# How to perform elementwise multiplication between two matrices with different size or summation between two matrices with the same size

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moh mor on 14 Dec 2023
Commented: Voss on 14 Dec 2023
Hello, imagine I have the following array:
f = 1:10;
x = -22:1:22;
y = -22:1:22;
[u,v] = meshgrid(x,y);
I wish to perform elementwise multiplication operation between 'f' and 'u' (I mean the final array must have numel(f)*numel(u) elements.) . How can I fo this efficiently (definitely I know how to do this using "for loop". this is time consuming.)? Moreover, Imagine that I want to sum "u" and "v" elementwisely which both of them have the same size (so the final array must have numel(u)*numel(v) elements.) . How to do this in order to have high speed?

Steven Lord on 14 Dec 2023
Let's look at the sizes of the arrays in question.
f = 1:10;
x = -22:1:22;
y = -22:1:22;
[u,v] = meshgrid(x,y);
whos f x y u v
Name Size Bytes Class Attributes f 1x10 80 double u 45x45 16200 double v 45x45 16200 double x 1x45 360 double y 1x45 360 double
I wish to perform elementwise multiplication operation between 'f' and 'u' (I mean the final array must have numel(f)*numel(u) elements.)
So do you specifically want the size of the output to be [10 45*45] = [10, 2025]? Since you're using a release that supports implicit expansion this is not that difficult.
A = reshape(f, numel(f), 1).*reshape(u, 1, numel(u));
whos A
Name Size Bytes Class Attributes A 10x2025 162000 double
How can I fo this efficiently (definitely I know how to do this using "for loop". this is time consuming.)? Moreover, Imagine that I want to sum "u" and "v" elementwisely which both of them have the same size (so the final array must have numel(u)*numel(v) elements.) . How to do this in order to have high speed?
So you want to just normally add u and v?
B = u+v;
whos B
Name Size Bytes Class Attributes B 45x45 16200 double
Or do you want to add each element of u to each element of v, not just corresponding elements?
C = reshape(u, numel(u), 1) + reshape(v, 1, numel(v));
whos C
Name Size Bytes Class Attributes C 2025x2025 32805000 double
moh mor on 14 Dec 2023
thank you

Voss on 14 Dec 2023
f = 1:10;
x = -22:1:22;
y = -22:1:22;
[u,v] = meshgrid(x,y);
whos
Name Size Bytes Class Attributes cmdout 1x33 66 char f 1x10 80 double u 45x45 16200 double v 45x45 16200 double x 1x45 360 double y 1x45 360 double
Note that u and v are 45x45 matrices, so each has 2025 elements.
Something along these lines may be what you are looking for:
fu = f(:).*u(:).'
fu = 10×2025
-22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -22 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -44 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -66 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -88 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -110 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -132 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -154 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -176 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -198 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220 -220
uv = u(:)+v(:).'
uv = 2025×2025
-44 -43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -44 -43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -44 -43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -44 -43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -44 -43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -44 -43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -44 -43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -44 -43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -44 -43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15 -44 -43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29 -28 -27 -26 -25 -24 -23 -22 -21 -20 -19 -18 -17 -16 -15
moh mor on 14 Dec 2023
thank you
Voss on 14 Dec 2023
You're welcome!

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