How to populate a matrix based on a function?

2018 3 4
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更新时间：2020 8 23
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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)

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Walter Roberson
Walter Roberson 2018-3-4

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[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;

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Shaun Pedicini
Shaun Pedicini 2018-3-4
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?
s s
s s 2020-8-23
It's so cumbersome to do this in matlab compared with the Mathematica function "Table".
Walter Roberson
Walter Roberson 2020-8-23
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;

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