BLAS/SRC/ctpmv.f(3)

🎀 BLAS/SRC/ctpmv.f 🎀

okay bestie, this is the Library Functions Manual page for BLAS/SRC/ctpmv.f — and it’s literally all about the BLAS subroutine CTPMV. No cap, it’s giving packed-triangular-matrix-vector energy. 💅✨

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🌸 NAME 🌸

BLAS/SRC/ctpmv.f — the manpage home of CTPMV, the BLAS routine that does triangular packed matrix-vector operations. 🫶

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

• subroutine ctpmv (uplo, trans, diag, n, ap, x, incx) — CTPMV

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💅 Function/Subroutine Documentation 💅

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

CTPMV — yes, that’s the icon. 👑

🎯 Purpose 🎯

okay so CTPMV performs one of these matrix-vector operations, fr fr:

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. Periodt. 💖

🧸 Parameters 🧸

• UPLO — CHARACTER*1. On entry, UPLO tells us whether the matrix is upper or lower triangular. Choose your fighter:
  • UPLO = 'U' or 'u' — A is an upper triangular matrix.
  • UPLO = 'L' or 'l' — A is a lower triangular matrix.
• TRANS — CHARACTER*1. On entry, TRANS says which operation is happening. The vibe check:
  • TRANS = 'N' or 'n' — x := A*x.
  • TRANS = 'T' or 't' — x := A**T*x.
  • TRANS = 'C' or 'c' — x := A**H*x.
• DIAG — CHARACTER*1. On entry, DIAG says whether A is unit triangular or not. Important little detail:
  • DIAG = 'U' or 'u' — A is assumed to be unit triangular.
  • DIAG = 'N' or 'n' — A is not assumed to be unit triangular.
• N — INTEGER. On entry, N specifies the order of the matrix A. N must be at least zero. No negative-era behavior here. 🚫
• AP — COMPLEX array, dimension at least ( ( n*( n + 1 ) )/2 ). This is the packed matrix bestie:
  • 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. Cute, convenient, iconic. 💫
• X — COMPLEX 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. The main character gets a glow-up in place. ✨
• INCX — INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Fr fr, do not test it. 😭

📝 Author 📝

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

🔍 Further Details 🔍

• Level 2 Blas routine.
• The vector and matrix arguments are not referenced when N = 0, or M = 0.
• The source says: -- 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.

📍 Definition at line 141 of file ctpmv.f.

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🤖 Author 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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💖 Final sign-off, bestie: this page is LAPACK Version 3.12.0, file BLAS/SRC/ctpmv.f(3), and the date in the write-up is 22-October-1986. Byeee, go slay some packed triangular matrices 💅✨