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linear extrapolation + spline interpolation with interp1
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Massimo
Dec 20, 2011, 10:41:07 AM12/20/11
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Hi,
I would like to know if there is a smart way to use interp1 and obtain spline interpolation and linear extrapolation at the same time.
Suppose, for simplicity, I have :
x=linspace(1,5,4); %my x
Y=[x.^2; x.^3; x.^4]; % my Y
xi=[linspace(0.5,5.5,20);linspace(0.2,6,20)]; %my xi
and I wanted to perform spline interpolation for values of xi inside the interval spanned by x (i.e. 1,5), and linear extrapolation for values of xi outside that interval.
The reason is that I believe that spline extrapolation would produce a bad approximation of the true function.
What I came up with is:
clear all
close all
clc
x=linspace(1,5,4); %my x
Y=[x.^2; x.^3; x.^4]; % my Y
xi=[linspace(0.5,5.5,20);linspace(0.2,6,20)]; %my xi
yi_final=zeros(size(xi,1),size(xi,2),size(Y,1)); %initialize yi
ind1=find(xi>min(x) & xi<max(x)); % index for interpolation
ind2=find(xi<=min(x) | xi>=max(x)); %index for extrapolation
yi_mix1=interp1(x,Y',xi(xi>min(x) & xi<max(x)),'spline','extrap'); %interpolate
yi_mix2=interp1(x,Y',xi(xi<=min(x) | xi>=max(x)),'linear','extrap'); %extrapolate
yi_final_temp=zeros(2,20); %initialize temporary variable
for i=1:size(Y,1) %for each Y
yi_final_temp(ind1)=yi_mix1(:,i); %locate interpolation values
yi_final_temp(ind2)=yi_mix2(:,i); %locate extrapolation values
yi_final(:,:,i)=yi_final_temp; %create yi of the same size as Matlab ND interpolation
end
Clearly this is not efficient because I have to call interp1 twice and because I use a for loop which, in a bigger problem, could slow things down...
Is there a better way to tell interp1 to use different methods for interpolation and extrapolation?
Thanks,
Massimo
I would like to know if there is a smart way to use interp1 and obtain spline interpolation and linear extrapolation at the same time.
Suppose, for simplicity, I have :
x=linspace(1,5,4); %my x
Y=[x.^2; x.^3; x.^4]; % my Y
xi=[linspace(0.5,5.5,20);linspace(0.2,6,20)]; %my xi
and I wanted to perform spline interpolation for values of xi inside the interval spanned by x (i.e. 1,5), and linear extrapolation for values of xi outside that interval.
The reason is that I believe that spline extrapolation would produce a bad approximation of the true function.
What I came up with is:
clear all
close all
clc
x=linspace(1,5,4); %my x
Y=[x.^2; x.^3; x.^4]; % my Y
xi=[linspace(0.5,5.5,20);linspace(0.2,6,20)]; %my xi
yi_final=zeros(size(xi,1),size(xi,2),size(Y,1)); %initialize yi
ind1=find(xi>min(x) & xi<max(x)); % index for interpolation
ind2=find(xi<=min(x) | xi>=max(x)); %index for extrapolation
yi_mix1=interp1(x,Y',xi(xi>min(x) & xi<max(x)),'spline','extrap'); %interpolate
yi_mix2=interp1(x,Y',xi(xi<=min(x) | xi>=max(x)),'linear','extrap'); %extrapolate
yi_final_temp=zeros(2,20); %initialize temporary variable
for i=1:size(Y,1) %for each Y
yi_final_temp(ind1)=yi_mix1(:,i); %locate interpolation values
yi_final_temp(ind2)=yi_mix2(:,i); %locate extrapolation values
yi_final(:,:,i)=yi_final_temp; %create yi of the same size as Matlab ND interpolation
end
Clearly this is not efficient because I have to call interp1 twice and because I use a for loop which, in a bigger problem, could slow things down...
Is there a better way to tell interp1 to use different methods for interpolation and extrapolation?
Thanks,
Massimo
Matt J
Dec 20, 2011, 10:50:08 AM12/20/11
to
"Massimo" <giov...@bc.edu> wrote in message <jcqaaj$2st$1...@newscl01ah.mathworks.com>...
Since you're using equi-spaced samples in x, then this tool might help you.
http://www.mathworks.com/matlabcentral/fileexchange/26292-regular-control-point-interpolation-matrix-with-boundary-conditions
It also gives some examples on setting up B-spline interpolators.
It doesn't have an option for linear extrapolation, but you might try the extrapolation options that it does have (e.g. 'mirror', 'rep') to see if they're good enough.
> Hi,
>
> I would like to know if there is a smart way to use interp1 and obtain spline interpolation and linear extrapolation at the same time.
>
> Suppose, for simplicity, I have :
>
> x=linspace(1,5,4); %my x
==================
>
> I would like to know if there is a smart way to use interp1 and obtain spline interpolation and linear extrapolation at the same time.
>
> Suppose, for simplicity, I have :
>
> x=linspace(1,5,4); %my x
Since you're using equi-spaced samples in x, then this tool might help you.
http://www.mathworks.com/matlabcentral/fileexchange/26292-regular-control-point-interpolation-matrix-with-boundary-conditions
It also gives some examples on setting up B-spline interpolators.
It doesn't have an option for linear extrapolation, but you might try the extrapolation options that it does have (e.g. 'mirror', 'rep') to see if they're good enough.
Matt J
Dec 20, 2011, 11:29:08 AM12/20/11
to
> Is there a better way to tell interp1 to use different methods for interpolation and extrapolation?
=================
On second thought, you should probably use
PP = interp1(X,Y,'spline','pp')
to obtain the corresponding piecewise polynomial. You can modify the PP to give you linear interpolation outside the boundaries of X. Then just use PPVAL.
Massimo
Dec 20, 2011, 1:46:08 PM12/20/11
to
> =================
>
> On second thought, you should probably use
>
> PP = interp1(X,Y,'spline','pp')
>
> to obtain the corresponding piecewise polynomial. You can modify the PP to give you linear interpolation outside the boundaries of X. Then just use PPVAL.
Thank you, I will look into that---not sure I know how to change the ppform yet--.
If I have problems I will post another message.
Massimo
Matt J
Dec 20, 2011, 2:52:08 PM12/20/11
to
> yi_mix1=interp1(x,Y',xi(xi>min(x) & xi<max(x)),'spline','extrap'); %interpolate
> yi_mix2=interp1(x,Y',xi(xi<=min(x) | xi>=max(x)),'linear','extrap'); %extrapolate
================
> yi_mix2=interp1(x,Y',xi(xi<=min(x) | xi>=max(x)),'linear','extrap'); %extrapolate
Note also that the SPLINE command allows you to do cubic spline fitting while enforcing certain slopes at the edges, in case that's useful.
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