forked from bartvdbraak/blender
4f1c674ee0
http://crd.lbl.gov/~xiaoye/SuperLU/ This is a library to solve sparse matrix systems (type A*x=B). It is able to solve large systems very FAST. Only the necessary parts of the library are included to limit file size and compilation time. This means the example files, fortran interface, test files, matlab interface, cblas library, complex number part and build system have been left out. All (gcc) warnings have been fixed too. This library will be used for LSCM UV unwrapping. With this library, LSCM unwrapping can be calculated in a split second, making the unwrapping proces much more interactive. Added OpenNL (Open Numerical Libary): http://www.loria.fr/~levy/OpenNL/ OpenNL is a library to easily construct and solve sparse linear systems. We use a stripped down version, as an interface to SuperLU. This library was kindly given to use by Bruno Levy.
332 lines
9.2 KiB
C
332 lines
9.2 KiB
C
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/*
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* -- SuperLU routine (version 3.0) --
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* Univ. of California Berkeley, Xerox Palo Alto Research Center,
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* and Lawrence Berkeley National Lab.
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* October 15, 2003
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*
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*/
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/*
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Copyright (c) 1994 by Xerox Corporation. All rights reserved.
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THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
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EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
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Permission is hereby granted to use or copy this program for any
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purpose, provided the above notices are retained on all copies.
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Permission to modify the code and to distribute modified code is
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granted, provided the above notices are retained, and a notice that
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the code was modified is included with the above copyright notice.
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*/
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#include "ssp_defs.h"
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/*
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* Function prototypes
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*/
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void susolve(int, int, float*, float*);
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void slsolve(int, int, float*, float*);
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void smatvec(int, int, int, float*, float*, float*);
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void
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sgstrs (trans_t trans, SuperMatrix *L, SuperMatrix *U,
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int *perm_c, int *perm_r, SuperMatrix *B,
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SuperLUStat_t *stat, int *info)
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{
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/*
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* Purpose
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* =======
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*
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* SGSTRS solves a system of linear equations A*X=B or A'*X=B
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* with A sparse and B dense, using the LU factorization computed by
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* SGSTRF.
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*
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* See supermatrix.h for the definition of 'SuperMatrix' structure.
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*
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* Arguments
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* =========
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*
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* trans (input) trans_t
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* Specifies the form of the system of equations:
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* = NOTRANS: A * X = B (No transpose)
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* = TRANS: A'* X = B (Transpose)
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* = CONJ: A**H * X = B (Conjugate transpose)
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*
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* L (input) SuperMatrix*
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* The factor L from the factorization Pr*A*Pc=L*U as computed by
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* sgstrf(). Use compressed row subscripts storage for supernodes,
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* i.e., L has types: Stype = SLU_SC, Dtype = SLU_S, Mtype = SLU_TRLU.
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*
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* U (input) SuperMatrix*
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* The factor U from the factorization Pr*A*Pc=L*U as computed by
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* sgstrf(). Use column-wise storage scheme, i.e., U has types:
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* Stype = SLU_NC, Dtype = SLU_S, Mtype = SLU_TRU.
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*
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* perm_c (input) int*, dimension (L->ncol)
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* Column permutation vector, which defines the
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* permutation matrix Pc; perm_c[i] = j means column i of A is
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* in position j in A*Pc.
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*
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* perm_r (input) int*, dimension (L->nrow)
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* Row permutation vector, which defines the permutation matrix Pr;
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* perm_r[i] = j means row i of A is in position j in Pr*A.
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*
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* B (input/output) SuperMatrix*
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* B has types: Stype = SLU_DN, Dtype = SLU_S, Mtype = SLU_GE.
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* On entry, the right hand side matrix.
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* On exit, the solution matrix if info = 0;
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*
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* stat (output) SuperLUStat_t*
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* Record the statistics on runtime and floating-point operation count.
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* See util.h for the definition of 'SuperLUStat_t'.
