DLASD5(3)

💖 DLASD5(3) — Library Functions Manual, but make it cute 💖

okay so bestie, welcome to DLASD5(3) from the Library Functions Manual — yes, the header folded itself in up here because we’re doing a vibe check, not a copy-paste 😌.

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🌸 NAME 🌸

The NAME section is literally this source path, no extra lore, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlasd5.f

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

• subroutine DLASD5 (i, d, z, delta, rho, dsigma, work) — DLASD5 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.

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🫶 Function/Subroutine Documentation 🫶

subroutine DLASD5 (integer i, double precision, dimension( 2 ) d, double
     precision, dimension( 2 ) z, double precision, dimension( 2 ) delta,
     double precision rho, double precision dsigma, double precision,
     dimension( 2 ) work)

DLASD5 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.

🌈 Purpose 🌈

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.

💅 Parameters 💅

• I — I is INTEGER. The index of the eigenvalue to be computed. I = 1 or I = 2.
• D — D is DOUBLE PRECISION array, dimension ( 2 ). The original eigenvalues. We assume 0 <= D(1) < D(2).
• Z — Z is DOUBLE PRECISION array, dimension ( 2 ). The components of the updating vector.
• DELTA — DELTA is DOUBLE PRECISION array, dimension ( 2 ). Contains (D(j) - sigma_I) in its j-th component. The vector DELTA contains the information necessary to construct the eigenvectors.
• RHO — RHO is DOUBLE PRECISION. The scalar in the symmetric updating formula.
• DSIGMA — DSIGMA is DOUBLE PRECISION. The computed sigma_I, the I-th updated eigenvalue.
• WORK — WORK is DOUBLE PRECISION array, dimension ( 2 ). WORK contains (D(j) + sigma_I) in its j-th component.

🌟 Author 🌟

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

🦋 Contributors 🦋

Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

Definition at line 115 of file dlasd5.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 DLASD5(3) moment 💖 — footer tea: LAPACK Version 3.12.0, from /home/abui...RC/dlasd5.f(3). No extra date stamp in the footer, just that source/version goodness. bye bestie, go slay those eigenvalues! 🫶