SRC/ztrti2.f(3)

💜 SRC/ztrti2.f(3) — from the Library Functions Manual, bestie

Okay so picture this: it's giving classic LAPACK manpage energy, and today's main character is ztrti2 — the unblocked, Level 2 BLAS little sister who inverts your complex triangular matrix. No cap. ✨

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine ztrti2 (uplo, diag, n, a, lda, info)

ZTRTI2 computes the inverse of a triangular matrix (unblocked algorithm). 🎀

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🦋 Function/Subroutine Documentation 🦋

subroutine ztrti2 (character uplo, character diag, integer n, complex*16,
    dimension( lda, * ) a, integer lda, integer info)

ZTRTI2 computes the inverse of a triangular matrix (unblocked algorithm). Periodt.

✨ Purpose ✨

So the actual job description, straight up:

!>
!> ZTRTI2 computes the inverse of a complex upper or lower triangular
!> matrix.
!>
!> This is the Level 2 BLAS version of the algorithm.
!>

Yeah — she's the Level 2 BLAS version of the algorithm. The unblocked one. The one who does it the honest way. 💅

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🌈 Parameters 🌈

• UPLO

!>          UPLO is CHARACTER*1
!>          Specifies whether the matrix A is upper or lower triangular.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>

This is the vibe check for your matrix — is A upper or lower triangular? 'U' means upper triangular, 'L' means lower triangular. Pick one, bestie, there's no in-between. 🙈

• DIAG

!>          DIAG is CHARACTER*1
!>          Specifies whether or not the matrix A is unit triangular.
!>          = 'N':  Non-unit triangular
!>          = 'U':  Unit triangular
!>

Is your matrix unit triangular or not? 'N' = non-unit triangular, 'U' = unit triangular. That's it, that's the whole flag. 🫶

• N

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>

The order of the matrix A. And it's N >= 0, so like, don't come at her with a negative order, that's not the move. 😭

• A

!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          On entry, the triangular matrix A.  If UPLO = 'U', the
!>          leading n by n upper triangular part of the array A contains
!>          the upper triangular matrix, and the strictly lower
!>          triangular part of A is not referenced.  If UPLO = 'L', the
!>          leading n by n lower triangular part of the array A contains
!>          the lower triangular matrix, and the strictly upper
!>          triangular part of A is not referenced.  If DIAG = 'U', the
!>          diagonal elements of A are also not referenced and are
!>          assumed to be 1.
!>
!>          On exit, the (triangular) inverse of the original matrix, in
!>          the same storage format.
!>

Okay this one's the star of the show — A is a COMPLEX*16 array, dimension (LDA,N). On entry it's your triangular matrix A:

• If UPLO = 'U', the leading n by n upper triangular part of A holds the upper triangular matrix, and the strictly lower triangular part of A is not referenced (she's not looking, leave it alone 💀).
• If UPLO = 'L', the leading n by n lower triangular part of A holds the lower triangular matrix, and the strictly upper triangular part of A is not referenced.
• If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.

On exit? The (triangular) inverse of the original matrix, in the same storage format. She literally ate and left no crumbs. 🔥

• LDA

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

The leading dimension of the array A. Constraint is LDA >= max(1,N) — respect it or catch an INFO complaint. ⭐

• INFO

!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -k, the k-th argument had an illegal value
!>

The receipts! INFO = 0 means a successful exit, slay. INFO < 0 means if INFO = -k, the k-th argument had an illegal value — so like, go look at argument number k, it's the problem, not her. 👑

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👑 Author 👑

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

Definition at line 109 of file ztrti2.f.

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🧚 Author 🧚

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