SRC/slarfg.f(3)

💖 NAME

Okay bestie, welcome to SRC/slarfg.f(3) — that's the Library Functions Manual page for SRC/slarfg.f. It's all about the slarfg subroutine, and it's giving Householder-reflector icon. No cap, we're getting through every detail together. 💅

✨ SYNOPSIS

Functions/Subroutines

       subroutine slarfg (n, alpha, x, incx, tau)
           SLARFG generates an elementary reflector (Householder matrix).

🛠️ Function/Subroutine Documentation

Full signature time — exactly as the source spells it:

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

SLARFG generates an elementary reflector (Householder matrix). That's the whole vibe. ✨

🧮 Purpose

The source says 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

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That's the whole page, bestie — LAPACK Version 3.12.0, source SRC/slarfg.f(3). Bye and slay 💖✨