table of contents
| hetri(3) | LAPACK | hetri(3) |
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.
= '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.
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.
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.
= '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.
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.
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, double precision, 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.
= '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.
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.
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.
= '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.
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.
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.
= '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.
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.
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.
= '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.
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.
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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