471 lines
13 KiB
C
471 lines
13 KiB
C
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/*! @file dutil.c
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* \brief Matrix utility functions
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*
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* <pre>
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* -- SuperLU routine (version 3.1) --
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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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* August 1, 2008
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*
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* Copyright (c) 1994 by Xerox Corporation. All rights reserved.
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*
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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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*
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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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* </pre>
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*/
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#include <math.h>
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#include "slu_ddefs.h"
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void
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dCreate_CompCol_Matrix(SuperMatrix *A, int m, int n, int nnz,
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double *nzval, int *rowind, int *colptr,
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Stype_t stype, Dtype_t dtype, Mtype_t mtype)
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{
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NCformat *Astore;
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A->Stype = stype;
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A->Dtype = dtype;
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A->Mtype = mtype;
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A->nrow = m;
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A->ncol = n;
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A->Store = (void *) SUPERLU_MALLOC( sizeof(NCformat) );
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if ( !(A->Store) ) ABORT("SUPERLU_MALLOC fails for A->Store");
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Astore = A->Store;
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Astore->nnz = nnz;
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Astore->nzval = nzval;
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Astore->rowind = rowind;
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Astore->colptr = colptr;
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}
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void
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dCreate_CompRow_Matrix(SuperMatrix *A, int m, int n, int nnz,
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double *nzval, int *colind, int *rowptr,
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Stype_t stype, Dtype_t dtype, Mtype_t mtype)
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{
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NRformat *Astore;
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A->Stype = stype;
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A->Dtype = dtype;
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A->Mtype = mtype;
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A->nrow = m;
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A->ncol = n;
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A->Store = (void *) SUPERLU_MALLOC( sizeof(NRformat) );
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if ( !(A->Store) ) ABORT("SUPERLU_MALLOC fails for A->Store");
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Astore = A->Store;
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Astore->nnz = nnz;
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Astore->nzval = nzval;
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Astore->colind = colind;
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Astore->rowptr = rowptr;
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}
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/*! \brief Copy matrix A into matrix B. */
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void
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dCopy_CompCol_Matrix(SuperMatrix *A, SuperMatrix *B)
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{
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NCformat *Astore, *Bstore;
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int ncol, nnz, i;
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B->Stype = A->Stype;
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B->Dtype = A->Dtype;
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B->Mtype = A->Mtype;
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B->nrow = A->nrow;;
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B->ncol = ncol = A->ncol;
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Astore = (NCformat *) A->Store;
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Bstore = (NCformat *) B->Store;
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Bstore->nnz = nnz = Astore->nnz;
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for (i = 0; i < nnz; ++i)
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((double *)Bstore->nzval)[i] = ((double *)Astore->nzval)[i];
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for (i = 0; i < nnz; ++i) Bstore->rowind[i] = Astore->rowind[i];
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for (i = 0; i <= ncol; ++i) Bstore->colptr[i] = Astore->colptr[i];
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}
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void
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dCreate_Dense_Matrix(SuperMatrix *X, int m, int n, double *x, int ldx,
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Stype_t stype, Dtype_t dtype, Mtype_t mtype)
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{
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DNformat *Xstore;
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X->Stype = stype;
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X->Dtype = dtype;
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X->Mtype = mtype;
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X->nrow = m;
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X->ncol = n;
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X->Store = (void *) SUPERLU_MALLOC( sizeof(DNformat) );
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if ( !(X->Store) ) ABORT("SUPERLU_MALLOC fails for X->Store");
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Xstore = (DNformat *) X->Store;
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Xstore->lda = ldx;
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Xstore->nzval = (double *) x;
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}
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void
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dCopy_Dense_Matrix(int M, int N, double *X, int ldx,
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double *Y, int ldy)
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{
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/*! \brief Copies a two-dimensional matrix X to another matrix Y.
