SRC/sla_gbamv.f(3)

okay bestie, welcome to SRC/sla_gbamv.f(3) — straight outta the Library Functions Manual 💅 this one is all about the sla_gbamv subroutine and it is lowkey iconic.

🌸 NAME 🌸

SRC/sla_gbamv.f

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✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

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

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

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🫶 Function/Subroutine Documentation 🫶

🦋 subroutine sla_gbamv 🦋

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

SLA_GBAMV performs a matrix-vector operation to calculate error bounds. no cap, that's the whole gig.

🎀 Purpose 🎀

okay so SLA_GBAMV 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. 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. that's the whole underflow-protection vibe ✨

🌈 Parameters 🌈

• TRANS — TRANS is INTEGER. On entry, TRANS specifies the operation to be performed as follows, and it is unchanged on exit:
  • 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)
• 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 REAL. On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
• AB — AB is REAL 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, 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 — I'm keeping it exactly as the manpage has it, bestie 🫶)
• X — X is REAL 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.
• BETA — BETA is REAL. 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 REAL 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 — 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 sla_gbamv.f 💅

Definition at line 185 of file sla_gbamv.f.

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💖 Author 💖

Generated automatically by Doxygen for LAPACK from the source code.

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mwah 💋 okay that's the whole page — footer vibes are LAPACK Version 3.12.0 and SRC/sla_gbamv.f(3), that's the source/version stamp. if a date was supposed to be there, it wasn't in this footer, so I'm not inventing one 💀✨ bye bestie! 🎀🦋