SRC/zla_geamv.f(3)

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version 3.12.1 · 7 versions
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Bestie, welcome to SRC/zla_geamv.f(3) 💅 — part of the Library Functions Manual, and yes, this is the page where Fortran has a whole matrix-vector main character moment.

🌸 NAME 🌸

SRC/zla_geamv.f — that’s the name, and it is serving exactly that. Iconic.

✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

Here’s the callable cutie:

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

ZLA_GEAMV computes a matrix-vector product using a general matrix to calculate error bounds.

💖 Function/Subroutine Documentation 💖

Meet the full signature, character-for-character:

subroutine zla_geamv (integer trans, integer m, integer n, double precision
    alpha, complex*16, dimension( lda, * ) a, integer lda, complex*16,
    dimension( * ) x, integer incx, double precision beta, double precision,
    dimension( * ) y, integer incy)

ZLA_GEAMV computes a matrix-vector product using a general matrix to calculate error bounds.

🔥 Purpose 🔥

Okay so here’s the lore: ZLA_GEAMV performs one of these matrix-vector operations:

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

where alpha and beta are scalars, x and y are vectors and A is an m by n matrix.

This function is primarily used in calculating error bounds — that’s the main character use case. To protect against underflow during evaluation, components in the resulting vector are perturbed away from zero by (N+1) times the underflow threshold. To prevent unnecessarily large errors for block-structure embedded in general matrices, zero components are not perturbed. A zero entry is considered if all multiplications involved in computing that entry have at least one zero multiplicand.

🌈 Parameters 🌈

Every parameter, no skips, no cap:

  • TRANS — TRANS is INTEGER. On entry, TRANS specifies the operation to be performed as follows: BLAS_NO_TRANS gives y := alpha*abs(A)*abs(x) + beta*abs(y), BLAS_TRANS gives y := alpha*abs(A**T)*abs(x) + beta*abs(y), and BLAS_CONJ_TRANS gives y := alpha*abs(A**T)*abs(x) + beta*abs(y). Unchanged on exit.
  • M — M is INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero. Unchanged on exit.
  • N — N is INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit.
  • ALPHA — ALPHA is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
  • 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. Unchanged on exit.
  • 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 ). Unchanged on exit.
  • X — X is COMPLEX*16 array. Its dimension is 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. Unchanged on exit.
  • INCX — INCX is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
  • BETA — BETA is DOUBLE PRECISION. On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. Unchanged on exit.
  • Y — Y is DOUBLE PRECISION array. Its dimension is ( 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.
  • INCY — INCY is INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.
💀 Also, fact-check bestie: Level 2 Blas routine.

👑 Author 👑

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

Definition at line 175 of file zla_geamv.f.

🦋 Author 🦋

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Catch you later, bestie — this page is from LAPACK, Version 3.12.0, and it’s for SRC/zla_geamv.f(3). Stay underflow-free 💅✨

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