[ellipsoids] r2759 committed - issue 133...

[ellip...@googlecode.com]

Revision: 2759
Author: anna.ata...@gmail.com
Date: Wed Mar 5 02:41:50 2014 UTC
Log: issue 133
Enhancement: committing finished work
http://code.google.com/p/ellipsoids/source/detail?r=2759

Added:

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_CopySaveProj.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_CopySaveTubes.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_CopySaveUnion.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_cat.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_fromQMScaledArrays.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_getDataProj.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_getDataTube.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_getDataUnion.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_getEllArrayProj.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_getEllArrayTube.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_getEllArrayUnion.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_getInfoProj.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_getInfoTube.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_getInfoUnion.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_isEqualProj.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_isEqualUnion.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_projectStaticTube.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_projectTube.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/getData.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/getDataForOneTube.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/getEllTube.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/getProj.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/getSameApprox.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/getUnion.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/getUnionExt.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/getUnionInt.m
Deleted:
/branches/issue_133_aatanesyan/doc/_build/latex/elltool_manual.aux
/branches/issue_133_aatanesyan/doc/_build/latex/elltool_manual.idx
/branches/issue_133_aatanesyan/doc/_build/latex/elltool_manual.log
/branches/issue_133_aatanesyan/doc/_build/latex/elltool_manual.out
/branches/issue_133_aatanesyan/doc/_build/latex/elltool_manual.pdf
/branches/issue_133_aatanesyan/doc/_build/latex/elltool_manual.toc
/branches/issue_133_aatanesyan/doc/_build/latex/python.ist

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_fromQArrays2.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_fromQMArrays2.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_fromQMScaledArrays1.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_fromQMScaledArrays2.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_getData.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_project.m
Modified:
/branches/issue_133_aatanesyan/doc/_build/html/_sources/chap_ellTube.txt
/branches/issue_133_aatanesyan/doc/_build/html/_sources/chap_functions.txt
/branches/issue_133_aatanesyan/doc/_build/html/_sources/chap_implement.txt
/branches/issue_133_aatanesyan/doc/_build/html/_sources/chap_reach.txt
/branches/issue_133_aatanesyan/doc/_build/html/chap_ellTube.html
/branches/issue_133_aatanesyan/doc/_build/html/chap_functions.html
/branches/issue_133_aatanesyan/doc/_build/html/chap_implement.html
/branches/issue_133_aatanesyan/doc/_build/html/main_manual.html
/branches/issue_133_aatanesyan/doc/_build/html/objects.inv
/branches/issue_133_aatanesyan/doc/_build/html/searchindex.js
/branches/issue_133_aatanesyan/doc/_build/latex/elltool_manual.tex
/branches/issue_133_aatanesyan/doc/chap_ellTube.rst
/branches/issue_133_aatanesyan/doc/chap_functions.rst
/branches/issue_133_aatanesyan/doc/chap_implement.rst
/branches/issue_133_aatanesyan/doc/chap_reach.rst

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+rels/AEllTubeProjectable.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+rels/ATypifiedAdjustedRel.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+rels/EllTube.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+rels/EllTubeBasic.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+rels/EllTubeProj.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+rels/EllTubeProjBasic.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+rels/EllTubeTouchCurveBasic.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+rels/EllTubeTouchCurveProjBasic.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+rels/EllUnionTube.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+rels/EllUnionTubeBasic.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+rels/EllUnionTubeStaticProj.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_cut1.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_cut2.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_fromEllArray.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_fromEllMArray.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_fromEllTubes.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_fromQArrays1.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_fromQMArrays1.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_interp.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_isEqual2.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_plot.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_plotExt.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_plotInt.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_projectStatic.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_projectToOrths1.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_projectToOrths2.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_scale.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_thinOutTuples.m

/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+mlunit/ExamplesTC.m

=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_CopySaveProj.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,35 @@
+EllProj = gras.ellapx.smartdb.test.examples.getProj();
+%
+% get a copy of the object
+%
+EllCopy = EllProj.getCopy();
+%
+% delete all the data from the object
+%
+EllProj.clearData();
+EllProj = gras.ellapx.smartdb.test.examples.getProj();
+%
+% create a copy of a specified object via calling a copy constructor for
+% the object class
+%
+Clone = EllProj.clone();
+%
+% remove all duplicate tuples from the relation
+%
+noDuplicate = Clone.removeDuplicateTuples();
+%
+% write a content of relation into Excel spreadsheet file
+%
+EllProj.writeToCSV('path');
+%
+% write a content of relation into Excel spreadsheet file
+%
+fileName = EllProj.writeToXLS('path');
+%
+% display a content of the given relation as a data grid UI component
+%
+EllProj.dispOnUI();
+%
+% put some textual information about object in screen
+%
+EllProj.display();
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_CopySaveTubes.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,52 @@
+nTubes=5;
+nPoints = 100;
+timeBeg=0;
+timeEnd=1;
+type = 2;
+EllTube=...
+
gras.ellapx.smartdb.test.examples.getEllTube(nTubes,timeBeg,timeEnd,type,nPoints);
+%
+% get a copy of the object
+%
+EllCopy = EllTube.getCopy();
+%
+% delete all the data from the object
+%
+EllTube.clearData();
+EllTube =...
+
gras.ellapx.smartdb.test.examples.getEllTube(nTubes,timeBeg,timeEnd,type,nPoints);
+%
+% create a copy of a specified object via calling a copy constructor for
+% the object class
+%
+Clone = EllTube.clone();
+%
+% remove all duplicate tuples from the relation
+%
+noDuplicate = Clone.removeDuplicateTuples();
+%
+% write a content of relation into Excel spreadsheet file
+%
+EllTube.writeToCSV('path');
+%
+% write a content of relation into Excel spreadsheet file
+%
+fileName = EllTube.writeToXLS('path');
+%
+% display a content of the given relation as a data grid UI component
+%
+EllTube.dispOnUI();
+%
+% put some textual information about object in screen
+%
+EllTube.display();
+
+
+
+
+
+
+
+
+
+
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_CopySaveUnion.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,35 @@
+EllUnion = gras.ellapx.smartdb.test.examples.getUnion();
+%
+% get a copy of the object
+%
+EllCopy = EllUnion.getCopy();
+%
+% delete all the data from the object
+%
+EllUnion.clearData();
+EllUnion = gras.ellapx.smartdb.test.examples.getUnion();
+%
+% create a copy of a specified object via calling a copy constructor for
+% the object class
+%
+Clone = EllUnion.clone();
+%
+% remove all duplicate tuples from the relation
+%
+noDuplicate = Clone.removeDuplicateTuples();
+%
+% write a content of relation into Excel spreadsheet file
+%
+EllUnion.writeToCSV('path');
+%
+% write a content of relation into Excel spreadsheet file
+%
+fileName = EllUnion.writeToXLS('path');
+%
+% display a content of the given relation as a data grid UI component
+%
+EllUnion.dispOnUI();
+%
+% put some textual information about object in screen
+%
+EllUnion.display();
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_cat.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,37 @@
+% An example of concatenating ellipsoid tube objects containing random
+% number of ellipsoid tubes (from one to ten tubes).
+%
+nTubes = randi(10,1);
+nPoints = 20;
+type = 1;
+timeBeg1 = 0;
+timeEnd1 = 1;
+firstEllTube =...
+
gras.ellapx.smartdb.test.examples.getEllTube(nTubes,timeBeg1,timeEnd1,type,nPoints);
+timeBeg2 = 1;
+timeEnd2 = 2;
+secondEllTube =...
+
gras.ellapx.smartdb.test.examples.getEllTube(nTubes,timeBeg2,timeEnd2,type,nPoints);
+%
+% Concatenating firstEllTube and secondEllTube on [timeBeg1, timeEnd2]
+% vector of time.
+%
+resEllTube = firstEllTube.cat(secondEllTube);
+%
+% Concatenating the same firstEllTube and secondEllTube on
[timeBeg1,timeEnd2]
+% vector of time, but the sTime and values of properties corresponding to
+% sTime are taken from secondEllTube.
+%
+resEllTube = firstEllTube.cat(secondEllTube,'isReplacedByNew',true);
+%
+% Concatenating the same firstEllTube and secondEllTube on
[timeBeg1,timeEnd2]
+% vector of time, but the sTime and values of properties corresponding to
+% sTime are taken from firstEllTube.
+%
+resEllTube = firstEllTube.cat(secondEllTube,'isReplacedByNew',false);
+%
+% Note that we cannot concatenate ellipsoid tubes with overlapping time
+% limits.
+%
+
+
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_fromQMScaledArrays.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,16 @@
+% An example of creating nTubes ellipsoid tube objects using
fromQMScaledArrays
+% function with the same type of approximation.
+[nTubes, nPoints, nDims, absTol, relTol, timeVec,...
+ sTime, lsGoodDirVec, ltGoodDirArray, aMat, qArrayList] = ...
+ gras.ellapx.smartdb.test.examples.getData();
+[approxSchemaDescr, approxSchemaName, approxType] = ...
+ gras.ellapx.smartdb.test.examples.getSameApprox();
+mArrayList=repmat({repmat(diag([0.1 0.2 0.3]),[1,1,nPoints])},...
+ 1,nTubes);
+scaleFactor = ones(1,nTubes);
+fromQMScaledArraysEllTube = ...
+ gras.ellapx.smartdb.rels.EllTube.fromQMScaledArrays(...
+ qArrayList,aMat,mArrayList,timeVec,...
+ ltGoodDirArray,sTime,approxType,approxSchemaName,...
+ approxSchemaDescr,absTol, relTol,...
+ scaleFactor);
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_getDataProj.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,3 @@
+% An example of GETDATA method's usage.
+ellTubeProj = gras.ellapx.smartdb.test.examples.getProj();
+data = ellTubeProj.getData();
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_getDataTube.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,9 @@
+% An example of GETDATA method's usage.
+nTubes=5;
+nPoints = 100;
+timeBeg=0;
+timeEnd=1;
+type = 2;
+EllTube=...
+
gras.ellapx.smartdb.test.examples.getEllTube(nTubes,timeBeg,timeEnd,type,nPoints);
+data = EllTube.getData();
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_getDataUnion.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,3 @@
+% An example of GETDATA method's usage.
+EllUnion = gras.ellapx.smartdb.test.examples.getUnion();
+data = EllUnion.getData();
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_getEllArrayProj.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,4 @@
+% An example of GETELLARRAY method's usage.
+EllProj = gras.ellapx.smartdb.test.examples.getProj();
+approxType = EllProj.approxType;
+data = EllProj.getEllArray(approxType);
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_getEllArrayTube.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,14 @@
+% An example of GETELLARRAY method's usage.
+[nTubes, nPoints, nDims, absTol, relTol, timeVec,...
+ sTime, lsGoodDirVec, ltGoodDirArray, aMat, qArrayList] = ...
+ gras.ellapx.smartdb.test.examples.getDataForOneTube();
+[approxSchemaDescr, approxSchemaName, approxType] = ...
+ gras.ellapx.smartdb.test.examples.getSameApprox();
+ellArray(nPoints) = ellipsoid();
+for iElem = 1:nPoints
+ ellArray(iElem) = ellipsoid(aMat(:,iElem), qArrayList{1}(:,:,iElem));
+end;
+fromEllArrayEllTube = gras.ellapx.smartdb.rels.EllTube.fromEllArray(...
+ ellArray,timeVec, ltGoodDirArray, sTime, approxType,...
+ approxSchemaName,approxSchemaDescr, absTol, relTol);
+data = fromEllArrayEllTube.getEllArray(approxType);
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_getEllArrayUnion.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,4 @@
+% An example of GETELLARRAY method's usage.
+EllUnion = gras.ellapx.smartdb.test.examples.getUnion();
+approxType = EllUnion.approxType;
+data = EllUnion.getEllArray(approxType);
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_getInfoProj.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,92 @@
+EllProj = gras.ellapx.smartdb.test.examples.getProj();
+%
+% get the list of field descriptions
+%
+Descr = EllProj.getFieldDescrList();
+%
+% get for given field a nested logical/cell array containing is-null
+% indicators for cell content. For example, for approxSchemaName field.
+%
+IsNull = EllProj.getFieldIsNull('approxSchemaName');
+%
+% get for given field logical vector determining whether value of this
+% field in each cell is null or not. For example, for approxSchemaName
field.
+%
+ValueIsNull = EllProj.getFieldIsValueNull('approxSchemaName');
+%
+% get the list of field names
+%
+Name = EllProj.getFieldNameList();
+%
+% project object with specified fields. For example, with fields that are
+% not to be cut or concatenated.
+%
+nameList = EllProj.getNoCatOrCutFieldsList();
+Proj = EllProj.getFieldProjection(nameList);
+%
+% get the list of field types
+%
+Type = EllProj.getFieldTypeList();
+%
+% get the list of field type specifications. Field type specification is a
+% sequence of type names corresponding to field value types starting with
+% the top level and going down into the nested content of a field (for a
+% field having a complex type).
+%
+TypeSpec = EllProj.getFieldTypeSpecList();
+% or
+TypeSpec = EllProj.getFieldTypeSpecList(nameList);
+%
+% get a matrix composed from the size vectorsfor the specified fields
+%
+ValueSizeMat = EllProj.getFieldValueSizeMat(nameList);
+%
+% get a vector indicating whether a particular field is composed of null
+% values completely
+%
+ValueNull = EllProj.getIsFieldValueNull(nameList);
+%
+% get a size vector for the specified dimensions. If no dimensions are
+% specified, a size vector for all dimensions up to minimum dimension is
+% returned
+MinDimensionSize = EllProj.getMinDimensionSize();
+%
+% get a minimum dimensionality for a given object
+%
+MinDimensionality = EllProj.getMinDimensionality();
+%
+% get a number of elements in a given object
+%
+NElems = EllProj.getNElems();
+%
+% get a number of fields in a given object
+%
+NFiedls = EllProj.getNFields();
+%
+% get a number of tuples in a given object
+%
+NTuples = EllProj.getNTuples();
+%
+% get sort index for all tuples of given relation with respect to some of
+% its fields
+%
+SortIndex = EllProj.getSortIndex(nameList);
+% also we can specify the direction of sorting ('asc' or 'desc')
+SortIndex = EllProj.getSortIndex(nameList,'Direction','asc');
+%
+% get tuples with given indices from given relation
+%
+Tuples = EllProj.getTuples(1);
+%
+% get tuples from given relation such that afixed index field contains
+% values from a given set of value
+%
+FilteredTuples = EllProj.getTuplesFilteredBy('sTime', 1);
+%
+% get internal representation for a set of unique tuples for given relation
+%
+UniqueData = EllProj.getUniqueData();
+%
+% get a relation containing the unique tuples from the original relation
+%
+UniqueTuples = EllProj.getUniqueTuples();
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_getInfoTube.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,98 @@
+nTubes=5;
+nPoints = 100;
+timeBeg=0;
+timeEnd=1;
+type = 2;
+EllTube=...
+
gras.ellapx.smartdb.test.examples.getEllTube(nTubes,timeBeg,timeEnd,type,nPoints);
+%
+% get the list of field descriptions
+%
+Descr = EllTube.getFieldDescrList();
+%
+% get for given field a nested logical/cell array containing is-null
+% indicators for cell content. For example, for approxSchemaName field.
+%
+IsNull = EllTube.getFieldIsNull('approxSchemaName');
+%
+% get for given field logical vector determining whether value of this
+% field in each cell is null or not. For example, for approxSchemaName
field.
+%
+ValueIsNull = EllTube.getFieldIsValueNull('approxSchemaName');
+%
+% get the list of field names
+%
+Name = EllTube.getFieldNameList();
+%
+% project object with specified fields. For example, with fields that are
+% not to be cut or concatenated.
+%
+nameList = EllTube.getNoCatOrCutFieldsList();
+Proj = EllTube.getFieldProjection(nameList);
+%
+% get the list of field types
+%
+Type = EllTube.getFieldTypeList();
+%
+% get the list of field type specifications. Field type specification is a
+% sequence of type names corresponding to field value types starting with
+% the top level and going down into the nested content of a field (for a
+% field having a complex type).
+%
+TypeSpec = EllTube.getFieldTypeSpecList();
+% or
+TypeSpec = EllTube.getFieldTypeSpecList(nameList);
+%
+% get a matrix composed from the size vectorsfor the specified fields
+%
+ValueSizeMat = EllTube.getFieldValueSizeMat(nameList);
+%
+% get a vector indicating whether a particular field is composed of null
+% values completely
+%
+ValueNull = EllTube.getIsFieldValueNull(nameList);
+%
+% get a size vector for the specified dimensions. If no dimensions are
+% specified, a size vector for all dimensions up to minimum dimension is
+% returned
+MinDimensionSize = EllTube.getMinDimensionSize();
+%
+% get a minimum dimensionality for a given object
+%
+MinDimensionality = EllTube.getMinDimensionality();
+%
+% get a number of elements in a given object
+%
+NElems = EllTube.getNElems();
+%
+% get a number of fields in a given object
+%
+NFiedls = EllTube.getNFields();
+%
+% get a number of tuples in a given object
+%
+NTuples = EllTube.getNTuples();
+%
+% get sort index for all tuples of given relation with respect to some of
+% its fields
+%
+SortIndex = EllTube.getSortIndex(nameList);
+% also we can specify the direction of sorting ('asc' or 'desc')
+SortIndex = EllTube.getSortIndex(nameList,'Direction','asc');
+%
+% get tuples with given indices from given relation
+%
+Tuples = EllTube.getTuples([1,2,3]);
+%
+% get tuples from given relation such that afixed index field contains
+% values from a given set of value
+%
+FilteredTuples = EllTube.getTuplesFilteredBy('sTime', 1);
+%
+% get internal representation for a set of unique tuples for given relation
+%
+UniqueData = EllTube.getUniqueData();
+%
+% get a relation containing the unique tuples from the original relation
+%
+UniqueTuples = EllTube.getUniqueTuples();
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_getInfoUnion.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,92 @@
+EllUnion = gras.ellapx.smartdb.test.examples.getUnion();
+%
+% get the list of field descriptions
+%
+Descr = EllUnion.getFieldDescrList();
+%
+% get for given field a nested logical/cell array containing is-null
+% indicators for cell content. For example, for approxSchemaName field.
+%
+IsNull = EllUnion.getFieldIsNull('approxSchemaName');
+%
+% get for given field logical vector determining whether value of this
+% field in each cell is null or not. For example, for approxSchemaName
field.
+%
+ValueIsNull = EllUnion.getFieldIsValueNull('approxSchemaName');
+%
+% get the list of field names
+%
+Name = EllUnion.getFieldNameList();
+%
+% project object with specified fields. For example, with fields that are
+% not to be cut or concatenated.
+%
+nameList = EllUnion.getNoCatOrCutFieldsList();
+Proj = EllUnion.getFieldProjection(nameList);
+%
+% get the list of field types
+%
+Type = EllUnion.getFieldTypeList();
+%
+% get the list of field type specifications. Field type specification is a
+% sequence of type names corresponding to field value types starting with
+% the top level and going down into the nested content of a field (for a
+% field having a complex type).
+%
+TypeSpec = EllUnion.getFieldTypeSpecList();
+% or
+TypeSpec = EllUnion.getFieldTypeSpecList(nameList);
+%
+% get a matrix composed from the size vectorsfor the specified fields
+%
+ValueSizeMat = EllUnion.getFieldValueSizeMat(nameList);
+%
+% get a vector indicating whether a particular field is composed of null
+% values completely
+%
+ValueNull = EllUnion.getIsFieldValueNull(nameList);
+%
+% get a size vector for the specified dimensions. If no dimensions are
+% specified, a size vector for all dimensions up to minimum dimension is
+% returned
+MinDimensionSize = EllUnion.getMinDimensionSize();
+%
+% get a minimum dimensionality for a given object
+%
+MinDimensionality = EllUnion.getMinDimensionality();
+%
+% get a number of elements in a given object
+%
+NElems = EllUnion.getNElems();
+%
+% get a number of fields in a given object
+%
+NFiedls = EllUnion.getNFields();
+%
+% get a number of tuples in a given object
+%
+NTuples = EllUnion.getNTuples();
+%
+% get sort index for all tuples of given relation with respect to some of
+% its fields
+%
+SortIndex = EllUnion.getSortIndex(nameList);
+% also we can specify the direction of sorting ('asc' or 'desc')
+SortIndex = EllUnion.getSortIndex(nameList,'Direction','asc');
+%
+% get tuples with given indices from given relation
+%
+Tuples = EllUnion.getTuples([1,2,3]);
+%
+% get tuples from given relation such that afixed index field contains
+% values from a given set of value
+%
+FilteredTuples = EllUnion.getTuplesFilteredBy('sTime', 1);
+%
+% get internal representation for a set of unique tuples for given relation
+%
+UniqueData = EllUnion.getUniqueData();
+%
+% get a relation containing the unique tuples from the original relation
+%
+UniqueTuples = EllUnion.getUniqueTuples();
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_isEqualProj.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,5 @@
+% An example of ISEQUAL method usage. The compared ellTubeProjections are
+% equal.
+firstProj = gras.ellapx.smartdb.test.examples.getProj();
+secondProj = gras.ellapx.smartdb.test.examples.getProj();
+res = firstProj.isEqual(secondProj);
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_isEqualUnion.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,6 @@
+% An example of ISEQUAL method usage. The compared ellTubeUnions are not
+% equal because one has external approximation, and the oter has internal
+% approximation.
+firstUnion = gras.ellapx.smartdb.test.examples.getUnionExt();
+secondUnion = gras.ellapx.smartdb.test.examples.getUnionInt();
+res = firstUnion.isEqual(secondUnion);
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_projectStaticTube.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,11 @@
+% Examples of calculating ellipsoid tube object static projection using
+% PROJECTSTATIC function.
+nTubes=1;
+nPoints = 20;
+timeBeg=0;
+timeEnd=1;
+type = 1;
+EllTube=...
+
gras.ellapx.smartdb.test.examples.getEllTube(nTubes,timeBeg,timeEnd,type,nPoints);
+projMat = [1 0; 0 1; 0 0]';
+ellTubeProjRel = EllTube.projectStatic(projMat);
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_projectTube.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,14 @@
+% An example of calculating ellipsoid tube object projection using PROJECT
+% method.
+nTubes=1;
+nPoints = 20;
+timeBeg=0;
+timeEnd=1;
+type = 1;
+EllTube=...
+
gras.ellapx.smartdb.test.examples.getEllTube(nTubes,timeBeg,timeEnd,type,nPoints);
+projType = gras.ellapx.enums.EProjType.Static;
+projMat = [1 0; 0 1; 0 0]';
+p = @gras.ellapx.smartdb.test.examples.fGetProjMat;
+[ellTubeProjRel,indProj2OrigVec] = EllTube.project(projType,...
+ {projMat},p);
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/getData.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,21 @@
+% This function returns the values of arguments, that are the same for
+% FROMQARRAYS, FROMQMARRAYS and FROMQMSCALEDARRAYS methods of creating an
+% ellipsoid tube object. Basically, this function creates a set of
+% arguments nessesary for creating an ellipsoid tube object containing
+% nTubes ellipsoid tubes. Here nTubes is a random natural number in the
+% range from one to ten.
+%
+function [nTubes, nPoints, nDims, absTol, relTol, timeVec,...
+ sTime, lsGoodDirVec, ltGoodDirArray, aMat, qArrayList] = getData()
+nTubes=randi(10,1);
+nPoints=20;
+nDims=3;
+absTol=0.001;
+relTol=0.001;
+timeVec=(1/nPoints):(1/nPoints):1;
+sTime=timeVec(randi(nPoints,1));
+lsGoodDirVec=[1;0;0];
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+aMat=zeros(nDims,nPoints);
+qArrayList=repmat({repmat(diag([0.1 0.2 0.3]),[1,1,nPoints])},1,nTubes);
+end
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/getDataForOneTube.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,19 @@
+% This function returns the values of arguments, that are needed to use
+% FROMELLARRAY and FROMELLMARRAY methods of creating an ellipsoid tube
+% object. Basically, this function creates a set of arguments nessesary for
+% creating an ellipsoid tube object containing one ellipsoid tube.
+%
+function [nTubes, nPoints, nDims, absTol, relTol, timeVec,...
+ sTime, lsGoodDirVec, ltGoodDirArray, aMat, qArrayList] =
getDataForOneTube()
+nTubes=1;
+nPoints=20;
+nDims=3;
+absTol=0.001;
+relTol=0.001;
+timeVec=(1/nPoints):(1/nPoints):1;
+sTime=timeVec(randi(nPoints,1));
+lsGoodDirVec=[1;0;0];
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+aMat=zeros(nDims,nPoints);
+qArrayList=repmat({repmat(diag([1 2 3]),[1,1,nPoints])},1,nTubes);
+end
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/getEllTube.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,28 @@
+% An example of creating an ellipsoid tube object containing nTubes
+% ellipsoid tubes from timeBegin to timeEnd time with specified type of
+% approximation.
+%
+function ellTube = getEllTube(nTubes,timeBeg,timeEnd,type,nPoints)
+nDims=3;
+absTol=0.001;
+relTol=0.001;
+timeVec=(timeBeg+1/nPoints):(1/nPoints):timeEnd;
+sTime=timeVec(randi(nPoints,1));
+lsGoodDirVec=[1;0;0];
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+aMat=zeros(nDims,nPoints);
+qArrayList=repmat({repmat(diag([1 2 3]),[1,1,nPoints])},1,nTubes);
+if type == 1
+ approxSchemaDescr='Internal';
+ approxSchemaName='Internal';
+ approxType=gras.ellapx.enums.EApproxType.Internal;
+else
+ approxSchemaDescr='External';
+ approxSchemaName='External';
+ approxType=gras.ellapx.enums.EApproxType.External;
+end
+ellTube=gras.ellapx.smartdb.rels.EllTube.fromQArrays(...
+ qArrayList, aMat, timeVec,...
+ ltGoodDirArray, sTime, approxType, approxSchemaName,...
+ approxSchemaDescr, absTol, relTol);
+end
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/getProj.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,14 @@
+function ellTubeProj = getProj()
+nTubes=1;
+nPoints = 20;
+timeBeg=0;
+timeEnd=1;
+type = 1;
+EllTube=...
+
gras.ellapx.smartdb.test.examples.getEllTube(nTubes,timeBeg,timeEnd,type,nPoints);
+projType = gras.ellapx.enums.EProjType.Static;
+projMat = [1 0; 0 1; 0 0]';
+p = @gras.ellapx.smartdb.test.examples.fGetProjMat;
+[ellTubeProj,indProj2OrigVec] = EllTube.project(projType,...
+ {projMat},p);
+end
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/getSameApprox.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,19 @@
+% This function returns the values of arguments, that specify the type of
+% approximation that will be used to create an ellipsoid tube object. It
+% will be a random type of approximation (Internal or External). These
+% arguments can be used while creating an ellipsoid tube object containing
+% one ellipsoid tube or several ellipsoid tubes with the same type of
+% approximation.
+%
+function [approxSchemaDescr, approxSchemaName, approxType] =
getSameApprox()
+ type = randi(2,1);
+ if type == 1
+ approxSchemaDescr='Internal';
+ approxSchemaName='Internal';
+ approxType=gras.ellapx.enums.EApproxType.Internal;
+ else
+ approxSchemaDescr='External';
+ approxSchemaName='External';
+ approxType=gras.ellapx.enums.EApproxType.External;
+ end
+end
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/getUnion.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,25 @@
+function unionEllTube = getUnion()
+% nTubes=10;
+% nPoints = 20;
+% timeBeg=1;
+% timeEnd=2;
+% type = 1;
+% ellTube = ...
+% gras.ellapx.smartdb.test.examples.getEllTube(nTubes,...
+% timeBeg,timeEnd,type,nPoints);
+% unionEllTube = ...
+% gras.ellapx.smartdb.rels.EllUnionTube.fromEllTubes(ellTube);
+aMat = [0 1; 0 0];
+bMat = eye(2);
+SUBounds = struct();
+SUBounds.center = {'sin(t)'; 'cos(t)'};
+SUBounds.shape = [9 0; 0 2];
+sys = elltool.linsys.LinSysContinuous(aMat, bMat, SUBounds);
+x0EllObj = ell_unitball(2);
+timeVec = [0 10];
+dirsMat = [1 0; 0 1]';
+rsObj = elltool.reach.ReachContinuous(sys, x0EllObj, dirsMat, timeVec);
+ellTubeObj = rsObj.getEllTubeRel();
+unionEllTube = ...
+ gras.ellapx.smartdb.rels.EllUnionTube.fromEllTubes(ellTubeObj);
+end
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/getUnionExt.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,12 @@
+function unionEllTube = getUnionExt()
+nTubes=10;
+nPoints = 20;
+timeBeg=1;
+timeEnd=2;
+type = 2;
+ellTube = ...
+ gras.ellapx.smartdb.test.examples.getEllTube(nTubes,...
+ timeBeg,timeEnd,type,nPoints);
+unionEllTube = ...
+ gras.ellapx.smartdb.rels.EllUnionTube.fromEllTubes(ellTube);
+end
=======================================
--- /dev/null
+++
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/getUnionInt.m
Wed Mar 5 02:41:50 2014 UTC
@@ -0,0 +1,12 @@
+function unionEllTube = getUnionInt()
+nTubes=10;
+nPoints = 20;
+timeBeg=1;
+timeEnd=2;
+type = 1;
+ellTube = ...
+ gras.ellapx.smartdb.test.examples.getEllTube(nTubes,...
+ timeBeg,timeEnd,type,nPoints);
+unionEllTube = ...
+ gras.ellapx.smartdb.rels.EllUnionTube.fromEllTubes(ellTube);
+end
=======================================
--- /branches/issue_133_aatanesyan/doc/_build/latex/elltool_manual.aux Tue
Feb 25 09:31:56 2014 UTC
+++ /dev/null
@@ -1,1280 +0,0 @@
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-\BOOKMARK [0][-]{chapter.1}{Introduction}{}% 1
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6
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[1][-]{section.10.5}{smartdb.relations.ATypifiedStaticRelation}{chapter.10}%
35
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[1][-]{section.10.6}{gras.ellapx.smartdb.rels.EllTube}{chapter.10}% 36
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[1][-]{section.10.7}{gras.ellapx.smartdb.rels.EllTubeProj}{chapter.10}% 37
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[1][-]{section.10.8}{gras.ellapx.smartdb.rels.EllUnionTube}{chapter.10}% 38
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39
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[1][-]{section.10.11}{elltool.reach.ReachContinuous}{chapter.10}% 41
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42
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[1][-]{section.10.15}{elltool.linsys.LinSysContinuous}{chapter.10}% 45
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47
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=======================================
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--- /branches/issue_133_aatanesyan/doc/_build/latex/elltool_manual.toc Tue
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=======================================
--- /branches/issue_133_aatanesyan/doc/_build/latex/python.ist Tue Feb 25
09:31:56 2014 UTC
+++ /dev/null
@@ -1,11 +0,0 @@
-line_max 100
-headings_flag 1
-heading_prefix " \\bigletter "
-
-preamble "\\begin{theindex}
-\\def\\bigletter#1{{\\Large\\sffamily#1}\\nopagebreak\\vspace{1mm}}
-
-"
-
-symhead_positive "{Symbols}"
-numhead_positive "{Numbers}"
=======================================
---
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_fromQArrays2.m
Mon Feb 24 01:41:07 2014 UTC
+++ /dev/null
@@ -1,23 +0,0 @@
-% An example of creating nTubes ellipsoid tube objects using fromQArrays
-% function with different types of approximation.
-nPoints=10;
-absTol=0.01;
-relTol=0.01;
-approxSchemaDescr={'Internal'; 'External'; 'External'};
-approxSchemaName={'Internal'; 'External'; 'External'};
-nDims=3;
-nTubes=3;
-lsGoodDirVec=[1;0;1];
-aMat=zeros(nDims,nPoints);
-timeVec=(1/nPoints):(1/nPoints):1;
-sTime=timeVec(randi(nPoints,1));
-approxType=[gras.ellapx.enums.EApproxType.Internal,...
- gras.ellapx.enums.EApproxType.External,...
- gras.ellapx.enums.EApproxType.External]';
-qArrayList=repmat({repmat(diag([1 2 3]),[1,1,nPoints])},...
- 1,nTubes);
-ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
-fromMatEllTube=gras.ellapx.smartdb.rels.EllTube.fromQArrays(...
- qArrayList, aMat, timeVec,...
- ltGoodDirArray, sTime, approxType, approxSchemaName,...
- approxSchemaDescr, absTol, relTol);
=======================================
---
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_fromQMArrays2.m
Mon Feb 24 01:41:07 2014 UTC
+++ /dev/null
@@ -1,25 +0,0 @@
-% An example of creating nTubes ellipsoid tube objects using fromQMArrays
-% function with different types of approximation.
-nPoints=10;
-absTol=0.01;
-relTol=0.01;
-approxSchemaDescr={'Internal'; 'External'; 'External'};
-approxSchemaName={'Internal'; 'External'; 'External'};
-nDims=3;
-nTubes=3;
-lsGoodDirVec=[1;0;1];
-aMat=zeros(nDims,nPoints);
-timeVec=(1/nPoints):(1/nPoints):1;
-sTime=timeVec(randi(nPoints,1));
-approxType=[gras.ellapx.enums.EApproxType.Internal,...
- gras.ellapx.enums.EApproxType.External,...
- gras.ellapx.enums.EApproxType.External]';
-mArrayList=repmat({repmat(diag([0.1 0.2 0.3]),[1,1,nPoints])},...
- 1,nTubes);
-qArrayList=repmat({repmat(diag([1 2 3]),[1,1,nPoints])},...
- 1,nTubes);
-ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
-fromMatMEllTube=gras.ellapx.smartdb.rels.EllTube.fromQMArrays(...
- qArrayList, aMat, mArrayList, timeVec,...
- ltGoodDirArray, sTime, approxType, approxSchemaName,...
- approxSchemaDescr, absTol, relTol);
=======================================
---
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_fromQMScaledArrays1.m
Mon Feb 24 01:41:07 2014 UTC
+++ /dev/null
@@ -1,26 +0,0 @@
-% An example of creating nTubes ellipsoid tube objects using
fromQMScaledArrays
-% function with the same type of approximation.
-nPoints=10;
-absTol=0.01;
-relTol=0.01;
-approxSchemaDescr='Internal';
-approxSchemaName='Internal';
-nDims=3;
-nTubes=5;
-lsGoodDirVec=[1;0;1];
-aMat=zeros(nDims,nPoints);
-timeVec=(1/nPoints):(1/nPoints):1;
-sTime=timeVec(randi(nPoints,1));
-approxType=gras.ellapx.enums.EApproxType.Internal;
-qArrayList=repmat({repmat(diag([1 2 3]),[1,1,nPoints])},...
- 1,nTubes);
-mArrayList=repmat({repmat(diag([0.1 0.2 0.3]),[1,1,nPoints])},...
- 1,nTubes);
-ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
-scaleFactor = ones(1,nTubes);
-fromQMScaledArraysEllTube = ...
- gras.ellapx.smartdb.rels.EllTube.fromQMScaledArrays(...
- qArrayList,aMat,mArrayList,timeVec,...
- ltGoodDirArray,sTime,approxType,approxSchemaName,...
- approxSchemaDescr,absTol, relTol,...
- scaleFactor);
=======================================
---
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_fromQMScaledArrays2.m
Mon Feb 24 01:41:07 2014 UTC
+++ /dev/null
@@ -1,28 +0,0 @@
-% An example of creating nTubes ellipsoid tube objects using
fromQMScaledArrays
-% function with different types of approximation.
-nPoints=10;
-absTol=0.01;
-relTol=0.01;
-approxSchemaDescr={'Internal'; 'Internal'; 'External'};
-approxSchemaName={'Internal'; 'Internal'; 'External'};
-nDims=3;
-nTubes=3;
-lsGoodDirVec=[1;0;1];
-aMat=zeros(nDims,nPoints);
-timeVec=(1/nPoints):(1/nPoints):1;
-sTime=timeVec(randi(nPoints,1));
-approxType=[gras.ellapx.enums.EApproxType.Internal,...
- gras.ellapx.enums.EApproxType.Internal,...
- gras.ellapx.enums.EApproxType.External]';
-qArrayList=repmat({repmat(diag([1 2 3]),[1,1,nPoints])},...
- 1,nTubes);
-mArrayList=repmat({repmat(diag([0.1 0.2 0.3]),[1,1,nPoints])},...
- 1,nTubes);
-ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
-scaleFactor = ones(1,nTubes);
-fromQMScaledArraysEllTube = ...
- gras.ellapx.smartdb.rels.EllTube.fromQMScaledArrays(...
- qArrayList,aMat,mArrayList,timeVec,...
- ltGoodDirArray,sTime,approxType,approxSchemaName,...
- approxSchemaDescr,absTol, relTol,...
- scaleFactor);
=======================================
---
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_getData.m
Mon Feb 24 20:42:41 2014 UTC
+++ /dev/null
@@ -1,21 +0,0 @@
-% An example of GETDATA method's usage.
-nPoints=10;
-absTol=0.01;
-relTol=0.01;
-approxSchemaDescr='Internal';
-approxSchemaName='Internal';
-nDims=3;
-nTubes=3;
-lsGoodDirVec=[1;0;1];
-aMat=zeros(nDims,nPoints);
-timeVec=(1/nPoints):(1/nPoints):1;
-sTime=timeVec(randi(nPoints,1));
-approxType=gras.ellapx.enums.EApproxType.Internal;
-qArrayList=repmat({repmat(diag([1 2 3]),[1,1,nPoints])},...
- 1,nTubes);
-ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
-fromMatEllTube=gras.ellapx.smartdb.rels.EllTube.fromQArrays(...
- qArrayList, aMat, timeVec,...
- ltGoodDirArray, sTime, approxType, approxSchemaName,...
- approxSchemaDescr, absTol, relTol);
-data = fromMatEllTube.getData();
=======================================
---
/branches/issue_133_aatanesyan/products/+gras/+ellapx/+smartdb/+test/+examples/example_project.m
Mon Feb 24 20:40:31 2014 UTC
+++ /dev/null
@@ -1,26 +0,0 @@
-% An example of calculating ellipsoid tube object projection using project
-% function.
-nPoints=5;
-absTol=0.01;
-relTol=0.01;
-approxSchemaDescr=char.empty(1,0);
-approxSchemaName=char.empty(1,0);
-nDims=3;
-nTubes=1;
-lsGoodDirVec=[1;0;1];
-aMat=zeros(nDims,nPoints);
-timeVec=1:nPoints;
-sTime=nPoints;
-approxType=gras.ellapx.enums.EApproxType.Internal;
-qArrayList=repmat({repmat(diag([1 2 3]),[1,1,nPoints])},...
- 1,nTubes);
-ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
-fromMatEllTube=gras.ellapx.smartdb.rels.EllTube.fromQArrays(...
- qArrayList, aMat, timeVec,...
- ltGoodDirArray, sTime, approxType, approxSchemaName,...
- approxSchemaDescr, absTol, relTol);
-projType = gras.ellapx.enums.EProjType.Static;
-projMat = [1 0; 0 1; 0 0]';
-p = @gras.ellapx.smartdb.test.examples.fGetProjMat;
-[ellTubeProjRel,indProj2OrigVec] = fromMatEllTube.project(projType,...
- {projMat},p);
=======================================
---
/branches/issue_133_aatanesyan/doc/_build/html/_sources/chap_ellTube.txt
Tue Feb 25 09:31:56 2014 UTC
+++
/branches/issue_133_aatanesyan/doc/_build/html/_sources/chap_ellTube.txt
Wed Mar 5 02:41:50 2014 UTC
@@ -1,115 +1,113 @@
-Ellipsoid tubes and touching curves
-===================================
+Ellipsoid tubes, unions and projections
+=======================================

-Touching curves
----------------
+There are two types of ellipsoid tube objects that we can work with using
*Ellipsoidal Toolbox*:

-One of the basic insruments in the *Ellipsoidal Toolbox* are classes,
which allow to work with touching curves. These are the curves along which
the internal and external ellipsoidal approximations are touching. In
*Ellipsoidal Toolbox* there are two basic classes (*EllTubeTouchCurveBasic*
and *EllTubeTouchCurveProjBasic*) which allow us to keep touching curves
and their projections. These classes do not add any functionality, that we
can use, while working with the toolbox, (They do not have public methods.)
but they are further used in other classes, which inherit these ones.
+- ellipsoidal tubes that are described in
*gras.ellapx.smartdb.rels.EllTube* class;

-*EllTubeTouchCurveBasic* class
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+- unions of ellipsoidal tubes by the instant of time described in
*gras.ellapx.smartdb.rels.EllUnionTube* class (see :ref:`formula
<union-label>`).

-This class allows us to keep touch point curve objects. This kind of
objects have a lot of different fields, which store the information about
the touching curve.
-The first field of our object is:
+The projections of ellipsoid tubes can be either static or dynamic. The
are described in gras.ellapx.smartdb.rels.EllTubeProj class. As for the
unions of ellipsoid tubes, they can only be projected on static subspaces.
These projections are described in
gras.ellapx.smartdb.rels.EllUnionTubeStaticProj class. For more information
about these types of projections and their differences and for examples see
this :ref:`link <section-label>`.

-- *dim*: In this field the dimension of the space in which the touching
- curves are defined is stored.
+Ellipsoid tubes
+---------------
+There is a whole variety of operations upon ellipsoid tubes in
*Ellipsoidal Toolbox*. We can, of course, create them. When the ellipsoid
tube object is created, we can cut them, concatenate, interpolate, plot and
project them and so on.

-Then there are several fields that are connecteld with time:
+The instruments to create ellipsoid tube objects are several functions:

-- *timeVec*: Time vector in which the the touching curves are defined;
+- *fromQArrays* method creates nEllTubes ellipsoid tube objects using an
array of ellipsoid matrices and an array of ellipsoid centers specified at
any point of time from timeVec;

-- *sTime*: Specific point of time which is best suited to describe good
direction;
+- *fromQMArrays* method acts the same way as *fromQArrays* method, except
for this one requires to specify an array of regularization marices
specified at any point of time from timeVec;

-- *indSTime*: The index of sTime point within timeVec is srored in this
field.
+- *fromQMScaledArrays* method acts the same way as *fromQMArrays* method,
except for this one requires to also specify a vector of scale factors
specified for every created ellipsoid tube;

-It should be said that the *good direction* is the direction along which
the internal and external approximations of ellipsoid tubes are touching.
Next several fields specify the type of approximation which was used? while
creating these touching curves:
+- *fromEllArray* method creates ellipsoid tube object using an array of
ellipsoids;

-- *approxSchemaName*: The name of the approximation schema;
+- *fromEllMArray* method creates ellipsoid tube object using an array of
ellipsoids and an array of regularisation matrices.

-- *approxSchemaDescr*: The description of the approximation schema;
+Basically we can divide these methods into two groups, based od what
objects they are using to create ellipsoid tube: an array of ellipsoid
matrices with an array of ellipsoid centers (by using these methods we can
create an ellipsoid tube object containing several ellipsoid tubes) or an
array of ellipsoids (by using these methods we can create an ellipsoid tube
object containing one ellipsoid tube). To illustrate the usage of these
methods we have to describe several functions, that will be used in the
process. Below are their descriptions.

