SRC/slaic1.f(3)

✨ SRC/slaic1.f(3) ✨

(Library Functions Manual, bestie — we're in the LAPACK math corner and it's giving incremental condition estimation 💅)

🌸 NAME 🌸

SRC/slaic1.f — the page for the slaic1 subroutine, the little routine with big singular-value energy.

💫 SYNOPSIS 💫

Functions/Subroutines

• subroutine slaic1 (job, j, x, sest, w, gamma, sestpr, s, c) — SLAIC1 applies one step of incremental condition estimation.

Full signature, exactly:

subroutine slaic1 (integer job, integer j, real, dimension( j ) x, real
    sest, real, dimension( j ) w, real gamma, real sestpr, real s, real c)

🎀 Function/Subroutine Documentation 🎀

subroutine slaic1 (integer job, integer j, real, dimension( j ) x, real
    sest, real, dimension( j ) w, real gamma, real sestpr, real s, real c)

SLAIC1 applies one step of incremental condition estimation.

Purpose

Okay bestie, here's the whole vibe: SLAIC1 applies one step of incremental condition estimation in its simplest version:

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

         twonorm(L*x) = sest

Then SLAIC1 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; = 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 REAL array, dimension (J); the j-vector x.
• SEST — SEST is REAL; estimated singular value of j by j matrix L.
• W — W is REAL array, dimension (J); the j-vector w.
• GAMMA — GAMMA is REAL; the diagonal element gamma.
• SESTPR — SESTPR is REAL; estimated singular value of (j+1) by (j+1) matrix Lhat.
• S — S is REAL; sine needed in forming xhat.
• C — C is REAL; 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 slaic1.f.

✨ Author ✨

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie. Sign-off: LAPACK Version 3.12.0, page SRC/slaic1.f(3). Stay slay and numerically stable. 💖