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| hetri_rook(3) | LAPACK | hetri_rook(3) |
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 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 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
Definition at line 127 of file chetri_rook.f.
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 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 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
Definition at line 128 of file csytri_rook.f.
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 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 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
Definition at line 128 of file dsytri_rook.f.
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 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 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
Definition at line 128 of file ssytri_rook.f.
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 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 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
Definition at line 127 of file zhetri_rook.f.
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 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 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
Definition at line 128 of file zsytri_rook.f.
Author
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