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path: root/DiskXYZ.py
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"""
Disk Post-Processing Classes.

Loads Raw Ramses Data. Processes F(X,Y,Z) -> F(X,Y) -> F(R).
Loads/Saves Reduced Data to Numpy File.
Plots Reduced F(X,Y), F(R) Data.

@todo - Plot w/ global figure handle.
@todo - Mass flow.
@todo - Status messages.
@todo - RZ-Integrate (rho)
@todo - Save plots.

Volker Hoffmann <volker@cheleb.net>
18 August 2013
"""

from pymses import RamsesOutput
from pymses.analysis import sample_points
from helpers import mkpoints_xyz, prof1d
from scipy.integrate import simps
import numpy as np
from math import pi
import matplotlib.pyplot as plt

# Helpers
twopi = 2.0 * np.pi

class DiskBase():
    """Declarations and Initialization Methods."""

    def __init__(self, iout=1):
        # Declarations
        self.pxy = None     # Coords for Sampling, (0,1)
        self.pxyz = None
        self.xy = {"x": None, "y": None}                # Wrapped Coords
        self.xyz = {"x": None, "y": None, "z": None}    # (0,boxlen)
        self.xy0 = {"x": None, "y": None}               # (-boxlen/2, boxlen/2)
        self.xyz0 = {"x": None, "y": None}
        self.rtz = {"r": None, "theta": None, "z": None}
        self.rt = {"r": None, "theta": None}
        self.info = None
        self.Q_xy = None
        self.Q_r = None
        self.P_xy = None
        self.P_r = None
        self.rho_xy = None; self.rho_xy_max = None; self.rho_xy_min = None
        self.rho_r = None; self.rho_r_no0_max = None; self.rho_r_no0_min = None
        self.mdot_r = None;
        self.mdot_r_abs_n0_max = None; self.mdot_r_abs_no0_min = None
        self.vcart_xyz = {"vx": None, "vy": None, "vz": None}
        self.vcart_xy = {"vx": None, "vy": None, "vz": None}
        self.vcart_r = {"vx": None, "vy": None, "vz": None}
        self.vcyl_xyz = {"vr": None, "vtheta": None, "vz": None}
        self.vcyl_xy = {"vr": None, "vtheta": None, "vz": None}
        self.vcyl_r = {"vr": None, "vtheta": None, "vz": None}
        self.dset = None
        self.dl = {"dx": None, "dy": None, "dz": None}
        self.rbins_edges = None
        self.rbins_centers = None
        self.mass_total = None      # Current Mass in Box
        self.mass_disk = None       # Current Mass in Disk
        self.mass_halo = None       # Current Mass in Halo
        self.mass_total_lost_to_halo = None     # Accumulated Mass Lost to Halo
        self.mass_total_lost_to_star = None     # Accumulated Mass Lost to Star
        self.angular_momentum_total = None
        self.angular_momentum_disk = None
        self.angular_momentum_halo = None
        self.angular_momentum_lost_to_halo = None
        self.angular_momentum_lost_to_star = None
        self.infall_rate = None     # Current Infall Rate (Msolar/yr)
        self.h_xy = None        # Scale Height (AU)
        self.T_mid_xy = None    # Midplane Temperature (T)
        self.T_mid_xy_max = None; self.T_mid_xy_min = None
        self.T_mid_r = None
        self.T_mid_r_max = None; self.T_mid_r_min = None
        self.Omega_xy = None    # Angular Velocity (1/TU) @todo: sort out units
        self.rho_mid_xy = None  # Midplane Volume Density (Msolar/AU^3)
        self.rho_mid_xy_max = None; self.rho_mid_xy_min = None
        self.n_mid_xy = None    # Midplane H2 Number Density (Number/cm^3)
        self.n_mid_xy_max = None; self.n_mid_xy_min = None
        self.n_mid_r = None
        self.n_mid_r_max = None; self.n_mid_r_min = None
        self.xe_mid_xy = None   # Midplane Electron Fraction (-)
        self.xe_mid_xy_max = None; self.xe_mid_xy_min = None
        self.xe_mid_r = None
        self.xe_mid_r_max = None; self.xe_mid_r_min = None
        self.etaB_mid_xy = None # Midplane Magnetic Diffusivity (AU^2/TU)
        self.ua2_mid_xy = None  # Midplane Alfven Velocity (AU/TU)
        self.ReM_mid_xy = None  # Midplane Magnetic Reynolds Number (-)
        self.ReM_mid_xy_max = None; self.ReM_mid_xy_min = None
        self.ReM_mid_r = None
        self.ReM_mid_r_max = None; self.ReM_mid_r_min = None

        # Boundary Conditions
        self.r_accrete = None
        self.rho0 = None
        self.rho0_frac_reset = None
        self.rho0_frac_floor = None

