SRC/slasv2.f(3)

💅 SRC/slasv2.f 💅

Okay bestie, welcome to the Library Functions Manual page for SRC/slasv2.f(3) — the NAME section below is SRC/slasv2.f, and the whole thing is giving tiny-subroutine, big singular-value-decomposition energy. 💖

🌸 NAME 🌸

SRC/slasv2.f

That's literally the whole NAME section. Short, iconic, periodt. ✨

🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

subroutine slasv2 (f, g, h, ssmin, ssmax, snr, csr, snl, csl)
    SLASV2 computes the singular value decomposition of a 2-by-2
    triangular matrix.

🧚 Function/Subroutine Documentation 🧚

🌟 subroutine slasv2 🌟

subroutine slasv2 (real f, real g, real h, real ssmin, real ssmax, real snr, real csr, real snl, real csl)

SLASV2 computes the singular value decomposition of a 2-by-2 triangular matrix. No cap, that's the whole assignment. 💅

🎯 Purpose 🎯

This is the actual Doxygen purpose block, matrix spacing and all — protect the alignment, it's iconic:

!>
!> SLASV2 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 REAL. The (1,1) element of the 2-by-2 matrix.
• G — G is REAL. The (1,2) element of the 2-by-2 matrix.
• H — H is REAL. The (2,2) element of the 2-by-2 matrix.
• SSMIN — SSMIN is REAL. abs(SSMIN) is the smaller singular value.
• SSMAX — SSMAX is REAL. abs(SSMAX) is the larger singular value.
• SNL — SNL is REAL. The source leaves it at that, bestie. 🫶
• CSL — CSL is REAL. The vector (CSL, SNL) is a unit left singular vector for the singular value abs(SSMAX).
• SNR — SNR is REAL. Same deal, no extra description in the source. 💅
• CSR — CSR is REAL. 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, any input with any output — the source said it, not me. 💅
• 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).
• In IEEE arithmetic, the code works correctly if one matrix element is infinite.
• Overflow will not occur unless the largest singular value itself overflows or is within a few ulps of overflow.
• Underflow is harmless if underflow is gradual. Otherwise, results may correspond to a matrix modified by perturbations of size near the underflow threshold.

Definition at line 135 of file slasv2.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

---

XOXO, bestie 💖 — this page is from LAPACK, Version 3.12.0, and it lives at SRC/slasv2.f(3). Now go slay those 2-by-2 triangular matrices! 🎀✨