{
    "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 visualise 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 orbital phase |\n",
                "| $\\Phi_\\theta$    | Polar orbital phase|\n",
                "| $\\Phi_r$    | Radial orbital 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",
                "| KerrEccEqFlux | 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 ($m_1$ and $m_2$) and the dimensionless spin parameter of the primary ($a$):"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 2,
            "metadata": {},
            "outputs": [],
            "source": [
                "m1 = 1e6  # Solar masses\n",
                "m2 = 1e1  # Solar masses\n",
                "a = 0.0  # For a Schwarzschild inspiral, the spin parameter is zero\n",
                "\n",
                "rhs.add_fixed_parameters(m1, m2, 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 $t_\\mathrm{rr} = t \\nu$, where $\\nu = \\mu / M$ is the mass ratio of the system (for $\\mu$ and $M$ as the reduced and total mass respectively). The RHS of the ODE is therefore defined such that the $(\\dot{p}, \\dot{e}, \\dot{x}_I)$ are scaled by $\\nu^{-1}$."
            ]
        },
        {
            "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": 4,
            "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': 'pex'}"
                        ]
                    },
                    "execution_count": 4,
                    "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": [
                "# Checking the model domain of validity\n",
                "\n",
                "ODE models that interpolate over pre-computed data can only be evaluated over a finite domain. The bounds of this domain can be verified with class methods. For instance, to check the maximum eccentricity at $p=10$ for this model, we write"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 5,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "0.755"
                        ]
                    },
                    "execution_count": 5,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "rhs.max_e(10.)"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Some models, such as `KerrEccEqFlux`, perform eccentricity tapering at low $p$ as this pre-computing data is prohibitively expensive in this region. Examining it over a wide range of $p$ for a single value of $a$, we can observe the taper kicking in at $\\sim p=13$."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 6,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "Text(0, 0.5, 'Maximum eccentricity')"
                        ]
                    },
                    "execution_count": 6,
                    "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": [
                "from few.trajectory.ode import KerrEccEqFlux\n",
                "import matplotlib.pyplot as plt\n",
                "import numpy as np\n",
                "\n",
                "rhs_kerr = KerrEccEqFlux()\n",
                "\n",
                "spin = 0.8\n",
                "\n",
                "p_lim_check = np.linspace(4., 20, 101)\n",
                "e_max = np.asarray([rhs_kerr.max_e(p_here, a=spin) for p_here in p_lim_check])\n",
                "plt.plot(p_lim_check, e_max)\n",
                "plt.xlabel(\"Semi-latus rectum\")\n",
                "plt.ylabel(\"Maximum eccentricity\")"
            ]
        },
        {
            "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": 7,
            "metadata": {},
            "outputs": [],
            "source": [
                "from few.trajectory.inspiral import EMRIInspiral"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 8,
            "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": 9,
            "metadata": {},
            "outputs": [],
            "source": [
                "m1 = 1e6\n",
                "m2 = 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 = [m1, m2, a, p0, e0, xI0]"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 10,
            "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": 11,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Delta_p: 0.002\n"
                    ]
                },
                {
                    "data": {
                        "text/plain": [
                            "8.388845174067683e-13"
                        ]
                    },
                    "execution_count": 11,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "from few.utils.geodesic 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 for a requested time duration"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "By using the keyword argument `T`, the trajectory to be computed until it reaches a desired time (in years)."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 12,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "(17366327.489808623, 3155814.97635456)"
