/* read a problem from a file; use %g for integers to avoid cs_long_t conflicts */ problem *get_problem (FILE *f, double tol) { cs_cl *T, *A, *C ; cs_long_t sym, m, n, mn, nz1, nz2 ; problem *Prob ; Prob = cs_cl_calloc (1, sizeof (problem)) ; if (!Prob) return (NULL) ; T = cs_cl_load (f) ; /* load triplet matrix T from a file */ Prob->A = A = cs_cl_compress (T) ; /* A = compressed-column form of T */ cs_cl_spfree (T) ; /* clear T */ if (!cs_cl_dupl (A)) return (free_problem (Prob)) ; /* sum up duplicates */ Prob->sym = sym = is_sym (A) ; /* determine if A is symmetric */ m = A->m ; n = A->n ; mn = CS_MAX (m,n) ; nz1 = A->p [n] ; cs_cl_dropzeros (A) ; /* drop zero entries */ nz2 = A->p [n] ; if (tol > 0) cs_cl_droptol (A, tol) ; /* drop tiny entries (just to test) */ Prob->C = C = sym ? make_sym (A) : A ; /* C = A + triu(A,1)', or C=A */ if (!C) return (free_problem (Prob)) ; printf ("\n--- Matrix: %g-by-%g, nnz: %g (sym: %g: nnz %g), norm: %8.2e\n", (double) m, (double) n, (double) (A->p [n]), (double) sym, (double) (sym ? C->p [n] : 0), cs_cl_norm (C)) ; if (nz1 != nz2) printf ("zero entries dropped: %g\n", (double) (nz1 - nz2)); if (nz2 != A->p [n]) printf ("tiny entries dropped: %g\n", (double) (nz2 - A->p [n])) ; Prob->b = cs_cl_malloc (mn, sizeof (cs_complex_t)) ; Prob->x = cs_cl_malloc (mn, sizeof (cs_complex_t)) ; Prob->resid = cs_cl_malloc (mn, sizeof (cs_complex_t)) ; return ((!Prob->b || !Prob->x || !Prob->resid) ? free_problem (Prob) : Prob) ; }
/* cs_sparse: convert triplet form into compress-column form sparse matrix */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { if (nargout > 1 || nargin != 3) { mexErrMsgTxt ("Usage: A = cs_sparse(i,j,x)") ; } if (mxIsComplex (pargin [2])) { #ifndef NCOMPLEX cs_cl *A, *C, *T, Tmatrix ; T = &Tmatrix ; /* get i,j,x and copy to triplet form */ T->nz = mxGetM (pargin [0]) ; T->p = cs_dl_mex_get_int (T->nz, pargin [0], &(T->n), 1) ; T->i = cs_dl_mex_get_int (T->nz, pargin [1], &(T->m), 1) ; cs_mex_check (1, T->nz, 1, 0, 0, 1, pargin [2]) ; T->x = cs_cl_mex_get_double (T->nz, pargin [2]) ; T->nzmax = T->nz ; C = cs_cl_compress (T) ; /* create sparse matrix C */ cs_cl_dupl (C) ; /* remove duplicates from C */ cs_cl_dropzeros (C) ; /* remove zeros from C */ A = cs_cl_transpose (C, -1) ; /* A=C.' */ cs_cl_spfree (C) ; pargout [0] = cs_cl_mex_put_sparse (&A) ; /* return A */ cs_free (T->p) ; cs_free (T->i) ; cs_free (T->x) ; /* free copy of complex values*/ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dl *A, *C, *T, Tmatrix ; T = &Tmatrix ; /* get i,j,x and copy to triplet form */ T->nz = mxGetM (pargin [0]) ; T->p = cs_dl_mex_get_int (T->nz, pargin [0], &(T->n), 1) ; T->i = cs_dl_mex_get_int (T->nz, pargin [1], &(T->m), 1) ; cs_mex_check (1, T->nz, 1, 0, 0, 1, pargin [2]) ; T->x = mxGetPr (pargin [2]) ; T->nzmax = T->nz ; C = cs_dl_compress (T) ; /* create sparse matrix C */ cs_dl_dupl (C) ; /* remove duplicates from C */ cs_dl_dropzeros (C) ; /* remove zeros from C */ A = cs_dl_transpose (C, 1) ; /* A=C' */ cs_dl_spfree (C) ; pargout [0] = cs_dl_mex_put_sparse (&A) ; /* return A */ cs_free (T->p) ; cs_free (T->i) ; } }
