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

!>          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 is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

!>          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.

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

!>          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 is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

!>          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.

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

!>          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 is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

!>          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.

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

!>          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 is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

!>          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.

Definition at line 108 of file ssptri.f.

subroutine zhptri (character uplo, integer n, complex16, dimension( ) ap, integer, dimension( * ) ipiv, complex16, 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 is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

!>          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.

Definition at line 108 of file zhptri.f.

subroutine zsptri (character uplo, integer n, complex16, dimension( ) ap, integer, dimension( * ) ipiv, complex16, 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 is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

!>          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.

Definition at line 108 of file zsptri.f.

Author

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