zgbequb.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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NAME

zgbequb.f  

SYNOPSIS


 

Functions/Subroutines


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

Function/Subroutine Documentation

 

subroutine zgbequb (integer M, integer N, integer KL, integer KU, complex*16, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) R, double precision, dimension( * ) C, double precision ROWCND, double precision COLCND, double precision AMAX, integer INFO)

ZGBEQUB

Purpose:

 ZGBEQUB 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 ZGEEQU by restricting the scaling factors
 to a power of the radix.  Barring over- and underflow, scaling by
 these factors introduces no additional rounding errors.  However, the
 scaled entries' magnitudes 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 COMPLEX*16 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:

June 2016

Definition at line 163 of file zgbequb.f.  

Author

Generated automatically by Doxygen for LAPACK from the source code.


 

Index

NAME
SYNOPSIS
Functions/Subroutines
Function/Subroutine Documentation
subroutine zgbequb (integer M, integer N, integer KL, integer KU, complex*16, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) R, double precision, dimension( * ) C, double precision ROWCND, double precision COLCND, double precision AMAX, integer INFO)
Author