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*/
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int i, j;
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for (j = 0; j < N; ++j)
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for (i = 0; i < M; ++i)
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Y[i + j*ldy] = X[i + j*ldx];
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}
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void
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dCreate_SuperNode_Matrix(SuperMatrix *L, int m, int n, int nnz,
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double *nzval, int *nzval_colptr, int *rowind,
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int *rowind_colptr, int *col_to_sup, int *sup_to_col,
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Stype_t stype, Dtype_t dtype, Mtype_t mtype)
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{
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SCformat *Lstore;
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L->Stype = stype;
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L->Dtype = dtype;
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L->Mtype = mtype;
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L->nrow = m;
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L->ncol = n;
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L->Store = (void *) SUPERLU_MALLOC( sizeof(SCformat) );
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if ( !(L->Store) ) ABORT("SUPERLU_MALLOC fails for L->Store");
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Lstore = L->Store;
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Lstore->nnz = nnz;
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Lstore->nsuper = col_to_sup[n];
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Lstore->nzval = nzval;
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Lstore->nzval_colptr = nzval_colptr;
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Lstore->rowind = rowind;
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Lstore->rowind_colptr = rowind_colptr;
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Lstore->col_to_sup = col_to_sup;
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Lstore->sup_to_col = sup_to_col;
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}
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/*! \brief Convert a row compressed storage into a column compressed storage.
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*/
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void
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dCompRow_to_CompCol(int m, int n, int nnz,
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double *a, int *colind, int *rowptr,
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double **at, int **rowind, int **colptr)
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{
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register int i, j, col, relpos;
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int *marker;
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/* Allocate storage for another copy of the matrix. */
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*at = (double *) doubleMalloc(nnz);
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*rowind = (int *) intMalloc(nnz);
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*colptr = (int *) intMalloc(n+1);
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marker = (int *) intCalloc(n);
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/* Get counts of each column of A, and set up column pointers */
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for (i = 0; i < m; ++i)
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for (j = rowptr[i]; j < rowptr[i+1]; ++j) ++marker[colind[j]];
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(*colptr)[0] = 0;
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for (j = 0; j < n; ++j) {
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(*colptr)[j+1] = (*colptr)[j] + marker[j];
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marker[j] = (*colptr)[j];
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}
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/* Transfer the matrix into the compressed column storage. */
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for (i = 0; i < m; ++i) {
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for (j = rowptr[i]; j < rowptr[i+1]; ++j) {
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col = colind[j];
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relpos = marker[col];
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(*rowind)[relpos] = i;
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(*at)[relpos] = a[j];
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++marker[col];
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}
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}
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SUPERLU_FREE(marker);
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}
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void
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dPrint_CompCol_Matrix(char *what, SuperMatrix *A)
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{
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NCformat *Astore;
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register int i,n;
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double *dp;
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printf("\nCompCol matrix %s:\n", what);
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printf("Stype %d, Dtype %d, Mtype %d\n", A->Stype,A->Dtype,A->Mtype);
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n = A->ncol;
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Astore = (NCformat *) A->Store;
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dp = (double *) Astore->nzval;
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printf("nrow %d, ncol %d, nnz %d\n", A->nrow,A->ncol,Astore->nnz);
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printf("nzval: ");
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for (i = 0; i < Astore->colptr[n]; ++i) printf("%f ", dp[i]);
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printf("\nrowind: ");
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for (i = 0; i < Astore->colptr[n]; ++i) printf("%d ", Astore->rowind[i]);
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printf("\ncolptr: ");
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for (i = 0; i <= n; ++i) printf("%d ", Astore->colptr[i]);
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printf("\n");
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fflush(stdout);
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}
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void
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dPrint_SuperNode_Matrix(char *what, SuperMatrix *A)
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{
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SCformat *Astore;
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register int i, j, k, c, d, n, nsup;
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double *dp;
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int *col_to_sup, *sup_to_col, *rowind, *rowind_colptr;
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printf("\nSuperNode matrix %s:\n", what);
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printf("Stype %d, Dtype %d, Mtype %d\n", A->Stype,A->Dtype,A->Mtype);
