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doubleGBauxiliary(3) LAPACK doubleGBauxiliary(3)

NAME

doubleGBauxiliary - double

SYNOPSIS

Functions


double precision function dlangb (NORM, N, KL, KU, AB, LDAB, WORK)
DLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix. 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.

Detailed Description

This is the group of double auxiliary functions for GB matrices

Function Documentation

double precision function dlangb (character NORM, integer N, integer KL, integer KU, double precision, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) WORK)

DLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general band matrix.

Purpose:


DLANGB returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of an
n by n band matrix A, with kl sub-diagonals and ku super-diagonals.

Returns

DLANGB


DLANGB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
(
( norm1(A), NORM = '1', 'O' or 'o'
(
( normI(A), NORM = 'I' or 'i'
(
( normF(A), NORM = 'F', 'f', 'E' or 'e'
where norm1 denotes the one norm of a matrix (maximum column sum),
normI denotes the infinity norm of a matrix (maximum row sum) and
normF denotes the Frobenius norm of a matrix (square root of sum of
squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.

Parameters

NORM


NORM is CHARACTER*1
Specifies the value to be returned in DLANGB as described
above.

N


N is INTEGER
The order of the matrix A. N >= 0. When N = 0, DLANGB is
set to zero.

KL


KL is INTEGER
The number of sub-diagonals of the matrix A. KL >= 0.

KU


KU is INTEGER
The number of super-diagonals of the matrix A. KU >= 0.

AB


AB is DOUBLE PRECISION array, dimension (LDAB,N)
The band matrix A, stored 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(n,j+kl).

LDAB


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

WORK


WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = 'I'; otherwise, WORK is not
referenced.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dlaqgb (integer M, integer N, integer KL, integer KU, double precision, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) R, double precision, dimension( * ) C, double precision ROWCND, double precision COLCND, double precision AMAX, character EQUED)

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


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.

KL


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

KU


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

AB


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


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.

Author

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