dutil.c

来自「SuperLU is a general purpose library for」· C语言 代码 · 共 473 行

/*! @file dutil.c
 * \brief Matrix utility functions
 *
 * <pre>
 * -- SuperLU routine (version 3.1) --
 * Univ. of California Berkeley, Xerox Palo Alto Research Center,
 * and Lawrence Berkeley National Lab.
 * August 1, 2008
 *
 * Copyright (c) 1994 by Xerox Corporation.  All rights reserved.
 *
 * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
 * EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.
 * 
 * Permission is hereby granted to use or copy this program for any
 * purpose, provided the above notices are retained on all copies.
 * Permission to modify the code and to distribute modified code is
 * granted, provided the above notices are retained, and a notice that
 * the code was modified is included with the above copyright notice.
 * </pre>
 */


#include <math.h>
#include "slu_ddefs.h"

void
dCreate_CompCol_Matrix(SuperMatrix *A, int m, int n, int nnz, 
		       double *nzval, int *rowind, int *colptr,
		       Stype_t stype, Dtype_t dtype, Mtype_t mtype)
{
    NCformat *Astore;

    A->Stype = stype;
    A->Dtype = dtype;
    A->Mtype = mtype;
    A->nrow = m;
    A->ncol = n;
    A->Store = (void *) SUPERLU_MALLOC( sizeof(NCformat) );
    if ( !(A->Store) ) ABORT("SUPERLU_MALLOC fails for A->Store");
    Astore = A->Store;
    Astore->nnz = nnz;
    Astore->nzval = nzval;
    Astore->rowind = rowind;
    Astore->colptr = colptr;
}

void
dCreate_CompRow_Matrix(SuperMatrix *A, int m, int n, int nnz, 
		       double *nzval, int *colind, int *rowptr,
		       Stype_t stype, Dtype_t dtype, Mtype_t mtype)
{
    NRformat *Astore;

    A->Stype = stype;
    A->Dtype = dtype;
    A->Mtype = mtype;
    A->nrow = m;
    A->ncol = n;
    A->Store = (void *) SUPERLU_MALLOC( sizeof(NRformat) );
    if ( !(A->Store) ) ABORT("SUPERLU_MALLOC fails for A->Store");
    Astore = A->Store;
    Astore->nnz = nnz;
    Astore->nzval = nzval;
    Astore->colind = colind;
    Astore->rowptr = rowptr;
}

/*! \brief Copy matrix A into matrix B. */
void
dCopy_CompCol_Matrix(SuperMatrix *A, SuperMatrix *B)
{
    NCformat *Astore, *Bstore;
    int      ncol, nnz, i;

    B->Stype = A->Stype;
    B->Dtype = A->Dtype;
    B->Mtype = A->Mtype;
    B->nrow  = A->nrow;;
    B->ncol  = ncol = A->ncol;
    Astore   = (NCformat *) A->Store;
    Bstore   = (NCformat *) B->Store;
    Bstore->nnz = nnz = Astore->nnz;
    for (i = 0; i < nnz; ++i)
	((double *)Bstore->nzval)[i] = ((double *)Astore->nzval)[i];
    for (i = 0; i < nnz; ++i) Bstore->rowind[i] = Astore->rowind[i];
    for (i = 0; i <= ncol; ++i) Bstore->colptr[i] = Astore->colptr[i];
}


void
dCreate_Dense_Matrix(SuperMatrix *X, int m, int n, double *x, int ldx,
		    Stype_t stype, Dtype_t dtype, Mtype_t mtype)
{
    DNformat    *Xstore;
    
    X->Stype = stype;
    X->Dtype = dtype;
    X->Mtype = mtype;
    X->nrow = m;
    X->ncol = n;
    X->Store = (void *) SUPERLU_MALLOC( sizeof(DNformat) );
    if ( !(X->Store) ) ABORT("SUPERLU_MALLOC fails for X->Store");
    Xstore = (DNformat *) X->Store;
    Xstore->lda = ldx;
    Xstore->nzval = (double *) x;
}

void
dCopy_Dense_Matrix(int M, int N, double *X, int ldx,
			double *Y, int ldy)
{
/*! \brief Copies a two-dimensional matrix X to another matrix Y.
 */
    int    i, j;
    
    for (j = 0; j < N; ++j)
        for (i = 0; i < M; ++i)
            Y[i + j*ldy] = X[i + j*ldx];
}

void
dCreate_SuperNode_Matrix(SuperMatrix *L, int m, int n, int nnz, 
			double *nzval, int *nzval_colptr, int *rowind,
			int *rowind_colptr, int *col_to_sup, int *sup_to_col,
			Stype_t stype, Dtype_t dtype, Mtype_t mtype)
{
    SCformat *Lstore;

