SRC/slaed5.f(3)

okay so this is SRC/slaed5.f(3) from the Library Functions Manual — manual-name name tag folded in, bestie, and we're talking about the little solver with main-character energy 💅

🌸 NAME 🌸

SRC/slaed5.f

🛰️ SYNOPSIS 🛰️

🧩 Functions/Subroutines 🧩

subroutine slaed5 (i, d, z, delta, rho, dlam)
    SLAED5 used by SSTEDC. Solves the 2-by-2 secular equation.

that's the whole synopsis vibe, no cap ✨

🧚 Function/Subroutine Documentation 🧚

subroutine slaed5 (integer i, real, dimension( 2 ) d, real, dimension( 2 )
z, real, dimension( 2 ) delta, real rho, real dlam)

SLAED5 used by SSTEDC. Solves the 2-by-2 secular equation.

✨ Purpose: ✨

okay so here's the lore: this subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix 🫶

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

the diagonal elements in the array D are assumed to satisfy:

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

we also assume RHO > 0 and that the Euclidean norm of the vector Z is one. preconditions, bestie — they're not optional 💖

🔢 Parameters 🔢

I

I is INTEGER. the index of the eigenvalue to be computed. I = 1 or I = 2.

D

D is REAL array, dimension (2). the original eigenvalues. we assume D(1) < D(2).

Z

Z is REAL array, dimension (2). the components of the updating vector.

DELTA

DELTA is REAL array, dimension (2). the vector DELTA contains the information necessary to construct the eigenvectors.

RHO

RHO is REAL. the scalar in the symmetric updating formula.

DLAM

DLAM is REAL. the computed lambda_I, the I-th updated eigenvalue.

✍️ 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 107 of file slaed5.f.

📜 Author 📜

Generated automatically by Doxygen for LAPACK from the source code.

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footer sign-off, bestie: the footer's whole energy is LAPACK Version 3.12.0 and source SRC/slaed5.f(3) — that's the cute little stamp at the very end 🫶💖