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

✨ NAME ✨

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

okay so this is a page from the Library Functions Manual, and it’s giving full main-character energy for dla_gbamv.f 💅. Yes bestie, that’s the whole path, and we are keeping it exactly as-is. 🫶

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💅 SYNOPSIS 💅

Functions/Subroutines

       subroutine DLA_GBAMV (trans, m, n, kl, ku, alpha, ab, ldab, x, incx,
           beta, y, incy)

DLA_GBAMV performs a matrix-vector operation to calculate error bounds. ✨

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🦋 Function/Subroutine Documentation 🦋

Here’s the full signature, and we’re not touching a single character of it, bestie:

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

DLA_GBAMV performs a matrix-vector operation to calculate error bounds. That’s the whole vibe, and honestly? Iconic. 👑

✨ Purpose: ✨

Okay so DLA_GBAMV performs one of these matrix-vector operations, and the formulas are staying exactly as written:

        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. 💖

🎀 Parameters 🎀

• 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. ✨

• 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 — is INTEGER. On entry, N specifies the number of columns of the matrix A. N must be at least zero. Unchanged on exit.
• KL — is INTEGER. The number of subdiagonals within the band of A. KL >= 0.
• KU — is INTEGER. The number of superdiagonals within the band of A. KU >= 0.
• ALPHA — is DOUBLE PRECISION. On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
• AB — is DOUBLE PRECISION 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 — is INTEGER. On entry, LDA specifies the first dimension of AB as declared in the calling (sub) program. LDAB must be at least max( 1, m ). Unchanged on exit. (Yes, the original says LDA there — we’re just reporting the lore. 💀)
• X — is DOUBLE PRECISION 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 — is INTEGER. On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.
• 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 — 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.
• INCY — is 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 185 of file dla_gbamv.f. ✨

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code. 💅

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okay bestie that’s the whole page. This footer is LAPACK Version 3.12.0 with page /home/abui...la_gbamv.f(3) — no separate date on this one, so no invented tea. Slay, stay hydrated, and don’t forget that INCX and INCY must not be zero. 💖✨