SRC/dlasv2.f(3)

📦
version 3.12.1 · 4 versions
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🌸 NAME 🌸

okay so bestie, this is SRC/dlasv2.f(3) from the LAPACK Library Functions Manual, and it's literally the page for dlasv2 — the routine that does the singular value decomposition of a 2-by-2 triangular matrix. main character energy, no cap 💅

✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

subroutine dlasv2 (f, g, h, ssmin, ssmax, snr, csr, snl, csl)

dlasv2 — DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix. slay.

💖 Function/Subroutine Documentation 💖

🌟 subroutine dlasv2 🌟

subroutine dlasv2 (double precision f, double precision g, double precision h,
    double precision ssmin, double precision ssmax, double precision snr,
    double precision csr, double precision snl, double precision csl)

DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix.

🎯 Purpose 🎯

okay so here's the whole vibe, bestie: DLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix

   [  F   G  ]
   [  0   H  ].

On return, abs(SSMAX) is the larger singular value, abs(SSMIN) is the smaller singular value, and (CSL,SNL) and (CSR,SNR) are the left and right singular vectors for abs(SSMAX), giving the decomposition

   [ CSL  SNL ] [  F   G  ] [ CSR -SNR ]  =  [ SSMAX   0   ]
   [-SNL  CSL ] [  0   H  ] [ SNR  CSR ]     [  0    SSMIN ].

🎀 Parameters 🎀

  • F — F is DOUBLE PRECISION. lowkey important: it's the (1,1) element of the 2-by-2 matrix.
  • G — G is DOUBLE PRECISION. it's the (1,2) element of the 2-by-2 matrix, bestie.
  • H — H is DOUBLE PRECISION. yup, the (2,2) element of the 2-by-2 matrix.
  • SSMIN — SSMIN is DOUBLE PRECISION. abs(SSMIN) is the smaller singular value. periodt.
  • SSMAX — SSMAX is DOUBLE PRECISION. abs(SSMAX) is the larger singular value. iconic.
  • SNL — SNL is DOUBLE PRECISION. (that's it, that's the description — no extra lore, bestie)
  • CSL — CSL is DOUBLE PRECISION. the vector (CSL, SNL) is a unit left singular vector for the singular value abs(SSMAX). 🦋
  • SNR — SNR is DOUBLE PRECISION. (again, no extra description in the source, so no invented lore)
  • CSR — CSR is DOUBLE PRECISION. the vector (CSR, SNR) is a unit right singular vector for the singular value abs(SSMAX). 🌈

🌟 Author 🌟

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

🔥 Further Details 🔥

  • Any input parameter may be aliased with any output parameter. yes bestie, aliasing is allowed — it's giving flexible.
  • Barring over/underflow and assuming a guard digit in subtraction, all output quantities are correct to within a few units in the last place (ulps). so, like, accuracy is cute but not infinite.
  • In IEEE arithmetic, the code works correctly if one matrix element is infinite. good to know, fr fr.
  • Overflow will not occur unless the largest singular value itself overflows or is within a few ulps of overflow. so don't panic unless the big one is already at the edge.
  • Underflow is harmless if underflow is gradual. Otherwise, results may correspond to a matrix modified by perturbations of size near the underflow threshold. ⚠️ so gradual underflow = fine; abrupt underflow = results might be a little haunted.

Definition at line 135 of file dlasv2.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

mwah 💋 that's the whole page, bestie — LAPACK Version 3.12.0 is the version stamped on this SRC/dlasv2.f(3) page, and it's literally iconic, no cap 🫶✨

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