Solving an array without for loops

I am trying to replace some "for-loops" in my code. I want to take a 3-D array (denoting X,Y, and Z) and turn the 3x1 array into a 3x'length' array where each column represents a new position. Once I generate an array with all my locations, I want to apply the array's values column by column. Again, I am NOT trying to use a "for-loop" for incrementing through each column of the "posittion array".

Another way to state this problem. I have two arrays,

Array_1= [3,length]

Array_2=[3, length_2]

I want to operate all of Array_2 with each column of Array_1.

The resulting array from the operation will be the same size as Array_1.

Answer 1

[Voss]

permute might be useful. Example:

Array_1 = rand(3,10); % size of Array_1: [3, 10]
Array_2 = rand(3,15); % size of Array_2: [3, 15]

temp_Array_1 = permute(Array_1,[1 3 2]); % size of temp_Array_1: [3,  1, 10]

temp_product = temp_Array_1.*Array_2;    % size of temp_product: [3, 15, 10]

temp_sum = sum(temp_product,2);          % size of temp_sum:     [3,  1, 10]

result = permute(temp_sum,[1 3 2]);      % size of result:       [3, 10]

whos

  Name              Size               Bytes  Class     Attributes

  Array_1           3x10                 240  double              
  Array_2           3x15                 360  double              
  cmdout            1x33                  66  char                
  result            3x10                 240  double              
  temp_Array_1      3x1x10               240  double              
  temp_product      3x15x10             3600  double              
  temp_sum          3x1x10               240  double              

[Lamont]

Thank you so much for these examples.

[Voss]

You're welcome!

Answer 2

[the cyclist]

Your question is stated abstractly enough that it is difficult to give specific advice (at least for me).

I think it is possible, though, that if you permute Array_2 so that length_2 extends into dimension 2, you might be able to do vectorized operations on Array_1 and Array_2, relying on implicit expansion.

Here is a trivial example:

rng default

% Input data
A = rand(3,7);
B = rand(3,5);

% Permute B to extend into 3rd dimension, instead of 2nd
B_p = permute(B,[1 3 2]);

% Perform an example operation that relies on implicit expansion
C = sum(A.*B_p,3);

% Show that C is now the size of original A
size(C)

ans = 1×2

3 7

[Lamont]

Thank you for your response.