SRC/cpptrf.f(3)

✨ SRC/cpptrf.f(3) — Library Functions Manual ✨

Okay bestie, welcome to the SRC/cpptrf.f(3) page from the Library Functions Manual 💖 This is the whole vibe, no cap.

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🌸 NAME 🌸

SRC/cpptrf.f — the main character file, periodt. She's giving subroutine energy and we're obsessed 👑

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🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

• subroutine cpptrf (uplo, n, ap, info) — this is the whole entire function, bestie. CPPTRF ate and left no crumbs 💅

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💜 Function/Subroutine Documentation 💜

🎀 subroutine cpptrf (character uplo, integer n, complex, dimension( * ) ap, integer info) 🎀

CPPTRF

🌟 Purpose:

CPPTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format. It's literally that girl 💖

The factorization has the form:

A = U**H * U,  if UPLO = 'U', or
A = L  * L**H,  if UPLO = 'L',

where U is an upper triangular matrix and L is lower triangular. No cap, that's the whole point 🫶

🍓 Parameters

• UPLO — UPLO is CHARACTER*1. She's telling you which triangle is stored, and you better listen:
  • = '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. Not me checking that N is non-negative, periodt 😌
• AP — AP is COMPLEX array, dimension (N*(N+1)/2). On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:
  • if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
  • if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.

See below for further details (yes, there's a whole example, keep scrolling bestie).

On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, in the same storage format as A. Iconic behavior, honestly 🔥

• INFO — INFO is INTEGER. The vibe check:
  • = 0: successful exit — we love a win 💖
  • < 0: if INFO = -i, the i-th argument had an illegal value — not me side-eyeing your arguments 🙈
  • > 0: if INFO = i, the leading principal minor of order i is not positive definite, and the factorization could not be completed. It's giving not positive definite, and honestly? Tragic 💀

🧚 Author

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

🌈 Further Details:

The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U':

Two-dimensional storage of the Hermitian matrix A:

   a11 a12 a13 a14
       a22 a23 a24
           a33 a34     (aij = conjg(aji))
               a44

Packed storage of the upper triangle of A:

AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

Literally so satisfying to look at, ngl 🦋

Definition at line 118 of file cpptrf.f. — she's got a designated spot in the source code, and she's serving it 💅

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code. The robots did their thing, and we respect the automation ✨

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And that's the tea, bestie 🎀 This page was brought to you by LAPACK Version 3.12.0 and the file SRC/cpptrf.f(3). No date in sight, but she's timeless 💖 Stay slaying, stay factorizing, and remember: positive definite matrices only 🫶