[sympycore] r1199 committed - Edited wiki page SteadyStateFluxAnalysis through web user interface.

[codesite...@google.com]

Revision: 1199
Author: pearu.peterson
Date: Tue Apr 12 12:01:06 2011
Log: Edited wiki page SteadyStateFluxAnalysis through web user
interface.
http://code.google.com/p/sympycore/source/detail?r=1199

Modified:
/wiki/SteadyStateFluxAnalysis.wiki

=======================================
--- /wiki/SteadyStateFluxAnalysis.wiki Fri Apr 8 03:45:33 2011
+++ /wiki/SteadyStateFluxAnalysis.wiki Tue Apr 12 12:01:06 2011
@@ -223,6 +223,34 @@
}}}
we see that the `kernel` matrix indeed defines the kernel of the
stoichiometry matrix.

+== Computing SVD kernel ==
+
+We can compute the kernel of this stoichiometry matrix with the SVD
algorithm:
+{{{
+>>> ex.compute_kernel_SVD()
+>>> fluxes, kernel_SVD = ex.get_kernel_SVD()
+}}}
+where `kernel_SVD` is a numpy ndarray object and `fluxes` is a list of
flux names. By definition, we have `fluxes = kernel_SVD * alpha` where
`alpha` defines a column vector of parameters.
+
+To view the kernel, one can use the following code
+{{{
+>>> alpha = ['a%s'%i for i in range(kernel_SVD.shape[1])]
+>>> print ex.label_matrix(Matrix(kernel_SVD.round(decimals=3)), fluxes,
alpha)
+ a0 a1 a2 a3 a4 a5
+ R_C_D 0.122 0.39 0.179 -0.389 -0.121 -0.511
+ R_B_C 0.381 -0.074 0.433 0.101 -0.354 -0.28
+ R_C -0.245 -0.1 0.194 0.637 -0.217 -0.118
+ R_C_E 0.505 -0.364 0.059 -0.146 -0.015 0.349
+ R_A_B 0 0.059 0.54 0.133 0.192 0.133
+ R_B_D -0.594 -0.255 0.255 -0.331 0.008 0.263
+ R_D_B -0.212 -0.388 0.147 -0.362 -0.538 -0.15
+ R_D_E -0.255 0.629 0.076 -0.071 -0.187 0.184
+ R_A 0 0.059 0.54 0.133 0.192 0.133
+ R_D -0.005 -0.106 0.211 -0.287 0.611 -0.283
+ R_E 0.25 0.265 0.135 -0.217 -0.202 0.533
+}}}
+Note that the columns of the SVD kernel are orthonormal.
+
== Viewing statistics ==

Finally, to view the statistics of kernel computations, execute