        # Output
        self.iout = iout
        # Sampling Volume, Options
        self.nx = 128; self.ny = 128; self.nz = 128; self.nrbins = 64
        self.center = 0.5; self.radius = 0.4; self.thickness = 0.2
        # self.rbin_min = 0; self.rbin_max = 5

    def init_constants(self):
        # Thermodynamic Stuff
        kB  = 1.3806488e-23    # m2 kg s-2 K-1 / Stefan Boltzmann Constant
        amu = 1.66053892e-27   # kg            / Atomic Mass Unit
        Rsp = kB / 2. / amu    # m2 s-2 K-1    / Specific Gas Constant for H2

        # Conversion Constants
        AU = 1.49598e11        # m
        yr = 3.15569e7         # s
        TU = 1./(twopi)        # yr
        Msolar = 1.99e30       # kg

        # Rescale Gas Constant to G=1
        Rsp = Rsp * (yr**2. / AU**2.)   # AU2 yr-2 K-2
        Rsp = Rsp * (TU**2.)            # AU2 TU-2 K-2

        # Hydrogen Mass
        mass_H2 = 2. * amu          # kg
        mass_H2 = mass_H2 / Msolar  # Solar Masses

        # Ratio of Specific Heats
        gamma = 1.4

        # Potassium Abundance (-7 = Solar Abundance)
        KH = -7.

        # Add to Object
        self.AU = AU
        self.yr = yr
        self.TU = TU
        self.Rsp = Rsp
        self.gamma = gamma
        self.mass_H2 = mass_H2
        self.KH = KH

    def init_cartesian_coords(self):
        self.xyz["x"] = self.pxyz[:,0] * self.info["boxlen"]
        self.xyz["y"] = self.pxyz[:,1] * self.info["boxlen"]
        self.xyz["z"] = self.pxyz[:,2] * self.info["boxlen"]
        self.xy["x"] = self.pxy[:,0] * self.info["boxlen"]
        self.xy["y"] = self.pxy[:,1] * self.info["boxlen"]
        self.xyz0["x"] = (self.pxyz[:,0] - 0.5) * self.info["boxlen"]
        self.xyz0["y"] = (self.pxyz[:,1] - 0.5) * self.info["boxlen"]
        self.xyz0["z"] = (self.pxyz[:,2] - 0.5) * self.info["boxlen"]
        self.xy0["x"] = (self.pxy[:,0] - 0.5) * self.info["boxlen"]
        self.xy0["y"] = (self.pxy[:,1] - 0.5) * self.info["boxlen"]

    def init_cylindrical_coords(self):
        self.rt["r"] = np.sqrt(self.xy0["x"]**2. + self.xy0["y"]**2.)
        self.rt["theta"] = np.arctan2(self.xy0["y"], self.xy0["x"])
        self.rtz["r"] = np.sqrt(self.xyz0["x"]**2. + self.xyz0["y"]**2.)
        self.rtz["theta"] = np.arctan2(self.xyz0["y"], self.xyz0["x"])
        self.rtz["z"] = self.xyz0["z"]

    def init_velocities(self):
        self.vcart_xyz["vx"] = self.dset["vel"][:,0]
        self.vcart_xyz["vy"] = self.dset["vel"][:,1]
        self.vcart_xyz["vz"] = self.dset["vel"][:,2]

    def init_rbins(self):
        self.rbin_min = 0.
        self.rbin_max = np.max(self.xy0["x"])
        self.rbins_edges = np.linspace(self.rbin_min, self.rbin_max,\
                                       self.nrbins + 1)
        self.rbins_centers = (self.rbins_edges[1:] + self.rbins_edges[:-1])/2.

class DiskIo(DiskBase):
    """Load/Save Methods."""

    def load_ramses(self):
        """Load **Raw** Data."""
        # Sampling Points
        self.pxyz, self.pxy, _, _, _, self.dl = \
            mkpoints_xyz(self.center,
                         self.radius,
                         self.thickness,
                         self.nx, self.ny, self.nz)
        # Read Data
        output = RamsesOutput(".", self.iout)
        source = output.amr_source(["rho", "vel", "P"])
        self.dset = sample_points(source, self.pxyz, use_C_code=False)
        # Populate Object Fields
        self.info = output.info
        for key in self.dl: self.dl[key] = self.dl[key] * self.info["boxlen"]
        self.init_constants()
        self.init_cartesian_coords()
        self.init_cylindrical_coords()
        self.init_velocities()
        self.init_rbins()
        self.convert_velocities()
        self.load_stats()
        self.load_boundary_conditions()

