DPTTRF(3)

💅 NAME 💅

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

okay so bestie, this is the manual page for dpttrf.f — yes that whole long path is genuinely the "name" up there, it's giving "my full government name" energy 😭 — and it lives in the Library Functions Manual section. It's the LAPACK girlies' page for the DPTTRF subroutine, and we're gonna walk through it together, no cap 🫶

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✨ SYNOPSIS ✨

Functions/Subroutines

• subroutine DPTTRF (n, d, e, info) — literally the whole lineup, and yes the description is just "DPTTRF" again, she's mysterious like that 💅

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🌸 Function/Subroutine Documentation 🌸

subroutine DPTTRF (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, integer info)

DPTTRF 👑 (again, the summary is just her name — main character energy fr fr)

🎀 Purpose

!> !> DPTTRF computes the L*D*LT factorization of a real symmetric !> positive definite tridiagonal matrix A. The factorization may also !> be regarded as having the form A = UT*D*U. !>

so basically she takes your real symmetric positive definite tridiagonal matrix A and factorizes it as L*D*L**T. and if you're more of a U girlie, that same factorization can also be regarded as having the form A = U**T*D*U. two icons, one routine, we love to see it ✨

🦋 Parameters

N

!> N is INTEGER !> The order of the matrix A. N >= 0. !>

N is an INTEGER and it's the order of the matrix A. she must be N >= 0, zero included, no negativity allowed 🙈

D

!> D is DOUBLE PRECISION array, dimension (N) !> On entry, the n diagonal elements of the tridiagonal matrix !> A. On exit, the n diagonal elements of the diagonal matrix !> D from the L*D*L**T factorization of A. !>

D is a DOUBLE PRECISION array, dimension (N). on entry? the n diagonal elements of the tridiagonal matrix A. on exit? the n diagonal elements of the diagonal matrix D from the L*D*L**T factorization of A. she's a glow-up, she's a transformation, she ate 💖

E

!> E is DOUBLE PRECISION array, dimension (N-1) !> On entry, the (n-1) subdiagonal elements of the tridiagonal !> matrix A. On exit, the (n-1) subdiagonal elements of the !> unit bidiagonal factor L from the L*D*LT factorization of A. !> E can also be regarded as the superdiagonal of the unit !> bidiagonal factor U from the UT*D*U factorization of A. !>

E is a DOUBLE PRECISION array, dimension (N-1) — note the -1, she's one shorter, that's not a typo bestie. on entry: the (n-1) subdiagonal elements of the tridiagonal matrix A. on exit: the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**T factorization of A. and plot twist — E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U**T*D*U factorization of A. versatile queen 🧚

INFO

!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -k, the k-th argument had an illegal value !> > 0: if INFO = k, the leading principal minor of order k !> is not positive; if k < N, the factorization could not !> be completed, while if k = N, the factorization was !> completed, but D(N) <= 0. !>

INFO is an INTEGER and she's the vibe check at the end, so listen up:

• = 0: successful exit. slay, we're done, go home 💅
• < 0: if INFO = -k, the k-th argument had an illegal value. someone passed something cursed 😭
• > 0: if INFO = k, the leading principal minor of order k is not positive. and here's the nuance, don't miss it — if k < N, the factorization could not be completed, while if k = N, the factorization was completed, but D(N) <= 0. so yeah, k = N still finished, it's just giving non-positive D(N) at the end 💀

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👑 Author 👑

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

the whole squad, credited, iconic 🌈

Definition at line 90 of file dpttrf.f.

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🙈 Author 🙈

Generated automatically by Doxygen for LAPACK from the source code.

(yes there are two Author sections, that's just how the page is built, we don't question the pipeline 🍓)

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okay and the cute little sign-off at the bottom: this is LAPACK, Version 3.12.0, and the file is that same dpttrf.f(3) path from the top — she began as she ended, full circle, periodt 🎀💜