CPPTRF(3)

💅 CPPTRF(3) 💅

okay so bestie, welcome to the cpptrf.f(3) page from the Library Functions Manual. this one is all about packed-format Cholesky and it's lowkey iconic once you see the storage pattern. 💖

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✨ NAME ✨

the name on the door is literally the source file path:

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

that's it, that's the name. 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine CPPTRF (uplo, n, ap, info) — CPPTRF

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🦋 Function/Subroutine Documentation 🦋

🫶 subroutine CPPTRF 🫶

the full signature is:

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

and yes, the routine is called CPPTRF — say it with me: CPPTRF. 🎀

💖 Purpose: 💖

CPPTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format. no cap.

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. periodt. ✨

💜 Parameters 💜

• UPLO — is CHARACTER*1.
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — is INTEGER. The order of the matrix A. N >= 0.
• AP — is COMPLEX 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 — 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 definite, and the factorization could not be completed.

bestie, that INFO > 0 case is the dramatic one: the factorization could not be completed. not a slay. 😭

👑 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 cpptrf.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. (yes, the page itself has main character energy. 💅)

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xoxo, bestie — this page is LAPACK Version 3.12.0 and its home is /home/abui...RC/cpptrf.f(3). go forth and pack that triangle. 🎀💖