-- *approxType*: The type of approximation (External, Internal,
NotDefined) is stored in this field.
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//getData.m
+ :language: matlab
+ :linenos:

-Then there are two fields which keep the absolute tolerance and relative
tolerance used to create this object (*absTolerance* and *relTolerance*,
respectively). And finally come the fields which allow us to keep the
touching curves and good directions:
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//getSameApprox.m
+ :language: matlab
+ :linenos:

-- *ltGoodDirMat* field stores the matrix of good direction vectors at any
point of time from timeVec;
+Using the three above mentioned functions we can describe an examples of
*fromQArrays*, *fromQMArrays* and *fromQMScaledArrays* methods' usage.

-- *lsGoodDirVec* field stores the good direction vector at sTime point of
time;
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromQArrays1.m
+ :language: matlab
+ :linenos:

-- *ltGoodDirNormVec* field stores the norm of good direction vectors at
any point of time from timeVec;
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromQArrays2.m
+ :language: matlab
+ :linenos:

-- *lsGoodDirNorm* field stores the norm of good direction vector at sTime
point of time;
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromQMArrays1.m
+ :language: matlab
+ :linenos:

-- *xTouchCurveMat* field stores the touch point curve for good direction
matrix;
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromQMArrays2.m
+ :language: matlab
+ :linenos:

-- *xTouchOpCurveMat* field stores the touch point curve oposite to the
xTouchCurveMat touch point curve;
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromQMScaledArrays.m
+ :language: matlab
+ :linenos:

-- *xsTouchVec* field stores the touch point at sTime point of time;
+To use *fromEllArray* and *fromEllMArray* methods we nave to describe one
more auxiliary function (as these methods create an ellipsoid tube object
containing only one ellipsoid tube and we can not use *getData* function,
because it returns data for crating random number of ellipsoid tubes).

-- *xsTouchOpVec* field stores a point opposite to the xsTouchVec touch
point;
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//getDataForOneTube.m
+ :language: matlab
+ :linenos:

-- *isLsTouch* field stores a logical variable which indicates whether a
touch takes place along good direction at sTime point of time;
+Now we can write examples of these methods' usage.

-- *isLtTouchVec* field stores a logical vector which indicates whether a
touch takes place along good direction at any point of time from
timeVec.
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromEllArray.m
+ :language: matlab
+ :linenos:

-*EllTubeTouchCurveProjBasic* class
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromEllMArray.m
+ :language: matlab
+ :linenos:

-This class allows us to keep the projections of touch point curves. This
kind of objects have a lot of different fields, which store the information
about the projection of touching curve. First of all it inherits all the
fields from *EllTubeTouchCurveBasic* class, and, secondly, it adds some of
its own fields. The inherited fields store the information about the
projection instead of the information about the original curve, but their
meaning is all the same.
-The first group of new fields is connected to the type of projection and
the space on which the curve is projected:
+As we can see in all these examples, we can specify how many ellipsoid
tubes we want to create, which type of arrpoximation to use. Also we can
create ellipsoid tube objects, which will contain several ellipsoid tubes
with different types of approximation.

-- *projSMat* field stores the projection matrix at sTime point of time;
+After creation of ellipsoid tube objects we can do several operations with
them. Below is the *getEllTube* function that create an ellipsoid tube
object containing one or several ellipsoid tubes with specified type of
approximation, on specified time vector with specified time points. This
function will be used further down to illustrate other methods that we can
use while working with ellipsoid tube objects.

-- *projArray* field stores an array of projection matrices at any point
of time from timVec;
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//getEllTube.m
+ :language: matlab
+ :linenos:

-- *projType* field stores the type of projection (Static or
DynamicAlongGoodCurve).
+As we have created an ellipsoid tube object, we can get all the types of
differet data about it. There is a set of methods that can give information
about the data stored in the object and give access to it.

-And then come the new fields which store some information about the
original curve:
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_getDataTube.m
+ :language: matlab
+ :linenos:

-- *ltGoodDirNormOrigVec* field stores the norm of the original good
direction vectors at any point of time from timeVec;
-- *lsGoodDirNormOrig* field stores the norm of the original good
direction vector at sTime point of time;
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_getEllArrayTube.m
+ :language: matlab
+ :linenos:

-- *ltGoodDirOrigMat* field stores the matrix of the original good
direction vectors at any point of time from timeVec;
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_getInfoTube.m
+ :language: matlab
+ :linenos:

-- *lsGoodDirOrigVec* field stores the original good direction vector at
sTime point of time;
+Also we can copy the object, clear all the data, save it in a file:

-- *ltGoodDirNormOrigProjVec* field stores the norm of the projection of
the original good direction curve;
-
-- *ltGoodDirOrigProjMat* field stores the projectition of the original
good direction curve.
-
-Ellipsoidal tubes
------------------
-
-Other basic insrument in the *Ellipsoidal Toolbox* are classes, which
allow to work with ellipsoidal tubes. In *Ellipsoidal Toolbox* there are
four classes (*EllTubeBasic*, *EllTube*, *EllTubeProjBasic* and
*EllTubeProj*) which give us the needed functionality to work with
ellipsoid tube objects.
-
-*EllTubeBasic* class
-~~~~~~~~~~~~~~~~~~~~
-
-This class inherits its fields from *EllTubeTouchCurveBasic* class and
adds some new fields which are:
-
-- *QArray* field which stores an array of nTimePoints ellipsoid matrices.
Each element from this
- array specifies an ellipsoid matrix at nTimePoint point of time. Here
nTimePoints is number of elements in *timeVec* (It is one of the fields
inherited from *EllTubeTouchCurveBasic* class.);
-
-- *aMat* field which stores an array of nTimePoints ellipsoid centers.
Each center is specified for nTimePoint point of time;
-
-- scaleFactor field which stores the scale for the created ellipsoid tube;
-
-- MArray field which stores an array of nTimePoints regularization
matrices. Each element from this array specifies a regularization
matrix at nTimePoint point of time.
-
-This class gives us some methods which can be used to work with
ellipsoidal tubes. For example, if we have already created ellipsoid tube
object using one timeVec vector of time, then we can interpolate this tube,
using new time vector. Take notice that we have to make sure that the first
and the last elements in old and new vectors of time are the same.
-
-..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_interp.m
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_CopySaveTubes.m
:language: matlab
:linenos:

-Other method that we can use is *THINOUTTUPLES* method. It allows us to
thin out the already created ellipsoid tube, by saving only the ellipsoids
at specified points of time.
+As we have created the object, we can work with it. Below is the example
of concatenating ellipsoid tube objects. We can concatenate objects
containing one or several ellipsoid tubes with the same type of
approximation.

-..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_thinOutTuples.m
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_cat.m
:language: matlab
:linenos:

-Then we can also cut the created ellipsoid tube, leaving only part of it
at specified vector of time or point of time. Below are the exmples:
+As we can concatenate ellipsoid tubes, it is logical to be possible to cut
ellipsoid tubes, leaving only part of it at specified vector of time or
point of time. Below are the exmples:

..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_cut1.m
:language: matlab
@@ -119,139 +117,171 @@
:language: matlab
:linenos:

-*EllTube* class
-~~~~~~~~~~~~~~~
+After cutting, we can interpolate the resulting tube, using new time
vector. Take notice that we have to make sure that the first and the last
elements in old and new vectors of time are the same.

-This class inherits its fields from *EllTubeBasic* class. It does not have
any new fields, but adds some functionality. First of all it gives us the
instruments to create ellipsoid tube objects. Here are these methods:
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_interp.m
+ :language: matlab
+ :linenos:

-- *fromQArrays* - creates nEllTubes ellipsoid tube objects using an array
of ellipsoid matrices and an array of ellipsoid centers specified at
any point of time from timeVec;
+After that we can thin out the new ellipsoid tube, removing ellipsoids at
sertain points of time.

-- *fromQMArrays* - acts the same way as *fromQArrays* method, except for
this one requires to specify an array of regularization marices
specified at any point of time from timeVec;
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_thinOutTuples.m
+ :language: matlab
+ :linenos:

-- *fromQMScaledArrays* - acts the same way as *fromQMArrays* method,
except for this one requires to also specify a vector of scale
factors specified for every created ellipsoid tube;
+Then we can also calculate new scale factor for specified fields:

-- *fromEllArray* - creates ellipsoid tube object using an array of
ellipsoids;
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_scale.m
+ :language: matlab
+ :linenos:

-- *fromEllMArray* - creates ellipsoid tube object using an array of
ellipsoids and an array of regularisation matrices.
+Also we can compare objects using method *isEqual*.

-Basically we can divide these methods into two groups, based od what
objects they are using to create ellipsoid tube: an array of ellipsoid
matrices and an array of ellipsoid centers or an array of ellipsoids. Below
are some examples of the usage of these functions.
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_isEqual1.m
+ :language: matlab
+ :linenos:

-..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromQArrays1.m
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_isEqual2.m
:language: matlab
:linenos:

-..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromQArrays2.m
+At last there are several methods for projecting ellipsoid tubes on the
specified spaces. The first method projects the ellipsoid tube on specified
space creating the specified type of projection.
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_projectTube.m
:language: matlab
:linenos:

-..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromQMArrays1.m
+The second method projects the ellipsoid tube onto subspace defined by
vectors of standart basis with indices specified in indVec.
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_projectToOrths1.m
:language: matlab
:linenos:

-..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromQMScaledArrays1.m
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_projectToOrths2.m
:language: matlab
:linenos:

-..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromEllArray.m
+Also there is a method for calculating only static projections.
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_projectStaticTube.m
:language: matlab
:linenos:

-..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromEllMArray.m
+For creating the projection matrix a special function is used in all of
these examples.
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//fGetProjMat.m
:language: matlab
:linenos:

-As we can see in these examples, we can specify how many ellipsoid tubes
we want to create, which type of arrpoximation to use. also we can create
ellipsoid tube objects, which will contain several ellipsoid tubes with
different types of approximation.
-We can also use *project* and *projectToOrths* methods to project our
ellipsoid tubes on the specified spaces. The first metod projects the
ellipsoid tube on specified space creating the specified type of projection.
+Unions of ellipsoid tubes
+-------------------------
+
+As with ellipsoid tube objects there are several methods that we can use
while working with ellipsoid tube unions. First of all we can create
ellipsoid tube unions using *fromEllTubes* method:

-..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_project.m
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromEllTubes.m
:language: matlab
:linenos:

-The second method projects the ellipsoid tube onto subspace defined by
vectors of standart basis with indices specified in indVec.
+From here on we will use the *getUnion* function so we can get ellipsoid
tube union and work with it further on. As we have created an ellipsoid
tube object, we can get all the types of differet data about it. There is a
set of methods that can give information about the data stored in the
object and give access to it.

-..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_projectToOrths1.m
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_getDataUnion.m
:language: matlab
:linenos:

-..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_projectToOrths2.m
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_getEllArrayUnion.m
:language: matlab
:linenos:

-*EllTubeProjBasic* class
-~~~~~~~~~~~~~~~~~~~~~~~~
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_getInfoUnion.m
+ :language: matlab
+ :linenos:
+

-This class inherits its fields from *EllTubeBasic* and
*EllTubeTouchCurveProjBasic* classes. It does not have any new fields, but
holds not the original values of the fields, which were the values of the
original ellipsoid tube, it holds the values of the projection. We can use
*plot*, *plotInt* or *plotExt* methods to plot the projections.
+Also we can copy the object, clear all the data, save it in a file.

-..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_plot.m
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_CopySaveUnion.m
:language: matlab
:linenos:

-..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_plotInt.m
+Also we can compare ellipsoid tube union objects using *isEqual* method.
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_isEqualUnion.m
:language: matlab
:linenos:

-..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_plotExt.m
+At last, as it has already been said ellipsoid tube union objects can be
projected only on static subspaces. It can be done in two ways.
+
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_project.m
:language: matlab
:linenos:

-All the three methods have several properties connected to the properties
of the image, for example: transparency, color, line width and so on.
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_projectStatic.m
+ :language: matlab
+ :linenos:

-*EllTubeProj* class
-~~~~~~~~~~~~~~~~~~~
+As for ellipsoid tube projections a special function is used to create the
projection matrix for ellipsoid tube union objects:

-This class doesn't add any functionality to the *EllTubeProjBasic* class.
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//fGetProjMat.m
+ :language: matlab
+ :linenos:

-Unions of ellipsoidal tubes
----------------------------
+Projections of ellipsoid tubes and unions
+-----------------------------------------

-The last classes which will be discussed in this chapter are classes,
operating with unions of ellipsoid tubes. These are *EllUnionTubeBasic*,
*EllUnionTube* and *EllUnionTubeStaticProj* classes.
+As it has already been said we can create either static or dynamic
projections for ellipsoid tubes and only static projections for unions of
ellipsoid tubes. There are several methods in *Ellipsoidal Toolbox* for
that. Most of them has already been described:

-*EllUnionTubeBasic* class
-~~~~~~~~~~~~~~~~~~~~~~~~~
+- *project*, *projectStatic* and *projectToOrths* for ellipsoid tubes;

-This class allows us to keep and work with unions of ellipsoid tubes. The
fields of this class are:
+- *project* and *projectStatic* for unions of ellipsoid tubes.

-- *ellUnionTimeDirection* which stores the direction in time along which
union is performed;
+It should be mentioned that from here on all the examples are written for
ellipsoid tube projections, but their usage is the same for ellipsoid tube
union projections. We wiil use *getProj* function to create ellipsoid tube
projection that we will work with.

-- *timeTouchEndVec* which stores the points of time when touch is occured
in good direction;
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_getProj.m
+ :language: matlab
+ :linenos:

-- *timeTouchOpEndVec* which stores the points of time when touch is
occured in direction opposite to good direction;
+As with ellipsoid tubes and unions of ellipsoid tubes we can get all the
types of differet data about projections. There is a set of methods that
can give information about the data stored in the object and give access to
it.

-- *isLsTouchOp* which stores a logical variable which indicates whether a
touch takes place along the direction opposite to the good direction at
sTime point of time;

-- *isLtTouchOpVec* which stores a logical variable which indicates
whether a touch takes place along the direction opposite to the good
direction at any point of time from timeVec.
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_getDataProj.m
+ :language: matlab
+ :linenos:

-This class does not have any public methods.
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_getEllArrayProj.m
+ :language: matlab
+ :linenos:

-*EllUnionTube* class
-~~~~~~~~~~~~~~~~~~~~
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_getInfoProj.m
+ :language: matlab
+ :linenos:

-This class inherits its fields from *EllUnionTubeBasic* and *EllTubeBasic*
classes. Unlike *EllUnionTubeBasic* class, this class has one public method
- *fromEllTubes* method, which allows us to create an ellUnionTube object
using ellipsoid tubes.
+Also we can copy the object, clear all the data, save it in a file.

-..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_fromEllTubes.m
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_CopySaveProj.m
:language: matlab
:linenos:

-*EllUnionTubeStaticProj* class
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-The last class connected to ellUnionTube objects is
*EllUnionTubeStaticProj* class. It inherits the fields and methods of
*EllUnionTubeBasic* and *EllTubeProjBasic* classes and allows us to work
with the static projections of ellUnionTubes.
+Also we can compare ellipsoid tube union objects using *isEqual* method.

-*TypifiedByFieldCodeRel* class
-----------------------------
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_isEqualProj.m
+ :language: matlab
+ :linenos:

-This is the last class that should be mentioned in this chapter. It is
inherited by *EllTube*, *EllTubeProj*, *EllUnionTube* and
*EllUnionTubeStaticProj* classes and adds some methods to them. For example
we can use *getData* method.
+And finally we can plot out results using one of three methods: *plot*,
*plotExt* (for external approximation) or *plotInt* (for internal
approximation).

-..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_getData.m
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_plot.m
:language: matlab
:linenos:

-Or we can compare objects from above mentioned classes using method
*isEqual*.
-
-..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_isEqual1.m
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_plotInt.m
:language: matlab
:linenos:

-..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_isEqual2.m
+..
literalinclude:: ../products/+gras/+ellapx/+smartdb/+test/+examples//example_plotExt.m
:language: matlab
:linenos:
+
+All the three methods have several properties connected to the properties
of the image, for example: transparency, color, line width and so on.
+
+To read more about the differences of these projections :ref:`goto
<goto-label>`. Also there you can find some illustrations for both ellTube
projections and ellUnionTube projections.
+
=======================================
---
/branches/issue_133_aatanesyan/doc/_build/html/_sources/chap_functions.txt
Thu Feb 6 19:00:52 2014 UTC
+++
/branches/issue_133_aatanesyan/doc/_build/html/_sources/chap_functions.txt
Wed Mar 5 02:41:50 2014 UTC
@@ -6762,34 +6762,58 @@

::

- EllTube - class which keeps ellipsoidal tubes
+ A class which allows to work with ellipsoid tube objects.

Fields:
- QArray:cell[1, nElem] - Array of ellipsoid matrices
- aMat:cell[1, nElem] - Array of ellipsoid centers
- scaleFactor:double[1, 1] - Tube scale factor
- MArray:cell[1, nElem] - Array of regularization ellipsoid matrices
- dim :double[1, 1] - Dimensionality
- sTime:double[1, 1] - Time s
- approxSchemaName:cell[1,] - Name
- approxSchemaDescr:cell[1,] - Description
- approxType:gras.ellapx.enums.EApproxType - Type of approximation
- (external, internal, not defined)
- timeVec:cell[1, m] - Time vector
- calcPrecision:double[1, 1] - Calculation precision
- indSTime:double[1, 1] - index of sTime within timeVec
- ltGoodDirMat:cell[1, nElem] - Good direction curve
- lsGoodDirVec:cell[1, nElem] - Good direction at time s
- ltGoodDirNormVec:cell[1, nElem] - Norm of good direction curve
- lsGoodDirNorm:double[1, 1] - Norm of good direction at time s
- xTouchCurveMat:cell[1, nElem] - Touch point curve for good
- direction
- xTouchOpCurveMat:cell[1, nElem] - Touch point curve for direction
- opposite to good direction
- xsTouchVec:cell[1, nElem] - Touch point at time s
- xsTouchOpVec :cell[1, nElem] - Touch point at time s
+ QArray: cell[1,1] of double[nDims,nDims,nTimePoints] -
+ a 3-dimentional matrix in which each of nTimePoints slices is a
+ double[nDims,nDims] ellipsoid matrix at nTimePoint point of time.
+ Here nTimePoints is number of elements in timeVec.
+ aMat: cell[1,nTimePoints] of double[nDims,1] - a 2-dimentional matrix
+ in which each of nTimePoints columns is a
+ double[nDims, 1] ellipsoid center. Each center is specified for
+ nTimePoint point of time
+ scaleFactor: double[1, 1] - scale for the created ellipsoid tube
+ MArray: cell[1,1] of double[nDims,nDims,nTimePoints] -
+ a 3-dimentional matrix in which each of nTimePoints slices is
+ a double[nDims,nDims] regularization matrix at nTimePoint point
+ of time.
+ dim: double[1, 1] - the dimension of the space in which the touching
+ curves are defined
+ sTime: double[1, 1] - specific point of time which is best suited to
+ describe good direction
+ approxSchemaName: cell[1, 1] of char[1,] - name of the
+ approximation schema
+ approxSchemaDescr: cell[1, 1] of char[1,] - description of the
+ approximation schema
+ approxType: gras.ellapx.enums.EApproxType[1,1] - type of approximation
+ (External, Internal, NotDefined)
+ timeVec: double[1, nTimePoints] - time vector
+ absTolerance: double[1, 1] - absolute tolerance
+ relTolerance: double[1, 1] - relative tolerance
+ indSTime: double[1, 1] - index of sTime point within timeVec
+ ltGoodDirMat: cell[1, nTimePoints] of double[nDims, 1] - matrix of
+ good direction vectors at any point of time from timeVec
+ lsGoodDirVec: cell[1, 1] of double[nDims, 1] - good direction vector
+ at sTime point of time
+ ltGoodDirNormVec: cell[1, 1] of double[1, nTimePoints] - norm of good
+ direction vector at any point of time from timeVec
+ lsGoodDirNorm: double[1, 1] - norm of good direction vector at
+ sTime point of time
+ xTouchCurveMat: cell[1, nTimePoints] of double[nDims, 1] - touch
+ point curve for good direction matrix
+ xTouchOpCurveMat: cell[1, nTimePoints] of double[nDims, 1] - touch
+ point curve oposite to the xTouchCurveMat touch point curve
+ xsTouchVec: cell[1, 1] of double[nDims, 1] - touch point at sTime
+ point of time
+ xsTouchOpVec: cell[1, 1] of double[nDims, 1] - a point opposite to
+ the xsTouchVec touch point
+ isLsTouch: logical[1, 1] - a logical variable which indicates whether
+ a touch takes place along good direction at sTime point of time
+ isLtTouchVec: cell[1, 1] of logical[nTimePoints, 1] - a logical
+ vector which indicates whether a touch takes place along good
+ direction at any point of time from timeVec

- TODO: correct description of the fields in
gras.ellapx.smartdb.rels.EllTube



@@ -6903,32 +6927,58 @@
gras.ellapx.smartdb.rels.EllTube.cut
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

+::

+ CUT - extracts the piece of the ellipsoid tube object from given
+ start point of time to given end point of time.
+
+ Input:
+ regular:
+ self.
+ cutTimeVec: double[1, 2] / double[1, 1] - time interval to cut
+
+ Output:
+ cutEllTubeRel: gras.ellapx.smartdb.rels.EllTube[1, 1] -
+ ellipsoid tube which is created from the original one by
+ cutting it from given start point of time to given end
+ point of time
+
+
+

gras.ellapx.smartdb.rels.EllTube.fromEllArray
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

::

- FROMELLARRAY - creates a relation object using an array of ellipsoids
+ FROMELLARRAY - creates ellipsoid tube object using an
+ array of ellipsoids.

Input:
regular:
- qEllArray: ellipsoid[nDim1, nDim2, ..., nDimN] - array of ellipsoids
+ qEllArray: double[nDims,nDims,nTimePoints] - array of
+ ellipsoids. Each element from double[nDims,nDims,nTimePoints]
+ array specifies double[nDims,nDims] ellipsoid at nTimePoint
+ point of time. Here nTimePoints is number of elements
+ in timeVec.
+ timeVec: cell[1,1] of double[1,nTimePoints] - time vector
+ ltGoodDirArray: cell[nEllTubes,1] of double[nDim, nTimePoints] -
+ cell of nEllTubes arrays of nTimePoints good direction
+ vectors at any point of time from timeVec
+ sTime: double[1,1] - specific point of time from timeVec
+ which is best suited to describe good direction
+ approxType: gras.ellapx.enums.EApproxType[1,1] - type
+ of approximation (External, Internal, NotDefined).
+ approxSchemaName: char[1,] - name of the approximation schema
+ approxSchemaDescr: char[1,] - description of the
+ approximation schema. It is possible
+ absTol:double[1, 1] - absolute tolerance
+ relTol:double[1, 1] - relative tolerance

- optional:
- timeVec:cell[1, m] - time vector
- ltGoodDirArray:cell[1, nElem] - good direction at time s
- sTime:double[1, 1] - time s
- approxType:gras.ellapx.enums.EApproxType - type of approximation
- (external, internal, not defined)
- approxSchemaName:cell[1,] - name of the schema
- approxSchemaDescr:cell[1,] - description of the schema
- calcPrecision:double[1, 1] - calculation precision
+ Output:
+ ellTubeRel: gras.ellapx.smartdb.rels.EllTube[1, 1] - constructed
+ ellipsoid tube object

- Output:
- ellTubeRel: smartdb.relation.StaticRelation[1, 1] - constructed
relation
- object



@@ -6937,29 +6987,39 @@

::

- FROMELLMARRAY - creates a relation object using an array of ellipsoids.
- This method uses regularizer in the form of a matrix
- function.
+ FROMELLMARRAY - creates ellipsoid tube object using an
+ array of ellipsoids and an array of regularisation matrices.

Input:
regular:
- qEllArray: ellipsoid[nDim1, nDim2, ..., nDimN] - array of ellipsoids
- ellMArr: double[nDim1, nDim2, ..., nDimN] - regularization ellipsoid
- matrices
+ qEllArray: double[nDims,nDims,nTimePoints] - array of
+ ellipsoids. Each element from double[nDims,nDims,nTimePoints]
+ array specifies double[nDims,nDims] ellipsoid at nTimePoint
+ point of time. Here nTimePoints is number of elements
+ in timeVec.
+ ellMArr: double[nDims,nDims,nTimePoints] - an array of nTimePoints
+ regularization matrices of double[nDims,nDims] type.
+ Each element from double[nDims,nDims,nTimePoints] array
+ specifies double[nDim,nDim] regularization matrix at
+ nTimePoint point of time.
+ timeVec: cell[1,1] of double[1,nTimePoints] - time vector
+ ltGoodDirArray: cell[nEllTubes,1] of double[nDim, nTimePoints] -
+ cell of nEllTubes arrays of nTimePoints good direction
+ vectors at any point of time from timeVec
+ sTime: double[1,1] - specific point of time from timeVec
+ which is best suited to describe good direction
+ approxType: gras.ellapx.enums.EApproxType[1,1] - type
+ of approximation (External, Internal, NotDefined).
+ approxSchemaName: char[1,] - name of the approximation schema
+ approxSchemaDescr: char[1,] - description of the
+ approximation schema. It is possible
+ absTol:double[1, 1] - absolute tolerance
+ relTol:double[1, 1] - relative tolerance

- optional:
- timeVec:cell[1, m] - time vector
- ltGoodDirArray:cell[1, nElem] - good direction at time s
- sTime:double[1, 1] - time s
- approxType:gras.ellapx.enums.EApproxType - type of approximation
- (external, internal, not defined)
- approxSchemaName:cell[1,] - name of the schema
- approxSchemaDescr:cell[1,] - description of the schema
- calcPrecision:double[1, 1] - calculation precision
+ Output:
+ ellTubeRel: gras.ellapx.smartdb.rels.EllTube[1, 1] - constructed
+ ellipsoid tube object

- Output:
- ellTubeRel: smartdb.relation.StaticRelation[1, 1] - constructed
relation
- object



@@ -6968,31 +7028,52 @@

::

- FROMQARRAYS - creates a relation object using an array of ellipsoids,
- described by the array of ellipsoid matrices and
- array of ellipsoid centers.This method used default
- scale factor.
+ FROMQARRAYS creates nEllTubes ellipsoid tube objects using an
+ array of ellipsoid matrices and an array of ellipsoid centers
+ specified at any point of time from timeVec.

Input:
regular:
- QArrayList: double[nDim1, nDim2, ..., nDimN] - array of ellipsoid
- matrices
- aMat: double[nDim1, nDim2, ..., nDimN] - array of ellipsoid centers
+ QArrayList: cell[nEllTubes,1] of double[nDims,nDims,nTimePoints] -
+ an array of nEllTubes 3-dimentional matrices in which
+ each of nTimePoints slices is a double[nDims,nDims]
+ ellipsoid matrix at nTimePoint point of time. Here
+ nTimePoints is number of elements in timeVec.
+ aMat: double[nDims, nTimePoints] - a 2-dimentional matrix
+ in which each of nTimePoints columns is a
+ double[nDims, 1] ellipsoid center. Each center is specified
+ for nTimePoint point of time
+ timeVec: cell[1,1] of double[1,nTimePoints] - time vector
+ ltGoodDirArray: cell[nEllTubes,1] of double[nDim, nTimePoints] -
+ cell of nEllTubes arrays of nTimePoints good direction
+ vectors at any point of time from timeVec
+ sTime: double[1,1] - specific point of time from timeVec
+ which is best suited to describe good direction
+ approxType: gras.ellapx.enums.EApproxType[1,1] /
+ / gras.ellapx.enums.EApproxType[1,nEllTubes] - type
+ of approximation (External, Internal, NotDefined).
+ It is possible either to specify one type of
+ approximation for all of nEllTubes ellipsoid tubes,
+ or specify the type of approximation for each of the
+ nEllTubes ellipsoid tubes separately.
+ approxSchemaName: char[1,] / cell[1,nEllTubes] of char[1,] -
+ name of the approximation schema. It is possible either
+ to specify one name of the approximation schema for
+ all of nEllTubes ellipsoid tubes, or specify the name
+ of the approximation schema for each of the nEllTubes
+ ellipsoid tubes separately.
+ approxSchemaDescr: char[1,] / cell[1,nEllTubes] of char[1,] -
+ description of the approximation schema. It is possible
+ either to specify one description of the approximation
+ schema for all of nEllTubes ellipsoid tubes, or specify
+ the description of the approximation schema for each
+ of the nEllTubes ellipsoid tubes separately.
+ absTol:double[1, 1] - absolute tolerance
+ relTol:double[1, 1] - relative tolerance
+ Output:
+ ellTubeRel: gras.ellapx.smartdb.rels.EllTube[1, 1] - constructed
+ ellipsoid tube object

- Optional:
- MArrayList:cell[1, nElem] - array of regularization ellipsoid
matrices
- timeVec:cell[1, m] - time vector
- ltGoodDirArray:cell[1, nElem] - good direction at time s
- sTime:double[1, 1] - time s
- approxType:gras.ellapx.enums.EApproxType - type of approximation
- (external, internal, not defined)
- approxSchemaName:cell[1,] - name of the schema
- approxSchemaDescr:cell[1,] - description of the schema
- calcPrecision:double[1, 1] - calculation precision
-
- Output:
- ellTubeRel: smartdb.relation.StaticRelation[1, 1] - constructed
relation
- object



@@ -7001,33 +7082,57 @@

::

- FROMQMARRAYS - creates a relation object using an array of ellipsoids,
- described by the array of ellipsoid matrices and
- array of ellipsoid centers. Also this method uses
- regularizer in the form of a matrix function. This
method
- used default scale factor.
+ FROMQMARRAYS creates nEllTubes ellipsoid tube objects using an
+ array of ellipsoid matrices, an array of ellipsoid centers
+ and an array of regularization marices specified at any point
+ of time from timeVec.

Input:
regular:
- QArrayList: double[nDim1, nDim2, ..., nDimN] - array of ellipsoid
- matrices
- aMat: double[nDim1, nDim2, ..., nDimN] - array of ellipsoid centers
- MArrayList: double[nDim1, nDim2, ..., nDimN] - ellipsoid matrices of
- regularization
-
- optional:
- timeVec:cell[1, m] - time vector
- ltGoodDirArray:cell[1, nElem] - good direction at time s
- sTime:double[1, 1] - time s
- approxType:gras.ellapx.enums.EApproxType - type of approximation
- (external, internal, not defined)
- approxSchemaName:cell[1,] - name of the schema
- approxSchemaDescr:cell[1,] - description of the schema
- calcPrecision:double[1, 1] - calculation precision
+ QArrayList: cell[nEllTubes,1] of double[nDims,nDims,nTimePoints] -
+ an array of nEllTubes 3-dimentional matrices in which
+ each of nTimePoints slices is a double[nDims,nDims]
+ ellipsoid matrix at nTimePoint point of time. Here
+ nTimePoints is number of elements in timeVec.
+ MArrayList: cell[nEllTubes,1] of double[nDims,nDims,nTimePoints] -
+ an array of nEllTubes 3-dimentional matrices in which
+ each of nTimePoints slices is a double[nDims,nDims]
+ regularization matrix at nTimePoint point of time.
+ aMat: double[nDims, nTimePoints] - a 2-dimentional matrix
+ in which each of nTimePoints columns is a
+ double[nDims, 1] ellipsoid center. Each center is specified
+ for nTimePoint point of time
+ timeVec: cell[1,1] of double[1,nTimePoints] - time vector
+ ltGoodDirArray: cell[nEllTubes,1] of double[nDim, nTimePoints] -
+ cell of nEllTubes arrays of nTimePoints good direction
+ vectors at any point of time from timeVec
+ sTime: double[1,1] - specific point of time from timeVec
+ which is best suited to describe good direction
+ approxType: gras.ellapx.enums.EApproxType[1,1] /
+ / gras.ellapx.enums.EApproxType[1,nEllTubes] - type
+ of approximation (External, Internal, NotDefined).
+ It is possible either to specify one type of
+ approximation for all of nEllTubes ellipsoid tubes,
+ or specify the type of approximation for each of the
+ nEllTubes ellipsoid tubes separately.
+ approxSchemaName: char[1,] / cell[1,nEllTubes] of char[1,] -
+ name of the approximation schema. It is possible either
+ to specify one name of the approximation schema for
+ all of nEllTubes ellipsoid tubes, or specify the name
+ of the approximation schema for each of the nEllTubes
+ ellipsoid tubes separately.
+ approxSchemaDescr: char[1,] / cell[1,nEllTubes] of char[1,] -
+ description of the approximation schema. It is possible
+ either to specify one description of the approximation
+ schema for all of nEllTubes ellipsoid tubes, or specify
+ the description of the approximation schema for each
+ of the nEllTubes ellipsoid tubes separately.
+ absTol:double[1, 1] - absolute tolerance
+ relTol:double[1, 1] - relative tolerance
+ Output:
+ ellTubeRel: gras.ellapx.smartdb.rels.EllTube[1, 1] - constructed
+ ellipsoid tube object

- Output:
- ellTubeRel: smartdb.relation.StaticRelation[1, 1] - constructed
relation
- object



@@ -7036,34 +7141,59 @@

::

- FROMQMSCALEDARRAYS - creates a relation object using an array of
ellipsoids,
- described by the array of ellipsoid matrices and
- array of ellipsoid centers. Also this method uses
- regularizer in the form of a matrix function.
-
+ FROMQMSCALEDARRAYS creates nEllTubes ellipsoid tube objects using an
+ array of ellipsoid matrices, an array of ellipsoid centers,
+ an array of regularization marices specified at any point
+ of time from timeVec and a vector of scale factors
+ specified for every created ellipsoid tube

Input:
regular:
- QArrayList: double[nDim1, nDim2, ..., nDimN] - array of ellipsoid
- matrices
- aMat: double[nDim1, nDim2, ..., nDimN] - array of ellipsoid centers
- MArrayList: double[nDim1, nDim2, ..., nDimN] - ellipsoid matrices
- of regularization
- scaleFactor:double[1, 1] - tube scale factor
-
- optional:
- timeVec:cell[1, m] - time vector
- ltGoodDirArray:cell[1, nElem] - good direction at time s
- sTime:double[1, 1] - time s
- approxType:gras.ellapx.enums.EApproxType - type of approximation
- (external, internal, not defined)
- approxSchemaName:cell[1,] - name of the schema
- approxSchemaDescr:cell[1,] - description of the schema
- calcPrecision:double[1, 1] - calculation precision
+ QArrayList: cell[nEllTubes,1] of double[nDims,nDims,nTimePoints] -
+ an array of nEllTubes 3-dimentional matrices in which
+ each of nTimePoints slices is a double[nDims,nDims]
+ ellipsoid matrix at nTimePoint point of time. Here
+ nTimePoints is number of elements in timeVec.
+ MArrayList: cell[nEllTubes,1] of double[nDims,nDims,nTimePoints] -
+ an array of nEllTubes 3-dimentional matrices in which
+ each of nTimePoints slices is a double[nDims,nDims]
+ regularization matrix at nTimePoint point of time.
+ aMat: double[nDims, nTimePoints] - a 2-dimentional matrix
+ in which each of nTimePoints columns is a
+ double[nDims, 1] ellipsoid center. Each center is specified
+ for nTimePoint point of time
+ timeVec: cell[1,1] of double[1,nTimePoints] - time vector
+ ltGoodDirArray: cell[nEllTubes,1] of double[nDim, nTimePoints] -
+ cell of nEllTubes arrays of nTimePoints good direction
+ vectors at any point of time from timeVec
+ sTime: double[1,1] - specific point of time from timeVec
+ which is best suited to describe good direction
+ approxType: gras.ellapx.enums.EApproxType[1,1] /
+ / gras.ellapx.enums.EApproxType[1,nEllTubes] - type
+ of approximation (External, Internal, NotDefined).
+ It is possible either to specify one type of
+ approximation for all of nEllTubes ellipsoid tubes,
+ or specify the type of approximation for each of the
+ nEllTubes ellipsoid tubes separately.
+ approxSchemaName: char[1,] / cell[1,nEllTubes] of char[1,] -
+ name of the approximation schema. It is possible either
+ to specify one name of the approximation schema for
+ all of nEllTubes ellipsoid tubes, or specify the name
+ of the approximation schema for each of the nEllTubes
+ ellipsoid tubes separately.
+ approxSchemaDescr: char[1,] / cell[1,nEllTubes] of char[1,] -
+ description of the approximation schema. It is possible
+ either to specify one description of the approximation
+ schema for all of nEllTubes ellipsoid tubes, or specify
+ the description of the approximation schema for each
+ of the nEllTubes ellipsoid tubes separately.
+ absTol:double[1, 1] - absolute tolerance
+ relTol:double[1, 1] - relative tolerance
+ scaleFactor:double[1,nTubes] - vector of scale factors

Output:
- ellTubeRel: smartdb.relation.StaticRelation[1, 1] - constructed
relation
- object
+ ellTubeRel: gras.ellapx.smartdb.rels.EllTube[1, 1] - constructed
+ ellipsoid tube object



@@ -7072,71 +7202,15 @@

::

- GETDATA - returns an indexed projection of CubeStruct object's content
-
+ GETDATA - gets data from ATypifiedAdjustedRel object
Input:
regular:
- self: CubeStruct [1,1] - the object
-
+ self.
+ varargin:
+ Output:
optional:
-
- subIndCVec:
- Case#1: numeric[1,]/numeric[,1]
-
- Case#2: cell[1,nDims]/cell[nDims,1] of double [nSubElem_i,1]
- for i=1,...,nDims
-
- -array of indices of field value slices that are selected
- to be returned; if not given (default),
- no indexation is performed

- Note!: numeric components of subIndVec are allowed to contain
- zeros which are be treated as they were references to null
- data slices
-
- dimVec: numeric[1,nDims]/numeric[nDims,1] - vector of dimension
- numbers corresponding to subIndCVec
-
- properties:
-
- fieldNameList: char[1,]/cell[1,nFields] of char[1,]
- list of field names to return
-
- structNameList: char[1,]/cell[1,nStructs] of char[1,]
- list of internal structures to return (by default it
- is {SData, SIsNull, SIsValueNull}
-
- replaceNull: logical[1,1] if true, null values are replaced with
- certain default values uniformly across all the cells,
- default value is false
-
- nullReplacements: cell[1,nReplacedFields] - list of null
- replacements for each of the fields
-
- nullReplacementFields: cell[1,nReplacedFields] - list of fields in
- which the nulls are to be replaced with the specified values,
- if not specified it is assumed that all fields are to be
- replaced
-
- NOTE!: all fields not listed in this parameter are replaced
with
- the default values
-
- checkInputs: logical[1,1] - true by default (input arguments are
- checked for correctness
-
- Output:
- regular:
- SData: struct [1,1] - structure containing values of
- fields at the selected slices, each field is an array
- containing values of the corresponding type
-
- SIsNull: struct [1,1] - structure containing a nested
- array with is-null indicators for each CubeStruct cell content

- SIsValueNull: struct [1,1] - structure containing a
- logical array [] for each of the fields (true
- means that a corresponding cell doesn't not contain
- any value



@@ -7146,17 +7220,20 @@

::

- GETELLARRAY - returns array of matrix's ellipsoid according to
- approxType
+ GETELLARRAY - returns array of ellipsoids according to
+ approxType

Input:
regular:
self.
- approxType:char[1,] - type of approximation(internal/external)
+ approxType: cell[nEllTubes, 1] of char[1,] - type of
+ approximation(internal/external)

Output:
- apprEllMat:double[nDim1,..., nDimN] - array of array of ellipsoid's
- matrices
+ apprEllMat: ellipsoid[nTimePoints, nEllTubes] - an array
+ of all the ellipsoids from all the ellipsoid tubes that
+ are stored in self object
+ timeVec: cell[1,1] of double[1,nTimePoints] - time vector



@@ -7192,51 +7269,89 @@
gras.ellapx.smartdb.rels.EllTube.getNoCatOrCutFieldsList
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

+::

+ GETNOCATORCUTFIELDSLIST - returns a list of fields of
+ EllTubeBasic object, which are not to be
+ concatenated or cut.
+
+ Input:
+ regular:
+ self.
+ Output:
+ fieldsList: cell[nFields, 1] of char[1, ] - list of fields
+ of EllTubeBasic object, which are not to be
+ concatenated or cut
+
+
+
+

gras.ellapx.smartdb.rels.EllTube.interp
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

+::

+ INTERP - interpolates ellipsoidal tube on a new time vector
+
+ Input:
+ regular:
+ self.
+ timeVec: double[1, nTimePoints] - sorted time vector to
+ interpolate on. Must begin with self.timeVec[1] and
+ end with self.timeVec[end]
+
+ Output:
+ interpEllTube: gras.ellapx.smartdb.rels.EllTubeBasic[1, 1] -
+ interpolated ellipsoidal tube
+
+

gras.ellapx.smartdb.rels.EllTube.isEqual
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

::

- ISEQUAL - compares current relation object with other relation object
and
- returns true if they are equal, otherwise it returns false
-
-
- Usage: isEq=isEqual(self,otherObj)
+ ISEQUAL - compares current relation object with other relation
+ object and returns true if they are equal, otherwise it returns
+ false.