    L->Stype = stype;
    L->Dtype = dtype;
    L->Mtype = mtype;
    L->nrow = m;
    L->ncol = n;
    L->Store = (void *) SUPERLU_MALLOC( sizeof(SCformat) );
    if ( !(L->Store) ) ABORT("SUPERLU_MALLOC fails for L->Store");
    Lstore = L->Store;
    Lstore->nnz = nnz;
    Lstore->nsuper = col_to_sup[n];
    Lstore->nzval = nzval;
    Lstore->nzval_colptr = nzval_colptr;
    Lstore->rowind = rowind;
    Lstore->rowind_colptr = rowind_colptr;
    Lstore->col_to_sup = col_to_sup;
    Lstore->sup_to_col = sup_to_col;

}


/*! \brief Convert a row compressed storage into a column compressed storage.
 */
void
dCompRow_to_CompCol(int m, int n, int nnz, 
		    double *a, int *colind, int *rowptr,
		    double **at, int **rowind, int **colptr)
{
    register int i, j, col, relpos;
    int *marker;

    /* Allocate storage for another copy of the matrix. */
    *at = (double *) doubleMalloc(nnz);
    *rowind = (int *) intMalloc(nnz);
    *colptr = (int *) intMalloc(n+1);
    marker = (int *) intCalloc(n);
    
    /* Get counts of each column of A, and set up column pointers */
    for (i = 0; i < m; ++i)
	for (j = rowptr[i]; j < rowptr[i+1]; ++j) ++marker[colind[j]];
    (*colptr)[0] = 0;
    for (j = 0; j < n; ++j) {
	(*colptr)[j+1] = (*colptr)[j] + marker[j];
	marker[j] = (*colptr)[j];
    }

    /* Transfer the matrix into the compressed column storage. */
    for (i = 0; i < m; ++i) {
	for (j = rowptr[i]; j < rowptr[i+1]; ++j) {
	    col = colind[j];
	    relpos = marker[col];
	    (*rowind)[relpos] = i;
	    (*at)[relpos] = a[j];
	    ++marker[col];
	}
    }

    SUPERLU_FREE(marker);
}


void
dPrint_CompCol_Matrix(char *what, SuperMatrix *A)
{
    NCformat     *Astore;
    register int i,n;
    double       *dp;
    
    printf("\nCompCol matrix %s:\n", what);
    printf("Stype %d, Dtype %d, Mtype %d\n", A->Stype,A->Dtype,A->Mtype);
    n = A->ncol;
    Astore = (NCformat *) A->Store;
    dp = (double *) Astore->nzval;
    printf("nrow %d, ncol %d, nnz %d\n", A->nrow,A->ncol,Astore->nnz);
    printf("nzval: ");
    for (i = 0; i < Astore->colptr[n]; ++i) printf("%f  ", dp[i]);
    printf("\nrowind: ");
    for (i = 0; i < Astore->colptr[n]; ++i) printf("%d  ", Astore->rowind[i]);
    printf("\ncolptr: ");
    for (i = 0; i <= n; ++i) printf("%d  ", Astore->colptr[i]);
    printf("\n");
    fflush(stdout);
}

void
dPrint_SuperNode_Matrix(char *what, SuperMatrix *A)
{
    SCformat     *Astore;
    register int i, j, k, c, d, n, nsup;
    double       *dp;
    int *col_to_sup, *sup_to_col, *rowind, *rowind_colptr;
    
