Man page - hetri_rook(3)

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Manual

hetri_rook

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine chetri_rook (character uplo, integer n, complex, dimension( lda,* ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( *) work, integer info)
subroutine csytri_rook (character uplo, integer n, complex, dimension( lda,* ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( *) work, integer info)
subroutine dsytri_rook (character uplo, integer n, double precision,dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,double precision, dimension( * ) work, integer info)
subroutine ssytri_rook (character uplo, integer n, real, dimension( lda, *) a, integer lda, integer, dimension( * ) ipiv, real, dimension( * )work, integer info)
subroutine zhetri_rook (character uplo, integer n, complex*16, dimension(lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16,dimension( * ) work, integer info)
subroutine zsytri_rook (character uplo, integer n, complex*16, dimension(lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16,dimension( * ) work, integer info)
Author

NAME

hetri_rook - {he,sy}tri_rook: triangular inverse

SYNOPSIS

Functions

subroutine chetri_rook (uplo, n, a, lda, ipiv, work, info)
CHETRI_ROOK computes the inverse of HE matrix using the factorization obtained with the bounded Bunch-Kaufman (’rook’) diagonal pivoting method.
subroutine csytri_rook (uplo, n, a, lda, ipiv, work, info)
CSYTRI_ROOK
subroutine dsytri_rook (uplo, n, a, lda, ipiv, work, info)
DSYTRI_ROOK
subroutine ssytri_rook (uplo, n, a, lda, ipiv, work, info)
SSYTRI_ROOK
subroutine zhetri_rook (uplo, n, a, lda, ipiv, work, info)
ZHETRI_ROOK computes the inverse of HE matrix using the factorization obtained with the bounded Bunch-Kaufman (’rook’) diagonal pivoting method.
subroutine zsytri_rook (uplo, n, a, lda, ipiv, work, info)
ZSYTRI_ROOK

Detailed Description

Function Documentation

subroutine chetri_rook (character uplo, integer n, complex, dimension( lda,* ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( *) work, integer info)

CHETRI_ROOK computes the inverse of HE matrix using the factorization obtained with the bounded Bunch-Kaufman (’rook’) diagonal pivoting method.

Purpose:

CHETRI_ROOK computes the inverse of a complex Hermitian indefinite matrix
A using the factorization A = U*D*U**H or A = L*D*L**H computed by
CHETRF_ROOK.

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= ’U’: Upper triangular, form is A = U*D*U**H;
= ’L’: 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)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by CHETRF_ROOK.

On exit, if INFO = 0, the (Hermitian) inverse of the original
matrix. If UPLO = ’U’, the upper triangular part of the
inverse is formed and the part of A below the diagonal is not
referenced; if UPLO = ’L’ the lower triangular part of the
inverse is formed and the part of A above the diagonal is
not referenced.

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.

WORK

WORK is COMPLEX array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
inverse could not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

November 2013, 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 csytri_rook (character uplo, integer n, complex, dimension( lda,* ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( *) work, integer info)

CSYTRI_ROOK

Purpose:

CSYTRI_ROOK computes the inverse of a complex symmetric
matrix A using the factorization A = U*D*U**T or A = L*D*L**T
computed by CSYTRF_ROOK.

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= ’U’: Upper triangular, form is A = U*D*U**T;
= ’L’: 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)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by CSYTRF_ROOK.

On exit, if INFO = 0, the (symmetric) inverse of the original
matrix. If UPLO = ’U’, the upper triangular part of the
inverse is formed and the part of A below the diagonal is not
referenced; if UPLO = ’L’ the lower triangular part of the
inverse is formed and the part of A above the diagonal is
not referenced.

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.

WORK

WORK is COMPLEX array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
inverse could not be computed.

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 dsytri_rook (character uplo, integer n, double precision,dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv,double precision, dimension( * ) work, integer info)

DSYTRI_ROOK

Purpose:

DSYTRI_ROOK computes the inverse of a real symmetric
matrix A using the factorization A = U*D*U**T or A = L*D*L**T
computed by DSYTRF_ROOK.

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= ’U’: Upper triangular, form is A = U*D*U**T;
= ’L’: 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)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by DSYTRF_ROOK.

On exit, if INFO = 0, the (symmetric) inverse of the original
matrix. If UPLO = ’U’, the upper triangular part of the
inverse is formed and the part of A below the diagonal is not
referenced; if UPLO = ’L’ the lower triangular part of the
inverse is formed and the part of A above the diagonal is
not referenced.

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.

WORK

WORK 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
> 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
inverse could not be computed.

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 ssytri_rook (character uplo, integer n, real, dimension( lda, *) a, integer lda, integer, dimension( * ) ipiv, real, dimension( * )work, integer info)

SSYTRI_ROOK

Purpose:

SSYTRI_ROOK computes the inverse of a real symmetric
matrix A using the factorization A = U*D*U**T or A = L*D*L**T
computed by SSYTRF_ROOK.

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= ’U’: Upper triangular, form is A = U*D*U**T;
= ’L’: 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)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by SSYTRF_ROOK.

On exit, if INFO = 0, the (symmetric) inverse of the original
matrix. If UPLO = ’U’, the upper triangular part of the
inverse is formed and the part of A below the diagonal is not
referenced; if UPLO = ’L’ the lower triangular part of the
inverse is formed and the part of A above the diagonal is
not referenced.

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.

WORK

WORK is REAL array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
inverse could not be computed.

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 zhetri_rook (character uplo, integer n, complex*16, dimension(lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16,dimension( * ) work, integer info)

ZHETRI_ROOK computes the inverse of HE matrix using the factorization obtained with the bounded Bunch-Kaufman (’rook’) diagonal pivoting method.

Purpose:

ZHETRI_ROOK computes the inverse of a complex Hermitian indefinite matrix
A using the factorization A = U*D*U**H or A = L*D*L**H computed by
ZHETRF_ROOK.

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= ’U’: Upper triangular, form is A = U*D*U**H;
= ’L’: 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)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by ZHETRF_ROOK.

On exit, if INFO = 0, the (Hermitian) inverse of the original
matrix. If UPLO = ’U’, the upper triangular part of the
inverse is formed and the part of A below the diagonal is not
referenced; if UPLO = ’L’ the lower triangular part of the
inverse is formed and the part of A above the diagonal is
not referenced.

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_ROOK.

WORK

WORK is COMPLEX*16 array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
inverse could not be computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

November 2013, 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 zsytri_rook (character uplo, integer n, complex*16, dimension(lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16,dimension( * ) work, integer info)

ZSYTRI_ROOK

Purpose:

ZSYTRI_ROOK computes the inverse of a complex symmetric
matrix A using the factorization A = U*D*U**T or A = L*D*L**T
computed by ZSYTRF_ROOK.

Parameters

UPLO

UPLO is CHARACTER*1
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix.
= ’U’: Upper triangular, form is A = U*D*U**T;
= ’L’: 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)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by ZSYTRF_ROOK.

On exit, if INFO = 0, the (symmetric) inverse of the original
matrix. If UPLO = ’U’, the upper triangular part of the
inverse is formed and the part of A below the diagonal is not
referenced; if UPLO = ’L’ the lower triangular part of the
inverse is formed and the part of A above the diagonal is
not referenced.

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.

WORK

WORK is COMPLEX*16 array, dimension (N)

INFO

INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
inverse could not be computed.

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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