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Namespace astrea::math

Namespace List > astrea > math

Public Functions

Type Name
constexpr mp_units::quantity< mp_units::one, Rep > assoc_legendre (const unsigned int & n, const unsigned int & m, const mp_units::quantity< R, Rep > & q) noexcept
T atan3 (T y, T x)
mp_units::QuantityOf< mp_units::dimensionless > auto cosh (const mp_units::quantity< R, Rep > & q) noexcept
constexpr mp_units::quantity< mp_units::one, Rep > cyl_bessel_j (const Rep & nu, const mp_units::quantity< R, Rep > & q) noexcept
double evaluate_chebyshev_derivative (double x, double lb, double ub, const std::array< double, N > & coeff, double extrapolationTol=1.0e-6)
Evaluate the derivative of the Chebyshev polynomial at the specified value, x, which must be in the range [lb, ub], using Clenshaw's recurrence formula.
double evaluate_chebyshev_derivative (double x, const std::array< double, N > & boundsCoeff, double extrapolationTol=1.0e-6)
Evaluate the derivative of the Chebyshev polynomial at the specified value, x, which must be in the range [lb, ub], using Clenshaw's recurrence formula.
double evaluate_chebyshev_polynomial (const double & x, const double & lb, const double & ub, const std::array< double, N > & coeff, const double & coeffZeroFactor=0.5, const double & extrapolationTol=1.0e-6)
Evaluate the Chebyshev polynomial at the specified value, x, which must be in the range [lb, ub], using Clenshaw's recurrence formula.
double evaluate_chebyshev_polynomial (const double & x, const std::array< double, N > & boundsCoeff, const double & coeffZeroFactor=0.5, const double & extrapolationTol=1.0e-6)
Evaluate the Chebyshev polynomial at the specified value, x, which must be in the range [lb, ub], using Clenshaw's recurrence formula.
Y fast_interpolate (const std::array< X, 2 > & x, const std::array< Y, 2 > & y, const X & sx)
Fast linear interpolation for two points, with bounds checking.
Y interpolate (const std::vector< X > & x, const std::vector< Y > & y, const X & sx)
Linear interpolation for a single point, with bounds checking.
mp_units::quantity< R, Rep > max (const mp_units::quantity< R, Rep > & q1, const mp_units::quantity< R, Rep > & q2) noexcept
mp_units::quantity< R, Rep > min (const mp_units::quantity< R, Rep > & q1, const mp_units::quantity< R, Rep > & q2) noexcept
constexpr bool nearly_equal (const mp_units::quantity< R1, Rep > & x, const mp_units::quantity< R2, Rep > & y, const mp_units::quantity< mp_units::one, Rep > & relTol=0.0 *mp_units::one, const mp_units::quantity< mp_units::one, Rep > & absTol=0.0 *mp_units::one) noexcept
Check if two quantities of the same unit are nearly equal within a relative tolerance.
mp_units::quantity< mp_units::one, Rep > pow (const mp_units::quantity< R, Rep > & q, const mp_units::quantity< R, Rep > & n) noexcept
requires requires (Rep v)
Computes the sinc function for a given angle in radians.
mp_units::QuantityOf< mp_units::dimensionless > auto sinc (const mp_units::quantity< R, Rep > & q) noexcept
mp_units::QuantityOf< mp_units::dimensionless > auto sinh (const mp_units::quantity< R, Rep > & q) noexcept
double transform_from_chebyshev_range (const double & x, const double & lb, const double & ub)
Transform variable from the Chebyshev range of [-1, 1] to the range [lb, ub].
double transform_to_chebyshev_range (const double & x, const double & lb, const double & ub)
Transform variable from the range [lb, ub] to the Chebyshev range of [-1, 1].

