Merging/Multiplying Functions

Hello, I haven't figured out to find a way to create a new function out of multiplying 2 functions, for example:

fun1 = @(x) sin(x);
fun2 = @(x) cos(x);
*I want to create fun3 out of them so that -* 
fun3 = @(x) sin(x)*cos(x)

The reason I'm asking this is that if I define fun3 as-

fun3 = @(x) fun1(x)*fun2(x)

and obviously it doesn't turn into-

fun3=@(x) sin(x)*cos(x)

thus I can't integrate fun3-

integral(fun3,0,5) ~= int(sin(x)*cos(x),x,0,5)

Matlab just says-

Error using  * 
Inner matrix dimensions must agree.

Thank you

Answer 1

[Star Strider]

You need to use element-wise operations here, using the dot (.) operator for element-wise multiplication, (.*).

This works:

fun1 = @(x) sin(x);
fun2 = @(x) cos(x);
fun3 = @(x) fun1(x).*fun2(x);
int_fun3 = integral(fun3, 0, 5)

int_fun3 =
   459.7679e-003

See the documentation on Array vs. Matrix Operations for a full discussion.

[yuval]

Thanks, didn't realize that was the issue.

[Star Strider]

My pleasure.

Many people don’t, and I suspect everyone has encountered the problem themselves at least once. (I have.)

[JacobsonRadical]

Great Answer. I've also been confused by this for a while. You saved me!

[Star Strider]

Thank you!

[Grant Peel]

Does this method work with 2 dimensional functions:

fun1 = @(x,y) sin(x)*sin(y);

fun2 = @(x,y) xy;

fun3 = @(x,y) fun1(x,y).*fun2(x,y);

integral2(fun3, 0,1,0,1)

[Star Strider]

@Grant Peel —

The easiest way to find out is to first fully vectorise the constituent equations, and then try it —

fun1 = @(x,y) sin(x).*sin(y);
fun2 = @(x,y) x.*y;
fun3 = @(x,y) fun1(x,y).*fun2(x,y);
int_fun3 = integral2(fun3, 0,1,0,1)

int_fun3 = 0.0907

It seems that it does!

.