ZTPMV(3)

💅 NAME 💅

So bestie, you opened page ztpmv.f(3) out of the LAPACK Library Functions Manual, and the star of the show is this file right here:

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

That's it, that's the name. It's giving "my whole identity is a build path" and honestly? Iconic. 🎀

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✨ SYNOPSIS ✨

Functions/Subroutines

Okay so the whole vibe:

subroutine ZTPMV (uplo, trans, diag, n, ap, x, incx)
    ZTPMV

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🦋 Function/Subroutine Documentation 🦋

subroutine ZTPMV

Here's the full signature, no cap, character for character:

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

ZTPMV 🌸

⭐ Purpose ⭐

Okay so literally, ZTPMV performs one of these matrix-vector operations:

x := A*x,   or   x := A**T*x,   or   x := A**H*x,

where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix, supplied in packed form. Packed form! She's compact, she's efficient, she's not wasting a single element on those zeros. Obsessed. 💜

🎀 Parameters 🎀

• UPLO — it's a CHARACTER*1. On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix, like this:
  • UPLO = 'U' or 'u' → A is an upper triangular matrix.
  • UPLO = 'L' or 'l' → A is a lower triangular matrix.
• TRANS — also a CHARACTER*1. On entry, TRANS specifies the operation to be performed, and your choices are:
  • TRANS = 'N' or 'n' → x := A*x.
  • TRANS = 'T' or 't' → x := A**T*x.
  • TRANS = 'C' or 'c' → x := A**H*x.
• DIAG — yeah, CHARACTER*1 again. 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 — an 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. 🧚
• AP — a COMPLEX*16 array, dimension at least ( ( n*( n + 1 ) )/2 ). This is the packed triangle, and the packing order is very much the main character here:
  • 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.
  • Heads up: when DIAG = 'U' or 'u', the diagonal elements of A are not referenced, but are assumed to be unity. So don't bother storing them, bestie, nobody's checking. 🙈
• X — a COMPLEX*16 array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). Before entry, the incremented array X must contain the n element vector x. On exit, X is overwritten with the transformed vector x. She goes in as one thing and comes out as another, it's giving transformation arc. 🦋
• INCX — an INTEGER. On entry, INCX specifies the increment for the elements of X. And listen: INCX must not be zero. Do not do it. 🚫

👑 Author 👑

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

The whole squad. Respect. 🫶

🔥 Further Details: 🔥

• Level 2 Blas routine.
• The vector and matrix arguments are not referenced when N = 0, or M = 0 — yep, that's literally what it says, I'm just reading the page to you. 💀
• -- 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 and still serving. The longevity. The legacy. Periodt. ⭐

Definition at line 141 of file ztpmv.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. (Yes, a robot wrote this one. She's doing her best. 😭)

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And that's the whole page, bestie — cute sign-off time: this was LAPACK Version 3.12.0, page /home/abui...SRC/ztpmv.f(3). Go forth and pack your triangles correctly. 💖✨🎀