Man page - gecon(3)

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Manual

gecon

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cgecon (character norm, integer n, complex, dimension( lda, * )a, integer lda, real anorm, real rcond, complex, dimension( * ) work,real, dimension( * ) rwork, integer info)
subroutine dgecon (character norm, integer n, double precision, dimension(lda, * ) a, integer lda, double precision anorm, double precisionrcond, double precision, dimension( * ) work, integer, dimension( * )iwork, integer info)
subroutine sgecon (character norm, integer n, real, dimension( lda, * ) a,integer lda, real anorm, real rcond, real, dimension( * ) work,integer, dimension( * ) iwork, integer info)
subroutine zgecon (character norm, integer n, complex*16, dimension( lda, *) a, integer lda, double precision anorm, double precision rcond,complex*16, dimension( * ) work, double precision, dimension( * )rwork, integer info)
Author

NAME

gecon - gecon: condition number estimate

SYNOPSIS

Functions

subroutine cgecon (norm, n, a, lda, anorm, rcond, work, rwork, info)
CGECON
subroutine dgecon (norm, n, a, lda, anorm, rcond, work, iwork, info)
DGECON
subroutine sgecon (norm, n, a, lda, anorm, rcond, work, iwork, info)
SGECON
subroutine zgecon (norm, n, a, lda, anorm, rcond, work, rwork, info)
ZGECON

Detailed Description

Function Documentation

subroutine cgecon (character norm, integer n, complex, dimension( lda, * )a, integer lda, real anorm, real rcond, complex, dimension( * ) work,real, dimension( * ) rwork, integer info)

CGECON

Purpose:

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

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.

A

A is COMPLEX array, dimension (LDA,N)
The factors L and U from the factorization A = P*L*U
as computed by CGETRF.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).

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 (2*N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
NaNs are illegal values for ANORM, and they propagate to
the output parameter RCOND.
Infinity is illegal for ANORM, and it propagates to the output
parameter RCOND as 0.
= 1: if RCOND = NaN, or
RCOND = Inf, or
the computed norm of the inverse of A is 0.
In the latter, RCOND = 0 is returned.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dgecon (character norm, integer n, double precision, dimension(lda, * ) a, integer lda, double precision anorm, double precisionrcond, double precision, dimension( * ) work, integer, dimension( * )iwork, integer info)

DGECON

Purpose:

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

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.

A

A is DOUBLE PRECISION array, dimension (LDA,N)
The factors L and U from the factorization A = P*L*U
as computed by DGETRF.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).

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 (4*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.
NaNs are illegal values for ANORM, and they propagate to
the output parameter RCOND.
Infinity is illegal for ANORM, and it propagates to the output
parameter RCOND as 0.
= 1: if RCOND = NaN, or
RCOND = Inf, or
the computed norm of the inverse of A is 0.
In the latter, RCOND = 0 is returned.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine sgecon (character norm, integer n, real, dimension( lda, * ) a,integer lda, real anorm, real rcond, real, dimension( * ) work,integer, dimension( * ) iwork, integer info)

SGECON

Purpose:

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

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.

A

A is REAL array, dimension (LDA,N)
The factors L and U from the factorization A = P*L*U
as computed by SGETRF.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).

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 (4*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.
NaNs are illegal values for ANORM, and they propagate to
the output parameter RCOND.
Infinity is illegal for ANORM, and it propagates to the output
parameter RCOND as 0.
= 1: if RCOND = NaN, or
RCOND = Inf, or
the computed norm of the inverse of A is 0.
In the latter, RCOND = 0 is returned.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zgecon (character norm, integer n, complex*16, dimension( lda, *) a, integer lda, double precision anorm, double precision rcond,complex*16, dimension( * ) work, double precision, dimension( * )rwork, integer info)

ZGECON

Purpose:

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

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.

A

A is COMPLEX*16 array, dimension (LDA,N)
The factors L and U from the factorization A = P*L*U
as computed by ZGETRF.

LDA

LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).

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 (2*N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value.
NaNs are illegal values for ANORM, and they propagate to
the output parameter RCOND.
Infinity is illegal for ANORM, and it propagates to the output
parameter RCOND as 0.
= 1: if RCOND = NaN, or
RCOND = Inf, or
the computed norm of the inverse of A is 0.
In the latter, RCOND = 0 is returned.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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