Input:
regular:
- self: ARelation [1,1] - current relation object
- otherObj: ARelation [1,1] - other relation object
+ self.
+ otherObj: ARelation [1,1] - other relation object

properties:
- checkFieldOrder/isFieldOrderCheck: logical [1,1] - if true, then
fields
- in compared relations must be in the same order, otherwise the
- order is not important (false by default)
- checkTupleOrder: logical[1,1] - if true, then the tuples in the
- compared relations are expected to be in the same order,
- otherwise the order is not important (false by default)
-
- maxTolerance: double [1,1] - maximum allowed tolerance
-
+ checkFieldOrder/isFieldOrderCheck: logical [1,1] - if true,
+ then fields in compared relations must be in the same
+ order, otherwise the order is not important (false by
+ default)
+ checkTupleOrder: logical[1,1] - if true, then the tuples
+ in the compared relations are expected to be in the same
+ order, otherwise the order is not important (false by
+ default)
+ maxTolerance: double [1,1] - maximum allowed tolerance
+ maxRelativeTolerance: double [1,1] - maximum allowed relative
+ tolerance
compareMetaDataBackwardRef: logical[1,1] if true, the CubeStruct's
referenced from the meta data objects are also compared
-
- maxRelativeTolerance: double [1,1] - maximum allowed
- relative tolerance
+ notComparedFieldList: cell[1,nFields] of char[1,] - list
+ of fields that are not to be compared
+ areTimeBoundsCompared: logical[1,1] - if false,
+ ellipsoidal tubes are compared on intersection of
+ definition domains

Output:
- isEq: logical[1,1] - result of comparison
- reportStr: char[1,] - report of comparsion
+ isOk: logical[1, 1] - logical vector elements of
+ which take OK value if the fields in self and otherRel
+ are equal and otherwise it takes FALSE value
+ reportStr: char[1, ] - a report string which contains more
+ detailed information about inequal fields in self and
+ otherRel objects

-
-
+
+
+

gras.ellapx.smartdb.rels.EllTube.plot
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
@@ -7248,9 +7363,13 @@

Input:
regular:
- self:
+ self.
+ optional:
plObj: smartdb.disp.RelationDataPlotter[1,1] - plotter
object used for displaying ellipsoidal tubes
+ Output:
+ plObj: smartdb.disp.RelationDataPlotter[1,1] - plotter
+ object used for displaying ellipsoidal tubes



@@ -7259,97 +7378,72 @@

::

- PROJECT - computes projection of the relation object onto given time
- dependent subspase
+ PROJECT - projects ellipsoid tube onto subspace
+
Input:
regular:
self.
- projType: gras.ellapx.enums.EProjType[1,1] -
- type of the projection, can be
- 'Static' and 'DynamicAlongGoodCurve'
- projMatList: cell[1,nProj] of double[nSpDim,nDim] - list of
- projection matrices, not necessarily orthogonal
- fGetProjMat: function_handle[1,1] - function which creates
- vector of the projection
- matrices
- Input:
- regular:
- projMat:double[nDim, mDim] - matrix of the projection at the
- instant of time
- timeVec:double[1, nDim] - time interval
- optional:
- sTime:double[1,1] - instant of time
- Output:
- projOrthMatArray:double[1, nSpDim] - vector of the projection
- matrices
- projOrthMatTransArray:double[nSpDim, 1] - transposed vector of
- the projection matrices
+ projType: gras.ellapx.enums.EProjType[1, 1] - type of
+ projection. It can be Static or DynamicAlongGoodCurve.
+ projMatList: double[nDims, nDims] - subspace defined by
+ its basis vectors on which ellipsoid tube has to be
+ projected
+ fGetProjMat: cell_fun[1, ] - function that is used to
+ get the projection.
+
Output:
- ellTubeProjRel: gras.ellapx.smartdb.rels.EllTubeProj[1, 1]/
- gras.ellapx.smartdb.rels.EllTubeUnionProj[1, 1] -
- projected ellipsoidal tube
+ ellTubeProjRel: gras.ellapx.smartdb.rels.EllTubeProj[1, 1] -
+ ellipsoid tube projection
+ indProj2OrigVec: double[1, ] - vector of indices

- indProj2OrigVec:cell[nDim, 1] - index of the line number from
- which is obtained the projection
-
- Example:
- function example
- aMat = [0 1; 0 0]; bMat = eye(2);
- SUBounds = struct();
- SUBounds.center = {'sin(t)'; 'cos(t)'};
- SUBounds.shape = [9 0; 0 2];
- sys = elltool.linsys.LinSysContinuous(aMat, bMat, SUBounds);
- x0EllObj = ell_unitball(2);
- timeVec = [0 10];
- dirsMat = [1 0; 0 1]';
- rsObj = elltool.reach.ReachContinuous(sys, x0EllObj, dirsMat,
timeVec);
- ellTubeObj = rsObj.getEllTubeRel();
- unionEllTube = ...
- gras.ellapx.smartdb.rels.EllUnionTube.fromEllTubes(ellTubeObj);
- projMatList = {[1 0;0 1]};
- projType = gras.ellapx.enums.EProjType.Static;
- statEllTubeProj = unionEllTube.project(projType,projMatList,...
- @fGetProjMat);
- plObj=smartdb.disp.RelationDataPlotter();
- statEllTubeProj.plot(plObj);
- end
-
- function
[projOrthMatArray,projOrthMatTransArray]=fGetProjMat(projMat,...
- timeVec,varargin)
- nTimePoints=length(timeVec);
- projOrthMatArray=repmat(projMat,[1,1,nTimePoints]);
- projOrthMatTransArray=repmat(projMat.',[1,1,nTimePoints]);
- end



gras.ellapx.smartdb.rels.EllTube.projectStatic
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

+::

+ PROJECTSTATIC - computes a static projection of the relation
+ object onto static subspaces specified by static matrices
+
+ Input:
+ regular:
+ self.
+ projMatList: double[nSpDims,nDims]/cell[1,nProjs]
+ of double[nSpDims,nDims] - list of not necessarily orthogonal
+ projection matrices
+
+ Output:
+ ellTubeProjRel: smartdb.relation.StaticRelation[1, 1]/
+ smartdb.relation.DynamicRelation[1, 1]- projected relation
+ indProj2OrigVec:cell[nDims, 1] - index of the line number from
+ which is obtained the projection
+
+
+

gras.ellapx.smartdb.rels.EllTube.projectToOrths
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

::

- PROJECTTOORTHS - project elltube onto subspace defined by
- vectors of standart basis with indices specified in indVec
+ PROJECTTOORTHS - projects ellipsoid tube onto subspace defined
+ by vectors of standart basis with indices specified in
+ indVec.

Input:
regular:
- self: gras.ellapx.smartdb.rels.EllTube[1, 1] - elltube
- object
- indVec: double[1, nProjDims] - indices specifying a subset of
- standart basis
+ self.
+ indVec: double[1, nProjDims] - indices specifying a subset
+ of standart basis
optional:
projType: gras.ellapx.enums.EProjType[1, 1] - type of
- projection
+ projection. Default option is Static.

Output:
- regular:
- ellTubeProjRel: gras.ellapx.smartdb.rels.EllTubeProj[1, 1] -
- elltube projection
+ ellTubeProjRel: gras.ellapx.smartdb.rels.EllTubeProj[1, 1] -
+ ellipsoid tube projection

Example:
ellTubeProjRel = ellTubeRel.projectToOrths([1,2])
@@ -7363,56 +7457,68 @@

::

- SCALE - scales relation object
+ SCALE - calculates new value of scaleFactor for fields from
+ fieldNameList using fCalcFactor function

- Input:
+ Input:
regular:
- self.
- fCalcFactor - function which calculates factor for
- fields in fieldNameList
- Input:
- regular:
- fieldNameList: char/cell[1,] of char - a list of fields
- for which factor will be calculated
- Output:
- factor:double[1, 1] - calculated factor
-
- fieldNameList:cell[1,nElem]/char[1,] - names of the fields
+ self.
+ fCalcFactor: function_handle[1, 1] - function which calculates
+ scaleFactor for fields in fieldNameList
+ fieldNameList: char[1, ]/cell[1,nFields] of char[1, ] -
+ a list of field or nFields fields for which scale factor
+ will be calculated

Output:
- none
+ none.

- Example:
- nPoints=5;
- calcPrecision=0.001;
- approxSchemaDescr=char.empty(1,0);
- approxSchemaName=char.empty(1,0);
- nDims=3;
- nTubes=1;
- lsGoodDirVec=[1;0;1];
- aMat=zeros(nDims,nPoints);
- timeVec=1:nPoints;
- sTime=nPoints;
- approxType=gras.ellapx.enums.EApproxType.Internal;
- qArrayList=repmat({repmat(diag([1 2 3]),[1,1,nPoints])},1,nTubes);
- ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
- fromMatEllTube=...
- gras.ellapx.smartdb.rels.EllTube.fromQArrays(qArrayList,...
- aMat, timeVec,ltGoodDirArray, sTime, approxType,...
- approxSchemaName, approxSchemaDescr, calcPrecision);
- fromMatEllTube.scale(@(varargin)2,{});



gras.ellapx.smartdb.rels.EllTube.sortDetermenistically
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

+::

+ SORTDETERMENISTICALLY - sorts fields of ATypifiedAdjustedRel
+ object using specified maximal tolerance
+ Input:
+ regular:
+ self.
+ maxTolerance: double[1, 1] - maximal tolerance that is
+ used while sorting elements of self object.
+ Output:
+ none.
+
+
+
+

gras.ellapx.smartdb.rels.EllTube.thinOutTuples
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

+::

+ THINOUTTUPLES - thins ellipsoid tube object using vector of
+ indices specified by the user. The function returns new
+ ellipsoid tube object containing only ellipsoids from the
+ original ellipsoid tube with indices specified in indVec.
+
+ Input:
+ regular:
+ self.
+ indVec: double[nIndices, 1] - indices of ellipsoids which
+ are to be included in new ellipsoid tube object
+
+ Output:
+ thinnedEllTubeRel: gras.ellapx.smartdb.rels.EllTubeBasic[1, 1] -
+ new ellipsoid tube object containing only ellipsoids from
+ self EllTube object with indices specified in indVec
+
+
+
+
+

gras.ellapx.smartdb.rels.EllTubeProj
------------------------------------
@@ -7422,43 +7528,79 @@

::

- EllTubeProj - class which keeps ellipsoidal tube's projection
-
+ A class which allows to work with projections of ellipsoid tube objects.
+
Fields:
- QArray:cell[1, nElem] - Array of ellipsoid matrices
- aMat:cell[1, nElem] - Array of ellipsoid centers
- scaleFactor:double[1, 1] - Tube scale factor
- MArray:cell[1, nElem] - Array of regularization ellipsoid matrices
- dim :double[1, 1] - Dimensionality
- sTime:double[1, 1] - Time s
- approxSchemaName:cell[1,] - Name
- approxSchemaDescr:cell[1,] - Description
- approxType:gras.ellapx.enums.EApproxType - Type of approximation
- (external, internal, not defined)
- timeVec:cell[1, m] - Time vector
- calcPrecision:double[1, 1] - Calculation precision
- indSTime:double[1, 1] - index of sTime within timeVec
- ltGoodDirMat:cell[1, nElem] - Good direction curve
- lsGoodDirVec:cell[1, nElem] - Good direction at time s
- ltGoodDirNormVec:cell[1, nElem] - Norm of good direction curve
- lsGoodDirNorm:double[1, 1] - Norm of good direction at time s
- xTouchCurveMat:cell[1, nElem] - Touch point curve for good
- direction
- xTouchOpCurveMat:cell[1, nElem] - Touch point curve for direction
- opposite to good direction
- xsTouchVec:cell[1, nElem] - Touch point at time s
- xsTouchOpVec:cell[1, nElem] - Touch point at time s
- projSTimeMat: cell[1, 1] - Projection matrix at time s
- projType:gras.ellapx.enums.EProjType - Projection type
- ltGoodDirNormOrigVec:cell[1, 1] - Norm of the original (not
- projected) good direction curve
- lsGoodDirNormOrig:double[1, 1] - Norm of the original (not
- projected)good direction at time s
- lsGoodDirOrigVec:cell[1, 1] - Original (not projected) good
- direction at time s
+ QArray: cell[1,1] of double[nDims,nDims,nTimePoints] -
+ a 3-dimentional matrix in which each of nTimePoints slices is a
+ double[nDims,nDims] projection of an ellipsoid matrix on specified
+ subspace at nTimePoint point of time. Here nTimePoints is number
+ of elements in timeVec.
+ aMat: cell[1,nTimePoints] of double[nDims,1] - a 2-dimentional matrix
+ in which each of nTimePoints columns is a projection of
+ an ellipsoid center. Each center is specified for
+ nTimePoint point of time
+ scaleFactor: double[1, 1] - scale for the created ellipsoid tube
+ MArray: cell[1,1] of double[nDims,nDims,nTimePoints] -
+ a 3-dimentional matrix in which each of nTimePoints slices is a
+ double[nDims,nDims] projection of a regularization matrix on
specified
+ subspace at nTimePoint point of time.
+ dim: double[1, 1] - the dimension of the space on which the touching
+ curves are projected
+ sTime: double[1, 1] - specific point of time which is best suited to
+ describe good direction
+ approxSchemaName: cell[1, 1] of char[1,] - name of the
+ approximation schema
+ approxSchemaDescr: cell[1, 1] of char[1,] - description of the
+ approximation schema
+ approxType: gras.ellapx.enums.EApproxType[1,1] - type of approximation
+ (External, Internal, NotDefined)
+ timeVec: double[1, nTimePoints] - time vector
+ absTolerance: double[1, 1] - absolute tolerance
+ relTolerance: double[1, 1] - relative tolerance
+ indSTime: double[1, 1] - index of sTime point within timeVec
+ ltGoodDirMat: cell[1, nTimePoints] of double[nDims, 1] - matrix of
+ the projections of good direction vectors on the specified space
+ at any point of time from timeVec
+ lsGoodDirVec: cell[1, 1] of double[nDims, 1] - the projection of good
+ direction vector on the specified space at sTime point of time
+ ltGoodDirNormVec: cell[1, 1] of double[1, nTimePoints] - norm of the
+ projections of good direction vectors on the specified space at
***The diff for this file has been truncated for email.***
=======================================
---
/branches/issue_133_aatanesyan/doc/_build/html/_sources/chap_implement.txt
Tue Nov 19 13:44:20 2013 UTC
+++
/branches/issue_133_aatanesyan/doc/_build/html/_sources/chap_implement.txt
Wed Mar 5 02:41:50 2014 UTC
@@ -1,4 +1,4 @@
-Implementation
+Implementation
==============

Operations with ellipsoids
@@ -391,6 +391,8 @@
default optimization package included in the distribution of the
*Ellipsoidal Toolbox* is SeDuMi ([STUR1999]_, [SDMHP]_).

+.. _section-label:
+
Operations with ellipsoidal tubes
---------------------------------

@@ -400,7 +402,11 @@
gras.ellapx.smartdb.rels.EllUnionTube is used to store tubes by the
instant of time:

-.. math:: {\mathcal X}_{U}[t]=\bigcup \limits_{\tau\leqslant t}{\mathcal
X}[\tau],
+.. _union-label:
+
+.. math::
+
+ {\mathcal X}_{U}[t]=\bigcup \limits_{\tau\leqslant t}{\mathcal X}[\tau],

where :math:`{\mathcal X}[\tau]` is single ellipsoidal tube. The class
gras.ellapx.smartdb.rels.EllTubeProj is used to describe the projection
@@ -432,6 +438,8 @@
:language: matlab
:linenos:

+.. _goto-label:
+
We can compute the projection of the ellipsoidal
tube onto time-dependent subspace.

=======================================
--- /branches/issue_133_aatanesyan/doc/_build/html/_sources/chap_reach.txt
Mon Feb 24 20:40:31 2014 UTC
+++ /branches/issue_133_aatanesyan/doc/_build/html/_sources/chap_reach.txt
Wed Mar 5 02:41:50 2014 UTC
@@ -1,4 +1,4 @@
-Reachability
+Reachability
============

Basics of Reachability Analysis
=======================================
--- /branches/issue_133_aatanesyan/doc/_build/html/chap_ellTube.html Tue
Feb 25 09:31:56 2014 UTC
+++ /branches/issue_133_aatanesyan/doc/_build/html/chap_ellTube.html Wed
Mar 5 02:41:50 2014 UTC
@@ -6,7 +6,7 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />

- <title>Ellipsoid tubes and touching curves &mdash; Ellipsoidal Toolbox
2.0 beta 1 documentation</title>
+ <title>Ellipsoid tubes, unions and projections &mdash; Ellipsoidal
Toolbox 2.0 beta 1 documentation</title>

<link rel="stylesheet" href="_static/default.css" type="text/css" />
<link rel="stylesheet" href="_static/pygments.css" type="text/css" />
@@ -49,79 +49,26 @@
<div class="bodywrapper">
<div class="body">

