/*! @file zlaqgs.c * \brief Equlibrates a general sprase matrix * *
* -- SuperLU routine (version 2.0) -- * Univ. of California Berkeley, Xerox Palo Alto Research Center, * and Lawrence Berkeley National Lab. * November 15, 1997 * * Modified from LAPACK routine ZLAQGE **/ /* * File name: zlaqgs.c * History: Modified from LAPACK routine ZLAQGE */ #include
* Purpose * ======= * * ZLAQGS equilibrates a general sparse M by N matrix A using the row and * scaling factors in the vectors R and C. * * See supermatrix.h for the definition of 'SuperMatrix' structure. * * Arguments * ========= * * A (input/output) SuperMatrix* * On exit, the equilibrated matrix. See EQUED for the form of * the equilibrated matrix. The type of A can be: * Stype = NC; Dtype = SLU_Z; Mtype = GE. * * R (input) double*, dimension (A->nrow) * The row scale factors for A. * * C (input) double*, dimension (A->ncol) * The column scale factors for A. * * ROWCND (input) double * Ratio of the smallest R(i) to the largest R(i). * * COLCND (input) double * Ratio of the smallest C(i) to the largest C(i). * * AMAX (input) double * Absolute value of largest matrix entry. * * EQUED (output) char* * Specifies the form of equilibration that was done. * = 'N': No equilibration * = 'R': Row equilibration, i.e., A has been premultiplied by * diag(R). * = 'C': Column equilibration, i.e., A has been postmultiplied * by diag(C). * = 'B': Both row and column equilibration, i.e., A has been * replaced by diag(R) * A * diag(C). * * Internal Parameters * =================== * * THRESH is a threshold value used to decide if row or column scaling * should be done based on the ratio of the row or column scaling * factors. If ROWCND < THRESH, row scaling is done, and if * COLCND < THRESH, column scaling is done. * * LARGE and SMALL are threshold values used to decide if row scaling * should be done based on the absolute size of the largest matrix * element. If AMAX > LARGE or AMAX < SMALL, row scaling is done. * * ===================================================================== **/ void zlaqgs(SuperMatrix *A, double *r, double *c, double rowcnd, double colcnd, double amax, char *equed) { #define THRESH (0.1) /* Local variables */ NCformat *Astore; doublecomplex *Aval; int i, j, irow; double large, small, cj; double temp; /* Quick return if possible */ if (A->nrow <= 0 || A->ncol <= 0) { *(unsigned char *)equed = 'N'; return; } Astore = A->Store; Aval = Astore->nzval; /* Initialize LARGE and SMALL. */ small = dlamch_("Safe minimum") / dlamch_("Precision"); large = 1. / small; if (rowcnd >= THRESH && amax >= small && amax <= large) { if (colcnd >= THRESH) *(unsigned char *)equed = 'N'; else { /* Column scaling */ for (j = 0; j < A->ncol; ++j) { cj = c[j]; for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) { zd_mult(&Aval[i], &Aval[i], cj); } } *(unsigned char *)equed = 'C'; } } else if (colcnd >= THRESH) { /* Row scaling, no column scaling */ for (j = 0; j < A->ncol; ++j) for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) { irow = Astore->rowind[i]; zd_mult(&Aval[i], &Aval[i], r[irow]); } *(unsigned char *)equed = 'R'; } else { /* Row and column scaling */ for (j = 0; j < A->ncol; ++j) { cj = c[j]; for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) { irow = Astore->rowind[i]; temp = cj * r[irow]; zd_mult(&Aval[i], &Aval[i], temp); } } *(unsigned char *)equed = 'B'; } return; } /* zlaqgs */