    def load_npz(self):
        """Load **Reduced** Data.."""
        npz = np.load("DiskXY_%05d.npz" % self.iout)
        self.nx = npz["nx"]; self.ny = npz["ny"]; self.nz = npz["nz"]
        self.xy = npz["xy"][()]; self.xy0 = npz["xy0"][()];
        self.rt = npz["rt"][()]
        self.rbins_edges = npz["rbins_edges"]
        self.rbins_centers = npz["rbins_centers"]
        self.rbin_min = npz["rbin_min"]; self.rbin_max = npz["rbin_max"]
        self.vcart_xy = npz["vcart_xy"][()]; self.vcyl_xy = npz["vcyl_xy"][()]
        self.vcart_r = npz["vcart_r"][()]; self.vcyl_r = npz["vcyl_r"][()]
        self.rho_xy = npz["rho_xy"]; self.rho_r = npz["rho_r"]
        self.rho_xy_max = npz["rho_xy_max"]
        self.rho_xy_min = npz["rho_xy_min"]
        self.rho_r_no0_max = npz["rho_r_no0_max"]
        self.rho_r_no0_min = npz["rho_r_no0_min"]
        self.Q_xy = npz["Q_xy"]; self.Q_r = npz["Q_r"]
        self.mdot_r = npz["mdot_r"]
        self.mdot_r_abs_no0_max = npz["mdot_r_abs_no0_max"]
        self.mdot_r_abs_no0_min = npz["mdot_r_abs_no0_min"]
        self.mass_total = npz["mass_total"]
        self.mass_disk = npz["mass_disk"]
        self.mass_halo = npz["mass_halo"]
        self.mass_total_lost_to_halo = npz["mass_total_lost_to_halo"]
        self.mass_total_lost_to_star = npz["mass_total_lost_to_star"]
        self.angular_momentum_total = npz["angular_momentum_total"]
        self.angular_momentum_disk = npz["angular_momentum_disk"]
        self.angular_momentum_halo = npz["angular_momentum_halo"]
        self.angular_momentum_lost_to_star = npz["angular_momentum_lost_to_star"]
        self.angular_momentum_lost_to_halo = npz["angular_momentum_lost_to_halo"]
        self.infall_rate = npz["infall_rate"]
        self.info = npz["info"][()]
        self.h_xy = npz["h_xy"]
        self.T_mid_xy = npz["T_mid_xy"]
        self.Omega_xy = npz["Omega_xy"]
        self.rho_mid_xy = npz["rho_mid_xy"]
        self.n_mid_xy = npz["n_mid_xy"]
        self.xe_mid_xy = npz["xe_mid_xy"]
        self.etaB_mid_xy = npz["etaB_mid_xy"]
        self.ua2_mid_xy = npz["ua2_mid_xy"]
        self.ReM_mid_xy = npz["ReM_mid_xy"]
        self.T_mid_r = npz["T_mid_r"]
        self.xe_mid_r = npz["xe_mid_r"]
        self.n_mid_r = npz["n_mid_r"]
        self.ReM_mid_r = npz["ReM_mid_r"]
        self.r_accrete = npz["r_accrete"]
        self.rho0 = npz["rho0"]
        self.rho0_frac_reset = npz["rho0_frac_reset"]
        self.rho0_frac_floor = npz["rho0_frac_floor"]

    def load_boundary_conditions(self):
        """Load Boundary Conditions."""
        fpath = "output_%05d" % self.iout
        fmydisk = "mydisk_%05d.txt" % self.iout
        ff = "./%s/%s" % ( fpath, fmydisk )
        with open(ff, 'r') as f:
            lines = f.readlines()
            self.r_accrete = float(lines[13].strip().split(" | ")[1])
            self.rho0 = float(lines[14].strip().split(" | ")[1])
            self.rho0_frac_reset = float(lines[15].strip().split(" | ")[1])
            self.rho0_frac_floor = float(lines[16].strip().split(" | ")[1])

    def load_stats(self):
        """Load Stats."""
        fpath = "output_%05d" % self.iout
        fmydisk = "mydisk_%05d.txt" % self.iout
        ff = "./%s/%s" % ( fpath, fmydisk )
        fid = open(ff, 'r')
        lines = fid.readlines()
        fid.close()
        l2 = lines[2]
        l3 = lines[3]
        l4 = lines[4]
        l5 = lines[5]
        l6 = lines[6]
        l7 = lines[7]
        l8 = lines[8] # L_lost_star
        l9 = lines[9] # L_lost_halo
        l10 = lines[10] # L_disk
        l11 = lines[11] # L_halo
        l12 = lines[12] # L_tot
        self.infall_rate = float(l7[11:33]) * 2. * pi
        self.mass_total = float(l6[11:33])
        self.mass_disk = float(l4[11:33])
        self.mass_halo = float(l5[11:33])
        self.mass_total_lost_to_halo = float(l3[11:33])
        self.mass_total_lost_to_star = float(l2[11:33])
        self.angular_momentum_total = float(l12[11:33])
        self.angular_momentum_disk = float(l10[11:33])
        self.angular_momentum_halo = float(l11[11:33])
        self.angular_momentum_lost_to_star = float(l8[11:33])
        self.angular_momentum_lost_to_halo = float(l9[11:33])

