SLASV2(3)

okay so this is SLASV2(3), and yes bestie, it lives in the Library Functions Manual 💅✨

💖 NAME 💖

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/slasv2.f

That's the source file, no cap. 🫶

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🌸 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. iconic behavior honestly 😭👑

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💅 Function/Subroutine Documentation 💅

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. periodt. ✨

🎀 Purpose 🎀

okay so the whole point is this: 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 ].

like, the math is mathing 💜🔥

🌈 Parameters 🌈

• F is REAL — the (1,1) element of the 2-by-2 matrix.
• G is REAL — the (1,2) element of the 2-by-2 matrix.
• H is REAL — the (2,2) element of the 2-by-2 matrix.
• SSMIN is REAL — abs(SSMIN) is the smaller singular value.
• SSMAX is REAL — abs(SSMAX) is the larger singular value.
• SNL is REAL.
• CSL is REAL — the vector (CSL, SNL) is a unit left singular vector for the singular value abs(SSMAX).
• SNR is REAL.
• 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, really, they can overlap 👀
• 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. slay 💀✨
• 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. so like, gradual underflow? fine. otherwise? chaotic energy 😭

Definition at line 135 of file slasv2.f.

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⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code.

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That's the whole page, bestie! Footer sign-off: LAPACK Version 3.12.0 and /home/abui...RC/slasv2.f(3) — that's the source/version energy, and there's no date line up in here, so we're not inventing one 🎀💖🫶