larfgp(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

🌸 NAME 🌸

larfgp — larfgp: generate Householder reflector, beta ≥ 0. ✨

This is the larfgp(3) page from the Library Functions Manual — LAPACK's very own reflector generator, and we're gonna go through it with bestie-level detail. 🫶

✨ SYNOPSIS ✨

🎀 Functions 🎀

  • subroutine clarfgp (n, alpha, x, incx, tau) — CLARFGP generates an elementary reflector (Householder matrix) with non-negative beta. 💅
  • subroutine dlarfgp (n, alpha, x, incx, tau) — DLARFGP generates an elementary reflector (Householder matrix) with non-negative beta. 💅
  • subroutine slarfgp (n, alpha, x, incx, tau) — SLARFGP generates an elementary reflector (Householder matrix) with non-negative beta. 💅
  • subroutine zlarfgp (n, alpha, x, incx, tau) — ZLARFGP generates an elementary reflector (Householder matrix) with non-negative beta. 💅

🦋 Detailed Description 🦋

okay so this section is literally empty in the original — no extra lore, no hidden detail, just a blank space doing its little thing. moving on, bestie. 💀

🔥 Function Documentation 🔥

💖 subroutine clarfgp (integer n, complex alpha, complex, dimension( * ) x, integer incx, complex tau) 💖

CLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.

Purpose:

CLARFGP 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, beta is real and non-negative, 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. 🫶

🌸 Parameters 🌸

  • N — N is INTEGER. The order of the elementary reflector.
  • ALPHA — ALPHA is COMPLEX. On entry, the value alpha. On exit, it is overwritten with the value beta.
  • X — X is COMPLEX 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. The value tau.

👑 Author 👑

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

Definition at line 103 of file clarfgp.f.

💖 subroutine dlarfgp (integer n, double precision alpha, double precision, dimension( * ) x, integer incx, double precision tau) 💖

DLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.

Purpose:

DLARFGP 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, beta is non-negative, 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. 🫶

🌸 Parameters 🌸

  • N — N is INTEGER. The order of the elementary reflector.
  • ALPHA — ALPHA is DOUBLE PRECISION. On entry, the value alpha. On exit, it is overwritten with the value beta.
  • X — X is DOUBLE PRECISION 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 DOUBLE PRECISION. The value tau.

👑 Author 👑

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

Definition at line 103 of file dlarfgp.f.

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

SLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.

Purpose:

SLARFGP 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, beta is non-negative, 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. 🫶

🌸 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 103 of file slarfgp.f.

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

ZLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.

Purpose:

ZLARFGP 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, beta is real and non-negative, 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. 🫶

🌸 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 103 of file zlarfgp.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

okay that's the whole page, bestie! the footer says LAPACK and Version 3.12.0, and there's literally no date printed on this one — so that's the source/version sign-off, no date bestie. periodt. 💅✨

📦 where this page comes from