Man page - hecon_rook(3)

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Manual

hecon_rook

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine checon_rook (character uplo, integer n, complex, dimension( lda,* ) a, integer lda, integer, dimension( * ) ipiv, real anorm, realrcond, complex, dimension( * ) work, integer info)
subroutine csycon_rook (character uplo, integer n, complex, dimension( lda,* ) a, integer lda, integer, dimension( * ) ipiv, real anorm, realrcond, complex, dimension( * ) work, integer info)
subroutine dsycon_rook (character uplo, integer n, double precision,dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,double precision anorm, double precision rcond, double precision,dimension( * ) work, integer, dimension( * ) iwork, integer info)
subroutine ssycon_rook (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_rook (character uplo, integer n, complex*16, dimension(lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precisionanorm, double precision rcond, complex*16, dimension( * ) work, integerinfo)
subroutine zsycon_rook (character uplo, integer n, complex*16, dimension(lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precisionanorm, double precision rcond, complex*16, dimension( * ) work, integerinfo)
Author

NAME

hecon_rook - {he,sy}con_rook: condition number estimate

SYNOPSIS

Functions

subroutine checon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, info)
CHECON_ROOK estimates the reciprocal of the condition number fort HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges)
subroutine csycon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, info)
CSYCON_ROOK
subroutine dsycon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, iwork, info)
DSYCON_ROOK
subroutine ssycon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, iwork, info)
SSYCON_ROOK
subroutine zhecon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, info)
ZHECON_ROOK estimates the reciprocal of the condition number fort HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges)
subroutine zsycon_rook (uplo, n, a, lda, ipiv, anorm, rcond, work, info)
ZSYCON_ROOK

Detailed Description

Function Documentation

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

CHECON_ROOK estimates the reciprocal of the condition number fort HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges)

Purpose:

CHECON_ROOK 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_ROOK.

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_ROOK.

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_ROOK.

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.

Contributors:

December 2016, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

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

CSYCON_ROOK

Purpose:

CSYCON_ROOK 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_ROOK.

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_ROOK.

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_ROOK.

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.

Contributors:

April 2012, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

subroutine dsycon_rook (character uplo, integer n, double precision,dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,double precision anorm, double precision rcond, double precision,dimension( * ) work, integer, dimension( * ) iwork, integer info)

DSYCON_ROOK

Purpose:

DSYCON_ROOK 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_ROOK.

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_ROOK.

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_ROOK.

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.

Contributors:

April 2012, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

subroutine ssycon_rook (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_ROOK

Purpose:

SSYCON_ROOK 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_ROOK.

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_ROOK.

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_ROOK.

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.

Contributors:

December 2016, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

subroutine zhecon_rook (character uplo, integer n, complex*16, dimension(lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precisionanorm, double precision rcond, complex*16, dimension( * ) work, integerinfo)

ZHECON_ROOK estimates the reciprocal of the condition number fort HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges)

Purpose:

ZHECON_ROOK 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_ROOK.

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 CHETRF_ROOK.

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_ROOK.

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.

Contributors:

June 2017, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

subroutine zsycon_rook (character uplo, integer n, complex*16, dimension(lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precisionanorm, double precision rcond, complex*16, dimension( * ) work, integerinfo)

ZSYCON_ROOK

Purpose:

ZSYCON_ROOK 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_ROOK.

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_ROOK.

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_ROOK.

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.

Contributors:

December 2016, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley

September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
School of Mathematics,
University of Manchester

Author

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