num::GivensRotation Struct Reference

Givens plane rotation: G = [c, s; -s, c]. More...

#include <small_matrix.hpp>

Public Member Functions
constexpr void	apply (real &x, real &y) const noexcept
	Apply G from the left: [x; y] <- G * [x; y].
constexpr void	apply_t (real &x, real &y) const noexcept
	Apply G^T (inverse rotation): [x; y] <- G^T * [x; y].
constexpr SmallMatrix< 2, 2 >	as_matrix () const noexcept
	Return the 2x2 rotation matrix.

Static Public Member Functions
static constexpr GivensRotation	from (real a, real b) noexcept

Public Attributes
real	c
real	s

Detailed Description

Givens plane rotation: G = [c, s; -s, c].

Constructed so that G * [a; b]^T = [r; 0] with r = hypot(a, b).

auto g = GivensRotation::from(h_jj, h_jj1);  // zero H[j,j+1] in GMRES
g.apply(g_j, g_j1);                           // rotate RHS vector too

Definition at line 144 of file small_matrix.hpp.

Member Function Documentation

apply()

constexpr void num::GivensRotation::apply ( real &  x, real &  y  ) const

inlineconstexprnoexcept

Apply G from the left: [x; y] <- G * [x; y].

Definition at line 158 of file small_matrix.hpp.

References c, num::ipow(), and s.

apply_t()

constexpr void num::GivensRotation::apply_t ( real &  x, real &  y  ) const

inlineconstexprnoexcept

Apply G^T (inverse rotation): [x; y] <- G^T * [x; y].

Definition at line 165 of file small_matrix.hpp.

References c, num::ipow(), and s.

as_matrix()

constexpr SmallMatrix< 2, 2 > num::GivensRotation::as_matrix ( ) const

inlineconstexprnoexcept

Return the 2x2 rotation matrix.

Definition at line 172 of file small_matrix.hpp.

References c, and s.

from()

static constexpr GivensRotation num::GivensRotation::from ( real  a, real  b  )

inlinestaticconstexprnoexcept

Compute (c,s) such that G*[a;b] = [r;0], r = hypot(a,b). Stable for any (a,b) including b==0.

Definition at line 149 of file small_matrix.hpp.

References num::ipow().

Member Data Documentation

c

real num::GivensRotation::c

Definition at line 145 of file small_matrix.hpp.

Referenced by apply(), apply_t(), and as_matrix().

s

real num::GivensRotation::s

Definition at line 145 of file small_matrix.hpp.

Referenced by apply(), apply_t(), and as_matrix().

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The documentation for this struct was generated from the following file:

• /home/runner/work/numerics/numerics/include/core/small_matrix.hpp