Class WKBSolver¶

Defined in File wkbsolver.hpp

Inheritance Relationships¶

Derived Types¶

public WKBSolver1 (Class WKBSolver1)
public WKBSolver2 (Class WKBSolver2)
public WKBSolver3 (Class WKBSolver3)

Class Documentation¶

class WKBSolver¶

Class to carry out WKB steps of varying orders.

Subclassed by WKBSolver1, WKBSolver2, WKBSolver3

Public Functions

WKBSolver()¶

WKBSolver(de_system &de_sys, int order)¶

Eigen::Matrix<std::complex<double>, 3, 2> step(std::complex<double> x0, std::complex<double> dx0, double t0, double h0, const Eigen::Matrix<std::complex<double>, 6, 1> &ws, const Eigen::Matrix<std::complex<double>, 6, 1> &gs, const Eigen::Matrix<std::complex<double>, 5, 1> &ws5, const Eigen::Matrix<std::complex<double>, 5, 1> &gs5)¶

Computes a WKB step of a given order and returns the solution and its local error estimate.

Parameters

x0[in] – value of the solution \(x(t)\) at the start of the step
dx0[in] – value of the derivative of the solution \(\frac{dx}{dt}\) at the start of the step
t0[in] – value of independent variable (time) at the start of the step
h0[in] – size of the step (solution will be given at t+t0)
ws[in] – vector of 6 evaulations of the frequency term at the Gauss-Lobatto nodes, this is necessary for Gauss-Lobatto integration, which in turn is needed to calculate the WKB series
gs[in] – vector of 6 evaluations of the friction term
ws5[in] – vector of 5 evaluations of the friction term at the nodes of 5th order Gauss-Lobatto quadrature, this is needed to compute the error on Gauss-Lobatto quadrature, and in turn the WKB series
gs5[in] – vector of 5 evaluations of the friction term

Returns

a matrix, whose rows are:

\( x, \dot{x}\) at t0+h0 as an nth order WKB estimate
\( \Delta_{\mathrm{trunc}}x, \Delta_{\mathrm{trunc}}\dot{x}\) at t0+h0, defined as the difference between an nth and (n-1)th order WKB estimate
\( \Delta_{\mathrm{int}}x, \Delta_{\mathrm{int}}\dot{x}\) at t0+h0, defined as the local error coming from those terms in the WKB series that involved numerical integrals

void dense_step(double t0, const std::list<double> &dots, std::list<std::complex<double>> &doxs, std::list<std::complex<double>> &dodxs)¶

Computes dense output at a set of timepoints within a step.

Parameters

t0[in] – value of independent variable (time) at the start of the step
dots[in] – sequence of timepoints at which dense output is to be generated
doxs[in, out] – dense output for the solution \(x(t)\)
dodxs[in, out] – dense output for the derivative of the solution \(\dot{x}\)

Eigen::Matrix<double, 6, 1> dense_weights_6(double t)¶

Eigen::Matrix<double, 6, 1> dense_weights_derivs_6(double t)¶

std::complex<double> dense_integrate(const Eigen::Matrix<double, 6, 1> &denseweights6, const Eigen::Matrix<std::complex<double>, 6, 1> &integrand6)¶

std::complex<double> dense_interpolate(const Eigen::Matrix<double, 6, 1> &denseweights6, const Eigen::Matrix<std::complex<double>, 6, 1> &integrand6)¶

Public Members

Eigen::Matrix<std::complex<double>, 7, 1> x_vdm¶

Protected Functions

void d1w1()¶

void d1w2()¶

void d1w3()¶

void d1w4()¶

void d1w5()¶

void d1w6()¶

void d2w1()¶

void d2w2()¶

void d2w3()¶

void d2w4()¶

void d2w5()¶

void d2w6()¶

void d3w1()¶

void d3w2()¶

void d3w3()¶

void d3w4()¶

void d3w5()¶

void d3w6()¶

void d4w1()¶

void d1g1()¶

void d1g2()¶

void d1g3()¶

void d1g4()¶

void d1g5()¶

void d1g6()¶

void d2g1()¶

void d2g2()¶

void d2g3()¶

void d2g4()¶

void d2g5()¶

void d2g6()¶

void d3g1()¶

void d1w2_5()¶

void d1w3_5()¶

void d1w4_5()¶

virtual void dds()¶

virtual void dsi()¶

virtual void dsf()¶

virtual void s()¶

void fp()¶

void fm()¶

void dfpi()¶

void dfmi()¶

void dfpf()¶

void dfmf()¶

void ddfp()¶

void ddfm()¶

void ap()¶

void am()¶

void bp()¶

void bm()¶

Eigen::Matrix<std::complex<double>, 2, 1> integrate(const Eigen::Matrix<std::complex<double>, 6, 1> &integrand6, const Eigen::Matrix<std::complex<double>, 5, 1> &integrand5)¶