    def load_npz_minmax(self):
        """Load Min/Max on **Reduced** Data."""
        npz = np.load("DiskXY_%05d.npz" % self.iout)
        self.rho_xy_max = npz["rho_xy_max"]
        self.rho_xy_min = npz["rho_xy_min"]
        self.rho_r_no0_max = npz["rho_r_no0_max"]
        self.rho_r_no0_min = npz["rho_r_no0_min"]
        self.mdot_r_abs_no0_max = npz["mdot_r_abs_no0_max"]
        self.mdot_r_abs_no0_min = npz["mdot_r_abs_no0_min"]
        self.rho_mid_xy_max = npz["rho_mid_xy_max"]
        self.rho_mid_xy_min = npz["rho_mid_xy_min"]
        self.T_mid_xy_max = npz["T_mid_xy_max"]
        self.T_mid_xy_min = npz["T_mid_xy_min"]
        self.xe_mid_xy_max = npz["xe_mid_xy_max"]
        self.xe_mid_xy_min = npz["xe_mid_xy_min"]
        self.n_mid_xy_max = npz["n_mid_xy_max"]
        self.n_mid_xy_min = npz["n_mid_xy_min"]
        self.ReM_mid_xy_max = npz["ReM_mid_xy_max"]
        self.ReM_mid_xy_min = npz["ReM_mid_xy_min"]
        self.T_mid_r_max = npz["T_mid_r_max"]
        self.T_mid_r_min = npz["T_mid_r_min"]
        self.xe_mid_r_max = npz["xe_mid_r_max"]
        self.xe_mid_r_min = npz["xe_mid_r_min"]
        self.n_mid_r_max = npz["n_mid_r_max"]
        self.n_mid_r_min = npz["n_mid_r_min"]
        self.ReM_mid_r_max = npz["ReM_mid_r_max"]
        self.ReM_mid_r_min = npz["ReM_mid_r_min"]

    def load_npz_stats(self):
        """Load Mass Stats Only."""
        npz = np.load("DiskXY_%05d.npz" % self.iout)
        self.mass_total = npz["mass_total"]
        self.mass_disk = npz["mass_disk"]
        self.mass_halo = npz["mass_halo"]
        self.mass_total_lost_to_halo = npz["mass_total_lost_to_halo"]
        self.mass_total_lost_to_star = npz["mass_total_lost_to_star"]
        self.infall_rate = npz["infall_rate"]
        self.angular_momentum_total = npz["angular_momentum_total"]
        self.angular_momentum_disk = npz["angular_momentum_disk"]
        self.angular_momentum_halo = npz["angular_momentum_halo"]
        self.angular_momentum_lost_to_star = npz["angular_momentum_lost_to_star"]
        self.angular_momentum_lost_to_halo = npz["angular_momentum_lost_to_halo"]
        self.info = npz["info"][()]

    def save_npz(self):
        """Save **Reduced** Data."""
        np.savez("DiskXY_%05d.npz" % self.iout, \
            nx = self.nx, ny = self.ny, nz = self.nz, \
            xy = self.xy, xy0 = self.xy0, rt = self.rt, \
            rbins_edges = self.rbins_edges, \
            rbins_centers = self.rbins_centers, \
            rbin_min = self.rbin_min, rbin_max = self.rbin_max, \
            vcart_xy = self.vcart_xy, vcyl_xy = self.vcyl_xy, \
            vcart_r = self.vcart_r, vcyl_r = self.vcyl_r, \
            rho_xy = self.rho_xy, rho_r = self.rho_r, \
            rho_xy_max = self.rho_xy_max, rho_xy_min = self.rho_xy_min, \
            rho_r_no0_max = self.rho_r_no0_max, \
            rho_r_no0_min = self.rho_r_no0_min, \
            Q_xy = self.Q_xy, Q_r = self.Q_r, \
            mdot_r = self.mdot_r, \
            mdot_r_abs_no0_max = self.mdot_r_abs_no0_max, \
            mdot_r_abs_no0_min = self.mdot_r_abs_no0_min, \
            mass_total = self.mass_total, \
            mass_disk = self.mass_disk, \
            mass_halo = self.mass_halo, \
            mass_total_lost_to_halo = self.mass_total_lost_to_halo, \
            mass_total_lost_to_star = self.mass_total_lost_to_star, \
            angular_momentum_disk = self.angular_momentum_disk, \
            angular_momentum_halo = self.angular_momentum_halo, \
            angular_momentum_total = self.angular_momentum_total, \
            angular_momentum_lost_to_halo = self.angular_momentum_lost_to_halo, \
            angular_momentum_lost_to_star = self.angular_momentum_lost_to_star, \
            infall_rate = self.infall_rate, \
            info = self.info, \
            h_xy = self.h_xy, \
            T_mid_xy = self.T_mid_xy, \
            T_mid_xy_max = self.T_mid_xy_max, T_mid_xy_min = self.T_mid_xy_min, \
            Omega_xy = self.Omega_xy, \
            rho_mid_xy = self.rho_mid_xy, \
            rho_mid_xy_max = self.rho_mid_xy_max, rho_mid_xy_min = self.rho_mid_xy_min, \
            n_mid_xy = self.n_mid_xy, \
            n_mid_xy_max = self.n_mid_xy_max, n_mid_xy_min = self.n_mid_xy_min, \
            xe_mid_xy = self.xe_mid_xy, \
            xe_mid_xy_max = self.xe_mid_xy_max, xe_mid_xy_min = self.xe_mid_xy_min, \
            etaB_mid_xy = self.etaB_mid_xy, \
            ua2_mid_xy = self.ua2_mid_xy, \
            ReM_mid_xy = self.ReM_mid_xy, \
            ReM_mid_xy_max = self.ReM_mid_xy_max, ReM_mid_xy_min = self.ReM_mid_xy_min, \
            T_mid_r = self.T_mid_r, \
            T_mid_r_max = self.T_mid_r_max, T_mid_r_min = self.T_mid_r_min, \
            xe_mid_r = self.xe_mid_r, \
            xe_mid_r_max = self.xe_mid_r_max, xe_mid_r_min = self.xe_mid_r_min, \
            n_mid_r = self.n_mid_r, \
            n_mid_r_max = self.n_mid_r_max, n_mid_r_min = self.n_mid_r_min, \
            ReM_mid_r = self.ReM_mid_r, \
            ReM_mid_r_max = self.ReM_mid_r_max, ReM_mid_r_min = self.ReM_mid_r_min, \
            r_accrete = self.r_accrete, \
            rho0 = self.rho0, \
            rho0_frac_reset = self.rho0_frac_reset, \
            rho0_frac_floor = self.rho0_frac_floor \
            )

