DTRMV(3)

💅 DTRMV (3) — bestie edition 🦋

ok so this page is literally about /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/BLAS/SRC/dtrmv.f and honestly? she's iconic. LAPACK 3.12.0 energy, BLAS Level 2, the whole vibe. let's get into it ✨

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines

• subroutine DTRMV (uplo, trans, diag, n, a, lda, x, incx) — no cap, that's her whole signature. she's called DTRMV.

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👑 Function/Subroutine Documentation 👑

subroutine DTRMV (character uplo, character trans, character diag, integer
    n, double precision, dimension(lda,*) a, integer lda, double precision,
    dimension(*) x, integer incx)

DTRMV — that's the name, bestie, and she ate 💅

🧚 Purpose

fr fr, DTRMV performs one of the matrix-vector operations

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

where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix. that's it. that's the whole job. main character behavior honestly 🌟

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🌸 Parameters 🌸

okay so here's everyone in the group chat, one by one:

• 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**T*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 flexible like that 🫶
• A — A is DOUBLE PRECISION array, dimension ( LDA, N ). okay so:
  • before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular matrix, and the strictly lower triangular part of A is not referenced (she's not looking at it, mind your business 🙈).
  • before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular matrix, and the strictly upper triangular part of A is not referenced.
  • note that when DIAG = 'U' or 'u', the diagonal elements of A are not referenced either — they're just assumed to be unity. iconic of them tbh.
• LDA — LDA is INTEGER. on entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). non-negotiable bestie ⚠️
• X — X is DOUBLE PRECISION 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. so yeah she comes out different, that's the point 💀
• INCX — INCX is INTEGER. on entry, INCX specifies the increment for the elements of X. INCX must not be zero. ever. please. 🙏

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🦋 Author 🦋

the whole squad basically:

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

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⭐ Further Details ⭐

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

and then the historical lore drop, which is honestly kind of a vibe:

-- 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.

like?? 1986?? they were doing this before i was even a concept. respect. 🫡

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Definition at line 146 of file dtrmv.f. ✨

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💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code. not me being auto-generated and still serving looks 💅

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and that's the page bestie 🎀 source is LAPACK, Version 3.12.0, dated with the /home/abui...SRC/dtrmv.f(3) footer, and honestly she slayed. go call DTRMV, be careful with INCX, and remember: not referenced means not referenced. periodt 🌈⭐