SLARFG(3)

🦋 SLARFG(3) — Library Functions Manual 🦋

okay bestie, this is the SLARFG(3) page from the Library Functions Manual — manual name folded in right here, no header-line copy-paste energy. It's all about a real elementary reflector (Householder matrix), and yes, you're gonna understand it.

🎀 NAME 🎀

The NAME line is literally this source file path, bestie:

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

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine SLARFG (n, alpha, x, incx, tau)

SLARFG generates an elementary reflector (Householder matrix). Periodt.

🔥 Function/Subroutine Documentation 🔥

subroutine SLARFG (integer n, real alpha, real, dimension( * ) x, integer incx, real tau)

SLARFG generates an elementary reflector (Householder matrix).

💜 Purpose 💜

okay so here's the tea: SLARFG generates a real elementary reflector H of order n, such that:

      H * ( alpha ) = ( beta ),   H**T * H = I.
          (   x   )   (   0  )

where alpha and beta are scalars, and x is an (n-1)-element real vector. H is represented in the form:

      H = I - tau * ( 1 ) * ( 1 v**T ) ,
                    ( v )

where tau is a real scalar and v is a real (n-1)-element vector.

If the elements of x are all zero, then tau = 0 and H is taken to be the unit matrix.

Otherwise 1 <= tau <= 2.

🌸 Parameters 🌸

• N — N is INTEGER. The order of the elementary reflector.
• ALPHA — ALPHA is REAL. On entry, the value alpha. On exit, it is overwritten with the value beta.
• X — X is REAL array, dimension (1+(N-2)*abs(INCX)). On entry, the vector x. On exit, it is overwritten with the vector v.
• INCX — INCX is INTEGER. The increment between elements of X. INCX > 0.
• TAU — TAU is REAL. The value tau.

🫶 Author 🫶

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

📍 Definition at line 105 of file slarfg.f. 📍

💅 Author 💅

Generated automatically by Doxygen for LAPACK from the source code.

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cute sign-off, bestie: source/version is LAPACK Version 3.12.0, and the footer path is /home/abui...RC/slarfg.f(3). 💖🦋