MATLAB index exceeds matrix dimensions error.

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JLK
JLK 2015-8-14
评论： JLK 2015-8-14
I have created the following script to specifically implement piecewise quadratic interpolation. The script seems to work for several inputs however for the examples shown below I recieve an error: index exceeds matrix dimensions.
SCRIPT:
function [p,px,pxx] = quadinterp(x, xj, fj)
n = length(xj);
[~,j] = histc(x,xj);
j(x>=xj(n)) = n-1;
j(x<xj(1)) = 1;
p = fj(j).*((x - xj(j+1)).*(x-xj(j+2)))./((xj(j) - xj(j+1)).*(xj(j) - xj(j+2))) ...
+ fj(j+1).*((x - xj(j)).*(x-xj(j+2)))./((xj(j+1) - xj(j)).*(xj(j+1) - xj(j+2)))...
+ fj(j+2).*((x - xj(j)).*(x-xj(j+1)))./((xj(j+2) - xj(j)).*(xj(j+2) - xj(j+1)));
px = fj(j).*(2*x-xj(j+1)-xj(j+2))./((xj(j) - xj(j+1)).*(xj(j) - xj(j+2))) ...
+ fj(j+1).*(2*x-xj(j)-xj(j+2))./((xj(j+1) - xj(j)).*(xj(j+1) - xj(j+2)))...
+ fj(j+2).*((2*x-xj(j)-xj(j+1)))./((xj(j+2) - xj(j)).*(xj(j+2) - xj(j+1)));
pxx = fj(j).*2./((xj(j) - xj(j+1)).*(xj(j) - xj(j+2))) ...
+ fj(j+1).*2./((xj(j+1) - xj(j)).*(xj(j+1) - xj(j+2)))...
+ fj(j+2).*(2)./((xj(j+2) - xj(j)).*(xj(j+2) - xj(j+1)));
The following inputs give correct solutions:
xj = [1 5 9 11 13];
fj = [xj].^2;
x = linspace(2,10,13);
The following outputs give the error:
xj = [1 5 9 11 13];
fj = [xj].^2;
x = linspace(1,12,13);
&
xj = linspace(0, 2,5);
fj = xj.^2;
x = linspace(0, 2, 20);
Any help is greatly appreciated.

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回答（1 个）

Azzi Abdelmalek
Azzi Abdelmalek 2015-8-14
Check this line
p = fj(j).*((x - xj(j+1)).*(x-xj(j+2)))./((xj(j) - xj(j+1)).*(xj(j) - xj(j+2))) ...
+ fj(j+1).*((x - xj(j)).*(x-xj(j+2)))./((xj(j+1) - xj(j)).*(xj(j+1) - xj(j+2)))...
+ fj(j+2).*((x - xj(j)).*(x-xj(j+1)))./((xj(j+2) - xj(j)).*(xj(j+2) - xj(j+1)))
you have
j=[1 1 1 1 1 2 2 2 2 3 3 4 4]
the max value of j is 4, and the size of xj is 5, when you type xj(j+2), you are asking for x([3 3 3 3 3 4 4 4 4 5 5 6 6]), x(6) can't be calculated, because the size of xj is [1 6]
  1 个评论
JLK
JLK 2015-8-14
Thanks for your input.
Is there anyway of correcting this without changing the line
p = fj(j).*((x - xj(j+1)).*(x-xj(j+2)))./((xj(j) - xj(j+1)).*(xj(j) - xj(j+2))) ...
+ fj(j+1).*((x - xj(j)).*(x-xj(j+2)))./((xj(j+1) - xj(j)).*(xj(j+1) - xj(j+2)))...
+ fj(j+2).*((x - xj(j)).*(x-xj(j+1)))./((xj(j+2) - xj(j)).*(xj(j+2) - xj(j+1)))
as this is the formula for lagrange interpolation

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