SRC/dlasd4.f(3)

SRC/dlasd4.f(3) 💅✨

okay so we’re lowkey in the Library Functions Manual, and this whole page is about SRC/dlasd4.f(3). Buckle up bestie, it’s giving Fortran subroutine main-character energy. 🫶

NAME ✨

SRC/dlasd4.f — that’s the name, periodt. 💖

SYNOPSIS 🫶

Functions/Subroutines 🧚

subroutine dlasd4 (n, i, d, z, delta, rho, sigma, work, info)
    DLASD4 computes the square root of the i-th updated eigenvalue of a
    positive symmetric rank-one modification to a positive diagonal
    matrix. Used by dbdsdc.

Function/Subroutine Documentation 🎀

subroutine dlasd4 (integer n, integer i, double precision, dimension( * ) d,
    double precision, dimension( * ) z, double precision, dimension( * )
    delta, double precision rho, double precision sigma, double precision,
    dimension( * ) work, integer info)

DLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by dbdsdc. 👑

Purpose: 🔥

okay so here’s the whole point, bestie: this subroutine computes the square root of the I-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix whose entries are given as the squares of the corresponding entries in the array d, and that

        0 <= 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 ) * 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; it’s the length of all arrays. 👑
• I — I is INTEGER; it’s the index of the eigenvalue to be computed, and 1 <= I <= N. 🎯
• D — D is DOUBLE PRECISION array, dimension ( N ); these are the original eigenvalues. It is assumed that they are in order, 0 <= D(I) < D(J) for I < J. 🌈
• Z — Z is DOUBLE PRECISION array, dimension ( N ); these are the components of the updating vector. 🦋
• DELTA — DELTA is DOUBLE PRECISION array, dimension ( N ). If N .ne. 1, DELTA contains (D(j) - sigma_I) in its j-th component. If N = 1, then DELTA(1) = 1. The vector DELTA contains the information necessary to construct the (singular) eigenvectors. 💀
• RHO — RHO is DOUBLE PRECISION; it’s the scalar in the symmetric updating formula. 🍓
• SIGMA — SIGMA is DOUBLE PRECISION; it’s the computed sigma_I, the I-th updated eigenvalue. ⭐
• WORK — WORK is DOUBLE PRECISION array, dimension ( N ). If N .ne. 1, WORK contains (D(j) + sigma_I) in its j-th component. If N = 1, then WORK( 1 ) = 1. 🧚
• INFO — INFO is INTEGER
  • = 0: successful exit
  • > 0: if INFO = 1, the updating process failed. 😭

Internal Parameters: 🧚

• ORGATI — logical variable (origin-at-i?) 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

• SWTCH3 — logical variable (switch-for-3-poles?) for noting if we are working with THREE poles! 🔥
• MAXIT — 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 152 of file dlasd4.f. 📌

Author (auto-generated) 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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okay that’s the whole page, bestie 🫶 the footer vibes are LAPACK Version 3.12.0, SRC/dlasd4.f(3) — auto-generated by Doxygen for LAPACK from the source code, and it’s iconic. mwah 💋✨