SLAIC1(3)

💅 SLAIC1(3) — incremental condition estimation, but make it cute ✨

okay so bestie, welcome to the slaic1.f(3) page from the Library Functions Manual — yes, the one with the absolute mouthful of a path. we're talking about SLAIC1, a Fortran subroutine that applies one step of incremental condition estimation. linear algebra? in this economy? slay. 🫶

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slaic1.f

that's it. that's the NAME section. iconic minimalism, no notes. 💅

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

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

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👑 Function/Subroutine Documentation 👑

🫶 subroutine SLAIC1 🫶

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. periodt. 💖

💖 Purpose 💖

okay so here's the actual lore: SLAIC1 applies one step of incremental condition estimation in its simplest version:

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 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. 👑

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 — 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. 🔥

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. 🤖💅

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okay that's the whole page, bestie. signed off with LAPACK, Version 3.12.0, and the footer path /home/abui...RC/slaic1.f(3) — no date was listed, just this cute little source/version flex. mwah 💋✨