/*
* -- SuperLU routine (version 3.0) --
* Univ. of California Berkeley, Xerox Palo Alto Research Center,
* and Lawrence Berkeley National Lab.
* October 15, 2003
*
*/
/*
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.
*/
#include <math.h>
#include "slu_cdefs.h"
void
cCreate_CompCol_Matrix(SuperMatrix *A, int m, int n, int nnz,
complex *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
cCreate_CompRow_Matrix(SuperMatrix *A, int m, int n, int nnz,
complex *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;
}
/* Copy matrix A into matrix B. */
void
cCopy_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)
((complex *)Bstore->nzval)[i] = ((complex *)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
cCreate_Dense_Matrix(SuperMatrix *X, int m, int n, complex *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 = (complex *) x;
}
void
cCopy_Dense_Matrix(int M, int N, complex *X, int ldx,
complex *Y, int ldy)
{
/*
*
* Purpose
* =======
*
* 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
cCreate_SuperNode_Matrix(SuperMatrix *L, int m, int n, int nnz,
complex *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;
}
/*
* Convert a row compressed storage into a column compressed storage.
*/
void
cCompRow_to_CompCol(int m, int n, int nnz,
complex *a, int *colind, int *rowptr,
complex **at, int **rowind, int **colptr)
{
register int i, j, col, relpos;
int *marker;
/* Allocate storage for another copy of the matrix. */
*at = (complex *) complexMalloc(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
cPrint_CompCol_Matrix(char *what, SuperMatrix *A)
{
NCformat *Astore;
register int i,n;
float *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 = (float *) Astore->nzval;
printf("nrow %d, ncol %d, nnz %d\n", A->nrow,A->ncol,Astore->nnz);
printf("nzval: ");
for (i = 0; i < 2*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
cPrint_SuperNode_Matrix(char *what, SuperMatrix *A)
{
SCformat *Astore;
register int i, j, k, c, d, n, nsup;
float *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 = (float *) 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\t%e\n", rowind[i], j, dp[d], dp[d+1]);
d += 2;
}
}
}
#if 0
for (i = 0; i < 2*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
cPrint_Dense_Matrix(char *what, SuperMatrix *A)
{
DNformat *Astore;
register int i, j, lda = Astore->lda;
float *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 = (float *) 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 < 2*A->nrow; ++i) printf("%f ", dp[i + j*2*lda]);
printf("\n");
}
printf("\n");
fflush(stdout);
}
/*
* Diagnostic print of column "jcol" in the U/L factor.
*/
void
cprint_lu_col(char *msg, int jcol, int pivrow, int *xprune, GlobalLU_t *Glu)
{
int i, k, fsupc;
int *xsup, *supno;
int *xlsub, *lsub;
complex *lusup;
int *xlusup;
complex *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, %10.4f\n", usub[i], ucol[i].r, ucol[i].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, %10.4f\n", lsub[i], lusup[k].r, lusup[k].i);
i++; k++;
}
fflush(stdout);
}
/*
* Check whether tempv[] == 0. This should be true before and after
* calling any numeric routines, i.e., "panel_bmod" and "column_bmod".
*/
void ccheck_tempv(int n, complex *tempv)
{
int i;
for (i = 0; i < n; i++) {
if ((tempv[i].r != 0.0) || (tempv[i].i != 0.0))
{
fprintf(stderr,"tempv[%d] = {%f, %f}\n", i, tempv[i].r, tempv[i].i);
ABORT("ccheck_tempv");
}
}
}
void
cGenXtrue(int n, int nrhs, complex *x, int ldx)
{
int i, j;
for (j = 0; j < nrhs; ++j)
for (i = 0; i < n; ++i) {
x[i + j*ldx].r = 1.0;
x[i + j*ldx].i = 0.0;
}
}
/*
* Let rhs[i] = sum of i-th row of A, so the solution vector is all 1's
*/
void
cFillRHS(trans_t trans, int nrhs, complex *x, int ldx,
SuperMatrix *A, SuperMatrix *B)
{
NCformat *Astore;
complex *Aval;
DNformat *Bstore;
complex *rhs;
complex one = {1.0, 0.0};
complex zero = {0.0, 0.0};
int ldc;
char transc[1];
Astore = A->Store;
Aval = (complex *) Astore->nzval;
Bstore = B->Store;
rhs = Bstore->nzval;
ldc = Bstore->lda;
if ( trans == NOTRANS ) *(unsigned char *)transc = 'N';
else *(unsigned char *)transc = 'T';
sp_cgemm(transc, "N", A->nrow, nrhs, A->ncol, one, A,
x, ldx, zero, rhs, ldc);
}
/*
* Fills a complex precision array with a given value.
*/
void
cfill(complex *a, int alen, complex dval)
{
register int i;
for (i = 0; i < alen; i++) a[i] = dval;
}
/*
* Check the inf-norm of the error vector
*/
void cinf_norm_error(int nrhs, SuperMatrix *X, complex *xtrue)
{
DNformat *Xstore;
float err, xnorm;
complex *Xmat, *soln_work;
complex temp;
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++) {
c_sub(&temp, &soln_work[i], &xtrue[i]);
err = SUPERLU_MAX(err, c_abs(&temp));
xnorm = SUPERLU_MAX(xnorm, c_abs(&soln_work[i]));
}
err = err / xnorm;
printf("||X - Xtrue||/||X|| = %e\n", err);
}
}
/* Print performance of the code. */
void
cPrintPerf(SuperMatrix *L, SuperMatrix *U, mem_usage_t *mem_usage,
float rpg, float rcond, float *ferr,
float *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_complex_vec(char *what, int n, complex *vec)
{
int i;
printf("%s: n %d\n", what, n);
for (i = 0; i < n; ++i) printf("%d\t%f%f\n", i, vec[i].r, vec[i].i);
return 0;
}
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