SRC/zla_gbamv.f(3)

💅 SRC/zla_gbamv.f — the zla_gbamv manual page, bestie edition

okay so this is the man page for SRC/zla_gbamv.f from the LAPACK library manual, and honestly? she's a whole vibe. buckle up 🎀

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✨ SYNOPSIS ✨

🦋 Functions/Subroutines

• subroutine zla_gbamv (trans, m, n, kl, ku, alpha, ab, ldab, x, incx, beta, y, incy) — ZLA_GBAMV performs a matrix-vector operation to calculate error bounds.

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💜 Function/Subroutine Documentation 💜

🌸 the subroutine herself

subroutine zla_gbamv (integer trans, integer m, integer n, integer kl,
    integer ku, double precision alpha, complex*16, dimension( ldab, * ) ab,
    integer ldab, complex*16, dimension( * ) x, integer incx, double
    precision beta, double precision, dimension( * ) y, integer incy)

ZLA_GBAMV performs a matrix-vector operation to calculate error bounds. periodt. that's the whole job description and she does it flawlessly 💅

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🎯 Purpose

okay so here's the tea, bestie — ZLA_GBAMV performs one of the 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. no cap 🧢

this function is primarily used in calculating error bounds. and like, 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. iykyk 🔥

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👑 Parameters 👑

💫 TRANS

TRANS is INTEGER

on entry, TRANS specifies the operation to be performed as follows:

BLAS_NO_TRANS      y := alpha*abs(A)*abs(x) + beta*abs(y)
BLAS_TRANS         y := alpha*abs(A**T)*abs(x) + beta*abs(y)
BLAS_CONJ_TRANS    y := alpha*abs(A**T)*abs(x) + beta*abs(y)

unchanged on exit. slay ✨

💫 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.

💫 KL

KL is INTEGER

the number of subdiagonals within the band of A. KL >= 0. 🫶

💫 KU

KU is INTEGER

the number of superdiagonals within the band of A. KU >= 0. 🫶

💫 ALPHA

ALPHA is DOUBLE PRECISION

on entry, ALPHA specifies the scalar alpha. unchanged on exit.

💫 AB

AB is COMPLEX*16 array, dimension ( LDAB, n )

before entry, the leading m by n part of the array AB must contain the matrix of coefficients. unchanged on exit.

💫 LDAB

LDAB is INTEGER

on entry, LDAB specifies the first dimension of AB as declared in the calling (sub) program. LDAB must be at least max( 1, m ). unchanged on exit. don't skip this one bestie, she's load-bearing 😭

💫 X

X is COMPLEX*16 array, dimension

( 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. not zero, okay? zero is not the move here 🙈

💫 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. little shortcut, we love her 🌈

💫 Y

Y is DOUBLE PRECISION array, dimension

( 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 literally just leaves, iconic 💀

💫 INCY

INCY is INTEGER

on entry, INCY specifies the increment for the elements of Y. INCY must not be zero. unchanged on exit. same rule as INCX, no zeros allowed ⭐

📌 Level 2 Blas routine. (yes, that note is part of the parameter block, keeping it exactly where it lives 🎀)

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🧚 Author 🧚

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

Definition at line 186 of file zla_gbamv.f. go look, she's right there 👑

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🌟 sign-off 🌟

this page was generated automatically by Doxygen for LAPACK straight from the source code, and it's LAPACK Version 3.12.0 energy all the way, dated right there in the SRC/zla_gbamv.f(3) footer. bye bestie, go perturb some components (but not the zero ones) 💖✨🎀🦋