SPTTRF(3)

✨ SPTTRF 💅 (like, the whole glow-up)

okay so real talk bestie — this page is from the LAPACK library manual, and the star of the show lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/spttrf.f. yes that's a real path, no I did not make it up 😭

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🎀 NAME 🎀

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

that's it. that's the name. she's literally just a file path and honestly? iconic. 👑

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🦋 SYNOPSIS 🦋

Functions/Subroutines

here's the lineup, no cap:

subroutine SPTTRF (n, d, e, info)
    SPTTRF

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🌸 Function/Subroutine Documentation 🌸

okay so the actual signature, bestie — look at her:

subroutine SPTTRF (integer n, real, dimension( * ) d, real, dimension( * )
    e, integer info)
    SPTTRF

💖 Purpose 💖

!> !> SPTTRF 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, you can also read it as A = U**T*D*U. same energy, different vibe check. ✨

🌈 Parameters 🌈

okay buckle up, here's everybody:

• N — N is INTEGER. she's the order of the matrix A, and the rule is N >= 0. no negatives, periodt. 🚫
• D — D is REAL array, dimension (N). on the way in, these are the n diagonal elements of the tridiagonal matrix A. on the way out? she's the n diagonal elements of the diagonal matrix D from the L*D*L**T factorization of A. glow-up complete, honestly. 💅
• E — E is REAL array, dimension (N-1). on entry she holds the (n-1) subdiagonal elements of the tridiagonal matrix A. on exit she's 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! 🦋

note the dimension is (N-1), not N. one less. don't come for me, that's just what she is. 🙈

• INFO — INFO is INTEGER, and she's the one who tells you how it went:
  • = 0: successful exit. slay. ✅
  • < 0: if INFO = -k, the k-th argument had an illegal value. so like, you passed her something cursed. 💀
  • > 0: if INFO = k, the leading principal minor of order k is not positive. and here's the nuance bestie — if k < N, the factorization could not be completed; while if k = N, the factorization was completed, but D(N) <= 0. so close but so real. 😭

👑 Author 👑

the whole academic squad behind this:

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

⭐ Definition at line 90 of file spttrf.f. ⭐

line 90, file spttrf.f. if you were wondering where to look, there she is. 🔥

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🍓 Author 🍓

Generated automatically by Doxygen for LAPACK from the source code.

not a human, a machine. she was born automated and she's thriving. 🧚

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💜 the cute lil sign-off 💜

k so this little masterpiece is from LAPACK, Version 3.12.0, and the page footer path vibes were /home/abui...RC/spttrf.f(3) — the (3) ofc meaning she's a section-3 library function, iykyk. that's the whole page bestie, you ate, go factorize something tridiagonal 🌸🫶✨