laed5(3)

💖 NAME 💖

okay so bestie, meet laed5(3) from the Library Functions Manual — she’s here, she’s iconic, and she does exactly one little 2x2 job. Periodt. 💅

laed5 - laed5: D&C step: secular equation, 2x2 🎀

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✨ SYNOPSIS ✨

Functions

• subroutine dlaed5 (i, d, z, delta, rho, dlam) — DLAED5 used by DSTEDC. Solves the 2-by-2 secular equation. 🔥
• subroutine slaed5 (i, d, z, delta, rho, dlam) — SLAED5 used by SSTEDC. Solves the 2-by-2 secular equation. 🦋

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📚 Detailed Description 📚

okay so the Detailed Description section is literally just a heading in the original — no extra prose, no hidden lore, no side quest. We go straight to the function docs, bestie. ✨

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🧮 Function Documentation 🧮

subroutine dlaed5

subroutine dlaed5 (integer i, double precision, dimension( 2 ) d, double precision, dimension( 2 ) z, double precision, dimension( 2 ) delta, double precision rho, double precision dlam)

DLAED5 used by DSTEDC. Solves the 2-by-2 secular equation.

Purpose:

!>
!> 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.
!>

Parameters

I — which eigenvalue are we computing? It’s I = 1 or I = 2, no in-between, bestie. 💅

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

D — the original eigenvalues, and yes, we assume D(1) < D(2).

!>          D is DOUBLE PRECISION array, dimension (2)
!>         The original eigenvalues.  We assume D(1) < D(2).
!>

Z — the components of the updating vector. 🦋

!>          Z is DOUBLE PRECISION array, dimension (2)
!>         The components of the updating vector.
!>

DELTA — the vector that carries the info needed to construct the eigenvectors.

!>          DELTA is DOUBLE PRECISION array, dimension (2)
!>         The vector DELTA contains the information necessary
!>         to construct the eigenvectors.
!>

RHO — the scalar in the symmetric updating formula.

!>          RHO is DOUBLE PRECISION
!>         The scalar in the symmetric updating formula.
!>

DLAM — the computed lambda_I, aka the I-th updated eigenvalue. ✨

!>          DLAM is DOUBLE PRECISION
!>         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 dlaed5.f.

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subroutine slaed5

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:

!>
!> 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.
!>

Parameters

I — same energy, same job: this is the index of the eigenvalue, and it’s I = 1 or I = 2. 💖

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

D — the original eigenvalues. We assume D(1) < D(2), no cap.

!>          D is REAL array, dimension (2)
!>         The original eigenvalues.  We assume D(1) < D(2).
!>

Z — the components of the updating vector. 🎀

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

DELTA — all the info you need to construct the eigenvectors.

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

RHO — the scalar in the symmetric updating formula. 🌸

!>          RHO is REAL
!>         The scalar in the symmetric updating formula.
!>

DLAM — the computed lambda_I, the I-th updated eigenvalue. 👑

!>          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.

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👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole laed5(3) page, bestie — straight from the LAPACK source, Version 3.12.0 💖✨ no cap.