?hetri_3
?hetri_3
Computes the inverse of a complex Hermitian matrix using the factorization computed by
?hetrf_rk
.lapack_int
LAPACKE_chetri_3
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_float
*
A
,
lapack_int
lda
,
const
lapack_complex_float
*
e
,
const
lapack_int
*
ipiv
);
lapack_int
LAPACKE_zhetri_3
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_double
*
A
,
lapack_int
lda
,
const
lapack_complex_double
*
e
,
const
lapack_int
*
ipiv
);
Description
?hetri_3
computes the inverse of a complex Hermitian matrix A using the factorization computed by ?hetrf_rk
: A = P*U*D*(UH
)*(PT
) or A = P*L*D*(LH
)*(PT
), where U (or L) is a unit upper (or lower) triangular matrix, UH
(or LH
) is the conjugate of U (or L), P is a permutation matrix, PT
is the transpose of P, and D is a Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.?hetri_3
sets the leading dimension of the workspace before calling ?hetri_3x
, which actually computes the inverse.This is the blocked version of the algorithm, calling Level-3 BLAS.
Input Parameters
- matrix_layout
- Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
- uplo
- Specifies whether the details of the factorization are stored as an upper or lower triangular matrix.
- ='U': The upper triangle of A is stored.
- ='L': The lower triangle of A is stored.
- n
- The order of the matrix A.n≥ 0.
- A
- Array of size max(1,On entry, diagonal of the block diagonal matrix D and factor U or L as computed bylda*n).?hetrf_rk:
- Onlydiagonal elements of the Hermitian block diagonal matrix D on the diagonal of A; that is, D(k,k) = A(k,k). Superdiagonal (or subdiagonal) elements of D should be provided on entry in arraye.
- Ifuplo='U', factor U in the superdiagonal part of A. Ifuplo='L', factor L is the subdiagonal part of A.
- lda
- The leading dimension of the arrayA.
- e
- Array of sizeOn entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks. Ifn.uplo='U', e(i) = D(i-1,i),i=2:N, and e(1) is not referenced. Ifuplo='L', e(i) = D(i+1,i),i=1:N-1, and e(n) is not referenced.For 1-by-1 diagonal block D(k), where 1 ≤k≤n, the elemente[k-1] is not referenced in both theuplo='U'anduplo='L'cases.
- ipiv
- Array of sizeDetails of the interchanges and the block structure of D as determined byn.?hetrf_rk.
Output Parameters
- A
- On exit, ifinfo= 0, the Hermitian inverse of the original matrix. Ifuplo='U', the upper triangular part of the inverse is formed and the part of A below the diagonal is not referenced. Ifuplo='L', the lower triangular part of the inverse is formed and the part of A above the diagonal is not referenced.
Return Values
This function returns a value
info
.= 0: Successful exit.
< 0: If , the i
info
= -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.