Multiplying a 2d matrix with each slice of 3d matrix

What is the fastest way multiply a 2d matrix with each slice of a 3d matrix?

x = rand(1000,200);
F = rand(100,1000,10);

b = zeros(100,200,10);
for i = 1:10
    b(:,:,i) = F(:,:,i)*x;
end

[Shravankumar P]

I would like to have the transposed F. i.e., F=F'; is it possible.

[Matt J]

@Shravankumar

MTIMESX has input flags that let you say whether you want the multiplication with F, F', or F.'

Answer 1

[Andrei Bobrov]

f1 = size(F);
x1 = size(x);
b = reshape(sum(bsxfun(@times,reshape(F,[f1(1),1,f1(2:3)]),...
                      reshape(x',1,x1(2),[])),3),f1(1),x1(2),[]);

[Ray M]

Great Solution, the solution you have provided is equivalent to:

for i = 1:whatever

b(:,:,i) = F(:,:,i) * x;

end

How would you produce the trasnpose multiplication effect (assuming correct sizes)?

for i = 1:whatever

b(:,:,i) = x * F(:,:,i);

end

[Ray M]

Nevermind! I got it :)

Answer 2

[Steven Lord]

In release R2020b we introduced the pagemtimes function for this purpose.

[Image Analyst]

Too bad it doesn't work with uint8 images (yet)

% Works
maskedRgbImage = bsxfun(@times, rgbImage, cast(mask, 'like', rgbImage));
% Doesn't work
maskedRgbImage = pagemtimes(rgbImage, cast(mask, 'like', rgbImage)); % R2020b and later.

Error using pagemtimes

Invalid data types. Input arrays must be double or single.

Error in test (line 10)

maskedRgbImage = pagemtimes(rgbImage, cast(mask, 'like', rgbImage)); % R2020b and later.

It would be great for using a logical 2-D mask image and a 2-D gray scale, or 3-D color, or N-d volumetric image. Can you put in that suggestion?

[Ray M]

I am not sure if this meant to be a reply to my question under Andrei Bobrov solution, but it does not appear so. I am simply interested in performing a single matrix multiplication by slices of a 3D matrix with the use of bsxfun as follows:

mat_mxn * 3Dmat_nxkxl

and

3Dmat_mxnxk * mat_nxh

1) We note that A * B ~= B * A. Note that Andrei Bobrov solution just does 3Dmat_mxnxk * mat_mxh.

2) @times in bsxfun perform .* not * and that is why Andrei Bobrov does a sum as well.

Thanks

[Steven Lord]

@Image Analyst Your bsxfun call is calling times not mtimes. times can work with implicit expansion.

A = int16(magic(4));
B = repmat(A, 1, 1, 3);
C = A.*B

C = 4×4×3 int16 array
C(:,:,1) =

   256     4     9   169
    25   121   100    64
    81    49    36   144
    16   196   225     1


C(:,:,2) =

   256     4     9   169
    25   121   100    64
    81    49    36   144
    16   196   225     1


C(:,:,3) =

   256     4     9   169
    25   121   100    64
    81    49    36   144
    16   196   225     1

mtimes isn't fully defined for integer arrays. If mtimes doesn't work pagemtimes probably shouldn't.

D = A*A % errors

Error using *
MTIMES (*) is not fully supported for integer classes. At least one argument must be scalar.

Answer 3

[Edric Ellis]

With Parallel Computing Toolbox, you can perform this on the GPU using PAGEFUN.

[Nils Melchert]

Is there the possibility to get a minimal example for exactly this use case? I am struggling with the same thing.

Answer 4

[Matt J]

See MTIMESX.

[Matt J]

Søren sønderby Commented:

I briefly looked at MTIMESX but I didn't find any installation instructions for OSX.

How would you do it using GPU?

[Matt J]

How would you do it using GPU?

You could make a GPU implementation of the for-loop in your original post. Simply pre-convert F, x, and b to gpuArray objects.

[Image Analyst]

To use GPU computing you also need the Parallel Computing Toolbox. Have you purchased that?

[Matt J]

Also, for small array dimensions like what you've shown, a GPU-driven version might not be faster than on the CPU. Matrix multiplications in MATLAB are already very well-multithreaded on the CPU.

[Søren sønderby]

I have the GPU toolbox (academic license). Do you have any experience installing MTIMESX on os x?

[Image Analyst]

The Mathworks does not make any toolbox by the name "GPU Toolbox". If you have one, it must have been written by some third party company.

[Søren sønderby]

I meant i have the Parallel Computing Toolbox

[Matt J]

Do you have any experience installing MTIMESX on os x

Don't see why it would be different than Windows, except I'm not sure that SPEEDOMP would be supported. What happens when you try to compile with mtimesx_build?

[Søren sønderby]

It fails with the following output:

Non-PC auto build is not currently supported. You will have to
manually compile the mex routine. E.g., as follows:

>> blas_lib = 'the_actual_path_and_name_of_your_systems_BLAS_library'
>> mex('-DDEFINEUNIX','mtimesx.c',blas_lib)

or

>> mex('-DDEFINEUNIX','-largeArrayDims','mtimesx.c',blas_lib)

I tried to google the blas library path on osx 10.7.5 with no luck so far.

Answer 5

[Image Analyst]

You can do it easily if the number of rows and columns in your 3D and 2D match, which they don't in your example:

rows = 1000;
columns = 200;
slices = 10;
x = rand(rows, columns);
F = rand(rows, columns, slices);
b = zeros(rows, columns, slices);
for slice = 1 : slices
    b(:,:, slice) = F(:,:, slice) .* x; % Use dot star, not just star.
end

If the number of rows and columns are different you need to make some decisions about exactly where you want to multiply, if one is smaller than the other, or one extends out past the other.

[Image Analyst]

Alternate way. Not sure which is faster:

% Mask the 3D image called "image3D" with 2D image called "mask".
masked3DImage = bsxfun(@times, image3D, cast(mask, class(image3D)));