SRC/dla_gbamv.f(3)

💖 NAME 💖

SRC/dla_gbamv.f

okay bestie, this page is from the Library Functions Manual and the title is SRC/dla_gbamv.f(3) — yes, we're in LAPACK-adjacent land and DLA_GBAMV is the main character 💅✨

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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 🌈

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.

🍓 Purpose 🍓

okay so DLA_GBAMV performs one of these matrix-vector operations, no cap:

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 — 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 — 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 — 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.
• X — 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 — 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 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 185 of file dla_gbamv.f.

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💀 Author 💀

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