SRC/claic1.f(3)

📦
version 3.12.1 · 7 versions
, in arch rolling

💖 NAME 🎀

SRC/claic1.f — bestie, this is the page for that file, and it's giving Library Functions Manual. It's the home of CLAIC1, which does one step of incremental condition estimation. Iconic behavior, honestly. ✨

🌸 SYNOPSIS 🌸

Functions/Subroutines

  • subroutine claic1 (job, j, x, sest, w, gamma, sestpr, s, c) — CLAIC1 applies one step of incremental condition estimation.

👑 Function/Subroutine Documentation 👑

subroutine claic1 (integer job, integer j, complex, dimension( j ) x, real sest, complex, dimension( j ) w, complex gamma, real sestpr, complex s, complex c)

CLAIC1 applies one step of incremental condition estimation. Literally the main character of this page. 💅

✨ Purpose ✨

Okay so here's the whole point, no cap: CLAIC1 applies one step of incremental condition estimation in its simplest version:

Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j lower triangular matrix L, such that

twonorm(L*x) = sest

Then CLAIC1 computes sestpr, s, c such that the vector

         [ s*x ]
  xhat = [  c  ]

is an approximate singular vector of

         [ L      0  ]
  Lhat = [ w**H gamma ]

in the sense that

twonorm(Lhat*xhat) = sestpr.

Depending on JOB, an estimate for the largest or smallest singular value is computed.

Note that [s c]**H and sestpr**2 is an eigenpair of the system

diag(sest*sest, 0) + [alpha  gamma] * [ conjg(alpha) ]
                                      [ conjg(gamma) ]

where alpha = x**H*w.

🎀 Parameters 🎀

  • JOB — JOB is INTEGER. = 1: an estimate for the largest singular value is computed. = 2: an estimate for the smallest singular value is computed.
  • J — J is INTEGER. Length of X and W.
  • X — X is COMPLEX array, dimension (J). The j-vector x.
  • SEST — SEST is REAL. Estimated singular value of j by j matrix L.
  • W — W is COMPLEX array, dimension (J). The j-vector w.
  • GAMMA — GAMMA is COMPLEX. The diagonal element gamma.
  • SESTPR — SESTPR is REAL. Estimated singular value of (j+1) by (j+1) matrix Lhat.
  • S — S is COMPLEX. Sine needed in forming xhat.
  • C — C is COMPLEX. Cosine needed in forming xhat.

🫶 Author 🫶

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

Definition at line 134 of file claic1.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

Later bestie 💅 — this whole vibe check comes from LAPACK Version 3.12.0, source SRC/claic1.f(3). The footer didn't include a literal date, so that's the timestamp tea. 🫶🎀

📦 where this page comes from