Man page - hecon(3)

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Manual

hecon

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine checon (character uplo, integer n, complex, dimension( lda, * )a, integer lda, integer, dimension( * ) ipiv, real anorm, real rcond,complex, dimension( * ) work, integer info)
subroutine csycon (character uplo, integer n, complex, dimension( lda, * )a, integer lda, integer, dimension( * ) ipiv, real anorm, real rcond,complex, dimension( * ) work, integer info)
subroutine dsycon (character uplo, integer n, double precision, dimension(lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precisionanorm, double precision rcond, double precision, dimension( * ) work,integer, dimension( * ) iwork, integer info)
subroutine ssycon (character uplo, integer n, real, dimension( lda, * ) a,integer lda, integer, dimension( * ) ipiv, real anorm, real rcond,real, dimension( * ) work, integer, dimension( * ) iwork, integer info)
subroutine zhecon (character uplo, integer n, complex*16, dimension( lda, *) a, integer lda, integer, dimension( * ) ipiv, double precision anorm,double precision rcond, complex*16, dimension( * ) work, integer info)
subroutine zsycon (character uplo, integer n, complex*16, dimension( lda, *) a, integer lda, integer, dimension( * ) ipiv, double precision anorm,double precision rcond, complex*16, dimension( * ) work, integer info)
Author

NAME

hecon - {he,sy}con: condition number estimate

SYNOPSIS

Functions

subroutine checon (uplo, n, a, lda, ipiv, anorm, rcond, work, info)
CHECON
subroutine csycon (uplo, n, a, lda, ipiv, anorm, rcond, work, info)
CSYCON
subroutine dsycon (uplo, n, a, lda, ipiv, anorm, rcond, work, iwork, info)
DSYCON
subroutine ssycon (uplo, n, a, lda, ipiv, anorm, rcond, work, iwork, info)
SSYCON
subroutine zhecon (uplo, n, a, lda, ipiv, anorm, rcond, work, info)
ZHECON
subroutine zsycon (uplo, n, a, lda, ipiv, anorm, rcond, work, info)
ZSYCON

Detailed Description

Function Documentation

subroutine checon (character uplo, integer n, complex, dimension( lda, * )a, integer lda, integer, dimension( * ) ipiv, real anorm, real rcond,complex, dimension( * ) work, integer info)

CHECON

Purpose:

CHECON estimates the reciprocal of the condition number of a complex
Hermitian matrix A using the factorization A = U*D*U**H or
A = L*D*L**H computed by CHETRF.

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

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= ā€™Uā€™: Upper triangular, form is A = U*D*U**H;
= ā€™Lā€™: Lower triangular, form is A = L*D*L**H.

N

N is INTEGER
The order of the matrix A. N >= 0.

A

A is COMPLEX array, dimension (LDA,N)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by CHETRF.

LDA

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

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CHETRF.

ANORM

ANORM is REAL
The 1-norm of the original matrix A.

RCOND

RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.

WORK

WORK is COMPLEX array, dimension (2*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 csycon (character uplo, integer n, complex, dimension( lda, * )a, integer lda, integer, dimension( * ) ipiv, real anorm, real rcond,complex, dimension( * ) work, integer info)

CSYCON

Purpose:

CSYCON estimates the reciprocal of the condition number (in the
1-norm) of a complex symmetric matrix A using the factorization
A = U*D*U**T or A = L*D*L**T computed by CSYTRF.

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

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= ā€™Uā€™: Upper triangular, form is A = U*D*U**T;
= ā€™Lā€™: Lower triangular, form is A = L*D*L**T.

N

N is INTEGER
The order of the matrix A. N >= 0.

A

A is COMPLEX array, dimension (LDA,N)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by CSYTRF.

LDA

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

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CSYTRF.

ANORM

ANORM is REAL
The 1-norm of the original matrix A.

RCOND

RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.

