Man page - gbequ(3)

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Manual

gbequ

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cgbequ (integer m, integer n, integer kl, integer ku, complex,dimension( ldab, * ) ab, integer ldab, real, dimension( * ) r, real,dimension( * ) c, real rowcnd, real colcnd, real amax, integer info)
subroutine dgbequ (integer m, integer n, integer kl, integer ku, doubleprecision, dimension( ldab, * ) ab, integer ldab, double precision,dimension( * ) r, double precision, dimension( * ) c, double precisionrowcnd, double precision colcnd, double precision amax, integer info)
subroutine sgbequ (integer m, integer n, integer kl, integer ku, real,dimension( ldab, * ) ab, integer ldab, real, dimension( * ) r, real,dimension( * ) c, real rowcnd, real colcnd, real amax, integer info)
subroutine zgbequ (integer m, integer n, integer kl, integer ku,complex*16, dimension( ldab, * ) ab, integer ldab, double precision,dimension( * ) r, double precision, dimension( * ) c, double precisionrowcnd, double precision colcnd, double precision amax, integer info)
Author

NAME

gbequ - gbequ: equilibration

SYNOPSIS

Functions

subroutine cgbequ (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info)
CGBEQU
subroutine dgbequ (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info)
DGBEQU
subroutine sgbequ (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info)
SGBEQU
subroutine zgbequ (m, n, kl, ku, ab, ldab, r, c, rowcnd, colcnd, amax, info)
ZGBEQU

Detailed Description

Function Documentation

subroutine cgbequ (integer m, integer n, integer kl, integer ku, complex,dimension( ldab, * ) ab, integer ldab, real, dimension( * ) r, real,dimension( * ) c, real rowcnd, real colcnd, real amax, integer info)

CGBEQU

Purpose:

CGBEQU 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 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 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 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.

subroutine dgbequ (integer m, integer n, integer kl, integer ku, doubleprecision, dimension( ldab, * ) ab, integer ldab, double precision,dimension( * ) r, double precision, dimension( * ) c, double precisionrowcnd, double precision colcnd, double precision amax, integer info)

DGBEQU

Purpose:

DGBEQU 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 DOUBLE PRECISION 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

Univ. of Colorado Denver

NAG Ltd.

subroutine sgbequ (integer m, integer n, integer kl, integer ku, real,dimension( ldab, * ) ab, integer ldab, real, dimension( * ) r, real,dimension( * ) c, real rowcnd, real colcnd, real amax, integer info)

SGBEQU

Purpose:

SGBEQU 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 REAL 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 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 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.

subroutine zgbequ (integer m, integer n, integer kl, integer ku,complex*16, dimension( ldab, * ) ab, integer ldab, double precision,dimension( * ) r, double precision, dimension( * ) c, double precisionrowcnd, double precision colcnd, double precision amax, integer info)

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

Univ. of Colorado Denver

NAG Ltd.

Author

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