                        ]
                    },
                    "execution_count": 12,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "import matplotlib.pyplot as plt\n",
                "import numpy as np\n",
                "\n",
                "T = 0.1  # duration of trajectory in years (as defined by few.utils.constants.YRSID_SI)\n",
                "\n",
                "t_trunc, p_trunc, e_trunc, xI_trunc, Phi_phi_trunc, Phi_theta_trunc, Phi_r_trunc = traj_model(*traj_pars, T=T)\n",
                "\n",
                "t[-1], t_trunc[-1]"
            ]
        },
        {
            "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": 13,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "t1 max: 19999900.0 t2 max: 4713600.0\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": 16,
            "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: 454.85645146086296\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": 18,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "((15780,), (6,))"
                        ]
                    },
                    "execution_count": 18,
                    "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": 19,
            "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": [
                "We can also set a maximum time-step during adaptive integration:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 20,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "(1869829.3568359115, 79645.72327024862)"
                        ]
                    },
                    "execution_count": 20,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": [
                "t_adaptive = traj_model(*traj_pars, T=1.)[0]\n",
                "t_adaptive_capped = traj_model(*traj_pars, T=1., max_step_size=86400)[0]\n",
                "np.max(np.diff(t_adaptive)), np.max(np.diff(t_adaptive_capped))"
            ]
        },
        {
            "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": 21,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "-5.704414718366024e-11"
                        ]
                    },
                    "execution_count": 21,
                    "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": 22,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "(53, 32, 2.7758617626716386e-09)"
                        ]
                    },
                    "execution_count": 22,
                    "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 $(E, L, Q)$ via the `integrate_constants_of_motion` keyword. 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": 19,
            "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: [31, 44]\n",
                        "(ELQ, pex) phase difference: 3.871961234835908e-05\n"
                    ]
                }
            ],
            "source": [
                "m1 = 1e6\n",
                "m2 = 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(m1, m2, 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": [
                "### 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": 24,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "p0_new = 13.05941726854163 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 = EMRIInspiral(func=SchwarzEccFlux)\n",
                "\n",
                "# Set initial parameters\n",
                "m1 = 1e6\n",
                "m2 = 5e1\n",
                "a=0.0\n",
                "e0 = 0.7\n",
                "xI0=1.0\n",
                "\n",
                "traj_args = [m1, m2, a, e0, xI0]\n",
                "traj_kwargs = {}\n",
                "\n",
                "t_out = 1.5\n",
                "# Run trajectory\n",
                "p0_new = get_p_at_t(\n",
                "    traj,\n",
                "    t_out,\n",
                "    traj_args,\n",
                "    #index_of_a=2, # specifies the position of the index as it appears in the argument of traj\n",
                "    #index_of_p=3,\n",
                "    #index_of_e=4,\n",
                "    #index_of_x=5,\n",
                "    traj_kwargs=traj_kwargs,\n",
                "    xtol=1e-15,\n",
                "    rtol=1e-15,\n",
                "    bounds=None,\n",
                ")\n",
                "\n",
                "print(\n",
                "    \"p0_new = {} will create a waveform that is {} years long, given the other input parameters.\".format(\n",
                "        p0_new, t_out\n",
                "    )\n",
                ")"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "#### Get $m_2$ based on desired duration of trajectory"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Similarly, if you have a desired length of trajectory to analyze, this function will give you the value of $m_2$ that corresponds to the proper evolution time."
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 25,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "m2_new = 9.810595038283548 will create a waveform that is 1.5 years long, given the other input parameters.\n"
                    ]
                }
            ],
            "source": [
                "from few.utils.utility import get_m2_at_t\n",
                "\n",
                "traj = EMRIInspiral(func=SchwarzEccFlux)\n",
                "\n",
                "# Set initial parameters\n",
                "m1 = 1e6\n",
                "m2 = 5e1\n",
                "a=0.0\n",
                "e0 = 0.7\n",
                "xI0=1.0\n",
                "\n",
                "traj_args = [m1, 0.0, p0, e0, 1.0]\n",
                "traj_kwargs = {}\n",
                "index_of_m2 = 1\n",
                "\n",
                "t_out = 1.5\n",
                "# Run trajectory\n",
                "m2_new = get_m2_at_t(\n",
                "    traj,\n",
                "    t_out,\n",
                "    traj_args,\n",
                "    index_of_m2 = index_of_m2,\n",
                "    traj_kwargs=traj_kwargs,\n",
                "    xtol=1e-15,\n",
                "    rtol=1e-15,\n",
                "    bounds=None,\n",
                ")\n",
                "\n",
                "print(\n",
                "    \"m2_new = {} will create a waveform that is {} years long, given the other input parameters.\".format(\n",
                "        m2_new, t_out\n",
                "    )\n",
                ")"
            ]
        },
        {
            "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. "
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "#### Defining a new trajectory model"
            ]
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": [
                "Let's implement a Post-Newtonian trajectory in Schwarzschild eccentric as an example:"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 27,
            "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",
                "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",
                "    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": 29,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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",
                        "text/plain": [
                            "<Figure size 640x480 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "m1 = 1e6\n",
                "m2 = 1e2\n",
                "p0 = 10.0\n",
                "e0 = 0.7\n",
                "T = 1.0\n",
                "\n",
                "traj = EMRIInspiral(func=SchwarzEccFlux)\n",
                "flux = traj(m1, m2, 0.0, p0, e0, 1.0, T=T, dt=10.0)\n",
                "p,e = flux[1:3]\n",
                "\n",
                "traj_PN = EMRIInspiral(func=Schwarzschild_PN)\n",
                "flux_PN = traj_PN(m1, m2, a, p0, e0, xI0, T=T, dt=10.0)\n",
                "p_PN, e_PN = flux_PN[1:3]\n",
                "\n",
                "plt.plot(p, e, label=\"flux\")\n",
                "plt.plot(p_PN, e_PN, label=\"pn\")\n",
                "plt.ylabel(\"e\")\n",
                "plt.xlabel(\"p\")\n",
                "\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": 33,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": [
                            "(-0.011514135697943613, -0.011629277054923049)"
                        ]
                    },
                    "execution_count": 33,
                    "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",
                "\n",
                "\n",
                "m1 = 1e6\n",
                "m2 = 1e2\n",
                "a = 0.7\n",
                "p = 10.0\n",
                "e = 0.3\n",
                "xI = 1.0\n",
                "\n",
                "additional_args = [\n",
                "    0.01,\n",
                "]\n",
                "\n",
                "# Example usage\n",
                "# Example usage\n",
                "original_ode = KerrEccEqFlux()\n",
                "original_ode.add_fixed_parameters(m1, m2, a)\n",
                "\n",
                "modified_ode = ModifiedKerrEccEqFlux()\n",
                "modified_ode.add_fixed_parameters(m1, m2, a, additional_args)\n",
                "\n",
                "original_ode([p, e, xI])[0], modified_ode([p, e, xI])[0]"
            ]
        },
        {
            "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": 34,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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",
                        "text/plain": [
                            "<Figure size 640x480 with 1 Axes>"
                        ]
                    },
                    "metadata": {},
                    "output_type": "display_data"
