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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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| subroutine zsytri_3 | ( | character | uplo, |
| integer | n, | ||
| complex*16, dimension( lda, * ) | a, | ||
| integer | lda, | ||
| complex*16, dimension( * ) | e, | ||
| integer, dimension( * ) | ipiv, | ||
| complex*16, dimension( * ) | work, | ||
| integer | lwork, | ||
| integer | info | ||
| ) |
ZSYTRI_3
Download ZSYTRI_3 + dependencies [TGZ] [ZIP] [TXT]
ZSYTRI_3 computes the inverse of a complex symmetric indefinite
matrix A using the factorization computed by ZSYTRF_RK or ZSYTRF_BK:
A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),
where U (or L) is unit upper (or lower) triangular matrix,
U**T (or L**T) is the transpose of U (or L), P is a permutation
matrix, P**T is the transpose of P, and D is symmetric and block
diagonal with 1-by-1 and 2-by-2 diagonal blocks.
ZSYTRI_3 sets the leading dimension of the workspace before calling
ZSYTRI_3X that actually computes the inverse. This is the blocked
version of the algorithm, calling Level 3 BLAS. | [in] | UPLO | UPLO is CHARACTER*1
Specifies whether the details of the factorization are
stored as an upper or lower triangular matrix.
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored. |
| [in] | N | N is INTEGER
The order of the matrix A. N >= 0. |
| [in,out] | A | A is COMPLEX*16 array, dimension (LDA,N)
On entry, diagonal of the block diagonal matrix D and
factors U or L as computed by ZSYTRF_RK and ZSYTRF_BK:
a) ONLY diagonal elements of the symmetric block diagonal
matrix D on the diagonal of A, i.e. D(k,k) = A(k,k);
(superdiagonal (or subdiagonal) elements of D
should be provided on entry in array E), and
b) If UPLO = 'U': factor U in the superdiagonal part of A.
If UPLO = 'L': factor L in the subdiagonal part of A.
On exit, if INFO = 0, the symmetric inverse of the original
matrix.
If UPLO = 'U': the upper triangular part of the inverse
is formed and the part of A below the diagonal is not
referenced;
If UPLO = 'L': the lower triangular part of the inverse
is formed and the part of A above the diagonal is not
referenced. |
| [in] | LDA | LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N). |
| [in] | E | E is COMPLEX*16 array, dimension (N)
On entry, contains the superdiagonal (or subdiagonal)
elements of the symmetric block diagonal matrix D
with 1-by-1 or 2-by-2 diagonal blocks, where
If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.
NOTE: For 1-by-1 diagonal block D(k), where
1 <= k <= N, the element E(k) is not referenced in both
UPLO = 'U' or UPLO = 'L' cases. |
| [in] | IPIV | IPIV is INTEGER array, dimension (N)
Details of the interchanges and the block structure of D
as determined by ZSYTRF_RK or ZSYTRF_BK. |
| [out] | WORK | WORK is COMPLEX*16 array, dimension (N+NB+1)*(NB+3).
On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
| [in] | LWORK | LWORK is INTEGER
The length of WORK. LWORK >= (N+NB+1)*(NB+3).
If LDWORK = -1, then a workspace query is assumed;
the routine only calculates the optimal size of the optimal
size of the WORK array, returns this value as the first
entry of the WORK array, and no error message related to
LWORK is issued by XERBLA. |
| [out] | 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. |
November 2017, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley Definition at line 168 of file zsytri_3.f.
1.9.7