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n = A->ncol;
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Astore = (SCformat *) A->Store;
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dp = (double *) Astore->nzval;
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col_to_sup = Astore->col_to_sup;
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sup_to_col = Astore->sup_to_col;
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rowind_colptr = Astore->rowind_colptr;
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rowind = Astore->rowind;
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printf("nrow %d, ncol %d, nnz %d, nsuper %d\n",
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A->nrow,A->ncol,Astore->nnz,Astore->nsuper);
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printf("nzval:\n");
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for (k = 0; k <= Astore->nsuper; ++k) {
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c = sup_to_col[k];
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nsup = sup_to_col[k+1] - c;
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for (j = c; j < c + nsup; ++j) {
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d = Astore->nzval_colptr[j];
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for (i = rowind_colptr[c]; i < rowind_colptr[c+1]; ++i) {
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printf("%d\t%d\t%e\n", rowind[i], j, dp[d++]);
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}
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}
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}
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#if 0
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for (i = 0; i < Astore->nzval_colptr[n]; ++i) printf("%f ", dp[i]);
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#endif
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printf("\nnzval_colptr: ");
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for (i = 0; i <= n; ++i) printf("%d ", Astore->nzval_colptr[i]);
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printf("\nrowind: ");
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for (i = 0; i < Astore->rowind_colptr[n]; ++i)
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printf("%d ", Astore->rowind[i]);
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printf("\nrowind_colptr: ");
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for (i = 0; i <= n; ++i) printf("%d ", Astore->rowind_colptr[i]);
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printf("\ncol_to_sup: ");
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for (i = 0; i < n; ++i) printf("%d ", col_to_sup[i]);
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printf("\nsup_to_col: ");
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for (i = 0; i <= Astore->nsuper+1; ++i)
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printf("%d ", sup_to_col[i]);
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printf("\n");
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fflush(stdout);
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}
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void
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dPrint_Dense_Matrix(char *what, SuperMatrix *A)
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{
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DNformat *Astore = (DNformat *) A->Store;
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register int i, j, lda = Astore->lda;
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double *dp;
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printf("\nDense matrix %s:\n", what);
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printf("Stype %d, Dtype %d, Mtype %d\n", A->Stype,A->Dtype,A->Mtype);
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dp = (double *) Astore->nzval;
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printf("nrow %d, ncol %d, lda %d\n", A->nrow,A->ncol,lda);
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printf("\nnzval: ");
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for (j = 0; j < A->ncol; ++j) {
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for (i = 0; i < A->nrow; ++i) printf("%f ", dp[i + j*lda]);
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printf("\n");
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}
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printf("\n");
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fflush(stdout);
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}
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/*! \brief Diagnostic print of column "jcol" in the U/L factor.
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*/
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void
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dprint_lu_col(char *msg, int jcol, int pivrow, int *xprune, GlobalLU_t *Glu)
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{
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int i, k, fsupc;
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int *xsup, *supno;
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int *xlsub, *lsub;
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double *lusup;
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int *xlusup;
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double *ucol;
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int *usub, *xusub;
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xsup = Glu->xsup;
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supno = Glu->supno;
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lsub = Glu->lsub;
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xlsub = Glu->xlsub;
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lusup = Glu->lusup;
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xlusup = Glu->xlusup;
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ucol = Glu->ucol;
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usub = Glu->usub;
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xusub = Glu->xusub;
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printf("%s", msg);
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printf("col %d: pivrow %d, supno %d, xprune %d\n",
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jcol, pivrow, supno[jcol], xprune[jcol]);
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printf("\tU-col:\n");
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for (i = xusub[jcol]; i < xusub[jcol+1]; i++)
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printf("\t%d%10.4f\n", usub[i], ucol[i]);
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printf("\tL-col in rectangular snode:\n");
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fsupc = xsup[supno[jcol]]; /* first col of the snode */
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i = xlsub[fsupc];
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k = xlusup[jcol];
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while ( i < xlsub[fsupc+1] && k < xlusup[jcol+1] ) {
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printf("\t%d\t%10.4f\n", lsub[i], lusup[k]);
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i++; k++;
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}
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fflush(stdout);
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}
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/*! \brief Check whether tempv[] == 0. This should be true before and after calling any numeric routines, i.e., "panel_bmod" and "column_bmod".
