SRC/zla_syamv.f(3)

🌸 SRC/zla_syamv.f 🌸

ok so this is a page from the LAPACK manual (Library Functions Manual), and bestie, it's all about one iconic little subroutine. buckle up 💅

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✨ NAME ✨

SRC/zla_syamv.f — no cap, that's the whole name, it's giving "I let my work speak for itself" 💁‍♀️

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine zla_syamv (uplo, n, alpha, a, lda, x, incx, beta, y, incy) — ZLA_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds. that's her job, that's what she does 🫶

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✨ Function/Subroutine Documentation ✨

subroutine zla_syamv (integer uplo, 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_SYAMV computes a matrix-vector product using a symmetric indefinite matrix to calculate error bounds. literally her whole personality 🔥

💖 Purpose 💖

ok so ZLA_SYAMV performs the matrix-vector operation:

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

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

This function is primarily used in calculating error bounds. 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. 🧠✨ (yes this is the deep lore, pay attention)

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🌈 Parameters 🌈

⭐ UPLO

UPLO is INTEGER. On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows:

• UPLO = BLAS_UPPER — Only the upper triangular part of A is to be referenced.
• UPLO = BLAS_LOWER — Only the lower triangular part of A is to be referenced.

Unchanged on exit. (she stays exactly how you left her 💖)

⭐ 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, n ). Unchanged on exit. don't skimp on this one bestie, it's a hard requirement 😤

⭐ X

X is COMPLEX*16 array, dimension at least ( 1 + ( n - 1 )*abs( INCX ) ). 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. (free pass on setting Y, we love a shortcut ✨)

⭐ Y

Y is DOUBLE PRECISION array, dimension ( 1 + ( n - 1 )*abs( INCY ) ). 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. she gets a whole glow-up on the way out 💫

⭐ INCY

INCY is INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit. 🚨

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✨ Author ✨

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

the whole squad pulled up for this one 🫶👑

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✨ Further Details ✨

Level 2 Blas routine.

-- 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. -- Modified for the absolute-value product, April 2006 Jason Riedy, UC Berkeley

legends. absolute legends. the way they were doing linear algebra before some of us were even born 😭👑

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Definition at line 177 of file zla_syamv.f.

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✨ Author ✨

Generated automatically by Doxygen for LAPACK from the source code. (not a human, just a little robot doing its best 🤖💖)

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ok that's the whole page bestie, go forth and compute those error bounds 💅✨ LAPACK, Version 3.12.0, dated SRC/zla_syamv.f(3) — mwah, bye! 🎀🦋💜