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 zgbequ.f(3) LAPACK zgbequ.f(3)

zgbequ.f -

# SYNOPSIS

## Functions/Subroutines

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

ZGBEQU

# Function/Subroutine Documentation

## subroutine zgbequ (integerM, integerN, integerKL, integerKU, complex*16, dimension( ldab, * )AB, integerLDAB, double precision, dimension( * )R, double precision, dimension( * )C, double precisionROWCND, double precisionCOLCND, double precisionAMAX, integerINFO)

ZGBEQU
Purpose:
``` ZGBEQU 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 COMPLEX*16 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
NAG Ltd.
Date:
November 2011
Definition at line 154 of file zgbequ.f.

# Author

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