# zlaqge.f - Man Page

SRC/zlaqge.f

## Synopsis

### Functions/Subroutines

subroutine **zlaqge** (m, n, a, lda, r, c, rowcnd, colcnd, amax, equed)**ZLAQGE** scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.

## Function/Subroutine Documentation

### subroutine zlaqge (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) r, double precision, dimension( * ) c, double precision rowcnd, double precision colcnd, double precision amax, character equed)

**ZLAQGE** scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.

**Purpose:**

ZLAQGE equilibrates a general M by N matrix A using the row and column scaling factors in the vectors R and C.

**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*16 array, dimension (LDA,N) On entry, the M by N matrix A. On exit, the equilibrated matrix. See EQUED for the form of the equilibrated matrix.

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

*R*R is DOUBLE PRECISION array, dimension (M) The row scale factors for A.

*C*C is DOUBLE PRECISION array, dimension (N) The column scale factors for A.

*ROWCND*ROWCND is DOUBLE PRECISION Ratio of the smallest R(i) to the largest R(i).

*COLCND*COLCND is DOUBLE PRECISION Ratio of the smallest C(i) to the largest C(i).

*AMAX*AMAX is DOUBLE PRECISION Absolute value of largest matrix entry.

*EQUED*EQUED is CHARACTER*1 Specifies the form of equilibration that was done. = 'N': No equilibration = 'R': Row equilibration, i.e., A has been premultiplied 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 = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).

**Internal 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.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **141** of file **zlaqge.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zlaqge(3) is an alias of zlaqge.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK