SLAED4(3)

💅 SLAED4(3) — Library Functions Manual, but make it a bestie explainer ✨

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slaed4.f

✨ 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 (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. 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 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 (Doxygen’s autograph era) 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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Cute sign-off, bestie: source/version/path footer vibes are LAPACK — Version 3.12.0 — /home/abui...RC/slaed4.f(3). The original footer didn’t print a date, so I’m not inventing one 😭💖