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

💖 NAME

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

okay so this is literally the file for CLARFGP, from the Library Functions Manual — bestie, it's the LAPACK source file and it's the whole entire personality of this page 💅

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✨ SYNOPSIS

Functions/Subroutines

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

CLARFGP generates an elementary reflector (Householder matrix) with non-negative beta. no cap, that's the whole gig 🎀

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🦋 Function/Subroutine 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. like, that's it, that's the function 🌸

👑 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.
!>

so basically ✨ H is H = I - tau * ( 1 ) * ( 1 v**H ) with ( v ) stacked under it, tau is a complex scalar, v is a complex (n-1)-element vector — and H is not hermitian, don't @ me 🙈. and if every element of x is zero AND alpha is real? then tau = 0 and H is just the unit matrix, iconic behavior fr fr 💀

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🫶 Parameters

• N — N is INTEGER. it's the order of the elementary reflector. main character number 👑
• ALPHA — ALPHA is COMPLEX. on entry, it's the value alpha. on exit, it gets overwritten with the value beta — so yeah, it does not survive, she's changed 💅✨
• X — X is COMPLEX array, dimension (1+(N-2)*abs(INCX)). on entry, the vector x. on exit, it's overwritten with the vector v. same deal, glow-up on the way out 🦋
• INCX — INCX is INTEGER. the increment between elements of X, and INCX > 0 bestie, that's a hard requirement, not a vibe suggestion 🌸
• TAU — TAU is COMPLEX. the value tau. that's the whole description, she speaks for herself 🎀

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🌈 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

(the whole squad 🫶)

Definition at line 103 of file clarfgp.f.

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⭐ Author

Generated automatically by Doxygen for LAPACK from the source code. not a human, just a robot doing her little thing 🤖✨

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and that's the tea ☕ — <rainbow>LAPACK, Version 3.12.0</rainbow>, straight from /home/abui.../clarfgp.f(3). mwah, go call your Householder reflectors responsibly 💖🎀🦋