NAME¶

CGEEQU - computes row and column scalings intended to equilibrate 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 equilibrate an M-by-N 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.

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 smallest 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 underflow, 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