ZHPTRI(3F) ZHPTRI(3F)
ZHPTRI - compute 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
SUBROUTINE ZHPTRI( UPLO, N, AP, IPIV, WORK, INFO )
CHARACTER UPLO
INTEGER INFO, N
INTEGER IPIV( * )
COMPLEX*16 AP( * ), WORK( * )
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.
UPLO (input) 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 (input) INTEGER
The order of the matrix A. N >= 0.
AP (input/output) 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 (input) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D as
determined by ZHPTRF.
WORK (workspace) COMPLEX*16 array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Page 1
ZHPTRI(3F) ZHPTRI(3F)
> 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
inverse could not be computed.
ZHPTRI(3F) ZHPTRI(3F)
ZHPTRI - compute 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
SUBROUTINE ZHPTRI( UPLO, N, AP, IPIV, WORK, INFO )
CHARACTER UPLO
INTEGER INFO, N
INTEGER IPIV( * )
COMPLEX*16 AP( * ), WORK( * )
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.
UPLO (input) 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 (input) INTEGER
The order of the matrix A. N >= 0.
AP (input/output) 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 (input) INTEGER array, dimension (N)
Details of the interchanges and the block structure of D as
determined by ZHPTRF.
WORK (workspace) COMPLEX*16 array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Page 1
ZHPTRI(3F) ZHPTRI(3F)
> 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
inverse could not be computed.
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