void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { if (nargout > 1 || nargin < 2 || nargin > 4) { mexErrMsgTxt ("Usage: C = cs_add(A,B,alpha,beta)") ; } if (mxIsComplex (pargin [0]) || mxIsComplex (pargin [1]) || (nargin > 2 && mxIsComplex (pargin [2])) || (nargin > 3 && mxIsComplex (pargin [3]))) { #ifndef NCOMPLEX cs_complex_t alpha, beta ; cs_cl Amatrix, Bmatrix, *A, *B, *C, *D ; A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */ B = cs_cl_mex_get_sparse (&Bmatrix, 0, pargin [1]) ; /* get B */ alpha = (nargin < 3) ? 1 : get_complex (pargin [2]) ; /* get alpha */ beta = (nargin < 4) ? 1 : get_complex (pargin [3]) ; /* get beta */ C = cs_cl_add (A,B,alpha,beta) ; /* C = alpha*A + beta *B */ cs_cl_dropzeros (C) ; /* drop zeros */ D = cs_cl_transpose (C, 1) ; /* sort result via double transpose */ cs_cl_spfree (C) ; C = cs_cl_transpose (D, 1) ; cs_cl_spfree (D) ; pargout [0] = cs_cl_mex_put_sparse (&C) ; /* return C */ #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { double alpha, beta ; cs_dl Amatrix, Bmatrix, *A, *B, *C, *D ; A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ B = cs_dl_mex_get_sparse (&Bmatrix, 0, 1, pargin [1]) ; /* get B */ alpha = (nargin < 3) ? 1 : mxGetScalar (pargin [2]) ; /* get alpha */ beta = (nargin < 4) ? 1 : mxGetScalar (pargin [3]) ; /* get beta */ C = cs_dl_add (A,B,alpha,beta) ; /* C = alpha*A + beta *B */ cs_dl_dropzeros (C) ; /* drop zeros */ D = cs_dl_transpose (C, 1) ; /* sort result via double transpose */ cs_dl_spfree (C) ; C = cs_dl_transpose (D, 1) ; cs_dl_spfree (D) ; pargout [0] = cs_dl_mex_put_sparse (&C) ; /* return C */ } }
/* cs_lu: sparse LU factorization, with optional fill-reducing ordering */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT n, order, *p ; double tol ; if (nargout > 4 || nargin > 3 || nargin < 1) { mexErrMsgTxt ("Usage: [L,U,p,q] = cs_lu (A,tol)") ; } if (nargin == 2) /* determine tol and ordering */ { tol = mxGetScalar (pargin [1]) ; order = (nargout == 4) ? 1 : 0 ; /* amd (A+A'), or natural */ } else { tol = 1 ; order = (nargout == 4) ? 2 : 0 ; /* amd(S'*S) w/dense rows or I */ } if (mxIsComplex (pargin [0])) { #ifndef NCOMPLEX cs_cls *S ; cs_cln *N ; cs_cl Amatrix, *A, *D ; A = cs_cl_mex_get_sparse (&Amatrix, 1, pargin [0]) ; /* get A */ n = A->n ; S = cs_cl_sqr (order, A, 0) ; /* symbolic ordering, no QR bound */ N = cs_cl_lu (A, S, tol) ; /* numeric factorization */ if (!N) mexErrMsgTxt ("cs_lu failed (singular, or out of memory)") ; cs_cl_free (A->x) ; /* complex copy no longer needed */ cs_cl_dropzeros (N->L) ; /* drop zeros from L and sort it */ D = cs_cl_transpose (N->L, 1) ; cs_cl_spfree (N->L) ; N->L = cs_cl_transpose (D, 1) ; cs_cl_spfree (D) ; cs_cl_dropzeros (N->U) ; /* drop zeros from U and sort it */ D = cs_cl_transpose (N->U, 1) ; cs_cl_spfree (N->U) ; N->U = cs_cl_transpose (D, 1) ; cs_cl_spfree (D) ; p = cs_cl_pinv (N->pinv, n) ; /* p=pinv' */ pargout [0] = cs_cl_mex_put_sparse (&(N->L)) ; /* return L */ pargout [1] = cs_cl_mex_put_sparse (&(N->U)) ; /* return U */ pargout [2] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */ /* return Q */ if (nargout == 4) pargout [3] = cs_dl_mex_put_int (S->q, n, 1, 0) ; cs_cl_nfree (N) ; cs_cl_sfree (S) ; #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dls *S ; cs_dln *N ; cs_dl Amatrix, *A, *D ; A = cs_dl_mex_get_sparse (&Amatrix, 1, 1, pargin [0]) ; /* get A */ n = A->n ; S = cs_dl_sqr (order, A, 0) ; /* symbolic ordering, no QR bound */ N = cs_dl_lu (A, S, tol) ; /* numeric factorization */ if (!N) mexErrMsgTxt ("cs_lu failed (singular, or out of memory)") ; cs_dl_dropzeros (N->L) ; /* drop zeros from L and sort it */ D = cs_dl_transpose (N->L, 1) ; cs_dl_spfree (N->L) ; N->L = cs_dl_transpose (D, 1) ; cs_dl_spfree (D) ; cs_dl_dropzeros (N->U) ; /* drop zeros from U and sort it */ D = cs_dl_transpose (N->U, 1) ; cs_dl_spfree (N->U) ; N->U = cs_dl_transpose (D, 1) ; cs_dl_spfree (D) ; p = cs_dl_pinv (N->pinv, n) ; /* p=pinv' */ pargout [0] = cs_dl_mex_put_sparse (&(N->L)) ; /* return L */ pargout [1] = cs_dl_mex_put_sparse (&(N->U)) ; /* return U */ pargout [2] = cs_dl_mex_put_int (p, n, 1, 1) ; /* return p */ /* return Q */ if (nargout == 4) pargout [3] = cs_dl_mex_put_int (S->q, n, 1, 0) ; cs_dl_nfree (N) ; cs_dl_sfree (S) ; } }
/* cs_qr: sparse QR factorization */ void mexFunction ( int nargout, mxArray *pargout [ ], int nargin, const mxArray *pargin [ ] ) { CS_INT m, n, order, *p ; if (nargout > 5 || nargin != 1) { mexErrMsgTxt ("Usage: [V,beta,p,R,q] = cs_qr(A)") ; } order = (nargout == 5) ? 3 : 0 ; /* determine ordering */ m = mxGetM (pargin [0]) ; n = mxGetN (pargin [0]) ; if (m < n) mexErrMsgTxt ("A must have # rows >= # columns") ; if (mxIsComplex (pargin [0])) { #ifndef NCOMPLEX cs_cls *S ; cs_cln *N ; cs_cl Amatrix, *A, *D ; A = cs_cl_mex_get_sparse (&Amatrix, 0, pargin [0]) ; /* get A */ S = cs_cl_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/ N = cs_cl_qr (A, S) ; /* numeric QR factorization */ cs_free (A->x) ; if (!N) mexErrMsgTxt ("qr failed") ; cs_cl_dropzeros (N->L) ; /* drop zeros from V and sort */ D = cs_cl_transpose (N->L, 1) ; cs_cl_spfree (N->L) ; N->L = cs_cl_transpose (D, 1) ; cs_cl_spfree (D) ; cs_cl_dropzeros (N->U) ; /* drop zeros from R and sort */ D = cs_cl_transpose (N->U, 1) ; cs_cl_spfree (N->U) ; N->U = cs_cl_transpose (D, 1) ; cs_cl_spfree (D) ; m = N->L->m ; /* m may be larger now */ p = cs_cl_pinv (S->pinv, m) ; /* p = pinv' */ pargout [0] = cs_cl_mex_put_sparse (&(N->L)) ; /* return V */ cs_dl_mex_put_double (n, N->B, &(pargout [1])) ; /* return beta */ pargout [2] = cs_dl_mex_put_int (p, m, 1, 1) ; /* return p */ pargout [3] = cs_cl_mex_put_sparse (&(N->U)) ; /* return R */ pargout [4] = cs_dl_mex_put_int (S->q, n, 1, 0) ; /* return q */ cs_cl_nfree (N) ; cs_cl_sfree (S) ; #else mexErrMsgTxt ("complex matrices not supported") ; #endif } else { cs_dls *S ; cs_dln *N ; cs_dl Amatrix, *A, *D ; A = cs_dl_mex_get_sparse (&Amatrix, 0, 1, pargin [0]) ; /* get A */ S = cs_dl_sqr (order, A, 1) ; /* symbolic QR ordering & analysis*/ N = cs_dl_qr (A, S) ; /* numeric QR factorization */ if (!N) mexErrMsgTxt ("qr failed") ; cs_dl_dropzeros (N->L) ; /* drop zeros from V and sort */ D = cs_dl_transpose (N->L, 1) ; cs_dl_spfree (N->L) ; N->L = cs_dl_transpose (D, 1) ; cs_dl_spfree (D) ; cs_dl_dropzeros (N->U) ; /* drop zeros from R and sort */ D = cs_dl_transpose (N->U, 1) ; cs_dl_spfree (N->U) ; N->U = cs_dl_transpose (D, 1) ; cs_dl_spfree (D) ; m = N->L->m ; /* m may be larger now */ p = cs_dl_pinv (S->pinv, m) ; /* p = pinv' */ pargout [0] = cs_dl_mex_put_sparse (&(N->L)) ; /* return V */ cs_dl_mex_put_double (n, N->B, &(pargout [1])) ; /* return beta */ pargout [2] = cs_dl_mex_put_int (p, m, 1, 1) ; /* return p */ pargout [3] = cs_dl_mex_put_sparse (&(N->U)) ; /* return R */ pargout [4] = cs_dl_mex_put_int (S->q, n, 1, 0) ; /* return q */ cs_dl_nfree (N) ; cs_dl_sfree (S) ; } }