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NAME CGEEQU - compute row and column scalings intended to equili- brate an M by N matrix A and reduce its condition number SYNOPSIS SUBROUTINE CGEEQU( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO ) INTEGER INFO, LDA, M, N REAL AMAX, COLCND, ROWCND REAL C( * ), R( * ) COMPLEX A( LDA, * ) PURPOSE CGEEQU computes row and column scalings intended to equili- brate an M by N matrix A and reduce its condition number. R returns the row scale factors and C the column scale fac- tors, chosen to try to make the largest entry 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. 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) COMPLEX array, dimension (LDA,N) The M-by-N matrix whose equilibration factors are to be computed. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,M). R (output) REAL array, dimension (M) If INFO = 0 or INFO > M, R contains the row scale factors for A. C (output) REAL array, dimension (N) If INFO = 0, C contains the column scale factors for A. ROWCND (output) REAL 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) REAL If INFO = 0, COLCND contains the ratio of the smal- lest C(i) to the largest C(i). If COLCND >= 0.1, it is not worth scaling by C. AMAX (output) REAL Absolute value of largest matrix element. If AMAX is very close to overflow or very close to under- flow, the matrix should be scaled. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, and i is <= M: the i-th row of A is exactly zero > M: the (i-M)-th column of A is exactly zero