DLAIC1(3)

okay so this is DLAIC1(3) from the Library Functions Manual, and the source path folded in near the top is /home/abui...RC/dlaic1.f(3) 💖. Yes bestie, we’re doing incremental condition estimation and it’s lowkey iconic.

💖 NAME 💖

/home/abui...RC/dlaic1.f(3) — that’s the file path, and this page is all about DLAIC1.

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine DLAIC1 (job, j, x, sest, w, gamma, sestpr, s, c)
    DLAIC1 applies one step of incremental condition estimation.

🦋 Function/Subroutine Documentation 🦋

subroutine DLAIC1 (integer job, integer j, double precision, dimension( j ) x, double precision sest, double precision, dimension( j ) w, double precision gamma, double precision sestpr, double precision s, double precision c)

DLAIC1 applies one step of incremental condition estimation.

🎀 Purpose 🎀

Okay so here’s the whole cute math situation. DLAIC1 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 DLAIC1 computes sestpr, s, c such that the vector

         [ s*x ]
  xhat = [  c  ]

is an approximate singular vector of

         [ L       0  ]
  Lhat = [ w**T 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]**T and sestpr**2 is an eigenpair of the system

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

where alpha = x**T*w.

🌸 Parameters 🌸

• JOB — JOB is INTEGER. Vibe check: = 1 means an estimate for the largest singular value is computed. = 2 means an estimate for the smallest singular value is computed.
• J — J is INTEGER; length of X and W.
• X — X is DOUBLE PRECISION array, dimension (J); the j-vector x.
• SEST — SEST is DOUBLE PRECISION; estimated singular value of j by j matrix L.
• W — W is DOUBLE PRECISION array, dimension (J); the j-vector w.
• GAMMA — GAMMA is DOUBLE PRECISION; the diagonal element gamma.
• SESTPR — SESTPR is DOUBLE PRECISION; estimated singular value of (j+1) by (j+1) matrix Lhat.
• S — S is DOUBLE PRECISION; sine needed in forming xhat.
• C — C is DOUBLE PRECISION; cosine needed in forming xhat.

👑 Author 👑

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

Definition at line 133 of file dlaic1.f.

💅 Author 💅

Generated automatically by Doxygen for LAPACK from the source code.

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💖 that’s the page, bestie! Footer vibes: LAPACK Version 3.12.0, source path /home/abui...RC/dlaic1.f(3), and we’re out — periodt. ✨