table of contents
hptri(3) | Library Functions Manual | 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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 108 of file chptri.f.
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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 108 of file csptri.f.
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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 108 of file dsptri.f.
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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 108 of file ssptri.f.
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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 108 of file zhptri.f.
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 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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 108 of file zsptri.f.
Author¶
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