- <div class="section" id="ellipsoid-tubes-and-touching-curves">
-<h1>Ellipsoid tubes and touching curves<a class="headerlink"
href="#ellipsoid-tubes-and-touching-curves" title="Permalink to this
headline">¶</a></h1>
-<div class="section" id="touching-curves">
-<h2>Touching curves<a class="headerlink" href="#touching-curves"
title="Permalink to this headline">¶</a></h2>
-<p>One of the basic insruments in the <em>Ellipsoidal Toolbox</em> are
classes, which allow to work with touching curves. These are the curves
along which the internal and external ellipsoidal approximations are
touching. In <em>Ellipsoidal Toolbox</em> there are two basic classes
(<em>EllTubeTouchCurveBasic</em> and <em>EllTubeTouchCurveProjBasic</em>)
which allow us to keep touching curves and their projections. These classes
do not add any functionality, that we can use, while working with the
toolbox, (They do not have public methods.) but they are further used in
other classes, which inherit these ones.</p>
-<div class="section" id="elltubetouchcurvebasic-class">
-<h3><em>EllTubeTouchCurveBasic</em> class<a class="headerlink"
href="#elltubetouchcurvebasic-class" title="Permalink to this
headline">¶</a></h3>
-<p>This class allows us to keep touch point curve objects. This kind of
objects have a lot of different fields, which store the information about
the touching curve.
-The first field of our object is:</p>
+ <div class="section" id="ellipsoid-tubes-unions-and-projections">
+<h1>Ellipsoid tubes, unions and projections<a class="headerlink"
href="#ellipsoid-tubes-unions-and-projections" title="Permalink to this
headline">¶</a></h1>
+<p>There are two types of ellipsoid tube objects that we can work with
using <em>Ellipsoidal Toolbox</em>:</p>
<ul class="simple">
-<li><em>dim</em>: In this field the dimension of the space in which the
touching
-curves are defined is stored.</li>
+<li>ellipsoidal tubes that are described in
<em>gras.ellapx.smartdb.rels.EllTube</em> class;</li>
+<li>unions of ellipsoidal tubes by the instant of time described in
<em>gras.ellapx.smartdb.rels.EllUnionTube</em> class (see <a
class="reference internal"
href="chap_implement.html#union-label"><em>formula</em></a>).</li>
</ul>
-<p>Then there are several fields that are connecteld with time:</p>
+<p>The projections of ellipsoid tubes can be either static or dynamic. The
are described in gras.ellapx.smartdb.rels.EllTubeProj class. As for the
unions of ellipsoid tubes, they can only be projected on static subspaces.
These projections are described in
gras.ellapx.smartdb.rels.EllUnionTubeStaticProj class. For more information
about these types of projections and their differences and for examples see
this <a class="reference internal"
href="chap_implement.html#section-label"><em>link</em></a>.</p>
+<div class="section" id="ellipsoid-tubes">
+<h2>Ellipsoid tubes<a class="headerlink" href="#ellipsoid-tubes"
title="Permalink to this headline">¶</a></h2>
+<p>There is a whole variety of operations upon ellipsoid tubes in
<em>Ellipsoidal Toolbox</em>. We can, of course, create them. When the
ellipsoid tube object is created, we can cut them, concatenate,
interpolate, plot and project them and so on.</p>
+<p>The instruments to create ellipsoid tube objects are several
functions:</p>
<ul class="simple">
-<li><em>timeVec</em>: Time vector in which the the touching curves are
defined;</li>
-<li><em>sTime</em>: Specific point of time which is best suited to
describe good direction;</li>
-<li><em>indSTime</em>: The index of sTime point within timeVec is srored
in this field.</li>
+<li><em>fromQArrays</em> method creates nEllTubes ellipsoid tube objects
using an array of ellipsoid matrices and an array of ellipsoid centers
specified at any point of time from timeVec;</li>
+<li><em>fromQMArrays</em> method acts the same way as <em>fromQArrays</em>
method, except for this one requires to specify an array of regularization
marices specified at any point of time from timeVec;</li>
+<li><em>fromQMScaledArrays</em> method acts the same way as
<em>fromQMArrays</em> method, except for this one requires to also specify
a vector of scale factors specified for every created ellipsoid tube;</li>
+<li><em>fromEllArray</em> method creates ellipsoid tube object using an
array of ellipsoids;</li>
+<li><em>fromEllMArray</em> method creates ellipsoid tube object using an
array of ellipsoids and an array of regularisation matrices.</li>
</ul>
-<p>It should be said that the <em>good direction</em> is the direction
along which the internal and external approximations of ellipsoid tubes are
touching. Next several fields specify the type of approximation which was
used? while creating these touching curves:</p>
-<ul class="simple">
-<li><em>approxSchemaName</em>: The name of the approximation schema;</li>
-<li><em>approxSchemaDescr</em>: The description of the approximation
schema;</li>
-<li><em>approxType</em>: The type of approximation (External, Internal,
NotDefined) is stored in this field.</li>
-</ul>
-<p>Then there are two fields which keep the absolute tolerance and
relative tolerance used to create this object (<em>absTolerance</em> and
<em>relTolerance</em>, respectively). And finally come the fields which
allow us to keep the touching curves and good directions:</p>
-<ul class="simple">
-<li><em>ltGoodDirMat</em> field stores the matrix of good direction
vectors at any point of time from timeVec;</li>
-<li><em>lsGoodDirVec</em> field stores the good direction vector at sTime
point of time;</li>
-<li><em>ltGoodDirNormVec</em> field stores the norm of good direction
vectors at any point of time from timeVec;</li>
-<li><em>lsGoodDirNorm</em> field stores the norm of good direction vector
at sTime point of time;</li>
-<li><em>xTouchCurveMat</em> field stores the touch point curve for good
direction matrix;</li>
-<li><em>xTouchOpCurveMat</em> field stores the touch point curve oposite
to the xTouchCurveMat touch point curve;</li>
-<li><em>xsTouchVec</em> field stores the touch point at sTime point of
time;</li>
-<li><em>xsTouchOpVec</em> field stores a point opposite to the xsTouchVec
touch point;</li>
-<li><em>isLsTouch</em> field stores a logical variable which indicates
whether a touch takes place along good direction at sTime point of
time;</li>
-<li><em>isLtTouchVec</em> field stores a logical vector which indicates
whether a touch takes place along good direction at any point of
time from timeVec.</li>
-</ul>
-</div>
-<div class="section" id="elltubetouchcurveprojbasic-class">
-<h3><em>EllTubeTouchCurveProjBasic</em> class<a class="headerlink"
href="#elltubetouchcurveprojbasic-class" title="Permalink to this
headline">¶</a></h3>
-<p>This class allows us to keep the projections of touch point curves.
This kind of objects have a lot of different fields, which store the
information about the projection of touching curve. First of all it
inherits all the fields from <em>EllTubeTouchCurveBasic</em> class, and,
secondly, it adds some of its own fields. The inherited fields store the
information about the projection instead of the information about the
original curve, but their meaning is all the same.
-The first group of new fields is connected to the type of projection and
the space on which the curve is projected:</p>
-<ul class="simple">
-<li><em>projSMat</em> field stores the projection matrix at sTime point of
time;</li>
-<li><em>projArray</em> field stores an array of projection matrices at any
point of time from timVec;</li>
-<li><em>projType</em> field stores the type of projection (Static or
DynamicAlongGoodCurve).</li>
-</ul>
-<p>And then come the new fields which store some information about the
original curve:</p>
-<ul class="simple">
-<li><em>ltGoodDirNormOrigVec</em> field stores the norm of the original
good direction vectors at any point of time from timeVec;</li>
-<li><em>lsGoodDirNormOrig</em> field stores the norm of the original good
direction vector at sTime point of time;</li>
-<li><em>ltGoodDirOrigMat</em> field stores the matrix of the original good
direction vectors at any point of time from timeVec;</li>
-<li><em>lsGoodDirOrigVec</em> field stores the original good direction
vector at sTime point of time;</li>
-<li><em>ltGoodDirNormOrigProjVec</em> field stores the norm of the
projection of the original good direction curve;</li>
-<li><em>ltGoodDirOrigProjMat</em> field stores the projectition of the
original good direction curve.</li>
-</ul>
-</div>
-</div>
-<div class="section" id="ellipsoidal-tubes">
-<h2>Ellipsoidal tubes<a class="headerlink" href="#ellipsoidal-tubes"
title="Permalink to this headline">¶</a></h2>
-<p>Other basic insrument in the <em>Ellipsoidal Toolbox</em> are classes,
which allow to work with ellipsoidal tubes. In <em>Ellipsoidal Toolbox</em>
there are four classes (<em>EllTubeBasic</em>, <em>EllTube</em>,
<em>EllTubeProjBasic</em> and <em>EllTubeProj</em>) which give us the
needed functionality to work with ellipsoid tube objects.</p>
-<div class="section" id="elltubebasic-class">
-<h3><em>EllTubeBasic</em> class<a class="headerlink"
href="#elltubebasic-class" title="Permalink to this headline">¶</a></h3>
-<p>This class inherits its fields from <em>EllTubeTouchCurveBasic</em>
class and adds some new fields which are:</p>
-<ul class="simple">
-<li><em>QArray</em> field which stores an array of nTimePoints ellipsoid
matrices. Each element from this
-array specifies an ellipsoid matrix at nTimePoint point of time. Here
nTimePoints is number of elements in <em>timeVec</em> (It is one of the
fields inherited from <em>EllTubeTouchCurveBasic</em> class.);</li>
-<li><em>aMat</em> field which stores an array of nTimePoints ellipsoid
centers. Each center is specified for nTimePoint point of time;</li>
-<li>scaleFactor field which stores the scale for the created ellipsoid
tube;</li>
-<li>MArray field which stores an array of nTimePoints regularization
matrices. Each element from this array specifies a regularization
matrix at nTimePoint point of time.</li>
-</ul>
-<p>This class gives us some methods which can be used to work with
ellipsoidal tubes. For example, if we have already created ellipsoid tube
object using one timeVec vector of time, then we can interpolate this tube,
using new time vector. Take notice that we have to make sure that the first
and the last elements in old and new vectors of time are the same.</p>
+<p>Basically we can divide these methods into two groups, based od what
objects they are using to create ellipsoid tube: an array of ellipsoid
matrices with an array of ellipsoid centers (by using these methods we can
create an ellipsoid tube object containing several ellipsoid tubes) or an
array of ellipsoids (by using these methods we can create an ellipsoid tube
object containing one ellipsoid tube). To illustrate the usage of these
methods we have to describe several functions, that will be used in the
process. Below are their descriptions.</p>
<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
2
3
@@ -142,38 +89,29 @@
18
19
20
-21
-22
-23
-24
-25</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of usage of INTERP function from EllTubeBasic class.
In this</span>
-<span class="c">% example an ellipsoid tube object is created, using
oldTimeVec time</span>
-<span class="c">% vector. Then it is interpolated on newTimeVec time
vector.</span>
-<span class="n">nPoints</span><span class="p">=</span><span
class="mi">10</span><span class="p">;</span>
-<span class="n">absTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">relTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">approxSchemaDescr</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
-<span class="n">approxSchemaName</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
-<span class="n">nDims</span><span class="p">=</span><span
class="mi">3</span><span class="p">;</span>
-<span class="n">nTubes</span><span class="p">=</span><span
class="mi">1</span><span class="p">;</span>
-<span class="n">lsGoodDirVec</span><span class="p">=[</span><span
class="mi">1</span><span class="p">;</span><span class="mi">0</span><span
class="p">;</span><span class="mi">1</span><span class="p">];</span>
-<span class="n">aMat</span><span class="p">=</span><span
class="nb">zeros</span><span class="p">(</span><span
class="n">nDims</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">);</span>
-<span class="n">timeVec</span><span class="p">=(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):</span><span
class="mi">1</span><span class="p">;</span>
-<span class="n">sTime</span><span class="p">=</span><span
class="n">timeVec</span><span class="p">(</span><span
class="n">randi</span><span class="p">(</span><span
class="n">nPoints</span><span class="p">,</span><span
class="mi">1</span><span class="p">));</span>
-<span class="n">approxType</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">Internal</span><span class="p">;</span>
-<span class="n">qArrayList</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">({</span><span
class="nb">repmat</span><span class="p">(</span><span
class="nb">diag</span><span class="p">([</span><span class="mi">1</span>
<span class="mi">2</span> <span class="mi">3</span><span
class="p">]),[</span><span class="mi">1</span><span class="p">,</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">])},</span><span
class="c">...</span>
- <span class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">);</span>
-<span class="n">ltGoodDirArray</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">(</span><span
class="n">lsGoodDirVec</span><span class="p">,[</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">]);</span>
-<span class="n">fromMatEllTube</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">rels</span><span class="p">.</span><span
class="n">EllTube</span><span class="p">.</span><span
class="n">fromQArrays</span><span class="p">(</span><span
class="c">...</span>
- <span class="n">qArrayList</span><span class="p">,</span> <span
class="n">aMat</span><span class="p">,</span> <span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
- <span class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">sTime</span><span class="p">,</span> <span
class="n">approxType</span><span class="p">,</span> <span
class="n">approxSchemaName</span><span class="p">,</span><span
class="c">...</span>
- <span class="n">approxSchemaDescr</span><span class="p">,</span> <span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">);</span>
-<span class="n">newnPoints</span><span class="p">=</span><span
class="mi">100</span><span class="p">;</span>
-<span class="n">newTimeVec</span> <span class="p">=</span> <span
class="p">(</span><span class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">newnPoints</span><span class="p">):</span><span
class="mi">1</span><span class="p">;</span>
-<span class="n">interpEllTube</span> <span class="p">=</span> <span
class="n">fromMatEllTube</span><span class="p">.</span><span
class="n">interp</span><span class="p">(</span><span
class="n">newTimeVec</span><span class="p">);</span>
+21</pre></div></td><td class="code"><div class="highlight"><pre>% This
function returns the values of arguments, that are the same for
+% FROMQARRAYS, FROMQMARRAYS and FROMQMSCALEDARRAYS methods of creating an
+% ellipsoid tube object. Basically, this function creates a set of
+% arguments nessesary for creating an ellipsoid tube object containing
+% nTubes ellipsoid tubes. Here nTubes is a random natural number in the
+% range from one to ten.
+%
+function [nTubes, nPoints, nDims, absTol, relTol, timeVec,...
+ sTime, lsGoodDirVec, ltGoodDirArray, aMat, qArrayList] = getData()
+nTubes=randi(10,1);
+nPoints=20;
+nDims=3;
+absTol=0.001;
+relTol=0.001;
+timeVec=(1/nPoints):(1/nPoints):1;
+sTime=timeVec(randi(nPoints,1));
+lsGoodDirVec=[1;0;0];
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+aMat=zeros(nDims,nPoints);
+qArrayList=repmat({repmat(diag([0.1 0.2 0.3]),[1,1,nPoints])},1,nTubes);
+end
</pre></div>
</td></tr></table></div>
-<p>Other method that we can use is <em>THINOUTTUPLES</em> method. It
allows us to thin out the already created ellipsoid tube, by saving only
the ellipsoids at specified points of time.</p>
<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
2
3
@@ -192,40 +130,28 @@
16
17
18
-19
-20
-21
-22
-23
-24
-25</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of usage of THINOUTTUPLES function from EllTubeBasic
class. In</span>
-<span class="c">% this example an ellipsoid tube object is created, using
TimeVec time</span>
-<span class="c">% vector. Then it is thinned out using indVec vector of
indices of elements</span>
-<span class="c">% from timeVec.</span>
-<span class="n">nPoints</span><span class="p">=</span><span
class="mi">10</span><span class="p">;</span>
-<span class="n">absTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">relTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">approxSchemaDescr</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
-<span class="n">approxSchemaName</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
-<span class="n">nDims</span><span class="p">=</span><span
class="mi">3</span><span class="p">;</span>
-<span class="n">nTubes</span><span class="p">=</span><span
class="mi">1</span><span class="p">;</span>
-<span class="n">lsGoodDirVec</span><span class="p">=[</span><span
class="mi">1</span><span class="p">;</span><span class="mi">0</span><span
class="p">;</span><span class="mi">1</span><span class="p">];</span>
-<span class="n">aMat</span><span class="p">=</span><span
class="nb">zeros</span><span class="p">(</span><span
class="n">nDims</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">);</span>
-<span class="n">timeVec</span><span class="p">=(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):</span><span
class="mi">1</span><span class="p">;</span>
-<span class="n">sTime</span><span class="p">=</span><span
class="n">timeVec</span><span class="p">(</span><span
class="n">randi</span><span class="p">(</span><span
class="n">nPoints</span><span class="p">,</span><span
class="mi">1</span><span class="p">));</span>
-<span class="n">approxType</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">Internal</span><span class="p">;</span>
-<span class="n">qArrayList</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">({</span><span
class="nb">repmat</span><span class="p">(</span><span
class="nb">diag</span><span class="p">([</span><span class="mi">1</span>
<span class="mi">2</span> <span class="mi">3</span><span
class="p">]),[</span><span class="mi">1</span><span class="p">,</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">])},</span><span
class="c">...</span>
- <span class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">);</span>
-<span class="n">ltGoodDirArray</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">(</span><span
class="n">lsGoodDirVec</span><span class="p">,[</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">]);</span>
-<span class="n">fromMatEllTube</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">rels</span><span class="p">.</span><span
class="n">EllTube</span><span class="p">.</span><span
class="n">fromQArrays</span><span class="p">(</span><span
class="c">...</span>
- <span class="n">qArrayList</span><span class="p">,</span> <span
class="n">aMat</span><span class="p">,</span> <span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
- <span class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">sTime</span><span class="p">,</span> <span
class="n">approxType</span><span class="p">,</span> <span
class="n">approxSchemaName</span><span class="p">,</span><span
class="c">...</span>
- <span class="n">approxSchemaDescr</span><span class="p">,</span> <span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">);</span>
-<span class="n">indVec</span> <span class="p">=</span> <span
class="n">randi</span><span class="p">(</span><span
class="n">nPoints</span><span class="p">,</span><span
class="mi">1</span><span class="p">,</span><span class="mi">5</span><span
class="p">);</span>
-<span class="n">thinOutEllTube</span> <span class="p">=</span> <span
class="n">fromMatEllTube</span><span class="p">.</span><span
class="n">thinOutTuples</span><span class="p">(</span><span
class="n">indVec</span><span class="p">);</span>
+19</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% This function returns the values of arguments, that specify the
type of</span>
+<span class="c">% approximation that will be used to create an ellipsoid
tube object. It</span>
+<span class="c">% will be a random type of approximation (Internal or
External). These</span>
+<span class="c">% arguments can be used while creating an ellipsoid tube
object containing</span>
+<span class="c">% one ellipsoid tube or several ellipsoid tubes with the
same type of</span>
+<span class="c">% approximation.</span>
+<span class="c">%</span>
+<span class="k">function</span><span class="w"> </span>[approxSchemaDescr,
approxSchemaName, approxType] <span class="p">=</span><span class="w">
</span><span class="nf">getSameApprox</span><span class="p">()</span><span
class="w"></span>
+<span class="w"> </span><span class="n">type</span> <span
class="p">=</span> <span class="n">randi</span><span
class="p">(</span><span class="mi">2</span><span class="p">,</span><span
class="mi">1</span><span class="p">);</span>
+ <span class="k">if</span> <span class="n">type</span> <span
class="o">==</span> <span class="mi">1</span>
+ <span class="n">approxSchemaDescr</span><span
class="p">=</span><span class="s">&#39;Internal&#39;</span><span
class="p">;</span>
+ <span class="n">approxSchemaName</span><span
class="p">=</span><span class="s">&#39;Internal&#39;</span><span
class="p">;</span>
+ <span class="n">approxType</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">Internal</span><span class="p">;</span>
+ <span class="k">else</span>
+ <span class="n">approxSchemaDescr</span><span
class="p">=</span><span class="s">&#39;External&#39;</span><span
class="p">;</span>
+ <span class="n">approxSchemaName</span><span
class="p">=</span><span class="s">&#39;External&#39;</span><span
class="p">;</span>
+ <span class="n">approxType</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">External</span><span class="p">;</span>
+ <span class="k">end</span>
+<span class="k">end</span>
</pre></div>
</td></tr></table></div>
-<p>Then we can also cut the created ellipsoid tube, leaving only part of
it at specified vector of time or point of time. Below are the exmples:</p>
+<p>Using the three above mentioned functions we can describe an examples
of <em>fromQArrays</em>, <em>fromQMArrays</em> and
<em>fromQMScaledArrays</em> methods&#8217; usage.</p>
<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
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@@ -236,43 +162,17 @@
8
9
10
-11
-12
-13
-14
-15
-16
-17
-18
-19
-20
-21
-22
-23
-24</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of usage of CUT function from EllTubeBasic class.
In</span>
-<span class="c">% this example an ellipsoid tube object is created, using
TimeVec time</span>
-<span class="c">% vector. Then it is cut using cutTimeVec time
vector.</span>
-<span class="n">nPoints</span><span class="p">=</span><span
class="mi">10</span><span class="p">;</span>
-<span class="n">absTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">relTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">approxSchemaDescr</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
-<span class="n">approxSchemaName</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
-<span class="n">nDims</span><span class="p">=</span><span
class="mi">3</span><span class="p">;</span>
-<span class="n">nTubes</span><span class="p">=</span><span
class="mi">1</span><span class="p">;</span>
-<span class="n">lsGoodDirVec</span><span class="p">=[</span><span
class="mi">1</span><span class="p">;</span><span class="mi">0</span><span
class="p">;</span><span class="mi">1</span><span class="p">];</span>
-<span class="n">aMat</span><span class="p">=</span><span
class="nb">zeros</span><span class="p">(</span><span
class="n">nDims</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">);</span>
-<span class="n">timeVec</span><span class="p">=(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):</span><span
class="mi">1</span><span class="p">;</span>
-<span class="n">sTime</span><span class="p">=</span><span
class="n">timeVec</span><span class="p">(</span><span
class="n">randi</span><span class="p">(</span><span
class="n">nPoints</span><span class="p">,</span><span
class="mi">1</span><span class="p">));</span>
-<span class="n">approxType</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">Internal</span><span class="p">;</span>
-<span class="n">qArrayList</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">({</span><span
class="nb">repmat</span><span class="p">(</span><span
class="nb">diag</span><span class="p">([</span><span class="mi">1</span>
<span class="mi">2</span> <span class="mi">3</span><span
class="p">]),[</span><span class="mi">1</span><span class="p">,</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">])},</span><span
class="c">...</span>
- <span class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">);</span>
-<span class="n">ltGoodDirArray</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">(</span><span
class="n">lsGoodDirVec</span><span class="p">,[</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">]);</span>
+11</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of creating nTubes ellipsoid tube objects using
fromQArrays</span>
+<span class="c">% function with the same type of approximation.</span>
+<span class="p">[</span><span class="n">nTubes</span><span
class="p">,</span> <span class="n">nPoints</span><span class="p">,</span>
<span class="n">nDims</span><span class="p">,</span> <span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">,</span> <span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
+ <span class="n">sTime</span><span class="p">,</span> <span
class="n">lsGoodDirVec</span><span class="p">,</span> <span
class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">aMat</span><span class="p">,</span> <span
class="n">qArrayList</span><span class="p">]</span> <span
class="p">=</span> <span class="c">...</span>
+ <span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">test</span><span class="p">.</span><span
class="n">examples</span><span class="p">.</span><span
class="n">getData</span><span class="p">();</span>
+<span class="p">[</span><span class="n">approxSchemaDescr</span><span
class="p">,</span> <span class="n">approxSchemaName</span><span
class="p">,</span> <span class="n">approxType</span><span
class="p">]</span> <span class="p">=</span> <span class="c">...</span>
+ <span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">test</span><span class="p">.</span><span
class="n">examples</span><span class="p">.</span><span
class="n">getSameApprox</span><span class="p">();</span>
<span class="n">fromMatEllTube</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">rels</span><span class="p">.</span><span
class="n">EllTube</span><span class="p">.</span><span
class="n">fromQArrays</span><span class="p">(</span><span
class="c">...</span>
<span class="n">qArrayList</span><span class="p">,</span> <span
class="n">aMat</span><span class="p">,</span> <span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
<span class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">sTime</span><span class="p">,</span> <span
class="n">approxType</span><span class="p">,</span> <span
class="n">approxSchemaName</span><span class="p">,</span><span
class="c">...</span>
<span class="n">approxSchemaDescr</span><span class="p">,</span> <span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">);</span>
-<span class="n">cutTimeVec</span> <span class="p">=</span> <span
class="p">[</span><span class="n">timeVec</span><span
class="p">(</span><span class="mi">2</span><span class="p">)</span> <span
class="n">timeVec</span><span class="p">(</span><span
class="mi">7</span><span class="p">)];</span>
-<span class="n">cutVecEllTube</span> <span class="p">=</span> <span
class="n">fromMatEllTube</span><span class="p">.</span><span
class="n">cut</span><span class="p">(</span><span
class="n">cutTimeVec</span><span class="p">);</span>
</pre></div>
</td></tr></table></div>
<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
@@ -297,24 +197,22 @@
20
21
22
-23
-24
-25</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of usage of CUT function from EllTubeBasic class.
In</span>
-<span class="c">% this example an ellipsoid tube object is created, using
TimeVec time</span>
-<span class="c">% vector. Then it is cut using cutTimePoint point</span>
-<span class="c">% of time.</span>
+23</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of creating nTubes ellipsoid tube objects using
fromQArrays</span>
+<span class="c">% function with different types of approximation.</span>
<span class="n">nPoints</span><span class="p">=</span><span
class="mi">10</span><span class="p">;</span>
<span class="n">absTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
<span class="n">relTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">approxSchemaDescr</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
-<span class="n">approxSchemaName</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
+<span class="n">approxSchemaDescr</span><span class="p">={</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span> <span
class="s">&#39;External&#39;</span><span class="p">;</span> <span
class="s">&#39;External&#39;</span><span class="p">};</span>
+<span class="n">approxSchemaName</span><span class="p">={</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span> <span
class="s">&#39;External&#39;</span><span class="p">;</span> <span
class="s">&#39;External&#39;</span><span class="p">};</span>
<span class="n">nDims</span><span class="p">=</span><span
class="mi">3</span><span class="p">;</span>
-<span class="n">nTubes</span><span class="p">=</span><span
class="mi">1</span><span class="p">;</span>
+<span class="n">nTubes</span><span class="p">=</span><span
class="mi">3</span><span class="p">;</span>
<span class="n">lsGoodDirVec</span><span class="p">=[</span><span
class="mi">1</span><span class="p">;</span><span class="mi">0</span><span
class="p">;</span><span class="mi">1</span><span class="p">];</span>
<span class="n">aMat</span><span class="p">=</span><span
class="nb">zeros</span><span class="p">(</span><span
class="n">nDims</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">);</span>
<span class="n">timeVec</span><span class="p">=(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):</span><span
class="mi">1</span><span class="p">;</span>
<span class="n">sTime</span><span class="p">=</span><span
class="n">timeVec</span><span class="p">(</span><span
class="n">randi</span><span class="p">(</span><span
class="n">nPoints</span><span class="p">,</span><span
class="mi">1</span><span class="p">));</span>
-<span class="n">approxType</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">Internal</span><span class="p">;</span>
+<span class="n">approxType</span><span class="p">=[</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">Internal</span><span class="p">,</span><span class="c">...</span>
+ <span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">External</span><span class="p">,</span><span class="c">...</span>
+ <span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">External</span><span class="p">]</span><span
class="o">&#39;</span><span class="p">;</span>
<span class="n">qArrayList</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">({</span><span
class="nb">repmat</span><span class="p">(</span><span
class="nb">diag</span><span class="p">([</span><span class="mi">1</span>
<span class="mi">2</span> <span class="mi">3</span><span
class="p">]),[</span><span class="mi">1</span><span class="p">,</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">])},</span><span
class="c">...</span>
<span class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">);</span>
<span class="n">ltGoodDirArray</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">(</span><span
class="n">lsGoodDirVec</span><span class="p">,[</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">]);</span>
@@ -322,22 +220,8 @@
<span class="n">qArrayList</span><span class="p">,</span> <span
class="n">aMat</span><span class="p">,</span> <span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
<span class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">sTime</span><span class="p">,</span> <span
class="n">approxType</span><span class="p">,</span> <span
class="n">approxSchemaName</span><span class="p">,</span><span
class="c">...</span>
<span class="n">approxSchemaDescr</span><span class="p">,</span> <span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">);</span>
-<span class="n">cutTimePoint</span> <span class="p">=</span> <span
class="n">timeVec</span><span class="p">(</span><span
class="n">randi</span><span class="p">(</span><span
class="n">nPoints</span><span class="p">,</span><span
class="mi">1</span><span class="p">));</span>
-<span class="n">cutPointEllTube</span> <span class="p">=</span> <span
class="n">fromMatEllTube</span><span class="p">.</span><span
class="n">cut</span><span class="p">(</span><span
class="n">cutTimePoint</span><span class="p">);</span>
</pre></div>
</td></tr></table></div>
-</div>
-<div class="section" id="elltube-class">
-<h3><em>EllTube</em> class<a class="headerlink" href="#elltube-class"
title="Permalink to this headline">¶</a></h3>
-<p>This class inherits its fields from <em>EllTubeBasic</em> class. It
does not have any new fields, but adds some functionality. First of all it
gives us the instruments to create ellipsoid tube objects. Here are these
methods:</p>
-<ul class="simple">
-<li><em>fromQArrays</em> - creates nEllTubes ellipsoid tube objects using
an array of ellipsoid matrices and an array of ellipsoid centers
specified at any point of time from timeVec;</li>
-<li><em>fromQMArrays</em> - acts the same way as <em>fromQArrays</em>
method, except for this one requires to specify an array of
regularization marices specified at any point of time from timeVec;</li>
-<li><em>fromQMScaledArrays</em> - acts the same way as
<em>fromQMArrays</em> method, except for this one requires to also
specify a vector of scale factors specified for every created ellipsoid
tube;</li>
-<li><em>fromEllArray</em> - creates ellipsoid tube object using an array
of ellipsoids;</li>
-<li><em>fromEllMArray</em> - creates ellipsoid tube object using an array
of ellipsoids and an array of regularisation matrices.</li>
-</ul>
-<p>Basically we can divide these methods into two groups, based od what
objects they are using to create ellipsoid tube: an array of ellipsoid
matrices and an array of ellipsoid centers or an array of ellipsoids. Below
are some examples of the usage of these functions.</p>
<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
2
3
@@ -350,33 +234,17 @@
10
11
12
-13
-14
-15
-16
-17
-18
-19
-20
-21</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of creating nTubes ellipsoid tube objects using
fromQArrays</span>
+13</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of creating nTubes ellipsoid tube objects using
fromQMArrays</span>
<span class="c">% function with the same type of approximation.</span>
-<span class="n">nPoints</span><span class="p">=</span><span
class="mi">10</span><span class="p">;</span>
-<span class="n">absTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">relTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">approxSchemaDescr</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
-<span class="n">approxSchemaName</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
-<span class="n">nDims</span><span class="p">=</span><span
class="mi">3</span><span class="p">;</span>
-<span class="n">nTubes</span><span class="p">=</span><span
class="mi">3</span><span class="p">;</span>
-<span class="n">lsGoodDirVec</span><span class="p">=[</span><span
class="mi">1</span><span class="p">;</span><span class="mi">0</span><span
class="p">;</span><span class="mi">1</span><span class="p">];</span>
-<span class="n">aMat</span><span class="p">=</span><span
class="nb">zeros</span><span class="p">(</span><span
class="n">nDims</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">);</span>
-<span class="n">timeVec</span><span class="p">=(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):</span><span
class="mi">1</span><span class="p">;</span>
-<span class="n">sTime</span><span class="p">=</span><span
class="n">timeVec</span><span class="p">(</span><span
class="n">randi</span><span class="p">(</span><span
class="n">nPoints</span><span class="p">,</span><span
class="mi">1</span><span class="p">));</span>
-<span class="n">approxType</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">Internal</span><span class="p">;</span>
-<span class="n">qArrayList</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">({</span><span
class="nb">repmat</span><span class="p">(</span><span
class="nb">diag</span><span class="p">([</span><span class="mi">1</span>
<span class="mi">2</span> <span class="mi">3</span><span
class="p">]),[</span><span class="mi">1</span><span class="p">,</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">])},</span><span
class="c">...</span>
+<span class="p">[</span><span class="n">nTubes</span><span
class="p">,</span> <span class="n">nPoints</span><span class="p">,</span>
<span class="n">nDims</span><span class="p">,</span> <span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">,</span> <span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
+ <span class="n">sTime</span><span class="p">,</span> <span
class="n">lsGoodDirVec</span><span class="p">,</span> <span
class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">aMat</span><span class="p">,</span> <span
class="n">qArrayList</span><span class="p">]</span> <span
class="p">=</span> <span class="c">...</span>
+ <span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">test</span><span class="p">.</span><span
class="n">examples</span><span class="p">.</span><span
class="n">getData</span><span class="p">();</span>
+<span class="p">[</span><span class="n">approxSchemaDescr</span><span
class="p">,</span> <span class="n">approxSchemaName</span><span
class="p">,</span> <span class="n">approxType</span><span
class="p">]</span> <span class="p">=</span> <span class="c">...</span>
+ <span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">test</span><span class="p">.</span><span
class="n">examples</span><span class="p">.</span><span
class="n">getSameApprox</span><span class="p">();</span>
+<span class="n">mArrayList</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">({</span><span
class="nb">repmat</span><span class="p">(</span><span
class="nb">diag</span><span class="p">([</span><span class="mf">0.1</span>
<span class="mf">0.2</span> <span class="mf">0.3</span><span
class="p">]),[</span><span class="mi">1</span><span class="p">,</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">])},</span><span
class="c">...</span>
<span class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">);</span>
-<span class="n">ltGoodDirArray</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">(</span><span
class="n">lsGoodDirVec</span><span class="p">,[</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">]);</span>
-<span class="n">fromMatEllTube</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">rels</span><span class="p">.</span><span
class="n">EllTube</span><span class="p">.</span><span
class="n">fromQArrays</span><span class="p">(</span><span
class="c">...</span>
- <span class="n">qArrayList</span><span class="p">,</span> <span
class="n">aMat</span><span class="p">,</span> <span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
+<span class="n">fromMatMEllTube</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">rels</span><span class="p">.</span><span
class="n">EllTube</span><span class="p">.</span><span
class="n">fromQMArrays</span><span class="p">(</span><span
class="c">...</span>
+ <span class="n">qArrayList</span><span class="p">,</span> <span
class="n">aMat</span><span class="p">,</span> <span
class="n">mArrayList</span><span class="p">,</span> <span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
<span class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">sTime</span><span class="p">,</span> <span
class="n">approxType</span><span class="p">,</span> <span
class="n">approxSchemaName</span><span class="p">,</span><span
class="c">...</span>
<span class="n">approxSchemaDescr</span><span class="p">,</span> <span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">);</span>
</pre></div>
@@ -403,7 +271,9 @@
20
21
22
-23</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of creating nTubes ellipsoid tube objects using
fromQArrays</span>
+23
+24
+25</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of creating nTubes ellipsoid tube objects using
fromQMArrays</span>
<span class="c">% function with different types of approximation.</span>
<span class="n">nPoints</span><span class="p">=</span><span
class="mi">10</span><span class="p">;</span>
<span class="n">absTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
@@ -419,11 +289,13 @@
<span class="n">approxType</span><span class="p">=[</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">Internal</span><span class="p">,</span><span class="c">...</span>
<span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">External</span><span class="p">,</span><span class="c">...</span>
<span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">External</span><span class="p">]</span><span
class="o">&#39;</span><span class="p">;</span>
+<span class="n">mArrayList</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">({</span><span
class="nb">repmat</span><span class="p">(</span><span
class="nb">diag</span><span class="p">([</span><span class="mf">0.1</span>
<span class="mf">0.2</span> <span class="mf">0.3</span><span
class="p">]),[</span><span class="mi">1</span><span class="p">,</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">])},</span><span
class="c">...</span>
+ <span class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">);</span>
<span class="n">qArrayList</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">({</span><span
class="nb">repmat</span><span class="p">(</span><span
class="nb">diag</span><span class="p">([</span><span class="mi">1</span>
<span class="mi">2</span> <span class="mi">3</span><span
class="p">]),[</span><span class="mi">1</span><span class="p">,</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">])},</span><span
class="c">...</span>
<span class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">);</span>
<span class="n">ltGoodDirArray</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">(</span><span
class="n">lsGoodDirVec</span><span class="p">,[</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">]);</span>
-<span class="n">fromMatEllTube</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">rels</span><span class="p">.</span><span
class="n">EllTube</span><span class="p">.</span><span
class="n">fromQArrays</span><span class="p">(</span><span
class="c">...</span>
- <span class="n">qArrayList</span><span class="p">,</span> <span
class="n">aMat</span><span class="p">,</span> <span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
+<span class="n">fromMatMEllTube</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">rels</span><span class="p">.</span><span
class="n">EllTube</span><span class="p">.</span><span
class="n">fromQMArrays</span><span class="p">(</span><span
class="c">...</span>
+ <span class="n">qArrayList</span><span class="p">,</span> <span
class="n">aMat</span><span class="p">,</span> <span
class="n">mArrayList</span><span class="p">,</span> <span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
<span class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">sTime</span><span class="p">,</span> <span
class="n">approxType</span><span class="p">,</span> <span
class="n">approxSchemaName</span><span class="p">,</span><span
class="c">...</span>
<span class="n">approxSchemaDescr</span><span class="p">,</span> <span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">);</span>
</pre></div>
@@ -443,38 +315,25 @@
13
14
15
-16
-17
-18
-19
-20
-21
-22
-23</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of creating nTubes ellipsoid tube objects using
fromQMArrays</span>
+16</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of creating nTubes ellipsoid tube objects using
fromQMScaledArrays</span>
<span class="c">% function with the same type of approximation.</span>
-<span class="n">nPoints</span><span class="p">=</span><span
class="mi">10</span><span class="p">;</span>
-<span class="n">absTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">relTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">approxSchemaDescr</span><span class="p">=</span><span
class="s">&#39;External&#39;</span><span class="p">;</span>
-<span class="n">approxSchemaName</span><span class="p">=</span><span
class="s">&#39;External&#39;</span><span class="p">;</span>
-<span class="n">nDims</span><span class="p">=</span><span
class="mi">3</span><span class="p">;</span>
-<span class="n">nTubes</span><span class="p">=</span><span
class="mi">3</span><span class="p">;</span>
-<span class="n">lsGoodDirVec</span><span class="p">=[</span><span
class="mi">1</span><span class="p">;</span><span class="mi">0</span><span
class="p">;</span><span class="mi">1</span><span class="p">];</span>
-<span class="n">aMat</span><span class="p">=</span><span
class="nb">zeros</span><span class="p">(</span><span
class="n">nDims</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">);</span>
-<span class="n">timeVec</span><span class="p">=(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):</span><span
class="mi">1</span><span class="p">;</span>
-<span class="n">sTime</span><span class="p">=</span><span
class="n">timeVec</span><span class="p">(</span><span
class="n">randi</span><span class="p">(</span><span
class="n">nPoints</span><span class="p">,</span><span
class="mi">1</span><span class="p">));</span>
-<span class="n">approxType</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">External</span><span class="p">;</span>
+<span class="p">[</span><span class="n">nTubes</span><span
class="p">,</span> <span class="n">nPoints</span><span class="p">,</span>
<span class="n">nDims</span><span class="p">,</span> <span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">,</span> <span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
+ <span class="n">sTime</span><span class="p">,</span> <span
class="n">lsGoodDirVec</span><span class="p">,</span> <span
class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">aMat</span><span class="p">,</span> <span
class="n">qArrayList</span><span class="p">]</span> <span
class="p">=</span> <span class="c">...</span>
+ <span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">test</span><span class="p">.</span><span
class="n">examples</span><span class="p">.</span><span
class="n">getData</span><span class="p">();</span>
+<span class="p">[</span><span class="n">approxSchemaDescr</span><span
class="p">,</span> <span class="n">approxSchemaName</span><span
class="p">,</span> <span class="n">approxType</span><span
class="p">]</span> <span class="p">=</span> <span class="c">...</span>
+ <span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">test</span><span class="p">.</span><span
class="n">examples</span><span class="p">.</span><span
class="n">getSameApprox</span><span class="p">();</span>
<span class="n">mArrayList</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">({</span><span
class="nb">repmat</span><span class="p">(</span><span
class="nb">diag</span><span class="p">([</span><span class="mf">0.1</span>
<span class="mf">0.2</span> <span class="mf">0.3</span><span
class="p">]),[</span><span class="mi">1</span><span class="p">,</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">])},</span><span
class="c">...</span>
<span class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">);</span>
-<span class="n">qArrayList</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">({</span><span
class="nb">repmat</span><span class="p">(</span><span
class="nb">diag</span><span class="p">([</span><span class="mi">1</span>
<span class="mi">2</span> <span class="mi">3</span><span
class="p">]),[</span><span class="mi">1</span><span class="p">,</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">])},</span><span
class="c">...</span>
- <span class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">);</span>
-<span class="n">ltGoodDirArray</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">(</span><span
class="n">lsGoodDirVec</span><span class="p">,[</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">]);</span>
-<span class="n">fromMatMEllTube</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">rels</span><span class="p">.</span><span
class="n">EllTube</span><span class="p">.</span><span
class="n">fromQMArrays</span><span class="p">(</span><span
class="c">...</span>
- <span class="n">qArrayList</span><span class="p">,</span> <span
class="n">aMat</span><span class="p">,</span> <span
class="n">mArrayList</span><span class="p">,</span> <span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
- <span class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">sTime</span><span class="p">,</span> <span
class="n">approxType</span><span class="p">,</span> <span
class="n">approxSchemaName</span><span class="p">,</span><span
class="c">...</span>
- <span class="n">approxSchemaDescr</span><span class="p">,</span> <span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">);</span>
+<span class="n">scaleFactor</span> <span class="p">=</span> <span
class="nb">ones</span><span class="p">(</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">);</span>
+<span class="n">fromQMScaledArraysEllTube</span> <span class="p">=</span>
<span class="c">...</span>
+ <span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">rels</span><span class="p">.</span><span
class="n">EllTube</span><span class="p">.</span><span
class="n">fromQMScaledArrays</span><span class="p">(</span><span
class="c">...</span>
+ <span class="n">qArrayList</span><span class="p">,</span><span
class="n">aMat</span><span class="p">,</span><span
class="n">mArrayList</span><span class="p">,</span><span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
+ <span class="n">ltGoodDirArray</span><span class="p">,</span><span
class="n">sTime</span><span class="p">,</span><span
class="n">approxType</span><span class="p">,</span><span
class="n">approxSchemaName</span><span class="p">,</span><span
class="c">...</span>
+ <span class="n">approxSchemaDescr</span><span class="p">,</span><span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">,</span><span class="c">...</span>
+ <span class="n">scaleFactor</span><span class="p">);</span>
</pre></div>
</td></tr></table></div>
+<p>To use <em>fromEllArray</em> and <em>fromEllMArray</em> methods we nave
to describe one more auxiliary function (as these methods create an
ellipsoid tube object containing only one ellipsoid tube and we can not use
<em>getData</em> function, because it returns data for crating random
number of ellipsoid tubes).</p>
<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
2
3
@@ -493,41 +352,28 @@
16
17
18
-19
-20
-21
-22
-23
-24
-25
-26</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of creating nTubes ellipsoid tube objects using
fromQMScaledArrays</span>
-<span class="c">% function with the same type of approximation.</span>
-<span class="n">nPoints</span><span class="p">=</span><span
class="mi">10</span><span class="p">;</span>
-<span class="n">absTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">relTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">approxSchemaDescr</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
-<span class="n">approxSchemaName</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
-<span class="n">nDims</span><span class="p">=</span><span
class="mi">3</span><span class="p">;</span>
-<span class="n">nTubes</span><span class="p">=</span><span
class="mi">5</span><span class="p">;</span>
-<span class="n">lsGoodDirVec</span><span class="p">=[</span><span
class="mi">1</span><span class="p">;</span><span class="mi">0</span><span
class="p">;</span><span class="mi">1</span><span class="p">];</span>
-<span class="n">aMat</span><span class="p">=</span><span
class="nb">zeros</span><span class="p">(</span><span
class="n">nDims</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">);</span>
-<span class="n">timeVec</span><span class="p">=(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):</span><span
class="mi">1</span><span class="p">;</span>
-<span class="n">sTime</span><span class="p">=</span><span
class="n">timeVec</span><span class="p">(</span><span
class="n">randi</span><span class="p">(</span><span
class="n">nPoints</span><span class="p">,</span><span
class="mi">1</span><span class="p">));</span>
-<span class="n">approxType</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">Internal</span><span class="p">;</span>
-<span class="n">qArrayList</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">({</span><span
class="nb">repmat</span><span class="p">(</span><span
class="nb">diag</span><span class="p">([</span><span class="mi">1</span>
<span class="mi">2</span> <span class="mi">3</span><span
class="p">]),[</span><span class="mi">1</span><span class="p">,</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">])},</span><span
class="c">...</span>
- <span class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">);</span>
-<span class="n">mArrayList</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">({</span><span
class="nb">repmat</span><span class="p">(</span><span
class="nb">diag</span><span class="p">([</span><span class="mf">0.1</span>
<span class="mf">0.2</span> <span class="mf">0.3</span><span
class="p">]),[</span><span class="mi">1</span><span class="p">,</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">])},</span><span
class="c">...</span>
- <span class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">);</span>
-<span class="n">ltGoodDirArray</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">(</span><span
class="n">lsGoodDirVec</span><span class="p">,[</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">]);</span>
-<span class="n">scaleFactor</span> <span class="p">=</span> <span
class="nb">ones</span><span class="p">(</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">);</span>
-<span class="n">fromQMScaledArraysEllTube</span> <span class="p">=</span>
<span class="c">...</span>
- <span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">rels</span><span class="p">.</span><span
class="n">EllTube</span><span class="p">.</span><span
class="n">fromQMScaledArrays</span><span class="p">(</span><span
class="c">...</span>
- <span class="n">qArrayList</span><span class="p">,</span><span
class="n">aMat</span><span class="p">,</span><span
class="n">mArrayList</span><span class="p">,</span><span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
- <span class="n">ltGoodDirArray</span><span class="p">,</span><span
class="n">sTime</span><span class="p">,</span><span
class="n">approxType</span><span class="p">,</span><span
class="n">approxSchemaName</span><span class="p">,</span><span
class="c">...</span>
- <span class="n">approxSchemaDescr</span><span class="p">,</span><span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">,</span><span class="c">...</span>
- <span class="n">scaleFactor</span><span class="p">);</span>
+19</pre></div></td><td class="code"><div class="highlight"><pre>% This
function returns the values of arguments, that are needed to use
+% FROMELLARRAY and FROMELLMARRAY methods of creating an ellipsoid tube
+% object. Basically, this function creates a set of arguments nessesary for
+% creating an ellipsoid tube object containing one ellipsoid tube.
+%
+function [nTubes, nPoints, nDims, absTol, relTol, timeVec,...
+ sTime, lsGoodDirVec, ltGoodDirArray, aMat, qArrayList] =
getDataForOneTube()
+nTubes=1;
+nPoints=20;
+nDims=3;
+absTol=0.001;
+relTol=0.001;
+timeVec=(1/nPoints):(1/nPoints):1;
+sTime=timeVec(randi(nPoints,1));
+lsGoodDirVec=[1;0;0];
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+aMat=zeros(nDims,nPoints);
+qArrayList=repmat({repmat(diag([1 2 3]),[1,1,nPoints])},1,nTubes);
+end
</pre></div>
</td></tr></table></div>
+<p>Now we can write examples of these methods&#8217; usage.</p>
<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
2
3
@@ -541,37 +387,19 @@
11
12
13
-14
-15
-16
-17
-18
-19
-20
-21
-22
-23</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of creating nTubes ellipsoid tube objects using
fromEllArray</span>
+14</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of creating nTubes ellipsoid tube objects using
fromEllArray</span>
<span class="c">% function.</span>
-<span class="n">nPoints</span><span class="p">=</span><span
class="mi">10</span><span class="p">;</span>
-<span class="n">absTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">relTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">approxSchemaDescr</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
-<span class="n">approxSchemaName</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
-<span class="n">nDims</span><span class="p">=</span><span
class="mi">3</span><span class="p">;</span>
-<span class="n">nTubes</span><span class="p">=</span><span
class="mi">1</span><span class="p">;</span>
-<span class="n">lsGoodDirVec</span><span class="p">=[</span><span
class="mi">1</span><span class="p">;</span><span class="mi">0</span><span
class="p">;</span><span class="mi">1</span><span class="p">];</span>
-<span class="n">timeVec</span><span class="p">=(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):</span><span
class="mi">1</span><span class="p">;</span>
-<span class="n">sTime</span><span class="p">=</span><span
class="n">timeVec</span><span class="p">(</span><span
class="n">randi</span><span class="p">(</span><span
class="n">nPoints</span><span class="p">,</span><span
class="mi">1</span><span class="p">));</span>
-<span class="n">approxType</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">Internal</span><span class="p">;</span>
+<span class="p">[</span><span class="n">nTubes</span><span
class="p">,</span> <span class="n">nPoints</span><span class="p">,</span>
<span class="n">nDims</span><span class="p">,</span> <span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">,</span> <span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
+ <span class="n">sTime</span><span class="p">,</span> <span
class="n">lsGoodDirVec</span><span class="p">,</span> <span
class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">aMat</span><span class="p">,</span> <span
class="n">qArrayList</span><span class="p">]</span> <span
class="p">=</span> <span class="c">...</span>
+ <span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">test</span><span class="p">.</span><span
class="n">examples</span><span class="p">.</span><span
class="n">getDataForOneTube</span><span class="p">();</span>
+<span class="p">[</span><span class="n">approxSchemaDescr</span><span
class="p">,</span> <span class="n">approxSchemaName</span><span
class="p">,</span> <span class="n">approxType</span><span
class="p">]</span> <span class="p">=</span> <span class="c">...</span>
+ <span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">test</span><span class="p">.</span><span
class="n">examples</span><span class="p">.</span><span
class="n">getSameApprox</span><span class="p">();</span>
<span class="n">ellArray</span><span class="p">(</span><span
class="n">nPoints</span><span class="p">)</span> <span class="p">=</span>
<span class="n">ellipsoid</span><span class="p">();</span>
-<span class="n">aMat</span><span class="p">=</span><span
class="nb">zeros</span><span class="p">(</span><span
class="n">nDims</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">);</span>
-<span class="n">qArrayList</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">({</span><span
class="nb">repmat</span><span class="p">(</span><span
class="nb">diag</span><span class="p">([</span><span class="mi">1</span>
<span class="mi">2</span> <span class="mi">3</span><span
class="p">]),[</span><span class="mi">1</span><span class="p">,</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">])},</span><span
class="mi">1</span><span class="p">,</span><span class="mi">1</span><span
class="p">);</span>
<span class="k">for</span> <span class="n">iElem</span> <span
class="p">=</span> <span class="mi">1</span><span class="p">:</span><span
class="n">nPoints</span>
<span class="n">ellArray</span><span class="p">(</span><span
class="n">iElem</span><span class="p">)</span> <span class="p">=</span>
<span class="n">ellipsoid</span><span class="p">(</span><span
class="n">aMat</span><span class="p">(:,</span><span
class="n">iElem</span><span class="p">),</span> <span
class="n">qArrayList</span><span class="p">{</span><span
class="mi">1</span><span class="p">}(:,:,</span><span
class="n">iElem</span><span class="p">));</span>
<span class="k">end</span><span class="p">;</span>
-<span class="n">ellnArray</span> <span class="p">=</span> <span
class="nb">repmat</span><span class="p">(</span><span
class="n">ellArray</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">,</span><span
class="mi">1</span><span class="p">);</span>
<span class="n">fromEllArrayEllTube</span> <span class="p">=</span> <span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">rels</span><span class="p">.</span><span
class="n">EllTube</span><span class="p">.</span><span
class="n">fromEllArray</span><span class="p">(</span><span
class="c">...</span>
- <span class="n">ellnArray</span><span class="p">,</span><span
class="n">timeVec</span><span class="p">,</span> <span
class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">sTime</span><span class="p">,</span> <span
class="n">approxType</span><span class="p">,</span><span
class="c">...</span>
+ <span class="n">ellArray</span><span class="p">,</span><span
class="n">timeVec</span><span class="p">,</span> <span
class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">sTime</span><span class="p">,</span> <span
class="n">approxType</span><span class="p">,</span><span
class="c">...</span>
<span class="n">approxSchemaName</span><span class="p">,</span><span
class="n">approxSchemaDescr</span><span class="p">,</span> <span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">);</span>
</pre></div>
</td></tr></table></div>
@@ -590,48 +418,26 @@
13
14
15
-16
-17
-18
-19
-20
-21
-22
-23
-24
-25
-26
-27</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of creating nTubes ellipsoid tube objects using
fromEllMArray</span>
+16</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of creating nTubes ellipsoid tube objects using
fromEllMArray</span>
<span class="c">% function.</span>
-<span class="n">nPoints</span><span class="p">=</span><span
class="mi">10</span><span class="p">;</span>
-<span class="n">absTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">relTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">approxSchemaDescr</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
-<span class="n">approxSchemaName</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
-<span class="n">nDims</span><span class="p">=</span><span
class="mi">3</span><span class="p">;</span>
-<span class="n">nTubes</span><span class="p">=</span><span
class="mi">1</span><span class="p">;</span>
-<span class="n">lsGoodDirVec</span><span class="p">=[</span><span
class="mi">1</span><span class="p">;</span><span class="mi">0</span><span
class="p">;</span><span class="mi">1</span><span class="p">];</span>
-<span class="n">timeVec</span><span class="p">=(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):</span><span
class="mi">1</span><span class="p">;</span>
-<span class="n">sTime</span><span class="p">=</span><span
class="n">timeVec</span><span class="p">(</span><span
class="n">randi</span><span class="p">(</span><span
class="n">nPoints</span><span class="p">,</span><span
class="mi">1</span><span class="p">));</span>
-<span class="n">approxType</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">Internal</span><span class="p">;</span>
+<span class="p">[</span><span class="n">nTubes</span><span
class="p">,</span> <span class="n">nPoints</span><span class="p">,</span>
<span class="n">nDims</span><span class="p">,</span> <span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">,</span> <span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
+ <span class="n">sTime</span><span class="p">,</span> <span
class="n">lsGoodDirVec</span><span class="p">,</span> <span
class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">aMat</span><span class="p">,</span> <span
class="n">qArrayList</span><span class="p">]</span> <span
class="p">=</span> <span class="c">...</span>
+ <span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">test</span><span class="p">.</span><span
class="n">examples</span><span class="p">.</span><span
class="n">getDataForOneTube</span><span class="p">();</span>
+<span class="p">[</span><span class="n">approxSchemaDescr</span><span
class="p">,</span> <span class="n">approxSchemaName</span><span
class="p">,</span> <span class="n">approxType</span><span
class="p">]</span> <span class="p">=</span> <span class="c">...</span>
+ <span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">test</span><span class="p">.</span><span
class="n">examples</span><span class="p">.</span><span
class="n">getSameApprox</span><span class="p">();</span>
<span class="n">ellArray</span><span class="p">(</span><span
class="n">nPoints</span><span class="p">)</span> <span class="p">=</span>
<span class="n">ellipsoid</span><span class="p">();</span>
-<span class="n">aMat</span><span class="p">=</span><span
class="nb">zeros</span><span class="p">(</span><span
class="n">nDims</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">);</span>
-<span class="n">qArrayList</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">({</span><span
class="nb">repmat</span><span class="p">(</span><span
class="nb">diag</span><span class="p">([</span><span class="mi">1</span>
<span class="mi">2</span> <span class="mi">3</span><span
class="p">]),[</span><span class="mi">1</span><span class="p">,</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">])},</span><span
class="mi">1</span><span class="p">,</span><span class="mi">1</span><span
class="p">);</span>
<span class="k">for</span> <span class="n">iElem</span> <span
class="p">=</span> <span class="mi">1</span><span class="p">:</span><span
class="n">nPoints</span>
<span class="n">ellArray</span><span class="p">(</span><span
class="n">iElem</span><span class="p">)</span> <span class="p">=</span>
<span class="n">ellipsoid</span><span class="p">(</span><span
class="n">aMat</span><span class="p">(:,</span><span
class="n">iElem</span><span class="p">),</span> <span
class="n">qArrayList</span><span class="p">{</span><span
class="mi">1</span><span class="p">}(:,:,</span><span
class="n">iElem</span><span class="p">));</span>
<span class="k">end</span><span class="p">;</span>
-<span class="n">ellnArray</span> <span class="p">=</span> <span
class="nb">repmat</span><span class="p">(</span><span
class="n">ellArray</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">,</span><span
class="mi">1</span><span class="p">);</span>
<span class="n">mArrayList</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">({</span><span
class="nb">repmat</span><span class="p">(</span><span
class="nb">diag</span><span class="p">([</span><span class="mf">0.1</span>
<span class="mf">0.2</span> <span class="mf">0.3</span><span
class="p">]),[</span><span class="mi">1</span><span class="p">,</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">])},</span><span
class="c">...</span>
<span class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">);</span>
-<span class="n">fromEllMArrayEllTube</span><span class="p">=</span><span
class="c">...</span>
- <span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">rels</span><span class="p">.</span><span
class="n">EllTube</span><span class="p">.</span><span
class="n">fromEllMArray</span><span class="p">(</span><span
class="c">...</span>
- <span class="n">ellArray</span><span class="p">,</span> <span
class="n">mArrayList</span><span class="p">{</span><span
class="mi">1</span><span class="p">},</span> <span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
- <span class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">sTime</span><span class="p">,</span> <span
class="n">approxType</span><span class="p">,</span> <span
class="n">approxSchemaName</span><span class="p">,</span><span
class="c">...</span>
- <span class="n">approxSchemaDescr</span><span class="p">,</span> <span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">);</span>
+<span class="n">fromEllArrayEllTube</span> <span class="p">=</span> <span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">rels</span><span class="p">.</span><span
class="n">EllTube</span><span class="p">.</span><span
class="n">fromEllArray</span><span class="p">(</span><span
class="c">...</span>
+ <span class="n">ellArray</span><span class="p">,</span><span
class="n">timeVec</span><span class="p">,</span> <span
class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">sTime</span><span class="p">,</span> <span
class="n">approxType</span><span class="p">,</span><span
class="c">...</span>
+ <span class="n">approxSchemaName</span><span class="p">,</span><span
class="n">approxSchemaDescr</span><span class="p">,</span> <span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">);</span>
</pre></div>
</td></tr></table></div>
-<p>As we can see in these examples, we can specify how many ellipsoid
tubes we want to create, which type of arrpoximation to use. also we can
create ellipsoid tube objects, which will contain several ellipsoid tubes
with different types of approximation.
-We can also use <em>project</em> and <em>projectToOrths</em> methods to
project our ellipsoid tubes on the specified spaces. The first metod
projects the ellipsoid tube on specified space creating the specified type
of projection.</p>
+<p>As we can see in all these examples, we can specify how many ellipsoid
tubes we want to create, which type of arrpoximation to use. Also we can
create ellipsoid tube objects, which will contain several ellipsoid tubes
with different types of approximation.</p>
+<p>After creation of ellipsoid tube objects we can do several operations
with them. Below is the <em>getEllTube</em> function that create an
ellipsoid tube object containing one or several ellipsoid tubes with
specified type of approximation, on specified time vector with specified
time points. This function will be used further down to illustrate other
methods that we can use while working with ellipsoid tube objects.</p>
<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
2
3
@@ -657,35 +463,58 @@
23
24
25
-26</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of calculating ellipsoid tube object projection
using project</span>
-<span class="c">% function.</span>
-<span class="n">nPoints</span><span class="p">=</span><span
class="mi">5</span><span class="p">;</span>
-<span class="n">absTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">relTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">approxSchemaDescr</span><span class="p">=</span><span
class="n">char</span><span class="p">.</span><span
class="n">empty</span><span class="p">(</span><span
class="mi">1</span><span class="p">,</span><span class="mi">0</span><span
class="p">);</span>
-<span class="n">approxSchemaName</span><span class="p">=</span><span
class="n">char</span><span class="p">.</span><span
class="n">empty</span><span class="p">(</span><span
class="mi">1</span><span class="p">,</span><span class="mi">0</span><span
class="p">);</span>
+26
+27
+28</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of creating an ellipsoid tube object containing
nTubes</span>
+<span class="c">% ellipsoid tubes from timeBegin to timeEnd time with
specified type of</span>
+<span class="c">% approximation.</span>
+<span class="c">%</span>
+<span class="k">function</span><span class="w"> </span>ellTube <span
class="p">=</span><span class="w"> </span><span
class="nf">getEllTube</span><span
class="p">(</span>nTubes,timeBeg,timeEnd,type,nPoints<span
class="p">)</span><span class="w"></span>
<span class="n">nDims</span><span class="p">=</span><span
class="mi">3</span><span class="p">;</span>
-<span class="n">nTubes</span><span class="p">=</span><span
class="mi">1</span><span class="p">;</span>
-<span class="n">lsGoodDirVec</span><span class="p">=[</span><span
class="mi">1</span><span class="p">;</span><span class="mi">0</span><span
class="p">;</span><span class="mi">1</span><span class="p">];</span>
-<span class="n">aMat</span><span class="p">=</span><span
class="nb">zeros</span><span class="p">(</span><span
class="n">nDims</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">);</span>
-<span class="n">timeVec</span><span class="p">=</span><span
class="mi">1</span><span class="p">:</span><span
class="n">nPoints</span><span class="p">;</span>
-<span class="n">sTime</span><span class="p">=</span><span
class="n">nPoints</span><span class="p">;</span>
-<span class="n">approxType</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">Internal</span><span class="p">;</span>
-<span class="n">qArrayList</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">({</span><span
class="nb">repmat</span><span class="p">(</span><span
class="nb">diag</span><span class="p">([</span><span class="mi">1</span>
<span class="mi">2</span> <span class="mi">3</span><span
class="p">]),[</span><span class="mi">1</span><span class="p">,</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">])},</span><span
class="c">...</span>
- <span class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">);</span>
+<span class="n">absTol</span><span class="p">=</span><span
class="mf">0.001</span><span class="p">;</span>
+<span class="n">relTol</span><span class="p">=</span><span
class="mf">0.001</span><span class="p">;</span>
+<span class="n">timeVec</span><span class="p">=(</span><span
class="n">timeBeg</span><span class="o">+</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):</span><span
class="n">timeEnd</span><span class="p">;</span>
+<span class="n">sTime</span><span class="p">=</span><span
class="n">timeVec</span><span class="p">(</span><span
class="n">randi</span><span class="p">(</span><span
class="n">nPoints</span><span class="p">,</span><span
class="mi">1</span><span class="p">));</span>
+<span class="n">lsGoodDirVec</span><span class="p">=[</span><span
class="mi">1</span><span class="p">;</span><span class="mi">0</span><span
class="p">;</span><span class="mi">0</span><span class="p">];</span>
<span class="n">ltGoodDirArray</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">(</span><span
class="n">lsGoodDirVec</span><span class="p">,[</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">]);</span>
-<span class="n">fromMatEllTube</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">rels</span><span class="p">.</span><span
class="n">EllTube</span><span class="p">.</span><span
class="n">fromQArrays</span><span class="p">(</span><span
class="c">...</span>
+<span class="n">aMat</span><span class="p">=</span><span
class="nb">zeros</span><span class="p">(</span><span
class="n">nDims</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">);</span>
+<span class="n">qArrayList</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">({</span><span
class="nb">repmat</span><span class="p">(</span><span
class="nb">diag</span><span class="p">([</span><span class="mi">1</span>
<span class="mi">2</span> <span class="mi">3</span><span
class="p">]),[</span><span class="mi">1</span><span class="p">,</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">])},</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">);</span>
+<span class="k">if</span> <span class="n">type</span> <span
class="o">==</span> <span class="mi">1</span>
+ <span class="n">approxSchemaDescr</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
+ <span class="n">approxSchemaName</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
+ <span class="n">approxType</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">Internal</span><span class="p">;</span>
+<span class="k">else</span>
+ <span class="n">approxSchemaDescr</span><span class="p">=</span><span
class="s">&#39;External&#39;</span><span class="p">;</span>
+ <span class="n">approxSchemaName</span><span class="p">=</span><span
class="s">&#39;External&#39;</span><span class="p">;</span>
+ <span class="n">approxType</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">External</span><span class="p">;</span>
+<span class="k">end</span>
+<span class="n">ellTube</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">rels</span><span class="p">.</span><span
class="n">EllTube</span><span class="p">.</span><span
class="n">fromQArrays</span><span class="p">(</span><span
class="c">...</span>
<span class="n">qArrayList</span><span class="p">,</span> <span
class="n">aMat</span><span class="p">,</span> <span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
<span class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">sTime</span><span class="p">,</span> <span
class="n">approxType</span><span class="p">,</span> <span
class="n">approxSchemaName</span><span class="p">,</span><span
class="c">...</span>
<span class="n">approxSchemaDescr</span><span class="p">,</span> <span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">);</span>
-<span class="n">projType</span> <span class="p">=</span> <span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EProjType</span><span class="p">.</span><span
class="n">Static</span><span class="p">;</span>
-<span class="n">projMat</span> <span class="p">=</span> <span
class="p">[</span><span class="mi">1</span> <span class="mi">0</span><span
class="p">;</span> <span class="mi">0</span> <span class="mi">1</span><span
class="p">;</span> <span class="mi">0</span> <span class="mi">0</span><span
class="p">]</span><span class="o">&#39;</span><span class="p">;</span>
-<span class="n">p</span> <span class="p">=</span> <span
class="p">@</span><span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">test</span><span class="p">.</span><span
class="n">examples</span><span class="p">.</span><span
class="n">fGetProjMat</span><span class="p">;</span>
-<span class="p">[</span><span class="n">ellTubeProjRel</span><span
class="p">,</span><span class="n">indProj2OrigVec</span><span
class="p">]</span> <span class="p">=</span> <span
class="n">fromMatEllTube</span><span class="p">.</span><span
class="n">project</span><span class="p">(</span><span
class="n">projType</span><span class="p">,</span><span class="c">...</span>
- <span class="p">{</span><span class="n">projMat</span><span
class="p">},</span><span class="n">p</span><span class="p">);</span>
+<span class="k">end</span>
</pre></div>
</td></tr></table></div>
-<p>The second method projects the ellipsoid tube onto subspace defined by
vectors of standart basis with indices specified in indVec.</p>
+<p>As we have created an ellipsoid tube object, we can get all the types
of differet data about it. There is a set of methods that can give
information about the data stored in the object and give access to it.</p>
+<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre>1
+2
+3
+4
+5
+6
+7
+8
+9</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of GETDATA method&#39;s usage.</span>
+<span class="n">nTubes</span><span class="p">=</span><span
class="mi">5</span><span class="p">;</span>
+<span class="n">nPoints</span> <span class="p">=</span> <span
class="mi">100</span><span class="p">;</span>
+<span class="n">timeBeg</span><span class="p">=</span><span
class="mi">0</span><span class="p">;</span>
+<span class="n">timeEnd</span><span class="p">=</span><span
class="mi">1</span><span class="p">;</span>
+<span class="n">type</span> <span class="p">=</span> <span
class="mi">2</span><span class="p">;</span>
+<span class="n">EllTube</span><span class="p">=</span><span
class="c">...</span>
+ <span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">test</span><span class="p">.</span><span
class="n">examples</span><span class="p">.</span><span
class="n">getEllTube</span><span class="p">(</span><span
class="n">nTubes</span><span class="p">,</span><span
class="n">timeBeg</span><span class="p">,</span><span
class="n">timeEnd</span><span class="p">,</span><span
class="n">type</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">);</span>
+<span class="n">data</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getData</span><span class="p">();</span>
+</pre></div>
+</td></tr></table></div>
<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
2
3
@@ -695,6 +524,35 @@
7
8
9
+10
+11
+12
+13
+14</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% An example of GETELLARRAY method&#39;s usage.</span>
+<span class="p">[</span><span class="n">nTubes</span><span
class="p">,</span> <span class="n">nPoints</span><span class="p">,</span>
<span class="n">nDims</span><span class="p">,</span> <span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">,</span> <span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
+ <span class="n">sTime</span><span class="p">,</span> <span
class="n">lsGoodDirVec</span><span class="p">,</span> <span
class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">aMat</span><span class="p">,</span> <span
class="n">qArrayList</span><span class="p">]</span> <span
class="p">=</span> <span class="c">...</span>
+ <span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">test</span><span class="p">.</span><span
class="n">examples</span><span class="p">.</span><span
class="n">getDataForOneTube</span><span class="p">();</span>
+<span class="p">[</span><span class="n">approxSchemaDescr</span><span
class="p">,</span> <span class="n">approxSchemaName</span><span
class="p">,</span> <span class="n">approxType</span><span
class="p">]</span> <span class="p">=</span> <span class="c">...</span>
+ <span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">test</span><span class="p">.</span><span
class="n">examples</span><span class="p">.</span><span
class="n">getSameApprox</span><span class="p">();</span>
+<span class="n">ellArray</span><span class="p">(</span><span
class="n">nPoints</span><span class="p">)</span> <span class="p">=</span>
<span class="n">ellipsoid</span><span class="p">();</span>
+<span class="k">for</span> <span class="n">iElem</span> <span
class="p">=</span> <span class="mi">1</span><span class="p">:</span><span
class="n">nPoints</span>
+ <span class="n">ellArray</span><span class="p">(</span><span
class="n">iElem</span><span class="p">)</span> <span class="p">=</span>
<span class="n">ellipsoid</span><span class="p">(</span><span
class="n">aMat</span><span class="p">(:,</span><span
class="n">iElem</span><span class="p">),</span> <span
class="n">qArrayList</span><span class="p">{</span><span
class="mi">1</span><span class="p">}(:,:,</span><span
class="n">iElem</span><span class="p">));</span>
+<span class="k">end</span><span class="p">;</span>
+<span class="n">fromEllArrayEllTube</span> <span class="p">=</span> <span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">rels</span><span class="p">.</span><span
class="n">EllTube</span><span class="p">.</span><span
class="n">fromEllArray</span><span class="p">(</span><span
class="c">...</span>
+ <span class="n">ellArray</span><span class="p">,</span><span
class="n">timeVec</span><span class="p">,</span> <span
class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">sTime</span><span class="p">,</span> <span
class="n">approxType</span><span class="p">,</span><span
class="c">...</span>
+ <span class="n">approxSchemaName</span><span class="p">,</span><span
class="n">approxSchemaDescr</span><span class="p">,</span> <span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">);</span>
+<span class="n">data</span> <span class="p">=</span> <span
class="n">fromEllArrayEllTube</span><span class="p">.</span><span
class="n">getEllArray</span><span class="p">(</span><span
class="n">approxType</span><span class="p">);</span>
+</pre></div>
+</td></tr></table></div>
+<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
+ 2
+ 3
+ 4
+ 5
+ 6
+ 7
+ 8
+ 9
10
11
12
@@ -710,33 +568,180 @@
22
23
24
-25</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% Examples of calculating ellipsoid tube object projection to
basic orths </span>
-<span class="c">% using PROJECTTOORTHS function. This is an example of
projectToOrths usage </span>
-<span class="c">% with one input variable. The default value of projection
type is used.</span>
-<span class="n">nPoints</span><span class="p">=</span><span
class="mi">10</span><span class="p">;</span>
-<span class="n">absTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">relTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">approxSchemaDescr</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
-<span class="n">approxSchemaName</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
-<span class="n">nDims</span><span class="p">=</span><span
class="mi">3</span><span class="p">;</span>
-<span class="n">nTubes</span><span class="p">=</span><span
class="mi">1</span><span class="p">;</span>
-<span class="n">lsGoodDirVec</span><span class="p">=[</span><span
class="mi">1</span><span class="p">;</span><span class="mi">0</span><span
class="p">;</span><span class="mi">1</span><span class="p">];</span>
-<span class="n">aMat</span><span class="p">=</span><span
class="nb">zeros</span><span class="p">(</span><span
class="n">nDims</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">);</span>
-<span class="n">timeVec</span><span class="p">=(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):</span><span
class="mi">1</span><span class="p">;</span>
-<span class="n">sTime</span><span class="p">=</span><span
class="n">timeVec</span><span class="p">(</span><span
class="n">randi</span><span class="p">(</span><span
class="n">nPoints</span><span class="p">,</span><span
class="mi">1</span><span class="p">));</span>
-<span class="n">approxType</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">Internal</span><span class="p">;</span>
-<span class="n">qArrayList</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">({</span><span
class="nb">repmat</span><span class="p">(</span><span
class="nb">diag</span><span class="p">([</span><span class="mi">1</span>
<span class="mi">2</span> <span class="mi">3</span><span
class="p">]),[</span><span class="mi">1</span><span class="p">,</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">])},</span><span
class="c">...</span>
- <span class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">);</span>
-<span class="n">ltGoodDirArray</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">(</span><span
class="n">lsGoodDirVec</span><span class="p">,[</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">]);</span>
-<span class="n">fromMatEllTube</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">rels</span><span class="p">.</span><span
class="n">EllTube</span><span class="p">.</span><span
class="n">fromQArrays</span><span class="p">(</span><span
class="c">...</span>
- <span class="n">qArrayList</span><span class="p">,</span> <span
class="n">aMat</span><span class="p">,</span> <span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
- <span class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">sTime</span><span class="p">,</span> <span
class="n">approxType</span><span class="p">,</span> <span
class="n">approxSchemaName</span><span class="p">,</span><span
class="c">...</span>
- <span class="n">approxSchemaDescr</span><span class="p">,</span> <span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">);</span>
-<span class="n">ellTubeProjRel</span> <span class="p">=</span> <span
class="n">fromMatEllTube</span><span class="p">.</span><span
class="n">projectToOrths</span><span class="p">([</span><span
class="mi">1</span><span class="p">,</span><span class="mi">2</span><span
class="p">]);</span>
-<span class="n">plObj</span><span class="p">=</span><span
class="n">smartdb</span><span class="p">.</span><span
class="nb">disp</span><span class="p">.</span><span
class="n">RelationDataPlotter</span><span class="p">();</span>
-<span class="n">ellTubeProjRel</span><span class="p">.</span><span
class="n">plot</span><span class="p">(</span><span
class="n">plObj</span><span class="p">);</span>
+25
+26
+27
+28
+29
+30
+31
+32
+33
+34
+35
+36
+37
+38
+39
+40
+41
+42
+43
+44
+45
+46
+47
+48
+49
+50
+51
+52
+53
+54
+55
+56
+57
+58
+59
+60
+61
+62
+63
+64
+65
+66
+67
+68
+69
+70
+71
+72
+73
+74
+75
+76
+77
+78
+79
+80
+81
+82
+83
+84
+85
+86
+87
+88
+89
+90
+91
+92
+93
+94
+95
+96
+97
+98</pre></div></td><td class="code"><div class="highlight"><pre><span
class="n">nTubes</span><span class="p">=</span><span
class="mi">5</span><span class="p">;</span>
+<span class="n">nPoints</span> <span class="p">=</span> <span
class="mi">100</span><span class="p">;</span>
+<span class="n">timeBeg</span><span class="p">=</span><span
class="mi">0</span><span class="p">;</span>
+<span class="n">timeEnd</span><span class="p">=</span><span
class="mi">1</span><span class="p">;</span>
+<span class="n">type</span> <span class="p">=</span> <span
class="mi">2</span><span class="p">;</span>
+<span class="n">EllTube</span><span class="p">=</span><span
class="c">...</span>
+ <span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">test</span><span class="p">.</span><span
class="n">examples</span><span class="p">.</span><span
class="n">getEllTube</span><span class="p">(</span><span
class="n">nTubes</span><span class="p">,</span><span
class="n">timeBeg</span><span class="p">,</span><span
class="n">timeEnd</span><span class="p">,</span><span
class="n">type</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">);</span>
+<span class="c">%</span>
+<span class="c">% get the list of field descriptions</span>
+<span class="c">%</span>
+<span class="n">Descr</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getFieldDescrList</span><span class="p">();</span>
+<span class="c">%</span>
+<span class="c">% get for given field a nested logical/cell array
containing is-null </span>
+<span class="c">% indicators for cell content. For example, for
approxSchemaName field.</span>
+<span class="c">%</span>
+<span class="n">IsNull</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getFieldIsNull</span><span class="p">(</span><span
class="s">&#39;approxSchemaName&#39;</span><span class="p">);</span>
+<span class="c">%</span>
+<span class="c">% get for given field logical vector determining whether
value of this </span>
+<span class="c">% field in each cell is null or not. For example, for
approxSchemaName field.</span>
+<span class="c">%</span>
+<span class="n">ValueIsNull</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getFieldIsValueNull</span><span class="p">(</span><span
class="s">&#39;approxSchemaName&#39;</span><span class="p">);</span>
+<span class="c">%</span>
+<span class="c">% get the list of field names</span>
+<span class="c">%</span>
+<span class="n">Name</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getFieldNameList</span><span class="p">();</span>
+<span class="c">%</span>
+<span class="c">% project object with specified fields. For example, with
fields that are</span>
+<span class="c">% not to be cut or concatenated.</span>
+<span class="c">%</span>
+<span class="n">nameList</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getNoCatOrCutFieldsList</span><span class="p">();</span>
+<span class="n">Proj</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getFieldProjection</span><span class="p">(</span><span
class="n">nameList</span><span class="p">);</span>
+<span class="c">%</span>
+<span class="c">% get the list of field types</span>
+<span class="c">%</span>
+<span class="n">Type</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getFieldTypeList</span><span class="p">();</span>
+<span class="c">%</span>
+<span class="c">% get the list of field type specifications. Field type
specification is a </span>
+<span class="c">% sequence of type names corresponding to field value
types starting with </span>
+<span class="c">% the top level and going down into the nested content of
a field (for a </span>
+<span class="c">% field having a complex type).</span>
+<span class="c">%</span>
+<span class="n">TypeSpec</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getFieldTypeSpecList</span><span class="p">();</span>
+<span class="c">% or</span>
+<span class="n">TypeSpec</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getFieldTypeSpecList</span><span class="p">(</span><span
class="n">nameList</span><span class="p">);</span>
+<span class="c">%</span>
+<span class="c">% get a matrix composed from the size vectorsfor the
specified fields</span>
+<span class="c">%</span>
+<span class="n">ValueSizeMat</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getFieldValueSizeMat</span><span class="p">(</span><span
class="n">nameList</span><span class="p">);</span>
+<span class="c">%</span>
+<span class="c">% get a vector indicating whether a particular field is
composed of null </span>
+<span class="c">% values completely</span>
+<span class="c">%</span>
+<span class="n">ValueNull</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getIsFieldValueNull</span><span class="p">(</span><span
class="n">nameList</span><span class="p">);</span>
+<span class="c">%</span>
+<span class="c">% get a size vector for the specified dimensions. If no
dimensions are </span>
+<span class="c">% specified, a size vector for all dimensions up to
minimum dimension is </span>
+<span class="c">% returned</span>
+<span class="n">MinDimensionSize</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getMinDimensionSize</span><span class="p">();</span>
+<span class="c">%</span>
+<span class="c">% get a minimum dimensionality for a given object</span>
+<span class="c">%</span>
+<span class="n">MinDimensionality</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getMinDimensionality</span><span class="p">();</span>
+<span class="c">%</span>
+<span class="c">% get a number of elements in a given object</span>
+<span class="c">%</span>
+<span class="n">NElems</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getNElems</span><span class="p">();</span>
+<span class="c">%</span>
+<span class="c">% get a number of fields in a given object</span>
+<span class="c">%</span>
+<span class="n">NFiedls</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getNFields</span><span class="p">();</span>
+<span class="c">%</span>
+<span class="c">% get a number of tuples in a given object</span>
+<span class="c">%</span>
+<span class="n">NTuples</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getNTuples</span><span class="p">();</span>
+<span class="c">%</span>
+<span class="c">% get sort index for all tuples of given relation with
respect to some of </span>
+<span class="c">% its fields</span>
+<span class="c">%</span>
+<span class="n">SortIndex</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getSortIndex</span><span class="p">(</span><span
class="n">nameList</span><span class="p">);</span>
+<span class="c">% also we can specify the direction of sorting
(&#39;asc&#39; or &#39;desc&#39;)</span>
+<span class="n">SortIndex</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getSortIndex</span><span class="p">(</span><span
class="n">nameList</span><span class="p">,</span><span
class="s">&#39;Direction&#39;</span><span class="p">,</span><span
class="s">&#39;asc&#39;</span><span class="p">);</span>
+<span class="c">%</span>
+<span class="c">% get tuples with given indices from given relation</span>
+<span class="c">%</span>
+<span class="n">Tuples</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getTuples</span><span class="p">([</span><span
class="mi">1</span><span class="p">,</span><span class="mi">2</span><span
class="p">,</span><span class="mi">3</span><span class="p">]);</span>
+<span class="c">%</span>
+<span class="c">% get tuples from given relation such that afixed index
field contains </span>
+<span class="c">% values from a given set of value</span>
+<span class="c">%</span>
+<span class="n">FilteredTuples</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getTuplesFilteredBy</span><span class="p">(</span><span
class="s">&#39;sTime&#39;</span><span class="p">,</span> <span
class="mi">1</span><span class="p">);</span>
+<span class="c">%</span>
+<span class="c">% get internal representation for a set of unique tuples
for given relation</span>
+<span class="c">%</span>
+<span class="n">UniqueData</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getUniqueData</span><span class="p">();</span>
+<span class="c">%</span>
+<span class="c">% get a relation containing the unique tuples from the
original relation</span>
+<span class="c">%</span>
+<span class="n">UniqueTuples</span> <span class="p">=</span> <span
class="n">EllTube</span><span class="p">.</span><span
class="n">getUniqueTuples</span><span class="p">();</span>
</pre></div>
</td></tr></table></div>
+<p>Also we can copy the object, clear all the data, save it in a file:</p>
<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
2
3
@@ -762,38 +767,67 @@
23
24
25
-26</pre></div></td><td class="code"><div class="highlight"><pre><span
class="c">% Examples of calculating ellipsoid tube object projection to
basic orths </span>
-<span class="c">% using PROJECTTOORTHS function. This is an example of
projectToOrths usage </span>
-<span class="c">% with specified projection type.</span>
-<span class="n">nPoints</span><span class="p">=</span><span
class="mi">10</span><span class="p">;</span>
-<span class="n">absTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">relTol</span><span class="p">=</span><span
class="mf">0.01</span><span class="p">;</span>
-<span class="n">approxSchemaDescr</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
-<span class="n">approxSchemaName</span><span class="p">=</span><span
class="s">&#39;Internal&#39;</span><span class="p">;</span>
-<span class="n">nDims</span><span class="p">=</span><span
class="mi">3</span><span class="p">;</span>
-<span class="n">nTubes</span><span class="p">=</span><span
class="mi">1</span><span class="p">;</span>
-<span class="n">lsGoodDirVec</span><span class="p">=[</span><span
class="mi">1</span><span class="p">;</span><span class="mi">0</span><span
class="p">;</span><span class="mi">1</span><span class="p">];</span>
-<span class="n">aMat</span><span class="p">=</span><span
class="nb">zeros</span><span class="p">(</span><span
class="n">nDims</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">);</span>
-<span class="n">timeVec</span><span class="p">=(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):(</span><span
class="mi">1</span><span class="o">/</span><span
class="n">nPoints</span><span class="p">):</span><span
class="mi">1</span><span class="p">;</span>
-<span class="n">sTime</span><span class="p">=</span><span
class="n">timeVec</span><span class="p">(</span><span
class="n">randi</span><span class="p">(</span><span
class="n">nPoints</span><span class="p">,</span><span
class="mi">1</span><span class="p">));</span>
-<span class="n">approxType</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EApproxType</span><span class="p">.</span><span
class="n">Internal</span><span class="p">;</span>
-<span class="n">qArrayList</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">({</span><span
class="nb">repmat</span><span class="p">(</span><span
class="nb">diag</span><span class="p">([</span><span class="mi">1</span>
<span class="mi">2</span> <span class="mi">3</span><span
class="p">]),[</span><span class="mi">1</span><span class="p">,</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">])},</span><span
class="c">...</span>
- <span class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">);</span>
-<span class="n">ltGoodDirArray</span><span class="p">=</span><span
class="nb">repmat</span><span class="p">(</span><span
class="n">lsGoodDirVec</span><span class="p">,[</span><span
class="mi">1</span><span class="p">,</span><span
class="n">nTubes</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">]);</span>
-<span class="n">fromMatEllTube</span><span class="p">=</span><span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">rels</span><span class="p">.</span><span
class="n">EllTube</span><span class="p">.</span><span
class="n">fromQArrays</span><span class="p">(</span><span
class="c">...</span>
- <span class="n">qArrayList</span><span class="p">,</span> <span
class="n">aMat</span><span class="p">,</span> <span
class="n">timeVec</span><span class="p">,</span><span class="c">...</span>
- <span class="n">ltGoodDirArray</span><span class="p">,</span> <span
class="n">sTime</span><span class="p">,</span> <span
class="n">approxType</span><span class="p">,</span> <span
class="n">approxSchemaName</span><span class="p">,</span><span
class="c">...</span>
- <span class="n">approxSchemaDescr</span><span class="p">,</span> <span
class="n">absTol</span><span class="p">,</span> <span
class="n">relTol</span><span class="p">);</span>
-<span class="n">projType</span> <span class="p">=</span> <span
class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">enums</span><span class="p">.</span><span
class="n">EProjType</span><span class="p">.</span><span
class="n">DynamicAlongGoodCurve</span><span class="p">;</span>
-<span class="n">ellTubeProjRel</span> <span class="p">=</span> <span
class="n">fromMatEllTube</span><span class="p">.</span><span
class="n">projectToOrths</span><span class="p">([</span><span
class="mi">1</span><span class="p">,</span><span class="mi">2</span><span
class="p">],</span> <span class="n">projType</span><span class="p">);</span>
-<span class="n">plObj</span><span class="p">=</span><span
class="n">smartdb</span><span class="p">.</span><span
class="nb">disp</span><span class="p">.</span><span
class="n">RelationDataPlotter</span><span class="p">();</span>
-<span class="n">ellTubeProjRel</span><span class="p">.</span><span
class="n">plot</span><span class="p">(</span><span
class="n">plObj</span><span class="p">);</span>
+26
+27
+28
+29
+30
+31
+32
+33
+34
+35
+36
+37
+38
+39
+40
+41
+42</pre></div></td><td class="code"><div class="highlight"><pre><span
class="n">nTubes</span><span class="p">=</span><span
class="mi">5</span><span class="p">;</span>
+<span class="n">nPoints</span> <span class="p">=</span> <span
class="mi">100</span><span class="p">;</span>
+<span class="n">timeBeg</span><span class="p">=</span><span
class="mi">0</span><span class="p">;</span>
+<span class="n">timeEnd</span><span class="p">=</span><span
class="mi">1</span><span class="p">;</span>
+<span class="n">type</span> <span class="p">=</span> <span
class="mi">2</span><span class="p">;</span>
+<span class="n">EllTube</span><span class="p">=</span><span
class="c">...</span>
+ <span class="n">gras</span><span class="p">.</span><span
class="n">ellapx</span><span class="p">.</span><span
class="n">smartdb</span><span class="p">.</span><span
class="n">test</span><span class="p">.</span><span
class="n">examples</span><span class="p">.</span><span
class="n">getEllTube</span><span class="p">(</span><span
class="n">nTubes</span><span class="p">,</span><span
class="n">timeBeg</span><span class="p">,</span><span
class="n">timeEnd</span><span class="p">,</span><span
class="n">type</span><span class="p">,</span><span
class="n">nPoints</span><span class="p">);</span>
***The diff for this file has been truncated for email.***
=======================================
--- /branches/issue_133_aatanesyan/doc/_build/html/chap_functions.html Mon
Feb 24 20:40:31 2014 UTC
+++ /branches/issue_133_aatanesyan/doc/_build/html/chap_functions.html Wed
Mar 5 02:41:50 2014 UTC
@@ -6078,34 +6078,57 @@
<h2>gras.ellapx.smartdb.rels.EllTube<a class="headerlink"
href="#gras-ellapx-smartdb-rels-elltube" title="Permalink to this
headline">¶</a></h2>
<div class="section" id="gras-ellapx-smartdb-rels-elltube-elltube">
<h3>gras.ellapx.smartdb.rels.EllTube.EllTube<a class="headerlink"
href="#gras-ellapx-smartdb-rels-elltube-elltube" title="Permalink to this
headline">¶</a></h3>
-<div class="highlight-python"><div class="highlight"><pre>EllTube - class
which keeps ellipsoidal tubes
+<div class="highlight-python"><div class="highlight"><pre>A class which
allows to work with ellipsoid tube objects.

Fields:
- QArray:cell[1, nElem] - Array of ellipsoid matrices
- aMat:cell[1, nElem] - Array of ellipsoid centers
- scaleFactor:double[1, 1] - Tube scale factor
- MArray:cell[1, nElem] - Array of regularization ellipsoid matrices
- dim :double[1, 1] - Dimensionality
- sTime:double[1, 1] - Time s
- approxSchemaName:cell[1,] - Name
- approxSchemaDescr:cell[1,] - Description
- approxType:gras.ellapx.enums.EApproxType - Type of approximation
- (external, internal, not defined)
- timeVec:cell[1, m] - Time vector
- calcPrecision:double[1, 1] - Calculation precision
- indSTime:double[1, 1] - index of sTime within timeVec
- ltGoodDirMat:cell[1, nElem] - Good direction curve
- lsGoodDirVec:cell[1, nElem] - Good direction at time s
- ltGoodDirNormVec:cell[1, nElem] - Norm of good direction curve
- lsGoodDirNorm:double[1, 1] - Norm of good direction at time s
- xTouchCurveMat:cell[1, nElem] - Touch point curve for good
- direction
- xTouchOpCurveMat:cell[1, nElem] - Touch point curve for direction
- opposite to good direction
- xsTouchVec:cell[1, nElem] - Touch point at time s
- xsTouchOpVec :cell[1, nElem] - Touch point at time s
-
- TODO: correct description of the fields in
gras.ellapx.smartdb.rels.EllTube
+ QArray: cell[1,1] of double[nDims,nDims,nTimePoints] -
+ a 3-dimentional matrix in which each of nTimePoints slices is a
+ double[nDims,nDims] ellipsoid matrix at nTimePoint point of time.
+ Here nTimePoints is number of elements in timeVec.
+ aMat: cell[1,nTimePoints] of double[nDims,1] - a 2-dimentional matrix
+ in which each of nTimePoints columns is a
+ double[nDims, 1] ellipsoid center. Each center is specified for
+ nTimePoint point of time
+ scaleFactor: double[1, 1] - scale for the created ellipsoid tube
+ MArray: cell[1,1] of double[nDims,nDims,nTimePoints] -
+ a 3-dimentional matrix in which each of nTimePoints slices is
+ a double[nDims,nDims] regularization matrix at nTimePoint point
+ of time.
+ dim: double[1, 1] - the dimension of the space in which the touching
+ curves are defined
+ sTime: double[1, 1] - specific point of time which is best suited to
+ describe good direction
+ approxSchemaName: cell[1, 1] of char[1,] - name of the
+ approximation schema
+ approxSchemaDescr: cell[1, 1] of char[1,] - description of the
+ approximation schema
+ approxType: gras.ellapx.enums.EApproxType[1,1] - type of approximation
+ (External, Internal, NotDefined)
+ timeVec: double[1, nTimePoints] - time vector
+ absTolerance: double[1, 1] - absolute tolerance
+ relTolerance: double[1, 1] - relative tolerance
+ indSTime: double[1, 1] - index of sTime point within timeVec
+ ltGoodDirMat: cell[1, nTimePoints] of double[nDims, 1] - matrix of
+ good direction vectors at any point of time from timeVec
+ lsGoodDirVec: cell[1, 1] of double[nDims, 1] - good direction vector
+ at sTime point of time
+ ltGoodDirNormVec: cell[1, 1] of double[1, nTimePoints] - norm of good
+ direction vector at any point of time from timeVec
+ lsGoodDirNorm: double[1, 1] - norm of good direction vector at
+ sTime point of time
+ xTouchCurveMat: cell[1, nTimePoints] of double[nDims, 1] - touch
+ point curve for good direction matrix
+ xTouchOpCurveMat: cell[1, nTimePoints] of double[nDims, 1] - touch
+ point curve oposite to the xTouchCurveMat touch point curve
+ xsTouchVec: cell[1, 1] of double[nDims, 1] - touch point at sTime
+ point of time
+ xsTouchOpVec: cell[1, 1] of double[nDims, 1] - a point opposite to
+ the xsTouchVec touch point
+ isLsTouch: logical[1, 1] - a logical variable which indicates whether
+ a touch takes place along good direction at sTime point of time
+ isLtTouchVec: cell[1, 1] of logical[nTimePoints, 1] - a logical
+ vector which indicates whether a touch takes place along good
+ direction at any point of time from timeVec
</pre></div>
</div>
<p>See the description of the following methods in <a class="reference
internal"
href="#smartdb-relations-atypifiedstaticrelation">smartdb.relations.ATypifiedStaticRelation</a>
for smartdb.relations.ATypifiedStaticRelation:</p>
@@ -6211,237 +6234,282 @@
</div>
<div class="section" id="gras-ellapx-smartdb-rels-elltube-cut">
<h3>gras.ellapx.smartdb.rels.EllTube.cut<a class="headerlink"
href="#gras-ellapx-smartdb-rels-elltube-cut" title="Permalink to this
headline">¶</a></h3>
+<div class="highlight-python"><div class="highlight"><pre>CUT - extracts
the piece of the ellipsoid tube object from given
+start point of time to given end point of time.
+
+Input:
+ regular:
+ self.
+ cutTimeVec: double[1, 2] / double[1, 1] - time interval to cut
+
+Output:
+ cutEllTubeRel: gras.ellapx.smartdb.rels.EllTube[1, 1] -
+ ellipsoid tube which is created from the original one by
+ cutting it from given start point of time to given end
+ point of time
+</pre></div>
+</div>
</div>
<div class="section" id="gras-ellapx-smartdb-rels-elltube-fromellarray">
<h3>gras.ellapx.smartdb.rels.EllTube.fromEllArray<a class="headerlink"
href="#gras-ellapx-smartdb-rels-elltube-fromellarray" title="Permalink to
this headline">¶</a></h3>
-<div class="highlight-python"><div class="highlight"><pre>FROMELLARRAY -
creates a relation object using an array of ellipsoids
+<div class="highlight-python"><div class="highlight"><pre>FROMELLARRAY -
creates ellipsoid tube object using an
+array of ellipsoids.

Input:
regular:
- qEllArray: ellipsoid[nDim1, nDim2, ..., nDimN] - array of ellipsoids
-
- optional:
- timeVec:cell[1, m] - time vector
- ltGoodDirArray:cell[1, nElem] - good direction at time s
- sTime:double[1, 1] - time s
- approxType:gras.ellapx.enums.EApproxType - type of approximation
- (external, internal, not defined)
- approxSchemaName:cell[1,] - name of the schema
- approxSchemaDescr:cell[1,] - description of the schema
- calcPrecision:double[1, 1] - calculation precision
+ qEllArray: double[nDims,nDims,nTimePoints] - array of
+ ellipsoids. Each element from double[nDims,nDims,nTimePoints]
+ array specifies double[nDims,nDims] ellipsoid at nTimePoint
+ point of time. Here nTimePoints is number of elements
+ in timeVec.
+ timeVec: cell[1,1] of double[1,nTimePoints] - time vector
+ ltGoodDirArray: cell[nEllTubes,1] of double[nDim, nTimePoints] -
+ cell of nEllTubes arrays of nTimePoints good direction
+ vectors at any point of time from timeVec
+ sTime: double[1,1] - specific point of time from timeVec
+ which is best suited to describe good direction
+ approxType: gras.ellapx.enums.EApproxType[1,1] - type
+ of approximation (External, Internal, NotDefined).
+ approxSchemaName: char[1,] - name of the approximation schema
+ approxSchemaDescr: char[1,] - description of the
+ approximation schema. It is possible
+ absTol:double[1, 1] - absolute tolerance
+ relTol:double[1, 1] - relative tolerance

Output:
- ellTubeRel: smartdb.relation.StaticRelation[1, 1] - constructed relation
- object
+ ellTubeRel: gras.ellapx.smartdb.rels.EllTube[1, 1] - constructed
+ ellipsoid tube object
</pre></div>
</div>
</div>
<div class="section" id="gras-ellapx-smartdb-rels-elltube-fromellmarray">
<h3>gras.ellapx.smartdb.rels.EllTube.fromEllMArray<a class="headerlink"
href="#gras-ellapx-smartdb-rels-elltube-fromellmarray" title="Permalink to
this headline">¶</a></h3>
-<div class="highlight-python"><div class="highlight"><pre>FROMELLMARRAY -
creates a relation object using an array of ellipsoids.
- This method uses regularizer in the form of a matrix
- function.
+<div class="highlight-python"><div class="highlight"><pre>FROMELLMARRAY -
creates ellipsoid tube object using an
+array of ellipsoids and an array of regularisation matrices.

Input:
regular:
- qEllArray: ellipsoid[nDim1, nDim2, ..., nDimN] - array of ellipsoids
- ellMArr: double[nDim1, nDim2, ..., nDimN] - regularization ellipsoid
- matrices
-
- optional:
- timeVec:cell[1, m] - time vector
- ltGoodDirArray:cell[1, nElem] - good direction at time s
- sTime:double[1, 1] - time s
- approxType:gras.ellapx.enums.EApproxType - type of approximation
- (external, internal, not defined)
- approxSchemaName:cell[1,] - name of the schema
- approxSchemaDescr:cell[1,] - description of the schema
- calcPrecision:double[1, 1] - calculation precision
+ qEllArray: double[nDims,nDims,nTimePoints] - array of
+ ellipsoids. Each element from double[nDims,nDims,nTimePoints]
+ array specifies double[nDims,nDims] ellipsoid at nTimePoint
+ point of time. Here nTimePoints is number of elements
+ in timeVec.
+ ellMArr: double[nDims,nDims,nTimePoints] - an array of nTimePoints
+ regularization matrices of double[nDims,nDims] type.
+ Each element from double[nDims,nDims,nTimePoints] array
+ specifies double[nDim,nDim] regularization matrix at
+ nTimePoint point of time.
+ timeVec: cell[1,1] of double[1,nTimePoints] - time vector
+ ltGoodDirArray: cell[nEllTubes,1] of double[nDim, nTimePoints] -
+ cell of nEllTubes arrays of nTimePoints good direction
+ vectors at any point of time from timeVec
+ sTime: double[1,1] - specific point of time from timeVec
+ which is best suited to describe good direction
+ approxType: gras.ellapx.enums.EApproxType[1,1] - type
+ of approximation (External, Internal, NotDefined).
+ approxSchemaName: char[1,] - name of the approximation schema
+ approxSchemaDescr: char[1,] - description of the
+ approximation schema. It is possible
+ absTol:double[1, 1] - absolute tolerance
+ relTol:double[1, 1] - relative tolerance

Output:
- ellTubeRel: smartdb.relation.StaticRelation[1, 1] - constructed relation
- object
+ ellTubeRel: gras.ellapx.smartdb.rels.EllTube[1, 1] - constructed
+ ellipsoid tube object
</pre></div>
</div>
</div>
<div class="section" id="gras-ellapx-smartdb-rels-elltube-fromqarrays">
<h3>gras.ellapx.smartdb.rels.EllTube.fromQArrays<a class="headerlink"
href="#gras-ellapx-smartdb-rels-elltube-fromqarrays" title="Permalink to
this headline">¶</a></h3>
-<div class="highlight-python"><div class="highlight"><pre>FROMQARRAYS -
creates a relation object using an array of ellipsoids,
- described by the array of ellipsoid matrices and
- array of ellipsoid centers.This method used default
- scale factor.
+<div class="highlight-python"><div class="highlight"><pre>FROMQARRAYS
creates nEllTubes ellipsoid tube objects using an
+array of ellipsoid matrices and an array of ellipsoid centers
+specified at any point of time from timeVec.

Input:
regular:
- QArrayList: double[nDim1, nDim2, ..., nDimN] - array of ellipsoid
- matrices
- aMat: double[nDim1, nDim2, ..., nDimN] - array of ellipsoid centers
-
-Optional:
- MArrayList:cell[1, nElem] - array of regularization ellipsoid matrices
- timeVec:cell[1, m] - time vector
- ltGoodDirArray:cell[1, nElem] - good direction at time s
- sTime:double[1, 1] - time s
- approxType:gras.ellapx.enums.EApproxType - type of approximation
- (external, internal, not defined)
- approxSchemaName:cell[1,] - name of the schema
- approxSchemaDescr:cell[1,] - description of the schema
- calcPrecision:double[1, 1] - calculation precision
-
+ QArrayList: cell[nEllTubes,1] of double[nDims,nDims,nTimePoints] -
+ an array of nEllTubes 3-dimentional matrices in which
+ each of nTimePoints slices is a double[nDims,nDims]
+ ellipsoid matrix at nTimePoint point of time. Here
+ nTimePoints is number of elements in timeVec.
+ aMat: double[nDims, nTimePoints] - a 2-dimentional matrix
+ in which each of nTimePoints columns is a
+ double[nDims, 1] ellipsoid center. Each center is specified
+ for nTimePoint point of time
+ timeVec: cell[1,1] of double[1,nTimePoints] - time vector
+ ltGoodDirArray: cell[nEllTubes,1] of double[nDim, nTimePoints] -
+ cell of nEllTubes arrays of nTimePoints good direction
+ vectors at any point of time from timeVec
+ sTime: double[1,1] - specific point of time from timeVec
+ which is best suited to describe good direction
+ approxType: gras.ellapx.enums.EApproxType[1,1] /
+ / gras.ellapx.enums.EApproxType[1,nEllTubes] - type
+ of approximation (External, Internal, NotDefined).
+ It is possible either to specify one type of
+ approximation for all of nEllTubes ellipsoid tubes,
+ or specify the type of approximation for each of the
+ nEllTubes ellipsoid tubes separately.
+ approxSchemaName: char[1,] / cell[1,nEllTubes] of char[1,] -
+ name of the approximation schema. It is possible either
+ to specify one name of the approximation schema for
+ all of nEllTubes ellipsoid tubes, or specify the name
+ of the approximation schema for each of the nEllTubes
+ ellipsoid tubes separately.
+ approxSchemaDescr: char[1,] / cell[1,nEllTubes] of char[1,] -
+ description of the approximation schema. It is possible
+ either to specify one description of the approximation
+ schema for all of nEllTubes ellipsoid tubes, or specify
+ the description of the approximation schema for each
+ of the nEllTubes ellipsoid tubes separately.
+ absTol:double[1, 1] - absolute tolerance
+ relTol:double[1, 1] - relative tolerance
Output:
- ellTubeRel: smartdb.relation.StaticRelation[1, 1] - constructed relation
- object
+ ellTubeRel: gras.ellapx.smartdb.rels.EllTube[1, 1] - constructed
+ ellipsoid tube object
</pre></div>
</div>
</div>
<div class="section" id="gras-ellapx-smartdb-rels-elltube-fromqmarrays">
<h3>gras.ellapx.smartdb.rels.EllTube.fromQMArrays<a class="headerlink"
href="#gras-ellapx-smartdb-rels-elltube-fromqmarrays" title="Permalink to
this headline">¶</a></h3>
-<div class="highlight-python"><div class="highlight"><pre>FROMQMARRAYS -
creates a relation object using an array of ellipsoids,
- described by the array of ellipsoid matrices and
- array of ellipsoid centers. Also this method uses
- regularizer in the form of a matrix function. This method
- used default scale factor.
+<div class="highlight-python"><div class="highlight"><pre>FROMQMARRAYS
creates nEllTubes ellipsoid tube objects using an
+array of ellipsoid matrices, an array of ellipsoid centers
+and an array of regularization marices specified at any point
+of time from timeVec.

Input:
regular:
- QArrayList: double[nDim1, nDim2, ..., nDimN] - array of ellipsoid
- matrices
- aMat: double[nDim1, nDim2, ..., nDimN] - array of ellipsoid centers
- MArrayList: double[nDim1, nDim2, ..., nDimN] - ellipsoid matrices of
- regularization
-
- optional:
- timeVec:cell[1, m] - time vector
- ltGoodDirArray:cell[1, nElem] - good direction at time s
- sTime:double[1, 1] - time s
- approxType:gras.ellapx.enums.EApproxType - type of approximation
- (external, internal, not defined)
- approxSchemaName:cell[1,] - name of the schema
- approxSchemaDescr:cell[1,] - description of the schema
- calcPrecision:double[1, 1] - calculation precision
-
+ QArrayList: cell[nEllTubes,1] of double[nDims,nDims,nTimePoints] -
+ an array of nEllTubes 3-dimentional matrices in which
+ each of nTimePoints slices is a double[nDims,nDims]
+ ellipsoid matrix at nTimePoint point of time. Here
+ nTimePoints is number of elements in timeVec.
+ MArrayList: cell[nEllTubes,1] of double[nDims,nDims,nTimePoints] -
+ an array of nEllTubes 3-dimentional matrices in which
+ each of nTimePoints slices is a double[nDims,nDims]
+ regularization matrix at nTimePoint point of time.
+ aMat: double[nDims, nTimePoints] - a 2-dimentional matrix
+ in which each of nTimePoints columns is a
+ double[nDims, 1] ellipsoid center. Each center is specified
+ for nTimePoint point of time
+ timeVec: cell[1,1] of double[1,nTimePoints] - time vector
+ ltGoodDirArray: cell[nEllTubes,1] of double[nDim, nTimePoints] -
+ cell of nEllTubes arrays of nTimePoints good direction
+ vectors at any point of time from timeVec
+ sTime: double[1,1] - specific point of time from timeVec
+ which is best suited to describe good direction
+ approxType: gras.ellapx.enums.EApproxType[1,1] /
+ / gras.ellapx.enums.EApproxType[1,nEllTubes] - type
+ of approximation (External, Internal, NotDefined).
+ It is possible either to specify one type of
+ approximation for all of nEllTubes ellipsoid tubes,
+ or specify the type of approximation for each of the
+ nEllTubes ellipsoid tubes separately.
+ approxSchemaName: char[1,] / cell[1,nEllTubes] of char[1,] -
+ name of the approximation schema. It is possible either
+ to specify one name of the approximation schema for
+ all of nEllTubes ellipsoid tubes, or specify the name
+ of the approximation schema for each of the nEllTubes
+ ellipsoid tubes separately.
+ approxSchemaDescr: char[1,] / cell[1,nEllTubes] of char[1,] -
+ description of the approximation schema. It is possible
+ either to specify one description of the approximation
+ schema for all of nEllTubes ellipsoid tubes, or specify
+ the description of the approximation schema for each
+ of the nEllTubes ellipsoid tubes separately.
+ absTol:double[1, 1] - absolute tolerance
+ relTol:double[1, 1] - relative tolerance
Output:
- ellTubeRel: smartdb.relation.StaticRelation[1, 1] - constructed relation
- object
+ ellTubeRel: gras.ellapx.smartdb.rels.EllTube[1, 1] - constructed
+ ellipsoid tube object
</pre></div>
</div>
</div>
<div class="section"
id="gras-ellapx-smartdb-rels-elltube-fromqmscaledarrays">
<h3>gras.ellapx.smartdb.rels.EllTube.fromQMScaledArrays<a
class="headerlink"
href="#gras-ellapx-smartdb-rels-elltube-fromqmscaledarrays"
title="Permalink to this headline">¶</a></h3>
-<div class="highlight-python"><div
class="highlight"><pre>FROMQMSCALEDARRAYS - creates a relation object
using an array of ellipsoids,
- described by the array of ellipsoid matrices and
- array of ellipsoid centers. Also this method uses
- regularizer in the form of a matrix function.
-
+<div class="highlight-python"><div
class="highlight"><pre>FROMQMSCALEDARRAYS creates nEllTubes ellipsoid tube
objects using an
+array of ellipsoid matrices, an array of ellipsoid centers,
+an array of regularization marices specified at any point
+of time from timeVec and a vector of scale factors
+specified for every created ellipsoid tube

Input:
regular:
- QArrayList: double[nDim1, nDim2, ..., nDimN] - array of ellipsoid
- matrices
- aMat: double[nDim1, nDim2, ..., nDimN] - array of ellipsoid centers
- MArrayList: double[nDim1, nDim2, ..., nDimN] - ellipsoid matrices
- of regularization
- scaleFactor:double[1, 1] - tube scale factor
-
- optional:
- timeVec:cell[1, m] - time vector
- ltGoodDirArray:cell[1, nElem] - good direction at time s
- sTime:double[1, 1] - time s
- approxType:gras.ellapx.enums.EApproxType - type of approximation
- (external, internal, not defined)
- approxSchemaName:cell[1,] - name of the schema
- approxSchemaDescr:cell[1,] - description of the schema
- calcPrecision:double[1, 1] - calculation precision
+ QArrayList: cell[nEllTubes,1] of double[nDims,nDims,nTimePoints] -
+ an array of nEllTubes 3-dimentional matrices in which
+ each of nTimePoints slices is a double[nDims,nDims]
+ ellipsoid matrix at nTimePoint point of time. Here
+ nTimePoints is number of elements in timeVec.
+ MArrayList: cell[nEllTubes,1] of double[nDims,nDims,nTimePoints] -
+ an array of nEllTubes 3-dimentional matrices in which
+ each of nTimePoints slices is a double[nDims,nDims]
+ regularization matrix at nTimePoint point of time.
+ aMat: double[nDims, nTimePoints] - a 2-dimentional matrix
+ in which each of nTimePoints columns is a
+ double[nDims, 1] ellipsoid center. Each center is specified
+ for nTimePoint point of time
+ timeVec: cell[1,1] of double[1,nTimePoints] - time vector
+ ltGoodDirArray: cell[nEllTubes,1] of double[nDim, nTimePoints] -
+ cell of nEllTubes arrays of nTimePoints good direction
+ vectors at any point of time from timeVec
+ sTime: double[1,1] - specific point of time from timeVec
+ which is best suited to describe good direction
+ approxType: gras.ellapx.enums.EApproxType[1,1] /
+ / gras.ellapx.enums.EApproxType[1,nEllTubes] - type
+ of approximation (External, Internal, NotDefined).
+ It is possible either to specify one type of
+ approximation for all of nEllTubes ellipsoid tubes,
+ or specify the type of approximation for each of the
+ nEllTubes ellipsoid tubes separately.
+ approxSchemaName: char[1,] / cell[1,nEllTubes] of char[1,] -
+ name of the approximation schema. It is possible either
+ to specify one name of the approximation schema for
+ all of nEllTubes ellipsoid tubes, or specify the name
+ of the approximation schema for each of the nEllTubes
+ ellipsoid tubes separately.
+ approxSchemaDescr: char[1,] / cell[1,nEllTubes] of char[1,] -
+ description of the approximation schema. It is possible
+ either to specify one description of the approximation
+ schema for all of nEllTubes ellipsoid tubes, or specify
+ the description of the approximation schema for each
+ of the nEllTubes ellipsoid tubes separately.
+ absTol:double[1, 1] - absolute tolerance
+ relTol:double[1, 1] - relative tolerance
+ scaleFactor:double[1,nTubes] - vector of scale factors

Output:
- ellTubeRel: smartdb.relation.StaticRelation[1, 1] - constructed relation
- object
+ ellTubeRel: gras.ellapx.smartdb.rels.EllTube[1, 1] - constructed
+ ellipsoid tube object
</pre></div>
</div>
</div>
<div class="section" id="gras-ellapx-smartdb-rels-elltube-getdata">
<h3>gras.ellapx.smartdb.rels.EllTube.getData<a class="headerlink"
href="#gras-ellapx-smartdb-rels-elltube-getdata" title="Permalink to this
headline">¶</a></h3>
-<div class="highlight-python"><div class="highlight"><pre>GETDATA -
returns an indexed projection of CubeStruct object&#39;s content
-
+<div class="highlight-python"><div class="highlight"><pre>GETDATA - gets
data from ATypifiedAdjustedRel object
Input:
regular:
- self: CubeStruct [1,1] - the object
-
- optional:
-
- subIndCVec:
- Case#1: numeric[1,]/numeric[,1]
-
- Case#2: cell[1,nDims]/cell[nDims,1] of double [nSubElem_i,1]
- for i=1,...,nDims
-
- -array of indices of field value slices that are selected
- to be returned; if not given (default),
- no indexation is performed
-
- Note!: numeric components of subIndVec are allowed to contain
- zeros which are be treated as they were references to null
- data slices
-
- dimVec: numeric[1,nDims]/numeric[nDims,1] - vector of dimension
- numbers corresponding to subIndCVec
-
- properties:
-
- fieldNameList: char[1,]/cell[1,nFields] of char[1,]
- list of field names to return
-
- structNameList: char[1,]/cell[1,nStructs] of char[1,]
- list of internal structures to return (by default it
- is {SData, SIsNull, SIsValueNull}
-
- replaceNull: logical[1,1] if true, null values are replaced with
- certain default values uniformly across all the cells,
- default value is false
-
- nullReplacements: cell[1,nReplacedFields] - list of null
- replacements for each of the fields
-
- nullReplacementFields: cell[1,nReplacedFields] - list of fields in
- which the nulls are to be replaced with the specified values,
- if not specified it is assumed that all fields are to be
- replaced
-
- NOTE!: all fields not listed in this parameter are replaced with
- the default values
-
- checkInputs: logical[1,1] - true by default (input arguments are
- checked for correctness
-
+ self.
+ varargin:
Output:
- regular:
- SData: struct [1,1] - structure containing values of
- fields at the selected slices, each field is an array
- containing values of the corresponding type
-
- SIsNull: struct [1,1] - structure containing a nested
- array with is-null indicators for each CubeStruct cell content
-
- SIsValueNull: struct [1,1] - structure containing a
- logical array [] for each of the fields (true
- means that a corresponding cell doesn&#39;t not contain
- any value
+ optional:
</pre></div>
</div>
</div>
<div class="section" id="gras-ellapx-smartdb-rels-elltube-getellarray">
<h3>gras.ellapx.smartdb.rels.EllTube.getEllArray<a class="headerlink"
href="#gras-ellapx-smartdb-rels-elltube-getellarray" title="Permalink to
this headline">¶</a></h3>
-<div class="highlight-python"><div class="highlight"><pre>GETELLARRAY -
returns array of matrix&#39;s ellipsoid according to
- approxType
+<div class="highlight-python"><div class="highlight"><pre>GETELLARRAY -
returns array of ellipsoids according to
+approxType

Input:
regular:
self.
- approxType:char[1,] - type of approximation(internal/external)
+ approxType: cell[nEllTubes, 1] of char[1,] - type of
+ approximation(internal/external)

Output:
- apprEllMat:double[nDim1,..., nDimN] - array of array of ellipsoid&#39;s
- matrices
+ apprEllMat: ellipsoid[nTimePoints, nEllTubes] - an array
+ of all the ellipsoids from all the ellipsoid tubes that
+ are stored in self object
+ timeVec: cell[1,1] of double[1,nTimePoints] - time vector
</pre></div>
</div>
</div>
@@ -6471,42 +6539,75 @@
</div>
<div class="section"
id="gras-ellapx-smartdb-rels-elltube-getnocatorcutfieldslist">
<h3>gras.ellapx.smartdb.rels.EllTube.getNoCatOrCutFieldsList<a
class="headerlink"
href="#gras-ellapx-smartdb-rels-elltube-getnocatorcutfieldslist"
title="Permalink to this headline">¶</a></h3>
+<div class="highlight-python"><div
class="highlight"><pre>GETNOCATORCUTFIELDSLIST - returns a list of fields of
+EllTubeBasic object, which are not to be
+concatenated or cut.
+
+Input:
+ regular:
+ self.
+Output:
+ fieldsList: cell[nFields, 1] of char[1, ] - list of fields
+ of EllTubeBasic object, which are not to be
+ concatenated or cut
+</pre></div>
+</div>
</div>
<div class="section" id="gras-ellapx-smartdb-rels-elltube-interp">
<h3>gras.ellapx.smartdb.rels.EllTube.interp<a class="headerlink"
href="#gras-ellapx-smartdb-rels-elltube-interp" title="Permalink to this
headline">¶</a></h3>
+<div class="highlight-python"><div class="highlight"><pre>INTERP -
interpolates ellipsoidal tube on a new time vector
+
+Input:
+ regular:
+ self.
+ timeVec: double[1, nTimePoints] - sorted time vector to
+ interpolate on. Must begin with self.timeVec[1] and
+ end with self.timeVec[end]
+
+Output:
+ interpEllTube: gras.ellapx.smartdb.rels.EllTubeBasic[1, 1] -
+ interpolated ellipsoidal tube
+</pre></div>
+</div>
</div>
<div class="section" id="gras-ellapx-smartdb-rels-elltube-isequal">
<h3>gras.ellapx.smartdb.rels.EllTube.isEqual<a class="headerlink"
href="#gras-ellapx-smartdb-rels-elltube-isequal" title="Permalink to this
headline">¶</a></h3>
-<div class="highlight-python"><div class="highlight"><pre>ISEQUAL -
compares current relation object with other relation object and
- returns true if they are equal, otherwise it returns false
-
-
-Usage: isEq=isEqual(self,otherObj)
+<div class="highlight-python"><div class="highlight"><pre>ISEQUAL -
compares current relation object with other relation
+object and returns true if they are equal, otherwise it returns
+false.