                }
            ],
            "source": [
                "m1 = 1e6\n",
                "m2 = 1e2\n",
                "a = 0.7\n",
                "p0 = 10.0\n",
                "e0 = 0.3\n",
                "xI0 = 1.0\n",
                "\n",
                "traj_modified = EMRIInspiral(func=ModifiedKerrEccEqFlux)\n",
                "flux_modified = traj_modified(m1, m2, a, p0, e0, xI0, 0.01, T=T, dt=10.0)\n",
                "\n",
                "traj = EMRIInspiral(func=KerrEccEqFlux)\n",
                "flux = traj(m1, m2, a, p0, e0, xI0, T=T, dt=10.0)\n",
                "\n",
                "plt.plot(flux[1], flux[2], label=\"flux + mod\")\n",
                "plt.plot(flux_modified[1], flux_modified[2], label=\"flux\", 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": 35,
            "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://dx.doi.org/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 and add GW contribution\n",
                "        ydot[0] = ydot[0] + LdotAcc / dL_dp\n",
                "\n",
                "\n",
                "m1 = 1e6\n",
                "m2 = 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(func=KerrEccEqFlux, integrate_constants_of_motion=False)\n",
                "flux = traj(m1, m2, a, p0, e0, xI0, T=T, dt=2.0)\n",
                "\n",
                "traj_accretionDisk = EMRIInspiral(func=KerrEccEqFluxAccretionDisk, integrate_constants_of_motion=False)\n",
                "flux_accretionDisk = traj_accretionDisk(m1, m2, a, p0, e0, xI0, 0.0, 8.0, T=T, dt=2.0)\n",
                "\n",
                "plt.plot(flux[0] / 86400, flux[4], label=\"flux\")\n",
                "plt.plot(flux_accretionDisk[0] / 86400, flux_accretionDisk[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": 36,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "Requirement already satisfied: pastamarkers in /Users/c.chapman-bird@bham.ac.uk/miniconda3/envs/few2.0rc1/lib/python3.12/site-packages (0.1.0)\n",
                        "Requirement already satisfied: matplotlib<4.0.0,>=3.4.3 in /Users/c.chapman-bird@bham.ac.uk/miniconda3/envs/few2.0rc1/lib/python3.12/site-packages (from pastamarkers) (3.10.1)\n",
                        "Requirement already satisfied: numpy<2.0.0,>=1.21.2 in /Users/c.chapman-bird@bham.ac.uk/miniconda3/envs/few2.0rc1/lib/python3.12/site-packages (from pastamarkers) (1.26.4)\n",
                        "Requirement already satisfied: contourpy>=1.0.1 in /Users/c.chapman-bird@bham.ac.uk/miniconda3/envs/few2.0rc1/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 /Users/c.chapman-bird@bham.ac.uk/miniconda3/envs/few2.0rc1/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 /Users/c.chapman-bird@bham.ac.uk/miniconda3/envs/few2.0rc1/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 /Users/c.chapman-bird@bham.ac.uk/miniconda3/envs/few2.0rc1/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 /Users/c.chapman-bird@bham.ac.uk/miniconda3/envs/few2.0rc1/lib/python3.12/site-packages (from matplotlib<4.0.0,>=3.4.3->pastamarkers) (24.2)\n",
                        "Requirement already satisfied: pillow>=8 in /Users/c.chapman-bird@bham.ac.uk/miniconda3/envs/few2.0rc1/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 /Users/c.chapman-bird@bham.ac.uk/miniconda3/envs/few2.0rc1/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 /Users/c.chapman-bird@bham.ac.uk/miniconda3/envs/few2.0rc1/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 /Users/c.chapman-bird@bham.ac.uk/miniconda3/envs/few2.0rc1/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": 41,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": [
                        "p0_new = 12.876302295341677 will create a waveform that is 2.0 years long, given the other input parameters.\n",
                        "4e-06\n",
                        "Time taken for trajectory: 0.05723714828491211\n",
                        "Time taken for flux_accretionDisk: 0.09399986267089844\n",
                        "p0_new = 14.288498630733283 will create a waveform that is 3.0 years long, given the other input parameters.\n",
                        "4e-06\n",
                        "Time taken for trajectory: 0.06962704658508301\n",
                        "Time taken for flux_accretionDisk: 0.08910298347473145\n",
                        "p0_new = 15.382138510647557 will create a waveform that is 4.0 years long, given the other input parameters.\n",
                        "4e-06\n",
                        "Time taken for trajectory: 0.07811617851257324\n",
                        "Time taken for flux_accretionDisk: 0.06440186500549316\n",
                        "p0_new = 16.286887612296823 will create a waveform that is 5.0 years long, given the other input parameters.\n",
                        "4e-06\n",
