CTPSV(3)

💜 CTPSV(3) — like, the LAPACK BLAS routine, bestie 💜

okay so this page lives in the LAPACK manual (Version 3.12.0, if we're being precise, and we are) and it's literally all about one little workhorse from BLAS/SRC/ctpsv.f. she's a Level 2 BLAS icon, no cap. let's get into it 🫶

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/BLAS/SRC/ctpsv.f — that's the file, that's the whole vibe. she's a .f file, she solves triangular systems, she's booked and busy 💅

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine CTPSV (uplo, trans, diag, n, ap, x, incx) — yep. that's her. that's the whole call. CTPSV.

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🎀 Function/Subroutine Documentation 🎀

subroutine CTPSV (character uplo, character trans, character diag, integer &
   n, complex, dimension(*) ap, complex, dimension(*) x, integer incx)

CTPSV. say it with me. CTPSV. iconic behavior honestly ⭐

🦋 Purpose 🦋

okay so here's the tea, straight from the source with the !> markup and everything:

!>
!> CTPSV  solves one of the systems of equations
!>
!>    A*x = b,   or   A**T*x = b,   or   A**H*x = b,
!>
!> where b and x are n element vectors and A is an n by n unit, or
!> non-unit, upper or lower triangular matrix, supplied in packed form.
!>
!> No test for singularity or near-singularity is included in this
!> routine. Such tests must be performed before calling this routine.
!>

so like. she solves for x. she is not checking whether your matrix is singular or near-singular, bestie — that is not her job and she said what she said 😭 you gotta do that test before you call her. do not come for her if your matrix was messy going in. 🫶

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💖 Parameters 💖

okay this is the part where we go one by one, and yes i'm gonna be thorough, because every single one of these matters:

• UPLO — UPLO is CHARACTER*1. on entry, UPLO specifies whether the matrix is an upper or lower triangular matrix, like so:
  • UPLO = 'U' or 'u' → A is an upper triangular matrix.
  • UPLO = 'L' or 'l' → A is a lower triangular matrix.
• TRANS — TRANS is CHARACTER*1. on entry, TRANS specifies the equations to be solved, as follows:
  • TRANS = 'N' or 'n' → A*x = b.
  • TRANS = 'T' or 't' → A**T*x = b.
  • TRANS = 'C' or 'c' → A**H*x = b.
• DIAG — DIAG is CHARACTER*1. on entry, DIAG specifies whether or not A is unit triangular, like:
  • DIAG = 'U' or 'u' → A is assumed to be unit triangular.
  • DIAG = 'N' or 'n' → A is not assumed to be unit triangular.
• N — N is INTEGER. on entry, N specifies the order of the matrix A. N must be at least zero. (zero is allowed! she's chill like that. negative? no ma'am.)
• AP — AP is COMPLEX array, dimension at least ( ( n*( n + 1 ) )/2 ). this is the packed matrix and the packing order is very specific, so listen up:
  • before entry with UPLO = 'U' or 'u', the array AP must contain the upper triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) respectively, and so on.
  • before entry with UPLO = 'L' or 'l', the array AP must contain the lower triangular matrix packed sequentially, column by column, so that AP( 1 ) contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) respectively, and so on.
  • note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced, but are assumed to be unity. so don't stress about what's sitting on that diagonal, she's not even looking at it 👀
• X — X is COMPLEX array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). before entry, the incremented array X must contain the n element right-hand side vector b. on exit, X is overwritten with the solution vector x. she replaces it. no copy, no take-backs, that's the deal 💀
• INCX — INCX is INTEGER. on entry, INCX specifies the increment for the elements of X. INCX must not be zero. fr fr. zero is not a vibe here.

⚠️ heads up bestie: INCX must not be zero, N must be at least zero, and the singularity check? not included. that one's on you. 😌

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👑 Author 👑

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

a whole collab. the avengers of numerical linear algebra, honestly 🌈

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🔥 Further Details 🔥

!>
!>  Level 2 Blas routine.
!>
!>  -- Written on 22-October-1986.
!>     Jack Dongarra, Argonne National Lab.
!>     Jeremy Du Croz, Nag Central Office.
!>     Sven Hammarling, Nag Central Office.
!>     Richard Hanson, Sandia National Labs.
!>

Level 2 Blas routine. written on 22-October-1986 by Jack Dongarra (Argonne National Lab), Jeremy Du Croz (Nag Central Office), Sven Hammarling (Nag Central Office) and Richard Hanson (Sandia National Labs). 1986!! she's vintage, she's a classic, she's been serving since before most of us existed and she still hits 💅✨

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⭐ Definition ⭐

Definition at line 143 of file ctpsv.f.

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🌷 Author (the other one) 🌷

Generated automatically by Doxygen for LAPACK from the source code. not a human, just a robot doing her little documentation thing, and honestly? she ate. 🎀

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k that's the whole page, mwah 💋 — this was LAPACK, Version 3.12.0, and the file is ctpsv.f(3), courtesy of our fave automatic doc generator. go solve your triangular systems responsibly, bestie. 🦋💖