SGTTRS(3)

🌸 SGTTRS (3) — the tridiagonal-solve bestie we deserve ✨

ok so this is a page from the Library Functions Manual, and the star of the show lives at /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sgttrs.f — yes that's a whole mouthful, she's got a long address, we still love her 💖

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✨ NAME ✨

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

that's it. that's the name. she's a file path and she's iconic for it 🎀

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🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine SGTTRS (trans, n, nrhs, dl, d, du, du2, ipiv, b, ldb, info)

SGTTRS 💫 (yes the heading literally just says her name again, main character energy fr)

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👑 Function/Subroutine Documentation 👑

subroutine SGTTRS (character trans, integer n, integer nrhs, real,
    dimension( * ) dl, real, dimension( * ) d, real, dimension( * ) du,
    real, dimension( * ) du2, integer, dimension( * ) ipiv, real, dimension(
    ldb, * ) b, integer ldb, integer info)

SGTTRS (she said it twice, she's confident 💅)

🌈 Purpose 🌈

ok so listen bestie, here's the vibe:

!>
!> SGTTRS solves one of the systems of equations
!>    A*X = B  or  A**T*X = B,
!> with a tridiagonal matrix A using the LU factorization computed
!> by SGTTRF.
!>

so basically she takes your system of equations — either A*X = B or A**T*X = B — with a tridiagonal matrix A, and she solves it using the LU factorization that SGTTRF already computed for you. no cap, that's the whole job 🫶

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🎀 Parameters 🎀

• TRANS — TRANS is CHARACTER*1. this tells her which form of the system of equations you want, and your options are:
  • = 'N': A * X = B (No transpose)
  • = 'T': A**T* X = B (Transpose)
  • = 'C': A**T* X = B (Conjugate transpose = Transpose)

(yes 'T' and 'C' do the same thing here, that's not a typo, that's just how it is 💀)

• N — N is INTEGER. the order of the matrix A. literally just how big she is ✨
• NRHS — NRHS is INTEGER. the number of right hand sides, i.e., the number of columns of the matrix B. and important: NRHS >= 0. she does not do negative columns, don't even try 🙈
• DL — DL is REAL array, dimension (N-1). the (n-1) multipliers that define the matrix L from the LU factorization of A. the L girlies 💜
• D — D is REAL array, dimension (N). the n diagonal elements of the upper triangular matrix U from the LU factorization of A. the diagonal queen 👑
• DU — DU is REAL array, dimension (N-1). the (n-1) elements of the first super-diagonal of U. first super-diagonal, so fancy 🎀
• DU2 — DU2 is REAL array, dimension (N-2). the (n-2) elements of the second super-diagonal of U. okay second super-diagonal, she's showing off now ✨
• IPIV — IPIV is INTEGER array, dimension (N). the pivot indices; for 1 <= i <= n, row i of the matrix was interchanged with row IPIV(i). and here's the tea: IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required. so she's never out here swapping rows all wild, she keeps it neighbors-only 🫶
• B — B is REAL array, dimension (LDB,NRHS). on entry, the matrix of right hand side vectors B. on exit, B is overwritten by the solution vectors X. so like… she eats your B and leaves X behind. she ate and left no crumbs fr fr 🔥
• LDB — LDB is INTEGER. the leading dimension of the array B. and LDB >= max(1,N) — gotta be at least that, no discussion 💅
• INFO — INFO is INTEGER. the receipts:
  • = 0: successful exit 🎉
  • < 0: if INFO = -i, the i-th argument had an illegal value 😭 (so INFO tells you which argument acted up, helpful king)

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🌸 Author 🌸

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

a whole squad, we love a collaborative effort 💖

Definition at line 136 of file sgttrs.f. (iykyk, she's anchored to line 136 exactly, don't @ me)

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⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. so nobody hand-wrote this bad boy, a robot did it and honestly? slay 🤖✨

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ok that's the whole page bestie, go solve your tridiagonal systems, you got this 💜🦋

LAPACK — Version 3.12.0 — /home/abui...RC/sgttrs.f(3) 🎀 that's the version, that's the date string, that's the sign-off, mwah 💋