DLASD4(3)

💜 DLASD4(3) — the LAPACK manual page, but make it make sense

okay so bestie, this is DLASD4 from LAPACK Version 3.12.0, and the source file is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlasd4.f. Yes that whole path. It's giving "compiled in a build directory and we're all just living in it" 😭 but that literally is the NAME section, so here we are. 🎀

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✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dlasd4.f

that's it. that's the name. the whole path. iconic honestly. 💅

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🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine DLASD4 (n, i, d, z, delta, rho, sigma, work, info)

okay so what does it DO — 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. periodt. 🔥

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🌸 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)

again for the people in the back: 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. slay. ✨

💖 Purpose:

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 fortran 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 fortran 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.

the way that the method just *approximates the rational functions in the secular equation by simpler interpolating rational functions*… lowkey obsessed with her ngl 🧚

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🎀 Parameters 🎀

• N — N is INTEGER. The length of all arrays. every single one. 🫶
• 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, 0 <= D(I) < D(J) for I < J. so don't come in here with unsorted eigenvalues, bestie, the assumption is load-bearing. 😭
• 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. note: singular eigenvectors, fr fr, that's what it says. 🙈
• RHO — RHO is DOUBLE PRECISION. The scalar in the symmetric updating formula.
• SIGMA — SIGMA is DOUBLE PRECISION. The computed sigma_I, the I-th updated eigenvalue. the main character of this whole operation honestly 👑
• 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. Status check, bestie:
  • = 0: successful exit ✨
  • > 0: if INFO = 1, the updating process failed. 💀

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🌈 Internal Parameters: 🌈

Logical variable ORGATI (origin-at-i?) is used for distinguishing whether D(i) or D(i+1) is treated as the origin. fortran 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.

not the variable literally named "switch-for-3-poles" 😭😭 she has range and she has THREE POLES. iykyk. 💅

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⭐ 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.

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💫 Author (the meta one) 💫

Generated automatically by Doxygen for LAPACK from the source code.

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ngl bestie, if you're reading a manpage for a LAPACK subroutine that approximates rational functions in a secular equation, you are highkey built different. go drink some water. 🍓

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LAPACK — Version 3.12.0 — /home/abui...RC/dlasd4.f(3) 🌸 that's the sign-off, mwah, bye, go sort your eigenvalues 💜