class DiskReduceBase(DiskIo):
    """General Reduction Methods."""

    def integrate(self, data_xyz):
        """Numerical Z-Integrator."""
        """@todo - Weight function support."""
        data_xy = np.zeros(self.nx * self.ny)
        idx_lo = 0
        for ii in range(self.pxy.shape[0]):
            idx_hi = idx_lo + self.nz
            data_xy[ii] = simps(data_xyz[idx_lo:idx_hi], dx=self.dl["dz"])
            idx_lo = idx_hi
        return data_xy

    def average(self, data_xyz, weights_xyz=None):
        """Z-Averaging. Supports Weight Function."""
        if weights_xyz == None:
            weights_xyz = self.weights(np.ones(data_xyz.shape))
        data_xy = np.zeros(self.nx * self.ny)
        idx_lo = 0
        for ii in range(self.pxy.shape[0]):
            idx_hi = idx_lo + self.nz
            data_xy[ii] = np.sum(data_xyz[idx_lo:idx_hi] * \
                                 weights_xyz[idx_lo:idx_hi])
            idx_lo = idx_hi
        return data_xy

    def weights(self, weights_xyz):
        """Create Weight Function."""
        weights_xyz = weights_xyz.reshape(self.nx, self.ny, self.nz)
        weights_sum = np.sum(weights_xyz, axis=2)
        weights_sum = weights_sum[:,:,None]
        weights_sum = weights_sum * np.ones([self.nx, self.ny, self.nz])
        weights_xyz = weights_xyz / weights_sum
        weights_xyz = weights_xyz.reshape(self.nz * self.ny * self.nx)
        return weights_xyz

class DiskReduce(DiskReduceBase):
    """Specific Reduction Methods."""

    def integrate_to_rho_xy(self):
        """Z-Integrate Volume Density. Gives Surface Density."""
        self.rho_xy = self.integrate(self.dset["rho"])
        self.rho_xy[np.isnan(self.Omega_xy)] = np.nan
        self.rho_xy_max = np.nanmax(self.rho_xy)
        self.rho_xy_min = np.nanmin(self.rho_xy)

    def average_to_rho_r(self):
        """Theta-Averaged Surface Density."""
        self.rho_r = prof1d(self.rt["r"], self.rho_xy, self.rbins_edges)
        self.rho_r_no0_max = np.nanmax(self.rho_r[self.rho_r!=0])
        self.rho_r_no0_min = np.nanmin(self.rho_r[self.rho_r!=0])

    def integrate_to_P_xy(self):
        """Z-Integrate 3D Pressure Density. Gives 2D Pressure."""
        self.P_xy = self.integrate(self.dset["P"])

    def convert_velocities(self):
        """Cylindrical Coordinate Components of Velocities."""
        cos_theta = np.cos(self.rtz["theta"])
        sin_theta = np.sin(self.rtz["theta"])
        self.vcyl_xyz["vr"] = self.vcart_xyz["vx"] * cos_theta + \
                              self.vcart_xyz["vy"] * sin_theta
        self.vcyl_xyz["vtheta"] = - self.vcart_xyz["vx"] * sin_theta + \
                                    self.vcart_xyz["vy"] * cos_theta
        self.vcyl_xyz["vz"] = self.vcart_xyz["vz"]