Public Functions Documentation

function assoc_legendre

constexpr mp_units::quantity< mp_units::one, Rep > astrea::math::assoc_legendre (
    const unsigned int & n,
    const unsigned int & m,
    const mp_units::quantity< R, Rep > & q
) noexcept

function atan3

template<typename T>
T astrea::math::atan3 (
    T y,
    T x
)

function cosh

inline mp_units::QuantityOf< mp_units::dimensionless > auto astrea::math::cosh (
    const mp_units::quantity< R, Rep > & q
) noexcept

function cyl_bessel_j

constexpr mp_units::quantity< mp_units::one, Rep > astrea::math::cyl_bessel_j (
    const Rep & nu,
    const mp_units::quantity< R, Rep > & q
) noexcept

function evaluate_chebyshev_derivative

Evaluate the derivative of the Chebyshev polynomial at the specified value, x, which must be in the range [lb, ub], using Clenshaw's recurrence formula. 

template<size_t N>
double astrea::math::evaluate_chebyshev_derivative (
    double x,
    double lb,
    double ub,
    const std::array< double, N > & coeff,
    double extrapolationTol=1.0e-6
)

Numerical Recipes in Fortran 77: The Art of Scientific Computing, Page 189, Routine chder

Parameters:

  • x Value at which the Chebyshev polynomial is to be evaluated at
  • lb Lower bound of the function range
  • ub Upper bound of the function range
  • coeff Chebyshev coefficients evaluated using chebyshev_coefficients function
  • extrapolationTol Tolerance for the maximum distance x can be outside of [lb, ub] range before exception is thrown.

Returns:

Corresponding Chebyshev coefficient values

Template parameters:

  • N Size of the array

Exception:

  • std::invalid_argument If coeff has less than one value, or if extrapolation occurs

function evaluate_chebyshev_derivative

Evaluate the derivative of the Chebyshev polynomial at the specified value, x, which must be in the range [lb, ub], using Clenshaw's recurrence formula. 

template<size_t N>
double astrea::math::evaluate_chebyshev_derivative (
    double x,
    const std::array< double, N > & boundsCoeff,
    double extrapolationTol=1.0e-6
)

Note:

The lb, ub, and Chebyshev coefficients are stored in the same array here, which is used for planetary coefficients from CSpice

Numerical Recipes in Fortran 77: The Art of Scientific Computing, Page 189, Routine chder

Parameters:

  • x Value at which the Chebyshev polynomial is to be evaluated at
  • boundsCoeff Vector containing lb, ub, and Chebyshev coefficients evaluated using chebyshev_coefficients function
  • extrapolationTol Tolerance for the maximum distance x can be outside of [lb, ub] range before exception is thrown.

Returns:

Corresponding Chebyshev coefficient values

Template parameters:

  • N Size of the array

Exception:

  • std::invalid_argument If coeff has less than one value, or if extrapolation occurs

function evaluate_chebyshev_polynomial

Evaluate the Chebyshev polynomial at the specified value, x, which must be in the range [lb, ub], using Clenshaw's recurrence formula. 

template<std::size_t N>
double astrea::math::evaluate_chebyshev_polynomial (
    const double & x,
    const double & lb,
    const double & ub,
    const std::array< double, N > & coeff,
    const double & coeffZeroFactor=0.5,
    const double & extrapolationTol=1.0e-6
)

Numerical Recipes in Fortran 77: The Art of Scientific Computing, Page 187-188, Routine chebev

Parameters:

  • x Value at which the Chebyshev polynomial is to be evaluated at
  • lb Lower bound of the function range
  • ub Upper bound of the function range
  • coeff Chebyshev coefficients evaluated using chebyshev_coefficients function
  • coeffZeroFactor Factor to multiply coeff[0] by. Numerical Recipes has this at 0.5, but for CSpice the coeff[0] has already been multiplied by 0.5, so set factor to 1.0
  • extrapolationTol Tolerance for the maximum distance x can be outside of [lb, ub] range before exception is thrown.

