SRC/dlasd5.f(3)

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🎀 SRC/dlasd5.f(3) 🎀

hey bestie, welcome to the Library Functions Manual page for SRC/dlasd5.f — yes, that's the whole title vibe. this is the dlasd5 subroutine's little corner of LAPACK, and we're gonna read it together like a group chat, no cap. 💅

🌸 NAME 🌸

SRC/dlasd5.f — literally the name, bestie. that's it. that's the section. 🫶

✨ 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.

💖 Function/Subroutine Documentation 💖

🧚 subroutine dlasd5 — the full signature 🧚

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 🍓

ok so 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. periodt. 💅

🎀 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.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

okay bye bestie 🫶 this whole thing is LAPACK, Version 3.12.0, and the file SRC/dlasd5.f(3) — see ya! ✨💜

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