    def average_velocities_to_xy(self):
        """Z-Average Velocity Components. Density Weighted."""
        weights_xyz = self.weights(self.dset["rho"])
        self.vcart_xy["vx"] = self.average(self.vcart_xyz["vx"], weights_xyz)
        self.vcart_xy["vy"] = self.average(self.vcart_xyz["vy"], weights_xyz)
        self.vcart_xy["vz"] = self.average(self.vcart_xyz["vz"], weights_xyz)
        self.vcyl_xy["vr"] = self.average(self.vcyl_xyz["vr"], weights_xyz)
        self.vcyl_xy["vtheta"] = self.average(self.vcyl_xyz["vtheta"], weights_xyz)
        self.vcyl_xy["vz"] = self.average(self.vcyl_xyz["vz"], weights_xyz)

    def average_velocities_to_r(self):
        """Theta-Averaged Velocity Components."""
        self.vcart_r["vx"] = \
            prof1d(self.rt["r"], self.vcart_xy["vx"], self.rbins_edges)
        self.vcart_r["vy"] = \
            prof1d(self.rt["r"], self.vcart_xy["vy"], self.rbins_edges)
        self.vcart_r["vz"] = \
            prof1d(self.rt["r"], self.vcart_xy["vz"], self.rbins_edges)
        self.vcyl_r["vr"] = \
            prof1d(self.rt["r"], self.vcyl_xy["vr"], self.rbins_edges)
        self.vcyl_r["vtheta"] = \
            prof1d(self.rt["r"], self.vcyl_xy["vtheta"], self.rbins_edges)
        self.vcyl_r["vz"] = \
            prof1d(self.rt["r"], self.vcyl_xy["vz"], self.rbins_edges)

    def compute_cs2_xy(self):
        self.cs2_xy = self.P_xy / self.rho_xy
        self.cs2_xy[np.isnan(self.Omega_xy)] = np.nan

    def compute_Omega_xy(self):
        self.Omega_xy = self.vcyl_xy["vtheta"] / self.rt["r"]
        self.Omega_xy[self.Omega_xy <= 1.0e-6] = np.nan

    def compute_h_xy(self):
        self.h_xy = np.sqrt(self.cs2_xy) / self.Omega_xy

    def compute_T_mid_xy(self):
        self.T_mid_xy = self.cs2_xy / self.gamma / self.Rsp
        self.T_mid_xy[np.isnan(self.Omega_xy)] = np.nan
        self.T_mid_xy_max = np.nanmax(self.T_mid_xy)
        self.T_mid_xy_min = np.nanmin(self.T_mid_xy)

    def compute_rho_mid_xy(self):
        self.rho_mid_xy = self.rho_xy / (np.sqrt(twopi) * self.h_xy)
        self.rho_mid_xy_max = np.nanmax(self.rho_mid_xy)
        self.rho_mid_xy_min = np.nanmin(self.rho_mid_xy)

    def compute_n_mid_xy(self):
        """
        Volumetric Midplane Number Density.
        """
        # (Msolar / AU^3) / Msolar = 1/AU^3
        self.n_mid_xy = self.rho_mid_xy / self.mass_H2
        self.n_mid_xy = self.n_mid_xy / self.AU**3.          # 1/m^3
        self.n_mid_xy = self.n_mid_xy / 100.**3.             # 1/cm^3
        self.n_mid_xy_max = np.nanmax(self.n_mid_xy)
        self.n_mid_xy_min = np.nanmin(self.n_mid_xy)

    def compute_xe_mid_xy(self):
        """
        Midplane Electron Fraction.
        """
        self.xe_mid_xy = 6.47e-13 * np.sqrt(10.0**self.KH) * \
                         (self.T_mid_xy / 1.0e3)**(0.75) * \
                         (2.4e15 / self.n_mid_xy)**(0.5) * \
                         np.exp(-25188. / self.T_mid_xy) / 1.15e-11
        # Prevent Underflows!
        self.xe_mid_xy[self.xe_mid_xy == 0.0]    = 1.0e-30
        self.xe_mid_xy[self.xe_mid_xy < 1.0e-30] = 1.0e-30
        self.xe_mid_xy_max = np.nanmax(self.xe_mid_xy)
        self.xe_mid_xy_min = np.nanmin(self.xe_mid_xy)

    def compute_magnetic_diffusivity(self):
        """
        Magnetic Diffusivity.
        """
        self.etaB_mid_xy = \
            230. / self.xe_mid_xy * np.sqrt(self.T_mid_xy)       # cm^2 / s
        self.etaB_mid_xy = self.etaB_mid_xy / 1000. / 1000       # m^2  / s
        self.etaB_mid_xy = self.etaB_mid_xy / self.AU / self.AU  # AU^2 / s
        self.etaB_mid_xy = self.etaB_mid_xy * self.yr            # AU^2 / yr
        self.etaB_mid_xy = self.etaB_mid_xy * self.TU            # AU^2 / TU

    def compute_alfven_speed_mid_xy(self):
        """
        Midplane Alfven Speed.

