Functions
double precision function dlangb (NORM, N, KL, KU, AB, LDAB, WORK)
DLANGB returns the value of the 1norm, Frobenius norm, infinitynorm, 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 1norm, Frobenius norm, infinitynorm, 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 subdiagonals and ku superdiagonals.
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.
NN is INTEGER The order of the matrix A. N >= 0. When N = 0, DLANGB is set to zero.
KLKL is INTEGER The number of subdiagonals of the matrix A. KL >= 0.
KUKU is INTEGER The number of superdiagonals of the matrix A. KU >= 0.
ABAB is DOUBLE PRECISION array, dimension (LDAB,N) The band matrix A, stored in rows 1 to KL+KU+1. The jth column of A is stored in the jth column of the array AB as follows: AB(ku+1+ij,j) = A(i,j) for max(1,jku)<=i<=min(n,j+kl).
LDABLDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1.
WORKWORK 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
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.
NN is INTEGER The number of columns of the matrix A. N >= 0.
KLKL is INTEGER The number of subdiagonals within the band of A. KL >= 0.
KUKU is INTEGER The number of superdiagonals within the band of A. KU >= 0.
ABAB is DOUBLE PRECISION array, dimension (LDAB,N) On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The jth column of A is stored in the jth column of the array AB as follows: AB(ku+1+ij,j) = A(i,j) for max(1,jku)<=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.
LDABLDAB is INTEGER The leading dimension of the array AB. LDA >= KL+KU+1.
RR is DOUBLE PRECISION array, dimension (M) The row scale factors for A.
CC is DOUBLE PRECISION array, dimension (N) The column scale factors for A.
ROWCNDROWCND is DOUBLE PRECISION Ratio of the smallest R(i) to the largest R(i).
COLCNDCOLCND is DOUBLE PRECISION Ratio of the smallest C(i) to the largest C(i).
AMAXAMAX is DOUBLE PRECISION Absolute value of largest matrix entry.
EQUEDEQUED 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
Author
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