DPPTRF(3)

🌸 NAME 🌸

Okay so bestie, this is DPPTRF(3) from the Library Functions Manual, and the NAME section is literally this source path — no cap:

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

It’s giving “the file that documents DPPTRF,” and DPPTRF computes the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format. ✨💅

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✨ SYNOPSIS ✨

Functions/Subroutines 🫶

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

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🫶 Function/Subroutine Documentation 🫶

Main-character signature, exactly as written:

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

🎯 Purpose:

Bestie, here’s the whole point: DPPTRF 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 — 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 DOUBLE PRECISION 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 dpptrf.f. 📍

🤖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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Catch ya later, bestie 💖🫶 — this page is LAPACK Version 3.12.0, and the footer path is /home/abui...RC/dpptrf.f(3). No date showed up in the footer, so that’s the whole vibe. Slay. 🌟