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NAME SLAQGE - equilibrate a general M by N matrix A using the row and scaling factors in the vectors R and C SYNOPSIS SUBROUTINE SLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, EQUED ) CHARACTER EQUED INTEGER LDA, M, N REAL AMAX, COLCND, ROWCND REAL A( LDA, * ), C( * ), R( * ) PURPOSE SLAQGE equilibrates a general M by N matrix A using the row and scaling factors in the vectors R and C. ARGUMENTS M (input) INTEGER The number of rows of the matrix A. M >= 0. N (input) INTEGER The number of columns of the matrix A. N >= 0. A (input/output) REAL array, dimension (LDA,N) On entry, the M by N matrix A. On exit, the equili- brated matrix. See EQUED for the form of the equilibrated matrix. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(M,1). R (input) REAL array, dimension (M) The row scale factors for A. C (input) REAL array, dimension (N) The column scale factors for A. ROWCND (input) REAL Ratio of the smallest R(i) to the largest R(i). COLCND (input) REAL Ratio of the smallest C(i) to the largest C(i). AMAX (input) REAL Absolute value of largest matrix entry. EQUED (output) CHARACTER*1 Specifies the form of equilibration that was done. = 'N': No equilibration = 'R': Row equilibration, i.e., A has been premul- tiplied 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 = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C). 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.