I have an Anonymous Function and want to integrate it

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Yang
Yang 2014-11-18
评论： Mike Hosea 2014-11-20
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.

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回答（2 个）

Adam
Adam 2014-11-18
编辑：Adam 2014-11-18
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.
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Yang
Yang 2014-11-18
Thanks Adam,
what is myMatrix?
Could u give me more details?
now I have
A = @ (x) [x 2*x;3*x 4*x]; >> quadv(A,0,1)
ans =
0.5000 1.0000
1.5000 2.0000
Could u just integrate A(1,1)?
Adam
Adam 2014-11-18
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 2014-11-18
clear all
close all
clc;
syms x
A=[x 2*x;3*x 4*x];
int(A(1,1),0,1)
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MA
MA 2014-11-18
for numerical integration you can use quad , quadl or double(int())
syms x
A=[x 2*x;3*x 4*x];
double(int(A(1,1),0,1))
Mike Hosea
Mike Hosea 2014-11-20
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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