SRC/zlaic1.f(3)

🦋 SRC/zlaic1.f(3) — like, the LAPACK girlies' own manual page ✨

okay bestie, so this is page SRC/zlaic1.f(3) from the LAPACK manual, and I'm gonna walk you through it like we're on FaceTime at 1am. no cap, it's actually so good. 💖

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✨ NAME ✨

SRC/zlaic1.f — that's the file, that's the whole name, periodt. 🎀

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🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine zlaic1 (job, j, x, sest, w, gamma, sestpr, s, c) — ZLAIC1 applies one step of incremental condition estimation. and that's literally the whole vibe 💅

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👑 Function/Subroutine Documentation 👑

subroutine zlaic1 (integer job, integer j, complex*16, dimension( j ) x, double precision sest, complex*16, dimension( j ) w, complex*16 gamma, double precision sestpr, complex*16 s, complex*16 c)

ZLAIC1 applies one step of incremental condition estimation. (iconic behaviour, honestly)

Purpose:

so here's the tea, fr fr — ZLAIC1 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 ZLAIC1 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. (pick your fighter 💀)

also quick note bestie — [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*16 array, dimension (J)
  • The j-vector x.
• SEST — SEST is DOUBLE PRECISION
  • Estimated singular value of j by j matrix L.
• W — W is COMPLEX*16 array, dimension (J)
  • The j-vector w.
• GAMMA — GAMMA is COMPLEX*16
  • The diagonal element gamma.
• SESTPR — SESTPR is DOUBLE PRECISION
  • Estimated singular value of (j+1) by (j+1) matrix Lhat.
• S — S is COMPLEX*16
  • Sine needed in forming xhat.
• C — C is COMPLEX*16
  • Cosine needed in forming xhat.

ok but literally every one of these parameters ate, no crumbs left. 🌈

Author

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

Definition at line 134 of file zlaic1.f. ⭐

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💜 Author 💜

Generated automatically by Doxygen for LAPACK from the source code. (the robots did this one, not me 🙈)

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and that's the whole page bestie!! mwah 💋 — this little masterpiece is brought to you by LAPACK, Version 3.12.0, on page SRC/zlaic1.f(3). go forth and estimate some conditions, you absolute main character 👑💖