Input:
regular:
- self: ARelation [1,1] - current relation object
- otherObj: ARelation [1,1] - other relation object
+ self.
+ otherObj: ARelation [1,1] - other relation object

properties:
- checkFieldOrder/isFieldOrderCheck: logical [1,1] - if true, then fields
- in compared relations must be in the same order, otherwise the
- order is not important (false by default)
- checkTupleOrder: logical[1,1] - if true, then the tuples in the
- compared relations are expected to be in the same order,
- otherwise the order is not important (false by default)
-
+ checkFieldOrder/isFieldOrderCheck: logical [1,1] - if true,
+ then fields in compared relations must be in the same
+ order, otherwise the order is not important (false by
+ default)
+ checkTupleOrder: logical[1,1] - if true, then the tuples
+ in the compared relations are expected to be in the same
+ order, otherwise the order is not important (false by
+ default)
maxTolerance: double [1,1] - maximum allowed tolerance
-
+ maxRelativeTolerance: double [1,1] - maximum allowed relative
+ tolerance
compareMetaDataBackwardRef: logical[1,1] if true, the CubeStruct&#39;s
referenced from the meta data objects are also compared
-
- maxRelativeTolerance: double [1,1] - maximum allowed
- relative tolerance
+ notComparedFieldList: cell[1,nFields] of char[1,] - list
+ of fields that are not to be compared
+ areTimeBoundsCompared: logical[1,1] - if false,
+ ellipsoidal tubes are compared on intersection of
+ definition domains

Output:
- isEq: logical[1,1] - result of comparison
- reportStr: char[1,] - report of comparsion
+ isOk: logical[1, 1] - logical vector elements of
+ which take OK value if the fields in self and otherRel
+ are equal and otherwise it takes FALSE value
+ reportStr: char[1, ] - a report string which contains more
+ detailed information about inequal fields in self and
+ otherRel objects
</pre></div>
</div>
</div>
@@ -6517,100 +6618,76 @@

Input:
regular:
- self:
+ self.
+ optional:
plObj: smartdb.disp.RelationDataPlotter[1,1] - plotter
object used for displaying ellipsoidal tubes
+Output:
+ plObj: smartdb.disp.RelationDataPlotter[1,1] - plotter
+ object used for displaying ellipsoidal tubes
</pre></div>
</div>
</div>
<div class="section" id="gras-ellapx-smartdb-rels-elltube-project">
<h3>gras.ellapx.smartdb.rels.EllTube.project<a class="headerlink"
href="#gras-ellapx-smartdb-rels-elltube-project" title="Permalink to this
headline">¶</a></h3>
-<div class="highlight-python"><div class="highlight"><pre>PROJECT -
computes projection of the relation object onto given time
- dependent subspase
+<div class="highlight-python"><div class="highlight"><pre>PROJECT -
projects ellipsoid tube onto subspace
+
Input:
regular:
self.
- projType: gras.ellapx.enums.EProjType[1,1] -
- type of the projection, can be
- &#39;Static&#39; and &#39;DynamicAlongGoodCurve&#39;
- projMatList: cell[1,nProj] of double[nSpDim,nDim] - list of
- projection matrices, not necessarily orthogonal
- fGetProjMat: function_handle[1,1] - function which creates
- vector of the projection
- matrices
- Input:
- regular:
- projMat:double[nDim, mDim] - matrix of the projection at the
- instant of time
- timeVec:double[1, nDim] - time interval
- optional:
- sTime:double[1,1] - instant of time
- Output:
- projOrthMatArray:double[1, nSpDim] - vector of the projection
- matrices
- projOrthMatTransArray:double[nSpDim, 1] - transposed vector of
- the projection matrices
-Output:
- ellTubeProjRel: gras.ellapx.smartdb.rels.EllTubeProj[1, 1]/
- gras.ellapx.smartdb.rels.EllTubeUnionProj[1, 1] -
- projected ellipsoidal tube
+ projType: gras.ellapx.enums.EProjType[1, 1] - type of
+ projection. It can be Static or DynamicAlongGoodCurve.
+ projMatList: double[nDims, nDims] - subspace defined by
+ its basis vectors on which ellipsoid tube has to be
+ projected
+ fGetProjMat: cell_fun[1, ] - function that is used to
+ get the projection.

- indProj2OrigVec:cell[nDim, 1] - index of the line number from
- which is obtained the projection
-
-Example:
- function example
- aMat = [0 1; 0 0]; bMat = eye(2);
- SUBounds = struct();
- SUBounds.center = {&#39;sin(t)&#39;; &#39;cos(t)&#39;};
- SUBounds.shape = [9 0; 0 2];
- sys = elltool.linsys.LinSysContinuous(aMat, bMat, SUBounds);
- x0EllObj = ell_unitball(2);
- timeVec = [0 10];
- dirsMat = [1 0; 0 1]&#39;;
- rsObj = elltool.reach.ReachContinuous(sys, x0EllObj, dirsMat, timeVec);
- ellTubeObj = rsObj.getEllTubeRel();
- unionEllTube = ...
- gras.ellapx.smartdb.rels.EllUnionTube.fromEllTubes(ellTubeObj);
- projMatList = {[1 0;0 1]};
- projType = gras.ellapx.enums.EProjType.Static;
- statEllTubeProj = unionEllTube.project(projType,projMatList,...
- @fGetProjMat);
- plObj=smartdb.disp.RelationDataPlotter();
- statEllTubeProj.plot(plObj);
-end
-
-function [projOrthMatArray,projOrthMatTransArray]=fGetProjMat(projMat,...
- timeVec,varargin)
- nTimePoints=length(timeVec);
- projOrthMatArray=repmat(projMat,[1,1,nTimePoints]);
- projOrthMatTransArray=repmat(projMat.&#39;,[1,1,nTimePoints]);
- end
+Output:
+ ellTubeProjRel: gras.ellapx.smartdb.rels.EllTubeProj[1, 1] -
+ ellipsoid tube projection
+ indProj2OrigVec: double[1, ] - vector of indices
</pre></div>
</div>
</div>
<div class="section" id="gras-ellapx-smartdb-rels-elltube-projectstatic">
<h3>gras.ellapx.smartdb.rels.EllTube.projectStatic<a class="headerlink"
href="#gras-ellapx-smartdb-rels-elltube-projectstatic" title="Permalink to
this headline">¶</a></h3>
+<div class="highlight-python"><div class="highlight"><pre>PROJECTSTATIC -
computes a static projection of the relation
+object onto static subspaces specified by static matrices
+
+Input:
+ regular:
+ self.
+ projMatList: double[nSpDims,nDims]/cell[1,nProjs]
+ of double[nSpDims,nDims] - list of not necessarily orthogonal
+ projection matrices
+
+Output:
+ ellTubeProjRel: smartdb.relation.StaticRelation[1, 1]/
+ smartdb.relation.DynamicRelation[1, 1]- projected relation
+ indProj2OrigVec:cell[nDims, 1] - index of the line number from
+ which is obtained the projection
+</pre></div>
+</div>
</div>
<div class="section" id="gras-ellapx-smartdb-rels-elltube-projecttoorths">
<h3>gras.ellapx.smartdb.rels.EllTube.projectToOrths<a class="headerlink"
href="#gras-ellapx-smartdb-rels-elltube-projecttoorths" title="Permalink to
this headline">¶</a></h3>
-<div class="highlight-python"><div class="highlight"><pre>PROJECTTOORTHS -
project elltube onto subspace defined by
-vectors of standart basis with indices specified in indVec
+<div class="highlight-python"><div class="highlight"><pre>PROJECTTOORTHS -
projects ellipsoid tube onto subspace defined
+by vectors of standart basis with indices specified in
+indVec.

Input:
regular:
- self: gras.ellapx.smartdb.rels.EllTube[1, 1] - elltube
- object
- indVec: double[1, nProjDims] - indices specifying a subset of
- standart basis
+ self.
+ indVec: double[1, nProjDims] - indices specifying a subset
+ of standart basis
optional:
projType: gras.ellapx.enums.EProjType[1, 1] - type of
- projection
+ projection. Default option is Static.

Output:
- regular:
- ellTubeProjRel: gras.ellapx.smartdb.rels.EllTubeProj[1, 1] -
- elltube projection
+ ellTubeProjRel: gras.ellapx.smartdb.rels.EllTubeProj[1, 1] -
+ ellipsoid tube projection

Example:
ellTubeProjRel = ellTubeRel.projectToOrths([1,2])
@@ -6621,95 +6698,134 @@
</div>
<div class="section" id="gras-ellapx-smartdb-rels-elltube-scale">
<h3>gras.ellapx.smartdb.rels.EllTube.scale<a class="headerlink"
href="#gras-ellapx-smartdb-rels-elltube-scale" title="Permalink to this
headline">¶</a></h3>
-<div class="highlight-python"><div class="highlight"><pre>SCALE - scales
relation object
+<div class="highlight-python"><div class="highlight"><pre>SCALE -
calculates new value of scaleFactor for fields from
+fieldNameList using fCalcFactor function

- Input:
+Input:
regular:
- self.
- fCalcFactor - function which calculates factor for
- fields in fieldNameList
- Input:
- regular:
- fieldNameList: char/cell[1,] of char - a list of fields
- for which factor will be calculated
- Output:
- factor:double[1, 1] - calculated factor
-
- fieldNameList:cell[1,nElem]/char[1,] - names of the fields
+ self.
+ fCalcFactor: function_handle[1, 1] - function which calculates
+ scaleFactor for fields in fieldNameList
+ fieldNameList: char[1, ]/cell[1,nFields] of char[1, ] -
+ a list of field or nFields fields for which scale factor
+ will be calculated

Output:
- none
-
-Example:
- nPoints=5;
- calcPrecision=0.001;
- approxSchemaDescr=char.empty(1,0);
- approxSchemaName=char.empty(1,0);
- nDims=3;
- nTubes=1;
- lsGoodDirVec=[1;0;1];
- aMat=zeros(nDims,nPoints);
- timeVec=1:nPoints;
- sTime=nPoints;
- approxType=gras.ellapx.enums.EApproxType.Internal;
- qArrayList=repmat({repmat(diag([1 2 3]),[1,1,nPoints])},1,nTubes);
- ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
- fromMatEllTube=...
- gras.ellapx.smartdb.rels.EllTube.fromQArrays(qArrayList,...
- aMat, timeVec,ltGoodDirArray, sTime, approxType,...
- approxSchemaName, approxSchemaDescr, calcPrecision);
- fromMatEllTube.scale(@(varargin)2,{});
+ none.
</pre></div>
</div>
</div>
<div class="section"
id="gras-ellapx-smartdb-rels-elltube-sortdetermenistically">
<h3>gras.ellapx.smartdb.rels.EllTube.sortDetermenistically<a
class="headerlink"
href="#gras-ellapx-smartdb-rels-elltube-sortdetermenistically"
title="Permalink to this headline">¶</a></h3>
+<div class="highlight-python"><div
class="highlight"><pre>SORTDETERMENISTICALLY - sorts fields of
ATypifiedAdjustedRel
+object using specified maximal tolerance
+Input:
+ regular:
+ self.
+ maxTolerance: double[1, 1] - maximal tolerance that is
+ used while sorting elements of self object.
+Output:
+ none.
+</pre></div>
+</div>
</div>
<div class="section" id="gras-ellapx-smartdb-rels-elltube-thinouttuples">
<h3>gras.ellapx.smartdb.rels.EllTube.thinOutTuples<a class="headerlink"
href="#gras-ellapx-smartdb-rels-elltube-thinouttuples" title="Permalink to
this headline">¶</a></h3>
+<div class="highlight-python"><div class="highlight"><pre>THINOUTTUPLES -
thins ellipsoid tube object using vector of
+indices specified by the user. The function returns new
+ellipsoid tube object containing only ellipsoids from the
+original ellipsoid tube with indices specified in indVec.
+
+Input:
+ regular:
+ self.
+ indVec: double[nIndices, 1] - indices of ellipsoids which
+ are to be included in new ellipsoid tube object
+
+Output:
+ thinnedEllTubeRel: gras.ellapx.smartdb.rels.EllTubeBasic[1, 1] -
+ new ellipsoid tube object containing only ellipsoids from
+ self EllTube object with indices specified in indVec
+</pre></div>
+</div>
</div>
</div>
<div class="section" id="gras-ellapx-smartdb-rels-elltubeproj">
<h2>gras.ellapx.smartdb.rels.EllTubeProj<a class="headerlink"
href="#gras-ellapx-smartdb-rels-elltubeproj" title="Permalink to this
headline">¶</a></h2>
<div class="section" id="gras-ellapx-smartdb-rels-elltubeproj-elltubeproj">
<h3>gras.ellapx.smartdb.rels.EllTubeProj.EllTubeProj<a class="headerlink"
href="#gras-ellapx-smartdb-rels-elltubeproj-elltubeproj" title="Permalink
to this headline">¶</a></h3>
-<div class="highlight-python"><div class="highlight"><pre>EllTubeProj -
class which keeps ellipsoidal tube&#39;s projection
+<div class="highlight-python"><div class="highlight"><pre>A class which
allows to work with projections of ellipsoid tube objects.

Fields:
- QArray:cell[1, nElem] - Array of ellipsoid matrices
- aMat:cell[1, nElem] - Array of ellipsoid centers
- scaleFactor:double[1, 1] - Tube scale factor
- MArray:cell[1, nElem] - Array of regularization ellipsoid matrices
- dim :double[1, 1] - Dimensionality
- sTime:double[1, 1] - Time s
- approxSchemaName:cell[1,] - Name
- approxSchemaDescr:cell[1,] - Description
- approxType:gras.ellapx.enums.EApproxType - Type of approximation
- (external, internal, not defined)
- timeVec:cell[1, m] - Time vector
- calcPrecision:double[1, 1] - Calculation precision
- indSTime:double[1, 1] - index of sTime within timeVec
- ltGoodDirMat:cell[1, nElem] - Good direction curve
- lsGoodDirVec:cell[1, nElem] - Good direction at time s
- ltGoodDirNormVec:cell[1, nElem] - Norm of good direction curve
- lsGoodDirNorm:double[1, 1] - Norm of good direction at time s
- xTouchCurveMat:cell[1, nElem] - Touch point curve for good
- direction
- xTouchOpCurveMat:cell[1, nElem] - Touch point curve for direction
- opposite to good direction
- xsTouchVec:cell[1, nElem] - Touch point at time s
- xsTouchOpVec:cell[1, nElem] - Touch point at time s
- projSTimeMat: cell[1, 1] - Projection matrix at time s
- projType:gras.ellapx.enums.EProjType - Projection type
- ltGoodDirNormOrigVec:cell[1, 1] - Norm of the original (not
- projected) good direction curve
- lsGoodDirNormOrig:double[1, 1] - Norm of the original (not
- projected)good direction at time s
- lsGoodDirOrigVec:cell[1, 1] - Original (not projected) good
- direction at time s
-
-TODO: correct description of the fields in
- gras.ellapx.smartdb.rels.EllTubeProj
+ QArray: cell[1,1] of double[nDims,nDims,nTimePoints] -
+ a 3-dimentional matrix in which each of nTimePoints slices is a
+ double[nDims,nDims] projection of an ellipsoid matrix on specified
+ subspace at nTimePoint point of time. Here nTimePoints is number
+ of elements in timeVec.
+ aMat: cell[1,nTimePoints] of double[nDims,1] - a 2-dimentional matrix
+ in which each of nTimePoints columns is a projection of
+ an ellipsoid center. Each center is specified for
+ nTimePoint point of time
+ scaleFactor: double[1, 1] - scale for the created ellipsoid tube
+ MArray: cell[1,1] of double[nDims,nDims,nTimePoints] -
+ a 3-dimentional matrix in which each of nTimePoints slices is a
+ double[nDims,nDims] projection of a regularization matrix on
specified
+ subspace at nTimePoint point of time.
+ dim: double[1, 1] - the dimension of the space on which the touching
+ curves are projected
+ sTime: double[1, 1] - specific point of time which is best suited to
+ describe good direction
+ approxSchemaName: cell[1, 1] of char[1,] - name of the
+ approximation schema
+ approxSchemaDescr: cell[1, 1] of char[1,] - description of the
+ approximation schema
+ approxType: gras.ellapx.enums.EApproxType[1,1] - type of approximation
+ (External, Internal, NotDefined)
+ timeVec: double[1, nTimePoints] - time vector
+ absTolerance: double[1, 1] - absolute tolerance
+ relTolerance: double[1, 1] - relative tolerance
+ indSTime: double[1, 1] - index of sTime point within timeVec
+ ltGoodDirMat: cell[1, nTimePoints] of double[nDims, 1] - matrix of
+ the projections of good direction vectors on the specified space
+ at any point of time from timeVec
+ lsGoodDirVec: cell[1, 1] of double[nDims, 1] - the projection of good
+ direction vector on the specified space at sTime point of time
+ ltGoodDirNormVec: cell[1, 1] of double[1, nTimePoints] - norm of the
+ projections of good direction vectors on the specified space at
+ any point of time from timeVec
+ lsGoodDirNorm: double[1, 1] - norm of the projection of good direction
+ vector on the specified space at sTime point of time
+ xTouchCurveMat: cell[1, nTimePoints] of double[nDims, 1] - the projection
+ of touch point curve on the specified space for good direction matrix
+ xTouchOpCurveMat: cell[1, nTimePoints] of double[nDims, 1] - the
projection
+ of touch point curve oposite to the xTouchCurveMat touch point curve
+ xsTouchVec: cell[1, 1] of double[nDims, 1] - the projection of touch
+ point at sTime point of time
+ xsTouchOpVec: cell[1, 1] of double[nDims, 1] - the projection of a
+ point opposite to the xsTouchVec touch point
+ isLsTouch: logical[1, 1] - a logical variable which indicates whether
+ a touch takes place along good direction at sTime point of time
+ isLsTouchVec: cell[1, 1] of logical[nTimePoints, 1] - a logical
+ vector which indicates whether a touch takes place along good
+ direction at any point of time from timeVec
+ projSMat: cell[1, 1] of double[nDims, nDims] - projection matrix at
+ sTime point of time
+ projArray: cell[nTimePoints, 1] of double[nDims, nDims] - an array
+ of projection matrices at any point of time from timVec
+ projType: gras.ellapx.enums.EProjType[1, 1] - type of projection
+ (Static, DynamicAlongGoodCurve)
+ ltGoodDirNormOrigVec: cell[1, 1] of double[1, nTimePoints] - norm
+ of the original good direction vectors at any point of time from
timeVec
+ lsGoodDirNormOrig: double[1, 1] - norm of the original good direction
+ vector at sTime point of time
+ ltGoodDirOrigMat: cell[1, nTimePoints] of double[nDims, 1] - matrix
+ of the original good direction vectors at any point of time from
timeVec
+ lsGoodDirOrigVec: cell[1, 1] of double[nDims, 1] - the original good
+ direction vector at sTime point of time
+ ltGoodDirNormOrigProjVec: cell[1, 1] of double[1, nTimePoints] - norm
+ of the projection of the original good direction curve
+ ltGoodDirOrigProjMat: cell[1, 1] of double[nDims, nTimePoints] - the
+ projectition of the original good direction curve
</pre></div>
</div>
<p>See the description of the following methods in <a class="reference
internal"
href="#smartdb-relations-atypifiedstaticrelation">smartdb.relations.ATypifiedStaticRelation</a>
for smartdb.relations.ATypifiedStaticRelation:</p>
@@ -6779,90 +6895,50 @@
</div>
<div class="section" id="gras-ellapx-smartdb-rels-elltubeproj-cut">
<h3>gras.ellapx.smartdb.rels.EllTubeProj.cut<a class="headerlink"
href="#gras-ellapx-smartdb-rels-elltubeproj-cut" title="Permalink to this
headline">¶</a></h3>
+<div class="highlight-python"><div class="highlight"><pre>CUT - extracts
the piece of the ellipsoid tube object from given
+start point of time to given end point of time.
+
+Input:
+ regular:
+ self.
+ cutTimeVec: double[1, 2] / double[1, 1] - time interval to cut
+
+Output:
+ cutEllTubeRel: gras.ellapx.smartdb.rels.EllTube[1, 1] -
+ ellipsoid tube which is created from the original one by
+ cutting it from given start point of time to given end
+ point of time
+</pre></div>
+</div>
</div>
<div class="section" id="gras-ellapx-smartdb-rels-elltubeproj-getdata">
***The diff for this file has been truncated for email.***
=======================================
--- /branches/issue_133_aatanesyan/doc/_build/html/chap_implement.html Mon
Feb 24 20:40:31 2014 UTC
+++ /branches/issue_133_aatanesyan/doc/_build/html/chap_implement.html Wed
Mar 5 02:41:50 2014 UTC
@@ -333,9 +333,9 @@
</td></tr></table></div>
<div class="figure" id="minksumpic">
<a class="reference internal image-reference"
href="_images/chapter05_section01_minksum.png"><img alt="minksum"
src="_images/chapter05_section01_minksum.png" style="width: 40%;" /></a>
-<p class="caption">Figure 15: The geometric sum of ellipsoids.</p>
+<p class="caption">Figure 45: The geometric sum of ellipsoids.</p>
</div>
-<p><a href="#minksumpic">Figure 15</a> displays the geometric sum of
ellipsoids. If
+<p><a href="#minksumpic">Figure 45</a> displays the geometric sum of
ellipsoids. If
the dimension of the space in which the ellipsoids are defined exceeds
<img class="math"
src="_images/math/b9b358d9bbdf54c3d9aef7554638822d996c21ea.png" alt="3"/>,
an error is returned. The result of the geometric sum
operation is not generally an ellipsoid, but it can be approximated by
@@ -417,9 +417,9 @@
</td></tr></table></div>
<div class="figure" id="minkdiffpic">
<a class="reference internal image-reference"
href="_images/chapter05_section01_minkdiff.png"><img alt="minkdiff"
src="_images/chapter05_section01_minkdiff.png" style="width: 40%;" /></a>
-<p class="caption">Figure 16: The geometric difference of ellipsoids.</p>
+<p class="caption">Figure 46: The geometric difference of ellipsoids.</p>
</div>
-<p><a href="#minkdiffpic">Figure 16</a> shows the geometric difference of
ellipsoids.</p>
+<p><a href="#minkdiffpic">Figure 46</a> shows the geometric difference of
ellipsoids.</p>
<p>Similar to minksum, minkdiff is there for visualization purpose. It
works only for dimensions <img class="math"
src="_images/math/123e375e88da91240024aaf085abee194c4a2d06.png" alt="1"/>,
<img class="math"
src="_images/math/15c663954a3e059d1f876bc8a4621de376038c96.png" alt="2"/>
and <img class="math"
src="_images/math/b9b358d9bbdf54c3d9aef7554638822d996c21ea.png" alt="3"/>,
and for
higher dimensions it returns an error. For arbitrary dimensions, the
@@ -505,9 +505,9 @@
</td></tr></table></div>
<div class="figure" id="minkpic">
<a class="reference internal image-reference"
href="_images/chapter05_section01_minkpmminkmp.png"><img alt="minkpmminkmp"
src="_images/chapter05_section01_minkpmminkmp.png" style="width: 100%;"
/></a>
-<p class="caption">Figure 17: Implementation of operations
&#8216;sum-difference&#8217; and &#8216;difference-sum&#8217;.</p>
+<p class="caption">Figure 47: Implementation of operations
&#8216;sum-difference&#8217; and &#8216;difference-sum&#8217;.</p>
</div>
-<p>Figure <a href="#minkpic"> 17</a> displays results of
+<p>Figure <a href="#minkpic"> 47</a> displays results of
the implementation of minkpm and minkmp operations.</p>
<p>Similarly, operation ’sum-difference’ described in section <a
class="reference internal"
href="chap_ellcalc.html#sum-diff-label"><em>Geometric
Sum-Difference</em></a> is implemented in functions
minkpm, minkpm_ea, minkpm_ia, the first one of which is used for
@@ -968,13 +968,13 @@
<em>Ellipsoidal Toolbox</em> is SeDuMi (<a class="reference internal"
href="chap_install.html#stur1999" id="id7">[STUR1999]</a>, <a
class="reference internal" href="chap_install.html#sdmhp"
id="id8">[SDMHP]</a>).</p>
</div>
<div class="section" id="operations-with-ellipsoidal-tubes">
-<h2>Operations with ellipsoidal tubes<a class="headerlink"
href="#operations-with-ellipsoidal-tubes" title="Permalink to this
headline">¶</a></h2>
+<span id="section-label"></span><h2>Operations with ellipsoidal tubes<a
class="headerlink" href="#operations-with-ellipsoidal-tubes"
title="Permalink to this headline">¶</a></h2>
<p>There are several classes in <em>Ellipsoidal Toolbox</em> for
operations with
ellipsoidal tubes. The class gras.ellapx.smartdb.rels.EllTube is used to
describe ellipsoidal tubes. The class
gras.ellapx.smartdb.rels.EllUnionTube is used to store tubes by the
instant of time:</p>
-<div class="math">
+<div class="math" id="union-label">
<p><img src="_images/math/53ca07410d079433f63db3afd5fd5ba975724616.png"
alt="{\mathcal X}_{U}[t]=\bigcup \limits_{\tau\leqslant t}{\mathcal
X}[\tau],"/></p>
</div><p>where <img class="math"
src="_images/math/456d10b00ec6c948f7306d194e252da674e291d1.png"
alt="{\mathcal X}[\tau]"/> is single ellipsoidal tube. The class
gras.ellapx.smartdb.rels.EllTubeProj is used to describe the projection
@@ -1110,13 +1110,13 @@
end
</pre></div>
</td></tr></table></div>
-<p>We can compute the projection of the ellipsoidal
+<p id="goto-label">We can compute the projection of the ellipsoidal
tube onto time-dependent subspace.</p>
<div class="figure" id="statdyn-proj">
<a class="reference internal image-reference"
href="_images/chapter05_section03_reachTubeStatProjreachTubeDynProj.png"><img
alt="reachTubeStatProjreachTubeDynProj"
src="_images/chapter05_section03_reachTubeStatProjreachTubeDynProj.png"
style="width: 100%;" /></a>
-<p class="caption">Figure 18: Static and dynamic projections of the
ellipsoidal tube.</p>
+<p class="caption">Figure 48: Static and dynamic projections of the
ellipsoidal tube.</p>
</div>
-<p>Figure <a href="#statdyn-proj"> 18</a> displays static and dynamic
projections.
+<p>Figure <a href="#statdyn-proj"> 48</a> displays static and dynamic
projections.
Also we can see projections of good directions for ellipsoidal tubes.</p>
<p>We can compute tubes by the instant of time using
methodfromEllTubes:</p>
<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
@@ -1176,9 +1176,9 @@
</td></tr></table></div>
<div class="figure" id="uniontubestatproj">
<a class="reference internal image-reference"
href="_images/chapter05_section03_unionTubeStatProj.png"><img
alt="unionTubeStatProj"
src="_images/chapter05_section03_unionTubeStatProj.png" style="width: 70%;"
/></a>
-<p class="caption">Figure 19: Ellipsoidal tubes by the instant of time.</p>
+<p class="caption">Figure 49: Ellipsoidal tubes by the instant of time.</p>
</div>
-<p><a href="#uniontubestatproj">Figure 19</a> shows projection of
ellipsoidal
+<p><a href="#uniontubestatproj">Figure 49</a> shows projection of
ellipsoidal
tubes by the instant of time.</p>
<p>Also we can get initial data from the resulting tube:</p>
<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre>1
@@ -1227,9 +1227,9 @@
</td></tr></table></div>
<div class="figure" id="disppic">
<a class="reference internal image-reference"
href="_images/chapter05_section03_dispPic.png"><img alt="disp"
src="_images/chapter05_section03_dispPic.png" style="width: 50%;" /></a>
-<p class="caption">Figure 20: Content of the ellipsoidal tube.</p>
+<p class="caption">Figure 50: Content of the ellipsoidal tube.</p>
</div>
-<p><a href="#disppic">Figure 20</a>
+<p><a href="#disppic">Figure 50</a>
displays all fields of the ellipsoidal tube.</p>
<p>There are several methods to find the tubes with necessary
parameters.</p>
<div class="highlight-matlab"><table class="highlighttable"><tr><td
class="linenos"><div class="linenodiv"><pre> 1
=======================================
--- /branches/issue_133_aatanesyan/doc/_build/html/main_manual.html Mon Feb
24 20:40:31 2014 UTC
+++ /branches/issue_133_aatanesyan/doc/_build/html/main_manual.html Wed
Mar 5 02:41:50 2014 UTC
@@ -107,26 +107,10 @@
<li class="toctree-l2"><a class="reference internal"
href="chap_examples.html#hybrid-system">Hybrid System</a></li>
</ul>
</li>
-<li class="toctree-l1"><a class="reference internal"
href="chap_ellTube.html">Ellipsoid tubes and touching curves</a><ul>
-<li class="toctree-l2"><a class="reference internal"
href="chap_ellTube.html#touching-curves">Touching curves</a><ul>
-<li class="toctree-l3"><a class="reference internal"
href="chap_ellTube.html#elltubetouchcurvebasic-class"><em>EllTubeTouchCurveBasic</em>
class</a></li>
-<li class="toctree-l3"><a class="reference internal"
href="chap_ellTube.html#elltubetouchcurveprojbasic-class"><em>EllTubeTouchCurveProjBasic</em>
class</a></li>
-</ul>
-</li>
-<li class="toctree-l2"><a class="reference internal"
href="chap_ellTube.html#ellipsoidal-tubes">Ellipsoidal tubes</a><ul>
-<li class="toctree-l3"><a class="reference internal"
href="chap_ellTube.html#elltubebasic-class"><em>EllTubeBasic</em>
class</a></li>
-<li class="toctree-l3"><a class="reference internal"
href="chap_ellTube.html#elltube-class"><em>EllTube</em> class</a></li>
-<li class="toctree-l3"><a class="reference internal"
href="chap_ellTube.html#elltubeprojbasic-class"><em>EllTubeProjBasic</em>
class</a></li>
-<li class="toctree-l3"><a class="reference internal"
href="chap_ellTube.html#elltubeproj-class"><em>EllTubeProj</em>
class</a></li>
-</ul>
-</li>
-<li class="toctree-l2"><a class="reference internal"
href="chap_ellTube.html#unions-of-ellipsoidal-tubes">Unions of ellipsoidal
tubes</a><ul>
-<li class="toctree-l3"><a class="reference internal"
href="chap_ellTube.html#elluniontubebasic-class"><em>EllUnionTubeBasic</em>
class</a></li>
-<li class="toctree-l3"><a class="reference internal"
href="chap_ellTube.html#elluniontube-class"><em>EllUnionTube</em>
class</a></li>
-<li class="toctree-l3"><a class="reference internal"
href="chap_ellTube.html#elluniontubestaticproj-class"><em>EllUnionTubeStaticProj</em>
class</a></li>
-</ul>
-</li>
-<li class="toctree-l2"><a class="reference internal"
href="chap_ellTube.html#typifiedbyfieldcoderel-class"><em>TypifiedByFieldCodeRel</em>
class</a></li>
+<li class="toctree-l1"><a class="reference internal"
href="chap_ellTube.html">Ellipsoid tubes, unions and projections</a><ul>
+<li class="toctree-l2"><a class="reference internal"
href="chap_ellTube.html#ellipsoid-tubes">Ellipsoid tubes</a></li>
+<li class="toctree-l2"><a class="reference internal"
href="chap_ellTube.html#unions-of-ellipsoid-tubes">Unions of ellipsoid
tubes</a></li>
+<li class="toctree-l2"><a class="reference internal"
href="chap_ellTube.html#projections-of-ellipsoid-tubes-and-unions">Projections
of ellipsoid tubes and unions</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal"
href="chap_summary.html">Summary and Outlook</a></li>
=======================================
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--- /branches/issue_133_aatanesyan/doc/_build/html/searchindex.js Mon Feb
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5 02:41:50 2014 UTC
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and
Outlook","Ellipsoid tubes and touching curves","Ellipsoidal
Calculus","Acknowledgement","Installation","Reachability","Function
Reference","Introduction","Welcome to Ellipsoidal Toolbox
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and
Outlook","Ellipsoid tubes, unions and projections","Ellipsoidal
Calculus","Acknowledgement","Installation","Reachability","Function
Reference","Introduction","Welcome to Ellipsoidal Toolbox
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=======================================
--- /branches/issue_133_aatanesyan/doc/_build/latex/elltool_manual.tex Mon
Feb 24 20:40:31 2014 UTC
+++ /branches/issue_133_aatanesyan/doc/_build/latex/elltool_manual.tex Wed
Mar 5 02:41:50 2014 UTC
@@ -17,7 +17,7 @@


\title{Ellipsoidal Toolbox}
-\date{February 25, 2014}
+\date{March 05, 2014}
\release{2.0 beta 1}
\author{Peter Gagarinov, Alex A. Kurzhanskiy}
\newcommand{\sphinxlogo}{}
@@ -3283,7 +3283,7 @@
\capstart

\includegraphics[width=0.400\linewidth]{chapter05_section01_minksum.png}
-\caption{Figure 15: The geometric sum of
ellipsoids.}\label{chap_implement:minksumpic}\end{figure}
+\caption{Figure 45: The geometric sum of
ellipsoids.}\label{chap_implement:minksumpic}\end{figure}

\hyperref[chap_implement:minksumpic]{Figure
\ref*{chap_implement:minksumpic}} displays the geometric sum of ellipsoids.
If
the dimension of the space in which the ellipsoids are defined exceeds
@@ -3343,7 +3343,7 @@
\capstart

\includegraphics[width=0.400\linewidth]{chapter05_section01_minkdiff.png}
-\caption{Figure 16: The geometric difference of
ellipsoids.}\label{chap_implement:minkdiffpic}\end{figure}
+\caption{Figure 46: The geometric difference of
ellipsoids.}\label{chap_implement:minkdiffpic}\end{figure}

\hyperref[chap_implement:minkdiffpic]{Figure
\ref*{chap_implement:minkdiffpic}} shows the geometric difference of
ellipsoids.

@@ -3405,7 +3405,7 @@
\capstart


\includegraphics[width=1.000\linewidth]{chapter05_section01_minkpmminkmp.png}
-\caption{Figure 17: Implementation of operations `sum-difference' and
`difference-sum'.}\label{chap_implement:minkpic}\end{figure}
+\caption{Figure 47: Implementation of operations `sum-difference' and
`difference-sum'.}\label{chap_implement:minkpic}\end{figure}

Figure \hyperref[chap_implement:minkpic]{ \ref*{chap_implement:minkpic}}
displays results of
the implementation of minkpm and minkmp operations.
@@ -3737,13 +3737,13 @@


\section{Operations with ellipsoidal tubes}
-\label{chap_implement:operations-with-ellipsoidal-tubes}
+\label{chap_implement:section-label}\label{chap_implement:operations-with-ellipsoidal-tubes}
There are several classes in \emph{Ellipsoidal Toolbox} for operations with
ellipsoidal tubes. The class gras.ellapx.smartdb.rels.EllTube is used to
describe ellipsoidal tubes. The class
gras.ellapx.smartdb.rels.EllUnionTube is used to store tubes by the
instant of time:
-\begin{gather}
+\phantomsection\label{chap_implement:union-label}\begin{gather}
\begin{split}{\mathcal X}_{U}[t]=\bigcup \limits_{\tau\leqslant
t}{\mathcal X}[\tau],\end{split}\notag
\end{gather}
where \({\mathcal X}[\tau]\) is single ellipsoidal tube. The class
@@ -3830,7 +3830,7 @@
projOrthMatTransArray=repmat(projMat.\PYGZsq{},[1,1,nTimePoints]);
end
\end{Verbatim}
-
+\phantomsection\label{chap_implement:goto-label}
We can compute the projection of the ellipsoidal
tube onto time-dependent subspace.
\begin{figure}[htbp]
@@ -3838,7 +3838,7 @@
\capstart


\includegraphics[width=1.000\linewidth]{chapter05_section03_reachTubeStatProjreachTubeDynProj.png}
-\caption{Figure 18: Static and dynamic projections of the ellipsoidal
tube.}\label{chap_implement:statdyn-proj}\end{figure}
+\caption{Figure 48: Static and dynamic projections of the ellipsoidal
tube.}\label{chap_implement:statdyn-proj}\end{figure}

Figure \hyperref[chap_implement:statdyn-proj]{
\ref*{chap_implement:statdyn-proj}} displays static and dynamic projections.
Also we can see projections of good directions for ellipsoidal tubes.
@@ -3879,7 +3879,7 @@
\capstart


\includegraphics[width=0.700\linewidth]{chapter05_section03_unionTubeStatProj.png}
-\caption{Figure 19: Ellipsoidal tubes by the instant of
time.}\label{chap_implement:uniontubestatproj}\end{figure}
+\caption{Figure 49: Ellipsoidal tubes by the instant of
time.}\label{chap_implement:uniontubestatproj}\end{figure}

\hyperref[chap_implement:uniontubestatproj]{Figure
\ref*{chap_implement:uniontubestatproj}} shows projection of ellipsoidal
tubes by the instant of time.
@@ -3919,7 +3919,7 @@
\capstart

\includegraphics[width=0.500\linewidth]{chapter05_section03_dispPic.png}
-\caption{Figure 20: Content of the ellipsoidal
tube.}\label{chap_implement:disppic}\end{figure}
+\caption{Figure 50: Content of the ellipsoidal
tube.}\label{chap_implement:disppic}\end{figure}

\hyperref[chap_implement:disppic]{Figure \ref*{chap_implement:disppic}}
displays all fields of the ellipsoidal tube.
@@ -5336,256 +5336,126 @@
the guard is not actually reached, because the state evolves according
to the green region.

-
-\chapter{Ellipsoid tubes and touching curves}
-\label{chap_ellTube::doc}\label{chap_ellTube:ellipsoid-tubes-and-touching-curves}
-
-\section{Touching curves}
-\label{chap_ellTube:touching-curves}
-One of the basic insruments in the \emph{Ellipsoidal Toolbox} are classes,
which allow to work with touching curves. These are the curves along which
the internal and external ellipsoidal approximations are touching. In
\emph{Ellipsoidal Toolbox} there are two basic classes
(\emph{EllTubeTouchCurveBasic} and \emph{EllTubeTouchCurveProjBasic}) which
allow us to keep touching curves and their projections. These classes do
not add any functionality, that we can use, while working with the toolbox,
(They do not have public methods.) but they are further used in other
classes, which inherit these ones.

