ZPTTS2(3)

💅 ZPTTS2(3) — like, the whole glow-up

okay so bestie, buckle up, because this is a page from the Library Functions Manual and it's about to be your new fave ✨ It's ZPTTS2, and she solves things. Literally. Tridiagonal things. 💖

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✨ SYNOPSIS ✨

Functions/Subroutines 🎀

subroutine ZPTTS2 (iuplo, n, nrhs, d, e, b, ldb)

ZPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf. 🫶

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🌸 Function/Subroutine Documentation 🌸

💫 the actual signature, no cap 💫

subroutine ZPTTS2 (integer iuplo, integer n, integer nrhs, double precision,
    dimension( * ) d, complex*16, dimension( * ) e, complex*16, dimension(
    ldb, * ) b, integer ldb)

ZPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf. (yes she says it twice, she's consistent, we love that for her 👑)

🦋 Purpose 🦋

!>
!> ZPTTS2 solves a tridiagonal system of the form
!>    A * X = B
!> using the factorization A = U**H *D*U or A = L*D*L**H computed by ZPTTRF.
!> D is a diagonal matrix specified in the vector D, U (or L) is a unit
!> bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
!> the vector E, and X and B are N by NRHS matrices.
!>

so like, A * X = B, she factors it as A = U**H *D*U or A = L*D*L**H (courtesy of ZPTTRF), D is the diagonal vibe living in the vector D, U (or L) is a unit bidiagonal queen whose superdiagonal (or subdiagonal) is chillin' in the vector E, and X and B are N by NRHS matrices. iconic. ✨

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🎀 Parameters 🎀

🌈 IUPLO 🌈

!>          IUPLO is INTEGER
!>          Specifies the form of the factorization and whether the
!>          vector E is the superdiagonal of the upper bidiagonal factor
!>          U or the subdiagonal of the lower bidiagonal factor L.
!>          = 1:  A = U**H *D*U, E is the superdiagonal of U
!>          = 0:  A = L*D*L**H, E is the subdiagonal of L
!>

• IUPLO is INTEGER 👑 — she picks which factorization form you're on and whether E is the superdiagonal of the upper bidiagonal factor U or the subdiagonal of the lower bidiagonal factor L.
  • = 1: A = U**H *D*U, and E is the superdiagonal of U 💜
  • = 0: A = L*D*L**H, and E is the subdiagonal of L 💜

🍓 N 🍓

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

• N is INTEGER — the order of the tridiagonal matrix A. And bestie, N >= 0. fr fr. ✨

🧚 NRHS 🧚

!>          NRHS is INTEGER
!>          The number of right hand sides, i.e., the number of columns
!>          of the matrix B.  NRHS >= 0.
!>

• NRHS is INTEGER — the number of right hand sides, aka how many columns the matrix B has. NRHS >= 0, no exceptions 💅

💀 D 💀

!>          D is DOUBLE PRECISION array, dimension (N)
!>          The n diagonal elements of the diagonal matrix D from the
!>          factorization A = U**H *D*U or A = L*D*L**H.
!>

• D is a DOUBLE PRECISION array, dimension (N) — she holds the n diagonal elements of the diagonal matrix D from the factorization A = U**H *D*U or A = L*D*L**H. main character energy, honestly 🌟

🔥 E 🔥

!>          E is COMPLEX*16 array, dimension (N-1)
!>          If IUPLO = 1, the (n-1) superdiagonal elements of the unit
!>          bidiagonal factor U from the factorization A = U**H*D*U.
!>          If IUPLO = 0, the (n-1) subdiagonal elements of the unit
!>          bidiagonal factor L from the factorization A = L*D*L**H.
!>

• E is a COMPLEX*16 array, dimension (N-1) — she's feral but specific:
  • if IUPLO = 1, she's the (n-1) superdiagonal elements of the unit bidiagonal factor U from A = U**H*D*U 🌸
  • if IUPLO = 0, she's the (n-1) subdiagonal elements of the unit bidiagonal factor L from A = L*D*L**H 🌸

🦋 B 🦋

!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          On entry, the right hand side vectors B for the system of
!>          linear equations.
!>          On exit, the solution vectors, X.
!>

• B is a COMPLEX*16 array, dimension (LDB,NRHS) — a whole transformation arc 😭
  • on entry: the right hand side vectors B for the system of linear equations
  • on exit: the solution vectors, X — she ate and left no crumbs 💅

🎀 LDB 🎀

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max(1,N).
!>

• LDB is INTEGER — the leading dimension of the array B, and it's gotta be LDB >= max(1,N). periodt. 👑

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👑 Author 👑

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

the whole squad, we stan 🫶

Definition at line 112 of file zptts2.f. ✨

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💖 Author (the meta one) 💖

Generated automatically by Doxygen for LAPACK from the source code. not a human, just vibes 🤖💅

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🧚 quick heads-up bestie: shoutout to the NAME section of the original, which was just the path /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zptts2.f — she's literally just a file path, that's her whole identity, and honestly? relatable. 🙈

and that's the page!! 💖 LAPACK, Version 3.12.0, dated alongside /home/abui...RC/zptts2.f(3) — slay, bye, drink water 🍓