{
    "cells": [
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "## Tutorial: Fast self-forced trajectories"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "An essential component of the FastEMRIWaveforms (FEW) framework is the rapid evaluation of the inspiral trajectory of the secondary compact object. FEW provides the tools required for users to generate and visualiase these trajectories. Users can also implement their own trajectory models to incorporate additional physics (such as environmental effects or modifications to gravity). We will demonstrate these capabilities in this tutorial."
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### ODE classes"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "#### Parameter conventions"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "FEW constructs trajectories by integrating the equations of motion of the compact binary; these are a system of ordinary differential equations (ODEs) that describe the evolution of the following parameters:\n",
                "\n",
                "| Parameter    | Definition |\n",
                "| :--------: | ------- |\n",
                "| $p$  | (Dimensionless) semi-latus rectum|\n",
                "| $e$ | Eccentricity |\n",
                "| $x_I$    | Cosine of the inclination of the orbital plane|\n",
                "| $\\Phi_\\phi$    | Azimuthal GW phase |\n",
                "| $\\Phi_\\theta$    | Polar GW phase|\n",
                "| $\\Phi_r$    | Radial GW phase|\n",
                "\n",
                "The ODE system can be integrated efficiently with adaptive Runge-Kutta techniques. These solvers obtain trajectories by integrating the right-hand side (RHS) of the ODE with respect to a time parameter."
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "#### Stock trajectory models\n",
                "\n",
                "In order to handle the necessary information for evaluating the RHS of the ODE, FEW defines ODE classes. The following stock options are available:\n",
                "\n",
                "| Model    | Features |  Notes |\n",
                "| :--------: | ------- | ------- |\n",
                "| KerrEqEccFlux | Adiabatic; equatorial eccentric inspiral with spinning primary| Our most up-to-date model |\n",
                "| SchwarzEccFlux  | Adiabatic; inspiral with non-spinning primary | An older model (currently outdated) |\n",
                "| PN5    | Post-Newtonian; eccentric inclined inspirals with spinning primary | Most complete model, but inaccurate for larger $e$ and/or lower $p$|\n"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "#### Obtaining the right-hand side of the trajectory ODE"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "As an example, let's examine the SchwarzEccFlux model:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 1,
            "metadata": {},
            "outputs": [],
            "source": [
                "from few.trajectory.ode import SchwarzEccFlux\n",
                "\n",
                "rhs = SchwarzEccFlux()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Before evaluating the RHS, we must first define the parameters of the system that remain fixed during an inspiral. At adiabatic order, these are the component masses ($M$ and $\\mu$) and the dimensionless spin parameter of the primary ($a$):"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 2,
            "metadata": {},
            "outputs": [],
            "source": [
                "M = 1e6  # Solar masses\n",
                "mu = 1e1  # Solar masses\n",
                "a = 0.0  # For a Schwarzschild inspiral, the spin parameter is zero\n",
                "\n",
                "rhs.add_fixed_parameters(M, mu, a)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "We can then access the ODE derivatives:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 3,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "(-0.017771723696175704,\n",
                            " -0.000779281500397855,\n",
                            " 0.0,\n",
                            " 0.028647063536752972,\n",
                            " 0.028647063536752972,\n",
                            " 0.018040932375307846)"
                        ]
                    },
                    "execution_count": 3,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "p = 10.0\n",
                "e = 0.3\n",
                "x = 1.0  # Schwarzschild inspiral is equatorial by definition\n",
                "\n",
                "pdot, edot, xIdot, Omega_phi, Omega_theta, Omega_r = rhs([p, e, x])\n",
                "pdot, edot, xIdot, Omega_phi, Omega_theta, Omega_r"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "FEW integrates trajectories on the radiation-reaction timescale $t_\\mathrm{rr} = t \\epsilon$, where $\\epsilon = \\mu / M$ is the mass ratio of the system. The RHS of the ODE is therefore defined such that the $(\\dot{p}, \\dot{e}, \\dot{x}_I)$ are scaled by $\\epsilon^{-1}$. We can easily undo this rescaling if required:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 4,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "(-1.7771723696175706e-07,\n",
                            " -7.792815003978551e-09,\n",
                            " 0.0,\n",
                            " 0.028647063536752972,\n",
                            " 0.028647063536752972,\n",
                            " 0.018040932375307846)"
                        ]
                    },
                    "execution_count": 4,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "pdot, edot, xIdot, Omega_phi, Omega_theta, Omega_r = rhs([p, e, x], scale_by_eps=True)\n",
                "pdot, edot, xIdot, Omega_phi, Omega_theta, Omega_r"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "#### Checking the properties of an ODE system"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "The ODE class also defines a number of properties that describe the physical and systematic assumptions of the model:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 5,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "{'convert_Y': False,\n",
                            " 'equatorial': True,\n",
                            " 'circular': False,\n",
                            " 'supports_ELQ': True,\n",
                            " 'background': 'Schwarzschild',\n",
                            " 'separatrix_buffer_dist': 0.1,\n",
                            " 'nparams': 6,\n",
                            " 'flux_output_convention': 'ELQ'}"
                        ]
                    },
                    "execution_count": 5,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "from few.trajectory.ode.base import get_ode_properties\n",
                "\n",
                "get_ode_properties(rhs)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Trajectory evaluation"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "#### The EMRIInspiral class"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Trajectories are evaluated using the `EMRIInspiral` class, which interfaces with the underlying integrator classes and methods in order to integrate the trajectory from its initial conditions until either the maximum alloted duration elapses or pre-determined stopping conditions are satisfied.\n",
                "\n",
                "The `EMRIInspiral` class offers a number of features that can be adjusted according to the desired output. We will demonstrate these below, working with the `KerrEccEqFlux` trajectory model as an example."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 6,
            "metadata": {},
            "outputs": [],
            "source": [
                "from few.trajectory.inspiral import EMRIInspiral\n",
                "from few.trajectory.ode import KerrEccEqFlux"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 7,
            "metadata": {},
            "outputs": [],
            "source": [
                "# You can also instantiate this as EMRIInspiral(func=\"KerrEccEqFlux\") to save an import.\n",
                "traj_model = EMRIInspiral(func=KerrEccEqFlux)"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 8,
            "metadata": {},
            "outputs": [],
            "source": [
                "M = 1e6\n",
                "mu = 1e2\n",
                "a = 0.9  # This model supports a spinning primary compact object\n",
                "p0 = 10.0\n",
                "e0 = 0.8\n",
                "xI0 = 1.0  # +1 for prograde, -1 for retrograde inspirals\n",
                "\n",
                "T = 4.0  # duration of trajectory in years (as defined by few.utils.constants.YRSID_SI)\n",
                "\n",
                "traj_pars = [M, mu, a, p0, e0, xI0]"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 9,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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                        "text/plain": [
                            "<Figure size 1400x800 with 6 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "import matplotlib.pyplot as plt\n",
                "import numpy as np\n",
                "\n",
                "t, p, e, xI, Phi_phi, Phi_theta, Phi_r = traj_model(*traj_pars, T=T)\n",
                "\n",
                "fig, axes = plt.subplots(2, 3)\n",
                "plt.subplots_adjust(wspace=0.35)\n",
                "fig.set_size_inches(14, 8)\n",
                "axes = axes.ravel()\n",
                "\n",
                "ylabels = [r\"$e$\", r\"$p$\", r\"$e$\", r\"$\\Phi_\\phi$\", r\"$\\Phi_\\theta$\", r\"$\\Phi_r$\"]\n",
                "xlabels = [r\"$p$\", r\"$t$\", r\"$t$\", r\"$t$\", r\"$t$\", r\"$t$\"]\n",
                "ys = [e, p, e, Phi_phi, Phi_theta, Phi_r]\n",
                "xs = [p, t, t, t, t, t]\n",
                "\n",
                "for i, (ax, x, y, xlab, ylab) in enumerate(zip(axes, xs, ys, xlabels, ylabels)):\n",
                "    ax.plot(x, y)\n",
                "    ax.set_xlabel(xlab, fontsize=16)\n",
                "    ax.set_ylabel(ylab, fontsize=16)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "#### Trajectory stopping conditions"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "In principle, the inspiral trajectory continues until $p$ intersects with the separatrix, $p_\\mathrm{sep}(a, e, x_I)$. However, FEW truncates the inspiral at the buffer point $p_\\mathrm{stop} = p_\\mathrm{sep} + \\Delta p$ for numerical stability, performing a root-finding operation to place the last trajectory point within $\\sim 10^{-8}$ of $p_\\mathrm{stop}$. \n",
                "\n",
                "The size of $\\Delta p$ can vary based on the trajectory model, and can be obtained directly from the ODE object:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 10,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Delta_p: 0.05\n"
                    ]
                },
                {
                    "data": {
                        "text/plain": [
                            "1.9775479032091425e-09"
                        ]
                    },
