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231 lines
10 KiB
C++
231 lines
10 KiB
C++
//! \file math_functions.h
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//! A collection of elementary math functions.
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#ifndef OPENMC_MATH_FUNCTIONS_H
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#define OPENMC_MATH_FUNCTIONS_H
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#include <cmath>
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#include <cstdlib>
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#include "openmc/constants.h"
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#include "openmc/position.h"
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#include "openmc/random_lcg.h"
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namespace openmc {
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//==============================================================================
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//! Calculate the percentile of the standard normal distribution with a
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//! specified probability level.
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//!
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//! @param p The probability level
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//! @return The requested percentile
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//==============================================================================
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extern "C" double normal_percentile(double p);
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//==============================================================================
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//! Calculate the percentile of the Student's t distribution with a specified
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//! probability level and number of degrees of freedom.
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//!
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//! @param p The probability level
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//! @param df The degrees of freedom
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//! @return The requested percentile
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//==============================================================================
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extern "C" double t_percentile_c(double p, int df);
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//==============================================================================
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//! Calculate the n-th order Legendre polynomials at the value of x.
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//!
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//! @param n The maximum order requested
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//! @param x The value to evaluate at; x is expected to be within [-1,1]
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//! @param pnx The requested Legendre polynomials of order 0 to n (inclusive)
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//! evaluated at x.
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//==============================================================================
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extern "C" void calc_pn_c(int n, double x, double pnx[]);
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//==============================================================================
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//! Find the value of f(x) given a set of Legendre coefficients and the value
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//! of x.
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//!
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//! @param n The maximum order of the expansion
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//! @param data The polynomial expansion coefficient data; without the (2l+1)/2
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//! factor.
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//! @param x The value to evaluate at; x is expected to be within [-1,1]
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//! @return The requested Legendre polynomials of order 0 to n (inclusive)
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//! evaluated at x
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//==============================================================================
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extern "C" double evaluate_legendre(int n, const double data[], double x);
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//==============================================================================
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//! Calculate the n-th order real spherical harmonics for a given angle (in
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//! terms of (u,v,w)) for all 0<=n and -m<=n<=n.
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//!
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//! @param n The maximum order requested
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//! @param uvw[3] The direction the harmonics are requested at
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//! @param rn The requested harmonics of order 0 to n (inclusive)
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//! evaluated at uvw.
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//==============================================================================
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extern "C" void calc_rn_c(int n, const double uvw[3], double rn[]);
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//==============================================================================
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//! Calculate the n-th order modified Zernike polynomial moment for a given
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//! angle (rho, theta) location on the unit disk.
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//!
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//! This procedure uses the modified Kintner's method for calculating Zernike
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//! polynomials as outlined in Chong, C. W., Raveendran, P., & Mukundan,
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//! R. (2003). A comparative analysis of algorithms for fast computation of
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//! Zernike moments. Pattern Recognition, 36(3), 731-742.
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//! The normalization of the polynomials is such that the integral of Z_pq^2
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//! over the unit disk is exactly pi.
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//!
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//! @param n The maximum order requested
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//! @param rho The radial parameter to specify location on the unit disk
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//! @param phi The angle parameter to specify location on the unit disk
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//! @param zn The requested moments of order 0 to n (inclusive)
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//! evaluated at rho and phi.
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//==============================================================================
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extern "C" void calc_zn(int n, double rho, double phi, double zn[]);
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//==============================================================================
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//! Calculate only the even radial components of n-th order modified Zernike
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//! polynomial moment with azimuthal dependency m = 0 for a given angle
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//! (rho, theta) location on the unit disk.
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//!
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//! Since m = 0, n could only be even orders. Z_q0 = R_q0
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//!
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//! This procedure uses the modified Kintner's method for calculating Zernike
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//! polynomials as outlined in Chong, C. W., Raveendran, P., & Mukundan,
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//! R. (2003). A comparative analysis of algorithms for fast computation of
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//! Zernike moments. Pattern Recognition, 36(3), 731-742.
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//! The normalization of the polynomials is such that the integral of Z_pq^2
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//! over the unit disk is exactly pi.
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//!
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//! @param n The maximum order requested
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//! @param rho The radial parameter to specify location on the unit disk
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//! @param phi The angle parameter to specify location on the unit disk
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//! @param zn_rad The requested moments of order 0 to n (inclusive)
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//! evaluated at rho and phi when m = 0.