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*
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* info (output) int*
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* = 0: successful exit
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* < 0: if info = -i, the i-th argument had an illegal value
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*
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*/
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#ifdef _CRAY
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_fcd ftcs1, ftcs2, ftcs3, ftcs4;
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#endif
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#ifdef USE_VENDOR_BLAS
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float alpha = 1.0, beta = 1.0;
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float *work_col;
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#endif
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DNformat *Bstore;
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float *Bmat;
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SCformat *Lstore;
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NCformat *Ustore;
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float *Lval, *Uval;
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int fsupc, nrow, nsupr, nsupc, luptr, istart, irow;
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int i, j, k, iptr, jcol, n, ldb, nrhs;
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float *work, *rhs_work, *soln;
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flops_t solve_ops;
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void sprint_soln();
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/* Test input parameters ... */
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*info = 0;
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Bstore = B->Store;
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ldb = Bstore->lda;
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nrhs = B->ncol;
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if ( trans != NOTRANS && trans != TRANS && trans != CONJ ) *info = -1;
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else if ( L->nrow != L->ncol || L->nrow < 0 ||
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L->Stype != SLU_SC || L->Dtype != SLU_S || L->Mtype != SLU_TRLU )
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*info = -2;
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else if ( U->nrow != U->ncol || U->nrow < 0 ||
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U->Stype != SLU_NC || U->Dtype != SLU_S || U->Mtype != SLU_TRU )
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*info = -3;
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else if ( ldb < SUPERLU_MAX(0, L->nrow) ||
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B->Stype != SLU_DN || B->Dtype != SLU_S || B->Mtype != SLU_GE )
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*info = -6;
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if ( *info ) {
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i = -(*info);
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xerbla_("sgstrs", &i);
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return;
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}
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n = L->nrow;
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work = floatCalloc(n * nrhs);
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if ( !work ) ABORT("Malloc fails for local work[].");
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soln = floatMalloc(n);
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if ( !soln ) ABORT("Malloc fails for local soln[].");
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Bmat = Bstore->nzval;
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Lstore = L->Store;
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Lval = Lstore->nzval;
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Ustore = U->Store;
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Uval = Ustore->nzval;
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solve_ops = 0;
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if ( trans == NOTRANS ) {
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/* Permute right hand sides to form Pr*B */
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for (i = 0; i < nrhs; i++) {
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rhs_work = &Bmat[i*ldb];
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for (k = 0; k < n; k++) soln[perm_r[k]] = rhs_work[k];
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for (k = 0; k < n; k++) rhs_work[k] = soln[k];
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}
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/* Forward solve PLy=Pb. */
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for (k = 0; k <= Lstore->nsuper; k++) {
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fsupc = L_FST_SUPC(k);
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istart = L_SUB_START(fsupc);
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nsupr = L_SUB_START(fsupc+1) - istart;
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nsupc = L_FST_SUPC(k+1) - fsupc;
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nrow = nsupr - nsupc;
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solve_ops += nsupc * (nsupc - 1) * nrhs;
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solve_ops += 2 * nrow * nsupc * nrhs;
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if ( nsupc == 1 ) {
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for (j = 0; j < nrhs; j++) {
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rhs_work = &Bmat[j*ldb];
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luptr = L_NZ_START(fsupc);
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for (iptr=istart+1; iptr < L_SUB_START(fsupc+1); iptr++){
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irow = L_SUB(iptr);
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++luptr;
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rhs_work[irow] -= rhs_work[fsupc] * Lval[luptr];
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}
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}
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} else {
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luptr = L_NZ_START(fsupc);
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#ifdef USE_VENDOR_BLAS
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#ifdef _CRAY
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ftcs1 = _cptofcd("L", strlen("L"));
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ftcs2 = _cptofcd("N", strlen("N"));
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ftcs3 = _cptofcd("U", strlen("U"));
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STRSM( ftcs1, ftcs1, ftcs2, ftcs3, &nsupc, &nrhs, &alpha,
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&Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
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SGEMM( ftcs2, ftcs2, &nrow, &nrhs, &nsupc, &alpha,
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&Lval[luptr+nsupc], &nsupr, &Bmat[fsupc], &ldb,
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&beta, &work[0], &n );
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#else
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strsm_("L", "L", "N", "U", &nsupc, &nrhs, &alpha,
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&Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
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sgemm_( "N", "N", &nrow, &nrhs, &nsupc, &alpha,
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&Lval[luptr+nsupc], &nsupr, &Bmat[fsupc], &ldb,
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&beta, &work[0], &n );
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#endif
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for (j = 0; j < nrhs; j++) {
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rhs_work = &Bmat[j*ldb];
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work_col = &work[j*n];
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iptr = istart + nsupc;
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for (i = 0; i < nrow; i++) {
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irow = L_SUB(iptr);
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rhs_work[irow] -= work_col[i]; /* Scatter */
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work_col[i] = 0.0;
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iptr++;
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}
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}
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#else
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for (j = 0; j < nrhs; j++) {
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rhs_work = &Bmat[j*ldb];
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slsolve (nsupr, nsupc, &Lval[luptr], &rhs_work[fsupc]);
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smatvec (nsupr, nrow, nsupc, &Lval[luptr+nsupc],
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&rhs_work[fsupc], &work[0] );
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iptr = istart + nsupc;
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for (i = 0; i < nrow; i++) {
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irow = L_SUB(iptr);
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rhs_work[irow] -= work[i];
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work[i] = 0.0;
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iptr++;
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}
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}
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#endif
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} /* else ... */
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} /* for L-solve */
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#ifdef DEBUG
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printf("After L-solve: y=\n");
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sprint_soln(n, Bmat);
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#endif
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/*
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* Back solve Ux=y.
