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Functions/Subroutines
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/Subroutine 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.

Download DLANGB + dependencies [TGZ] [ZIP] [TXT]

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:

[in]	NORM	NORM is CHARACTER*1 Specifies the value to be returned in DLANGB as described above.
[in]	N	N is INTEGER The order of the matrix A. N >= 0. When N = 0, DLANGB is set to zero.
[in]	KL	KL is INTEGER The number of sub-diagonals of the matrix A. KL >= 0.
[in]	KU	KU is INTEGER The number of super-diagonals of the matrix A. KU >= 0.
[in]	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).
[in]	LDAB	LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1.
[out]	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.

Date:: September 2012

Definition at line 124 of file dlangb.f.

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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.

Download DLAQGB + dependencies [TGZ] [ZIP] [TXT]

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:

[in]	M	M is INTEGER The number of rows of the matrix A. M >= 0.
[in]	N	N is INTEGER The number of columns of the matrix A. N >= 0.
[in]	KL	KL is INTEGER The number of subdiagonals within the band of A. KL >= 0.
[in]	KU	KU is INTEGER The number of superdiagonals within the band of A. KU >= 0.
[in,out]	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.
[in]	LDAB	LDAB is INTEGER The leading dimension of the array AB. LDA >= KL+KU+1.
[in]	R	R is DOUBLE PRECISION array, dimension (M) The row scale factors for A.
[in]	C	C is DOUBLE PRECISION array, dimension (N) The column scale factors for A.
[in]	ROWCND	ROWCND is DOUBLE PRECISION Ratio of the smallest R(i) to the largest R(i).
[in]	COLCND	COLCND is DOUBLE PRECISION Ratio of the smallest C(i) to the largest C(i).
[in]	AMAX	AMAX is DOUBLE PRECISION Absolute value of largest matrix entry.
[out]	EQUED	EQUED is CHARACTER1 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.

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Functions/Subroutines

Detailed Description

Function/Subroutine Documentation