Symmetries Namespace Reference

Functions
template<unsigned int N, typename T>
DEAL_II_ALWAYS_INLINE T	cos_arctan (const T &x) noexcept
	Compute cos(N * arctan(x)).
template<unsigned int N, typename T>
DEAL_II_ALWAYS_INLINE T	sin_arctan (const T &x) noexcept
	Compute sin(N * arctan(x)).
template<unsigned int N, typename T>
DEAL_II_ALWAYS_INLINE T	cos_theta (const T &nx, const T &ny) noexcept
	Compute cos(N * theta) where theta = arctan(ny/nx).
template<unsigned int N, typename T>
DEAL_II_ALWAYS_INLINE T	sin_theta (const T &nx, const T &ny) noexcept
	Compute sin(N * theta) where theta = arctan(ny/nx).
template<unsigned int N, typename T>
DEAL_II_ALWAYS_INLINE T	cos_psi (const T &nx, const T &ny, const T &nz) noexcept
	Compute cos(N * psi) where theta = arctan(sqrt(nx^2+ny^2)/ny).
template<unsigned int N, typename T>
DEAL_II_ALWAYS_INLINE T	sin_psi (const T &nx, const T &ny, const T &nz) noexcept
	Compute sin(N * psi) where theta = arctan(sqrt(nx^2+ny^2)/ny).

Function Documentation

cos_arctan()

template<unsigned int N, typename T>

DEAL_II_ALWAYS_INLINE T Symmetries::cos_arctan ( const T & x )

inlinenodiscardnoexcept

Compute cos(N * arctan(x)).

This function provides an efficient way to calculate symmetries like $cos(N arctan(\theta))$, where N is a known number at compile time.

Importantly, it doesn't always make sense to unroll the function with a Chebyshev polynomial due to the crossover point in multiplication operations and using the math library. We've found this to occur at N = 3, although your mileage will vary based on your architecture. TODO: Benchmark this better

cos_psi()

template<unsigned int N, typename T>

DEAL_II_ALWAYS_INLINE T Symmetries::cos_psi ( const T & nx, const T & ny, const T & nz )

inlinenodiscardnoexcept

Compute cos(N * psi) where theta = arctan(sqrt(nx^2+ny^2)/ny).

This function provides an efficient way to calculate symmetries like $cos(N arctan(\sqrt{n_x^2+n_y^2}/n_z))$, where N is a known number at compile time.

Importantly, it doesn't always make sense to unroll the function with a Chebyshev polynomial due to the crossover point in multiplication operations and using the math library. We've found this to occur at N = 5, although your mileage will vary based on your architecture. TODO: Benchmark this better

cos_theta()

template<unsigned int N, typename T>

DEAL_II_ALWAYS_INLINE T Symmetries::cos_theta ( const T & nx, const T & ny )

inlinenodiscardnoexcept

Compute cos(N * theta) where theta = arctan(ny/nx).

This function provides an efficient way to calculate symmetries like $cos(N arctan(n_y/n_x))$, where N is a known number at compile time.

Importantly, it doesn't always make sense to unroll the function with a Chebyshev polynomial due to the crossover point in multiplication operations and using the math library. We've found this to occur at N = 5, although your mileage will vary based on your architecture. TODO: Benchmark this better

sin_arctan()

template<unsigned int N, typename T>

DEAL_II_ALWAYS_INLINE T Symmetries::sin_arctan ( const T & x )

inlinenodiscardnoexcept

Compute sin(N * arctan(x)).

This function provides an efficient way to calculate symmetries like $sin(N arctan(\theta))$, where N is a known number at compile time.

Importantly, it doesn't always make sense to unroll the function with a Chebyshev polynomial due to the crossover point in multiplication operations and using the math library. We've found this to occur at N = 3, although your mileage will vary based on your architecture. TODO: Benchmark this better

sin_psi()

template<unsigned int N, typename T>

DEAL_II_ALWAYS_INLINE T Symmetries::sin_psi ( const T & nx, const T & ny, const T & nz )

inlinenodiscardnoexcept

Compute sin(N * psi) where theta = arctan(sqrt(nx^2+ny^2)/ny).

This function provides an efficient way to calculate symmetries like $sin(N arctan(\sqrt{n_x^2+n_y^2}/n_z))$, where N is a known number at compile time.

Importantly, it doesn't always make sense to unroll the function with a Chebyshev polynomial due to the crossover point in multiplication operations and using the math library. We've found this to occur at N = 5, although your mileage will vary based on your architecture. TODO: Benchmark this better

sin_theta()

template<unsigned int N, typename T>

DEAL_II_ALWAYS_INLINE T Symmetries::sin_theta ( const T & nx, const T & ny )

inlinenodiscardnoexcept

Compute sin(N * theta) where theta = arctan(ny/nx).

This function provides an efficient way to calculate symmetries like $sin(N arctan(n_y/n_x))$, where N is a known number at compile time.

Importantly, it doesn't always make sense to unroll the function with a Chebyshev polynomial due to the crossover point in multiplication operations and using the math library. We've found this to occur at N = 5, although your mileage will vary based on your architecture. TODO: Benchmark this better