dgbequb.f man page

dgbequb.f —

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

subroutine dgbequb (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)

DGBEQUB

Purpose:

DGBEQUB computes row and column scalings intended to equilibrate an
M-by-N 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 an absolute value of at most
the radix.

R(i) and C(j) are restricted to be a power of the radix 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.

This routine differs from DGEEQU by restricting the scaling factors
to a power of the radix.  Baring over- and underflow, scaling by
these factors introduces no additional rounding errors.  However, the
scaled entries' magnitured are no longer approximately 1 but lie
between sqrt(radix) and 1/sqrt(radix).

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(N,j+kl)

LDAB

LDAB is INTEGER
The leading dimension of the array A.  LDAB >= max(1,M).

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 160 of file dgbequb.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

dgbequb(3) is an alias of dgbequb.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK