Man page - gbcon(3)

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Manual

gbcon

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cgbcon (character norm, integer n, integer kl, integer ku,complex, dimension( ldab, * ) ab, integer ldab, integer, dimension( * )ipiv, real anorm, real rcond, complex, dimension( * ) work, real,dimension( * ) rwork, integer info)
subroutine dgbcon (character norm, integer n, integer kl, integer ku,double precision, dimension( ldab, * ) ab, integer ldab, integer,dimension( * ) ipiv, double precision anorm, double precision rcond,double precision, dimension( * ) work, integer, dimension( * ) iwork,integer info)
subroutine sgbcon (character norm, integer n, integer kl, integer ku, real,dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv,real anorm, real rcond, real, dimension( * ) work, integer, dimension(* ) iwork, integer info)
subroutine zgbcon (character norm, integer n, integer kl, integer ku,complex*16, dimension( ldab, * ) ab, integer ldab, integer, dimension(* ) ipiv, double precision anorm, double precision rcond, complex*16,dimension( * ) work, double precision, dimension( * ) rwork, integerinfo)
Author

NAME

gbcon - gbcon: condition number estimate

SYNOPSIS

Functions

subroutine cgbcon (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work, rwork, info)
CGBCON
subroutine dgbcon (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work, iwork, info)
DGBCON
subroutine sgbcon (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work, iwork, info)
SGBCON
subroutine zgbcon (norm, n, kl, ku, ab, ldab, ipiv, anorm, rcond, work, rwork, info)
ZGBCON

Detailed Description

Function Documentation

subroutine cgbcon (character norm, integer n, integer kl, integer ku,complex, dimension( ldab, * ) ab, integer ldab, integer, dimension( * )ipiv, real anorm, real rcond, complex, dimension( * ) work, real,dimension( * ) rwork, integer info)

CGBCON

Purpose:

CGBCON estimates the reciprocal of the condition number of a complex
general band matrix A, in either the 1-norm or the infinity-norm,
using the LU factorization computed by CGBTRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).

Parameters

NORM

NORM is CHARACTER*1
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= ā€™1ā€™ or ā€™Oā€™: 1-norm;
= ā€™Iā€™: Infinity-norm.

N

N is INTEGER
The order 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)
Details of the LU factorization of the band matrix A, as
computed by CGBTRF. U is stored as an upper triangular band
matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
the multipliers used during the factorization are stored in
rows KL+KU+2 to 2*KL+KU+1.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= 2*KL+KU+1.

IPIV

IPIV is INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= N, row i of the matrix was
interchanged with row IPIV(i).

ANORM

ANORM is REAL
If NORM = ā€™1ā€™ or ā€™Oā€™, the 1-norm of the original matrix A.
If NORM = ā€™Iā€™, the infinity-norm of the original matrix A.

RCOND

RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).

WORK

WORK is COMPLEX array, dimension (2*N)

RWORK

RWORK is REAL array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dgbcon (character norm, integer n, integer kl, integer ku,double precision, dimension( ldab, * ) ab, integer ldab, integer,dimension( * ) ipiv, double precision anorm, double precision rcond,double precision, dimension( * ) work, integer, dimension( * ) iwork,integer info)

DGBCON

Purpose:

DGBCON estimates the reciprocal of the condition number of a real
general band matrix A, in either the 1-norm or the infinity-norm,
using the LU factorization computed by DGBTRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).

Parameters

NORM

NORM is CHARACTER*1
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= ā€™1ā€™ or ā€™Oā€™: 1-norm;
= ā€™Iā€™: Infinity-norm.

N

N is INTEGER
The order 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)
Details of the LU factorization of the band matrix A, as
computed by DGBTRF. U is stored as an upper triangular band
matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
the multipliers used during the factorization are stored in
rows KL+KU+2 to 2*KL+KU+1.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= 2*KL+KU+1.

IPIV

IPIV is INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= N, row i of the matrix was
interchanged with row IPIV(i).

ANORM

ANORM is DOUBLE PRECISION
If NORM = ā€™1ā€™ or ā€™Oā€™, the 1-norm of the original matrix A.
If NORM = ā€™Iā€™, the infinity-norm of the original matrix A.

RCOND

RCOND is DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).

WORK

WORK is DOUBLE PRECISION array, dimension (3*N)

IWORK

IWORK is INTEGER array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine sgbcon (character norm, integer n, integer kl, integer ku, real,dimension( ldab, * ) ab, integer ldab, integer, dimension( * ) ipiv,real anorm, real rcond, real, dimension( * ) work, integer, dimension(* ) iwork, integer info)

SGBCON

Purpose:

SGBCON estimates the reciprocal of the condition number of a real
general band matrix A, in either the 1-norm or the infinity-norm,
using the LU factorization computed by SGBTRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).

Parameters

NORM

NORM is CHARACTER*1
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= ā€™1ā€™ or ā€™Oā€™: 1-norm;
= ā€™Iā€™: Infinity-norm.

N

N is INTEGER
The order 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)
Details of the LU factorization of the band matrix A, as
computed by SGBTRF. U is stored as an upper triangular band
matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
the multipliers used during the factorization are stored in
rows KL+KU+2 to 2*KL+KU+1.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= 2*KL+KU+1.

IPIV

IPIV is INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= N, row i of the matrix was
interchanged with row IPIV(i).

ANORM

ANORM is REAL
If NORM = ā€™1ā€™ or ā€™Oā€™, the 1-norm of the original matrix A.
If NORM = ā€™Iā€™, the infinity-norm of the original matrix A.

RCOND

RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).

WORK

WORK is REAL array, dimension (3*N)

IWORK

IWORK is INTEGER array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zgbcon (character norm, integer n, integer kl, integer ku,complex*16, dimension( ldab, * ) ab, integer ldab, integer, dimension(* ) ipiv, double precision anorm, double precision rcond, complex*16,dimension( * ) work, double precision, dimension( * ) rwork, integerinfo)

ZGBCON

Purpose:

ZGBCON estimates the reciprocal of the condition number of a complex
general band matrix A, in either the 1-norm or the infinity-norm,
using the LU factorization computed by ZGBTRF.

An estimate is obtained for norm(inv(A)), and the reciprocal of the
condition number is computed as
RCOND = 1 / ( norm(A) * norm(inv(A)) ).

Parameters

NORM

NORM is CHARACTER*1
Specifies whether the 1-norm condition number or the
infinity-norm condition number is required:
= ā€™1ā€™ or ā€™Oā€™: 1-norm;
= ā€™Iā€™: Infinity-norm.

N

N is INTEGER
The order 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)
Details of the LU factorization of the band matrix A, as
computed by ZGBTRF. U is stored as an upper triangular band
matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
the multipliers used during the factorization are stored in
rows KL+KU+2 to 2*KL+KU+1.

LDAB

LDAB is INTEGER
The leading dimension of the array AB. LDAB >= 2*KL+KU+1.

IPIV

IPIV is INTEGER array, dimension (N)
The pivot indices; for 1 <= i <= N, row i of the matrix was
interchanged with row IPIV(i).

ANORM

ANORM is DOUBLE PRECISION
If NORM = ā€™1ā€™ or ā€™Oā€™, the 1-norm of the original matrix A.
If NORM = ā€™Iā€™, the infinity-norm of the original matrix A.

RCOND

RCOND is DOUBLE PRECISION
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(norm(A) * norm(inv(A))).

WORK

WORK is COMPLEX*16 array, dimension (2*N)

RWORK

RWORK is DOUBLE PRECISION array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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