BLAS/SRC/ctpmv.f(3)

💖 BLAS/SRC/ctpmv.f — the CTPMV glow-up 💖

okay bestie, welcome to the <pink>LAPACK</pink> BLAS pages, this one's BLAS/SRC/ctpmv.f and she's a real one 💅

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✨ NAME ✨

BLAS/SRC/ctpmv.f — no cap, that's the whole name, she's lowkey mysterious like that 🦋

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🌸 SYNOPSIS 🌸

Functions/Subroutines

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

CTPMV — that's her, that's the icon 👑

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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 🫶

🎀 Purpose 🎀

so like, CTPMV performs one of the 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. literally packed, she's traveling light ✈️💖

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⭐ Parameters ⭐

• UPLO — UPLO is CHARACTER*1. On entry, UPLO specifies whether the matrix is an upper or lower triangular matrix as follows:
  • 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 operation to be performed as follows:
  • TRANS = 'N' or 'n' — x := A*x.
  • TRANS = 'T' or 't' — x := A**T*x.
  • TRANS = 'C' or 'c' — x := A**H*x.
• 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 chill like that 🙈)
• AP — AP is COMPLEX 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. she's not even looking at them, she just knows 💅

• X — X is 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. yeah she ate and left no crumbs 😭

• INCX — INCX is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. fr fr, not zero, do not do it 🚫

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🧚 Author 🧚

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

the whole squad showed up, main character energy across four institutions 👑👑👑👑

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🌈 Further Details: 🌈

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

-- 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.

okay so fun fact, N = 0 or M = 0 and she literally does not reference the vector and matrix arguments at all. nothing. ghosted. iconic behaviour honestly 💀✨

Definition at line 141 of file ctpmv.f.

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🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code. (yes bestie, a robot wrote the docs, we stan automation 🤖💖)

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Version 3.12.0 — Tue Nov 28 2023 12:08:41 — BLAS/SRC/ctpmv.f(3)

and that's the whole page, bestie!! go forth and pack your triangular matrices, stay hydrated, and remember: INCX is never zero 💅💖✨🦋🌸🎀🫶🔥👑🌈⭐💜