-
-\subsection{\emph{EllTubeTouchCurveBasic} class}
-\label{chap_ellTube:elltubetouchcurvebasic-class}
-This class allows us to keep touch point curve objects. This kind of
objects have a lot of different fields, which store the information about
the touching curve.
-The first field of our object is:
-\begin{itemize}
-\item {}
-\emph{dim}: In this field the dimension of the space in which the touching
-curves are defined is stored.
-
-\end{itemize}
-
-Then there are several fields that are connecteld with time:
-\begin{itemize}
-\item {}
-\emph{timeVec}: Time vector in which the the touching curves are defined;
-
-\item {}
-\emph{sTime}: Specific point of time which is best suited to describe good
direction;
-
-\item {}
-\emph{indSTime}: The index of sTime point within timeVec is srored in this
field.
-
-\end{itemize}
-
-It should be said that the \emph{good direction} is the direction along
which the internal and external approximations of ellipsoid tubes are
touching. Next several fields specify the type of approximation which was
used? while creating these touching curves:
-\begin{itemize}
-\item {}
-\emph{approxSchemaName}: The name of the approximation schema;
-
-\item {}
-\emph{approxSchemaDescr}: The description of the approximation schema;
-
-\item {}
-\emph{approxType}: The type of approximation (External, Internal,
NotDefined) is stored in this field.
-
-\end{itemize}
-
-Then there are two fields which keep the absolute tolerance and relative
tolerance used to create this object (\emph{absTolerance} and
\emph{relTolerance}, respectively). And finally come the fields which allow
us to keep the touching curves and good directions:
+\chapter{Ellipsoid tubes, unions and projections}
+\label{chap_ellTube::doc}\label{chap_ellTube:ellipsoid-tubes-unions-and-projections}
+There are two types of ellipsoid tube objects that we can work with using
\emph{Ellipsoidal Toolbox}:
\begin{itemize}
\item {}
-\emph{ltGoodDirMat} field stores the matrix of good direction vectors at
any point of time from timeVec;
-
-\item {}
-\emph{lsGoodDirVec} field stores the good direction vector at sTime point
of time;
-
-\item {}
-\emph{ltGoodDirNormVec} field stores the norm of good direction vectors at
any point of time from timeVec;
-
-\item {}
-\emph{lsGoodDirNorm} field stores the norm of good direction vector at
sTime point of time;
-
-\item {}
-\emph{xTouchCurveMat} field stores the touch point curve for good
direction matrix;
-
-\item {}
-\emph{xTouchOpCurveMat} field stores the touch point curve oposite to the
xTouchCurveMat touch point curve;
-
-\item {}
-\emph{xsTouchVec} field stores the touch point at sTime point of time;
-
-\item {}
-\emph{xsTouchOpVec} field stores a point opposite to the xsTouchVec touch
point;
-
-\item {}
-\emph{isLsTouch} field stores a logical variable which indicates whether a
touch takes place along good direction at sTime point of time;
+ellipsoidal tubes that are described in
\emph{gras.ellapx.smartdb.rels.EllTube} class;

\item {}
-\emph{isLtTouchVec} field stores a logical vector which indicates whether
a touch takes place along good direction at any point of time from
timeVec.
+unions of ellipsoidal tubes by the instant of time described in
\emph{gras.ellapx.smartdb.rels.EllUnionTube} class (see
{\hyperref[chap_implement:union-label]{\emph{formula}}}).

\end{itemize}

-
-\subsection{\emph{EllTubeTouchCurveProjBasic} class}
-\label{chap_ellTube:elltubetouchcurveprojbasic-class}
-This class allows us to keep the projections of touch point curves. This
kind of objects have a lot of different fields, which store the information
about the projection of touching curve. First of all it inherits all the
fields from \emph{EllTubeTouchCurveBasic} class, and, secondly, it adds
some of its own fields. The inherited fields store the information about
the projection instead of the information about the original curve, but
their meaning is all the same.
-The first group of new fields is connected to the type of projection and
the space on which the curve is projected:
-\begin{itemize}
-\item {}
-\emph{projSMat} field stores the projection matrix at sTime point of time;
-
-\item {}
-\emph{projArray} field stores an array of projection matrices at any point
of time from timVec;
+The projections of ellipsoid tubes can be either static or dynamic. The
are described in gras.ellapx.smartdb.rels.EllTubeProj class. As for the
unions of ellipsoid tubes, they can only be projected on static subspaces.
These projections are described in
gras.ellapx.smartdb.rels.EllUnionTubeStaticProj class. For more information
about these types of projections and their differences and for examples see
this {\hyperref[chap_implement:section-label]{\emph{link}}}.

-\item {}
-\emph{projType} field stores the type of projection (Static or
DynamicAlongGoodCurve).

-\end{itemize}
+\section{Ellipsoid tubes}
+\label{chap_ellTube:ellipsoid-tubes}
+There is a whole variety of operations upon ellipsoid tubes in
\emph{Ellipsoidal Toolbox}. We can, of course, create them. When the
ellipsoid tube object is created, we can cut them, concatenate,
interpolate, plot and project them and so on.

-And then come the new fields which store some information about the
original curve:
+The instruments to create ellipsoid tube objects are several functions:
\begin{itemize}
\item {}
-\emph{ltGoodDirNormOrigVec} field stores the norm of the original good
direction vectors at any point of time from timeVec;
+\emph{fromQArrays} method creates nEllTubes ellipsoid tube objects using
an array of ellipsoid matrices and an array of ellipsoid centers specified
at any point of time from timeVec;

\item {}
-\emph{lsGoodDirNormOrig} field stores the norm of the original good
direction vector at sTime point of time;
+\emph{fromQMArrays} method acts the same way as \emph{fromQArrays} method,
except for this one requires to specify an array of regularization marices
specified at any point of time from timeVec;

\item {}
-\emph{ltGoodDirOrigMat} field stores the matrix of the original good
direction vectors at any point of time from timeVec;
+\emph{fromQMScaledArrays} method acts the same way as \emph{fromQMArrays}
method, except for this one requires to also specify a vector of scale
factors specified for every created ellipsoid tube;

\item {}
-\emph{lsGoodDirOrigVec} field stores the original good direction vector at
sTime point of time;
+\emph{fromEllArray} method creates ellipsoid tube object using an array of
ellipsoids;

\item {}
-\emph{ltGoodDirNormOrigProjVec} field stores the norm of the projection of
the original good direction curve;
-
-\item {}
-\emph{ltGoodDirOrigProjMat} field stores the projectition of the original
good direction curve.
+\emph{fromEllMArray} method creates ellipsoid tube object using an array
of ellipsoids and an array of regularisation matrices.

\end{itemize}

-
-\section{Ellipsoidal tubes}
-\label{chap_ellTube:ellipsoidal-tubes}
-Other basic insrument in the \emph{Ellipsoidal Toolbox} are classes, which
allow to work with ellipsoidal tubes. In \emph{Ellipsoidal Toolbox} there
are four classes (\emph{EllTubeBasic}, \emph{EllTube},
\emph{EllTubeProjBasic} and \emph{EllTubeProj}) which give us the needed
functionality to work with ellipsoid tube objects.
-
-
-\subsection{\emph{EllTubeBasic} class}
-\label{chap_ellTube:elltubebasic-class}
-This class inherits its fields from \emph{EllTubeTouchCurveBasic} class
and adds some new fields which are:
-\begin{itemize}
-\item {}
-\emph{QArray} field which stores an array of nTimePoints ellipsoid
matrices. Each element from this
-array specifies an ellipsoid matrix at nTimePoint point of time. Here
nTimePoints is number of elements in \emph{timeVec} (It is one of the
fields inherited from \emph{EllTubeTouchCurveBasic} class.);
-
-\item {}
-\emph{aMat} field which stores an array of nTimePoints ellipsoid centers.
Each center is specified for nTimePoint point of time;
-
-\item {}
-scaleFactor field which stores the scale for the created ellipsoid tube;
-
-\item {}
-MArray field which stores an array of nTimePoints regularization matrices.
Each element from this array specifies a regularization matrix at
nTimePoint point of time.
-
-\end{itemize}
-
-This class gives us some methods which can be used to work with
ellipsoidal tubes. For example, if we have already created ellipsoid tube
object using one timeVec vector of time, then we can interpolate this tube,
using new time vector. Take notice that we have to make sure that the first
and the last elements in old and new vectors of time are the same.
+Basically we can divide these methods into two groups, based od what
objects they are using to create ellipsoid tube: an array of ellipsoid
matrices with an array of ellipsoid centers (by using these methods we can
create an ellipsoid tube object containing several ellipsoid tubes) or an
array of ellipsoids (by using these methods we can create an ellipsoid tube
object containing one ellipsoid tube). To illustrate the usage of these
methods we have to describe several functions, that will be used in the
process. Below are their descriptions.


\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
-\PYG{c}{\PYGZpc{} An example of usage of INTERP function from EllTubeBasic
class. In this}
-\PYG{c}{\PYGZpc{} example an ellipsoid tube object is created, using
oldTimeVec time}
-\PYG{c}{\PYGZpc{} vector. Then it is interpolated on newTimeVec time
vector.}
-\PYG{n}{nPoints}\PYG{p}{=}\PYG{l+m+mi}{10}\PYG{p}{;}
-\PYG{n}{absTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
-\PYG{n}{relTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
-\PYG{n}{approxSchemaDescr}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
-\PYG{n}{approxSchemaName}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
-\PYG{n}{nDims}\PYG{p}{=}\PYG{l+m+mi}{3}\PYG{p}{;}
-\PYG{n}{nTubes}\PYG{p}{=}\PYG{l+m+mi}{1}\PYG{p}{;}
-\PYG{n}{lsGoodDirVec}\PYG{p}{=}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{;}\PYG{l+m+mi}{0}\PYG{p}{;}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{;}
-\PYG{n}{aMat}\PYG{p}{=}\PYG{n+nb}{zeros}\PYG{p}{(}\PYG{n}{nDims}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{timeVec}\PYG{p}{=}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{l+m+mi}{1}\PYG{p}{;}
-\PYG{n}{sTime}\PYG{p}{=}\PYG{n}{timeVec}\PYG{p}{(}\PYG{n}{randi}\PYG{p}{(}\PYG{n}{nPoints}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{approxType}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EApproxType}\PYG{p}{.}\PYG{n}{Internal}\PYG{p}{;}
-\PYG{n}{qArrayList}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{p}{\PYGZob{}}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n+nb}{diag}\PYG{p}{(}\PYG{p}{[}\PYG{l+m+mi}{1}
\PYG{l+m+mi}{2}
\PYG{l+m+mi}{3}\PYG{p}{]}\PYG{p}{)}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{\PYGZcb{}}\PYG{p}{,}\PYG{c}{...}
- \PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{ltGoodDirArray}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n}{lsGoodDirVec}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{fromMatEllTube}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{rels}\PYG{p}{.}\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{fromQArrays}\PYG{p}{(}\PYG{c}{...}
- \PYG{n}{qArrayList}\PYG{p}{,} \PYG{n}{aMat}\PYG{p}{,}
\PYG{n}{timeVec}\PYG{p}{,}\PYG{c}{...}
- \PYG{n}{ltGoodDirArray}\PYG{p}{,} \PYG{n}{sTime}\PYG{p}{,}
\PYG{n}{approxType}\PYG{p}{,}
\PYG{n}{approxSchemaName}\PYG{p}{,}\PYG{c}{...}
- \PYG{n}{approxSchemaDescr}\PYG{p}{,} \PYG{n}{absTol}\PYG{p}{,}
\PYG{n}{relTol}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{newnPoints}\PYG{p}{=}\PYG{l+m+mi}{100}\PYG{p}{;}
-\PYG{n}{newTimeVec} \PYG{p}{=}
\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{newnPoints}\PYG{p}{)}\PYG{p}{:}\PYG{l+m+mi}{1}\PYG{p}{;}
-\PYG{n}{interpEllTube} \PYG{p}{=}
\PYG{n}{fromMatEllTube}\PYG{p}{.}\PYG{n}{interp}\PYG{p}{(}\PYG{n}{newTimeVec}\PYG{p}{)}\PYG{p}{;}
+\PYGZpc{} This function returns the values of arguments, that are the same
for
+\PYGZpc{} FROMQARRAYS, FROMQMARRAYS and FROMQMSCALEDARRAYS methods of
creating an
+\PYGZpc{} ellipsoid tube object. Basically, this function creates a set of
+\PYGZpc{} arguments nessesary for creating an ellipsoid tube object
containing
+\PYGZpc{} nTubes ellipsoid tubes. Here nTubes is a random natural number
in the
+\PYGZpc{} range from one to ten.
+\PYGZpc{}
+function [nTubes, nPoints, nDims, absTol, relTol, timeVec,...
+ sTime, lsGoodDirVec, ltGoodDirArray, aMat, qArrayList] = getData()
+nTubes=randi(10,1);
+nPoints=20;
+nDims=3;
+absTol=0.001;
+relTol=0.001;
+timeVec=(1/nPoints):(1/nPoints):1;
+sTime=timeVec(randi(nPoints,1));
+lsGoodDirVec=[1;0;0];
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+aMat=zeros(nDims,nPoints);
+qArrayList=repmat(\PYGZob{}repmat(diag([0.1 0.2
0.3]),[1,1,nPoints])\PYGZcb{},1,nTubes);
+end
\end{Verbatim}
-
-Other method that we can use is \emph{THINOUTTUPLES} method. It allows us
to thin out the already created ellipsoid tube, by saving only the
ellipsoids at specified points of time.


\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
-\PYG{c}{\PYGZpc{} An example of usage of THINOUTTUPLES function from
EllTubeBasic class. In}
-\PYG{c}{\PYGZpc{} this example an ellipsoid tube object is created, using
TimeVec time}
-\PYG{c}{\PYGZpc{} vector. Then it is thinned out using indVec vector of
indices of elements}
-\PYG{c}{\PYGZpc{} from timeVec.}
-\PYG{n}{nPoints}\PYG{p}{=}\PYG{l+m+mi}{10}\PYG{p}{;}
-\PYG{n}{absTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
-\PYG{n}{relTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
-\PYG{n}{approxSchemaDescr}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
-\PYG{n}{approxSchemaName}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
-\PYG{n}{nDims}\PYG{p}{=}\PYG{l+m+mi}{3}\PYG{p}{;}
-\PYG{n}{nTubes}\PYG{p}{=}\PYG{l+m+mi}{1}\PYG{p}{;}
-\PYG{n}{lsGoodDirVec}\PYG{p}{=}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{;}\PYG{l+m+mi}{0}\PYG{p}{;}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{;}
-\PYG{n}{aMat}\PYG{p}{=}\PYG{n+nb}{zeros}\PYG{p}{(}\PYG{n}{nDims}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{timeVec}\PYG{p}{=}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{l+m+mi}{1}\PYG{p}{;}
-\PYG{n}{sTime}\PYG{p}{=}\PYG{n}{timeVec}\PYG{p}{(}\PYG{n}{randi}\PYG{p}{(}\PYG{n}{nPoints}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{approxType}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EApproxType}\PYG{p}{.}\PYG{n}{Internal}\PYG{p}{;}
-\PYG{n}{qArrayList}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{p}{\PYGZob{}}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n+nb}{diag}\PYG{p}{(}\PYG{p}{[}\PYG{l+m+mi}{1}
\PYG{l+m+mi}{2}
\PYG{l+m+mi}{3}\PYG{p}{]}\PYG{p}{)}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{\PYGZcb{}}\PYG{p}{,}\PYG{c}{...}
- \PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{ltGoodDirArray}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n}{lsGoodDirVec}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{fromMatEllTube}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{rels}\PYG{p}{.}\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{fromQArrays}\PYG{p}{(}\PYG{c}{...}
- \PYG{n}{qArrayList}\PYG{p}{,} \PYG{n}{aMat}\PYG{p}{,}
\PYG{n}{timeVec}\PYG{p}{,}\PYG{c}{...}
- \PYG{n}{ltGoodDirArray}\PYG{p}{,} \PYG{n}{sTime}\PYG{p}{,}
\PYG{n}{approxType}\PYG{p}{,}
\PYG{n}{approxSchemaName}\PYG{p}{,}\PYG{c}{...}
- \PYG{n}{approxSchemaDescr}\PYG{p}{,} \PYG{n}{absTol}\PYG{p}{,}
\PYG{n}{relTol}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{indVec} \PYG{p}{=}
\PYG{n}{randi}\PYG{p}{(}\PYG{n}{nPoints}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{5}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{thinOutEllTube} \PYG{p}{=}
\PYG{n}{fromMatEllTube}\PYG{p}{.}\PYG{n}{thinOutTuples}\PYG{p}{(}\PYG{n}{indVec}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{} This function returns the values of arguments, that
specify the type of}
+\PYG{c}{\PYGZpc{} approximation that will be used to create an ellipsoid
tube object. It}
+\PYG{c}{\PYGZpc{} will be a random type of approximation (Internal or
External). These}
+\PYG{c}{\PYGZpc{} arguments can be used while creating an ellipsoid tube
object containing}
+\PYG{c}{\PYGZpc{} one ellipsoid tube or several ellipsoid tubes with the
same type of}
+\PYG{c}{\PYGZpc{} approximation.}
+\PYG{c}{\PYGZpc{}}
+\PYG{k}{function}\PYG{+w}{ }[approxSchemaDescr, approxSchemaName,
approxType] \PYG{p}{=}\PYG{+w}{
}\PYG{n+nf}{getSameApprox}\PYG{p}{(}\PYG{p}{)}
+\PYG{+w}{ }\PYG{n}{type} \PYG{p}{=}
\PYG{n}{randi}\PYG{p}{(}\PYG{l+m+mi}{2}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{;}
+ \PYG{k}{if} \PYG{n}{type} \PYG{o}{==} \PYG{l+m+mi}{1}
+
\PYG{n}{approxSchemaDescr}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
+
\PYG{n}{approxSchemaName}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
+
\PYG{n}{approxType}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EApproxType}\PYG{p}{.}\PYG{n}{Internal}\PYG{p}{;}
+ \PYG{k}{else}
+
\PYG{n}{approxSchemaDescr}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{External\PYGZsq{}}\PYG{p}{;}
+
\PYG{n}{approxSchemaName}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{External\PYGZsq{}}\PYG{p}{;}
+
\PYG{n}{approxType}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EApproxType}\PYG{p}{.}\PYG{n}{External}\PYG{p}{;}
+ \PYG{k}{end}
+\PYG{k}{end}
\end{Verbatim}

-Then we can also cut the created ellipsoid tube, leaving only part of it
at specified vector of time or point of time. Below are the exmples:
+Using the three above mentioned functions we can describe an examples of
\emph{fromQArrays}, \emph{fromQMArrays} and \emph{fromQMScaledArrays}
methods' usage.


\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
-\PYG{c}{\PYGZpc{} An example of usage of CUT function from EllTubeBasic
class. In}
-\PYG{c}{\PYGZpc{} this example an ellipsoid tube object is created, using
TimeVec time}
-\PYG{c}{\PYGZpc{} vector. Then it is cut using cutTimeVec time vector.}
-\PYG{n}{nPoints}\PYG{p}{=}\PYG{l+m+mi}{10}\PYG{p}{;}
-\PYG{n}{absTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
-\PYG{n}{relTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
-\PYG{n}{approxSchemaDescr}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
-\PYG{n}{approxSchemaName}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
-\PYG{n}{nDims}\PYG{p}{=}\PYG{l+m+mi}{3}\PYG{p}{;}
-\PYG{n}{nTubes}\PYG{p}{=}\PYG{l+m+mi}{1}\PYG{p}{;}
-\PYG{n}{lsGoodDirVec}\PYG{p}{=}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{;}\PYG{l+m+mi}{0}\PYG{p}{;}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{;}
-\PYG{n}{aMat}\PYG{p}{=}\PYG{n+nb}{zeros}\PYG{p}{(}\PYG{n}{nDims}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{timeVec}\PYG{p}{=}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{l+m+mi}{1}\PYG{p}{;}
-\PYG{n}{sTime}\PYG{p}{=}\PYG{n}{timeVec}\PYG{p}{(}\PYG{n}{randi}\PYG{p}{(}\PYG{n}{nPoints}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{approxType}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EApproxType}\PYG{p}{.}\PYG{n}{Internal}\PYG{p}{;}
-\PYG{n}{qArrayList}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{p}{\PYGZob{}}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n+nb}{diag}\PYG{p}{(}\PYG{p}{[}\PYG{l+m+mi}{1}
\PYG{l+m+mi}{2}
\PYG{l+m+mi}{3}\PYG{p}{]}\PYG{p}{)}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{\PYGZcb{}}\PYG{p}{,}\PYG{c}{...}
- \PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{ltGoodDirArray}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n}{lsGoodDirVec}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{} An example of creating nTubes ellipsoid tube objects
using fromQArrays}
+\PYG{c}{\PYGZpc{} function with the same type of approximation.}
+\PYG{p}{[}\PYG{n}{nTubes}\PYG{p}{,} \PYG{n}{nPoints}\PYG{p}{,}
\PYG{n}{nDims}\PYG{p}{,} \PYG{n}{absTol}\PYG{p}{,}
\PYG{n}{relTol}\PYG{p}{,} \PYG{n}{timeVec}\PYG{p}{,}\PYG{c}{...}
+ \PYG{n}{sTime}\PYG{p}{,} \PYG{n}{lsGoodDirVec}\PYG{p}{,}
\PYG{n}{ltGoodDirArray}\PYG{p}{,} \PYG{n}{aMat}\PYG{p}{,}
\PYG{n}{qArrayList}\PYG{p}{]} \PYG{p}{=} \PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getData}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{p}{[}\PYG{n}{approxSchemaDescr}\PYG{p}{,}
\PYG{n}{approxSchemaName}\PYG{p}{,} \PYG{n}{approxType}\PYG{p}{]}
\PYG{p}{=} \PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getSameApprox}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}

\PYG{n}{fromMatEllTube}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{rels}\PYG{p}{.}\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{fromQArrays}\PYG{p}{(}\PYG{c}{...}
\PYG{n}{qArrayList}\PYG{p}{,} \PYG{n}{aMat}\PYG{p}{,}
\PYG{n}{timeVec}\PYG{p}{,}\PYG{c}{...}
\PYG{n}{ltGoodDirArray}\PYG{p}{,} \PYG{n}{sTime}\PYG{p}{,}
\PYG{n}{approxType}\PYG{p}{,}
\PYG{n}{approxSchemaName}\PYG{p}{,}\PYG{c}{...}
\PYG{n}{approxSchemaDescr}\PYG{p}{,} \PYG{n}{absTol}\PYG{p}{,}
\PYG{n}{relTol}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{cutTimeVec} \PYG{p}{=}
\PYG{p}{[}\PYG{n}{timeVec}\PYG{p}{(}\PYG{l+m+mi}{2}\PYG{p}{)}
\PYG{n}{timeVec}\PYG{p}{(}\PYG{l+m+mi}{7}\PYG{p}{)}\PYG{p}{]}\PYG{p}{;}
-\PYG{n}{cutVecEllTube} \PYG{p}{=}
\PYG{n}{fromMatEllTube}\PYG{p}{.}\PYG{n}{cut}\PYG{p}{(}\PYG{n}{cutTimeVec}\PYG{p}{)}\PYG{p}{;}
\end{Verbatim}


\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
-\PYG{c}{\PYGZpc{} An example of usage of CUT function from EllTubeBasic
class. In}
-\PYG{c}{\PYGZpc{} this example an ellipsoid tube object is created, using
TimeVec time}
-\PYG{c}{\PYGZpc{} vector. Then it is cut using cutTimePoint point}
-\PYG{c}{\PYGZpc{} of time.}
+\PYG{c}{\PYGZpc{} An example of creating nTubes ellipsoid tube objects
using fromQArrays}
+\PYG{c}{\PYGZpc{} function with different types of approximation.}
\PYG{n}{nPoints}\PYG{p}{=}\PYG{l+m+mi}{10}\PYG{p}{;}
\PYG{n}{absTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
\PYG{n}{relTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
-\PYG{n}{approxSchemaDescr}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
-\PYG{n}{approxSchemaName}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
+\PYG{n}{approxSchemaDescr}\PYG{p}{=}\PYG{p}{\PYGZob{}}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{External\PYGZsq{}}\PYG{p}{;}
\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{External\PYGZsq{}}\PYG{p}{\PYGZcb{}}\PYG{p}{;}
+\PYG{n}{approxSchemaName}\PYG{p}{=}\PYG{p}{\PYGZob{}}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{External\PYGZsq{}}\PYG{p}{;}
\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{External\PYGZsq{}}\PYG{p}{\PYGZcb{}}\PYG{p}{;}
\PYG{n}{nDims}\PYG{p}{=}\PYG{l+m+mi}{3}\PYG{p}{;}
-\PYG{n}{nTubes}\PYG{p}{=}\PYG{l+m+mi}{1}\PYG{p}{;}
+\PYG{n}{nTubes}\PYG{p}{=}\PYG{l+m+mi}{3}\PYG{p}{;}

\PYG{n}{lsGoodDirVec}\PYG{p}{=}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{;}\PYG{l+m+mi}{0}\PYG{p}{;}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{;}

\PYG{n}{aMat}\PYG{p}{=}\PYG{n+nb}{zeros}\PYG{p}{(}\PYG{n}{nDims}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}

\PYG{n}{timeVec}\PYG{p}{=}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{l+m+mi}{1}\PYG{p}{;}

\PYG{n}{sTime}\PYG{p}{=}\PYG{n}{timeVec}\PYG{p}{(}\PYG{n}{randi}\PYG{p}{(}\PYG{n}{nPoints}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{approxType}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EApproxType}\PYG{p}{.}\PYG{n}{Internal}\PYG{p}{;}
+\PYG{n}{approxType}\PYG{p}{=}\PYG{p}{[}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EApproxType}\PYG{p}{.}\PYG{n}{Internal}\PYG{p}{,}\PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EApproxType}\PYG{p}{.}\PYG{n}{External}\PYG{p}{,}\PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EApproxType}\PYG{p}{.}\PYG{n}{External}\PYG{p}{]}\PYG{o}{\PYGZsq{}}\PYG{p}{;}

\PYG{n}{qArrayList}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{p}{\PYGZob{}}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n+nb}{diag}\PYG{p}{(}\PYG{p}{[}\PYG{l+m+mi}{1}
\PYG{l+m+mi}{2}
\PYG{l+m+mi}{3}\PYG{p}{]}\PYG{p}{)}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{\PYGZcb{}}\PYG{p}{,}\PYG{c}{...}
\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{)}\PYG{p}{;}

\PYG{n}{ltGoodDirArray}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n}{lsGoodDirVec}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{;}
@@ -5593,60 +5463,26 @@
\PYG{n}{qArrayList}\PYG{p}{,} \PYG{n}{aMat}\PYG{p}{,}
\PYG{n}{timeVec}\PYG{p}{,}\PYG{c}{...}
\PYG{n}{ltGoodDirArray}\PYG{p}{,} \PYG{n}{sTime}\PYG{p}{,}
\PYG{n}{approxType}\PYG{p}{,}
\PYG{n}{approxSchemaName}\PYG{p}{,}\PYG{c}{...}
\PYG{n}{approxSchemaDescr}\PYG{p}{,} \PYG{n}{absTol}\PYG{p}{,}
\PYG{n}{relTol}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{cutTimePoint} \PYG{p}{=}
\PYG{n}{timeVec}\PYG{p}{(}\PYG{n}{randi}\PYG{p}{(}\PYG{n}{nPoints}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{cutPointEllTube} \PYG{p}{=}
\PYG{n}{fromMatEllTube}\PYG{p}{.}\PYG{n}{cut}\PYG{p}{(}\PYG{n}{cutTimePoint}\PYG{p}{)}\PYG{p}{;}
\end{Verbatim}
-
-
-\subsection{\emph{EllTube} class}
-\label{chap_ellTube:elltube-class}
-This class inherits its fields from \emph{EllTubeBasic} class. It does not
have any new fields, but adds some functionality. First of all it gives us
the instruments to create ellipsoid tube objects. Here are these methods:
-\begin{itemize}
-\item {}
-\emph{fromQArrays} - creates nEllTubes ellipsoid tube objects using an
array of ellipsoid matrices and an array of ellipsoid centers specified
at any point of time from timeVec;
-
-\item {}
-\emph{fromQMArrays} - acts the same way as \emph{fromQArrays} method,
except for this one requires to specify an array of regularization
marices specified at any point of time from timeVec;
-
-\item {}
-\emph{fromQMScaledArrays} - acts the same way as \emph{fromQMArrays}
method, except for this one requires to also specify a vector of
scale factors specified for every created ellipsoid tube;
-
-\item {}
-\emph{fromEllArray} - creates ellipsoid tube object using an array of
ellipsoids;
-
-\item {}
-\emph{fromEllMArray} - creates ellipsoid tube object using an array of
ellipsoids and an array of regularisation matrices.
-
-\end{itemize}
-
-Basically we can divide these methods into two groups, based od what
objects they are using to create ellipsoid tube: an array of ellipsoid
matrices and an array of ellipsoid centers or an array of ellipsoids. Below
are some examples of the usage of these functions.


\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
-\PYG{c}{\PYGZpc{} An example of creating nTubes ellipsoid tube objects
using fromQArrays}
+\PYG{c}{\PYGZpc{} An example of creating nTubes ellipsoid tube objects
using fromQMArrays}
\PYG{c}{\PYGZpc{} function with the same type of approximation.}
-\PYG{n}{nPoints}\PYG{p}{=}\PYG{l+m+mi}{10}\PYG{p}{;}
-\PYG{n}{absTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
-\PYG{n}{relTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
-\PYG{n}{approxSchemaDescr}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
-\PYG{n}{approxSchemaName}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
-\PYG{n}{nDims}\PYG{p}{=}\PYG{l+m+mi}{3}\PYG{p}{;}
-\PYG{n}{nTubes}\PYG{p}{=}\PYG{l+m+mi}{3}\PYG{p}{;}
-\PYG{n}{lsGoodDirVec}\PYG{p}{=}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{;}\PYG{l+m+mi}{0}\PYG{p}{;}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{;}
-\PYG{n}{aMat}\PYG{p}{=}\PYG{n+nb}{zeros}\PYG{p}{(}\PYG{n}{nDims}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{timeVec}\PYG{p}{=}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{l+m+mi}{1}\PYG{p}{;}
-\PYG{n}{sTime}\PYG{p}{=}\PYG{n}{timeVec}\PYG{p}{(}\PYG{n}{randi}\PYG{p}{(}\PYG{n}{nPoints}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{approxType}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EApproxType}\PYG{p}{.}\PYG{n}{Internal}\PYG{p}{;}
-\PYG{n}{qArrayList}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{p}{\PYGZob{}}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n+nb}{diag}\PYG{p}{(}\PYG{p}{[}\PYG{l+m+mi}{1}
\PYG{l+m+mi}{2}
\PYG{l+m+mi}{3}\PYG{p}{]}\PYG{p}{)}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{\PYGZcb{}}\PYG{p}{,}\PYG{c}{...}
+\PYG{p}{[}\PYG{n}{nTubes}\PYG{p}{,} \PYG{n}{nPoints}\PYG{p}{,}
\PYG{n}{nDims}\PYG{p}{,} \PYG{n}{absTol}\PYG{p}{,}
\PYG{n}{relTol}\PYG{p}{,} \PYG{n}{timeVec}\PYG{p}{,}\PYG{c}{...}
+ \PYG{n}{sTime}\PYG{p}{,} \PYG{n}{lsGoodDirVec}\PYG{p}{,}
\PYG{n}{ltGoodDirArray}\PYG{p}{,} \PYG{n}{aMat}\PYG{p}{,}
\PYG{n}{qArrayList}\PYG{p}{]} \PYG{p}{=} \PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getData}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{p}{[}\PYG{n}{approxSchemaDescr}\PYG{p}{,}
\PYG{n}{approxSchemaName}\PYG{p}{,} \PYG{n}{approxType}\PYG{p}{]}
\PYG{p}{=} \PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getSameApprox}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{n}{mArrayList}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{p}{\PYGZob{}}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n+nb}{diag}\PYG{p}{(}\PYG{p}{[}\PYG{l+m+mf}{0.1}
\PYG{l+m+mf}{0.2}
\PYG{l+m+mf}{0.3}\PYG{p}{]}\PYG{p}{)}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{\PYGZcb{}}\PYG{p}{,}\PYG{c}{...}
\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{ltGoodDirArray}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n}{lsGoodDirVec}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{fromMatEllTube}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{rels}\PYG{p}{.}\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{fromQArrays}\PYG{p}{(}\PYG{c}{...}
- \PYG{n}{qArrayList}\PYG{p}{,} \PYG{n}{aMat}\PYG{p}{,}
\PYG{n}{timeVec}\PYG{p}{,}\PYG{c}{...}
+\PYG{n}{fromMatMEllTube}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{rels}\PYG{p}{.}\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{fromQMArrays}\PYG{p}{(}\PYG{c}{...}
+ \PYG{n}{qArrayList}\PYG{p}{,} \PYG{n}{aMat}\PYG{p}{,}
\PYG{n}{mArrayList}\PYG{p}{,} \PYG{n}{timeVec}\PYG{p}{,}\PYG{c}{...}
\PYG{n}{ltGoodDirArray}\PYG{p}{,} \PYG{n}{sTime}\PYG{p}{,}
\PYG{n}{approxType}\PYG{p}{,}
\PYG{n}{approxSchemaName}\PYG{p}{,}\PYG{c}{...}
\PYG{n}{approxSchemaDescr}\PYG{p}{,} \PYG{n}{absTol}\PYG{p}{,}
\PYG{n}{relTol}\PYG{p}{)}\PYG{p}{;}
\end{Verbatim}


\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
-\PYG{c}{\PYGZpc{} An example of creating nTubes ellipsoid tube objects
using fromQArrays}
+\PYG{c}{\PYGZpc{} An example of creating nTubes ellipsoid tube objects
using fromQMArrays}
\PYG{c}{\PYGZpc{} function with different types of approximation.}
\PYG{n}{nPoints}\PYG{p}{=}\PYG{l+m+mi}{10}\PYG{p}{;}
\PYG{n}{absTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
@@ -5662,30 +5498,6 @@

\PYG{n}{approxType}\PYG{p}{=}\PYG{p}{[}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EApproxType}\PYG{p}{.}\PYG{n}{Internal}\PYG{p}{,}\PYG{c}{...}

\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EApproxType}\PYG{p}{.}\PYG{n}{External}\PYG{p}{,}\PYG{c}{...}

\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EApproxType}\PYG{p}{.}\PYG{n}{External}\PYG{p}{]}\PYG{o}{\PYGZsq{}}\PYG{p}{;}
-\PYG{n}{qArrayList}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{p}{\PYGZob{}}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n+nb}{diag}\PYG{p}{(}\PYG{p}{[}\PYG{l+m+mi}{1}
\PYG{l+m+mi}{2}
\PYG{l+m+mi}{3}\PYG{p}{]}\PYG{p}{)}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{\PYGZcb{}}\PYG{p}{,}\PYG{c}{...}
- \PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{ltGoodDirArray}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n}{lsGoodDirVec}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{fromMatEllTube}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{rels}\PYG{p}{.}\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{fromQArrays}\PYG{p}{(}\PYG{c}{...}
- \PYG{n}{qArrayList}\PYG{p}{,} \PYG{n}{aMat}\PYG{p}{,}
\PYG{n}{timeVec}\PYG{p}{,}\PYG{c}{...}
- \PYG{n}{ltGoodDirArray}\PYG{p}{,} \PYG{n}{sTime}\PYG{p}{,}
\PYG{n}{approxType}\PYG{p}{,}
\PYG{n}{approxSchemaName}\PYG{p}{,}\PYG{c}{...}
- \PYG{n}{approxSchemaDescr}\PYG{p}{,} \PYG{n}{absTol}\PYG{p}{,}
\PYG{n}{relTol}\PYG{p}{)}\PYG{p}{;}
-\end{Verbatim}
-
-\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
-\PYG{c}{\PYGZpc{} An example of creating nTubes ellipsoid tube objects
using fromQMArrays}
-\PYG{c}{\PYGZpc{} function with the same type of approximation.}
-\PYG{n}{nPoints}\PYG{p}{=}\PYG{l+m+mi}{10}\PYG{p}{;}
-\PYG{n}{absTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
-\PYG{n}{relTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
-\PYG{n}{approxSchemaDescr}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{External\PYGZsq{}}\PYG{p}{;}
-\PYG{n}{approxSchemaName}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{External\PYGZsq{}}\PYG{p}{;}
-\PYG{n}{nDims}\PYG{p}{=}\PYG{l+m+mi}{3}\PYG{p}{;}
-\PYG{n}{nTubes}\PYG{p}{=}\PYG{l+m+mi}{3}\PYG{p}{;}
-\PYG{n}{lsGoodDirVec}\PYG{p}{=}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{;}\PYG{l+m+mi}{0}\PYG{p}{;}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{;}
-\PYG{n}{aMat}\PYG{p}{=}\PYG{n+nb}{zeros}\PYG{p}{(}\PYG{n}{nDims}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{timeVec}\PYG{p}{=}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{l+m+mi}{1}\PYG{p}{;}
-\PYG{n}{sTime}\PYG{p}{=}\PYG{n}{timeVec}\PYG{p}{(}\PYG{n}{randi}\PYG{p}{(}\PYG{n}{nPoints}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{approxType}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EApproxType}\PYG{p}{.}\PYG{n}{External}\PYG{p}{;}

\PYG{n}{mArrayList}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{p}{\PYGZob{}}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n+nb}{diag}\PYG{p}{(}\PYG{p}{[}\PYG{l+m+mf}{0.1}
\PYG{l+m+mf}{0.2}
\PYG{l+m+mf}{0.3}\PYG{p}{]}\PYG{p}{)}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{\PYGZcb{}}\PYG{p}{,}\PYG{c}{...}
\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{)}\PYG{p}{;}

\PYG{n}{qArrayList}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{p}{\PYGZob{}}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n+nb}{diag}\PYG{p}{(}\PYG{p}{[}\PYG{l+m+mi}{1}
\PYG{l+m+mi}{2}
\PYG{l+m+mi}{3}\PYG{p}{]}\PYG{p}{)}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{\PYGZcb{}}\PYG{p}{,}\PYG{c}{...}
@@ -5700,23 +5512,13 @@

\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
\PYG{c}{\PYGZpc{} An example of creating nTubes ellipsoid tube objects
using fromQMScaledArrays}
\PYG{c}{\PYGZpc{} function with the same type of approximation.}
-\PYG{n}{nPoints}\PYG{p}{=}\PYG{l+m+mi}{10}\PYG{p}{;}
-\PYG{n}{absTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
-\PYG{n}{relTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
-\PYG{n}{approxSchemaDescr}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
-\PYG{n}{approxSchemaName}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
-\PYG{n}{nDims}\PYG{p}{=}\PYG{l+m+mi}{3}\PYG{p}{;}
-\PYG{n}{nTubes}\PYG{p}{=}\PYG{l+m+mi}{5}\PYG{p}{;}
-\PYG{n}{lsGoodDirVec}\PYG{p}{=}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{;}\PYG{l+m+mi}{0}\PYG{p}{;}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{;}
-\PYG{n}{aMat}\PYG{p}{=}\PYG{n+nb}{zeros}\PYG{p}{(}\PYG{n}{nDims}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{timeVec}\PYG{p}{=}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{l+m+mi}{1}\PYG{p}{;}
-\PYG{n}{sTime}\PYG{p}{=}\PYG{n}{timeVec}\PYG{p}{(}\PYG{n}{randi}\PYG{p}{(}\PYG{n}{nPoints}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{approxType}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EApproxType}\PYG{p}{.}\PYG{n}{Internal}\PYG{p}{;}
-\PYG{n}{qArrayList}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{p}{\PYGZob{}}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n+nb}{diag}\PYG{p}{(}\PYG{p}{[}\PYG{l+m+mi}{1}
\PYG{l+m+mi}{2}
\PYG{l+m+mi}{3}\PYG{p}{]}\PYG{p}{)}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{\PYGZcb{}}\PYG{p}{,}\PYG{c}{...}
- \PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{)}\PYG{p}{;}
+\PYG{p}{[}\PYG{n}{nTubes}\PYG{p}{,} \PYG{n}{nPoints}\PYG{p}{,}
\PYG{n}{nDims}\PYG{p}{,} \PYG{n}{absTol}\PYG{p}{,}
\PYG{n}{relTol}\PYG{p}{,} \PYG{n}{timeVec}\PYG{p}{,}\PYG{c}{...}
+ \PYG{n}{sTime}\PYG{p}{,} \PYG{n}{lsGoodDirVec}\PYG{p}{,}
\PYG{n}{ltGoodDirArray}\PYG{p}{,} \PYG{n}{aMat}\PYG{p}{,}
\PYG{n}{qArrayList}\PYG{p}{]} \PYG{p}{=} \PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getData}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{p}{[}\PYG{n}{approxSchemaDescr}\PYG{p}{,}
\PYG{n}{approxSchemaName}\PYG{p}{,} \PYG{n}{approxType}\PYG{p}{]}
\PYG{p}{=} \PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getSameApprox}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}

\PYG{n}{mArrayList}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{p}{\PYGZob{}}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n+nb}{diag}\PYG{p}{(}\PYG{p}{[}\PYG{l+m+mf}{0.1}
\PYG{l+m+mf}{0.2}
\PYG{l+m+mf}{0.3}\PYG{p}{]}\PYG{p}{)}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{\PYGZcb{}}\PYG{p}{,}\PYG{c}{...}
\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{ltGoodDirArray}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n}{lsGoodDirVec}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{;}
\PYG{n}{scaleFactor} \PYG{p}{=}
\PYG{n+nb}{ones}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{)}\PYG{p}{;}
\PYG{n}{fromQMScaledArraysEllTube} \PYG{p}{=} \PYG{c}{...}

\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{rels}\PYG{p}{.}\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{fromQMScaledArrays}\PYG{p}{(}\PYG{c}{...}
@@ -5725,101 +5527,423 @@
\PYG{n}{approxSchemaDescr}\PYG{p}{,}\PYG{n}{absTol}\PYG{p}{,}
\PYG{n}{relTol}\PYG{p}{,}\PYG{c}{...}
\PYG{n}{scaleFactor}\PYG{p}{)}\PYG{p}{;}
\end{Verbatim}
+
+To use \emph{fromEllArray} and \emph{fromEllMArray} methods we nave to
describe one more auxiliary function (as these methods create an ellipsoid
tube object containing only one ellipsoid tube and we can not use
\emph{getData} function, because it returns data for crating random number
of ellipsoid tubes).
+
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
+\PYGZpc{} This function returns the values of arguments, that are needed
to use
+\PYGZpc{} FROMELLARRAY and FROMELLMARRAY methods of creating an ellipsoid
tube
+\PYGZpc{} object. Basically, this function creates a set of arguments
nessesary for
+\PYGZpc{} creating an ellipsoid tube object containing one ellipsoid tube.
+\PYGZpc{}
+function [nTubes, nPoints, nDims, absTol, relTol, timeVec,...
+ sTime, lsGoodDirVec, ltGoodDirArray, aMat, qArrayList] =
getDataForOneTube()
+nTubes=1;
+nPoints=20;
+nDims=3;
+absTol=0.001;
+relTol=0.001;
+timeVec=(1/nPoints):(1/nPoints):1;
+sTime=timeVec(randi(nPoints,1));
+lsGoodDirVec=[1;0;0];
+ltGoodDirArray=repmat(lsGoodDirVec,[1,nTubes,nPoints]);
+aMat=zeros(nDims,nPoints);
+qArrayList=repmat(\PYGZob{}repmat(diag([1 2
3]),[1,1,nPoints])\PYGZcb{},1,nTubes);
+end
+\end{Verbatim}
+
+Now we can write examples of these methods' usage.


