MATLAB Central Newsreader - How to calculate a matrix-based integral

How to calculate a matrix-based integral

Xueou Chen — Fri, 16 May 2008 06:31:02 -0400

I have a matrix-based integrand, i.e., including some
matrix calculations, like f(x) = A*B*C, A is a row vector,
B a matrix, C a column vector, all associated with x. and
f(x) still a single number function of x.

Now when I use function quadl to calculate int(f(x)), the
input x is always a vector, and it tells me error of matrix
dimention...

I have to calculate the above matrix formulas on paper to
avoid such errors. But f(x) actually includes matrix
inversion. 3 * 3 is still ok, then 4 * 4 matrix ... very
boring.

I think there are some other ways to do this better.

Re: How to calculate a matrix-based integral

John D'Errico — Fri, 16 May 2008 09:45:03 -0400

"Xueou Chen" <hicxo@sina.com> wrote in message
<g0j9n6$286$1@fred.mathworks.com>...
> I have a matrix-based integrand, i.e., including some
> matrix calculations, like f(x) = A*B*C, A is a row vector,
> B a matrix, C a column vector, all associated with x. and
> f(x) still a single number function of x.
>
> Now when I use function quadl to calculate int(f(x)), the
> input x is always a vector, and it tells me error of matrix
> dimention...

quadl can call your function with multiple
x values all at once. But, Matlab has a for
loop that you can use.

Put one inside your code, to compute your
function for each value of x that is passed
in.

John

Re: How to calculate a matrix-based integral

Xueou Chen — Mon, 19 May 2008 08:28:02 -0400

"John D'Errico" <woodchips@rochester.rr.com> wrote in
message <g0jl2v$mn6$1@fred.mathworks.com>...
> "Xueou Chen" <hicxo@sina.com> wrote in message
> <g0j9n6$286$1@fred.mathworks.com>...
> > I have a matrix-based integrand, i.e., including some
> > matrix calculations, like f(x) = A*B*C, A is a row
vector,
> > B a matrix, C a column vector, all associated with x.
and
> > f(x) still a single number function of x.
> >
> > Now when I use function quadl to calculate int(f(x)),
the
> > input x is always a vector, and it tells me error of
matrix
> > dimention...
>
> quadl can call your function with multiple
> x values all at once. But, Matlab has a for
> loop that you can use.
>
> Put one inside your code, to compute your
> function for each value of x that is passed
> in.
>
> John

thank you.

I have already tried this way before I posted here. It can
work anyway. But my integral is from -Inf to +Inf, the
exact integral range is decided by the precision
aotomatically. So there is a lot of calculations of my
integrand function. Then a for loop will slow down my codes
very much, so I posted here to find a better way.

hicxo

Re: How to calculate a matrix-based integral

John D'Errico — Mon, 19 May 2008 09:54:01 -0400

"Xueou Chen" <hicxo@sina.com> wrote in message
<g0rdmi$ko5$1@fred.mathworks.com>...

> I have already tried this way before I posted here. It can
> work anyway. But my integral is from -Inf to +Inf, the
> exact integral range is decided by the precision
> aotomatically. So there is a lot of calculations of my
> integrand function. Then a for loop will slow down my codes
> very much, so I posted here to find a better way.

If your integrand is such that you will
define different finite limits based on
your parameters, then this is impossible
to accomplish using quadl. Quadl is an
adaptive quadrature, but it uses only
one set of limits.

A for loop, external to the quadrature,
is then the solution.

John