laed4(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

🎀 laed4(3) — laed4: D&C step: secular equation nonlinear solver

💖 NAME

okay so laed4 is the manual-page name, and the one-liner is laed4: D&C step: secular equation nonlinear solver. That's the whole vibe. 💅

🌸 SYNOPSIS

Functions

  • subroutine dlaed4 (n, i, d, z, delta, rho, dlam, info) — DLAED4 used by DSTEDC. Finds a single root of the secular equation.
  • subroutine slaed4 (n, i, d, z, delta, rho, dlam, info) — SLAED4 used by SSTEDC. Finds a single root of the secular equation.

🦋 Detailed Description

bestie, there isn't an extra paragraph here in the original — the detailed tea lives in Function Documentation below. ✨

📚 Function Documentation

💜 subroutine dlaed4

subroutine dlaed4 (integer n, integer i, double precision, dimension( * ) d, double precision, dimension( * ) z, double precision, dimension( * ) delta, double precision rho, double precision dlam, integer info)

DLAED4 used by DSTEDC. Finds a single root of the secular equation.

✨ Purpose

okay so this subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that

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

and that RHO > 0. This is arranged by the calling routine, and is no loss in generality. The rank-one modified system is thus

diag( D )  +  RHO * Z * Z_transpose.

where we assume the Euclidean norm of Z is 1.

The method consists of approximating the rational functions in the secular equation by simpler interpolating rational functions.

🎀 Parameters

  • N — N is INTEGER. The length of all arrays.
  • I — I is INTEGER. The index of the eigenvalue to be computed. 1 <= I <= N.
  • D — D is DOUBLE PRECISION array, dimension (N). The original eigenvalues. It is assumed that they are in order, D(I) < D(J) for I < J.
  • Z — Z is DOUBLE PRECISION array, dimension (N). The components of the updating vector.
  • DELTA — DELTA is DOUBLE PRECISION array, dimension (N). If N > 2, DELTA contains (D(j) - lambda_I) in its j-th component. If N = 1, then DELTA(1) = 1. If N = 2, see DLAED5 for detail. The vector DELTA contains the information necessary to construct the eigenvectors by DLAED3 and DLAED9.
  • RHO — RHO is DOUBLE PRECISION. The scalar in the symmetric updating formula.
  • DLAM — DLAM is DOUBLE PRECISION. The computed lambda_I, the I-th updated eigenvalue.
  • INFO — INFO is INTEGER. = 0: successful exit. > 0: if INFO = 1, the updating process failed.

🔥 Internal Parameters:

  • Logical variable ORGATI (origin-at-i?) is used for distinguishing whether D(i) or D(i+1) is treated as the origin.
    • ORGATI = .true. — origin at i
    • ORGATI = .false. — origin at i+1
  • Logical variable SWTCH3 (switch-for-3-poles?) is for noting if we are working with THREE poles!
  • MAXIT is the maximum number of iterations allowed for each 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 144 of file dlaed4.f.

💙 subroutine slaed4

subroutine slaed4 (integer n, integer i, real, dimension( * ) d, real, dimension( * ) z, real, dimension( * ) delta, real rho, real dlam, integer info)

SLAED4 used by SSTEDC. Finds a single root of the secular equation.

✨ Purpose

okay so this subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that

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

and that RHO > 0. This is arranged by the calling routine, and is no loss in generality. The rank-one modified system is thus

diag( D )  +  RHO * Z * Z_transpose.

where we assume the Euclidean norm of Z is 1.

The method consists of approximating the rational functions in the secular equation by simpler interpolating rational functions.

🎀 Parameters

  • N — N is INTEGER. The length of all arrays.
  • I — I is INTEGER. The index of the eigenvalue to be computed. 1 <= I <= N.
  • D — D is REAL array, dimension (N). The original eigenvalues. It is assumed that they are in order, D(I) < D(J) for I < J.
  • Z — Z is REAL array, dimension (N). The components of the updating vector.
  • DELTA — DELTA is REAL array, dimension (N). If N > 2, DELTA contains (D(j) - lambda_I) in its j-th component. If N = 1, then DELTA(1) = 1. If N = 2, see SLAED5 for detail. The vector DELTA contains the information necessary to construct the eigenvectors by SLAED3 and SLAED9.
  • RHO — RHO is REAL. The scalar in the symmetric updating formula.
  • DLAM — DLAM is REAL. The computed lambda_I, the I-th updated eigenvalue.
  • INFO — INFO is INTEGER. = 0: successful exit. > 0: if INFO = 1, the updating process failed.

🔥 Internal Parameters:

  • Logical variable ORGATI (origin-at-i?) is used for distinguishing whether D(i) or D(i+1) is treated as the origin.
    • ORGATI = .true. — origin at i
    • ORGATI = .false. — origin at i+1
  • Logical variable SWTCH3 (switch-for-3-poles?) is for noting if we are working with THREE poles!
  • MAXIT is the maximum number of iterations allowed for each 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 144 of file slaed4.f.

👑 Author

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