SLASQ1(3)

🌸 SLASQ1(3) — Library Functions Manual 🌸

okay bestie, welcome to the SLASQ1(3) page from the Library Functions Manual 💅. The header path is /home/abui...RC/slasq1.f(3), and this whole page is about the Fortran subroutine that computes singular values of a real square bidiagonal matrix. It's used by sbdsqr, so yes, it's giving important side-character energy ✨.

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✨ NAME ✨

The NAME section is literally this path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slasq1.f

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✨ SYNOPSIS ✨

🌈 Functions/Subroutines 🌈

subroutine SLASQ1 (n, d, e, work, info)

SLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr. 🫶

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🦋 Function/Subroutine Documentation 🦋

Here's the full signature, bestie — every type and every dimension( * ) stays exactly where it belongs:

subroutine SLASQ1 (integer n, real, dimension( * ) d, real, dimension( * ) e, real, dimension( * ) work, integer info)

SLASQ1 computes the singular values of a real square bidiagonal matrix. Used by sbdsqr. 💖

🎀 Purpose 🎀

SLASQ1 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. 🔥

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.

yes, the citation really says “presented in by” and “described in , LAPACK Working Note” — I'm keeping it exactly as the page says, bestie. no editing the lore. 📚

💖 Parameters 💖

• N — INTEGER. The number of rows and columns in the matrix. N >= 0.
• D — REAL 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 — REAL 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.
• WORK — REAL array, dimension (4*N).
• INFO — 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 SLASQ1
    • = 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 slasq1.f.

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💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the page, bestie 🎀. footer sign-off: LAPACK Version 3.12.0, footer path /home/abui...RC/slasq1.f(3) — and ngl there's no date listed in that footer, so I'm not inventing one. periodt. 💜