Returns:

Corresponding Chebyshev coefficient values

Template parameters:

  • N Size of the array

Exception:

  • std::invalid_argument If coeff has less than one value, or if extrapolation occurs

function evaluate_chebyshev_polynomial

Evaluate the Chebyshev polynomial at the specified value, x, which must be in the range [lb, ub], using Clenshaw's recurrence formula. 

template<std::size_t N>
double astrea::math::evaluate_chebyshev_polynomial (
    const double & x,
    const std::array< double, N > & boundsCoeff,
    const double & coeffZeroFactor=0.5,
    const double & extrapolationTol=1.0e-6
)

Note:

The lb, ub, and Chebyshev coefficients are stored in the same array here, which is used for planetary coefficients from CSpice

Numerical Recipes in Fortran 77: The Art of Scientific Computing, Page 187-188, Routine chebev

Parameters:

  • x Value at which the Chebyshev polynomial is to be evaluated at
  • boundsCoeff Array containing lb, ub, and Chebyshev coefficients evaluated using chebyshev_coefficients function
  • coeffZeroFactor Factor to multiply coeff[0] by. Numerical Recipes has this at 0.5, but for CSpice the coeff[0] has already been multiplied by 0.5, so set factor to 1.0
  • extrapolationTol Tolerance for the maximum distance x can be outside of [lb, ub] range before exception is thrown.

Returns:

Corresponding Chebyshev coefficient values

Template parameters:

  • N Size of the array

Exception:

  • std::invalid_argument If coeff has less than one value, or if extrapolation occurs

function fast_interpolate

Fast linear interpolation for two points, with bounds checking. 

template<typename X, typename Y>
inline Y astrea::math::fast_interpolate (
    const std::array< X, 2 > & x,
    const std::array< Y, 2 > & y,
    const X & sx
)

Template parameters:

  • X Type of the x values (e.g. time).
  • Y Type of the y values (e.g. distance, angle). Must support arithmetic operations.

Parameters:

  • x Two x values corresponding to the y values. Must be in ascending order.
  • y Two y values corresponding to the x values.
  • sx The x value to interpolate at. Must be between x[0] and x[1].

Returns:

Y The interpolated y value at sx.

Exception:

  • std::runtime_error if sx is outside the bounds of x.

function interpolate

Linear interpolation for a single point, with bounds checking. 

template<typename X, typename Y>
inline Y astrea::math::interpolate (
    const std::vector< X > & x,
    const std::vector< Y > & y,
    const X & sx
)

Template parameters:

  • X Type of the x values (e.g. time).
  • Y Type of the y values (e.g. distance, angle). Must support arithmetic operations.

Parameters:

  • x Vector of x values corresponding to the y values. Must be in ascending order.
  • y Vector of y values corresponding to the x values.
  • sx The x value to interpolate at. Must be between x[0] and x.back().

Returns:

Y The interpolated y value at sx.

Exception:

  • std::runtime_error if sx is outside the bounds of x.

function max

inline mp_units::quantity< R, Rep > astrea::math::max (
    const mp_units::quantity< R, Rep > & q1,
    const mp_units::quantity< R, Rep > & q2
) noexcept

function min

inline mp_units::quantity< R, Rep > astrea::math::min (
    const mp_units::quantity< R, Rep > & q1,
    const mp_units::quantity< R, Rep > & q2
) noexcept

function nearly_equal

Check if two quantities of the same unit are nearly equal within a relative tolerance. 

template<auto R1, auto R2, typename Rep>
constexpr bool astrea::math::nearly_equal (
    const mp_units::quantity< R1, Rep > & x,
    const mp_units::quantity< R2, Rep > & y,
    const mp_units::quantity< mp_units::one, Rep > & relTol=0.0 *mp_units::one,
    const mp_units::quantity< mp_units::one, Rep > & absTol=0.0 *mp_units::one
) noexcept

Template parameters:

  • R The unit type (e.g., distance, time).
  • Rep The representation type (e.g., double).

