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

💖 NAME 💖

okay bestie, the header says /home/abui...la_heamv.f(3) and it's from the Library Functions Manual. The NAME section spells out the actual file path: /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/cla_heamv.f. That's the whole name vibe. 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

subroutine CLA_HEAMV (uplo, n, alpha, a, lda, x, incx, beta, y, incy)

CLA_HEAMV computes a matrix-vector product using a Hermitian indefinite matrix to calculate error bounds.

🌟 Function/Subroutine Documentation 🌟

subroutine CLA_HEAMV (integer uplo, integer n, real alpha, complex,
     dimension( lda, * ) a, integer lda, complex, dimension( * ) x, integer
     incx, real beta, real, dimension( * ) y, integer incy)

CLA_HEAMV computes a matrix-vector product using a Hermitian indefinite matrix to calculate error bounds.

🎯 Purpose 🎯

The original comment block literally starts like this — yes, it says CLA_SYAMV right there, bestie, not a typo from me:

!> CLA_SYAMV  performs the matrix-vector operation
!>
!>         y := alpha*abs(A)*abs(x) + beta*abs(y),
!>
!> where alpha and beta are scalars, x and y are vectors and A is an
!> n by n symmetric 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.
!>

So the operation is:

y := alpha*abs(A)*abs(x) + beta*abs(y),

where alpha and beta are scalars, x and y are vectors, and A is an n by n symmetric 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. Iconic little numerical-safety moment, no cap. 💅

🎀 Parameters 🎀

• UPLO — UPLO is INTEGER. On entry, UPLO specifies whether the upper or lower triangular part of the array A is to be referenced as follows: UPLO = BLAS_UPPER means only the upper triangular part of A is to be referenced; UPLO = BLAS_LOWER means only the lower triangular part of A is to be referenced. 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.
• ALPHA — ALPHA is REAL . On entry, ALPHA specifies the scalar alpha. Unchanged on exit.
• A — A is COMPLEX array, dimension ( LDA, n ). Before entry, the leading m by n part of the array A must contain the matrix of coefficients. Unchanged on exit. Yes, it says m by n — keep it exactly like that, bestie.
• LDA — LDA is INTEGER. On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. LDA must be at least max( 1, n ). Unchanged on exit.
• X — X is COMPLEX array, dimension ( 1 + ( n - 1 )*abs( INCX ) ). 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 + ( n - 1 )*abs( INCY ) ). 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.
• INCY — INCY is INTEGER. On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.

👑 Author 👑

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

🌈 Further Details 🌈

The source says:

!>
!>  Level 2 Blas routine.
!>
!>  -- Written on 22-October-1986.
!>     Jack Dongarra, Argonne National Lab.
!>     Jeremy Du Croz, Nag Central Office.
!>     Sven Hammarling, Nag Central Office.
!>     Richard Hanson, Sandia National Labs.
!>  -- Modified for the absolute-value product, April 2006
!>     Jason Riedy, UC Berkeley
!>

So: Level 2 Blas routine. It was written on 22-October-1986 by Jack Dongarra, Argonne National Lab; Jeremy Du Croz, Nag Central Office; Sven Hammarling, Nag Central Office; and Richard Hanson, Sandia National Labs. Then it was modified for the absolute-value product in April 2006 by Jason Riedy, UC Berkeley. History lesson ate. 🫶

Definition at line 176 of file cla_heamv.f.

💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie: LAPACK, Version 3.12.0, and the footer path /home/abui...la_heamv.f(3). Periodt. 💖🎀✨