SRC/csytri.f(3)

💜 SRC/csytri.f 💜

okay so bestie, gather round, because this is the manual page for SRC/csytri.f, straight out of the Library Functions Manual — and it's genuinely iconic. no cap. ✨

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🦋 NAME 🦋

SRC/csytri.f — that's it, that's the name, she's mysterious like that 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine csytri (uplo, n, a, lda, ipiv, work, info) — CSYTRI, the main character herself 👑

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🎀 Function/Subroutine Documentation 🎀

subroutine csytri 🧚

here's the whole glow-up, full signature, nothing skipped:

subroutine csytri (character uplo, integer n, complex, dimension( lda, * )
a, integer lda, integer, dimension( * ) ipiv, complex, dimension( * )
work, integer info)

CSYTRI ✨

Purpose:

!> !> CSYTRI computes the inverse of a complex symmetric indefinite matrix !> A using the factorization A = U*D*U**T or A = L*D*L**T computed by !> CSYTRF. !>

so yeah — she doesn't invent the factorization, she takes what CSYTRF already did and flips it into an inverse. team effort fr fr 🫶

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Parameters 🍓

• UPLO — UPLO is CHARACTER*1, and it's literally just telling you whether the factorization details are stored as an upper or lower triangular matrix:
  • = 'U': Upper triangular, form is A = U*D*U**T;
  • = 'L': Lower triangular, form is A = L*D*L**T.
• N — N is INTEGER, aka the order of the matrix A. and listen: N >= 0. respect the boundary bestie 💀
• A — A is COMPLEX array, dimension (LDA,N). on entry? it's the block diagonal matrix D plus the multipliers used to obtain the factor U or L as computed by CSYTRF. on exit, if INFO = 0, it's the (symmetric) inverse of the original matrix 😭 iconic transformation honestly. and the details, because they matter:
  • 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. and the rule is LDA >= max(1,N) — no wiggle room, she said what she said 💅
• IPIV — IPIV is INTEGER array, dimension (N). this one's carrying the details of the interchanges and the block structure of D as determined by CSYTRF. iykyk 🌈
• WORK — WORK is COMPLEX array, dimension (2*N) — just a workspace, doing her little job quietly, we love her 🎀
• INFO — INFO is INTEGER, the vibe check at the end:
  • = 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 💀

lowkey important: that last one is the "she's singular, the inverse is NOT happening" case. not a warning to gloss over, bestie — no inverse for you. 🔥

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👑 Author 👑

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

also: Definition at line 113 of file csytri.f. — go look, she's there 🌸

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⭐ Author (again, but make it doxygen) ⭐

Generated automatically by Doxygen for LAPACK from the source code. 🤖✨

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so that's the whole page angel, every flag, every dimension, every >= max(1,N), untouched and accounted for 💖

signing off from LAPACK, Version 3.12.0, dated SRC/csytri.f(3) — mwah, go invert something symmetric 🦋💅