dgbequ-f(3)

dgbequ.f –

Synopsis

Functions/Subroutines

subroutine dgbequ (M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO)
DGBEQU

Function/Subroutine Documentation

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

DGBEQU

Purpose:

 DGBEQU computes row and column scalings intended to equilibrate an
 M-by-N band matrix A and reduce its condition number. R returns the
 row scale factors and C the column scale factors, chosen to try to
 make the largest element in each row and column of the matrix B with
 elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
 R(i) and C(j) are restricted to be between SMLNUM = smallest safe
 number and BIGNUM = largest safe number. Use of these scaling
 factors is not guaranteed to reduce the condition number of A but
 works well in practice.

 

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)
 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(m,j+kl).

LDAB

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

R

 R is DOUBLE PRECISION array, dimension (M)
 If INFO = 0, or INFO > M, R contains the row scale factors
 for A.

C

 C is DOUBLE PRECISION array, dimension (N)
 If INFO = 0, C contains the column scale factors for A.

ROWCND

 ROWCND is DOUBLE PRECISION
 If INFO = 0 or INFO > M, ROWCND contains the ratio of the
 smallest R(i) to the largest R(i). If ROWCND >= 0.1 and
 AMAX is neither too large nor too small, it is not worth
 scaling by R.

COLCND

 COLCND is DOUBLE PRECISION
 If INFO = 0, COLCND contains the ratio of the smallest
 C(i) to the largest C(i). If COLCND >= 0.1, it is not
 worth scaling by C.

AMAX

 AMAX is DOUBLE PRECISION
 Absolute value of largest matrix element. If AMAX is very
 close to overflow or very close to underflow, the matrix
 should be scaled.

INFO

 INFO is INTEGER
 = 0: successful exit
 < 0: if INFO = -i, the i-th argument had an illegal value
 > 0: if INFO = i, and i is
 <= M: the i-th row of A is exactly zero
 > M: the (i-M)-th column of A is exactly zero

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 153 of file dgbequ.f.

Author

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