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    <p>If you look inside the <em><a href="http://www.mathworks.com/matlabcentral/fileexchange/16777-lapack/content/lapack.m" rel="nofollow noreferrer">lapack.m</a></em> file from the FEX submission mentioned, you will see a couple of examples on how to use the function:</p> <h3>Example: SVD decomposition using <a href="http://www.netlib.org/lapack/explore-html/dgesvd.f.html" rel="nofollow noreferrer">DGESVD</a>:</h3> <pre><code>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'; </code></pre> <p><em>(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)</em></p> <p>We get:</p> <pre><code>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 </code></pre> <p>Which is equivalent to MATLAB's own <a href="http://www.mathworks.com/help/matlab/ref/svd.html" rel="nofollow noreferrer">SVD</a> function:</p> <pre><code>[U,S,V] = svd(X); s = diag(S); </code></pre> <p>that gives:</p> <pre><code>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 </code></pre> <hr> <h1>EDIT:</h1> <p>For completeness, I show below an example of a MEX-function directly calling the Fortran interface of the DGESVD routine.</p> <p>The good news is that MATLAB provides <code>libmwlapack</code> and <code>libmwblas</code> libraries and two corresponding header files <code>blas.h</code> and <code>lapack.h</code> we can use. In fact, there is a page in the documentation explaining the process of <a href="http://www.mathworks.com/help/matlab/matlab_external/calling-lapack-and-blas-functions-from-mex-files.html" rel="nofollow noreferrer">calling BLAS/LAPACK functions from MEX-files</a>.</p> <p>In our case, <code>lapack.h</code> defines the following prototype:</p> <pre><code>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); </code></pre> <h3>svd_lapack.c</h3> <pre><code>#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 &gt; 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&lt;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", &amp;m, &amp;n, A, &amp;m, S, U, &amp;m, VT, &amp;n, &amp;workopt, &amp;lwork, &amp;info); lwork = (mwSignedIndex) workopt; work = (double *) mxMalloc(lwork * sizeof(double)); /* perform SVD decomposition */ dgesvd("A", "A", &amp;m, &amp;n, A, &amp;m, S, U, &amp;m, VT, &amp;n, work, &amp;lwork, &amp;info); /* cleanup */ mxFree(work); mxDestroyArray(in); /* check if call was successful */ if (info &lt; 0) { mexErrMsgTxt("Illegal values in arguments."); } else if (info &gt; 0) { mexErrMsgTxt("Failed to converge."); } } </code></pre> <p>On my 64-bit Windows, I compile the MEX-file as: <code>mex -largeArrayDims svd_lapack.c "C:\Program Files\MATLAB\R2013a\extern\lib\win64\microsoft\libmwlapack.lib"</code></p> <p>Here is a test:</p> <pre><code>&gt;&gt; X = rand(4,3); &gt;&gt; [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 </code></pre> <p>vs.</p> <pre><code>&gt;&gt; [U,S,V] = svd(X); &gt;&gt; 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 </code></pre> <p><em>(remember that the sign of the eigenvectors in <code>U</code> and <code>V</code> is arbitrary, so you might get flipped signs comparing the two)</em></p>
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    2. CO@Acorbe: I added an implementation of a MEX-file that directly calls the Fortran functions, so you can try it yourself and compare the speed... I did a quick test, and MATLAB's own `svd` is about twice as fast. I think this in part due to the overhead of calling MEX-functions as opposed to a builtin function. The advantage of the mentioned FEX submission is that you don't have to write a MEX-file for each LAPACK routine, their solution takes care of all the boilerplate code for you, into a single function!
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