SPPTRF(3)

hiii bestie 💖 okay so this is SPPTRF(3), from the Library Functions Manual, and the header path situation is /home/abui...RC/spptrf.f(3). we're about to get into packed Cholesky realness, no cap. ✨

🌸 NAME 🌸

the NAME section is literally this path, bestie:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/spptrf.f

---

✨ SYNOPSIS ✨

🧩 Functions/Subroutines 🧩

subroutine SPPTRF (uplo, n, ap, info)
    SPPTRF

---

💖 Function/Subroutine Documentation 💖

okay so the actual subroutine signature is giving main character energy:

subroutine SPPTRF (character uplo, integer n, real, dimension( * ) ap,
    integer info)
    SPPTRF

🎯 Purpose 🎯

SPPTRF computes the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format. 🔥

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. periodt. 💅

🧚 Parameters 🧚

• UPLO — CHARACTER*1
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — INTEGER
  • The order of the matrix A. N >= 0.
• AP — REAL array, dimension (N*(N+1)/2)
  • On entry, 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.

• INFO — INTEGER
  • = 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 spptrf.f.

---

🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

---

mwah 💋 this cutie's footer is LAPACK Version 3.12.0 plus /home/abui...RC/spptrf.f(3) — bye bestie, go slay some packed matrices! 🎀