numerics/SUPERLU/dutil.c

/*! \file
Copyright (c) 2003, The Regents of the University of California, through
Lawrence Berkeley National Laboratory (subject to receipt of any required
approvals from U.S. Dept. of Energy)

All rights reserved.

The source code is distributed under BSD license, see the file License.txt
at the top-level directory.
*/

/*! @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 = (DNformat *) A->Store;
    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);
    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   = (double *) Glu->lusup;
    xlusup  = Glu->xlusup;
    ucol    = (double *) 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\n",
	   mem_usage->for_lu/1e6, mem_usage->total_needed/1e6);
    printf("Number of memory expansions: %d\n", stat->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;
}