WORK

WORK is COMPLEX array, dimension (2*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 dsycon (character uplo, integer n, double precision, dimension(lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precisionanorm, double precision rcond, double precision, dimension( * ) work,integer, dimension( * ) iwork, integer info)

DSYCON

Purpose:

DSYCON estimates the reciprocal of the condition number (in the
1-norm) of a real symmetric matrix A using the factorization
A = U*D*U**T or A = L*D*L**T computed by DSYTRF.

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

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= ā€™Uā€™: Upper triangular, form is A = U*D*U**T;
= ā€™Lā€™: Lower triangular, form is A = L*D*L**T.

N

N is INTEGER
The order of the matrix A. N >= 0.

A

A is DOUBLE PRECISION array, dimension (LDA,N)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by DSYTRF.

LDA

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

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by DSYTRF.

ANORM

ANORM is DOUBLE PRECISION
The 1-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/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.

WORK

WORK is DOUBLE PRECISION array, dimension (2*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 ssycon (character uplo, integer n, real, dimension( lda, * ) a,integer lda, integer, dimension( * ) ipiv, real anorm, real rcond,real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

SSYCON

Purpose:

SSYCON estimates the reciprocal of the condition number (in the
1-norm) of a real symmetric matrix A using the factorization
A = U*D*U**T or A = L*D*L**T computed by SSYTRF.

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

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= ā€™Uā€™: Upper triangular, form is A = U*D*U**T;
= ā€™Lā€™: Lower triangular, form is A = L*D*L**T.

N

N is INTEGER
The order of the matrix A. N >= 0.

A

A is REAL array, dimension (LDA,N)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by SSYTRF.

LDA

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

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by SSYTRF.

ANORM

ANORM is REAL
The 1-norm of the original matrix A.

RCOND

RCOND is REAL
The reciprocal of the condition number of the matrix A,
computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.

WORK

WORK is REAL array, dimension (2*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 zhecon (character uplo, integer n, complex*16, dimension( lda, *) a, integer lda, integer, dimension( * ) ipiv, double precision anorm,double precision rcond, complex*16, dimension( * ) work, integer info)

ZHECON

Purpose:

ZHECON estimates the reciprocal of the condition number of a complex
Hermitian matrix A using the factorization A = U*D*U**H or
A = L*D*L**H computed by ZHETRF.

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

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= ā€™Uā€™: Upper triangular, form is A = U*D*U**H;
= ā€™Lā€™: Lower triangular, form is A = L*D*L**H.

N

N is INTEGER
The order of the matrix A. N >= 0.

A

A is COMPLEX*16 array, dimension (LDA,N)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by ZHETRF.

LDA

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

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by ZHETRF.

ANORM

ANORM is DOUBLE PRECISION
The 1-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/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.

WORK

WORK is COMPLEX*16 array, dimension (2*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 zsycon (character uplo, integer n, complex*16, dimension( lda, *) a, integer lda, integer, dimension( * ) ipiv, double precision anorm,double precision rcond, complex*16, dimension( * ) work, integer info)

ZSYCON

Purpose:

ZSYCON estimates the reciprocal of the condition number (in the
1-norm) of a complex symmetric matrix A using the factorization
A = U*D*U**T or A = L*D*L**T computed by ZSYTRF.

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

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= ā€™Uā€™: Upper triangular, form is A = U*D*U**T;
= ā€™Lā€™: Lower triangular, form is A = L*D*L**T.

N

N is INTEGER
The order of the matrix A. N >= 0.

A

A is COMPLEX*16 array, dimension (LDA,N)
The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by ZSYTRF.

LDA

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

IPIV

IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by ZSYTRF.

ANORM

ANORM is DOUBLE PRECISION
The 1-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/(ANORM * AINVNM), where AINVNM is an
estimate of the 1-norm of inv(A) computed in this routine.

WORK

WORK is COMPLEX*16 array, dimension (2*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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