SRC/zlarfg.f(3)

okay bestie, welcome to SRC/zlarfg.f(3) from the LAPACK Library Functions Manual — this page is about a complex elementary reflector (Householder matrix), and it’s giving linear algebra main character energy 💅✨

🌸 NAME 🌸

SRC/zlarfg.f

✨ SYNOPSIS ✨

🧚 Functions/Subroutines 🧚

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

🦋 Function/Subroutine Documentation 🦋

subroutine zlarfg (integer n, complex*16 alpha, complex*16, dimension( * )
    x, integer incx, complex*16 tau)

ZLARFG generates an elementary reflector (Householder matrix). 🫶

💖 Purpose 💖

okay so ZLARFG generates a complex elementary reflector H of order n, such that:

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

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

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

where tau is a complex scalar and v is a complex (n-1)-element vector. Note that H is not hermitian.

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

Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1. 💅

🎀 Parameters 🎀

• N — N is INTEGER; the order of the elementary reflector. 🫶
• ALPHA — ALPHA is COMPLEX*16; on entry, the value alpha; on exit, it is overwritten with the value beta. ✨
• X — X is COMPLEX*16 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 COMPLEX*16; the value tau. 🌸

👑 Author 👑

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

Definition at line 105 of file zlarfg.f. 📍

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code. 🧚

---

💖 that’s the whole page, bestie! source/version: LAPACK Version 3.12.0; page: SRC/zlarfg.f(3); date: the footer’s date slot is literally empty, so no invented date here. periodt. 💅✨