lasd5(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

💖 lasd5(3) — D&C step: secular equation, 2x2 💖

Okay bestie, welcome to lasd5(3) from the Library Functions Manual — it's giving tiny LAPACK helper energy, and it's literally all about the D&C step: secular equation, 2x2. No cap. ✨

🌸 NAME 🌸

lasd5 — lasd5: D&C step: secular equation, 2x2

✨ SYNOPSIS ✨

Functions

  • dlasd5 — 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.
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)
  • slasd5 — 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.
subroutine slasd5 (integer i, real, dimension( 2 ) d, real, dimension( 2 ) z, real, dimension( 2 ) delta, real rho, real dsigma, real, dimension( 2 ) work)

🦋 Detailed Description 🦋

No extra prose before the function docs, bestie — it goes straight into the function tea. 💅

👑 Function Documentation 👑

💅 subroutine dlasd5

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:

Okay so the whole point, bestie: 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, literally:

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 — INTEGER. The index of the eigenvalue to be computed. I = 1 or I = 2.
  • D — DOUBLE PRECISION array, dimension ( 2 ). The original eigenvalues. We assume 0 <= D(1) < D(2).
  • Z — DOUBLE PRECISION array, dimension ( 2 ). The components of the updating vector.
  • DELTA — 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 — DOUBLE PRECISION. The scalar in the symmetric updating formula.
  • DSIGMA — DOUBLE PRECISION. The computed sigma_I, the I-th updated eigenvalue.
  • WORK — 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.

🫶 subroutine slasd5

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.

Purpose:

Same iconic math energy, just the REAL girlie: 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, exactly:

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 — INTEGER. The index of the eigenvalue to be computed. I = 1 or I = 2.
  • D — REAL array, dimension (2). The original eigenvalues. We assume 0 <= D(1) < D(2).
  • Z — REAL array, dimension (2). The components of the updating vector.
  • DELTA — 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.
  • RHO — REAL. The scalar in the symmetric updating formula.
  • DSIGMA — REAL. The computed sigma_I, the I-th updated eigenvalue.
  • WORK — REAL 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 slasd5.f.

🌈 Author 🌈

  • Generated automatically by Doxygen for LAPACK from the source code.

Cute sign-off, bestie: this footer is LAPACK Version 3.12.0 for lasd5(3) — and there's no separate date printed on this page, so I'm not inventing one. Periodt. 💖🎀

📦 where this page comes from