SRC/dlaed4.f(3)

💅 SRC/dlaed4.f(3) — Library Functions Manual vibes 💅

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✨ NAME ✨

SRC/dlaed4.f

🌸 SYNOPSIS 🌸

Functions/Subroutines

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

🦋 Function/Subroutine Documentation 🦋

okay so here's the full signature, no cap:

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)

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

🎀 Purpose

Bestie, 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. Slay.

🌈 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.

🧚 Author

Generated automatically by Doxygen for LAPACK from the source code.

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