# zgbequ.f(3) [centos man page]

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

NAME
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
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       zgbequ.f(3)```

## Check Out this Related Man Page

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

NAME
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
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       zgbequ.f(3)```
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