CLAIC1(3)

💖 NAME 💖

okay so this is the claic1.f(3) page from the Library Functions Manual, and the file it's documenting is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/claic1.f. It's giving incremental condition estimation realness, and yes bestie, every detail is staying. 💅

✨ 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.

🌸 Purpose 🌸

Okay so here's the whole purpose, bestie—no skipping: 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 🍓

Every parameter, exactly as listed:

• 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 💜

Author squad:

• 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.

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That's the whole page, bestie! Footer tea: LAPACK Version 3.12.0, path /home/abui...RC/claic1.f(3). The footer doesn't list a date, so no invented date energy here—just the version and path, periodt. 💖✨