        @todo Could depend on field strength, etc.
              For now, just use some fraction of the sound speed.
        """
        factor = 0.5
        self.ua2_mid_xy = factor**2. * self.cs2_xy

    def compute_ReM_xy(self):
        """
        Midplane Magnetic Reynolds Number.
        """
        self.ReM_mid_xy = 2.0 * self.h_xy * \
                          np.sqrt(self.ua2_mid_xy) / self.etaB_mid_xy
        self.ReM_mid_xy_max = np.nanmax(self.ReM_mid_xy)
        self.ReM_mid_xy_min = np.nanmin(self.ReM_mid_xy)

    def average_to_ReM_mid_r(self):
        """Theta-Averaged Magnetic Reynolds Number."""
        self.ReM_mid_r = prof1d(self.rt["r"], self.ReM_mid_xy, self.rbins_edges)
        self.ReM_mid_r_max = np.nanmax(self.ReM_mid_r)
        self.ReM_mid_r_min = np.nanmin(self.ReM_mid_r)

    def average_to_T_mid_r(self):
        """Theta-Averaged Midplane Temperature."""
        self.T_mid_r = prof1d(self.rt["r"], self.T_mid_xy, self.rbins_edges)
        self.T_mid_r_max = np.nanmax(self.T_mid_r)
        self.T_mid_r_min = np.nanmin(self.T_mid_r)

    def average_to_n_mid_r(self):
        """Theta-Averaged Midplane Number Density."""
        self.n_mid_r = prof1d(self.rt["r"], self.n_mid_xy, self.rbins_edges)
        self.n_mid_r_max = np.nanmax(self.n_mid_r)
        self.n_mid_r_min = np.nanmin(self.n_mid_r)

    def average_to_xe_mid_r(self):
        """Theta-Averaged Midplane Electron Fraction."""
        self.xe_mid_r = prof1d(self.rt["r"], self.xe_mid_xy, self.rbins_edges)
        self.xe_mid_r_max = np.nanmax(self.xe_mid_r)
        self.xe_mid_r_min = np.nanmin(self.xe_mid_r)

    def compute_mdot_r(self):
        """Average Mass Flow."""
        """@todo Integrate Properly (rtz->rt->r). See Notes."""
        """Units: Mstar/code_time. 1yr =  code_time/2pi."""
        """So, Mstar*2*pi gives Mstar/yr. Convert in plot."""
        self.mdot_r = \
            2. * pi * self.vcyl_r["vr"] * self.rbins_centers * self.rho_r
        self.mdot_r_abs_no0_max = \
            np.nanmax(np.abs(self.mdot_r[self.mdot_r!=0]))
        self.mdot_r_abs_no0_min = \
            np.nanmin(np.abs(self.mdot_r[self.mdot_r!=0]))
        
    def compute_Q_xy(self):
        """Toomre-Q."""
        G = 1.0
        self.Q_xy = np.sqrt(self.cs2_xy) * self.Omega_xy / pi / G / self.rho_xy

    def average_to_Q_r(self):
        """Theta-Averaged Toomre-Q."""
        self.Q_r = prof1d(self.rt["r"], self.Q_xy, self.rbins_edges)

    def reduce_all(self):
        self.average_velocities_to_xy()
        self.average_velocities_to_r()
        self.compute_Omega_xy()
        self.integrate_to_P_xy()
        self.integrate_to_rho_xy()
        self.compute_cs2_xy()
        self.compute_T_mid_xy()
        self.compute_h_xy()
        self.compute_rho_mid_xy()
        self.compute_n_mid_xy()
        self.compute_xe_mid_xy()
        self.compute_magnetic_diffusivity()
        self.compute_alfven_speed_mid_xy()
        self.compute_ReM_xy()
        self.compute_Q_xy()
        self.average_to_rho_r()
        self.average_to_Q_r()
        self.average_to_xe_mid_r()
        self.average_to_ReM_mid_r()
        self.average_to_n_mid_r()
        self.average_to_T_mid_r()
        self.compute_mdot_r()

class DiskPlots(DiskReduce):
    """Plotting Routines."""

    def plot_ReM_mid_xy(self, ax_in=None, clim=None):
        ext = [np.min(self.xy0["x"]), np.max(self.xy0["x"]), \
               np.min(self.xy0["y"]), np.max(self.xy0["y"])]
        if not ax_in:
            fig = plt.figure()
            ax = fig.add_subplot(1,1,1)
        else:
            ax = ax_in
        im = ax.imshow(np.rot90(np.log10(self.ReM_mid_xy.reshape(self.nx, self.ny))), \
                       extent=ext, interpolation='none')
        ax.set_xlabel('X [AU]')
        ax.set_ylabel('Y [AU]')
        ax.set_title('Log10 Magnetic Reynolds Number [-]')
        ax.grid()
        if clim:
            im.set_clim(clim)
        plt.colorbar(im, ax=ax)
        if not ax_in:
            plt.show()