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//==============================================================================
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extern "C" void calc_zn_rad(int n, double rho, double zn_rad[]);
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//==============================================================================
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//! Rotate the direction cosines through a polar angle whose cosine is mu and
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//! through an azimuthal angle sampled uniformly.
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//!
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//! This is done with direct sampling rather than rejection sampling as is done
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//! in MCNP and Serpent.
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//!
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//! @param uvw[3] The initial, and final, direction vector
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//! @param mu The cosine of angle in lab or CM
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//! @param phi The azimuthal angle; will randomly chosen angle if a nullptr
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//! is passed
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//==============================================================================
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extern "C" void rotate_angle_c(double uvw[3], double mu, double* phi);
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Direction rotate_angle(Direction u, double mu, double* phi);
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//==============================================================================
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//! Samples an energy from the Maxwell fission distribution based on a direct
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//! sampling scheme.
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//!
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//! The probability distribution function for a Maxwellian is given as
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//! p(x) = 2/(T*sqrt(pi))*sqrt(x/T)*exp(-x/T). This PDF can be sampled using
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//! rule C64 in the Monte Carlo Sampler LA-9721-MS.
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//!
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//! @param T The tabulated function of the incoming energy
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//! @result The sampled outgoing energy
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//==============================================================================
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extern "C" double maxwell_spectrum(double T);
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//==============================================================================
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//! Samples an energy from a Watt energy-dependent fission distribution.
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//!
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//! Although fitted parameters exist for many nuclides, generally the
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//! continuous tabular distributions (LAW 4) should be used in lieu of the Watt
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//! spectrum. This direct sampling scheme is an unpublished scheme based on the
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//! original Watt spectrum derivation (See F. Brown's MC lectures).
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//!
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//! @param a Watt parameter a
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//! @param b Watt parameter b
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//! @result The sampled outgoing energy
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//==============================================================================
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extern "C" double watt_spectrum(double a, double b);
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//==============================================================================
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//! Doppler broadens the windowed multipole curvefit.
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//!
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//! The curvefit is a polynomial of the form a/E + b/sqrt(E) + c + d sqrt(E)...
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//!
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//! @param E The energy to evaluate the broadening at
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//! @param dopp sqrt(atomic weight ratio / kT) with kT given in eV
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//! @param n The number of components to the polynomial
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//! @param factors The output leading coefficient
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//==============================================================================
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extern "C" void broaden_wmp_polynomials_c(double E, double dopp, int n,
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double factors[]);
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//==============================================================================
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//! Constructs a natural cubic spline.
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//!
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//! Given a tabulated function y_i = f(x_i), this computes the second
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//! derivative of the interpolating function at each x_i, which can then be
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//! used in any subsequent calls to spline_interpolate or spline_integrate for
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//! the same set of x and y values.
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//!
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//! @param n Number of points
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//! @param x Values of the independent variable, which must be strictly
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//! increasing.
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//! @param y Values of the dependent variable.
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//! @param[out] z The second derivative of the interpolating function at each
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//! value of x.
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//==============================================================================
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extern "C" void spline_c(int n, const double x[], const double y[], double z[]);
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//==============================================================================
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//! Determine the cubic spline interpolated y-value for a given x-value.
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//!
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//! @param n Number of points
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//! @param x Values of the independent variable, which must be strictly
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//! increasing.
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//! @param y Values of the dependent variable.
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//! @param z The second derivative of the interpolating function at each
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//! value of x.
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//! @param xint Point at which to evaluate the cubic spline polynomial
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//! @result Interpolated value
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//==============================================================================
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extern "C" double spline_interpolate_c(int n, const double x[], const double y[],
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const double z[], double xint);
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//==============================================================================
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//! Evaluate the definite integral of the interpolating cubic spline between
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//! the given endpoints.
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//!
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//! @param n Number of points
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//! @param x Values of the independent variable, which must be strictly
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//! increasing.
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//! @param y Values of the dependent variable.
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//! @param z The second derivative of the interpolating function at each
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//! value of x.
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//! @param xa Lower limit of integration
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//! @param xb Upper limit of integration
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//! @result Integral
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//==============================================================================
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extern "C" double spline_integrate_c(int n, const double x[], const double y[],
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const double z[], double xa, double xb);
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} // namespace openmc
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#endif // OPENMC_MATH_FUNCTIONS_H
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