SPTTRSV(l)

✨ SPTTRSV(l) ✨

okay bestie sit DOWN because we're about to talk about SPTTRSV — a LAPACK routine, specifically from LAPACK version 2.0 💖 this is the SPTTRSV(l) manual page and she's giving linear algebra main character energy, no cap.

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🌸 NAME 🌸

SPTTRSV — solve one of the triangular systems L**T* X = B, or L * X = B,

(yes the comma is staying, we don't edit her 💅)

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🦋 SYNOPSIS 🦋

SUBROUTINE SPTTRSV( TRANS, N, NRHS, D, E, B, LDB, INFO )

    CHARACTER       TRANS

    INTEGER         INFO, LDB, N, NRHS

    REAL            D( * )

    REAL            B( LDB, * ), E( * )

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💜 PURPOSE 💜

so like, what does she even DO? SPTTRSV solves one of the triangular systems

L**T* X = B, or  L * X = B,

where L is the Cholesky factor of a Hermitian positive definite tridiagonal matrix A such that

A = L*D*L**H

and that factorization is computed by SPTTRF, just so you know where she came from 🫶

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🎀 ARGUMENTS 🎀

• TRANS (input) CHARACTER — tells us which form of the system of equations we're working with, like pick your fighter:
  • = 'N': L * X = B (No transpose)
  • = 'T': L**T * X = B (Transpose)
• N (input) INTEGER — the order of the tridiagonal matrix A. constraint: N >= 0. periodt.
• NRHS (input) INTEGER — the number of right hand sides, aka the number of columns of the matrix B. constraint: NRHS >= 0. yes she counted them herself 💅
• D (input) REAL array, dimension (N) — the n diagonal elements of the diagonal matrix D from the factorization computed by SPTTRF. 🍓
• E (input) COMPLEX array, dimension (N-1) — the (n-1) off-diagonal elements of the unit bidiagonal factor U or L from the factorization computed by SPTTRF (see UPLO). 🔥
• B (input/output) COMPLEX array, dimension (LDB,NRHS) — on entry, the right hand side matrix B. On exit, the solution matrix X. she literally transforms in front of you, iconic 💖
• LDB (input) INTEGER — the leading dimension of the array B. constraint: LDB >= max(1,N). do NOT skip this one, she WILL be upset 🙈
• INFO (output) INTEGER — the vibe check report:
  • = 0: successful exit ✨
  • < 0: if INFO = -i, the i-th argument had an illegal value 💀

bestie listen — if INFO comes back negative, something you passed in was not it. go back and look at argument number i. not me being the one to tell you, but she's judging a little. 😭

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🌈 that's the whole page, slay 🌈

this was a modified LAPACK routine, dated 12 May 1997, and you just read the SPTTRSV(l) page top to bottom. obsessed with you honestly. go solve a triangular system, you've got this 👑💜🧚