SRC/dlaic1.f(3)

🌈 SRC/dlaic1.f — Library Functions Manual 🌈

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✨ NAME ✨

SRC/dlaic1.f — that's the file, bestie. no cap.

🌸 SYNOPSIS 🌸

Functions/Subroutines

• subroutine dlaic1 (job, j, x, sest, w, gamma, sestpr, s, c) — DLAIC1 applies one step of incremental condition estimation. slay.

🫶 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. That's the whole vibe.

🧚 Purpose 🧚

Okay so picture this: DLAIC1 applies one step of incremental condition estimation in its simplest version. (yes, simplest — iconic behavior.)

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

twonorm(L*x) = sest

Then DLAIC1 computes sestpr, s, and 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. (yes, JOB is the switch, we'll get to it.)

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

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