                    "execution_count": 10,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "from few.utils.utility import get_separatrix\n",
                "\n",
                "Delta_p = KerrEccEqFlux().separatrix_buffer_dist\n",
                "print(\"Delta_p:\", Delta_p)\n",
                "p_sep = get_separatrix(a, e[-1], xI[-1])  # the separatrix at the trajectory end-point.\n",
                "p[-1] - (p_sep + Delta_p)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "#### Output on a requested time grid"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "In addition to the sparse output of the adaptive solver, the user can also construct trajectories on pre-defined time grids. For uniform grids, the sampling cadence $\\mathrm{d}t$ can be supplied and the grid will be constructed automatically. Non-uniform grids can be supplied via the `new_t` keyword argument. In either case, the `fix_t` keyword argument can be used to truncate the returned trajectory at its end-point."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 11,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "t1 max: 19999900.0 t2 max: 17361000.0\n"
                    ]
                },
                {
                    "data": {
                        "image/png": 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",
                        "text/plain": [
                            "<Figure size 640x480 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "dt = 100.0\n",
                "new_t = np.arange(0, 2e7, dt)\n",
                "\n",
                "# a warning will be thrown if the new_t array goes beyond the time array output from the trajectory\n",
                "t1, p1, e1, x1, Phi_phi1, Phi_theta1, Phi_r1 = traj_model(\n",
                "    *traj_pars, T=T, new_t=new_t, upsample=True\n",
                ")\n",
                "\n",
                "# you can cut the excess on these arrays by setting fix_t to True\n",
                "t2, p2, e2, x2, Phi_phi2, Phi_theta2, Phi_r2 = traj_model(\n",
                "    *traj_pars, T=T, new_t=new_t, upsample=True, fix_t=True\n",
                ")\n",
                "\n",
                "plt.plot(t1, Phi_phi1)\n",
                "plt.plot(t2, Phi_phi2, ls=\"--\")\n",
                "\n",
                "print(\"t1 max:\", t1.max(), \"t2 max:\", t2.max())"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "#### Return trajectory in dimensionless time coordinates"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Trajectories are returned in coordinate time by default, but may be obtained in dimensionless time units by passing `is_coordinate_time=False`:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 12,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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",
                        "text/plain": [
                            "<Figure size 640x480 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                },
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Dimensionless time step: 2.030254435033953\n"
                    ]
                }
            ],
            "source": [
                "t, p, e, x, Phi_phi, Phi_theta, Phi_r = traj_model(*traj_pars, in_coordinate_time=False)\n",
                "\n",
                "plt.plot(t, Phi_phi, label=r\"$\\Phi_\\phi$\")\n",
                "plt.plot(t, Phi_r, label=r\"$\\Phi_r$\")\n",
                "plt.legend(frameon=False)\n",
                "plt.show()\n",
                "print(\"Dimensionless time step:\", t[1] - t[0])"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "#### Integrating trajectories with a fixed time-step"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "The adaptive stepping of the solver can be disabled with the `DENSE_STEPPING` keyword argument, which switches to taking uniform steps of size `dt`. This is more expensive and memory-intensive than adaptive stepping."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 13,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "((15780,), (8,))"
                        ]
                    },
                    "execution_count": 13,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "T_dense = 0.005\n",
                "\n",
                "t_dense, p, e, x, Phi_phi, Phi_theta, Phi_r = traj_model(\n",
                "    *traj_pars, T=T_dense, DENSE_STEPPING=1\n",
                ")\n",
                "t_adaptive, p, e, x, Phi_phi, Phi_theta, Phi_r = traj_model(*traj_pars, T=T_dense)\n",
                "t_dense.shape, t_adaptive.shape"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "We can directly verify the accuracy of the adaptive solution by evaluating its output on the densely-stepped trajectory's time grid. The phase errors will be larger than the error in the orbital elements by a factor of $M / \\mu$ due to conventions chosen during integration:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 14,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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",
                        "text/plain": [
                            "<Figure size 640x480 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "t_dense, p, e, x, Phi_phi, Phi_theta, Phi_r = traj_model(\n",
                "    *traj_pars, T=T_dense, DENSE_STEPPING=1\n",
                ")\n",
                "t_adaptive, p_adaptive, e, x, Phi_phi_adaptive, Phi_theta, Phi_r = traj_model(\n",
                "    *traj_pars, T=T_dense, new_t=t_dense, upsample=True\n",
                ")\n",
                "\n",
                "plt.semilogy(t_dense, abs(Phi_phi_adaptive - Phi_phi), label=\"Phase error\")\n",
                "plt.semilogy(t_dense, abs(p_adaptive - p), label=\"p error\")\n",
                "plt.legend(frameon=False)\n",
                "plt.show()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "#### Evolving trajectories backwards in time"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Trajectories can also be evolved in reverse via the `integrate_backwards` keyword argument. Trajectories evolved in either direction will agree up to the numerical tolerance of the integrator:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 15,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "-3.977270068844518e-09"
                        ]
                    },
                    "execution_count": 15,
                    "metadata": {},
                    "output_type": "execute_result"
                },
                {
                    "data": {
                        "image/png": 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",
                        "text/plain": [
                            "<Figure size 640x480 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "traj_pars_back = traj_pars.copy()\n",
                "\n",
                "T = 0.55\n",
                "\n",
                "# forward\n",
                "t, p, e, xI, Phi_phi, Phi_theta, Phi_r = traj_model(*traj_pars, T=T)\n",
                "\n",
                "traj_pars_back[3] = p[-1]\n",
                "traj_pars_back[4] = e[-1]\n",
                "traj_pars_back[5] = xI[-1]\n",
                "\n",
                "# backward\n",
                "t_back, p_back, e_back, xI_back, Phi_phi_back, Phi_theta_back, Phi_r_back = traj_model(\n",
                "    *traj_pars_back, T=T, integrate_backwards=True\n",
                ")\n",
                "\n",
                "plt.plot(p, e)\n",
                "plt.plot(p_back, e_back, ls=\"--\")\n",
                "p_back[-1] - p[0]"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "#### Setting the integrator error tolerance"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "The integrator tolerance (which is an absolute tolerance) can be adjusted by setting the `err` keyword argument. Higher error tolerances reduce the number of points in the trajectory, but at the cost of numerical accuracy. Note that `err` is a _local_ error tolerance, not a global one, and must therefore be set conservatively with respect to the desired global error tolerance. The default setting of $10^{-11}$ is a reasonable value and should not need to be changed for typical scenarios. "
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 16,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "(64, 39, -1.5885511306379385e-07)"
                        ]
                    },
                    "execution_count": 16,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "p = traj_model(*traj_pars, T=T, err=1e-11)[1]\n",
                "p_hightol = traj_model(*traj_pars, T=T, err=1e-9)[1]\n",
                "\n",
                "p.size, p_hightol.size, (p[-1] - p_hightol[-1]).item()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "#### Integrating trajectories in $(E, L, Q)$ coordinates"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Trajectories can also be solved in the constants of motion parameterisation $(E, L, Q)$. This is supported for all stock trajectory models. Given input $(p_0, e_0, x_{I,0})$, the integrator converts these initial conditions to $(E, L, Q)$ and integrates these quantities alongside the inspiral phases. The output trajectory is converted back to $(p, e, x_I)$ coordinates if the keyword argument `convert_pex=True` (which it is by default).\n",
                "\n",
                "Integrating in $(E, L, Q)$ can offer some advantages, especially near the separatrix (see [Hughes 2024](https://arxiv.org/abs/2401.09577) for more information). Typically the trajectory also consists of fewer points than its $(p, e, x_I)$ counterpart, and is therefore faster to compute. However, it can also be numerically unstable for very small eccentricities, where small errors in the constants of motion can be amplified when transformed back to $(p, e, x_I)$. Usage of this method should be considered somewhat experimental, especially for eccentric and inclined (generic) inspirals."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 17,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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                        "text/plain": [
                            "<Figure size 1400x800 with 6 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                },
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "(ELQ, pex) trajectory lengths: [34, 48]\n",
                        "(ELQ, pex) phase difference: 0.0005445422793854959\n"
                    ]
                }
            ],
            "source": [
                "M = 1e6\n",
                "mu = 1e2\n",
                "a = 0.0\n",
                "p0 = 10.0\n",
                "e0 = 0.7\n",
                "xI0 = 1.0\n",
                "T = 1.0\n",
                "\n",
                "traj_model_ELQ = EMRIInspiral(func=SchwarzEccFlux, integrate_constants_of_motion=True)\n",
                "traj_model_pex = EMRIInspiral(func=SchwarzEccFlux, integrate_constants_of_motion=False)\n",
                "\n",
                "fig, axes = plt.subplots(2, 3, figsize=(14, 8))\n",
                "plt.subplots_adjust(wspace=0.35)\n",
                "axes = axes.ravel()\n",
                "ylabels = [r\"$e$\", r\"$p$\", r\"$e$\", r\"$\\Phi_\\phi$\", r\"$\\Phi_\\theta$\", r\"$\\Phi_r$\"]\n",
                "xlabels = [r\"$p$\", r\"$t$\", r\"$t$\", r\"$t$\", r\"$t$\", r\"$t$\"]\n",
                "\n",
                "lens = []\n",
                "phase_ends = []\n",
                "for traj_model, label, ls in zip(\n",
                "    [traj_model_ELQ, traj_model_pex], [\"ELQ\", \"pex\"], [\"-\", \"--\"]\n",
                "):\n",
                "    t, p, e, xI, Phi_phi, Phi_theta, Phi_r = traj_model(M, mu, a, p0, e0, xI0, T=T)\n",
                "\n",
                "    # Plot the results for comparison\n",
                "    ys = [e, p, e, Phi_phi, Phi_theta, Phi_r]\n",
                "    xs = [p, t, t, t, t, t]\n",
                "\n",
                "    for i, (ax, x, y, xlab, ylab) in enumerate(zip(axes, xs, ys, xlabels, ylabels)):\n",
                "        ax.plot(x, y, label=label, ls=ls)\n",
                "        ax.set_xlabel(xlab, fontsize=16)\n",
                "        ax.set_ylabel(ylab, fontsize=16)\n",
                "\n",
                "    lens.append(len(t))\n",
                "    phase_ends.append(Phi_phi[-1])\n",
                "axes[0].legend(frameon=False)\n",
                "\n",
                "plt.show()\n",
                "\n",
                "print(\"(ELQ, pex) trajectory lengths:\", lens)\n",
                "print(\"(ELQ, pex) phase difference:\", phase_ends[1] - phase_ends[0])"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### User-defined trajectory models"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "In addition to FEW's built-in trajectory models, users can readily implement their own models in the same framework.\n",
                "They can achieve this by:\n",
                "\n",
                "- Subclassing the `ODEBase` base class,\n",
                "  \n",
                "- Defining the `evaluate_rhs` method, and\n",
                "  \n",
                "- Updating any relevant properties of the model (by default, they are set for generic Kerr inspirals).\n",
                "  \n",
                "You do not need to handle any boundary checking in your modified class (e.g., ensuring quantities remain physical) as this is performed automatically by the base class. \n",
                "\n",
                "Let's implement a Post-Newtonian trajectory in Schwarzschild eccentric as an example:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 18,
            "metadata": {},
            "outputs": [],
            "source": [
                "# Some elliptic functions for evaluating geodesic frequencies\n",
                "from few.utils.elliptic import EllipK, EllipE, EllipPi\n",
                "\n",
                "# base classes\n",
                "from few.trajectory.ode.base import ODEBase\n",
                "\n",
                "\n",
                "# for common interface with C/mathematica\n",
                "def Power(x, n):\n",
                "    return x**n\n",
                "\n",
                "\n",
                "def Sqrt(x):\n",
                "    return np.sqrt(x)\n",
                "\n",
                "\n",
                "# this class defines the right-hand side of the ODE\n",
                "# we define the method \"evaluate_rhs\" according to our derivatives\n",
                "# we set the \"equatorial\" and \"background\" properties accordingly\n",
                "# we also set the \"flux_output_convention\" property to \"pex\" to tell the trajectory module what\n",
                "# the RHS derivatives correspond to\n",
                "class Schwarzschild_PN(ODEBase):\n",
                "    @property\n",
                "    def equatorial(self):\n",
                "        return True\n",
                "\n",
                "    @property\n",
                "    def background(self):\n",
                "        return \"Schwarzschild\"\n",
                "\n",
                "    @property\n",
                "    def flux_output_convention(self):\n",
                "        return \"pex\"\n",
                "\n",
                "    def evaluate_rhs(self, y):\n",
                "        # guard against bad integration steps\n",
                "        p, e, xI = y[:3]\n",
                "\n",
                "        # perform elliptic calculations\n",
                "        ellipE = EllipE(4 * e / (p - 6.0 + 2 * e))\n",
                "        ellipK = EllipK(4 * e / (p - 6.0 + 2 * e))\n",
                "        ellipPi1 = EllipPi(\n",
                "            16 * e / (12.0 + 8 * e - 4 * e * e - 8 * p + p * p),\n",
                "            4 * e / (p - 6.0 + 2 * e),\n",
                "        )\n",
                "        ellipPi2 = EllipPi(\n",
                "            2 * e * (p - 4) / ((1.0 + e) * (p - 6.0 + 2 * e)), 4 * e / (p - 6.0 + 2 * e)\n",
                "        )\n",
                "\n",
                "        # Azimuthal frequency\n",
                "        Omega_phi = (2 * Power(p, 1.5)) / (\n",
                "            Sqrt(-4 * Power(e, 2) + Power(-2 + p, 2))\n",
                "            * (\n",
                "                8\n",
                "                + (\n",
                "                    (\n",
                "                        -2\n",
                "                        * ellipPi2\n",
                "                        * (6 + 2 * e - p)\n",
                "                        * (3 + Power(e, 2) - p)\n",
                "                        * Power(p, 2)\n",
                "                    )\n",
                "                    / ((-1 + e) * Power(1 + e, 2))\n",
                "                    - (ellipE * (-4 + p) * Power(p, 2) * (-6 + 2 * e + p))\n",
                "                    / (-1 + Power(e, 2))\n",
                "                    + (\n",
                "                        ellipK\n",
                "                        * Power(p, 2)\n",
                "                        * (28 + 4 * Power(e, 2) - 12 * p + Power(p, 2))\n",
                "                    )\n",
                "                    / (-1 + Power(e, 2))\n",
                "                    + (\n",
                "                        4\n",
                "                        * (-4 + p)\n",
                "                        * p\n",
                "                        * (2 * (1 + e) * ellipK + ellipPi2 * (-6 - 2 * e + p))\n",
                "                    )\n",
                "                    / (1 + e)\n",
                "                    + 2\n",
                "                    * Power(-4 + p, 2)\n",
                "                    * (\n",
                "                        ellipK * (-4 + p)\n",
                "                        + (ellipPi1 * p * (-6 - 2 * e + p)) / (2 + 2 * e - p)\n",
                "                    )\n",
                "                )\n",
                "                / (ellipK * Power(-4 + p, 2))\n",
                "            )\n",
                "        )\n",
                "\n",
                "        # Post-Newtonian calculations\n",
                "        yPN = pow(Omega_phi, 2.0 / 3.0)\n",
                "\n",
                "        EdotPN = (\n",
                "            (96 + 292 * Power(e, 2) + 37 * Power(e, 4))\n",
                "            / (15.0 * Power(1 - Power(e, 2), 3.5))\n",
                "            * pow(yPN, 5)\n",
                "        )\n",
                "        LdotPN = (\n",
                "            (4 * (8 + 7 * Power(e, 2)))\n",
                "            / (5.0 * Power(-1 + Power(e, 2), 2))\n",
                "            * pow(yPN, 7.0 / 2.0)\n",
                "        )\n",
                "\n",
                "        # flux\n",
                "        Edot = -EdotPN\n",
                "        Ldot = -LdotPN\n",
                "\n",
                "        # time derivatives\n",
                "        pdot = (\n",
                "            -2\n",
                "            * (\n",
                "                Edot\n",
                "                * Sqrt((4 * Power(e, 2) - Power(-2 + p, 2)) / (3 + Power(e, 2) - p))\n",
                "                * (3 + Power(e, 2) - p)\n",
                "                * Power(p, 1.5)\n",
                "                + Ldot * Power(-4 + p, 2) * Sqrt(-3 - Power(e, 2) + p)\n",
                "            )\n",
                "        ) / (4 * Power(e, 2) - Power(-6 + p, 2))\n",
                "\n",
                "        edot = -(\n",
                "            (\n",
                "                Edot\n",
                "                * Sqrt((4 * Power(e, 2) - Power(-2 + p, 2)) / (3 + Power(e, 2) - p))\n",
                "                * Power(p, 1.5)\n",
                "                * (\n",
                "                    18\n",
                "                    + 2 * Power(e, 4)\n",
                "                    - 3 * Power(e, 2) * (-4 + p)\n",
                "                    - 9 * p\n",
                "                    + Power(p, 2)\n",
                "                )\n",
                "                + (-1 + Power(e, 2))\n",
                "                * Ldot\n",
                "                * Sqrt(-3 - Power(e, 2) + p)\n",
                "                * (12 + 4 * Power(e, 2) - 8 * p + Power(p, 2))\n",
                "            )\n",
                "            / (e * (4 * Power(e, 2) - Power(-6 + p, 2)) * p)\n",
                "        )\n",
                "\n",
                "        xIdot = 0.0\n",
                "\n",
                "        Phi_phi_dot = Omega_phi\n",
                "        Phi_theta_dot = Omega_phi\n",
                "\n",
                "        Phi_r_dot = (\n",
                "            p * Sqrt((-6 + 2 * e + p) / (-4 * Power(e, 2) + Power(-2 + p, 2))) * np.pi\n",
                "        ) / (\n",
                "            8 * ellipK\n",
                "            + (\n",
                "                (-2 * ellipPi2 * (6 + 2 * e - p) * (3 + Power(e, 2) - p) * Power(p, 2))\n",
                "                / ((-1 + e) * Power(1 + e, 2))\n",
                "                - (ellipE * (-4 + p) * Power(p, 2) * (-6 + 2 * e + p))\n",
                "                / (-1 + Power(e, 2))\n",
                "                + (ellipK * Power(p, 2) * (28 + 4 * Power(e, 2) - 12 * p + Power(p, 2)))\n",
                "                / (-1 + Power(e, 2))\n",
                "                + (\n",
                "                    4\n",
                "                    * (-4 + p)\n",
                "                    * p\n",
                "                    * (2 * (1 + e) * ellipK + ellipPi2 * (-6 - 2 * e + p))\n",
                "                )\n",
                "                / (1 + e)\n",
                "                + 2\n",
                "                * Power(-4 + p, 2)\n",
                "                * (\n",
                "                    ellipK * (-4 + p)\n",
                "                    + (ellipPi1 * p * (-6 - 2 * e + p)) / (2 + 2 * e - p)\n",
                "                )\n",
                "            )\n",
                "            / Power(-4 + p, 2)\n",
                "        )\n",
                "\n",
                "        dydt = [pdot, edot, xIdot, Phi_phi_dot, Phi_theta_dot, Phi_r_dot]\n",
                "\n",
                "        return dydt"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 19,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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55sLwv1664q8c2gYLroPsPVAn1JzdObR9BVReMykAuZEVK1ZYXYKIiJThl33ZJH6xhe9SjwDg7+vJPb1bMDQ26tyWrvgre9fDmzfAiaPQoAX860Oo1+Tvn7cGUwASERGxyN5j+Tz75TY++nEfAN52D4bGNuGe3i0IrOVdMb9k+3J49xZz1YLwTubszrX/5qM0F6AAdJ4Mw7C6hBpB10lE5HRZ+YXM/DqVeat3U+gwJ5u9Njqcsf1aE1m/Aie5/fldWDQKnMXQvDfcNB98yrE0hgtTACqn32dKzs/Px8/Pz+Jqqr/8fHOR2D/PMC0i4o5OFjmYt3oXM79OJeekObIrtlkDJl7Rho6NAiv2lyXPhKUPmf/c/gYY+DJ4VtBdJRegAFROdrudwMDAkvWxatWqVf4px92AYRjk5+dz8OBBAgMDNdO0iLg1h9Ng0Y/7mL5sG/uyTgDQJrQu4we0oVerhhX7PWIYsHwyfPe82Y4ZBfHT3GJ25/JQADoPoaGhAFok9BwEBgaWXC8REXdjGAYrtx/m/77YypYDOQCEBfiS0LcV113UCPvfHdn1Z44i+ORe+Okts91nMvS4321mdy4PBaDzYLPZCAsLIzg4mKKiIqvLqba8vLx050dE3NafR3bV9fXkrl4tGH5JBY3s+rPCfHjvVti+FGx2uOYF6PSviv89LkIB6G+w2+36ghcRkVL2HM3nmS9T+HjjfuDUyK67L29BvdqV1Acn/yi8NQj2rgNPX7hxLrQeUDm/y0VY/kBw5syZREVF4evrS0xMDOvWrTvr/llZWdx9992EhYXh4+NDq1atWLx4ccnP//Of/2Cz2Uq92rRpU9lvQ0RE3NyxvEKmfraZPs9+UxJ+BkaHk/RATx65ql3lhZ/svTCnvxl+fANg6McKP+fA0jtACxcuJCEhgVmzZhETE8OMGTOIj48nJSWF4ODg0/YvLCykb9++BAcH8/777xMREcHu3bsJDAwstd8FF1zA8uXLS9qenrrRJSIileNkkYPXv9vFf1ekcvy3kV2XtGjAxAFtaR8RULm//FAKzP8H5OyDuuFwy4cQ3LZyf6eLsDQZTJ8+nREjRjB8+HAAZs2axeeff86cOXOYMGHCafvPmTOHo0ePsnr16pJh1VFRUaft5+npqY63IiJSqRxOgw837GX6sm0cyDbX7Gob5s+EAW24rGVQ5Y8Q3rMO3rrJXNy0QUu45SMIjKzc3+lCLHsEVlhYyPr164mLiztVjIcHcXFxJCcnl3nMJ598QmxsLHfffTchISG0b9+eadOm4XA4Su23fft2wsPDadasGUOGDCE9Pf2stRQUFJCTk1PqJSIiUhbDMPg65SBXvvAtD77/MweyTxIe4Mv0my7k89E96FnRw9rLsm0pzLvGDD8RXeC2pQo/5WTZHaDDhw/jcDgICQkptT0kJIStW7eWecyOHTv46quvGDJkCIsXLyY1NZW77rqLoqIiJk+eDEBMTAxz586ldevWHDhwgClTpnDppZfyyy+/ULdu3TLPm5iYyJQpUyr2DYqIiMv5eW8WiYu3kryjktbsOhcb34aP7wbDAS36wk3zwLt21fxuF1KjOsc4nU6Cg4N59dVXsdvtdO7cmX379vH000+XBKABA051/OrYsSMxMTE0adKEd999l9tvv73M806cOJGEhISSdk5ODpGRStIiImJKP5LP01+m8OlPv43s8vTg1u5R3NWrecWt2XUuvnselk0y/7njILh2Jtg10/75sCwABQUFYbfbyczMLLU9MzPzjP13wsLCTptbpm3btmRkZFBYWIi39+kfwsDAQFq1akVqauoZa/Hx8cHHx+c834mIiLiqw7kFvPRVKm+u3U2Rw8Bmg39ER5DQrxWN6lXgml1/xemEZY9C8ktmO/Ye6DtVszv/DZZdOW9vbzp37kxSUlLJNqfTSVJSErGxsWUec8kll5CamorT6SzZtm3bNsLCwsoMPwC5ubmkpaURFhZWsW9ARERcVl5BMS8kbafnU18zd/UuihwGPVs15LPRPZg+KLpqw4+jCBb9+1T46TsV4p9Q+PmbLH0ElpCQwLBhw+jSpQvdunVjxowZ5OXllYwKGzp0KBERESQmJgIwatQoXnrpJcaMGcPo0aPZvn0706ZN49577y0559ixY7n66qtp0qQJ+/fvZ/Lkydjtdm6++WZL3qOIiNQcRQ4n73y/h+eXb+dwbgEAHSICmDigDd1bBFV9QYV58O5QSF1uzu587UyI1vdZRbA0AA0aNIhDhw4xadIkMjIyiI6OZsmSJSUdo9PT0/H4Q8KNjIxk6dKl3H///XTs2JGIiAjGjBnD+PHjS/bZu3cvN998M0eOHKFhw4b06NGDNWvW0LBhwyp/fyIiUjMYhsEXv2Tw9NIUdh7OA6BJg1o8GN+aK9qH4VHRa3adi7wj8NaNsG89ePrBTW9Aq35VX4eLshmGYVhdRHWTk5NDQEAA2dnZ+Pv7W12OiIhUojU7jpD4xVZ+2pMFQIPa3oyJa8ngro3x9rToMVNWOsy/Do5sB7968M/3ILKrNbXUIOX5/q5Ro8BEREQqypYDOTy1ZCtfpxwCoJa3nRGXNmPEZc2o42Ph12PmZlhwPRzfD/6NzNmdG7a2rh4XpQAkIiJuZV/WCaZ/uY0Pf9yLYYCnh42buzXm3j4taVjX4hHBu5Ph7UFwMhsatoF/fQABjaytyUUpAImIiFs4llfIzK9TeWPNbgqLzdHEV3YMY2y/1jQNqgYTCW75FD64A4pPQmQM3PwO1KpvdVUuSwFIRERcWn5hMa9/t4tZK9I4XmAuVhrbrAHjB7QhOjLQ2uJ+l/xfWPoQYEDLeLhxLnhX4VB7N6QAJCIiLqnI4eTdH/YwY/l2Dh03h7RX6WKl58LpgKUPw9qXzXbn4XDFM2DX13Nl0xUWERGXUtaQ9sj6fozt15qrO4ZbM6S9LIX58OEI2PqZ2Y6bApeMgeoQzNyAApCIiLiM1WmHefKLrfy0Nxswh7SP7t2Cf8Y0sW5Ie1lyD8Hbg2HfD2D3hoEvQ4cbrK7KrSgAiYhIjffr/myeXJLCym3VbEh7WQ6nwpvXw7Fd4BsIN78NTbpbXZXbqWafChERkXOXfiSfZ5el8PFGc5V2L7uNf3ZrzD29q8GQ9rLsToZ3boYTxyCwiTnMPail1VW5JQUgERGpcf68SjvANReG80C/VjRpUA2GtJfllw/ho3+DowAiOpvD3OsEW12V21IAEhGRGuP4ySJe+3Yn//t2B/mFDgAua9WQcfGtaR8RYHF1Z2AYsPoFWDbJbLe+Eq7/n4a5W0wBSEREqr2TRQ7eXJvOzK9TOZpXCMCFjQIY178Nl1ixSvu5chTDF+Pgh9lmO+bfED8NPOzW1iUKQCIiUn05nAYfbtjLjOXb2Zd1AoBmDWvzYL/W9G8fWj3m8jmTwjx4/zbYtgSwmcEn9i6rq5LfKACJiEi1YxgGyzZn8vTSFLYfzAUg1N+X+/u25PqLGuFpr0ZD2styPBPeugkObARPX7juVWh3rdVVyR8oAImISLWyZscRnlyylR/TswAI8PPi7subMzQ2Cl+vGvDo6OBWePNGyE6HWg3Mzs6R3ayuSv5EAUhERKqFX/dn89SSFL75bS4fPy87t/doyojLmhHg52Vxdedo57ewcIi5mnv95jDkPWjQ3OqqpAwKQCIiYqldh/OYvmwbn/xkzuXj6WHj5m6NGd2nBcF1fS2urhx+Wggf3w3OInM198FvQ+0GVlclZ6AAJCIiljh4/CQvJG3nnXV7KHaac/lcGx1OQt9qPJdPWQwDvn0GvnrcbLe7Fv7xCnj5WVuXnJUCkIiIVKnsE0W8ujKNOat2caLInMunV+uGPBjfmgvCq+lcPmfiKILPE2DDG2a7+2iIeww8qnknbVEAEhGRqnGi0MHc1buY9U0a2SeKAOjUOJDx/dtwcbMa+KjoZA68dyukJYHNAwY8Bd1GWF2VnCMFIBERqVSFxU4W/rCHF5O2c/B4AQAtg+vwYHxr+rYLqd5z+ZxJzn548ybI3AReteCGOdB6gNVVSTkoAImISKVwOA0++Wkfzy3bTvrRfAAa1fMjoW8rro2OwO5RA4MPQOav5jD3nH1QuyH8812IuMjqqqScFIBERKRC/T6J4bNfbiMl8zgADev6cG/vFgzq2hhvzxrcPybtK1g4FAqPQ1Arc5h7vSirq5LzoAAkIiIVZnXaYZ5emlIyiaG/ryf/7tWcW7tHUcu7hn/l/LgAPh0DzmJo0gMGLwC/elZXJeephn8aRUSkOvhpTxZPL01hVephwJzE8LYeUYy8rHnNmcTwTAwDViTCN0+a7Q43wrUzwdPH2rrkb1EAEhGR87Y98zjPfJnC0l8zAfCy2xgS04S7Lm9esyYxPJPiQvj0XvjpbbN96QNw+SMa5u4CFIBERKTc9hzN57nl21j04z6cBnjY4B+dGnFfXEsi69eyuryKkX8UFt4Cu1eBzQ5XTYfOt1pdlVQQBSARETlnB4+fZOZXqby1Lp0ihzl7c/8LQnmgXytahtS1uLoKdGibuZr7sZ3gXRdunAst46yuSiqQApCIiPyl7PwiXlmZxuvfnZq9+dKWQYzt15oLIwOtLa6ipX0N7w6DgmwIbAw3L4SQdlZXJRVMAUhERM4or6CYuat38co3aeScLAYgOjKQcf1b0715kMXVVYLvZ8PiB8FwmAuaDnoT6jS0uiqpBApAIiJympNFDt5cm87LK1I5nFsIQOuQuoyNb01c2+CaOXvz2TgdsPRhWPuy2e44CK5+AbxcoCO3lEkBSEREShQ5nLz3w15e/Go7B7JPAhDVoBb3923FVR3Da+7szWdzMgc+uB22f2m2ez8Cl44FVwt5Uorl4/hmzpxJVFQUvr6+xMTEsG7durPun5WVxd13301YWBg+Pj60atWKxYsX/61zioi4O4fT4KMf9xI3/Rse+mgTB7JPEhbgy/9d14FlCT1r9tIVZ3NsN8yJN8OPpx/cOA8ue1Dhxw1Yegdo4cKFJCQkMGvWLGJiYpgxYwbx8fGkpKQQHBx82v6FhYX07duX4OBg3n//fSIiIti9ezeBgYHnfU4REXdmGAZLf81g+rJtbMvMBSCojjd39WrBP2Ma4+tlt7jCSpS+Ft75J+QfhjqhcPPbWtPLjdgMwzCs+uUxMTF07dqVl156CQCn00lkZCSjR49mwoQJp+0/a9Ysnn76abZu3YqXV9kzi5b3nGXJyckhICCA7Oxs/P39z/PdiYhUX4ZhsHL7YZ79MoWf92YD5rIVd/Y0l62o7ePiPSR+fhc+vhschRDaEW5+BwIirK5K/qbyfH9b9gissLCQ9evXExd3al4FDw8P4uLiSE5OLvOYTz75hNjYWO6++25CQkJo374906ZNw+FwnPc5AQoKCsjJySn1EhFxVet2HmXQK2sYNmcdP+/Nppa3ndG9W/Dt+N7cfXkL1w4/Tid89Th8OMIMP22ugtuWKPy4Ics+5YcPH8bhcBASElJqe0hICFu3bi3zmB07dvDVV18xZMgQFi9eTGpqKnfddRdFRUVMnjz5vM4JkJiYyJQpU/7+mxIRqcZ+3pvFM19uY+W2QwB4e3ow9OImjOrVnAZ13GBdq8J8WPRv2Pyx2e5xP/SepGUt3FSNivlOp5Pg4GBeffVV7HY7nTt3Zt++fTz99NNMnjz5vM87ceJEEhISSto5OTlERkZWRMkiIpbbciCH55Zt48vN5npdnh42buoayejeLQgL8LO4uipyPAPeHgz7fwQPL7j6eeg0xOqqxEKWBaCgoCDsdjuZmZmltmdmZhIaGlrmMWFhYXh5eWG3n+qU17ZtWzIyMigsLDyvcwL4+Pjg4+MG//cjIm4l9WAuM5Zv47OfDwDmwKaB0RHcF9eSJg1qW1xdFTrwE7w1GI7vB7/6MGgBRF1idVViMcvu+3l7e9O5c2eSkpJKtjmdTpKSkoiNjS3zmEsuuYTU1FScTmfJtm3bthEWFoa3t/d5nVNExNXsPpJHwrsb6ffcNyXh58qOYSy7/zKeGxTtXuFny2cwp78ZfoJaw4gkhR8BLH4ElpCQwLBhw+jSpQvdunVjxowZ5OXlMXz4cACGDh1KREQEiYmJAIwaNYqXXnqJMWPGMHr0aLZv3860adO49957z/mcIiKual/WCV5M2s576/ficJoDfPu2C+H+uFa0C3ezEa2GAd/NgOVTAAOa9zYXNPUNsLgwqS4sDUCDBg3i0KFDTJo0iYyMDKKjo1myZElJJ+b09HQ8/tA5LTIykqVLl3L//ffTsWNHIiIiGDNmDOPHjz/nc4qIuJrMnJPM/DqVd9btodBh3iHv1bohCX1b0bFRoLXFWaG4ED67Dza+aba7joD+/wf2GtXtVSqZpfMAVVeaB0hEaoLDuQXMWpHG/DW7KSg2g0/35g14oF8rOjepb3F1Fsk7Au/eAru/A5sH9H8SYkZaXZVUkfJ8fysOi4jUMFn5hby6cgdzV+8iv9CcB61Lk3ok9Gvlmiu0n6tDKfDWTXBsF/j4ww2vQ8u4vzxM3JMCkIhIDZFzsojZ3+5kzqqdHC8oBqBjowAS+raiZ6uGrrdCe3mkJsF7w6EgGwKbwD/fheA2Vlcl1ZgCkIhINZdbUMy81bt4deUOsk8UAdAmtC4P9GtNXNtg9w4+AOtegy/Gg+GAyIth8JtQ243vhMk5UQASEamm8gqKmZe8i9dW7uBYvhl8WgTX4f64VgxoH4qHK67OXh6OYlj6EKx7xWxfeLM5waGn5nWTv6YAJCJSzeQXFvNG8m5eXbmDo3mFADQLqs29fVpy9YXh2N09+ACczDYfeaX9Nu9bn8nm0hbufjdMzpkCkIhINXGi0MH8Nbt45ZsdHPkt+EQ1qMW9fVpyzYXheNq1ZhVgdnJ+axAc2gqefnDdq9DuGqurkhpGAUhExGInCh28uXY3s75J43CuGXyaNKjF6N4tGRit4FPK7mRYOATyj0DdMLj5bQjvZHVVUgMpAImIWORkkYM316bz8oo0DucWABBZ34/RvVtyXacIBZ8/++kd+GQ0OAoh7EK4+R3wD7e6KqmhFIBERKrYySIHb68zg8/B42bwaVTPj3t7t+QfF0XgpeBTmtMJX02FVdPNdtur4R+vgLcbrWkmFU4BSESkipwscrDw+z38d0UqmTlm8IkI9GN07xZc37mRgk9ZCnLhozth62dm+9IH4PJHwEPXSv4eBSARkUpWUOzg3e/3MPPrNDJyTgJm8Ln78hbc0LkR3p76Mi/TsV3w9j/h4K9g94arX4Dom62uSlyEApCISCUpKHbw3g97+e/XqezPNoNPWIAvd1/eghu7NMLH025xhdXYzpXw7jA4cRTqhMCgBRDZzeqqxIUoAImIVLDCYifvrd/DzK9OBZ9Qf1/uvrw5N3WNVPA5G8MwZ3ZeMsGc2Tm8Ewx6EwIirK5MXIwCkIhIBSksdvLBhr289FUq+7JOABDi78NdvVowqGskvl4KPmdVXAiLH4ANb5jtDjfBNS+Al5+1dYlLUgASEfmbCoodvPvDXmatSCsJPg3r+nBXr+bc3K2xgs+5yD0IC2+BPWvA5gFxU6D7aM3sLJVGAUhE5Dz9Ppx91jdpJaO6guv6cGfP5gyJUfA5Z/t/hHeGQM4+8AmAG+ZAyzirqxIXpwAkIlJO+YXFvLkmnVdW7iiZwDAswJdRvZpzUxc96iqXTe/Dx3dD8Ulo0NKc2TmopdVViRtQABIROUe5BcXMT97Na9+eWqT09+Hs13eOUOfm8nA6fpvc8Dmz3aIv3DAbfAOsrUvchgKQiMhfyDlZxLzvdjH7u51k5RcB5lpdd1/egn900szN5XYyGz4YAduXmu1LxpiruXsoQErVUQASETmDrPxC5ny3i9e/28nxk8UANAuqzT29W2h19vN1JA3eHgyHt4GnL1zzInS8yeqqxA0pAImI/MnRvEL+9+0O3kjeTW6BGXxaBtdhdJ+WXNkhDLuHRiadl9Tl8P5t5h2guuEw+E2IuMjqqsRNKQCJiPzm0PECXvt2BwvW7Ca/0AFAm9C63NunJf0vCMVDwef8GAYkz4Rlj4LhhEbdzJmd64ZYXZm4MQUgEXF7mTkneeWbHby1bjcni5wAtI/w597eLYlrG6Lg83cUnYTP7oOf3jbbnf4FV04HTx9LyxJRABIRt7U/6wSzvknjne/3UFhsBp/oyEDG9GlJr9YNsWkSvr8n5wAsHAL71oPNDv0TodtITW4o1YICkIi4nR2Hcpn1TRof/biPIocBQJcm9bi3T0subRmk4FMR9v5gTm6YmwG+gXDTPGjWy+qqREooAImI2/h1fzb/XZHG4k0HMMzcw8XN6nNvn5bENmug4FNRNr4Fn94HjgJo2BZufgvqN7O6KpFSFIBExOX9sOsoM79O5euUQyXb4toGM6pXCzo3qWdhZS7GUQRLH4Z1r5jt1lfCda+AT11r6xIpgwKQiLgkwzBYuf0wM79OZd3OowB42OCqjuGM6tWctmH+FlfoYnIPwrvDIH212e45HnpOAA/NlSTVkwKQiLgUp9Ng6a8ZzFyRyi/7cgDwstu4oXMj7rysOVFBtS2u0AXt/cFcyf34fvCuC9e9Cm2usLoqkbNSABIRl1DkcPLxxv28vCKVtEN5APh52flnTGPuuLQpYQF+FlfootbPg8VjwVEIQa1g8FtazFRqBAUgEanRThY5ePeHPbzyzQ72ZZ0AwN/Xk1u7R3HrJU2pX9vb4gpdVHEBfDEO1s81222ugoEvg68eLUrNoAAkIjXS8ZNFLFiTzuxVOzica67MHlTHhzsubcqQmMbU9fWyuEIXlnMA3r0F9n4P2KD3I9AjQf19pEapFp/WmTNnEhUVha+vLzExMaxbt+6M+86dOxebzVbq5evrW2qfW2+99bR9+vfvX9lvQ0SqwNG8Qp79MoVL/u8rnlyylcO5hUQE+jH12gtYNf5y/t2zucJPZdqdDK9cZoYf3wAY8h5cNlbhR2ocy+8ALVy4kISEBGbNmkVMTAwzZswgPj6elJQUgoODyzzG39+flJSUknZZc3f079+f119/vaTt46Np10VqsvQj+fxv1Q7e/WFPyXIVzRvW5q5eLbgmOhwvrcxeuQwDvv8fLJkAzmIIvgAGL9D8PlJjWR6Apk+fzogRIxg+fDgAs2bN4vPPP2fOnDlMmDChzGNsNhuhoaFnPa+Pj89f7iMi1d+mvdm8stKcvND52+SFHSICuPvy5vRrpwVKq0TRSfg8ATa+abYvuA6ufQm8NaJOai5LA1BhYSHr169n4sSJJds8PDyIi4sjOTn5jMfl5ubSpEkTnE4nF110EdOmTeOCCy4otc+KFSsIDg6mXr169O7dm8cff5wGDRqUeb6CggIKCgpK2jk5OX/znYnI32EYBt9uP8wrK9P4LvVIyfaerRpyZ89mmrW5KmXtMfv77P8RbB4QNwW6j9Z6XlLjWRqADh8+jMPhICQkpNT2kJAQtm7dWuYxrVu3Zs6cOXTs2JHs7GyeeeYZunfvzq+//kqjRo0A8/HXddddR9OmTUlLS+Ohhx5iwIABJCcnY7fbTztnYmIiU6ZMqfg3KCLlUuxw8vmmA8z6ZgdbDpj/I2L3sHHNheGMuLQZ7cI1wqhK7VwJ790K+UfArz7cMAeaX251VSIVwmYYv6+IU/X2799PREQEq1evJjY2tmT7uHHj+Oabb1i7du1fnqOoqIi2bdty8803M3Xq1DL32bFjB82bN2f58uX06dPntJ+XdQcoMjKS7Oxs/P31B1eksuUXFvPu93t47dudJUPZ/bzsDO4Wye09mtKoXi2LK3QzhgFr/gtfPgqGA0I7wqAFUK+J1ZWJnFVOTg4BAQHn9P1t6R2goKAg7HY7mZmZpbZnZmaec/8dLy8vOnXqRGpq6hn3adasGUFBQaSmppYZgHx8fNRJWsQCR3ILmJe8mzeSd5GVXwRAg9re3No9in9d3IR6msOn6hXmw6f3wqb3zHbHwXD1DPDSRJLiWiwNQN7e3nTu3JmkpCQGDhwIgNPpJCkpiXvuueeczuFwONi0aRNXXHHmadf37t3LkSNHCAsLq4iyReRvSj+Sz2vfmiO6CorNEV1NGtRixKXNuKFzI3y9Tn9ULVXg2C5451+QuQlsdoifBjF3qr+PuCTLR4ElJCQwbNgwunTpQrdu3ZgxYwZ5eXklo8KGDh1KREQEiYmJADz22GNcfPHFtGjRgqysLJ5++ml2797NHXfcAZgdpKdMmcL1119PaGgoaWlpjBs3jhYtWhAfH2/Z+xQR+HlvFq+u3FFqRFfHRgH8u2dz4i8Ixa4RXdZJTYIPbocTx6BWENw0D6J6WF2VSKWxPAANGjSIQ4cOMWnSJDIyMoiOjmbJkiUlHaPT09Px+MMEW8eOHWPEiBFkZGRQr149OnfuzOrVq2nXrh0Adrudn3/+mXnz5pGVlUV4eDj9+vVj6tSpeswlYgGH02DZ5kzmrNrJul1HS7ZrRFc1YRjw3QxIegwMJ4RfBIPmQ0AjqysTqVSWdoKursrTiUpEypZXUMx7P+xhzne7SD+aD4Cnh42rLwxn5GXNaBum/7YsV5ALH98NmxeZ7U7/giueBS/fsx4mUl3VmE7QIuJ69medYF7yLt5am87xk8UABPh5MSSmMUNjowgN0JdrtXA4FRb+Cw5tAQ8vGPAkdLlN/X3EbSgAiUiF+GlPFrNX7eTzTQdw/NbBp2lQbW7r0ZTrL4qglrf+3FQbmz+GRXdD4XGoEwI3zYfGMVZXJVKl9BdJRM7b7/17Zq/awfe7jpVsj23WgNt7NKV3m2AtVVGdOIpg2WRYM9NsN7nEnNywrpYNEvejACQi5Xam/j3XXBjObT2a0j4iwOIK5TQ5++G94bBnjdnufi/0mQx2fQ2Ie9InX0TO2b6sE7yxehdvrTvVvyew1qn+PSH+6t9TLe1cCe/fBnmHwMcfBv4X2l5tdVUillIAEpGzMgyDNTuOMnf1TpZtziyZv6dZUG2Gq39P9eZ0wnfPwVePm0PcQ9rDTW9Ag+ZWVyZiOf3VEpEy5RcWs+jH/cxbvYuUzOMl27s3N/v3XN5a/XuqtRPH4KN/w7YlZjt6CFzxDHhrXTURUAASkT/ZczSfN5J3sfD7PeT89pjLz8vOdRdFMKx7FK1C6lpcofylAz/BwlsgazfYfeCKp+GioRriLvIHCkAigmEYfJd6hLmrd5K09SC/T4/auH4thsY24cYukQT4eVlbpPw1w4ANb8DiB8FRAIFNzEde4dFWVyZS7SgAibixvIJiPtywl3nJu0k9mFuy/dKWQQy/JIperfSYq8YozIfFY2Hjm2a71QD4x8vgV8/aukSqKQUgETeUevA4C9ak88H6vRwvMB9z1fa2c0PnRgztHkXzhnUsrlDK5UgavDvst1XcPaD3I3DJ/fCHdRRFpDQFIBE3UVDsYMkvGby1Np21O08tStosqDZDY5twfedG1PXVY64aZ8tnsGgUFORA7YZw/Wxo1tPqqkSqPQUgERe3+0geb61L570f9nI0rxAADxvEtQ1hyMVNuLRFkB5z1USOYkiaAqtfMNuRF8ONr4N/uLV1idQQCkAiLqjI4SRpy0HeXLubb7cfLtke6u/L4G6RDOoaSViAn4UVyt9yPMOc2HD3d2b74ruh7xSw6w6eyLlSABJxIfuyTrBwXTrvfL+Hg8cLAHPk82UtGzIkpjG92wTjaVe/kBpt1yoz/ORmgndduPYluGCg1VWJ1DgKQCI1nMNpsHLbId5cu5uvth4smak5qI43N3WJ5OZujYmsr8nvajzDMB93LZ8ChgOC25mruAe1sLoykRpJAUikhjqQfYL3f9jLO9/vYV/WiZLtsc0aMOTixvRrF4q3p+72uIST2bDoLtj6mdnuOBiumg7eta2tS6QGUwASqUEKi50s35LJuz/sYeW2QyV3ewL8vLihcyNu7taYFsEawu5SMjaZszof2wl2bxjwJHQerlmdRf4mBSCRGmBb5nEWfr+Hj37cVzKSC6Bb0/oM7hrJFR3C8PWyW1ihVIof34TPE6D4JAQ0hpvmQcRFVlcl4hIUgESqqewTRXz2837e+2EvG/dklWwPruvDDZ0bcWOXSJoG6RGISyo6CV88aC5rAdCiL1z3KtSqb21dIi5EAUikGil2OFm5/RAfrN/Hsi2ZFBY7AfD0sNG7TTCDukbSs1VDjeRyZUd3wrtDIeNnwAaXPwyXPqBZnUUqmAKQSDWweX8OH2zYy8cb93M4t6Bke+uQulzfOYJ/dGpEw7o+FlYoVSLlC/joTrPTc60GcP3/oHlvq6sScUkKQCIWycw5yac/7eeDDfvYciCnZHuD2t5cEx3O9Rc14oJwf2zq7Or6HMXw9ROwarrZbtQVbpwLAY0sLUvElSkAiVSh7PwivvjlAB9v3M+anUcwfhvF5W33oE/bYK6/qBE9WzfES4+43Ef2PvjgDkhfbbZj/g19p4Knt7V1ibg4BSCRSnai0MHyLZl8vHE/32w7SJHDKPlZlyb1uDY6nKsvDCewlr7w3M62L81HXieOmrM6X/M8tL/e6qpE3IICkEglKCh2sGr7YT77+QBLf80gv9BR8rM2oXW5JjqcqzuGa4Zmd+UogqTHTi1kGnYh3PA6NGhubV0ibkQBSKSCnCxysCLlEF/8coCkLQfJLSgu+Vmjen5cGx3ONRdG0Dq0roVViuWy0s21vPZ+b7a73Qn9poKnOrmLVCUFIJG/Ia+gmBUph1j8ywG+3nqw1J2eUH9f+rcP5ZrocDpFBqozs8CWz+Dju8xRXj4B5kKm7a6xuioRt6QAJFJO2flFfJ1ykC9+OcCKlEMU/DZXD0BEoB8D2ocyoEMYnSID8fBQ6BGguACWTYa1L5vtiM5wwxyoF2VpWSLuTAFI5BzsOZrPss2ZLNucybpdR3E4T3VkbtKgFgPah3FFh1A6RAToTo+UdnQHvDccDmw027H3QJ/JGuUlYrHzDkDffvstr7zyCmlpabz//vtEREQwf/58mjZtSo8ePSqyRpEqV+Rwsn73Mb7eepCvth5k+8HcUj9vFVKHfu1CuaJDGG3D6ir0SNl+/Qg+uRcKcsCvHgycBa37W12ViHCeAeiDDz7glltuYciQIfz4448UFJgz12ZnZzNt2jQWL15coUWKVIV9WSdYue0QK7cdYlXqYY6fPNWJ2e5ho0uTevRtF0LfdiE0aaA1uOQsik7C0ofgh9lmO/JiuGG2JjYUqUbOa7a1xx9/nFmzZvHaa6/h5eVVsv2SSy5hw4YN5T7fzJkziYqKwtfXl5iYGNatW3fGfefOnYvNZiv18vX1LbWPYRhMmjSJsLAw/Pz8iIuLY/v27eWuS1xbzskilm/O5D+f/ErvZ1dwyf99xcQPN/HFLxkcP1lM/dreXNcpghdv7sSGR/qy8M5Y7ri0mcKPnN3h7fC/uFPhp0cC3Pq5wo9INXNed4BSUlK47LLLTtseEBBAVlZWuc61cOFCEhISmDVrFjExMcyYMYP4+HhSUlIIDg4u8xh/f39SUlJK2n9+/PDUU0/xwgsvMG/ePJo2bcqjjz5KfHw8mzdvPi0sifvIKyjm+11HSd5xhOS0I/yyL5s/dOXB7mEjOjKQy1o25NJWQVzYKBC7OjFLefy0ED67H4ryoFYQXPcKtIizuioRKcN5BaDQ0FBSU1OJiooqtX3VqlU0a9asXOeaPn06I0aMYPjw4QDMmjWLzz//nDlz5jBhwoQyj7HZbISGhpb5M8MwmDFjBo888gjXXnstAG+88QYhISEsWrSIwYMHn3ZMQUFByWM8gJycnNP2kZrn4PGTbNh9jHU7j/HD7qP8uj+nVOdlgGZBtbm4eQMuaxlEbPMgAvy8znA2kbMozIcvHoQfF5jtqEvhutfAP8zaukTkjM4rAI0YMYIxY8YwZ84cbDYb+/fvJzk5mbFjx/Loo4+e83kKCwtZv349EydOLNnm4eFBXFwcycnJZzwuNzeXJk2a4HQ6ueiii5g2bRoXXHABADt37iQjI4O4uFP/1xUQEEBMTAzJycllBqDExESmTJlyznVL9ZNbUMzm/Tn8tCeLjb+99mWdOG2/iEA/ujdvQPcWDYhtFkRogO4Iyt90cAu8dysc2grYoOd46DkOPOxWVyYiZ3FeAWjChAk4nU769OlDfn4+l112GT4+PowdO5bRo0ef83kOHz6Mw+EgJCSk1PaQkBC2bt1a5jGtW7dmzpw5dOzYkezsbJ555hm6d+/Or7/+SqNGjcjIyCg5x5/P+fvP/mzixIkkJCSUtHNycoiMjDzn9yFVx+k02HvsBNsyj5OSeZwtB3LYvD+HnUfyShYW/Z3NBq1D6tI1qj5dourRJao+EYF+1hQurscwYOOb8PlYKD4BdULMuz7NelpdmYicg/MKQDabjYcffpgHH3yQ1NRUcnNzadeuHXXq1Kno+k4TGxtLbGxsSbt79+60bduWV155halTp57XOX18fPDx0TT01UVBsYODOQXsyzrBnqP57Dmaz84j+ew8nEvawTxOFDnKPC7U35cOjQKIjgykU2QgHRoFUNdXj7SkEhTkwucJ8PNCs93scrjuVahTdr9FEal+/tZEiN7e3rRr1+68jw8KCsJut5OZmVlqe2Zm5hn7+PyZl5cXnTp1IjU1FaDkuMzMTMLCTj1/z8zMJDo6+rxrlXPjdBrc8cYPBPh5EeDnRW0fO35edjztHnjYwGlAUbGTIoeTE0UOcgsc5Jwo4mheIUfyCjiSW8iRvMKz/g5vuwfNGtamdWhdWofW5YLwAC4I9yeojkKsVIGMTeYjryOpYPOAyx82R3p5nNegWhGxiKUzQXt7e9O5c2eSkpIYOHAgAE6nk6SkJO65555zOofD4WDTpk1cccUVADRt2pTQ0FCSkpJKAk9OTg5r165l1KhRlfE25A9yThbx1daDf/s83p4ehAf4Elm/Fo3q1SKqQS2aBtWmWcM6RDWohaddXzZSxQwDfpgDSyaCowDqhptz+zTpbnVlInIeLF8KIyEhgWHDhtGlSxe6devGjBkzyMvLKxkVNnToUCIiIkhMTATgscce4+KLL6ZFixZkZWXx9NNPs3v3bu644w7AfDx333338fjjj9OyZcuSYfDh4eElIUsqj7enB0/d0JFjeYXknCwir8DBySIHRQ4DAwMbNrw9bXh6eFDLx05tb0/q+npSv7Y3DWr7UL+2N2EBvgTW8tLsylJ9nMyGT8eYMzsDtOxnzupcu4G1dYnIebM8AA0aNIhDhw4xadIkMjIyiI6OZsmSJSWdmNPT0/H4w63lY8eOMWLECDIyMqhXrx6dO3dm9erVpR7FjRs3jry8PEaOHElWVhY9evRgyZIlmgOoCtTy9uSmLupALi5k3wZ4fzgc2wUenhD3H7j4bj3yEqnhbIbx57EzkpOTQ0BAANnZ2fj7+1tdjohYwemEtbNg2SRwFkFAY3MF98iuVlcmImdQnu9vy+8AiYhUO7kHYdEoSF1utttcBde+ZC5oKiIuQQFIROSPti8zw0/eIfD0hX6PQ9c7zImlRMRlKACJiIC5gvvy/8Dal812cDu4fjaEnP9UHyJSfSkAiYgc3Aof3AGZm8x2tzuh7xTw0szhIq5KAUhE3JdhwPrXYclD5nIWtRrAwJehVbzVlYlIJVMAEhH3lH8UPhkNWz8z2817m+Gn7rnNQi8iNZsCkIi4nx3fwEd3wvED4OH129w+d2luHxE3ogAkIu7DUQRfPwGrZgAGNGhpLmcRdqHVlYlIFVMAEhH3cCTN7Oi8f4PZvmgY9E8E79rW1iUillAAEhHXZhjw09uw+EEozAXfQLjmBWh3rdWViYiFFIBExHWdyILPE+CXD8x2kx5w3SsQ0MjSskTEegpAIuKa0teaj7yy08Fmh8snQo8E8LBbXZmIVAMKQCLiWhzF8O0z8M2TYDghsIk5o7MWMRWRP1AAEhHXkZUOH4yAPWvMdsdBcMUz4Hv2VaFFxP0oAImIa/jlA/j0fijIBu+6cOWzcOEgq6sSkWpKAUhEaraC4/DFeNj4ptmO6ALX/w/qN7W2LhGp1hSARKTm2rfe7Oh8dAdgg8vGQs/xYPeyujIRqeYUgESk5nE6YfUL8NVUcBaDfwRc9ypE9bC6MhGpIRSARKRmyd4Li0bBzpVmu+01cPXzUKu+tXWJSI2iACQiNcfP78HnD5gdnb1qwYAnodMtYLNZXZmI1DAKQCJS/Z04Zgaf32d0jugM/3gVglpYW5eI1FgKQCJSvaV9DYvuguP7zRmde46DS8eCXX++ROT86S+IiFRPRSdg+RRY+7LZrt8crnsNGnW2ti4RcQkKQCJS/ezfCB+OhMMpZrvL7dBvKnjXtrQsEXEdCkAiUn04HfDdDPh6mjm8vU4IXDsTWva1ujIRcTEKQCJSPRzdCR/9+9Q6Xm2ugqtfgNoNrK1LRFySApCIWMsw4McFsGQCFOaa63hd8RRceLOGt4tIpVEAEhHr5B2GT8fA1s/MduPu8I+XoV6UpWWJiOtTABIRa6QsgU/ugbxD4OEFvR+B7qPBw251ZSLiBhSARKRqFeTClw/D+rlmu2Fbcx2vsI6WliUi7kUBSESqzp7v4aORv63eDsTeA70fBS9fa+sSEbejACQilc9RBN88Bd8+A4bTXL194MvQrKfVlYmIm/KwugCAmTNnEhUVha+vLzExMaxbt+6cjnvnnXew2WwMHDiw1PZbb70Vm81W6tW/f/9KqFxE/tKhFJjdF1Y+ZYafDjfBqNUKPyJiKcvvAC1cuJCEhARmzZpFTEwMM2bMID4+npSUFIKDg8943K5duxg7diyXXnppmT/v378/r7/+eknbx8enwmsXkbNwOiB5Jnz1ODgKwDcArnoO2l9vdWUiItbfAZo+fTojRoxg+PDhtGvXjlmzZlGrVi3mzJlzxmMcDgdDhgxhypQpNGvWrMx9fHx8CA0NLXnVq1fvjOcrKCggJyen1EtE/oYjafD6FbDsUTP8tIiDu9Yo/IhItWFpACosLGT9+vXExcWVbPPw8CAuLo7k5OQzHvfYY48RHBzM7bfffsZ9VqxYQXBwMK1bt2bUqFEcOXLkjPsmJiYSEBBQ8oqMjDy/NyTi7pxOWPsKvHyJOaOzd11zNuch74N/uNXViYiUsPQR2OHDh3E4HISEhJTaHhISwtatW8s8ZtWqVcyePZuNGzee8bz9+/fnuuuuo2nTpqSlpfHQQw8xYMAAkpOTsdtPn2Nk4sSJJCQklLRzcnIUgkTK69hu+Phu2PWt2W56mbmOV2Bja+sSESmD5X2AyuP48ePccsstvPbaawQFBZ1xv8GDB5f8c4cOHejYsSPNmzdnxYoV9OnT57T9fXx81EdI5HwZhjmnz5ePmEtZeNWCvo+ZK7h7WP6UXUSkTJYGoKCgIOx2O5mZmaW2Z2ZmEhoaetr+aWlp7Nq1i6uvvrpkm9PpBMDT05OUlBSaN29+2nHNmjUjKCiI1NTUMgOQiJyn7H3wyWhISzLbjWPNuz4NTv/vUESkOrH0f8+8vb3p3LkzSUlJJducTidJSUnExsaetn+bNm3YtGkTGzduLHldc801XH755WzcuPGMj6327t3LkSNHCAsLq7T3IuJWDAM2vgX/jTXDj90H+j0Bt36u8CMiNYLlj8ASEhIYNmwYXbp0oVu3bsyYMYO8vDyGDx8OwNChQ4mIiCAxMRFfX1/at29f6vjAwECAku25ublMmTKF66+/ntDQUNLS0hg3bhwtWrQgPj6+St+biEs6nmkuYLrtC7Md0RkGzoKGraytS0SkHCwPQIMGDeLQoUNMmjSJjIwMoqOjWbJkSUnH6PT0dDzK0Y/Abrfz888/M2/ePLKysggPD6dfv35MnTpV/XxE/g7DgF8+gMVj4cQxcwHTyydC9zFgt/xPiYhIudgMwzCsLqK6ycnJISAggOzsbPz9/a0uR8R6eYfh8wTY/LHZDu0I/5gFIRdYW5eIyB+U5/tb/9smIme35VP49D7IPwwennDpWLhsLNi9rK5MROS8KQCJSNlOHIPF42DTu2a7YVvzrk94tKVliYhUBAUgETndti/N4e25GWDzgEvGQK+J4Kl+dCLiGhSAROSUk9mw9CH4cYHZbtASBr4MkV2trUtEpIIpAImIKe1r+PgeyNkL2ODiu6DPo+DlZ3VlIiIVTgFIxN2dzIZlk8zlLADqRZl3fZp0t7IqEZFKpQAk4s62L4dP74WcfWa76x0QNwV86lhbl4hIJVMAEnFHJ47B0odh45tmu14UXPMSNL3U0rJERKqKApCIu0n5wpzXJzcDs6/PKOj9CHjXtroyEZEqowAk4i7yj8IX42DTe2a7QQtz5fbGF1tbl4iIBRSARNzB5o/h8wcg75A5r0/sPXD5QxrhJSJuSwFIxJXlHjIXL928yGw3bGPe9WnUxdKyRESspgAk4ooMA35+F5aMNzs82+zQ437oOU6zOYuIoAAk4nqy9sBn90PqMrMd0gGufUlreImI/IECkIircDrhh9mw/D9QmAt2b+g53lzHSyu3i4iUogAk4goOp5qLl6avNtuRMea8Pg1bWVuXiEg1pQAkUpM5iiH5Rfg6ERwF4FUb4v5jzujs4WF1dSIi1ZYCkEhNdeBn+OQeOPCT2W7eB66eAYGNLS1LRKQmUAASqWmKTsLKp2DVDDAc4BsI/f8PLhwMNpvV1YmI1AgKQCI1ye7V8Mm9cGS72W43EK54GuoEW1qWiEhNowAkUhOcyILlk2H9XLNdJwSufBbaXm1lVSIiNZYCkEh1ZhjmMhZfjIPcTHNb51shbgr4BVpZmYhIjaYAJFJdZe8zl7FIWWy2G7SEq5+HqEusrUtExAUoAIlUN04HfD8bkh6DwuPg4WUuY3HpA+Dla3V1IiIuQQFIpDrJ3Ayf3gt7vzfbjbrBNS9AcFtr6xIRcTEKQCLVQdFJWPk0fDcDnMXgXRfiJkOX2zWhoYhIJVAAErHarlXw6Rg4kmq2W19pDm0PiLC2LhERF6YAJGKVE8dg2STY8IbZrhNiBp+212hCQxGRSqYAJFLVDAM2vQ9LJ0LeIXObhraLiFQpBSCRqnQkDT5PgB0rzHZQK7hqhoa2i4hUMQUgkapQXADfPQ8rnzFXbbf7wGUPwiX3gqeP1dWJiLgdBSCRyrZrFXx636n1u5pdbi5j0aC5pWWJiLizajG+dubMmURFReHr60tMTAzr1q07p+PeeecdbDYbAwcOLLXdMAwmTZpEWFgYfn5+xMXFsX379kqoXOQs8o7Aortg7pVm+KkdDNfPhls+UvgREbGY5QFo4cKFJCQkMHnyZDZs2MCFF15IfHw8Bw8ePOtxu3btYuzYsVx66aWn/eypp57ihRdeYNasWaxdu5batWsTHx/PyZMnK+ttiJxiGPDjAnipC2x8E7BBl9vgnu+hww0a4SUiUg3YDMMwrCwgJiaGrl278tJLLwHgdDqJjIxk9OjRTJgwocxjHA4Hl112GbfddhvffvstWVlZLFq0CDDv/oSHh/PAAw8wduxYALKzswkJCWHu3LkMHjz4tPMVFBRQUFBQ0s7JySEyMpLs7Gz8/f0r+B2LSzuUAp/dD7u/M9sh7c1OzpFdLS1LRMQd5OTkEBAQcE7f35beASosLGT9+vXExcWVbPPw8CAuLo7k5OQzHvfYY48RHBzM7bffftrPdu7cSUZGRqlzBgQEEBMTc8ZzJiYmEhAQUPKKjIz8G+9K3FLRCUiaCi9fYoYfr1rQdyqMXKHwIyJSDVnaCfrw4cM4HA5CQkJKbQ8JCWHr1q1lHrNq1Spmz57Nxo0by/x5RkZGyTn+fM7ff/ZnEydOJCEhoaT9+x0gkXOSmgSfPwDHdprtVgPgiqcgsLG1dYmIyBnVqFFgx48f55ZbbuG1114jKCiows7r4+ODj4+GIks55RyALx+GXz4w23XDzeDT5ir18xERqeYsDUBBQUHY7XYyMzNLbc/MzCQ0NPS0/dPS0ti1axdXX311yTan0wmAp6cnKSkpJcdlZmYSFhZW6pzR0dGV8C7E7TiKYd2r8PU0KDwONg+I+Tdc/hD41LW6OhEROQeW9gHy9vamc+fOJCUllWxzOp0kJSURGxt72v5t2rRh06ZNbNy4seR1zTXXcPnll7Nx40YiIyNp2rQpoaGhpc6Zk5PD2rVryzynSLmkr4FXe5rLWBQeh4guZj+f/okKPyIiNYjlj8ASEhIYNmwYXbp0oVu3bsyYMYO8vDyGDx8OwNChQ4mIiCAxMRFfX1/at29f6vjAwECAUtvvu+8+Hn/8cVq2bEnTpk159NFHCQ8PP22+IJFzlncYlk2GjQvMtl89iPsPdBoKHpbPJiEiIuVkeQAaNGgQhw4dYtKkSWRkZBAdHc2SJUtKOjGnp6fjUc4vmHHjxpGXl8fIkSPJysqiR48eLFmyBF9f38p4C+LKnE7YMBeWT4GTWea2i4ZCn/9A7QYWFiYiIn+H5fMAVUflmUdAXNj+H83RXfvWm+2QDnDVdIjsZm1dIiJSpvJ8f1t+B0ik2jmRBV89Dj/MBsMJ3nWh9yPQ9Q6w6z8ZERFXoL/mIr9zOuHnd2DZJMg7ZG7rcCP0exzqnj4qUUREai4FIBGA/Rth8YOw97eFeBu0NFdsb9bT0rJERKRyKACJe8s/+tvjrjmAAV61odd4iBkFnt5WVyciIpVEAUjck9MBP843R3edOGpua38D9JsK/uHW1iYiIpVOAUjcz971sPgBc5QXQHA7uOJpiOphbV0iIlJlFIDEfeQdhqQpsGE+YICPv7l8Rdc7wO5ldXUiIlKFFIDE9TkdZh+fr6bCyWxz24X/hL5ToE6wtbWJiIglFIDEte1eDV+Mg4xNZju0I1zxDDSOsbYuERGxlAKQuKbsveZ8Pr98YLZ9A6HPo9B5OHjYLS1NRESspwAkrqXoBKx+EVY9B0X5gA063wq9H9XaXSIiUkIBSFyDYcCWT+HLhyEr3dzWuDsMeBLCOlpbm4iIVDsKQFLzZW6GJeNh50qz7R9hzudzwXVgs1lbm4iIVEsKQFJz5R+FFYnw/WwwHGD3gUvGQI/7wLu21dWJiEg1pgAkNY/TAetfh6+eODWLc9trzEVL6zWxtjYREakRFICkZtm5EpZMhMxfzHbDtmY/Hy1aKiIi5aAAJDXDkTRzWPvWz8y2bwBc/gh0uQ3s+hiLiEj56JtDqreT2bDyaVgzC5xFYLND19uh10SoVd/q6kREpIZSAJLqyemADW/AV49D/mFzW/M+ED8NgttYW5uIiNR4CkBS/ez4BpY+dKqfT4OWZvBp2VfD2kVEpEIoAEn1cSQNvnwUUj43276B5qOurrdrtXYREalQCkBivTL7+dwBvSaon4+IiFQKBSCxjqMYNsyDr6ed6ufTIs583NWwtbW1iYiIS1MAkqpnGJC6HL58BA5tNbcFtTrVz0dERKSSKQBJ1cr81Qw+aV+Zbb/65qOuLrepn4+IiFQZBSCpGscz4esn4Mf5YDjB7g0xd8KlY8Ev0OrqRETEzSgASeUqzIc1M2HVDCjMNbe1Gwhx/4H6TS0sTERE3JkCkFQOpxM2vQtJj0HOPnNbRGezn0/ji62tTURE3J4CkFS8Hd+Y/XwyfjbbAZHmHZ8LrgMPD0tLExERAQUgqUgHt5oLlm5farZ9/OHSBIj5N3j5WVubiIjIHygAyd+Xe9Ccy2fDPLODs4cndLkdeo6H2g2srk5EROQ01eJ5xMyZM4mKisLX15eYmBjWrVt3xn0//PBDunTpQmBgILVr1yY6Opr58+eX2ufWW2/FZrOVevXv37+y34b7KcyHb56GFzrB+tfN8NPmKrhrLVzxlMKPiIhUW5bfAVq4cCEJCQnMmjWLmJgYZsyYQXx8PCkpKQQHB5+2f/369Xn44Ydp06YN3t7efPbZZwwfPpzg4GDi4+NL9uvfvz+vv/56SdvHx6dK3o9bcDrgp7fhqyfg+H5zW0Rn6PcENIm1tjYREZFzYDMMw7CygJiYGLp27cpLL70EgNPpJDIyktGjRzNhwoRzOsdFF13ElVdeydSpUwHzDlBWVhaLFi06r5pycnIICAggOzsbf3//8zqHy0pdDl9OgoO/mu3Axqc6OGuldhERsVB5vr8tfQRWWFjI+vXriYuLK9nm4eFBXFwcycnJf3m8YRgkJSWRkpLCZZddVupnK1asIDg4mNatWzNq1CiOHDlyxvMUFBSQk5NT6iV/cuBneGMgLLjeDD++AdDvcbjnB2h/vcKPiIjUKJY+Ajt8+DAOh4OQkJBS20NCQti6desZj8vOziYiIoKCggLsdjv//e9/6dv31BpS/fv357rrrqNp06akpaXx0EMPMWDAAJKTk7Hb7aedLzExkSlTplTcG3MlWXvMGZx/egcwzBmcu42ESx/QSu0iIlJjWd4H6HzUrVuXjRs3kpubS1JSEgkJCTRr1oxevXoBMHjw4JJ9O3ToQMeOHWnevDkrVqygT58+p51v4sSJJCQklLRzcnKIjIys9PdRrZ3Mhm+nw5qXwVFgbmt/A/R5FOpFWVqaiIjI32VpAAoKCsJut5OZmVlqe2ZmJqGhoWc8zsPDgxYtWgAQHR3Nli1bSExMLAlAf9asWTOCgoJITU0tMwD5+Piok/TvigvhhznwzZNw4qi5rUkP6PeY2dFZRETEBVjaB8jb25vOnTuTlJRUss3pdJKUlERs7LmPJnI6nRQUFJzx53v37uXIkSOEhYX9rXpdmmHArx/BzG6wZLwZfoJawc3vwK2fKfyIiIhLsfwRWEJCAsOGDaNLly5069aNGTNmkJeXx/DhwwEYOnQoERERJCYmAmZ/nS5dutC8eXMKCgpYvHgx8+fP5+WXXwYgNzeXKVOmcP311xMaGkpaWhrjxo2jRYsWpYbJyx+krzWXrtj72/xLtYPh8onQaSjYLf+IiIiIVDjLv90GDRrEoUOHmDRpEhkZGURHR7NkyZKSjtHp6el4/GH9qLy8PO666y727t2Ln58fbdq0YcGCBQwaNAgAu93Ozz//zLx588jKyiI8PJx+/foxdepUPeb6syNpsPw/sOUTs+1VC7qPNl8+dS0tTUREpDJZPg9QdeTy8wDlH4WVT8O618BZBDYP6PQv6PUQ+OsxoYiI1Ezl+f62/A6QVKHiQvj+NfjmKTiZZW5rEQd9p0JIO0tLExERqUoKQO7AMMzHXMsmw7Gd5rbgC6DfVGhx+qg4ERERV6cA5Or2b4QlEyF9tdmuEwKXP2w+8vI4fVJIERERd6AA5KqOZ0LSY7DxTcAATz+zc/MlY8CnjtXViYiIWEoByNUUF8Ca/8LKZ6Aw19zW4SaImwwBjaytTUREpJpQAHIl25fDF+PgaJrZjugM/Z+EyK7W1iUiIlLNKAC5gqM7YelDkLLYbNcJgb6PmXd+PCyd7FtERKRaUgCqyRxFkPwSrPg/KD4JHp4Q82/oOR58XXD+IhERkQqiAFRT7dsAn9wLmZvMdtSlcMUzENzG2rpERERqAAWgmqYgF76eBmtfBsMJfvWg3xMQ/U+w2ayuTkREpEZQAKpJdq2Cj0ZBdrrZ7nAjxCdCnYbW1iUiIlLDKADVBMUF8NXjsPpFwICAxnDVdGjZ1+rKREREaiQFoOru6E54dyhk/Gy2O90C/RO1WruIiMjfoABUnW1dDB/9Gwqywa8+XPMitL3K6qpERERqPAWg6sgwzBXbV0wz2426wY2vayZnERGRCqIAVN0UF8In98DPC812zL+h71Tw9La2LhEREReiAFSdFJ0w+/ts/xJsdrjyWegy3OqqREREXI4CUHVRXABvD4YdK8DTFwa9CS3jrK5KRETEJSkAVQdOJywaZYYf7zrwz4UQ1cPqqkRERFyWVsqsDpL+A798YK7lNfhNhR8REZFKpgBktR/mwHfPm/987Uxo1svSckRERNyBApCVDvwEX4w3//nyR+DCwdbWIyIi4iYUgKxSdALevx0chdD6CrhsrNUViYiIuA0FIKusSIQj26FOqPnoSyu5i4iIVBkFICtkbPptYVPgquegVn1r6xEREXEzCkBVzTBg8YNgOKHdQGhzhdUViYiIuB0FoKq25RNITwZPP4h/wupqRERE3JICUFVyFEPSY+Y/dx+txU1FREQsogBUlX56C46kQq0GcMm9VlcjIiLithSAqtKJLPPRV4/7waeu1dWIiIi4La0FVpUuuRc63gQ+/lZXIiIi4tYUgKpa3VCrKxAREXF71eIR2MyZM4mKisLX15eYmBjWrVt3xn0//PBDunTpQmBgILVr1yY6Opr58+eX2scwDCZNmkRYWBh+fn7ExcWxffv2yn4bIiIiUkNYHoAWLlxIQkICkydPZsOGDVx44YXEx8dz8ODBMvevX78+Dz/8MMnJyfz8888MHz6c4cOHs3Tp0pJ9nnrqKV544QVmzZrF2rVrqV27NvHx8Zw8ebKq3paIiIhUYzbDMAwrC4iJiaFr16689NJLADidTiIjIxk9ejQTJkw4p3NcdNFFXHnllUydOhXDMAgPD+eBBx5g7Fhzfa3s7GxCQkKYO3cugwf/9YKjOTk5BAQEkJ2djb+/+uuIiIjUBOX5/rb0DlBhYSHr168nLi6uZJuHhwdxcXEkJyf/5fGGYZCUlERKSgqXXXYZADt37iQjI6PUOQMCAoiJiTnjOQsKCsjJySn1EhEREddlaQA6fPgwDoeDkJCQUttDQkLIyMg443HZ2dnUqVMHb29vrrzySl588UX69u0LUHJcec6ZmJhIQEBAySsyMvLvvC0RERGp5izvA3Q+6taty8aNG/n+++954oknSEhIYMWKFed9vokTJ5KdnV3y2rNnT8UVKyIiItWOpcPgg4KCsNvtZGZmltqemZlJaOiZh4t7eHjQokULAKKjo9myZQuJiYn06tWr5LjMzEzCwsJKnTM6OrrM8/n4+ODj4/M3342IiIjUFJbeAfL29qZz584kJSWVbHM6nSQlJREbG3vO53E6nRQUFADQtGlTQkNDS50zJyeHtWvXluucIiIi4rosnwgxISGBYcOG0aVLF7p168aMGTPIy8tj+PDhAAwdOpSIiAgSExMBs79Oly5daN68OQUFBSxevJj58+fz8ssvA2Cz2bjvvvt4/PHHadmyJU2bNuXRRx8lPDycgQMHWvU2RUREpBqxPAANGjSIQ4cOMWnSJDIyMoiOjmbJkiUlnZjT09Px8Dh1oyovL4+77rqLvXv34ufnR5s2bViwYAGDBg0q2WfcuHHk5eUxcuRIsrKy6NGjB0uWLMHX17fK35+IiIhUP5bPA1QdaR4gERGRmqfGzAMkIiIiYgUFIBEREXE7lvcBqo5+fyqoGaFFRERqjt+/t8+ld48CUBmOHDkCoBmhRUREaqDjx48TEBBw1n0UgMpQv359wByB9lcX0B3k5OQQGRnJnj173L5TuK5Faboepel6nKJrUZquxymVeS0Mw+D48eOEh4f/5b4KQGX4fdh9QECA239Q/8jf31/X4ze6FqXpepSm63GKrkVpuh6nVNa1ONcbF+oELSIiIm5HAUhERETcjgJQGXx8fJg8ebIWSP2Nrscpuhal6XqUputxiq5Faboep1SXa6GZoEVERMTt6A6QiIiIuB0FIBEREXE7CkAiIiLidhSARERExO24ZQDat28f//rXv2jQoAF+fn506NCBH3744Yz7r1ixApvNdtorIyOjCquuHFFRUWW+t7vvvvuMx7z33nu0adMGX19fOnTowOLFi6uw4spV3usxd+7c0/b19fWt4qorh8Ph4NFHH6Vp06b4+fnRvHlzpk6d+pdr7KxYsYKLLroIHx8fWrRowdy5c6um4Ep2PtfDlf92HD9+nPvuu48mTZrg5+dH9+7d+f777896jKt+NqD818OVPhsrV67k6quvJjw8HJvNxqJFi0r93DAMJk2aRFhYGH5+fsTFxbF9+/a/PO/MmTOJiorC19eXmJgY1q1bV7GFG27m6NGjRpMmTYxbb73VWLt2rbFjxw5j6dKlRmpq6hmP+frrrw3ASElJMQ4cOFDycjgcVVh55Th48GCp97Rs2TIDML7++usy9//uu+8Mu91uPPXUU8bmzZuNRx55xPDy8jI2bdpUtYVXkvJej9dff93w9/cvdUxGRkbVFl1JnnjiCaNBgwbGZ599ZuzcudN47733jDp16hjPP//8GY/ZsWOHUatWLSMhIcHYvHmz8eKLLxp2u91YsmRJFVZeOc7nerjy346bbrrJaNeunfHNN98Y27dvNyZPnmz4+/sbe/fuLXN/V/5sGEb5r4crfTYWL15sPPzww8aHH35oAMZHH31U6uf/93//ZwQEBBiLFi0yfvrpJ+Oaa64xmjZtapw4ceKM53znnXcMb29vY86cOcavv/5qjBgxwggMDDQyMzMrrG63C0Djx483evToUa5jfv+gHjt2rHKKqkbGjBljNG/e3HA6nWX+/KabbjKuvPLKUttiYmKMO++8syrKq3J/dT1ef/11IyAgoGqLqiJXXnmlcdttt5Xadt111xlDhgw54zHjxo0zLrjgglLbBg0aZMTHx1dKjVXpfK6Hq/7tyM/PN+x2u/HZZ5+V2n7RRRcZDz/8cJnHuPJn43yuh6t+Nv4cgJxOpxEaGmo8/fTTJduysrIMHx8f4+233z7jebp162bcfffdJW2Hw2GEh4cbiYmJFVar2z0C++STT+jSpQs33ngjwcHBdOrUiddee+2cjo2OjiYsLIy+ffvy3XffVXKlVa+wsJAFCxZw2223YbPZytwnOTmZuLi4Utvi4+NJTk6uihKr1LlcD4Dc3FyaNGlCZGQk1157Lb/++msVVll5unfvTlJSEtu2bQPgp59+YtWqVQwYMOCMx7jy5+N8rsfvXO1vR3FxMQ6H47THvX5+fqxatarMY1z5s3E+1+N3rvbZ+LOdO3eSkZFR6t99QEAAMTExZ/x3X1hYyPr160sd4+HhQVxcXIV+XtwuAO3YsYOXX36Zli1bsnTpUkaNGsW9997LvHnzznhMWFgYs2bN4oMPPuCDDz4gMjKSXr16sWHDhiqsvPItWrSIrKwsbr311jPuk5GRQUhISKltISEhNfK59V85l+vRunVr5syZw8cff8yCBQtwOp10796dvXv3Vl2hlWTChAkMHjyYNm3a4OXlRadOnbjvvvsYMmTIGY850+cjJyeHEydOVHbJlep8roer/u2oW7cusbGxTJ06lf379+NwOFiwYAHJyckcOHCgzGNc+bNxPtfDVT8bf/b7d0N5vjcOHz6Mw+Go9O8at1sN3ul00qVLF6ZNmwZAp06d+OWXX5g1axbDhg0r85jWrVvTunXrknb37t1JS0vjueeeY/78+VVSd1WYPXs2AwYMIDw83OpSqoVzuR6xsbHExsaWtLt3707btm155ZVXmDp1alWUWWneffdd3nzzTd566y0uuOACNm7cyH333Ud4ePgZ/1txZedzPVz5b8f8+fO57bbbiIiIwG63c9FFF3HzzTezfv16q0uzRHmvhyt/NmoKt7sDFBYWRrt27Upta9u2Lenp6eU6T7du3UhNTa3I0iy1e/duli9fzh133HHW/UJDQ8nMzCy1LTMzk9DQ0Mosr8qd6/X4s9/vDLjCZ+PBBx8suevRoUMHbrnlFu6//34SExPPeMyZPh/+/v74+flVdsmV6nyuR1lc5W9H8+bN+eabb8jNzWXPnj2sW7eOoqIimjVrVub+rvzZgPJfj7K4ymfjj37/bijP90ZQUBB2u73Sv2vcLgBdcsklpKSklNq2bds2mjRpUq7zbNy4kbCwsIoszVKvv/46wcHBXHnllWfdLzY2lqSkpFLbli1bVuouiCs41+vxZw6Hg02bNrnEZyM/Px8Pj9J/Iux2O06n84zHuPLn43yuR1lc7W9H7dq1CQsL49ixYyxdupRrr722zP1c+bPxR+d6Pcriap8NgKZNmxIaGlrq331OTg5r16494797b29vOnfuXOoYp9NJUlJSxX5eKqw7dQ2xbt06w9PT03jiiSeM7du3G2+++aZRq1YtY8GCBSX7TJgwwbjllltK2s8995yxaNEiY/v27camTZuMMWPGGB4eHsby5cuteAsVzuFwGI0bNzbGjx9/2s9uueUWY8KECSXt7777zvD09DSeeeYZY8uWLcbkyZNdahi8YZTvekyZMsVYunSpkZaWZqxfv94YPHiw4evra/z6669VWXKlGDZsmBEREVEy7PvDDz80goKCjHHjxpXs8+f/Vn4f6vzggw8aW7ZsMWbOnOkyQ53P53q48t+OJUuWGF988YWxY8cO48svvzQuvPBCIyYmxigsLDQMw70+G4ZR/uvhSp+N48ePGz/++KPx448/GoAxffp048cffzR2795tGIY5DD4wMND4+OOPjZ9//tm49tprTxsG37t3b+PFF18sab/zzjuGj4+PMXfuXGPz5s3GyJEjjcDAwAqdZsTtApBhGMann35qtG/f3vDx8THatGljvPrqq6V+PmzYMKNnz54l7SeffNJo3ry54evra9SvX9/o1auX8dVXX1Vx1ZVn6dKlJfNR/FnPnj2NYcOGldr27rvvGq1atTK8vb2NCy64wPj888+rqNKqUZ7rcd999xmNGzc2vL29jZCQEOOKK64wNmzYUIXVVp6cnBxjzJgxRuPGjQ1fX1+jWbNmxsMPP2wUFBSU7PPn/1YMwxzeGx0dbXh7exvNmjUzXn/99aotvJKcz/Vw5b8dCxcuNJo1a2Z4e3sboaGhxt13321kZWWV/NydPhuGUf7r4Uqfjd+H9P/59fvfSqfTaTz66KNGSEiI4ePjY/Tp0+e0v69NmjQxJk+eXGrbiy++WPL3tVu3bsaaNWsqtG6bYfzFtK4iIiIiLsbt+gCJiIiIKACJiIiI21EAEhEREbejACQiIiJuRwFIRERE3I4CkIiIiLgdBSARERFxOwpAIiIi4nYUgERERMTtKACJiIiI21EAEhEREbfjaXUBIiJVoVevXrRv3x6A+fPn4+XlxahRo3jsscew2WwWVyciVU13gETEbcybNw9PT0/WrVvH888/z/Tp0/nf//5ndVkiYgGtBi8ibqFXr14cPHiQX3/9teSOz4QJE/jkk0/YvHmzxdWJSFXTHSARcRsXX3xxqcddsbGxbN++HYfDYWFVImIFBSARERFxOwpAIuI21q5dW6q9Zs0aWrZsid1ut6giEbGKApCIuI309HQSEhJISUnh7bff5sUXX2TMmDFWlyUiFtAweBFxG0OHDuXEiRN069YNu93OmDFjGDlypNVliYgFFIBExG14eXkxY8YMXn75ZatLERGL6RGYiIiIuB0FIBEREXE7mghRRERE3I7uAImIiIjbUQASERERt6MAJCIiIm5HAUhERETcjgKQiIiIuB0FIBEREXE7CkAiIiLidhSARERExO38Pz4TG4HHL8bAAAAAAElFTkSuQmCC",
                        "text/plain": [
                            "<Figure size 640x480 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "M = 1e6\n",
                "mu = 1e2\n",
                "p0 = 10.0\n",
                "e0 = 0.7\n",
                "T = 1.0\n",
                "\n",
                "traj = EMRIInspiral(func=Schwarzschild_PN)\n",
                "\n",
                "test = traj(M, mu, 0.0, p0, e0, 1.0, T=T, dt=10.0)\n",
                "\n",
                "traj2 = EMRIInspiral(func=SchwarzEccFlux)\n",
                "\n",
                "flux = traj2(M, mu, 0.0, p0, e0, 1.0, T=T, dt=10.0)\n",
                "\n",
                "p = test[1]\n",
                "e = test[2]\n",
                "\n",
                "plt.plot(flux[1], flux[2], label=\"flux\")\n",
                "plt.plot(p, e, label=\"pn\")\n",
                "plt.ylabel(\"e\")\n",
                "plt.xlabel(\"p\")\n",
                "\n",
                "plt.legend()\n",
                "plt.show()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "#### Modifying an existing trajectory model"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "In cases where the desired trajectory model can be expressed as a function of one that is supported out-of-the-box, the inbuilt model can be subclassed and supplemented as required by defining the `modify_rhs` method. This method takes as input the\n",
                "current system state and the corresponding derivatives produced by the model, which can then be modified as required. \n",
                "\n",
                "This method does not support a return argument for efficiency; the content of the first argument `derivs` should be modified in-place."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 20,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "array([-0.01162928, -0.00053601,  0.        ,  0.02761918,  0.02656476,\n",
                            "        0.02068311])"
                        ]
                    },
                    "execution_count": 20,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "from few.trajectory.ode.flux import KerrEccEqFlux\n",
                "\n",
                "\n",
                "class ModifiedKerrEccEqFlux(KerrEccEqFlux):\n",
                "    def modify_rhs(self, ydot, y):\n",
                "        # in-place modification of the derivatives\n",
                "        ydot[0] *= 1 + self.additional_args[0]\n",
                "        # ydot[1] *= (1 + self.additional_args[0]**0.5)\n",
                "\n",
                "\n",
                "M = 1e6\n",
                "mu = 1e2\n",
                "a = 0.7\n",
                "p = 10.0\n",
                "e = 0.3\n",
                "x = 1.0\n",
                "\n",
                "additional_args = [\n",
                "    0.01,\n",
                "]\n",
                "\n",
                "# Example usage\n",
                "modified_ode = ModifiedKerrEccEqFlux()\n",
                "modified_ode.add_fixed_parameters(M, mu, a, additional_args)\n",
                "\n",
                "modified_ode([p, e, x])"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "#### Passing additional arguments to a modified trajectory model"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "When calling a trajectory, the `additional_args` attribute of the ODE class will be populated with any positional arguments following $x_I$:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 21,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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",
