las2(3)

💅 NAME 💅

las2 — las2: 2x2 triangular SVD. And yes bestie, this whole page is las2(3) from the Library Functions Manual — iconic LAPACK behavior, no cap 💖

✨ SYNOPSIS ✨

🌈 Functions 🌈

• subroutine dlas2 (f, g, h, ssmin, ssmax) — DLAS2 computes singular values of a 2-by-2 triangular matrix.
• subroutine slas2 (f, g, h, ssmin, ssmax) — SLAS2 computes singular values of a 2-by-2 triangular matrix.

💖 Detailed Description 💖

The original section is literally just the heading, bestie — the real main-character energy is in Function Documentation below 🫶

🔥 Function Documentation 🔥

🎀 subroutine dlas2 (double precision f, double precision g, double precision h, double precision ssmin, double precision ssmax) 🎀

DLAS2 computes singular values of a 2-by-2 triangular matrix.

✨ Purpose: ✨

!>
!> DLAS2  computes the singular values of the 2-by-2 matrix
!>    [  F   G  ]
!>    [  0   H  ].
!> On return, SSMIN is the smaller singular value and SSMAX is the
!> larger singular value.
!>

🧚 Parameters 🧚

F — the exact param tea:

!>          F is DOUBLE PRECISION
!>          The (1,1) element of the 2-by-2 matrix.
!>

G — the exact param tea:

!>          G is DOUBLE PRECISION
!>          The (1,2) element of the 2-by-2 matrix.
!>

H — the exact param tea:

!>          H is DOUBLE PRECISION
!>          The (2,2) element of the 2-by-2 matrix.
!>

SSMIN — the exact param tea:

!>          SSMIN is DOUBLE PRECISION
!>          The smaller singular value.
!>

SSMAX — the exact param tea:

!>          SSMAX is DOUBLE PRECISION
!>          The larger singular value.
!>

👑 Author 👑

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

🌟 Further Details: 🌟

!>
!>  Barring over/underflow, all output quantities are correct to within
!>  a few units in the last place (ulps), even in the absence of a guard
!>  digit in addition/subtraction.
!>
!>  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 104 of file dlas2.f.

---

🎀 subroutine slas2 (real f, real g, real h, real ssmin, real ssmax) 🎀

SLAS2 computes singular values of a 2-by-2 triangular matrix.

✨ Purpose: ✨

!>
!> SLAS2  computes the singular values of the 2-by-2 matrix
!>    [  F   G  ]
!>    [  0   H  ].
!> On return, SSMIN is the smaller singular value and SSMAX is the
!> larger singular value.
!>

🧚 Parameters 🧚

F — the exact param tea:

!>          F is REAL
!>          The (1,1) element of the 2-by-2 matrix.
!>

G — the exact param tea:

!>          G is REAL
!>          The (1,2) element of the 2-by-2 matrix.
!>

H — the exact param tea:

!>          H is REAL
!>          The (2,2) element of the 2-by-2 matrix.
!>

SSMIN — the exact param tea:

!>          SSMIN is REAL
!>          The smaller singular value.
!>

SSMAX — the exact param tea:

!>          SSMAX is REAL
!>          The larger singular value.
!>

👑 Author 👑

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

🌟 Further Details: 🌟

!>
!>  Barring over/underflow, all output quantities are correct to within
!>  a few units in the last place (ulps), even in the absence of a guard
!>  digit in addition/subtraction.
!>
!>  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 104 of file slas2.f.

🌸 Author 🌸

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okay bye bestie 💖 source/version: LAPACK, Version 3.12.0; manual: las2(3); date: literally not in the footer, so I’m not making one up — periodt 🎀