Description |
MMX treats an N-D matrix of double precision values as a set of pages
of 2D matrices, and performs various matrix operations on those pages.
MMX uses multithreading over the higher dimensions to achieve good
performance. Full singleton expansion is available for most operations.
C = MMX('mult', A, B) is equivalent to the matlab loop
for i=1:N,
C(:,:,i) = A(:,:,i) * B(:,:,i);
end
Singleton expansion is enabled on all dimensions so for example if
A = randn(5,4,3,10,1);
B = randn(4,6,3,1 ,6);
C = zeros(5,6,3,10,6);
then C = mmx('mult',A,B) equivalent to
for i = 1:3
for j = 1:10
for k = 1:6
C(:,:,i,j,k) = A(:,:,i,j,1) * B(:,:,i,1,k);
end
end
end
C = MMX('mult', A, B, mod) and where mod is a modifier string, will
transpose one or both of A and B. Possible values for mod are
'tn', 'nt' and 'tt' where 't' stands for 'transposed' and 'n' for
'not-transposed'. For example
>> size(mmx('mult',randn(4,2),randn(4,2),'tn'))
ans = 2 2
C = MMX('square', A, []) will perform C = A*A'
C = MMX('square', A, [],'t') will perform C = A'*A
C = MMX('square', A, B) will perform C = 0.5*(A*B'+B*A')
C = MMX('square', A, B, 't') will perform C = 0.5*(A'*B+B'*A)
C = MMX('chol', A, []) will perform C = chol(A)
C = MMX('backslash', A, B) will perform C = A\B
Unlike other commands, 'backslash' does not support singleton
expansion. If A is square, mmx will use LU factorization, otherwise it
will use QR factorization. In the underdetermined case, (i.e. when
size(A,1) < size(A,2)), mmx will give the least-norm solution which
is equivalent to C = pinv(A)*B, unlike matlab's mldivide.
C = MMX('backslash', A, B, 'U') or MMX('backslash', A, B, 'L') will
perform C = A\B assuming that A is upper or lower triangular,
respectively.
C = MMX('backslash', A, B, 'P') will perform C = A\B assuming that A
is symmetric-positive-definite.
MMX(n) does thread control: mmx will automatically start a number of
threads equal to the number of available processors, however the
number can be set manually to n using the command mmx(n). mmx(0) will
clear the threads from memory.
IMPORTANT NOTE: The functions which assume special types of square
matrices as input ('chol' and 'backslash' for 'U','L' or 'P'
modifiers) do not check that the inputs are indeed what you say they
are, and produce no error if they are not. Caveat computator.
COMPILATION: To compile run 'build_mmx'. Type 'help build_mmx' to read
about compilation issues and options |