SRC/spptrf.f(3)

💖 NAME 💖

SRC/spptrf.f — okay bestie, this is the SRC/spptrf.f(3) page from the Library Functions Manual. The subroutine is SPPTRF and she’s giving major Cholesky factorization energy. ✨

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine spptrf (uplo, n, ap, info) — SPPTRF

🛠️ Function/Subroutine Documentation 🛠️

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

SPPTRF — iconic, no cap. Here’s the whole vibe:

🌸 Purpose 🌸

okay so 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.

💅 Parameters 💅

• UPLO — UPLO is CHARACTER*1
  • = '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 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 — INFO is 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.

---

xoxo, this page is from LAPACK Version 3.12.0, file SRC/spptrf.f(3). 💅✨