SRC/slaed4.f(3)

🎀 NAME 🎀

okay bestie, this page is from the Library Functions Manual and it’s all about SRC/slaed4.f 💖 like, a whole LAPACK subroutine page, no cap.

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

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

💅 Function/Subroutine Documentation 💅

🌟 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. literally iconic 💅

🧚 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 ⭐

Definition at line 144 of file slaed4.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

---

bye bestie 💖 this footer moment is brought to you by LAPACK Version 3.12.0 and the source path SRC/slaed4.f(3) — slay, periodt. ✨