\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
\PYG{c}{\PYGZpc{} An example of creating nTubes ellipsoid tube objects
using fromEllArray}
\PYG{c}{\PYGZpc{} function.}
-\PYG{n}{nPoints}\PYG{p}{=}\PYG{l+m+mi}{10}\PYG{p}{;}
-\PYG{n}{absTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
-\PYG{n}{relTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
-\PYG{n}{approxSchemaDescr}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
-\PYG{n}{approxSchemaName}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
-\PYG{n}{nDims}\PYG{p}{=}\PYG{l+m+mi}{3}\PYG{p}{;}
-\PYG{n}{nTubes}\PYG{p}{=}\PYG{l+m+mi}{1}\PYG{p}{;}
-\PYG{n}{lsGoodDirVec}\PYG{p}{=}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{;}\PYG{l+m+mi}{0}\PYG{p}{;}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{;}
-\PYG{n}{timeVec}\PYG{p}{=}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{l+m+mi}{1}\PYG{p}{;}
-\PYG{n}{sTime}\PYG{p}{=}\PYG{n}{timeVec}\PYG{p}{(}\PYG{n}{randi}\PYG{p}{(}\PYG{n}{nPoints}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{approxType}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EApproxType}\PYG{p}{.}\PYG{n}{Internal}\PYG{p}{;}
+\PYG{p}{[}\PYG{n}{nTubes}\PYG{p}{,} \PYG{n}{nPoints}\PYG{p}{,}
\PYG{n}{nDims}\PYG{p}{,} \PYG{n}{absTol}\PYG{p}{,}
\PYG{n}{relTol}\PYG{p}{,} \PYG{n}{timeVec}\PYG{p}{,}\PYG{c}{...}
+ \PYG{n}{sTime}\PYG{p}{,} \PYG{n}{lsGoodDirVec}\PYG{p}{,}
\PYG{n}{ltGoodDirArray}\PYG{p}{,} \PYG{n}{aMat}\PYG{p}{,}
\PYG{n}{qArrayList}\PYG{p}{]} \PYG{p}{=} \PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getDataForOneTube}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{p}{[}\PYG{n}{approxSchemaDescr}\PYG{p}{,}
\PYG{n}{approxSchemaName}\PYG{p}{,} \PYG{n}{approxType}\PYG{p}{]}
\PYG{p}{=} \PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getSameApprox}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
\PYG{n}{ellArray}\PYG{p}{(}\PYG{n}{nPoints}\PYG{p}{)} \PYG{p}{=}
\PYG{n}{ellipsoid}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{aMat}\PYG{p}{=}\PYG{n+nb}{zeros}\PYG{p}{(}\PYG{n}{nDims}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{qArrayList}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{p}{\PYGZob{}}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n+nb}{diag}\PYG{p}{(}\PYG{p}{[}\PYG{l+m+mi}{1}
\PYG{l+m+mi}{2}
\PYG{l+m+mi}{3}\PYG{p}{]}\PYG{p}{)}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{\PYGZcb{}}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{;}
\PYG{k}{for} \PYG{n}{iElem} \PYG{p}{=}
\PYG{l+m+mi}{1}\PYG{p}{:}\PYG{n}{nPoints}
\PYG{n}{ellArray}\PYG{p}{(}\PYG{n}{iElem}\PYG{p}{)} \PYG{p}{=}
\PYG{n}{ellipsoid}\PYG{p}{(}\PYG{n}{aMat}\PYG{p}{(}\PYG{p}{:}\PYG{p}{,}\PYG{n}{iElem}\PYG{p}{)}\PYG{p}{,}
\PYG{n}{qArrayList}\PYG{p}{\PYGZob{}}\PYG{l+m+mi}{1}\PYG{p}{\PYGZcb{}}\PYG{p}{(}\PYG{p}{:}\PYG{p}{,}\PYG{p}{:}\PYG{p}{,}\PYG{n}{iElem}\PYG{p}{)}\PYG{p}{)}\PYG{p}{;}
\PYG{k}{end}\PYG{p}{;}
-\PYG{n}{ellnArray} \PYG{p}{=}
\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n}{ellArray}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{;}
\PYG{n}{fromEllArrayEllTube} \PYG{p}{=}
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{rels}\PYG{p}{.}\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{fromEllArray}\PYG{p}{(}\PYG{c}{...}
- \PYG{n}{ellnArray}\PYG{p}{,}\PYG{n}{timeVec}\PYG{p}{,}
\PYG{n}{ltGoodDirArray}\PYG{p}{,} \PYG{n}{sTime}\PYG{p}{,}
\PYG{n}{approxType}\PYG{p}{,}\PYG{c}{...}
+ \PYG{n}{ellArray}\PYG{p}{,}\PYG{n}{timeVec}\PYG{p}{,}
\PYG{n}{ltGoodDirArray}\PYG{p}{,} \PYG{n}{sTime}\PYG{p}{,}
\PYG{n}{approxType}\PYG{p}{,}\PYG{c}{...}

\PYG{n}{approxSchemaName}\PYG{p}{,}\PYG{n}{approxSchemaDescr}\PYG{p}{,}
\PYG{n}{absTol}\PYG{p}{,} \PYG{n}{relTol}\PYG{p}{)}\PYG{p}{;}
\end{Verbatim}


\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
\PYG{c}{\PYGZpc{} An example of creating nTubes ellipsoid tube objects
using fromEllMArray}
\PYG{c}{\PYGZpc{} function.}
-\PYG{n}{nPoints}\PYG{p}{=}\PYG{l+m+mi}{10}\PYG{p}{;}
-\PYG{n}{absTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
-\PYG{n}{relTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
-\PYG{n}{approxSchemaDescr}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
-\PYG{n}{approxSchemaName}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
-\PYG{n}{nDims}\PYG{p}{=}\PYG{l+m+mi}{3}\PYG{p}{;}
-\PYG{n}{nTubes}\PYG{p}{=}\PYG{l+m+mi}{1}\PYG{p}{;}
-\PYG{n}{lsGoodDirVec}\PYG{p}{=}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{;}\PYG{l+m+mi}{0}\PYG{p}{;}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{;}
-\PYG{n}{timeVec}\PYG{p}{=}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{l+m+mi}{1}\PYG{p}{;}
-\PYG{n}{sTime}\PYG{p}{=}\PYG{n}{timeVec}\PYG{p}{(}\PYG{n}{randi}\PYG{p}{(}\PYG{n}{nPoints}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{approxType}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EApproxType}\PYG{p}{.}\PYG{n}{Internal}\PYG{p}{;}
+\PYG{p}{[}\PYG{n}{nTubes}\PYG{p}{,} \PYG{n}{nPoints}\PYG{p}{,}
\PYG{n}{nDims}\PYG{p}{,} \PYG{n}{absTol}\PYG{p}{,}
\PYG{n}{relTol}\PYG{p}{,} \PYG{n}{timeVec}\PYG{p}{,}\PYG{c}{...}
+ \PYG{n}{sTime}\PYG{p}{,} \PYG{n}{lsGoodDirVec}\PYG{p}{,}
\PYG{n}{ltGoodDirArray}\PYG{p}{,} \PYG{n}{aMat}\PYG{p}{,}
\PYG{n}{qArrayList}\PYG{p}{]} \PYG{p}{=} \PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getDataForOneTube}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{p}{[}\PYG{n}{approxSchemaDescr}\PYG{p}{,}
\PYG{n}{approxSchemaName}\PYG{p}{,} \PYG{n}{approxType}\PYG{p}{]}
\PYG{p}{=} \PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getSameApprox}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
\PYG{n}{ellArray}\PYG{p}{(}\PYG{n}{nPoints}\PYG{p}{)} \PYG{p}{=}
\PYG{n}{ellipsoid}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{aMat}\PYG{p}{=}\PYG{n+nb}{zeros}\PYG{p}{(}\PYG{n}{nDims}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{qArrayList}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{p}{\PYGZob{}}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n+nb}{diag}\PYG{p}{(}\PYG{p}{[}\PYG{l+m+mi}{1}
\PYG{l+m+mi}{2}
\PYG{l+m+mi}{3}\PYG{p}{]}\PYG{p}{)}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{\PYGZcb{}}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{;}
\PYG{k}{for} \PYG{n}{iElem} \PYG{p}{=}
\PYG{l+m+mi}{1}\PYG{p}{:}\PYG{n}{nPoints}
\PYG{n}{ellArray}\PYG{p}{(}\PYG{n}{iElem}\PYG{p}{)} \PYG{p}{=}
\PYG{n}{ellipsoid}\PYG{p}{(}\PYG{n}{aMat}\PYG{p}{(}\PYG{p}{:}\PYG{p}{,}\PYG{n}{iElem}\PYG{p}{)}\PYG{p}{,}
\PYG{n}{qArrayList}\PYG{p}{\PYGZob{}}\PYG{l+m+mi}{1}\PYG{p}{\PYGZcb{}}\PYG{p}{(}\PYG{p}{:}\PYG{p}{,}\PYG{p}{:}\PYG{p}{,}\PYG{n}{iElem}\PYG{p}{)}\PYG{p}{)}\PYG{p}{;}
\PYG{k}{end}\PYG{p}{;}
-\PYG{n}{ellnArray} \PYG{p}{=}
\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n}{ellArray}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{;}

\PYG{n}{mArrayList}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{p}{\PYGZob{}}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n+nb}{diag}\PYG{p}{(}\PYG{p}{[}\PYG{l+m+mf}{0.1}
\PYG{l+m+mf}{0.2}
\PYG{l+m+mf}{0.3}\PYG{p}{]}\PYG{p}{)}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{\PYGZcb{}}\PYG{p}{,}\PYG{c}{...}
\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{fromEllMArrayEllTube}\PYG{p}{=}\PYG{c}{...}
-
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{rels}\PYG{p}{.}\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{fromEllMArray}\PYG{p}{(}\PYG{c}{...}
- \PYG{n}{ellArray}\PYG{p}{,}
\PYG{n}{mArrayList}\PYG{p}{\PYGZob{}}\PYG{l+m+mi}{1}\PYG{p}{\PYGZcb{}}\PYG{p}{,}
\PYG{n}{timeVec}\PYG{p}{,}\PYG{c}{...}
- \PYG{n}{ltGoodDirArray}\PYG{p}{,} \PYG{n}{sTime}\PYG{p}{,}
\PYG{n}{approxType}\PYG{p}{,}
\PYG{n}{approxSchemaName}\PYG{p}{,}\PYG{c}{...}
- \PYG{n}{approxSchemaDescr}\PYG{p}{,} \PYG{n}{absTol}\PYG{p}{,}
\PYG{n}{relTol}\PYG{p}{)}\PYG{p}{;}
+\PYG{n}{fromEllArrayEllTube} \PYG{p}{=}
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{rels}\PYG{p}{.}\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{fromEllArray}\PYG{p}{(}\PYG{c}{...}
+ \PYG{n}{ellArray}\PYG{p}{,}\PYG{n}{timeVec}\PYG{p}{,}
\PYG{n}{ltGoodDirArray}\PYG{p}{,} \PYG{n}{sTime}\PYG{p}{,}
\PYG{n}{approxType}\PYG{p}{,}\PYG{c}{...}
+
\PYG{n}{approxSchemaName}\PYG{p}{,}\PYG{n}{approxSchemaDescr}\PYG{p}{,}
\PYG{n}{absTol}\PYG{p}{,} \PYG{n}{relTol}\PYG{p}{)}\PYG{p}{;}
\end{Verbatim}

-As we can see in these examples, we can specify how many ellipsoid tubes
we want to create, which type of arrpoximation to use. also we can create
ellipsoid tube objects, which will contain several ellipsoid tubes with
different types of approximation.
-We can also use \emph{project} and \emph{projectToOrths} methods to
project our ellipsoid tubes on the specified spaces. The first metod
projects the ellipsoid tube on specified space creating the specified type
of projection.
+As we can see in all these examples, we can specify how many ellipsoid
tubes we want to create, which type of arrpoximation to use. Also we can
create ellipsoid tube objects, which will contain several ellipsoid tubes
with different types of approximation.
+
+After creation of ellipsoid tube objects we can do several operations with
them. Below is the \emph{getEllTube} function that create an ellipsoid tube
object containing one or several ellipsoid tubes with specified type of
approximation, on specified time vector with specified time points. This
function will be used further down to illustrate other methods that we can
use while working with ellipsoid tube objects.


\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
-\PYG{c}{\PYGZpc{} An example of calculating ellipsoid tube object
projection using project}
-\PYG{c}{\PYGZpc{} function.}
-\PYG{n}{nPoints}\PYG{p}{=}\PYG{l+m+mi}{5}\PYG{p}{;}
-\PYG{n}{absTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
-\PYG{n}{relTol}\PYG{p}{=}\PYG{l+m+mf}{0.01}\PYG{p}{;}
-\PYG{n}{approxSchemaDescr}\PYG{p}{=}\PYG{n}{char}\PYG{p}{.}\PYG{n}{empty}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{0}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{approxSchemaName}\PYG{p}{=}\PYG{n}{char}\PYG{p}{.}\PYG{n}{empty}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{0}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{} An example of creating an ellipsoid tube object
containing nTubes}
+\PYG{c}{\PYGZpc{} ellipsoid tubes from timeBegin to timeEnd time with
specified type of}
+\PYG{c}{\PYGZpc{} approximation.}
+\PYG{c}{\PYGZpc{}}
+\PYG{k}{function}\PYG{+w}{ }ellTube \PYG{p}{=}\PYG{+w}{
}\PYG{n+nf}{getEllTube}\PYG{p}{(}nTubes,timeBeg,timeEnd,type,nPoints\PYG{p}{)}
\PYG{n}{nDims}\PYG{p}{=}\PYG{l+m+mi}{3}\PYG{p}{;}
-\PYG{n}{nTubes}\PYG{p}{=}\PYG{l+m+mi}{1}\PYG{p}{;}
-\PYG{n}{lsGoodDirVec}\PYG{p}{=}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{;}\PYG{l+m+mi}{0}\PYG{p}{;}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{;}
-\PYG{n}{aMat}\PYG{p}{=}\PYG{n+nb}{zeros}\PYG{p}{(}\PYG{n}{nDims}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{timeVec}\PYG{p}{=}\PYG{l+m+mi}{1}\PYG{p}{:}\PYG{n}{nPoints}\PYG{p}{;}
-\PYG{n}{sTime}\PYG{p}{=}\PYG{n}{nPoints}\PYG{p}{;}
-\PYG{n}{approxType}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EApproxType}\PYG{p}{.}\PYG{n}{Internal}\PYG{p}{;}
-\PYG{n}{qArrayList}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{p}{\PYGZob{}}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n+nb}{diag}\PYG{p}{(}\PYG{p}{[}\PYG{l+m+mi}{1}
\PYG{l+m+mi}{2}
\PYG{l+m+mi}{3}\PYG{p}{]}\PYG{p}{)}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{\PYGZcb{}}\PYG{p}{,}\PYG{c}{...}
- \PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{)}\PYG{p}{;}
+\PYG{n}{absTol}\PYG{p}{=}\PYG{l+m+mf}{0.001}\PYG{p}{;}
+\PYG{n}{relTol}\PYG{p}{=}\PYG{l+m+mf}{0.001}\PYG{p}{;}
+\PYG{n}{timeVec}\PYG{p}{=}\PYG{p}{(}\PYG{n}{timeBeg}\PYG{o}{+}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{n}{timeEnd}\PYG{p}{;}
+\PYG{n}{sTime}\PYG{p}{=}\PYG{n}{timeVec}\PYG{p}{(}\PYG{n}{randi}\PYG{p}{(}\PYG{n}{nPoints}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{)}\PYG{p}{;}
+\PYG{n}{lsGoodDirVec}\PYG{p}{=}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{;}\PYG{l+m+mi}{0}\PYG{p}{;}\PYG{l+m+mi}{0}\PYG{p}{]}\PYG{p}{;}

\PYG{n}{ltGoodDirArray}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n}{lsGoodDirVec}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{fromMatEllTube}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{rels}\PYG{p}{.}\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{fromQArrays}\PYG{p}{(}\PYG{c}{...}
+\PYG{n}{aMat}\PYG{p}{=}\PYG{n+nb}{zeros}\PYG{p}{(}\PYG{n}{nDims}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}
+\PYG{n}{qArrayList}\PYG{p}{=}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{p}{\PYGZob{}}\PYG{n+nb}{repmat}\PYG{p}{(}\PYG{n+nb}{diag}\PYG{p}{(}\PYG{p}{[}\PYG{l+m+mi}{1}
\PYG{l+m+mi}{2}
\PYG{l+m+mi}{3}\PYG{p}{]}\PYG{p}{)}\PYG{p}{,}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{]}\PYG{p}{)}\PYG{p}{\PYGZcb{}}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{n}{nTubes}\PYG{p}{)}\PYG{p}{;}
+\PYG{k}{if} \PYG{n}{type} \PYG{o}{==} \PYG{l+m+mi}{1}
+
\PYG{n}{approxSchemaDescr}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
+
\PYG{n}{approxSchemaName}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Internal\PYGZsq{}}\PYG{p}{;}
+
\PYG{n}{approxType}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EApproxType}\PYG{p}{.}\PYG{n}{Internal}\PYG{p}{;}
+\PYG{k}{else}
+
\PYG{n}{approxSchemaDescr}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{External\PYGZsq{}}\PYG{p}{;}
+
\PYG{n}{approxSchemaName}\PYG{p}{=}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{External\PYGZsq{}}\PYG{p}{;}
+
\PYG{n}{approxType}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EApproxType}\PYG{p}{.}\PYG{n}{External}\PYG{p}{;}
+\PYG{k}{end}
+\PYG{n}{ellTube}\PYG{p}{=}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{rels}\PYG{p}{.}\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{fromQArrays}\PYG{p}{(}\PYG{c}{...}
\PYG{n}{qArrayList}\PYG{p}{,} \PYG{n}{aMat}\PYG{p}{,}
\PYG{n}{timeVec}\PYG{p}{,}\PYG{c}{...}
\PYG{n}{ltGoodDirArray}\PYG{p}{,} \PYG{n}{sTime}\PYG{p}{,}
\PYG{n}{approxType}\PYG{p}{,}
\PYG{n}{approxSchemaName}\PYG{p}{,}\PYG{c}{...}
\PYG{n}{approxSchemaDescr}\PYG{p}{,} \PYG{n}{absTol}\PYG{p}{,}
\PYG{n}{relTol}\PYG{p}{)}\PYG{p}{;}
-\PYG{n}{projType} \PYG{p}{=}
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{enums}\PYG{p}{.}\PYG{n}{EProjType}\PYG{p}{.}\PYG{n}{Static}\PYG{p}{;}
-\PYG{n}{projMat} \PYG{p}{=} \PYG{p}{[}\PYG{l+m+mi}{1}
\PYG{l+m+mi}{0}\PYG{p}{;} \PYG{l+m+mi}{0} \PYG{l+m+mi}{1}\PYG{p}{;}
\PYG{l+m+mi}{0} \PYG{l+m+mi}{0}\PYG{p}{]}\PYG{o}{\PYGZsq{}}\PYG{p}{;}
-\PYG{n}{p} \PYG{p}{=}
\PYG{p}{@}\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{fGetProjMat}\PYG{p}{;}
-\PYG{p}{[}\PYG{n}{ellTubeProjRel}\PYG{p}{,}\PYG{n}{indProj2OrigVec}\PYG{p}{]}
\PYG{p}{=}
\PYG{n}{fromMatEllTube}\PYG{p}{.}\PYG{n}{project}\PYG{p}{(}\PYG{n}{projType}\PYG{p}{,}\PYG{c}{...}
-
\PYG{p}{\PYGZob{}}\PYG{n}{projMat}\PYG{p}{\PYGZcb{}}\PYG{p}{,}\PYG{n}{p}\PYG{p}{)}\PYG{p}{;}
+\PYG{k}{end}
\end{Verbatim}

-The second method projects the ellipsoid tube onto subspace defined by
vectors of standart basis with indices specified in indVec.
+As we have created an ellipsoid tube object, we can get all the types of
differet data about it. There is a set of methods that can give information
about the data stored in the object and give access to it.


\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
-\PYG{c}{\PYGZpc{} Examples of calculating ellipsoid tube object projection
to basic orths }
-\PYG{c}{\PYGZpc{} using PROJECTTOORTHS function. This is an example of
projectToOrths usage }
-\PYG{c}{\PYGZpc{} with one input variable. The default value of projection
type is used.}
+\PYG{c}{\PYGZpc{} An example of GETDATA method\PYGZsq{}s usage.}
+\PYG{n}{nTubes}\PYG{p}{=}\PYG{l+m+mi}{5}\PYG{p}{;}
+\PYG{n}{nPoints} \PYG{p}{=} \PYG{l+m+mi}{100}\PYG{p}{;}
+\PYG{n}{timeBeg}\PYG{p}{=}\PYG{l+m+mi}{0}\PYG{p}{;}
+\PYG{n}{timeEnd}\PYG{p}{=}\PYG{l+m+mi}{1}\PYG{p}{;}
+\PYG{n}{type} \PYG{p}{=} \PYG{l+m+mi}{2}\PYG{p}{;}
+\PYG{n}{EllTube}\PYG{p}{=}\PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getEllTube}\PYG{p}{(}\PYG{n}{nTubes}\PYG{p}{,}\PYG{n}{timeBeg}\PYG{p}{,}\PYG{n}{timeEnd}\PYG{p}{,}\PYG{n}{type}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}
+\PYG{n}{data} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getData}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\end{Verbatim}
+
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
+\PYG{c}{\PYGZpc{} An example of GETELLARRAY method\PYGZsq{}s usage.}
+\PYG{p}{[}\PYG{n}{nTubes}\PYG{p}{,} \PYG{n}{nPoints}\PYG{p}{,}
\PYG{n}{nDims}\PYG{p}{,} \PYG{n}{absTol}\PYG{p}{,}
\PYG{n}{relTol}\PYG{p}{,} \PYG{n}{timeVec}\PYG{p}{,}\PYG{c}{...}
+ \PYG{n}{sTime}\PYG{p}{,} \PYG{n}{lsGoodDirVec}\PYG{p}{,}
\PYG{n}{ltGoodDirArray}\PYG{p}{,} \PYG{n}{aMat}\PYG{p}{,}
\PYG{n}{qArrayList}\PYG{p}{]} \PYG{p}{=} \PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getDataForOneTube}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{p}{[}\PYG{n}{approxSchemaDescr}\PYG{p}{,}
\PYG{n}{approxSchemaName}\PYG{p}{,} \PYG{n}{approxType}\PYG{p}{]}
\PYG{p}{=} \PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getSameApprox}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{n}{ellArray}\PYG{p}{(}\PYG{n}{nPoints}\PYG{p}{)} \PYG{p}{=}
\PYG{n}{ellipsoid}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{k}{for} \PYG{n}{iElem} \PYG{p}{=}
\PYG{l+m+mi}{1}\PYG{p}{:}\PYG{n}{nPoints}
+ \PYG{n}{ellArray}\PYG{p}{(}\PYG{n}{iElem}\PYG{p}{)} \PYG{p}{=}
\PYG{n}{ellipsoid}\PYG{p}{(}\PYG{n}{aMat}\PYG{p}{(}\PYG{p}{:}\PYG{p}{,}\PYG{n}{iElem}\PYG{p}{)}\PYG{p}{,}
\PYG{n}{qArrayList}\PYG{p}{\PYGZob{}}\PYG{l+m+mi}{1}\PYG{p}{\PYGZcb{}}\PYG{p}{(}\PYG{p}{:}\PYG{p}{,}\PYG{p}{:}\PYG{p}{,}\PYG{n}{iElem}\PYG{p}{)}\PYG{p}{)}\PYG{p}{;}
+\PYG{k}{end}\PYG{p}{;}
+\PYG{n}{fromEllArrayEllTube} \PYG{p}{=}
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{rels}\PYG{p}{.}\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{fromEllArray}\PYG{p}{(}\PYG{c}{...}
+ \PYG{n}{ellArray}\PYG{p}{,}\PYG{n}{timeVec}\PYG{p}{,}
\PYG{n}{ltGoodDirArray}\PYG{p}{,} \PYG{n}{sTime}\PYG{p}{,}
\PYG{n}{approxType}\PYG{p}{,}\PYG{c}{...}
+
\PYG{n}{approxSchemaName}\PYG{p}{,}\PYG{n}{approxSchemaDescr}\PYG{p}{,}
\PYG{n}{absTol}\PYG{p}{,} \PYG{n}{relTol}\PYG{p}{)}\PYG{p}{;}
+\PYG{n}{data} \PYG{p}{=}
\PYG{n}{fromEllArrayEllTube}\PYG{p}{.}\PYG{n}{getEllArray}\PYG{p}{(}\PYG{n}{approxType}\PYG{p}{)}\PYG{p}{;}
+\end{Verbatim}
+
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
+\PYG{n}{nTubes}\PYG{p}{=}\PYG{l+m+mi}{5}\PYG{p}{;}
+\PYG{n}{nPoints} \PYG{p}{=} \PYG{l+m+mi}{100}\PYG{p}{;}
+\PYG{n}{timeBeg}\PYG{p}{=}\PYG{l+m+mi}{0}\PYG{p}{;}
+\PYG{n}{timeEnd}\PYG{p}{=}\PYG{l+m+mi}{1}\PYG{p}{;}
+\PYG{n}{type} \PYG{p}{=} \PYG{l+m+mi}{2}\PYG{p}{;}
+\PYG{n}{EllTube}\PYG{p}{=}\PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getEllTube}\PYG{p}{(}\PYG{n}{nTubes}\PYG{p}{,}\PYG{n}{timeBeg}\PYG{p}{,}\PYG{n}{timeEnd}\PYG{p}{,}\PYG{n}{type}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} get the list of field descriptions}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{Descr} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getFieldDescrList}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} get for given field a nested logical/cell array
containing is\PYGZhy{}null }
+\PYG{c}{\PYGZpc{} indicators for cell content. For example, for
approxSchemaName field.}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{IsNull} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getFieldIsNull}\PYG{p}{(}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{approxSchemaName\PYGZsq{}}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} get for given field logical vector determining whether
value of this }
+\PYG{c}{\PYGZpc{} field in each cell is null or not. For example, for
approxSchemaName field.}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{ValueIsNull} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getFieldIsValueNull}\PYG{p}{(}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{approxSchemaName\PYGZsq{}}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} get the list of field names}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{Name} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getFieldNameList}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} project object with specified fields. For example, with
fields that are}
+\PYG{c}{\PYGZpc{} not to be cut or concatenated.}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{nameList} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getNoCatOrCutFieldsList}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{n}{Proj} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getFieldProjection}\PYG{p}{(}\PYG{n}{nameList}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} get the list of field types}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{Type} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getFieldTypeList}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} get the list of field type specifications. Field type
specification is a }
+\PYG{c}{\PYGZpc{} sequence of type names corresponding to field value
types starting with }
+\PYG{c}{\PYGZpc{} the top level and going down into the nested content of
a field (for a }
+\PYG{c}{\PYGZpc{} field having a complex type).}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{TypeSpec} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getFieldTypeSpecList}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{} or}
+\PYG{n}{TypeSpec} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getFieldTypeSpecList}\PYG{p}{(}\PYG{n}{nameList}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} get a matrix composed from the size vectorsfor the
specified fields}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{ValueSizeMat} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getFieldValueSizeMat}\PYG{p}{(}\PYG{n}{nameList}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} get a vector indicating whether a particular field is
composed of null }
+\PYG{c}{\PYGZpc{} values completely}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{ValueNull} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getIsFieldValueNull}\PYG{p}{(}\PYG{n}{nameList}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} get a size vector for the specified dimensions. If no
dimensions are }
+\PYG{c}{\PYGZpc{} specified, a size vector for all dimensions up to
minimum dimension is }
+\PYG{c}{\PYGZpc{} returned}
+\PYG{n}{MinDimensionSize} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getMinDimensionSize}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} get a minimum dimensionality for a given object}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{MinDimensionality} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getMinDimensionality}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} get a number of elements in a given object}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{NElems} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getNElems}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} get a number of fields in a given object}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{NFiedls} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getNFields}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} get a number of tuples in a given object}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{NTuples} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getNTuples}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} get sort index for all tuples of given relation with
respect to some of }
+\PYG{c}{\PYGZpc{} its fields}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{SortIndex} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getSortIndex}\PYG{p}{(}\PYG{n}{nameList}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{} also we can specify the direction of sorting
(\PYGZsq{}asc\PYGZsq{} or \PYGZsq{}desc\PYGZsq{})}
+\PYG{n}{SortIndex} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getSortIndex}\PYG{p}{(}\PYG{n}{nameList}\PYG{p}{,}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{Direction\PYGZsq{}}\PYG{p}{,}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{asc\PYGZsq{}}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} get tuples with given indices from given relation}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{Tuples} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getTuples}\PYG{p}{(}\PYG{p}{[}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{l+m+mi}{2}\PYG{p}{,}\PYG{l+m+mi}{3}\PYG{p}{]}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} get tuples from given relation such that afixed index
field contains }
+\PYG{c}{\PYGZpc{} values from a given set of value}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{FilteredTuples} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getTuplesFilteredBy}\PYG{p}{(}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{sTime\PYGZsq{}}\PYG{p}{,}
\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} get internal representation for a set of unique tuples
for given relation}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{UniqueData} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getUniqueData}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} get a relation containing the unique tuples from the
original relation}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{UniqueTuples} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getUniqueTuples}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\end{Verbatim}
+
+Also we can copy the object, clear all the data, save it in a file:
+
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
+\PYG{n}{nTubes}\PYG{p}{=}\PYG{l+m+mi}{5}\PYG{p}{;}
+\PYG{n}{nPoints} \PYG{p}{=} \PYG{l+m+mi}{100}\PYG{p}{;}
+\PYG{n}{timeBeg}\PYG{p}{=}\PYG{l+m+mi}{0}\PYG{p}{;}
+\PYG{n}{timeEnd}\PYG{p}{=}\PYG{l+m+mi}{1}\PYG{p}{;}
+\PYG{n}{type} \PYG{p}{=} \PYG{l+m+mi}{2}\PYG{p}{;}
+\PYG{n}{EllTube}\PYG{p}{=}\PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getEllTube}\PYG{p}{(}\PYG{n}{nTubes}\PYG{p}{,}\PYG{n}{timeBeg}\PYG{p}{,}\PYG{n}{timeEnd}\PYG{p}{,}\PYG{n}{type}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} get a copy of the object}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{EllCopy} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{getCopy}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} delete all the data from the object}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{clearData}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{n}{EllTube} \PYG{p}{=}\PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getEllTube}\PYG{p}{(}\PYG{n}{nTubes}\PYG{p}{,}\PYG{n}{timeBeg}\PYG{p}{,}\PYG{n}{timeEnd}\PYG{p}{,}\PYG{n}{type}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} create a copy of a specified object via calling a copy
constructor for }
+\PYG{c}{\PYGZpc{} the object class}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{Clone} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{clone}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} remove all duplicate tuples from the relation}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{noDuplicate} \PYG{p}{=}
\PYG{n}{Clone}\PYG{p}{.}\PYG{n}{removeDuplicateTuples}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} write a content of relation into Excel spreadsheet file}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{writeToCSV}\PYG{p}{(}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{path\PYGZsq{}}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} write a content of relation into Excel spreadsheet file}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{fileName} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{writeToXLS}\PYG{p}{(}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{path\PYGZsq{}}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} display a content of the given relation as a data grid
UI component}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{dispOnUI}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} put some textual information about object in screen}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{display}\PYG{p}{(}\PYG{p}{)}\PYG{p}{;}
+\end{Verbatim}
+
+As we have created the object, we can work with it. Below is the example
of concatenating ellipsoid tube objects. We can concatenate objects
containing one or several ellipsoid tubes with the same type of
approximation.
+
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
+\PYG{c}{\PYGZpc{} An example of concatenating ellipsoid tube objects
containing random }
+\PYG{c}{\PYGZpc{} number of ellipsoid tubes (from one to ten tubes).}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{nTubes} \PYG{p}{=}
\PYG{n}{randi}\PYG{p}{(}\PYG{l+m+mi}{10}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{;}
+\PYG{n}{nPoints} \PYG{p}{=} \PYG{l+m+mi}{20}\PYG{p}{;}
+\PYG{n}{type} \PYG{p}{=} \PYG{l+m+mi}{1}\PYG{p}{;}
+\PYG{n}{timeBeg1} \PYG{p}{=} \PYG{l+m+mi}{0}\PYG{p}{;}
+\PYG{n}{timeEnd1} \PYG{p}{=} \PYG{l+m+mi}{1}\PYG{p}{;}
+\PYG{n}{firstEllTube} \PYG{p}{=}\PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getEllTube}\PYG{p}{(}\PYG{n}{nTubes}\PYG{p}{,}\PYG{n}{timeBeg1}\PYG{p}{,}\PYG{n}{timeEnd1}\PYG{p}{,}\PYG{n}{type}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}
+\PYG{n}{timeBeg2} \PYG{p}{=} \PYG{l+m+mi}{1}\PYG{p}{;}
+\PYG{n}{timeEnd2} \PYG{p}{=} \PYG{l+m+mi}{2}\PYG{p}{;}
+\PYG{n}{secondEllTube} \PYG{p}{=}\PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getEllTube}\PYG{p}{(}\PYG{n}{nTubes}\PYG{p}{,}\PYG{n}{timeBeg2}\PYG{p}{,}\PYG{n}{timeEnd2}\PYG{p}{,}\PYG{n}{type}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} Concatenating firstEllTube and secondEllTube on
[timeBeg1, timeEnd2]}
+\PYG{c}{\PYGZpc{} vector of time.}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{resEllTube} \PYG{p}{=}
\PYG{n}{firstEllTube}\PYG{p}{.}\PYG{n+nb}{cat}\PYG{p}{(}\PYG{n}{secondEllTube}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} Concatenating the same firstEllTube and secondEllTube on
[timeBeg1,timeEnd2]}
+\PYG{c}{\PYGZpc{} vector of time, but the sTime and values of properties
corresponding to }
+\PYG{c}{\PYGZpc{} sTime are taken from secondEllTube.}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{resEllTube} \PYG{p}{=}
\PYG{n}{firstEllTube}\PYG{p}{.}\PYG{n+nb}{cat}\PYG{p}{(}\PYG{n}{secondEllTube}\PYG{p}{,}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{isReplacedByNew\PYGZsq{}}\PYG{p}{,}\PYG{n}{true}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} Concatenating the same firstEllTube and secondEllTube on
[timeBeg1,timeEnd2]}
+\PYG{c}{\PYGZpc{} vector of time, but the sTime and values of properties
corresponding to }
+\PYG{c}{\PYGZpc{} sTime are taken from firstEllTube.}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{resEllTube} \PYG{p}{=}
\PYG{n}{firstEllTube}\PYG{p}{.}\PYG{n+nb}{cat}\PYG{p}{(}\PYG{n}{secondEllTube}\PYG{p}{,}\PYG{l+s}{\PYGZsq{}}\PYG{l+s}{isReplacedByNew\PYGZsq{}}\PYG{p}{,}\PYG{n}{false}\PYG{p}{)}\PYG{p}{;}
+\PYG{c}{\PYGZpc{}}
+\PYG{c}{\PYGZpc{} Note that we cannot concatenate ellipsoid tubes with
overlapping time}
+\PYG{c}{\PYGZpc{} limits.}
+\PYG{c}{\PYGZpc{}}
+\end{Verbatim}
+
+As we can concatenate ellipsoid tubes, it is logical to be possible to cut
ellipsoid tubes, leaving only part of it at specified vector of time or
point of time. Below are the exmples:
+
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
+\PYG{c}{\PYGZpc{} An example of usage of CUT function from EllTubeBasic
class. In}
+\PYG{c}{\PYGZpc{} this example an ellipsoid tube object is created, using
TimeVec time}
+\PYG{c}{\PYGZpc{} vector. Then it is cut using cutTimeVec time vector.}
+\PYG{c}{\PYGZpc{}}
+\PYG{n}{nTubes}\PYG{p}{=}\PYG{l+m+mi}{1}\PYG{p}{;}
+\PYG{n}{nPoints} \PYG{p}{=} \PYG{l+m+mi}{20}\PYG{p}{;}
+\PYG{n}{timeBeg}\PYG{p}{=}\PYG{l+m+mi}{0}\PYG{p}{;}
+\PYG{n}{timeEnd}\PYG{p}{=}\PYG{l+m+mi}{1}\PYG{p}{;}
+\PYG{n}{type} \PYG{p}{=} \PYG{l+m+mi}{1}\PYG{p}{;}
+\PYG{n}{EllTube}\PYG{p}{=}\PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getEllTube}\PYG{p}{(}\PYG{n}{nTubes}\PYG{p}{,}\PYG{n}{timeBeg}\PYG{p}{,}\PYG{n}{timeEnd}\PYG{p}{,}\PYG{n}{type}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}
+\PYG{n}{timeVec} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{timeVec}\PYG{p}{\PYGZob{}}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{p}{:}\PYG{p}{\PYGZcb{}}\PYG{p}{;}
+\PYG{n}{cutTimeVec} \PYG{p}{=}
\PYG{p}{[}\PYG{n}{timeVec}\PYG{p}{(}\PYG{l+m+mi}{2}\PYG{p}{)}
\PYG{n}{timeVec}\PYG{p}{(}\PYG{l+m+mi}{7}\PYG{p}{)}\PYG{p}{]}\PYG{p}{;}
+\PYG{n}{cutVecEllTube} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{cut}\PYG{p}{(}\PYG{n}{cutTimeVec}\PYG{p}{)}\PYG{p}{;}
+\end{Verbatim}
+
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
+\PYG{c}{\PYGZpc{} An example of usage of CUT function from EllTubeBasic
class. In}
+\PYG{c}{\PYGZpc{} this example an ellipsoid tube object is created, using
TimeVec time}
+\PYG{c}{\PYGZpc{} vector. Then it is cut using cutTimePoint point}
+\PYG{c}{\PYGZpc{} of time.}
+\PYG{n}{nTubes}\PYG{p}{=}\PYG{l+m+mi}{1}\PYG{p}{;}
+\PYG{n}{nPoints} \PYG{p}{=} \PYG{l+m+mi}{20}\PYG{p}{;}
+\PYG{n}{timeBeg}\PYG{p}{=}\PYG{l+m+mi}{0}\PYG{p}{;}
+\PYG{n}{timeEnd}\PYG{p}{=}\PYG{l+m+mi}{1}\PYG{p}{;}
+\PYG{n}{type} \PYG{p}{=} \PYG{l+m+mi}{1}\PYG{p}{;}
+\PYG{n}{EllTube}\PYG{p}{=}\PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getEllTube}\PYG{p}{(}\PYG{n}{nTubes}\PYG{p}{,}\PYG{n}{timeBeg}\PYG{p}{,}\PYG{n}{timeEnd}\PYG{p}{,}\PYG{n}{type}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}
+\PYG{n}{timeVec} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{timeVec}\PYG{p}{\PYGZob{}}\PYG{l+m+mi}{1}\PYG{p}{,}\PYG{p}{:}\PYG{p}{\PYGZcb{}}\PYG{p}{;}
+\PYG{n}{cutTimePoint} \PYG{p}{=}
\PYG{n}{timeVec}\PYG{p}{(}\PYG{n}{randi}\PYG{p}{(}\PYG{n+nb}{size}\PYG{p}{(}\PYG{n}{timeVec}\PYG{p}{,}\PYG{l+m+mi}{2}\PYG{p}{)}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{)}\PYG{p}{)}\PYG{p}{;}
+\PYG{n}{cutPointEllTube} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{cut}\PYG{p}{(}\PYG{n}{cutTimePoint}\PYG{p}{)}\PYG{p}{;}
+\end{Verbatim}
+
+After cutting, we can interpolate the resulting tube, using new time
vector. Take notice that we have to make sure that the first and the last
elements in old and new vectors of time are the same.
+
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
+\PYG{c}{\PYGZpc{} An example of usage of INTERP function. In this example
an ellipsoid tube}
+\PYG{c}{\PYGZpc{} object is created, using oldTimeVec time vector. Then it
is interpolated }
+\PYG{c}{\PYGZpc{} on newTimeVec time vector.}
+\PYG{n}{nTubes}\PYG{p}{=}\PYG{l+m+mi}{1}\PYG{p}{;}
+\PYG{n}{nPoints} \PYG{p}{=} \PYG{l+m+mi}{20}\PYG{p}{;}
+\PYG{n}{timeBeg}\PYG{p}{=}\PYG{l+m+mi}{0}\PYG{p}{;}
+\PYG{n}{timeEnd}\PYG{p}{=}\PYG{l+m+mi}{1}\PYG{p}{;}
+\PYG{n}{type} \PYG{p}{=} \PYG{l+m+mi}{1}\PYG{p}{;}
+\PYG{n}{EllTube}\PYG{p}{=}\PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getEllTube}\PYG{p}{(}\PYG{n}{nTubes}\PYG{p}{,}\PYG{n}{timeBeg}\PYG{p}{,}\PYG{n}{timeEnd}\PYG{p}{,}\PYG{n}{type}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}
+\PYG{n}{newnPoints}\PYG{p}{=}\PYG{l+m+mi}{50}\PYG{p}{;}
+\PYG{n}{newTimeVec} \PYG{p}{=}
\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{:}\PYG{p}{(}\PYG{l+m+mi}{1}\PYG{o}{/}\PYG{n}{newnPoints}\PYG{p}{)}\PYG{p}{:}\PYG{l+m+mi}{1}\PYG{p}{;}
+\PYG{n}{interpEllTube} \PYG{p}{=}
\PYG{n}{EllTube}\PYG{p}{.}\PYG{n}{interp}\PYG{p}{(}\PYG{n}{newTimeVec}\PYG{p}{)}\PYG{p}{;}
+\end{Verbatim}
+
+After that we can thin out the new ellipsoid tube, removing ellipsoids at
sertain points of time.
+
+\begin{Verbatim}[commandchars=\\\{\},numbers=left,firstnumber=1,stepnumber=1]
+\PYG{c}{\PYGZpc{} An example of usage of THINOUTTUPLES function from
EllTubeBasic class. In}
+\PYG{c}{\PYGZpc{} this example an ellipsoid tube object is created, using
TimeVec time}
+\PYG{c}{\PYGZpc{} vector. Then it is thinned out using indVec vector of
random indices of }
+\PYG{c}{\PYGZpc{} elements from timeVec.}
+\PYG{n}{nTubes}\PYG{p}{=}\PYG{l+m+mi}{1}\PYG{p}{;}
+\PYG{n}{nPoints} \PYG{p}{=} \PYG{l+m+mi}{20}\PYG{p}{;}
+\PYG{n}{timeBeg}\PYG{p}{=}\PYG{l+m+mi}{0}\PYG{p}{;}
+\PYG{n}{timeEnd}\PYG{p}{=}\PYG{l+m+mi}{1}\PYG{p}{;}
+\PYG{n}{type} \PYG{p}{=} \PYG{l+m+mi}{1}\PYG{p}{;}
+\PYG{n}{EllTube}\PYG{p}{=}\PYG{c}{...}
+
\PYG{n}{gras}\PYG{p}{.}\PYG{n}{ellapx}\PYG{p}{.}\PYG{n}{smartdb}\PYG{p}{.}\PYG{n}{test}\PYG{p}{.}\PYG{n}{examples}\PYG{p}{.}\PYG{n}{getEllTube}\PYG{p}{(}\PYG{n}{nTubes}\PYG{p}{,}\PYG{n}{timeBeg}\PYG{p}{,}\PYG{n}{timeEnd}\PYG{p}{,}\PYG{n}{type}\PYG{p}{,}\PYG{n}{nPoints}\PYG{p}{)}\PYG{p}{;}
+\PYG{n}{newnPoints}\PYG{p}{=}\PYG{l+m+mi}{50}\PYG{p}{;}
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