SRC/dlasq1.f(3)

💅 NAME

okay so this is SRC/dlasq1.f(3), the SRC/dlasq1.f page from the Library Functions Manual. Bestie, it's all about the DLASQ1 subroutine and its singular-value era. iconic.

✨ SYNOPSIS

Functions/Subroutines

subroutine dlasq1 (n, d, e, work, info)
    DLASQ1 computes the singular values of a real square bidiagonal
    matrix. Used by sbdsqr.

🎀 Function/Subroutine Documentation

subroutine dlasq1 (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( * ) work, integer info)

DLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr. slay.

🦋 Purpose

Okay so DLASQ1 computes the singular values of a real N-by-N bidiagonal matrix with diagonal D and off-diagonal E. The singular values are computed to high relative accuracy, in the absence of denormalization, underflow and overflow. no cap, that's the whole point.

The algorithm was first presented in by K. V. Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230, 1994, and the present implementation is described in , LAPACK Working Note.

🌸 Parameters

🌟 N

N is INTEGER. The number of rows and columns in the matrix. N >= 0.

🌟 D

D is DOUBLE PRECISION array, dimension (N). On entry, D contains the diagonal elements of the bidiagonal matrix whose SVD is desired. On normal exit, D contains the singular values in decreasing order.

🌟 E

E is DOUBLE PRECISION array, dimension (N). On entry, elements E(1:N-1) contain the off-diagonal elements of the bidiagonal matrix whose SVD is desired. On exit, E is overwritten. not me losing the original E though 😭

🌟 WORK

WORK is DOUBLE PRECISION array, dimension (4*N).

🌟 INFO

INFO is INTEGER.

• = 0: successful exit
• < 0: if INFO = -i, the i-th argument had an illegal value
• > 0: the algorithm failed
  • = 1: a split was marked by a positive value in E
  • = 2: current block of Z not diagonalized after 100*N iterations (in inner while loop) On exit D and E represent a matrix with the same singular values which the calling subroutine could use to finish the computation, or even feed back into DLASQ1
  • = 3: termination criterion of outer while loop not met (program created more than N unreduced blocks)

👑 Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 107 of file dlasq1.f.

👑 Author

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okay bestie, that's the whole page — footer vibes: LAPACK Version 3.12.0, page SRC/dlasq1.f(3). 💜✨