table of contents
| hptri(3) | LAPACK | hptri(3) |
NAME¶
hptri - {hp,sp}tri: triangular inverse
SYNOPSIS¶
Functions¶
subroutine chptri (uplo, n, ap, ipiv, work, info)
CHPTRI subroutine csptri (uplo, n, ap, ipiv, work, info)
CSPTRI subroutine dsptri (uplo, n, ap, ipiv, work, info)
DSPTRI subroutine ssptri (uplo, n, ap, ipiv, work, info)
SSPTRI subroutine zhptri (uplo, n, ap, ipiv, work, info)
ZHPTRI subroutine zsptri (uplo, n, ap, ipiv, work, info)
ZSPTRI
Detailed Description¶
Function Documentation¶
subroutine chptri (character uplo, integer n, complex, dimension( * ) ap, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer info)¶
CHPTRI
Purpose:
CHPTRI computes the inverse of a complex Hermitian indefinite matrix
A in packed storage using the factorization A = U*D*U**H or
A = L*D*L**H computed by CHPTRF.
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.
AP
AP is COMPLEX array, dimension (N*(N+1)/2)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by CHPTRF,
stored as a packed triangular matrix.
On exit, if INFO = 0, the (Hermitian) inverse of the original
matrix, stored as a packed triangular matrix. The j-th column
of inv(A) is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
if UPLO = 'L',
AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CHPTRF.
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 csptri (character uplo, integer n, complex, dimension( * ) ap, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer info)¶
CSPTRI
Purpose:
CSPTRI computes the inverse of a complex symmetric indefinite matrix
A in packed storage using the factorization A = U*D*U**T or
A = L*D*L**T computed by CSPTRF.
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.
AP
AP is COMPLEX array, dimension (N*(N+1)/2)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by CSPTRF,
stored as a packed triangular matrix.
On exit, if INFO = 0, the (symmetric) inverse of the original
matrix, stored as a packed triangular matrix. The j-th column
of inv(A) is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
if UPLO = 'L',
AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by CSPTRF.
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 dsptri (character uplo, integer n, double precision, dimension( * ) ap, integer, dimension( * ) ipiv, double precision, dimension( * ) work, integer info)¶
DSPTRI
Purpose:
DSPTRI computes the inverse of a real symmetric indefinite matrix
A in packed storage using the factorization A = U*D*U**T or
A = L*D*L**T computed by DSPTRF.
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.
AP
AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by DSPTRF,
stored as a packed triangular matrix.
On exit, if INFO = 0, the (symmetric) inverse of the original
matrix, stored as a packed triangular matrix. The j-th column
of inv(A) is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
if UPLO = 'L',
AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by DSPTRF.
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 ssptri (character uplo, integer n, real, dimension( * ) ap, integer, dimension( * ) ipiv, real, dimension( * ) work, integer info)¶
SSPTRI
Purpose:
SSPTRI computes the inverse of a real symmetric indefinite matrix
A in packed storage using the factorization A = U*D*U**T or
A = L*D*L**T computed by SSPTRF.
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.
AP
AP is REAL array, dimension (N*(N+1)/2)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by SSPTRF,
stored as a packed triangular matrix.
On exit, if INFO = 0, the (symmetric) inverse of the original
matrix, stored as a packed triangular matrix. The j-th column
of inv(A) is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
if UPLO = 'L',
AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by SSPTRF.
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 zhptri (character uplo, integer n, complex*16, dimension( * ) ap, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer info)¶
ZHPTRI
Purpose:
ZHPTRI computes the inverse of a complex Hermitian indefinite matrix
A in packed storage using the factorization A = U*D*U**H or
A = L*D*L**H computed by ZHPTRF.
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.
AP
AP is COMPLEX*16 array, dimension (N*(N+1)/2)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by ZHPTRF,
stored as a packed triangular matrix.
On exit, if INFO = 0, the (Hermitian) inverse of the original
matrix, stored as a packed triangular matrix. The j-th column
of inv(A) is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
if UPLO = 'L',
AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by ZHPTRF.
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 zsptri (character uplo, integer n, complex*16, dimension( * ) ap, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer info)¶
ZSPTRI
Purpose:
ZSPTRI computes the inverse of a complex symmetric indefinite matrix
A in packed storage using the factorization A = U*D*U**T or
A = L*D*L**T computed by ZSPTRF.
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.
AP
AP is COMPLEX*16 array, dimension (N*(N+1)/2)
On entry, the block diagonal matrix D and the multipliers
used to obtain the factor U or L as computed by ZSPTRF,
stored as a packed triangular matrix.
On exit, if INFO = 0, the (symmetric) inverse of the original
matrix, stored as a packed triangular matrix. The j-th column
of inv(A) is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = inv(A)(i,j) for 1<=i<=j;
if UPLO = 'L',
AP(i + (j-1)*(2n-j)/2) = inv(A)(i,j) for j<=i<=n.
IPIV
IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by ZSPTRF.
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.
Author¶
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| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |