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