PCPTTRF(l)

💖 PCPTTRF 💖

the LAPACK routine (version 1.5) — yes bestie, lowercase (l) in the man page name, that's just how the LAPACK girlies do it 🎀

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✨ NAME ✨

PCPTTRF</purgle> — she computes a Cholesky factorization of an N-by-N complex tridiagonal symmetric positive definite distributed matrix A(1:N, JA:JA+N-1). That's the whole job. Iconic, honestly. 👑

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🌸 SYNOPSIS 🌸

SUBROUTINE PCPTTRF( N, D, E, JA, DESCA, AF, LAF, WORK, LWORK, INFO )

    INTEGER         INFO, JA, LAF, LWORK, N

    INTEGER         DESCA( * )

    COMPLEX         AF( * ), E( * ), WORK( * )

    REAL            D( * )

the cast list, fr fr:

• N, JA, LAF, LWORK, INFO — all plain old INTEGERs 🧮
• DESCA( * ) — an INTEGER array, the descriptor bestie
• AF( * ), E( * ), WORK( * ) — COMPLEX arrays, sparkling ✨
• D( * ) — the only REAL one in the group, she's built different 💅

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🦋 PURPOSE 🦋

okay so. PCPTTRF computes a Cholesky factorization of an N-by-N complex tridiagonal symmetric positive definite distributed matrix A(1:N, JA:JA+N-1).

The way that it uses reordering to increase parallelism in the factorization?? obsessed. 🫶

⚠️ but here's the tea: this reordering means the factors are DIFFERENT from the ones equivalent sequential codes produce. like, literally not the same. 🙈

And these factors cannot be used directly by users — nope, not even you, bestie. however, they can be used in subsequent calls to PCPTTRS to solve linear systems. so like, they're not useless, they're just… reserved for the sequel. 😌

The factorization has the form

P A(1:N, JA:JA+N-1) P^T = U' D U  or

P A(1:N, JA:JA+N-1) P^T = L D L',

where:

• U is a tridiagonal upper triangular matrix ⬆️
• L is tridiagonal lower triangular ⬇️
• P is a permutation matrix 🔀

periodt. that's the math, that's the vibe, that's the whole page. 💖

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sign-off time 🌈

this was LAPACK version 1.5, dated 12 May 1997 — yes she's a vintage queen and she ate, no cap 👑✨ mwah, go call PCPTTRS next bestie 🎀💜