BLAS/SRC/zhemv.f(3)

✨ BLAS/SRC/zhemv.f(3) ✨

okay bestie, welcome to the LAPACK corner of the manual, specifically the little file known as BLAS/SRC/zhemv.f 🎀 this one is a whole icon and she's about to do math on your behalf, no cap.

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💖 NAME 💖

BLAS/SRC/zhemv.f — that's the file, that's the name, she's her 💅

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🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine zhemv (uplo, n, alpha, a, lda, x, incx, beta, y, incy)
    ZHEMV

like. that's the whole signature. one subroutine, ten arguments, zero chill. 👑

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🌸 Function/Subroutine Documentation 🌸

subroutine zhemv (character uplo, integer n, complex*16 alpha, complex*16, dimension(lda,*) a, integer lda, complex*16, dimension(*) x, integer incx, complex*16 beta, complex*16, dimension(*) y, integer incy)

ZHEMV

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🎯 Purpose:

ok so what does she actually DO. ZHEMV performs the matrix-vector operation

y := alpha*A*x + beta*y,

where alpha and beta are scalars, x and y are n element vectors, and A is an n by n hermitian matrix. that's it, that's the vibe ✨

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🧚 Parameters

• UPLO — she's a CHARACTER*1. On entry, UPLO tells you whether the upper or the lower triangular part of the array A is the one getting referenced, and here's the tea:
  • UPLO = 'U' or 'u' — only the upper triangular part of A is to be referenced. 🫶
  • UPLO = 'L' or 'l' — only the lower triangular part of A is to be referenced. 💜
• N — N is INTEGER. On entry, N is the order of the matrix A. and listen, N must be at least zero. no negatives, we don't do that here. 😌
• ALPHA — ALPHA is COMPLEX*16. On entry, ALPHA is the scalar alpha. she's just a little guy. 💖
• A — A is a COMPLEX*16 array, dimension ( LDA, N ). Before entry with UPLO = 'U' or 'u', the leading n by n upper triangular part of the array A must contain the upper triangular part of the hermitian matrix, and the strictly lower triangular part of A is not referenced. Before entry with UPLO = 'L' or 'l', the leading n by n lower triangular part of the array A must contain the lower triangular part of the hermitian matrix, and the strictly upper triangular part of A is not referenced. also note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero — so don't stress about those, bestie, she'll just assume zero. 🙈
• LDA — LDA is INTEGER. On entry, LDA is the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). that's the floor, don't go under it. ⭐
• X — X is 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. 🌈
• INCX — INCX is INTEGER. On entry, INCX is the increment for the elements of X. and INCX must not be zero. seriously. not zero. 💀
• BETA — BETA is COMPLEX*16. On entry, BETA is the scalar beta. and here's a fun fact: when BETA is supplied as zero, then Y need not be set on input. so you can just. not. 😌
• Y — Y is a COMPLEX*16 array, dimension at least ( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented array Y must contain the n element vector y. On exit, Y is overwritten by the updated vector y — so yes, she edits in place, that's her main character energy. 👑
• INCY — INCY is INTEGER. On entry, INCY is the increment for the elements of Y. INCY must not be zero. same rule, same energy. 🍓

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🎀 Author

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

look at that collective. iconic. all four of them. 💅

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🔥 Further Details:

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

so if N = 0, or M = 0, the vector and matrix arguments are simply not referenced. nothing happens. she's off the clock. 💤

-- 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.

written on 22-October-1986 by Jack Dongarra (Argonne National Lab.), Jeremy Du Croz (Nag Central Office), Sven Hammarling (Nag Central Office) and Richard Hanson (Sandia National Labs). the originators. the blueprint. the founding mothers and fathers of the vibe. 👑✨

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📍 Definition at line 153 of file zhemv.f.

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. she wasn't hand-written, she was manifested. 🦋

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okay that's the whole page bestie, you ate it, periodt. 🫶 this little doc shipped as Version 3.12.0, dated Tue Nov 28 2023 12:08:41, straight from BLAS/SRC/zhemv.f(3) — so go forth and multiply your hermitian matrices, mwah 💖✨