SRC/zpptrf.f(3)

Hey bestie! 💖 Welcome to SRC/zpptrf.f(3) from the Library Functions Manual — it's giving major "let's factor a complex Hermitian positive definite packed matrix" energy, and honestly? Iconic. ✨

🌸 NAME 🌸

SRC/zpptrf.f

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine zpptrf (uplo, n, ap, info) — ZPPTRF

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💅 Function/Subroutine Documentation 💅

👑 subroutine zpptrf 👑

subroutine zpptrf (character uplo, integer n, complex*16, dimension( * ) ap,
     integer info)

ZPPTRF

🎯 Purpose 🎯

Okay so ZPPTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format. 🫶

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. Slay. 💅

🌈 Parameters 🌈

• UPLO — UPLO is CHARACTER*1. It tells you which triangle of A is stored: = 'U': Upper triangle of A is stored; or = 'L': Lower triangle of A is stored. 🦋
• N — N is INTEGER. The order of the matrix A. N >= 0. 💜
• AP — AP is COMPLEX*16 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. ✨

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.

• INFO — INFO is INTEGER. Here's the vibe check:

= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
> 0:  if INFO = i, the leading principal minor of order i
      is not positive, and the factorization could not be
      completed.

🎀 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 ]

Definition at line 118 of file zpptrf.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 — LAPACK Version 3.12.0, page SRC/zpptrf.f(3). Bye, love you, go factor something positive definite. 💅✨