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*/
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for (k = Lstore->nsuper; k >= 0; k--) {
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fsupc = L_FST_SUPC(k);
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istart = L_SUB_START(fsupc);
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nsupr = L_SUB_START(fsupc+1) - istart;
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nsupc = L_FST_SUPC(k+1) - fsupc;
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luptr = L_NZ_START(fsupc);
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solve_ops += nsupc * (nsupc + 1) * nrhs;
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if ( nsupc == 1 ) {
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rhs_work = &Bmat[0];
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for (j = 0; j < nrhs; j++) {
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rhs_work[fsupc] /= Lval[luptr];
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rhs_work += ldb;
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}
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} else {
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#ifdef USE_VENDOR_BLAS
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#ifdef _CRAY
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ftcs1 = _cptofcd("L", strlen("L"));
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ftcs2 = _cptofcd("U", strlen("U"));
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ftcs3 = _cptofcd("N", strlen("N"));
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STRSM( ftcs1, ftcs2, ftcs3, ftcs3, &nsupc, &nrhs, &alpha,
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&Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
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#else
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strsm_("L", "U", "N", "N", &nsupc, &nrhs, &alpha,
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&Lval[luptr], &nsupr, &Bmat[fsupc], &ldb);
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#endif
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#else
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for (j = 0; j < nrhs; j++)
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susolve ( nsupr, nsupc, &Lval[luptr], &Bmat[fsupc+j*ldb] );
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#endif
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}
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for (j = 0; j < nrhs; ++j) {
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rhs_work = &Bmat[j*ldb];
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for (jcol = fsupc; jcol < fsupc + nsupc; jcol++) {
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solve_ops += 2*(U_NZ_START(jcol+1) - U_NZ_START(jcol));
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for (i = U_NZ_START(jcol); i < U_NZ_START(jcol+1); i++ ){
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irow = U_SUB(i);
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rhs_work[irow] -= rhs_work[jcol] * Uval[i];
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}
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}
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}
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} /* for U-solve */
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#ifdef DEBUG
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printf("After U-solve: x=\n");
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sprint_soln(n, Bmat);
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#endif
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/* Compute the final solution X := Pc*X. */
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for (i = 0; i < nrhs; i++) {
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rhs_work = &Bmat[i*ldb];
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for (k = 0; k < n; k++) soln[k] = rhs_work[perm_c[k]];
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for (k = 0; k < n; k++) rhs_work[k] = soln[k];
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}
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stat->ops[SOLVE] = solve_ops;
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} else { /* Solve A'*X=B or CONJ(A)*X=B */
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/* Permute right hand sides to form Pc'*B. */
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for (i = 0; i < nrhs; i++) {
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rhs_work = &Bmat[i*ldb];
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for (k = 0; k < n; k++) soln[perm_c[k]] = rhs_work[k];
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for (k = 0; k < n; k++) rhs_work[k] = soln[k];
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}
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stat->ops[SOLVE] = 0;
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for (k = 0; k < nrhs; ++k) {
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/* Multiply by inv(U'). */
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sp_strsv("U", "T", "N", L, U, &Bmat[k*ldb], stat, info);
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/* Multiply by inv(L'). */
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sp_strsv("L", "T", "U", L, U, &Bmat[k*ldb], stat, info);
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}
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/* Compute the final solution X := Pr'*X (=inv(Pr)*X) */
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for (i = 0; i < nrhs; i++) {
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rhs_work = &Bmat[i*ldb];
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for (k = 0; k < n; k++) soln[k] = rhs_work[perm_r[k]];
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for (k = 0; k < n; k++) rhs_work[k] = soln[k];
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}
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}
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SUPERLU_FREE(work);
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SUPERLU_FREE(soln);
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}
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/*
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* Diagnostic print of the solution vector
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*/
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void
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sprint_soln(int n, float *soln)
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{
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int i;
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for (i = 0; i < n; i++)
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printf("\t%d: %.4f\n", i, soln[i]);
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}
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