    printf("\nSuperNode matrix %s:\n", what);
    printf("Stype %d, Dtype %d, Mtype %d\n", A->Stype,A->Dtype,A->Mtype);
    n = A->ncol;
    Astore = (SCformat *) A->Store;
    dp = (double *) Astore->nzval;
    col_to_sup = Astore->col_to_sup;
    sup_to_col = Astore->sup_to_col;
    rowind_colptr = Astore->rowind_colptr;
    rowind = Astore->rowind;
    printf("nrow %d, ncol %d, nnz %d, nsuper %d\n", 
	   A->nrow,A->ncol,Astore->nnz,Astore->nsuper);
    printf("nzval:\n");
    for (k = 0; k <= Astore->nsuper; ++k) {
      c = sup_to_col[k];
      nsup = sup_to_col[k+1] - c;
      for (j = c; j < c + nsup; ++j) {
	d = Astore->nzval_colptr[j];
	for (i = rowind_colptr[c]; i < rowind_colptr[c+1]; ++i) {
	  printf("%d\t%d\t%e\n", rowind[i], j, dp[d++]);
	}
      }
    }
#if 0
    for (i = 0; i < Astore->nzval_colptr[n]; ++i) printf("%f  ", dp[i]);
#endif
    printf("\nnzval_colptr: ");
    for (i = 0; i <= n; ++i) printf("%d  ", Astore->nzval_colptr[i]);
    printf("\nrowind: ");
    for (i = 0; i < Astore->rowind_colptr[n]; ++i) 
        printf("%d  ", Astore->rowind[i]);
    printf("\nrowind_colptr: ");
    for (i = 0; i <= n; ++i) printf("%d  ", Astore->rowind_colptr[i]);
    printf("\ncol_to_sup: ");
    for (i = 0; i < n; ++i) printf("%d  ", col_to_sup[i]);
    printf("\nsup_to_col: ");
    for (i = 0; i <= Astore->nsuper+1; ++i) 
        printf("%d  ", sup_to_col[i]);
    printf("\n");
    fflush(stdout);
}

void
dPrint_Dense_Matrix(char *what, SuperMatrix *A)
{
    DNformat     *Astore;
    register int i, j, lda = Astore->lda;
    double       *dp;
    
    printf("\nDense matrix %s:\n", what);
    printf("Stype %d, Dtype %d, Mtype %d\n", A->Stype,A->Dtype,A->Mtype);
    Astore = (DNformat *) A->Store;
    dp = (double *) Astore->nzval;
    printf("nrow %d, ncol %d, lda %d\n", A->nrow,A->ncol,lda);
    printf("\nnzval: ");
    for (j = 0; j < A->ncol; ++j) {
        for (i = 0; i < A->nrow; ++i) printf("%f  ", dp[i + j*lda]);
        printf("\n");
    }
    printf("\n");
    fflush(stdout);
}

/*! \brief Diagnostic print of column "jcol" in the U/L factor.
 */
void
dprint_lu_col(char *msg, int jcol, int pivrow, int *xprune, GlobalLU_t *Glu)
{
    int     i, k, fsupc;
    int     *xsup, *supno;
    int     *xlsub, *lsub;
    double  *lusup;
    int     *xlusup;
    double  *ucol;
    int     *usub, *xusub;

    xsup    = Glu->xsup;
    supno   = Glu->supno;
    lsub    = Glu->lsub;
    xlsub   = Glu->xlsub;
    lusup   = Glu->lusup;
    xlusup  = Glu->xlusup;
    ucol    = Glu->ucol;
    usub    = Glu->usub;
    xusub   = Glu->xusub;
    
    printf("%s", msg);
    printf("col %d: pivrow %d, supno %d, xprune %d\n", 
	   jcol, pivrow, supno[jcol], xprune[jcol]);
    
    printf("\tU-col:\n");
    for (i = xusub[jcol]; i < xusub[jcol+1]; i++)
	printf("\t%d%10.4f\n", usub[i], ucol[i]);
    printf("\tL-col in rectangular snode:\n");
    fsupc = xsup[supno[jcol]];	/* first col of the snode */
    i = xlsub[fsupc];
    k = xlusup[jcol];
    while ( i < xlsub[fsupc+1] && k < xlusup[jcol+1] ) {
	printf("\t%d\t%10.4f\n", lsub[i], lusup[k]);
	i++; k++;
    }
    fflush(stdout);
}


/*! \brief Check whether tempv[] == 0. This should be true before and after calling any numeric routines, i.e., "panel_bmod" and "column_bmod". 
 */
void dcheck_tempv(int n, double *tempv)
{
    int i;
	
    for (i = 0; i < n; i++) {
	if (tempv[i] != 0.0) 
	{
	    fprintf(stderr,"tempv[%d] = %f\n", i,tempv[i]);
	    ABORT("dcheck_tempv");
	}
    }
}


void
dGenXtrue(int n, int nrhs, double *x, int ldx)
{
    int  i, j;
    for (j = 0; j < nrhs; ++j)
	for (i = 0; i < n; ++i) {
	    x[i + j*ldx] = 1.0;/* + (double)(i+1.)/n;*/
	}
}