                        "text/plain": [
                            "<Figure size 640x480 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "traj = EMRIInspiral(func=ModifiedKerrEccEqFlux)\n",
                "\n",
                "test = traj(M, mu, a, p, e, x, 0.01, T=T, dt=10.0)\n",
                "\n",
                "traj2 = EMRIInspiral(func=KerrEccEqFlux)\n",
                "\n",
                "flux = traj2(M, mu, a, p, e, x, T=T, dt=10.0)\n",
                "\n",
                "plt.plot(flux[1], flux[2], label=\"flux\")\n",
                "plt.plot(test[1], test[2], label=\"flux + mod\", ls=\"--\")\n",
                "plt.ylabel(\"e\")\n",
                "plt.xlabel(\"p\")\n",
                "\n",
                "plt.legend()\n",
                "plt.show()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "The flux-based stock models perform interpolation to obtain the integral fluxes $\\dot{E}$, $\\dot{L}_{z}$, and then apply a Jacobian transformation in order to obtain $\\dot{p}$, $\\dot{e}$ if these are the variables of integration (and they are by default). In some cases, the user may wish to adjust $\\dot{E}$, $\\dot{L}_z$ directly if the modifications desired are more easily computed in this parameterisation. This can be achieved similarly to what was shown above, but with the `modify_rhs_before_Jacobian` method:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 22,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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",
                        "text/plain": [
                            "<Figure size 640x480 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "# A physically-motivated example: dissipation of energy and angular momentum due to dynamical friction with an accretion disk\n",
                "# Modify the angular momentum derivative according to Eq(2.2) of https://journals.aps.org/prx/pdf/10.1103/PhysRevX.13.021035\n",
                "class KerrEccEqFluxAccretionDisk(KerrEccEqFlux):\n",
                "    def modify_rhs(self, ydot, y):\n",
                "        # in-place modification of the derivatives\n",
                "        LdotAcc = (\n",
                "            self.additional_args[0]\n",
                "            * pow(y[0] / 10.0, self.additional_args[1])\n",
                "            * 32.0\n",
                "            / 5.0\n",
                "            * pow(y[0], -7.0 / 2.0)\n",
                "        )\n",
                "        dL_dp = (\n",
                "            -3 * pow(a, 3)\n",
                "            + pow(a, 2) * (8 - 3 * y[0]) * np.sqrt(y[0])\n",
                "            + (-6 + y[0]) * pow(y[0], 2.5)\n",
                "            + 3 * a * y[0] * (-2 + 3 * y[0])\n",
                "        ) / (2.0 * pow(2 * a + (-3 + y[0]) * np.sqrt(y[0]), 1.5) * pow(y[0], 1.75))\n",
                "        # transform back to pdot from Ldot abd add GW contribution\n",
                "        # ydot[0] = (1+ LdotAcc/dL_dp) * ydot[0]\n",
                "        ydot[0] = ydot[0] + LdotAcc / dL_dp\n",
                "\n",
                "\n",
                "M = 1e6\n",
                "mu = 5e1\n",
                "a = 0.9\n",
                "p = 15.0\n",
                "# assume circular orbits, for extension to eccentricity see https://arxiv.org/pdf/2411.03436\n",
                "e = 0.0\n",
                "x = 1.0\n",
                "T = 4.0\n",
                "\n",
                "traj = EMRIInspiral(\n",
                "    func=KerrEccEqFluxAccretionDisk, integrate_constants_of_motion=False\n",
                ")\n",
                "\n",
                "test = traj(M, mu, a, p, e, x, 0.0, 8.0, T=T, dt=2.0)\n",
                "\n",
                "traj2 = EMRIInspiral(func=KerrEccEqFlux, integrate_constants_of_motion=False)\n",
                "\n",
                "flux = traj2(M, mu, a, p, e, x, T=T, dt=2.0)\n",
                "\n",
                "plt.plot(flux[0] / 86400, flux[4], label=\"flux\")\n",
                "plt.plot(test[0] / 86400, test[4], label=\"flux + mod\", ls=\"--\")\n",
                "plt.ylabel(r\"$\\Phi$\")\n",
                "plt.xlabel(\"t [days]\")\n",
                "\n",
                "plt.legend()\n",
                "plt.show()"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 23,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Requirement already satisfied: pastamarkers in /home/few/.local/few-venv/lib/python3.12/site-packages (0.1.0)\n",
                        "Requirement already satisfied: matplotlib<4.0.0,>=3.4.3 in /home/few/.local/few-venv/lib/python3.12/site-packages (from pastamarkers) (3.10.0)\n",
                        "Requirement already satisfied: numpy<2.0.0,>=1.21.2 in /home/few/.local/few-venv/lib/python3.12/site-packages (from pastamarkers) (1.26.4)\n",
                        "Requirement already satisfied: contourpy>=1.0.1 in /home/few/.local/few-venv/lib/python3.12/site-packages (from matplotlib<4.0.0,>=3.4.3->pastamarkers) (1.3.1)\n",
                        "Requirement already satisfied: cycler>=0.10 in /home/few/.local/few-venv/lib/python3.12/site-packages (from matplotlib<4.0.0,>=3.4.3->pastamarkers) (0.12.1)\n",
                        "Requirement already satisfied: fonttools>=4.22.0 in /home/few/.local/few-venv/lib/python3.12/site-packages (from matplotlib<4.0.0,>=3.4.3->pastamarkers) (4.56.0)\n",
                        "Requirement already satisfied: kiwisolver>=1.3.1 in /home/few/.local/few-venv/lib/python3.12/site-packages (from matplotlib<4.0.0,>=3.4.3->pastamarkers) (1.4.8)\n",
                        "Requirement already satisfied: packaging>=20.0 in /home/few/.local/few-venv/lib/python3.12/site-packages (from matplotlib<4.0.0,>=3.4.3->pastamarkers) (24.2)\n",
                        "Requirement already satisfied: pillow>=8 in /home/few/.local/few-venv/lib/python3.12/site-packages (from matplotlib<4.0.0,>=3.4.3->pastamarkers) (11.1.0)\n",
                        "Requirement already satisfied: pyparsing>=2.3.1 in /home/few/.local/few-venv/lib/python3.12/site-packages (from matplotlib<4.0.0,>=3.4.3->pastamarkers) (3.2.1)\n",
                        "Requirement already satisfied: python-dateutil>=2.7 in /home/few/.local/few-venv/lib/python3.12/site-packages (from matplotlib<4.0.0,>=3.4.3->pastamarkers) (2.9.0.post0)\n",
                        "Requirement already satisfied: six>=1.5 in /home/few/.local/few-venv/lib/python3.12/site-packages (from python-dateutil>=2.7->matplotlib<4.0.0,>=3.4.3->pastamarkers) (1.17.0)\n"
                    ]
                }
            ],
            "source": [
                "# some nice italian-style plotting\n",
                "!pip install pastamarkers"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 24,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "p0 = 12.141066507022591 will create a waveform that is 2.0 years long, given the other input parameters.\n",
                        "4e-06\n",
                        "Time taken for trajectory: 0.03345513343811035\n",
                        "Time taken for flux: 0.02951502799987793\n",
                        "p0 = 13.449285254725707 will create a waveform that is 3.0 years long, given the other input parameters.\n",
                        "4e-06\n",
                        "Time taken for trajectory: 0.034697771072387695\n",
                        "Time taken for flux: 0.029799699783325195\n",
                        "p0 = 14.462412588355715 will create a waveform that is 4.0 years long, given the other input parameters.\n",
                        "4e-06\n",
                        "Time taken for trajectory: 0.032881736755371094\n",
                        "Time taken for flux: 0.029918193817138672\n",
                        "p0 = 15.300552512965773 will create a waveform that is 5.0 years long, given the other input parameters.\n",
                        "4e-06\n",
                        "Time taken for trajectory: 0.03376007080078125\n",
                        "Time taken for flux: 0.029978513717651367\n",
                        "p0 = 16.02124072505033 will create a waveform that is 6.0 years long, given the other input parameters.\n",
                        "4e-06\n",
                        "Time taken for trajectory: 0.041049957275390625\n",
                        "Time taken for flux: 0.029675722122192383\n",
                        "p0 = 12.141066507022591 will create a waveform that is 2.0 years long, given the other input parameters.\n",
                        "1e-06\n",
                        "Time taken for trajectory: 0.0329432487487793\n",
                        "Time taken for flux: 0.028829574584960938\n",
                        "p0 = 13.449285254725707 will create a waveform that is 3.0 years long, given the other input parameters.\n",
                        "1e-06\n",
                        "Time taken for trajectory: 0.03320956230163574\n",
                        "Time taken for flux: 0.03012561798095703\n",
                        "p0 = 14.462412588355715 will create a waveform that is 4.0 years long, given the other input parameters.\n",
                        "1e-06\n",
                        "Time taken for trajectory: 0.036415815353393555\n",
                        "Time taken for flux: 0.03203415870666504\n",
                        "p0 = 15.300552512965773 will create a waveform that is 5.0 years long, given the other input parameters.\n",
                        "1e-06\n",
                        "Time taken for trajectory: 0.03495359420776367\n",
                        "Time taken for flux: 0.030391454696655273\n",
                        "p0 = 16.02124072505033 will create a waveform that is 6.0 years long, given the other input parameters.\n",
                        "1e-06\n",
                        "Time taken for trajectory: 0.036464691162109375\n",
                        "Time taken for flux: 0.030130863189697266\n"
                    ]
                }
            ],
            "source": [
                "# interpolate and compare the two trajectories\n",
                "from scipy.interpolate import interp1d\n",
                "from few.utils.utility import get_p_at_t\n",
                "from few.utils.constants import YRSID_SI\n",
                "from pastamarkers import markers\n",
                "import time\n",
                "\n",
                "traj_args = [M, mu, a, e0, 1.0]\n",
                "traj_kwargs = {}\n",
                "index_of_p = 3\n",
                "t_out = 1.5\n",
                "results = {\"orange\": [], \"blue\": []}\n",
                "for A, n, marker, col in zip(\n",
                "    [0.4e-5, 0.1e-5],\n",
                "    [59 / 10, 8.0],\n",
                "    [markers.tortellini, markers.ravioli],\n",
                "    [\"orange\", \"blue\"],\n",
                "):\n",
