SRC/dpptrf.f(3)

🌸 NAME 🌸

okay so this is the page for SRC/dpptrf.f, bestie — it's from the Library Functions Manual, and the header title is SRC/dpptrf.f(3). We're talking about DPPTRF, a LAPACK subroutine, and yes she's iconic. 🎀

🦋 SYNOPSIS 🦋

   Functions/Subroutines
       subroutine dpptrf (uplo, n, ap, info)
           DPPTRF

✨ Function/Subroutine Documentation ✨

Here's the signature, copied exactly so nobody comes for me:

   subroutine dpptrf (character uplo, integer n, double precision, dimension( *
       ) ap, integer info)
       DPPTRF

💖 Purpose 💖

DPPTRF computes the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format. No cap, that's the whole assignment. 💖

The factorization has the form

A = U**T * U,  if UPLO = 'U', or
A = L  * L**T,  if UPLO = 'L',

where U is an upper triangular matrix and L is lower triangular. Slay. ✨

🎀 Parameters 🎀

UPLO

UPLO is CHARACTER*1. The vibe is:

• = '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.

AP

AP is DOUBLE PRECISION array, dimension (N*(N+1)/2).

On entry, it's the upper or lower triangle of the symmetric 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**T*U or A = L*L**T, in the same storage format as A. Periodt. 💅

INFO

INFO is INTEGER. Here's the tea:

• = 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 symmetric matrix A:

     a11 a12 a13 a14
         a22 a23 a24
             a33 a34     (aij = 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 dpptrf.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code.

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🏁 cute sign-off: LAPACK, Version 3.12.0, SRC/dpptrf.f(3) — that's the footer, bestie. No date printed on this one, so don't come for me 🙈💜