                        "Time taken for trajectory: 0.0824270248413086\n",
                        "Time taken for flux_accretionDisk: 0.09103512763977051\n",
                        "p0_new = 17.064873248338337 will create a waveform that is 6.0 years long, given the other input parameters.\n",
                        "4e-06\n",
                        "Time taken for trajectory: 0.08822298049926758\n",
                        "Time taken for flux_accretionDisk: 0.06623005867004395\n",
                        "p0_new = 12.876302295341677 will create a waveform that is 2.0 years long, given the other input parameters.\n",
                        "1e-06\n",
                        "Time taken for trajectory: 0.0756220817565918\n",
                        "Time taken for flux_accretionDisk: 0.06400394439697266\n",
                        "p0_new = 14.288498630733283 will create a waveform that is 3.0 years long, given the other input parameters.\n",
                        "1e-06\n",
                        "Time taken for trajectory: 0.05479598045349121\n",
                        "Time taken for flux_accretionDisk: 0.0631108283996582\n",
                        "p0_new = 15.382138510647557 will create a waveform that is 4.0 years long, given the other input parameters.\n",
                        "1e-06\n",
                        "Time taken for trajectory: 0.05370283126831055\n",
                        "Time taken for flux_accretionDisk: 0.06365203857421875\n",
                        "p0_new = 16.286887612296823 will create a waveform that is 5.0 years long, given the other input parameters.\n",
                        "1e-06\n",
                        "Time taken for trajectory: 0.05735492706298828\n",
                        "Time taken for flux_accretionDisk: 0.08278703689575195\n",
                        "p0_new = 17.064873248338337 will create a waveform that is 6.0 years long, given the other input parameters.\n",
                        "1e-06\n",
                        "Time taken for trajectory: 0.07090592384338379\n",
                        "Time taken for flux_accretionDisk: 0.11389684677124023\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 = [m1, m2, a, e0, xI0]\n",
                "traj_kwargs = {}\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",
                "        p0_new = get_p_at_t(\n",
                "            traj,\n",
                "            t_out,\n",
                "            traj_args,\n",
                "            index_of_a=2,\n",
                "            index_of_p=3,\n",
                "            index_of_e=4,\n",
                "            index_of_x=5,\n",
                "            traj_kwargs=traj_kwargs,\n",
                "            xtol=1e-12,\n",
                "            rtol=1e-12,\n",
                "        )\n",
                "        print(\n",
                "            \"p0_new = {} will create a waveform that is {} years long, given the other input parameters.\".format(\n",
                "                p0_new, t_out\n",
                "            )\n",
                "        )\n",
                "\n",
                "        print(A)\n",
                "\n",
                "        T = 10.0\n",
                "        # T = t_out\n",
                "        tic = time.time()\n",
                "        flux = traj(m1, m2, a, p0_new, e0, xI0, T=T, dt=10.0)\n",
                "        toc = time.time()\n",
                "        print(\"Time taken for trajectory:\", toc - tic)\n",
                "        tic = time.time()\n",
                "        flux_accretionDisk = traj_accretionDisk(m1, m2, a, p0_new, e0, xI0, A, 8.0, T=T, dt=10.0)\n",
                "        toc = time.time()\n",
                "        print(\"Time taken for flux_accretionDisk:\", toc - tic)\n",
                "\n",
                "        interp_flux_accretionDisk = interp1d(flux_accretionDisk[0], flux_accretionDisk[4])\n",
                "        interp_flux = interp1d(flux[0], flux[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_flux_accretionDisk(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": 42,
            "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://dx.doi.org/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://dx.doi.org/10.1103/PhysRevX.13.021035))"
            ]
        },
        {
            "cell_type": "code",
            "execution_count": 43,
            "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",
                "plt.legend()\n",
                "plt.show()"
            ]
        }
    ],
    "metadata": {
        "kernelspec": {
            "display_name": "few2.0rc1",
            "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": "3.12.9"
        }
    },
    "nbformat": 4,
    "nbformat_minor": 2
}