SRC/zhetri2.f(3)

Welcome to the SRC/zhetri2.f(3) page from the Library Functions Manual — yes, that manual. We're about to get into zhetri2, and it's giving linear algebra main character energy. 💅

🌸 NAME 🌸

SRC/zhetri2.f — that's the page name, bestie. The function inside is zhetri2, and she's the star here. 🎀

✨ SYNOPSIS ✨

Here's the synopsis, no cap:

Functions/Subroutines
    subroutine zhetri2 (uplo, n, a, lda, ipiv, work, lwork, info)
        ZHETRI2

🫶 Function/Subroutine Documentation 🫶

This is the full call signature, exactly as the page gives it:

subroutine zhetri2 (character uplo, integer n, complex*16, dimension( lda, *
    ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( *
    ) work, integer lwork, integer info)
    ZHETRI2

🎀 Purpose 🎀

Okay so ZHETRI2 computes the inverse of a COMPLEX*16 hermitian indefinite matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZHETRF. Also, ZHETRI2 set the LEADING DIMENSION of the workspace before calling ZHETRI2X that actually computes the inverse. Slay. 💅

🍓 Parameters 🍓

Every parameter, every detail, let's go:

UPLO

UPLO is CHARACTER*1. It specifies whether the details of the factorization are stored as an upper or lower triangular matrix. The options are:

• = 'U': Upper triangular, form is A = U*D*U**T;
• = 'L': Lower triangular, form is A = L*D*L**T.

N

N is INTEGER. It's the order of the matrix A. Constraint: N >= 0.

A

A is COMPLEX*16 array, dimension (LDA,N). On entry, it holds the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZHETRF.

On exit, if INFO = 0, it's 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.

LDA

LDA is INTEGER. It's the leading dimension of the array A. Constraint: LDA >= max(1,N).

IPIV

IPIV is INTEGER array, dimension (N). It holds details of the interchanges and the block structure of D as determined by ZHETRF.

WORK

WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)).

LWORK

LWORK is INTEGER. It's the dimension of the array WORK.

Rules, periodt:

• If N = 0, LWORK >= 1, else LWORK >= (N+NB+1)*(NB+3).
• If LWORK = -1, then a workspace query is assumed; the routine calculates:
  • 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. Exit status tea:

• = 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 126 of file zhetri2.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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