NAME¶

CLAQGB - equilibrates a general M by N band matrix A with KL subdiagonals and KU superdiagonals using the row and scaling factors in the vectors R and C

SYNOPSIS¶

SUBROUTINE CLAQGB(

M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, EQUED )

CHARACTER EQUED INTEGER KL, KU, LDAB, M, N REAL AMAX, COLCND, ROWCND REAL C( * ), R( * ) COMPLEX AB( LDAB, * )

PURPOSE¶

CLAQGB equilibrates a general M by N band matrix A with KL subdiagonals and KU superdiagonals 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.

KL (input) INTEGER

The number of subdiagonals within the band of A. KL >= 0.

KU (input) INTEGER

The number of superdiagonals within the band of A. KU >= 0.

AB (input/output) COMPLEX array, dimension (LDAB,N)

On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl) On exit, the equilibrated matrix, in the same storage format as A. See EQUED for the form of the equilibrated matrix.

LDAB (input) INTEGER

The leading dimension of the array AB. LDA >= KL+KU+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 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 = 'B': Both row and column equilibration, i.e., A has been replaced by diag(R) * A * diag(C).

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.