CODEWITHSUNDEEP
matlabmatrixvectorfunctional-programming
Ben Kirwin
Ben Kirwin

Reputation: 164

Is there a two-dimensional 'map' equivalent in Matlab?

I'm trying to generate a matrix by applying a function to all combinations of elements of two vectors -- something like this:

A(i,j) = fun(X(i), Y(j));

Best solution I've found is to loop over all i and j, but I know that's bad style in Matlab. Any suggestions?

Upvotes: 2

Views: 445

Answers (1)

gnovice
gnovice

Reputation: 125874

This is basically what MESHGRID is for. It replicates vectors of values into meshes, and a function can then be applied to those meshed points. You can usually take advantage of matrix and element-wise array operations to avoid using a for loop to perform certain computations on the resulting meshes. Here's an example:

>> X = 1:4;  %# A sample X vector
>> Y = 1:5;  %# A sample Y vector
>> [xMat,yMat] = meshgrid(X,Y);  %# Create 2-D meshes from the vectors X and Y
>> fun = @(x,y) x.^y;   %# A sample function, which raises each element of x to
                        %#   the corresponding element of y power
>> A = fun(xMat,yMat)   %# Apply the function to compute A

A =

           1           2           3           4
           1           4           9          16
           1           8          27          64
           1          16          81         256
           1          32         243        1024

Notice that the first input to MESHGRID (i.e. X) is treated as running along the columns, while the second input (i.e. Y) is treated as running down the rows. This is generally desired if X and Y represent Cartesian coordinates and the matrix A is going to be plotted as a 3-D surface or mesh. However, you could also use the function NDGRID if you want this behavior "flipped". Here's the same example with NDGRID:

>> [xMat,yMat] = ndgrid(X,Y);
>> A = fun(xMat,yMat)

A =

           1           1           1           1           1
           2           4           8          16          32
           3           9          27          81         243
           4          16          64         256        1024

Notice that A is now a 4-by-5 matrix instead of a 5-by-4 matrix.

Upvotes: 2

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