BLAS/SRC/ztpsv.f(3)

💖 BLAS/SRC/ztpsv.f 💖

okay bestie, welcome to the ztpsv page from LAPACK's BLAS source — it lives at BLAS/SRC/ztpsv.f and it's lowkey one of the most useful little solvers in the whole triangle-squad. let's get into it 🦋

---

✨ NAME ✨

BLAS/SRC/ztpsv.f — no cap, that's the file, that's the name, that's the whole vibe 💅

---

🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine ztpsv (uplo, trans, diag, n, ap, x, incx) — literally the one and only ZTPSV 👑

---

🎀 Function/Subroutine Documentation 🎀

subroutine ztpsv (character uplo, character trans, character diag, integer n, complex*16, dimension(*) ap, complex*16, dimension(*) x, integer incx)

ZTPSV

---

🦋 Purpose 🦋

ok so ZTPSV solves one of these systems of equations, and you get to pick which one:

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. packed!! no full 2D array needed, she's efficient like that ✨

BIG WARNING BESTIE 🚨 no test for singularity or near-singularity is included in this routine. such tests must be performed before calling this routine. so if your matrix is sus, that's on you, not on her 🙈

---

💜 Parameters 💜

• 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, as follows:
  • 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 not gonna judge 🫶)
• AP — AP is COMPLEX*16 array, dimension at least ( ( n*( n + 1 ) )/2 ). 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. 🧚
• X — X is COMPLEX*16 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. 💫
• INCX — INCX is INTEGER. on entry, INCX specifies the increment for the elements of X. INCX must not be zero. not zero, bestie, she said what she said 💀

---

👑 Author 👑

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

---

🌈 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.

1986!! she's been slaying since before most of us were born, periodt 💅✨

---

📍 Definition

Definition at line 143 of file ztpsv.f.

---

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. (not a human, just a very diligent little robot 🎀)

---

and that's the whole page bestie!! no notes, she ate, we love a packed triangular solver with main character energy 🦋💖

Version 3.12.0 — Tue Nov 28 2023 12:08:41 — BLAS/SRC/ztpsv.f(3) 🫶 mwah, go solve something cute 💜