I have an Anonymous Function and want to integrate it

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.

Answer 1

[Adam]

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.

[Yang]

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]

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.

Answer 2

[MA]

clear all
close all
clc;
syms x 
A=[x 2*x;3*x 4*x];
int(A(1,1),0,1)

[Yang]

Thanks M.A.!

I think int is not as efficient as quad for very large problem, so do u know if I can use numerical integration to do it?

[MA]

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]

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.