
sgbequ.f(3) LAPACK sgbequ.f(3)
NAME
sgbequ.f 
SYNOPSIS
Functions/Subroutines
subroutine sgbequ (M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND, AMAX, INFO)
SGBEQU
Function/Subroutine Documentation
subroutine sgbequ (integerM, integerN, integerKL, integerKU, real, dimension( ldab, * )AB,
integerLDAB, real, dimension( * )R, real, dimension( * )C, realROWCND, realCOLCND,
realAMAX, integerINFO)
SGBEQU
Purpose:
SGBEQU computes row and column scalings intended to equilibrate an
MbyN 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 REAL 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(m,j+kl).
LDAB
LDAB is INTEGER
The leading dimension of the array AB. LDAB >= KL+KU+1.
R
R is REAL array, dimension (M)
If INFO = 0, or INFO > M, R contains the row scale factors
for A.
C
C is REAL array, dimension (N)
If INFO = 0, C contains the column scale factors for A.
ROWCND
ROWCND is REAL
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 REAL
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 REAL
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 ith argument had an illegal value
> 0: if INFO = i, and i is
<= M: the ith row of A is exactly zero
> M: the (iM)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 sgbequ.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 sgbequ.f(3) 
