dlaqgb-f(3)

dlaqgb.f –

Synopsis

Functions/Subroutines

subroutine dlaqgb (M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, EQUED)
DLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

Function/Subroutine Documentation

subroutine dlaqgb (integerM, integerN, integerKL, integerKU, double precision, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )R, double precision, dimension( * )C, double precisionROWCND, double precisionCOLCND, double precisionAMAX, characterEQUED)

DLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.

Purpose:

 DLAQGB 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.

Parameters:

 M is INTEGER
 The number of rows of the matrix A. M >= 0.

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

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

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

 AB is DOUBLE PRECISION 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

 LDAB is INTEGER
 The leading dimension of the array AB. LDA >= KL+KU+1.

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

 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 = 'B': Both row and column equilibration, i.e., A has been
 replaced by diag(R) * A * diag(C).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.

Date:

September 2012

Definition at line 159 of file dlaqgb.f.

Author

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