SLASD5(3)

💅 SLASD5(3) — the slasd5.f girlies rise

okay so bestie, welcome to SLASD5, a whole subroutine from the LAPACK fam (that's the Library Functions Manual energy, and yes we're in the section 3 files today 🎀).

Also can we talk about the NAME? The name of this file is literally just its whole address, main-character-coded:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slasd5.f

periodt. that's where she lives. 🏠✨

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✨ SYNOPSIS ✨

Functions/Subroutines

subroutine SLASD5 (i, d, z, delta, rho, dsigma, work)

SLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc. no cap, that's the whole vibe check. 🦋

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💖 Function/Subroutine Documentation 💖

subroutine SLASD5 (integer i, real, dimension( 2 ) d, real, dimension( 2 )
    z, real, dimension( 2 ) delta, real rho, real dsigma, real, dimension( 2
    ) work)

SLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc. (yes, we said it twice, she's consistent 💅)

🌸 Purpose:

okay so, the tea:

This subroutine computes the square root of the I-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix

           diag( D ) * diag( D ) +  RHO * Z * transpose(Z) .

The diagonal entries in the array D are assumed to satisfy

            0 <= D(i) < D(j)  for  i < j .

We also assume RHO > 0 and that the Euclidean norm of the vector Z is one. lowkey crucial, don't skip those assumptions bestie, they're the whole foundation of the fit 🧚✨

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🎀 Parameters 🎀

• I — I is INTEGER. The index of the eigenvalue to be computed. I = 1 or I = 2. that's it, only two options, very pick-me but make it math 💀
• D — D is REAL array, dimension (2). The original eigenvalues. We assume 0 <= D(1) < D(2). order matters, iconique 🙈
• Z — Z is REAL array, dimension (2). The components of the updating vector. the little update vector that could 🫶
• DELTA — DELTA is REAL array, dimension (2). Contains (D(j) - sigma_I) in its j-th component. The vector DELTA contains the information necessary to construct the eigenvectors. she's giving construction worker, but for eigenvectors 🏗️✨
• RHO — RHO is REAL. The scalar in the symmetric updating formula. just a scalar doing scalar things 💜
• DSIGMA — DSIGMA is REAL. The computed sigma_I, the I-th updated eigenvalue. the glow-up result, we love to see her 🔥
• WORK — WORK is REAL array, dimension (2). WORK contains (D(j) + sigma_I) in its j-th component. note: plus this time, not minus — DELTA took the minus, WORK took the plus, they're matching but opposite, it's giving twin flames 🌈

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👑 Author

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

four legends, one subroutine. the collab we didn't know we needed 🫶💖

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⭐ Contributors:

Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA. shoutout Ren-Cang, actual main character energy 👏✨

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🦋 Definition

Definition at line 115 of file slasd5.f. exact coordinates, iykyk 📍

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💫 Author (the meta one)

Generated automatically by Doxygen for LAPACK from the source code. not me being auto-generated, she's a bot but she's slaying 💅🤖

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fr fr bestie, keep those assumptions (0 <= D(i) < D(j) for i < j, RHO > 0, Z norm one) intact or the math does not math. no notes, just respect the constraints 🙏

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and that's the whole page 🎀 mwah 💋 — brought to you by LAPACK, Version 3.12.0, footer included, generated automatically by Doxygen for LAPACK from the source code. stay iconic, stay orthogonal 💜✨🌸