# cgeequb.f man page

cgeequb.f —

## Synopsis

### Functions/Subroutines

subroutine **cgeequb** (M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, INFO)**CGEEQUB**

## Function/Subroutine Documentation

### subroutine cgeequb (integerM, integerN, complex, dimension( lda, * )A, integerLDA, real, dimension( * )R, real, dimension( * )C, realROWCND, realCOLCND, realAMAX, integerINFO)

**CGEEQUB**

**Purpose:**

CGEEQUB 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 an absolute value of at most the radix. R(i) and C(j) are restricted to be a power of the radix 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. This routine differs from CGEEQU by restricting the scaling factors to a power of the radix. Baring over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled entries' magnitured are no longer approximately 1 but lie between sqrt(radix) and 1/sqrt(radix).

**Parameters:**-
*M*M is INTEGER The number of rows of the matrix A. M >= 0.

*N*N is INTEGER The number of columns of the matrix A. N >= 0.

*A*A is COMPLEX array, dimension (LDA,N) The M-by-N matrix whose equilibration factors are to be computed.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).

*R*R is REAL array, dimension (M) If INFO = 0 or INFO > M, R contains the row scale factors for A.

*C*C is REAL array, dimension (N) If INFO = 0, C contains the column scale factors for A.

*ROWCND*ROWCND is 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*COLCND is 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*AMAX is 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*INFO is 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

**Author:**-
Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**November 2011

Definition at line 147 of file cgeequb.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

cgeequb(3) is an alias of cgeequb.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK