DLASD8(3)

💖 DLASD8(3) — LAPACK manual but make it cute 💖

Okay so bestie, listen up, because this is literally the LAPACK manual page for DLASD8, and it's giving main character energy in the most niche way possible. We're talking Fortran subroutines, secular equations, and singular vectors. No cap, this is the good stuff. The manual name is LAPACK, and we're deep in the source file. Let me break it down for you. 🫶

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NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlasd8.f

Like, that's the whole path, bestie. It's literally where this file lives. Slay. 💅

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SYNOPSIS 🦋

Functions/Subroutines

subroutine DLASD8 (icompq, k, d, z, vf, vl, difl, difr, lddifr, dsigma,
    work, info)

DLASD8 finds the square roots of the roots of the secular equation, and stores, for each element in D, the distance to its two nearest poles. Used by sbdsdc. Highkey iconic. 👑

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Function/Subroutine Documentation 🌸

subroutine DLASD8 (integer icompq, integer k, double precision, dimension( *
) d, double precision, dimension( * ) z, double precision, dimension( *
) vf, double precision, dimension( * ) vl, double precision, dimension(
* ) difl, double precision, dimension( lddifr, * ) difr, integer lddifr,
double precision, dimension( * ) dsigma, double precision, dimension( *
) work, integer info)

DLASD8 finds the square roots of the roots of the secular equation, and stores, for each element in D, the distance to its two nearest poles. Used by sbdsdc. (Yes, I'm repeating myself, but it's literally the vibe.) 🌈

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Purpose 💜

Not me about to explain this like it's the most exciting thing ever — because it is. So DLASD8 finds the square roots of the roots of the secular equation, as defined by the values in DSIGMA and Z. It makes the appropriate calls to DLASD4, and stores, for each element in D, the distance to its two nearest poles (elements in DSIGMA). It also updates the arrays VF and VL, the first and last components of all the right singular vectors of the original bidiagonal matrix.

And yes, bestie, DLASD8 is called from DLASD6. That's the lore. 🎀

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Parameters 🧚

Okay so here's where it gets juicy. Every single parameter, coming at you:

• ICOMPQ — ICOMPQ is INTEGER. Specifies whether singular vectors are to be computed in factored form in the calling routine: = 0: Compute singular values only. = 1: Compute singular vectors in factored form as well. Like, pick your fighter. 💅
• K — K is INTEGER. The number of terms in the rational function to be solved by DLASD4. K >= 1. Periodt.
• D — D is DOUBLE PRECISION array, dimension ( K ). On output, D contains the updated singular values. Slay.
• Z — Z is DOUBLE PRECISION array, dimension ( K ). On entry, the first K elements of this array contain the components of the deflation-adjusted updating row vector. On exit, Z is updated. It's giving transformation. ✨
• VF — VF is DOUBLE PRECISION array, dimension ( K ). On entry, VF contains information passed through DBEDE8. On exit, VF contains the first K components of the first components of all right singular vectors of the bidiagonal matrix. Obsessed with the clarity. 🦋
• VL — VL is DOUBLE PRECISION array, dimension ( K ). On entry, VL contains information passed through DBEDE8. On exit, VL contains the first K components of the last components of all right singular vectors of the bidiagonal matrix. Twin energy with VF, honestly. 🫶
• DIFL — DIFL is DOUBLE PRECISION array, dimension ( K ). On exit, DIFL(I) = D(I) - DSIGMA(I). Literally that simple. 🔥
• DIFR — DIFR is DOUBLE PRECISION array, dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and dimension ( K ) if ICOMPQ = 0. On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not defined and will not be referenced. If ICOMPQ = 1, DIFR(1:K,2) is an array containing the normalizing factors for the right singular vector matrix. Not me warning you about DIFR(K,1) — do NOT touch it, it's undefined and will not be referenced, okay? 🙈
• LDDIFR — LDDIFR is INTEGER. The leading dimension of DIFR, must be at least K. No negotiation. 👑
• DSIGMA — DSIGMA is DOUBLE PRECISION array, dimension ( K ). On entry, the first K elements of this array contain the old roots of the deflated updating problem. These are the poles of the secular equation. The drama of it all. 🌸
• WORK — WORK is DOUBLE PRECISION array, dimension (3*K). Just workspace, bestie. Do your thing. 💖
• INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = 1, a singular value did not converge. Like, if you see INFO = 1, something didn't converge and you need to deal with it. No cap. 😭

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Author 🌟

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

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Contributors 🎀

Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA. Icons only. 💜

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Definition at line 162 of file dlasd8.f.

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Author ✨

Generated automatically by Doxygen for LAPACK from the source code. So like, a robot made this, but I'm here to make it cute. 🦋

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LAPACK — Version 3.12.0 — /home/abui...RC/dlasd8.f(3)

Okay that's the whole thing, bestie. You're welcome. Now go slay those singular values. 💅✨👑