Protected Attributes

Eigen::Matrix<double, 6, 1> glws6¶

Eigen::Matrix<double, 5, 1> glws5¶

Eigen::Matrix<double, 7, 1> d4w1_w¶

Eigen::Matrix<double, 6, 1> d1w1_w¶

Eigen::Matrix<double, 6, 1> d1w2_w¶

Eigen::Matrix<double, 6, 1> d1w3_w¶

Eigen::Matrix<double, 6, 1> d1w4_w¶

Eigen::Matrix<double, 6, 1> d1w5_w¶

Eigen::Matrix<double, 6, 1> d1w6_w¶

Eigen::Matrix<double, 6, 1> d2w1_w¶

Eigen::Matrix<double, 6, 1> d2w2_w¶

Eigen::Matrix<double, 6, 1> d2w3_w¶

Eigen::Matrix<double, 6, 1> d2w4_w¶

Eigen::Matrix<double, 6, 1> d2w5_w¶

Eigen::Matrix<double, 6, 1> d2w6_w¶

Eigen::Matrix<double, 6, 1> d3w1_w¶

Eigen::Matrix<double, 6, 1> d3w2_w¶

Eigen::Matrix<double, 6, 1> d3w3_w¶

Eigen::Matrix<double, 6, 1> d3w4_w¶

Eigen::Matrix<double, 6, 1> d3w5_w¶

Eigen::Matrix<double, 6, 1> d3w6_w¶

Eigen::Matrix<double, 6, 1> d1g1_w¶

Eigen::Matrix<double, 6, 1> d1g6_w¶

Eigen::Matrix<double, 6, 1> d2g1_w¶

Eigen::Matrix<double, 6, 1> d2g6_w¶

Eigen::Matrix<double, 6, 1> d3g1_w¶

Eigen::Matrix<double, 5, 1> d1w2_5_w¶

Eigen::Matrix<double, 5, 1> d1w3_5_w¶

Eigen::Matrix<double, 5, 1> d1w4_5_w¶

Eigen::Matrix<std::complex<double>, 7, 1> ws7_¶

Eigen::Matrix<std::complex<double>, 6, 1> ws_¶

Eigen::Matrix<std::complex<double>, 6, 1> gs_¶

Eigen::Matrix<std::complex<double>, 5, 1> ws5_¶

Eigen::Matrix<std::complex<double>, 5, 1> gs5_¶

std::complex<double> d1w1_¶

std::complex<double> d1w2_¶

std::complex<double> d1w3_¶

std::complex<double> d1w4_¶

std::complex<double> d1w5_¶

std::complex<double> d1w6_¶

std::complex<double> d2w1_¶

std::complex<double> d2w2_¶

std::complex<double> d2w3_¶

std::complex<double> d2w4_¶

std::complex<double> d2w5_¶

std::complex<double> d2w6_¶

std::complex<double> d3w1_¶

std::complex<double> d3w2_¶

std::complex<double> d3w3_¶

std::complex<double> d3w4_¶

std::complex<double> d3w5_¶

std::complex<double> d3w6_¶

std::complex<double> d4w1_¶

std::complex<double> d1g1_¶

std::complex<double> d1g2_¶

std::complex<double> d1g3_¶

std::complex<double> d1g4_¶

std::complex<double> d1g5_¶

std::complex<double> d1g6_¶

std::complex<double> d2g1_¶

std::complex<double> d2g2_¶

std::complex<double> d2g3_¶

std::complex<double> d2g4_¶

std::complex<double> d2g5_¶

std::complex<double> d2g6_¶

std::complex<double> d3g1_¶

std::complex<double> d1w2_5_¶

std::complex<double> d1w3_5_¶

std::complex<double> d1w4_5_¶

Eigen::Matrix<std::complex<double>, 6, 1> dws_¶

Eigen::Matrix<std::complex<double>, 6, 1> dgs_¶

Eigen::Matrix<std::complex<double>, 6, 1> d2ws_¶

Eigen::Matrix<std::complex<double>, 6, 1> d2gs_¶

Eigen::Matrix<std::complex<double>, 6, 1> d3ws_¶

Eigen::Matrix<std::complex<double>, 5, 1> dws5_¶

Eigen::Matrix<std::complex<double>, 1, 4> dds_¶

Eigen::Matrix<std::complex<double>, 1, 4> dsi_¶

Eigen::Matrix<std::complex<double>, 1, 4> dsf_¶

Eigen::Matrix<std::complex<double>, 1, 4> s_¶

Eigen::Matrix<std::complex<double>, 1, 4> s_error¶

std::complex<double> fp_¶

std::complex<double> fm_¶

std::complex<double> dfpi_¶

std::complex<double> dfmi_¶

std::complex<double> dfpf_¶

std::complex<double> dfmf_¶

std::complex<double> ddfp_¶

std::complex<double> ddfm_¶

std::complex<double> ap_¶

std::complex<double> am_¶

std::complex<double> bp_¶

std::complex<double> bm_¶

double h¶

std::complex<double> x¶

std::complex<double> dx¶

std::complex<double> ddx¶

int order_¶

std::complex<double> err_fp¶

std::complex<double> err_fm¶

std::complex<double> err_dfp¶

std::complex<double> err_dfm¶

std::list<std::complex<double>> doxs¶

std::list<std::complex<double>> dodxs¶

std::list<std::complex<double>> dows¶

Eigen::Matrix<std::complex<double>, 1, 4> dense_s_¶

Eigen::Matrix<std::complex<double>, 1, 4> dense_ds_¶

Eigen::Matrix<std::complex<double>, 1, 4> dense_ds_i¶

std::complex<double> dense_ap_¶

std::complex<double> dense_am_¶

std::complex<double> dense_bp_¶

std::complex<double> dense_bm_¶

Eigen::Matrix<double, 6, 6> integ_vandermonde¶

Eigen::Matrix<double, 6, 6> interp_vandermonde¶