I have an Anonymous Function and want to integrate it

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For a simple example, I have an Anonymous function A = @ (x) [x 2*x;3*x 4*x], and I want to integrate it from 0 to 1. If I use QUADV it will integrate the entire matrix A. However, it is not efficient for very large problem. I am wondering if there is a way that I can only integrate some specific terms, say only A(1,1).
The background is that I have a very large 80000 by 80000 matrix, and only a few terms need to be calculated.

Answers (2)

Adam
Adam on 18 Nov 2014
Edited: Adam on 18 Nov 2014
Can you not just call:
A( myMatrix(1,1) );
to evaluate just the first element of your matrix? Or
A( myMatrix( xStart:xEnd, yStart:yEnd ) );
to evaluate a rectangular subset of your matrix? Or any other form of indexing (especially linear indexing) to choose more specifically.
  2 Comments
Adam
Adam on 18 Nov 2014
I'm not familiar with using quadv so its usage does complicate matters a little though I would think it should be perfectly possible.
'myMatrix' is just a place holder for whatever your matrix is which I assumed was the input x though scanning through quadv it seems your function expects only a scalar input as x so I'm not sure where your matrix comes into it.

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MA
MA on 18 Nov 2014
clear all
close all
clc;
syms x
A=[x 2*x;3*x 4*x];
int(A(1,1),0,1)
  3 Comments
Mike Hosea
Mike Hosea on 20 Nov 2014
Quad, quadl, and quadv are all deprecated. The function is integral(), and for array valued problems, use the 'ArrayValued',true option.
It is easy to integrate selected terms in a way that unfortunately evaluates the entire matrix, anyway. The trick is to avoid that. I'm not sure how to do it in the general context.

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