Man page - hetri(3)

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Manual

hetri

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine chetri (character uplo, integer n, complex, dimension( lda, * )a, integer lda, integer, dimension( * ) ipiv, complex, dimension( * )work, integer info)
subroutine csytri (character uplo, integer n, complex, dimension( lda, * )a, integer lda, integer, dimension( * ) ipiv, complex, dimension( * )work, integer info)
subroutine dsytri (character uplo, integer n, double precision, dimension(lda, * ) a, integer lda, integer, dimension( * ) ipiv, doubleprecision, dimension( * ) work, integer info)
subroutine ssytri (character uplo, integer n, real, dimension( lda, * ) a,integer lda, integer, dimension( * ) ipiv, real, dimension( * ) work,integer info)
subroutine zhetri (character uplo, integer n, complex*16, dimension( lda, *) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension(* ) work, integer info)
subroutine zsytri (character uplo, integer n, complex*16, dimension( lda, *) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension(* ) work, integer info)
Author

NAME

hetri - {he,sy}tri: triangular inverse

SYNOPSIS

Functions

subroutine chetri (uplo, n, a, lda, ipiv, work, info)
CHETRI
subroutine csytri (uplo, n, a, lda, ipiv, work, info)
CSYTRI
subroutine dsytri (uplo, n, a, lda, ipiv, work, info)
DSYTRI
subroutine ssytri (uplo, n, a, lda, ipiv, work, info)
SSYTRI
subroutine zhetri (uplo, n, a, lda, ipiv, work, info)
ZHETRI
subroutine zsytri (uplo, n, a, lda, ipiv, work, info)
ZSYTRI

Detailed Description

Function Documentation

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

CHETRI

Purpose:

CHETRI 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.

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)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by CHETRF.

On exit, if INFO = 0, the (Hermitian) inverse of the original
matrix. If UPLO = ā€™Uā€™, the upper triangular part of the
inverse is formed and the part of A below the diagonal is not
referenced; if UPLO = ā€™Lā€™ 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.

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.

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

CSYTRI

Purpose:

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

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)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by CSYTRF.

On exit, if INFO = 0, the (symmetric) inverse of the original
matrix. If UPLO = ā€™Uā€™, the upper triangular part of the
inverse is formed and the part of A below the diagonal is not
referenced; if UPLO = ā€™Lā€™ 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.

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
> 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.

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

DSYTRI

Purpose:

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

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)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by DSYTRF.

On exit, if INFO = 0, the (symmetric) inverse of the original
matrix. If UPLO = ā€™Uā€™, the upper triangular part of the
inverse is formed and the part of A below the diagonal is not
referenced; if UPLO = ā€™Lā€™ 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.

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.

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

SSYTRI

Purpose:

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

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)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by SSYTRF.

On exit, if INFO = 0, the (symmetric) inverse of the original
matrix. If UPLO = ā€™Uā€™, the upper triangular part of the
inverse is formed and the part of A below the diagonal is not
referenced; if UPLO = ā€™Lā€™ 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.

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.

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

ZHETRI

Purpose:

ZHETRI 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.

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)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by ZHETRF.

On exit, if INFO = 0, the (Hermitian) inverse of the original
matrix. If UPLO = ā€™Uā€™, the upper triangular part of the
inverse is formed and the part of A below the diagonal is not
referenced; if UPLO = ā€™Lā€™ 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.

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.

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

ZSYTRI

Purpose:

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

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)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by ZSYTRF.

On exit, if INFO = 0, the (symmetric) inverse of the original
matrix. If UPLO = ā€™Uā€™, the upper triangular part of the
inverse is formed and the part of A below the diagonal is not
referenced; if UPLO = ā€™Lā€™ 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.

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
> 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.

Author

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