/*! @file sgsequ.c * \brief Computes row and column scalings * *
* -- 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 SGEEQU **/ /* * File name: sgsequ.c * History: Modified from LAPACK routine SGEEQU */ #include
* Purpose * ======= * * SGSEQU computes row and column scalings intended to equilibrate an * M-by-N sparse matrix A and reduce its condition number. R returns the row * scale factors and C the column scale factors, chosen to try to make * the largest element in each row and column of the matrix B with * elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1. * * R(i) and C(j) are restricted to be between SMLNUM = smallest safe * number and BIGNUM = largest safe number. Use of these scaling * factors is not guaranteed to reduce the condition number of A but * works well in practice. * * See supermatrix.h for the definition of 'SuperMatrix' structure. * * Arguments * ========= * * A (input) SuperMatrix* * The matrix of dimension (A->nrow, A->ncol) whose equilibration * factors are to be computed. The type of A can be: * Stype = SLU_NC; Dtype = SLU_S; Mtype = SLU_GE. * * R (output) float*, size A->nrow * If INFO = 0 or INFO > M, R contains the row scale factors * for A. * * C (output) float*, size A->ncol * If INFO = 0, C contains the column scale factors for A. * * ROWCND (output) float* * If INFO = 0 or INFO > M, ROWCND contains the ratio of the * smallest R(i) to the largest R(i). If ROWCND >= 0.1 and * AMAX is neither too large nor too small, it is not worth * scaling by R. * * COLCND (output) float* * If INFO = 0, COLCND contains the ratio of the smallest * C(i) to the largest C(i). If COLCND >= 0.1, it is not * worth scaling by C. * * AMAX (output) float* * Absolute value of largest matrix element. If AMAX is very * close to overflow or very close to underflow, the matrix * should be scaled. * * INFO (output) int* * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * > 0: if INFO = i, and i is * <= A->nrow: the i-th row of A is exactly zero * > A->ncol: the (i-M)-th column of A is exactly zero * * ===================================================================== **/ void sgsequ(SuperMatrix *A, float *r, float *c, float *rowcnd, float *colcnd, float *amax, int *info) { /* Local variables */ NCformat *Astore; float *Aval; int i, j, irow; float rcmin, rcmax; float bignum, smlnum; extern float slamch_(char *); /* Test the input parameters. */ *info = 0; if ( A->nrow < 0 || A->ncol < 0 || A->Stype != SLU_NC || A->Dtype != SLU_S || A->Mtype != SLU_GE ) *info = -1; if (*info != 0) { i = -(*info); xerbla_("sgsequ", &i); return; } /* Quick return if possible */ if ( A->nrow == 0 || A->ncol == 0 ) { *rowcnd = 1.; *colcnd = 1.; *amax = 0.; return; } Astore = A->Store; Aval = Astore->nzval; /* Get machine constants. */ smlnum = slamch_("S"); bignum = 1. / smlnum; /* Compute row scale factors. */ for (i = 0; i < A->nrow; ++i) r[i] = 0.; /* Find the maximum element in each row. */ for (j = 0; j < A->ncol; ++j) for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) { irow = Astore->rowind[i]; r[irow] = SUPERLU_MAX( r[irow], fabs(Aval[i]) ); } /* Find the maximum and minimum scale factors. */ rcmin = bignum; rcmax = 0.; for (i = 0; i < A->nrow; ++i) { rcmax = SUPERLU_MAX(rcmax, r[i]); rcmin = SUPERLU_MIN(rcmin, r[i]); } *amax = rcmax; if (rcmin == 0.) { /* Find the first zero scale factor and return an error code. */ for (i = 0; i < A->nrow; ++i) if (r[i] == 0.) { *info = i + 1; return; } } else { /* Invert the scale factors. */ for (i = 0; i < A->nrow; ++i) r[i] = 1. / SUPERLU_MIN( SUPERLU_MAX( r[i], smlnum ), bignum ); /* Compute ROWCND = min(R(I)) / max(R(I)) */ *rowcnd = SUPERLU_MAX( rcmin, smlnum ) / SUPERLU_MIN( rcmax, bignum ); } /* Compute column scale factors */ for (j = 0; j < A->ncol; ++j) c[j] = 0.; /* Find the maximum element in each column, assuming the row scalings computed above. */ for (j = 0; j < A->ncol; ++j) for (i = Astore->colptr[j]; i < Astore->colptr[j+1]; ++i) { irow = Astore->rowind[i]; c[j] = SUPERLU_MAX( c[j], fabs(Aval[i]) * r[irow] ); } /* Find the maximum and minimum scale factors. */ rcmin = bignum; rcmax = 0.; for (j = 0; j < A->ncol; ++j) { rcmax = SUPERLU_MAX(rcmax, c[j]); rcmin = SUPERLU_MIN(rcmin, c[j]); } if (rcmin == 0.) { /* Find the first zero scale factor and return an error code. */ for (j = 0; j < A->ncol; ++j) if ( c[j] == 0. ) { *info = A->nrow + j + 1; return; } } else { /* Invert the scale factors. */ for (j = 0; j < A->ncol; ++j) c[j] = 1. / SUPERLU_MIN( SUPERLU_MAX( c[j], smlnum ), bignum); /* Compute COLCND = min(C(J)) / max(C(J)) */ *colcnd = SUPERLU_MAX( rcmin, smlnum ) / SUPERLU_MIN( rcmax, bignum ); } return; } /* sgsequ */