SLASD4(3)

💅 SLASD4(3) — like, the whole manual, bestie ✨

okay so this page lives in the Library Functions Manual section, and its file is literally /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slasd4.f — that's the path, that's the name, that's the whole NAME section, slay 🎀

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✨ SYNOPSIS ✨

🌸 Functions/Subroutines

• subroutine SLASD4 (n, i, d, z, delta, rho, sigma, work, info) — SLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by sbdsdc.

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🦋 Function/Subroutine Documentation 🦋

subroutine SLASD4 (integer n, integer i, real, dimension( * ) d, real,
    dimension( * ) z, real, dimension( * ) delta, real rho, real sigma,
    real, dimension( * ) work, integer info)

SLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by sbdsdc. no cap, that's the whole gig 💜

🎀 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
!>
!>        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.
!>

so like, it's giving "find the square root of the I-th updated eigenvalue" of a positive symmetric rank-one modification to a positive diagonal matrix — and the diagonal entries are the squares of the entries in d. the ordering 0 <= D(i) < D(j) for i < j, plus RHO > 0, is all set up by whoever calls this routine, and it's no loss in generality, periodt. the rank-one modified system is diag( D ) * diag( D ) + RHO * Z * Z_transpose. and we're assuming the Euclidean norm of Z is 1. the method? approximating the rational functions in the secular equation by simpler interpolating rational functions. iconique 🔥

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💖 Parameters 💖

• N — N is INTEGER. The length of all arrays. that's it, that's the vibe.
• 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, 0 <= D(I) < D(J) for I < J. mind the ordering bestie, it's load-bearing 🙈
• Z — Z is REAL array, dimension ( N ). The components of the updating vector.
• DELTA — DELTA is REAL 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. yes the eigenvectors are singular, we love that for them 💀
• RHO — RHO is REAL. The scalar in the symmetric updating formula.
• SIGMA — SIGMA is REAL. The computed sigma_I, the I-th updated eigenvalue. the main character of this whole operation ngl 👑
• WORK — WORK is REAL 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. Exit status vibes:
  • = 0: successful exit 🌈
  • > 0: if INFO = 1, the updating process failed. 😭 it happens to the best of us.

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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.
!>
!>            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.
!>

okay so breaking the lore down for you 🧚

• The logical variable ORGATI (origin-at-i?) distinguishes whether D(i) or D(i+1) is treated as the origin.
  • ORGATI = .true. — origin at i
  • ORGATI = .false. — origin at i+1
• The logical variable SWTCH3 (switch-for-3-poles?) is for noting if we are working with THREE poles! three!! 🫶
• MAXIT is the maximum number of iterations allowed for each eigenvalue.

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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. legend behaviour, honestly 💅

Definition at line 152 of file slasd4.f.

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⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. (yes, a robot wrote this, and it ate 🤖✨)

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okay so that's the whole page!! this is LAPACK, Version 3.12.0, and the source file is /home/abui...RC/slasd4.f(3) — that's the date/version bit at the bottom, folded in all cute for you. bye bestie, go compute some eigenvalues 🦋💖