ZHETRI_3(3)

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zhetri_3.f — that's the source file this page is about, bestie.

This page is zhetri_3.f(3) from the Library Functions Manual, with the header path /home/abui.../zhetri_3.f(3). Slay.

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🦋 SYNOPSIS 🦋

   Functions/Subroutines
       subroutine ZHETRI_3 (uplo, n, a, lda, e, ipiv, work, lwork, info)
           ZHETRI_3

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💖 Function/Subroutine Documentation 💖

   subroutine ZHETRI_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)
       ZHETRI_3

🎯 Purpose

Okay so ZHETRI_3 computes the inverse of a complex Hermitian indefinite matrix A using the factorization computed by ZHETRF_RK or ZHETRF_BK:

A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T),

where U (or L) is unit upper (or lower) triangular matrix, U**H (or L**H) is the conjugate of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

ZHETRI_3 sets the leading dimension of the workspace before calling ZHETRI_3X that actually computes the inverse. This is the blocked version of the algorithm, calling Level 3 BLAS.

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🎀 Parameters

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.

N

N is INTEGER.

The order of the matrix A. N >= 0.

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 ZHETRF_RK and ZHETRF_BK:

• a) ONLY diagonal elements of the Hermitian 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 Hermitian 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.

LDA

LDA is INTEGER.

The leading dimension of the array A. LDA >= max(1,N).

E

E is COMPLEX*16 array, dimension (N).

On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian 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.

IPIV

IPIV is INTEGER array, dimension (N).

Details of the interchanges and the block structure of D as determined by ZHETRF_RK or ZHETRF_BK.

WORK

WORK is COMPLEX*16 array, dimension (N+NB+1)*(NB+3).

On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

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.

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.

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👑 Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

💜 Contributors

• November 2017, Igor Kozachenko,
• Computer Science Division,
• University of California, Berkeley

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📍 Definition

Definition at line 168 of file zhetri_3.f.

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🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie! Footer sign-off: LAPACK Version 3.12.0 and /home/abui.../zhetri_3.f(3) — that's the source/version line, and there's no separate date printed on it, so no invented date, periodt. 💅✨