/home/abui...la_gbamv.f(3)

💅 NAME 💅

Okay so bestie, this whole page is literally about one file — and its full government name is a whole journey:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zla_gbamv.f

Yes that's the actual name, no cap. It lives in the Library Functions Manual (that's the manual section, iykyk) and it's the home of ZLA_GBAMV, an iconic little workhorse from LAPACK. 🦋

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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. That's her whole job and she does it slayfully. 💅

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🎀 Function/Subroutine Documentation 🎀

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. she's giving utility function with main character energy. 👑

🌸 Purpose 🌸

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.

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. 🧚

Lowkey important: that "zero components are not perturbed" thing is the whole vibe check of this routine — it's not a bug, it's the design. Don't come for her.

💖 Parameters 💖

• TRANS — 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.

• M — INTEGER. On entry, M specifies the number of rows of the matrix A. M must be at least zero. Unchanged on exit.
• N — INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit.
• KL — INTEGER. The number of subdiagonals within the band of A. KL >= 0.
• KU — INTEGER. The number of superdiagonals within the band of A. KU >= 0.
• ALPHA — DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. Unchanged on exit. 🍓
• AB — 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 — 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.
• X — 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 — INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit. 🫶
• BETA — 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 — 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 is not referenced and the function performs a quick return. 💨
• INCY — INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.

Level 2 Blas routine. ✨

👑 Author 👑

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

Definition at line 186 of file zla_gbamv.f. 📍

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. Not me writing it by hand, bestie — the machines did this one. 🤖

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Anyway, that's the whole page, and honestly? She ate. 💀🔥

Sign-off era: this is LAPACK, Version 3.12.0, and yes, this page literally comes from /home/abui...la_gbamv.f(3) — the header and footer served their purpose so I'm folding them in here instead of copy-pasting them like a boring person. 🎀