/*! \brief Let rhs[i] = sum of i-th row of A, so the solution vector is all 1's
 */
void
dFillRHS(trans_t trans, int nrhs, double *x, int ldx,
         SuperMatrix *A, SuperMatrix *B)
{
    NCformat *Astore;
    double   *Aval;
    DNformat *Bstore;
    double   *rhs;
    double one = 1.0;
    double zero = 0.0;
    int      ldc;
    char transc[1];

    Astore = A->Store;
    Aval   = (double *) Astore->nzval;
    Bstore = B->Store;
    rhs    = Bstore->nzval;
    ldc    = Bstore->lda;
    
    if ( trans == NOTRANS ) *(unsigned char *)transc = 'N';
    else *(unsigned char *)transc = 'T';

    sp_dgemm(transc, "N", A->nrow, nrhs, A->ncol, one, A,
	     x, ldx, zero, rhs, ldc);

}

/*! \brief Fills a double precision array with a given value.
 */
void 
dfill(double *a, int alen, double dval)
{
    register int i;
    for (i = 0; i < alen; i++) a[i] = dval;
}



/*! \brief Check the inf-norm of the error vector 
 */
void dinf_norm_error(int nrhs, SuperMatrix *X, double *xtrue)
{
    DNformat *Xstore;
    double err, xnorm;
    double *Xmat, *soln_work;
    int i, j;

    Xstore = X->Store;
    Xmat = Xstore->nzval;

    for (j = 0; j < nrhs; j++) {
      soln_work = &Xmat[j*Xstore->lda];
      err = xnorm = 0.0;
      for (i = 0; i < X->nrow; i++) {
	err = SUPERLU_MAX(err, fabs(soln_work[i] - xtrue[i]));
	xnorm = SUPERLU_MAX(xnorm, fabs(soln_work[i]));
      }
      err = err / xnorm;
      printf("||X - Xtrue||/||X|| = %e\n", err);
    }
}



/*! \brief Print performance of the code. */
void
dPrintPerf(SuperMatrix *L, SuperMatrix *U, mem_usage_t *mem_usage,
           double rpg, double rcond, double *ferr,
           double *berr, char *equed, SuperLUStat_t *stat)
{
    SCformat *Lstore;
    NCformat *Ustore;
    double   *utime;
    flops_t  *ops;
    
    utime = stat->utime;
    ops   = stat->ops;
    
    if ( utime[FACT] != 0. )
	printf("Factor flops = %e\tMflops = %8.2f\n", ops[FACT],
	       ops[FACT]*1e-6/utime[FACT]);
    printf("Identify relaxed snodes	= %8.2f\n", utime[RELAX]);
    if ( utime[SOLVE] != 0. )
	printf("Solve flops = %.0f, Mflops = %8.2f\n", ops[SOLVE],
	       ops[SOLVE]*1e-6/utime[SOLVE]);
    
    Lstore = (SCformat *) L->Store;
    Ustore = (NCformat *) U->Store;
    printf("\tNo of nonzeros in factor L = %d\n", Lstore->nnz);
    printf("\tNo of nonzeros in factor U = %d\n", Ustore->nnz);
    printf("\tNo of nonzeros in L+U = %d\n", Lstore->nnz + Ustore->nnz);
	
    printf("L\\U MB %.3f\ttotal MB needed %.3f\texpansions %d\n",
	   mem_usage->for_lu/1e6, mem_usage->total_needed/1e6,
	   mem_usage->expansions);
	
    printf("\tFactor\tMflops\tSolve\tMflops\tEtree\tEquil\tRcond\tRefine\n");
    printf("PERF:%8.2f%8.2f%8.2f%8.2f%8.2f%8.2f%8.2f%8.2f\n",
	   utime[FACT], ops[FACT]*1e-6/utime[FACT],
	   utime[SOLVE], ops[SOLVE]*1e-6/utime[SOLVE],
	   utime[ETREE], utime[EQUIL], utime[RCOND], utime[REFINE]);
    
    printf("\tRpg\t\tRcond\t\tFerr\t\tBerr\t\tEquil?\n");
    printf("NUM:\t%e\t%e\t%e\t%e\t%s\n",
	   rpg, rcond, ferr[0], berr[0], equed);
    
}




print_double_vec(char *what, int n, double *vec)
{
    int i;
    printf("%s: n %d\n", what, n);
    for (i = 0; i < n; ++i) printf("%d\t%f\n", i, vec[i]);
    return 0;
}