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*/
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void dcheck_tempv(int n, double *tempv)
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{
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int i;
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for (i = 0; i < n; i++) {
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if (tempv[i] != 0.0)
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{
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fprintf(stderr,"tempv[%d] = %f\n", i,tempv[i]);
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ABORT("dcheck_tempv");
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}
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}
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}
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void
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dGenXtrue(int n, int nrhs, double *x, int ldx)
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{
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int i, j;
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for (j = 0; j < nrhs; ++j)
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for (i = 0; i < n; ++i) {
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x[i + j*ldx] = 1.0;/* + (double)(i+1.)/n;*/
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}
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}
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/*! \brief Let rhs[i] = sum of i-th row of A, so the solution vector is all 1's
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*/
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void
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dFillRHS(trans_t trans, int nrhs, double *x, int ldx,
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SuperMatrix *A, SuperMatrix *B)
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{
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NCformat *Astore;
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double *Aval;
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DNformat *Bstore;
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double *rhs;
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double one = 1.0;
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double zero = 0.0;
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int ldc;
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char transc[1];
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Astore = A->Store;
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Aval = (double *) Astore->nzval;
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Bstore = B->Store;
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rhs = Bstore->nzval;
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ldc = Bstore->lda;
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if ( trans == NOTRANS ) *(unsigned char *)transc = 'N';
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else *(unsigned char *)transc = 'T';
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sp_dgemm(transc, "N", A->nrow, nrhs, A->ncol, one, A,
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x, ldx, zero, rhs, ldc);
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}
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/*! \brief Fills a double precision array with a given value.
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*/
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void
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dfill(double *a, int alen, double dval)
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{
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register int i;
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for (i = 0; i < alen; i++) a[i] = dval;
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}
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/*! \brief Check the inf-norm of the error vector
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*/
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void dinf_norm_error(int nrhs, SuperMatrix *X, double *xtrue)
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{
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DNformat *Xstore;
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double err, xnorm;
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double *Xmat, *soln_work;
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int i, j;
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Xstore = X->Store;
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Xmat = Xstore->nzval;
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for (j = 0; j < nrhs; j++) {
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soln_work = &Xmat[j*Xstore->lda];
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err = xnorm = 0.0;
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for (i = 0; i < X->nrow; i++) {
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err = SUPERLU_MAX(err, fabs(soln_work[i] - xtrue[i]));
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xnorm = SUPERLU_MAX(xnorm, fabs(soln_work[i]));
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}
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err = err / xnorm;
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printf("||X - Xtrue||/||X|| = %e\n", err);
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}
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}
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/*! \brief Print performance of the code. */
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void
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dPrintPerf(SuperMatrix *L, SuperMatrix *U, mem_usage_t *mem_usage,
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double rpg, double rcond, double *ferr,
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double *berr, char *equed, SuperLUStat_t *stat)
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{
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SCformat *Lstore;
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NCformat *Ustore;
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double *utime;
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flops_t *ops;
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utime = stat->utime;
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ops = stat->ops;
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if ( utime[FACT] != 0. )
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printf("Factor flops = %e\tMflops = %8.2f\n", ops[FACT],
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ops[FACT]*1e-6/utime[FACT]);
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printf("Identify relaxed snodes = %8.2f\n", utime[RELAX]);
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if ( utime[SOLVE] != 0. )
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printf("Solve flops = %.0f, Mflops = %8.2f\n", ops[SOLVE],
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ops[SOLVE]*1e-6/utime[SOLVE]);
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Lstore = (SCformat *) L->Store;
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Ustore = (NCformat *) U->Store;
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printf("\tNo of nonzeros in factor L = %d\n", Lstore->nnz);
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printf("\tNo of nonzeros in factor U = %d\n", Ustore->nnz);
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printf("\tNo of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz);
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printf("L\\U MB %.3f\ttotal MB needed %.3f\n",
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mem_usage->for_lu/1e6, mem_usage->total_needed/1e6);
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printf("Number of memory expansions: %d\n", stat->expansions);
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printf("\tFactor\tMflops\tSolve\tMflops\tEtree\tEquil\tRcond\tRefine\n");
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printf("PERF:%8.2f%8.2f%8.2f%8.2f%8.2f%8.2f%8.2f%8.2f\n",
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utime[FACT], ops[FACT]*1e-6/utime[FACT],
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utime[SOLVE], ops[SOLVE]*1e-6/utime[SOLVE],
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utime[ETREE], utime[EQUIL], utime[RCOND], utime[REFINE]);
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printf("\tRpg\t\tRcond\t\tFerr\t\tBerr\t\tEquil?\n");
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printf("NUM:\t%e\t%e\t%e\t%e\t%s\n",
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rpg, rcond, ferr[0], berr[0], equed);
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}
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print_double_vec(char *what, int n, double *vec)
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{
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int i;
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printf("%s: n %d\n", what, n);
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for (i = 0; i < n; ++i) printf("%d\t%f\n", i, vec[i]);
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return 0;
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}
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|