BLAS/SRC/zgemv.f(3)

💖 NAME 💖

okay bestie, this page is BLAS/SRC/zgemv.f(3) — yep, that's the title — and it lives in the Library Functions Manual. It's all about zgemv, and she is ready to serve matrix-vector realness ✨

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✨ SYNOPSIS ✨

Functions/Subroutines

   subroutine zgemv (trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
       ZGEMV

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🎀 Function/Subroutine Documentation 🎀

   subroutine zgemv (character trans, integer m, 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)

ZGEMV

ZGEMV is the main character here. Periodt 💅

Purpose

okay so ZGEMV performs one of these matrix-vector operations, and you're gonna want to memorize the vibe:

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

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

where alpha and beta are scalars, x and y are vectors, and A is an m by n matrix. No cap, that's the whole glow-up 🦋

Parameters

• TRANS — TRANS is CHARACTER*1. On entry, TRANS tells the routine which operation to do, and the options are giving:
  • TRANS = 'N' or 'n' → y := alpha*A*x + beta*y.
  • TRANS = 'T' or 't' → y := alpha*A**T*x + beta*y.
  • TRANS = 'C' or 'c' → y := alpha*A**H*x + beta*y.
• M — M is INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero. Lowkey important: at least zero, bestie 🫶
• N — N is INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero. Same energy: at least zero 💖
• ALPHA — ALPHA is COMPLEX*16. On entry, ALPHA specifies the scalar alpha. That's it, that's the icon ✨
• A — A is COMPLEX*16 array, dimension ( LDA, N ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. She's the coefficient queen 👑
• 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, m ). Do not play with this, fr fr 🚨
• X — X is COMPLEX*16 array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n', and at least ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. Before entry, the incremented array X must contain the vector x. She's incremented, she's complex, she's booked and busy 🌸
• INCX — INCX is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Not zero. We do not do zero here 💀
• BETA — BETA is COMPLEX*16. On entry, BETA specifies the scalar beta. When BETA is supplied as zero, then Y need not be set on input. Cute shortcut, ngl ✨
• Y — Y is COMPLEX*16 array, dimension at least ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n', and at least ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. Before entry with BETA non-zero, the incremented array Y must contain the vector y. On exit, Y is overwritten by the updated vector y. If either m or n is zero, then Y not referenced and the function performs a quick return. She said quick return and meant it 💅
• INCY — INCY is INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Again: not zero, bestie 🫶

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.
• -- 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 159 of file zgemv.f.

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🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code.

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okay final vibe check, bestie: this page is from LAPACK Version 3.12.0, file BLAS/SRC/zgemv.f(3), and the routine itself was written on 22-October-1986. iconic, historic, complex*16-coded 💅✨🎀