                "    for t_out in [2.0, 3.0, 4.0, 5.0, 6.0]:\n",
                "        # obtain the initial p value for the desired trajectory duration, see below for futher explanations\n",
                "        p_new = get_p_at_t(\n",
                "            traj2,\n",
                "            t_out,\n",
                "            traj_args,\n",
                "            index_of_p=3,\n",
                "            index_of_a=2,\n",
                "            index_of_e=4,\n",
                "            index_of_x=5,\n",
                "            traj_kwargs={},\n",
                "            xtol=2e-12,\n",
                "            rtol=8.881784197001252e-16,\n",
                "        )\n",
                "        print(\n",
                "            \"p0 = {} will create a waveform that is {} years long, given the other input parameters.\".format(\n",
                "                p_new, t_out\n",
                "            )\n",
                "        )\n",
                "\n",
                "        print(A)\n",
                "\n",
                "        T = 10.0\n",
                "        # T = t_out\n",
                "        tic = time.time()\n",
                "        test = traj(M, mu, a, p_new, e, x, A, 8.0, T=T, dt=10.0)\n",
                "        toc = time.time()\n",
                "        print(\"Time taken for trajectory:\", toc - tic)\n",
                "        tic = time.time()\n",
                "        flux = traj2(M, mu, a, p_new, e, x, T=T, dt=10.0)\n",
                "        toc = time.time()\n",
                "        print(\"Time taken for flux:\", toc - tic)\n",
                "\n",
                "        interp_flux = interp1d(flux[0], flux[4])\n",
                "        interp_test = interp1d(test[0], test[4])\n",
                "\n",
                "        # t = np.arange(len(flux[0]))*dt\n",
                "        if t_out == 4.0:\n",
                "            label = f\"A={A}, n={n}\"\n",
                "        else:\n",
                "            label = None\n",
                "\n",
                "        # use the shortest trajectory as the reference\n",
                "        t_f = flux[0][-1]\n",
                "        delta_phi = interp_flux(t_f) - interp_test(t_f)\n",
                "        results[col].append((t_f / YRSID_SI, delta_phi, marker, label, col, toc - tic))\n",
                "\n",
                "for A, n, marker, col in zip(\n",
                "    [0.4e-5, 0.1e-5],\n",
                "    [59 / 10, 8.0],\n",
                "    [markers.tortellini, markers.ravioli],\n",
                "    [\"orange\", \"blue\"],\n",
                "):\n",
                "    results[col] = np.array(results[col])"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 25,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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",
                        "text/plain": [
                            "<Figure size 640x480 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "plt.title(\"Dephasing vs. time to plunge $t_p$ for different accretion disk parameters\")\n",
                "plt.scatter(\n",
                "    results[\"orange\"][:, 0],\n",
                "    results[\"orange\"][:, 1],\n",
                "    color=\"orange\",\n",
                "    marker=markers.tortellini,\n",
                "    label=results[\"orange\"][:, 3][2],\n",
                "    s=200,\n",
                "    linewidth=0.2,\n",
                ")\n",
                "plt.scatter(\n",
                "    results[\"blue\"][:, 0],\n",
                "    results[\"blue\"][:, 1],\n",
                "    color=\"blue\",\n",
                "    marker=markers.ravioli,\n",
                "    label=results[\"blue\"][:, 3][2],\n",
                "    s=200,\n",
                "    linewidth=0.2,\n",
                ")\n",
                "# plt.ylim(1e-3, 1e6)\n",
                "plt.ylabel(r\"$\\Delta \\Phi_{\\Phi}$\")\n",
                "plt.xlabel(\"$t_p$ [years]\")\n",
                "plt.grid()\n",
                "# import values from https://journals.aps.org/prx/pdf/10.1103/PhysRevX.13.021035 fig 1\n",
                "plt.scatter(\n",
                "    4,\n",
                "    1e2,\n",
                "    marker=markers.farfalle,\n",
                "    label=\"PhysRevX.13.021035\",\n",
                "    s=400,\n",
                "    linewidth=0.2,\n",
                ")\n",
                "plt.legend()\n",
                "plt.show()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "The dephasing $\\Delta \\Phi_{\\Phi}$ obtained from the difference between the final orbital phase of an evolution with and without migration torques in $\\alpha-$  or $\\beta-$ accretion disks. For $\\alpha-$disks, the slope is expected to be $n=8$, for $\\beta-$ disks, $n=59/10$. The obtained value in previous work for $t_p=4 yr$ is shown in the Figure as a tortellino (see fig 1 of [PhysRevX.13.021035](https://journals.aps.org/prx/pdf/10.1103/PhysRevX.13.021035))"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 26,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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",
                        "text/plain": [
                            "<Figure size 640x480 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "plt.scatter(\n",
                "    results[\"orange\"][:, 0],\n",
                "    results[\"orange\"][:, -1],\n",
                "    color=\"orange\",\n",
                "    marker=markers.tortellini,\n",
                "    label=results[\"orange\"][:, 3][2],\n",
                "    s=200,\n",
                "    linewidth=0.2,\n",
                ")\n",
                "plt.scatter(\n",
                "    results[\"blue\"][:, 0],\n",
                "    results[\"blue\"][:, -1],\n",
                "    color=\"blue\",\n",
                "    marker=markers.ravioli,\n",
                "    label=results[\"blue\"][:, 3][2],\n",
                "    s=200,\n",
                "    linewidth=0.2,\n",
                ")\n",
                "# plt.ylim(1e-3, 1e6)\n",
                "plt.ylabel(\"Timing [s]\")\n",
                "plt.xlabel(\"$t_p$ [years]\")\n",
                "plt.grid()\n",
                "# import values from https://journals.aps.org/prx/pdf/10.1103/PhysRevX.13.021035 fig 1\n",
                "plt.legend()\n",
                "plt.show()"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "User-defined trajectories can be readily implemented in waveform models in the FEW framework - see TODO."
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "### Trajectory-related utilities"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "#### Get $p_0$ based on desired duration of trajectory"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "If you have a desired length of trajectory to analyze, this function will give you the value of $p_0$ that corresponds to the proper evolution time."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 27,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "p0 = 13.059789978787903 will create a waveform that is 1.5 years long, given the other input parameters.\n"
                    ]
                }
            ],
            "source": [
                "from few.utils.utility import get_p_at_t\n",
                "\n",
                "traj_module = EMRIInspiral(func=SchwarzEccFlux)\n",
                "\n",
                "# set initial parameters\n",
                "M = 1e6\n",
                "mu = 5e1\n",
                "e0 = 0.7\n",
                "\n",
                "traj_args = [M, mu, 0.0, e0, 1.0]\n",
                "traj_kwargs = {}\n",
                "index_of_p = 3\n",
                "\n",
                "t_out = 1.5\n",
                "# run trajectory\n",
                "p_new = get_p_at_t(\n",
                "    traj_module,\n",
                "    t_out,\n",
                "    traj_args,\n",
                "    index_of_p=3,\n",
                "    index_of_a=2,\n",
                "    index_of_e=4,\n",
                "    index_of_x=5,\n",
                "    traj_kwargs={},\n",
                "    xtol=2e-12,\n",
                "    rtol=8.881784197001252e-16,\n",
                "    bounds=None,\n",
                ")\n",
                "\n",
                "print(\n",
                "    \"p0 = {} will create a waveform that is {} years long, given the other input parameters.\".format(\n",
                "        p_new, t_out\n",
                "    )\n",
                ")"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "#### Get $\\mu$ based on desired duration of trajectory"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "If you have a desired length of trajectory to analyze, this function will give you the value of $\\mu$ that corresponds to the proper evolution time."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 28,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "mu = 18.804307109481528 will create a waveform that is 1.5 years long, given the other input parameters.\n"
                    ]
                }
            ],
            "source": [
                "from few.utils.utility import get_mu_at_t\n",
                "\n",
                "traj_module = EMRIInspiral(func=SchwarzEccFlux)\n",
                "\n",
                "# set initial parameters\n",
                "M = 1e6\n",
                "p0 = 11.0\n",
                "e0 = 0.7\n",
                "\n",
                "traj_args = [M, 0.0, p0, e0, 1.0]\n",
                "traj_kwargs = {}\n",
                "index_of_mu = 1\n",
                "\n",
                "t_out = 1.5\n",
                "# run trajectory\n",
                "mu_new = get_mu_at_t(\n",
                "    traj_module,\n",
                "    t_out,\n",
                "    traj_args,\n",
                "    index_of_mu=index_of_mu,\n",
                "    traj_kwargs=traj_kwargs,\n",
                "    xtol=2e-12,\n",
                "    rtol=8.881784197001252e-16,\n",
                "    bounds=None,\n",
                ")\n",
                "\n",
                "print(\n",
                "    \"mu = {} will create a waveform that is {} years long, given the other input parameters.\".format(\n",
                "        mu_new, t_out\n",
                "    )\n",
                ")"
            ]
        }
    ],
    "metadata": {
        "kernelspec": {
            "display_name": "few_env",
            "language": "python",
            "name": "python3"
        },
        "language_info": {
            "codemirror_mode": {
                "name": "ipython",
                "version": 3
            },
            "file_extension": ".py",
            "mimetype": "text/x-python",
            "name": "python",
            "nbconvert_exporter": "python",
            "pygments_lexer": "ipython3",
            "version": "3.10.16"
        }
    },
    "nbformat": 4,
    "nbformat_minor": 2
}