I want to learn how to call the built-in LAPACK/BLAS routines in MATLAB. I have experience in MATLAB and mex files but I've actually no idea how to call LAPACK or BLAS libraries. I've found the gateway routines in file exchange that simplifies the calls since I don't have to write a mex file for any function such as this one. I need any toy example to learn the basic messaging between MATLAB and these built-in libraries. Any toy example such as matrix multiplication or LU decomposition is welcome.

回答1:

If you look inside the lapack.m file from the FEX submission mentioned, you will see a couple of examples on how to use the function:

Example: SVD decomposition using DGESVD:

X = rand(4,3);
[m,n] = size(X);
C = lapack('dgesvd', ...
     'A', 'A', ...           % compute ALL left/right singular vectors
      m, n, X, m, ...        % input MxN matrix
      zeros(n,1), ...        % output S array
      zeros(m), m, ...       % output U matrix
      zeros(n), n, ....      % output VT matrix
      zeros(5*m,1), 5*m, ... % workspace array
      0 ...                  % return value
);
[s,U,VT] = C{[7,8,10]};      % extract outputs
V = VT';

(Note: the reason we used those dummy variables for output variables is because Fortran functions expect all arguments to be passed by reference, but MEX-functions in MATLAB do not allow modifying their input, thus it's written to return copies of all inputs in a cell array with any modifications)

We get:

U =
     -0.44459      -0.6264     -0.54243       0.3402
     -0.61505     0.035348      0.69537      0.37004
     -0.41561     -0.26532      0.10543     -0.86357
     -0.50132      0.73211     -0.45948    -0.039753
s =
       2.1354
      0.88509
      0.27922
V =
     -0.58777      0.20822     -0.78178
      -0.6026     -0.75743      0.25133
     -0.53981      0.61882      0.57067

Which is equivalent to MATLAB's own SVD function:

[U,S,V] = svd(X);
s = diag(S);

that gives:

U =
     -0.44459      -0.6264     -0.54243       0.3402
     -0.61505     0.035348      0.69537      0.37004
     -0.41561     -0.26532      0.10543     -0.86357
     -0.50132      0.73211     -0.45948    -0.039753
s =
       2.1354
      0.88509
      0.27922
V =
     -0.58777      0.20822     -0.78178
      -0.6026     -0.75743      0.25133
     -0.53981      0.61882      0.57067

EDIT:

For completeness, I show below an example of a MEX-function directly calling the Fortran interface of the DGESVD routine.

The good news is that MATLAB provides libmwlapack and libmwblas libraries and two corresponding header files blas.h and lapack.h we can use. In fact, there is a page in the documentation explaining the process of calling BLAS/LAPACK functions from MEX-files.

In our case, lapack.h defines the following prototype:

extern void dgesvd(char *jobu, char *jobvt, 
  ptrdiff_t *m, ptrdiff_t *n, double *a, ptrdiff_t *lda,
  double *s, double *u, ptrdiff_t *ldu, double *vt, ptrdiff_t *ldvt,
  double *work, ptrdiff_t *lwork, ptrdiff_t *info);

svd_lapack.c

#include "mex.h"
#include "lapack.h"

void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
    mwSignedIndex m, n, lwork, info=0;
    double *A, *U, *S, *VT, *work;
    double workopt = 0;
    mxArray *in;

    /* verify input/output arguments */
    if (nrhs != 1) {
        mexErrMsgTxt("One input argument required.");
    }
    if (nlhs > 3) {
        mexErrMsgTxt("Too many output arguments.");
    }
    if (!mxIsDouble(prhs[0]) || mxIsComplex(prhs[0])) {
        mexErrMsgTxt("Input matrix must be real double matrix.");
    }

    /* duplicate input matrix (since its contents will be overwritten) */
    in = mxDuplicateArray(prhs[0]);

    /* dimensions of input matrix */
    m = mxGetM(in);
    n = mxGetN(in);

    /* create output matrices */
    plhs[0] = mxCreateDoubleMatrix(m, m, mxREAL);
    plhs[1] = mxCreateDoubleMatrix((m<n)?m:n, 1, mxREAL);
    plhs[2] = mxCreateDoubleMatrix(n, n, mxREAL);

    /* get pointers to data */
    A = mxGetPr(in);
    U = mxGetPr(plhs[0]);
    S = mxGetPr(plhs[1]);
    VT = mxGetPr(plhs[2]);

    /* query and allocate the optimal workspace size */
    lwork = -1;
    dgesvd("A", "A", &m, &n, A, &m, S, U, &m, VT, &n, &workopt, &lwork, &info);
    lwork = (mwSignedIndex) workopt;
    work = (double *) mxMalloc(lwork * sizeof(double));

    /* perform SVD decomposition */
    dgesvd("A", "A", &m, &n, A, &m, S, U, &m, VT, &n, work, &lwork, &info);

    /* cleanup */
    mxFree(work);
    mxDestroyArray(in);

    /* check if call was successful */
    if (info < 0) {
        mexErrMsgTxt("Illegal values in arguments.");
    } else if (info > 0) {
        mexErrMsgTxt("Failed to converge.");
    }
}

On my 64-bit Windows, I compile the MEX-file as: mex -largeArrayDims svd_lapack.c "C:\Program Files\MATLAB\R2013a\extern\lib\win64\microsoft\libmwlapack.lib"

Here is a test:

>> X = rand(4,3);
>> [U,S,VT] = svd_lapack(X)
U =
   -0.5964    0.4049    0.6870   -0.0916
   -0.3635    0.3157   -0.3975    0.7811
   -0.3514    0.3645   -0.6022   -0.6173
   -0.6234   -0.7769   -0.0861   -0.0199
S =
    1.0337
    0.5136
    0.0811
VT =
   -0.6065   -0.5151   -0.6057
    0.0192    0.7521   -0.6588
   -0.7949    0.4112    0.4462

vs.

>> [U,S,V] = svd(X);
>> U, diag(S), V'
U =
   -0.5964    0.4049    0.6870    0.0916
   -0.3635    0.3157   -0.3975   -0.7811
   -0.3514    0.3645   -0.6022    0.6173
   -0.6234   -0.7769   -0.0861    0.0199
ans =
    1.0337
    0.5136
    0.0811
ans =
   -0.6065   -0.5151   -0.6057
    0.0192    0.7521   -0.6588
   -0.7949    0.4112    0.4462

(remember that the sign of the eigenvectors in U and V is arbitrary, so you might get flipped signs comparing the two)

回答2:

A good/pratical example of how to use SVD in matlab is explained here: Transforming captured co-ordinates into screen co-ordinates

More on how to calculate svd in objective-c with lapack is written here calculate the V from A = USVt in objective-C with SVD from LAPACK in xcode