How to populate a matrix based on a function?

I have a 2d matrix of width 256 and height 128.

I also have some theoretical function: 127.5 * cos(pi * row_index) + col_index

I want to populate the cells of the matrix using this function so that the row_index/col_index pull from each cell as it is computed.

Ideally I need to use functions that can run against each cell in a matrix and also have access to the following variables:

1. Current Column Index
2. Current Row Index
3. Current Cell Value (I'm not using this in the earlier example, but I'd like to be able to use it in the future)

Answer 1

[Walter Roberson]

[RowIndices, ColumnIndices] = ndgrid(1:size(YourArray,1), 1:size(YourArray,2));

population_function = @(col_idx, row_idx, CurrentCellValue) 127.5 * cos(pi * row_index) + col_index;

populated_matrix = arrayfun(population_function, ColumnIndices, RowIndices, YourArray);

... But you will find that it is more efficient to just use vectorization:

[col_index, row_index] = ndgrid(1:size(YourArray,1), 1:size(YourArray,2));
populated_matrix = 127.5 * cos(pi * row_index) + col_index;

[Shaun Pedicini]

Thanks Walter, just to be clear on your vectorization example:

[col_index, row_index] = ndgrid(1:size(YourArray,1), 1:size(YourArray,2));
populated_matrix = 127.5 * cos(pi * row_index) + col_index;

It should be the other way around - [row_index, col_index], since indices are [row,col] in matlab, right?

[Walter Roberson]

Ah, yes, that is correct.

[s s]

It's so cumbersome to do this in matlab compared with the Mathematica function "Table".

[Walter Roberson]

You can also use

col_index = 1:size(YourArray,1);
row_index = 1:size(YourArray,2);
populated_matrix = 127.5 * cos(pi * row_index(:)) + col_index;