Parameters:

  • x First quantity to compare.
  • y Second quantity to compare.
  • relTol Relative tolerance for comparison.

Returns:

true if the two quantities are nearly equal within the specified tolerance.

Returns:

false if they are not nearly equal.

function pow

inline mp_units::quantity< mp_units::one, Rep > astrea::math::pow (
    const mp_units::quantity< R, Rep > & q,
    const mp_units::quantity< R, Rep > & n
) noexcept

function requires

Computes the sinc function for a given angle in radians. 

template<auto R, typename Rep>
requires astrea::math::requires (
    Rep v
)

Computes the associated Legendre function of the first kind.

Computes the Bessel function of the first kind of order zero.

Computes the hyperbolic sine of a given angle in radians.

Computes the hyperbolic cosine of a given angle in radians.

The sinc function is defined as sin(x)/x, where x is in radians. This function handles both integral and floating-point types.

Template parameters:

  • R The reference type for the angle (e.g., radian).
  • Rep The representation type (e.g., double, float).

Parameters:

  • q The angle in radians.

Returns:

The value of the sinc function at the given angle.

Template parameters:

  • R The reference type for the angle (e.g., radian).
  • Rep The representation type (e.g., double, float).

Parameters:

  • q The angle in radians.

Returns:

The value of the hyperbolic cosine at the given angle.

Template parameters:

  • R The reference type for the angle (e.g., radian).
  • Rep The representation type (e.g., double, float).

Parameters:

  • q The angle in radians.

Returns:

The value of the hyperbolic sine at the given angle.

This function computes the Bessel function of the first kind of order zero for a given value. It is defined as J_0(x) = (1/π) ∫_0^π cos(x sin(θ)) dθ.

Template parameters:

  • R The reference type for the input value (e.g., dimensionless).
  • Rep The representation type (e.g., double, float).

Parameters:

  • q The input value.

Returns:

The value of the Bessel function of the first kind of order zero at the given input.

This function computes the associated Legendre function P_n^m(x) for given n, m, and x. It is defined as P_n^m(x) = (1/2^n n!) (d/dx)^n ((1 - x^2)^n) P_m^n(x).

Template parameters:

  • R The reference type for the input value (e.g., dimensionless).
  • Rep The representation type (e.g., double, float).

Parameters:

  • n The degree of the polynomial.
  • m The order of the polynomial.
  • q The input value.

Returns:

The value of the associated Legendre function at the given input.

function sinc

inline mp_units::QuantityOf< mp_units::dimensionless > auto astrea::math::sinc (
    const mp_units::quantity< R, Rep > & q
) noexcept

function sinh

inline mp_units::QuantityOf< mp_units::dimensionless > auto astrea::math::sinh (
    const mp_units::quantity< R, Rep > & q
) noexcept

function transform_from_chebyshev_range

Transform variable from the Chebyshev range of [-1, 1] to the range [lb, ub]. 

double astrea::math::transform_from_chebyshev_range (
    const double & x,
    const double & lb,
    const double & ub
)

Numerical Recipes in Fortran 77: The Art of Scientific Computing, Page 186, Eq. 5.8.10

Parameters:

  • x Variable in the Chebyshev range
  • lb Lower bound of the function range
  • ub Upper bound of the function range

Returns:

Variable in the range [lb, ub]

function transform_to_chebyshev_range

Transform variable from the range [lb, ub] to the Chebyshev range of [-1, 1]. 

double astrea::math::transform_to_chebyshev_range (
    const double & x,
    const double & lb,
    const double & ub
)

Numerical Recipes in Fortran 77: The Art of Scientific Computing, Page 186, Eq. 5.8.10

Parameters:

  • x Variable in the range [lb, ub]
  • lb Lower bound of the function range
  • ub Upper bound of the function range

Returns:

Variable in the Chebyshev range [-1, 1]

The documentation for this class was generated from the following file astrea/math/math/chebyshev_util.cpp