    def plot_xe_mid_xy(self, ax_in=None, clim=None):
        ext = [np.min(self.xy0["x"]), np.max(self.xy0["x"]), \
               np.min(self.xy0["y"]), np.max(self.xy0["y"])]
        if not ax_in:
            fig = plt.figure()
            ax = fig.add_subplot(1,1,1)
        else:
            ax = ax_in
        im = ax.imshow(np.rot90(np.log10(self.xe_mid_xy.reshape(self.nx, self.ny))), \
                       extent=ext, interpolation='none')
        ax.set_xlabel('X [AU]')
        ax.set_ylabel('Y [AU]')
        ax.set_title('Log10 Midplane Electron Fraction [-]')
        ax.grid()
        if clim:
            im.set_clim(clim)
        plt.colorbar(im, ax=ax)
        if not ax_in:
            plt.show()

    def plot_n_mid_xy(self, ax_in=None, clim=None):
        ext = [np.min(self.xy0["x"]), np.max(self.xy0["x"]), \
               np.min(self.xy0["y"]), np.max(self.xy0["y"])]
        if not ax_in:
            fig = plt.figure()
            ax = fig.add_subplot(1,1,1)
        else:
            ax = ax_in
        im = ax.imshow(np.rot90(np.log10(self.n_mid_xy.reshape(self.nx, self.ny))), \
                       extent=ext, interpolation='none')
        ax.set_xlabel('X [AU]')
        ax.set_ylabel('Y [AU]')
        ax.set_title('Log10 Midplane H2 Number Density [1/cm^3]')
        ax.grid()
        if clim:
            im.set_clim(clim)
        plt.colorbar(im, ax=ax)
        if not ax_in:
            plt.show()

    def plot_T_mid_xy(self, ax_in=None, clim=None):
        ext = [np.min(self.xy0["x"]), np.max(self.xy0["x"]), \
               np.min(self.xy0["y"]), np.max(self.xy0["y"])]
        if not ax_in:
            fig = plt.figure()
            ax = fig.add_subplot(1,1,1)
        else:
            ax = ax_in
        im = ax.imshow(np.rot90(self.T_mid_xy.reshape(self.nx, self.ny)), \
                       extent=ext, interpolation='none')
        ax.set_xlabel('X [AU]')
        ax.set_ylabel('Y [AU]')
        ax.set_title('Midplane Temperature [K]')
        ax.grid()
        if clim:
            im.set_clim(clim)
        plt.colorbar(im, ax=ax)
        if not ax_in:
            plt.show()

    def plot_rho_xy(self, ax_in=None, clim=None):
        ext = [np.min(self.xy0["x"]), np.max(self.xy0["x"]), \
               np.min(self.xy0["y"]), np.max(self.xy0["y"])]
        if not ax_in:
            fig = plt.figure()
            ax = fig.add_subplot(1,1,1)
        else:
            ax = ax_in
        im = ax.imshow(np.rot90(np.log10(self.rho_xy.reshape(self.nx, self.ny))), \
                       extent=ext, interpolation='none')
        ax.set_xlabel('X [AU]')
        ax.set_ylabel('Y [AU]')
        ax.set_title('Log10 Surface Density [Mstar/AU^2]')
        ax.grid()
        if clim:
            im.set_clim(clim)
        plt.colorbar(im, ax=ax)
        if not ax_in:
            plt.show()

    def plot_T_mid_r(self, ax_in=None, ylim=None):
        # Cut Out Empty Bins
        T_mid_r = self.T_mid_r
        rbins_centers = self.rbins_centers
        T_mid_r[T_mid_r == 0.0] = np.nan
        rbins_centers = rbins_centers[~np.isnan(T_mid_r)]
        T_mid_r = T_mid_r[~np.isnan(T_mid_r)]
        # Plot
        if not ax_in:
            fig = plt.figure()
            ax = fig.add_subplot(1,1,1)
        else:
            ax = ax_in
        ax.plot(rbins_centers, T_mid_r, 'bs-')
        ax.set_yscale('linear')
        ax.set_xlabel('R [AU]')
        ax.set_ylabel('T [K]')
        ax.set_title('Midplane Temperature [K]')
        ax.grid()
        ax.set_xlim([self.rbin_min, self.rbin_max])
        if ylim:
            ax.set_ylim(ylim)
        if not ax_in:
            plt.show()

    def plot_xe_mid_r(self, ax_in=None, ylim=None):
        # Cut Out Empty Bins
        xe_mid_r = self.xe_mid_r
        rbins_centers = self.rbins_centers
        xe_mid_r[xe_mid_r == 0.0] = np.nan
        rbins_centers = rbins_centers[~np.isnan(xe_mid_r)]
        xe_mid_r = xe_mid_r[~np.isnan(xe_mid_r)]
        # Plot
        if not ax_in:
            fig = plt.figure()
            ax = fig.add_subplot(1,1,1)
        else:
            ax = ax_in
        ax.plot(rbins_centers, xe_mid_r, 'bs-')
        ax.set_yscale('log')
        ax.set_xlabel('R [AU]')
        ax.set_ylabel('Log10 xe [-]')
        ax.set_title('Log10 Midplane Electron Fraction [-]')
        ax.grid()
        ax.set_xlim([self.rbin_min, self.rbin_max])
        if ylim:
            ax.set_ylim(ylim)
        if not ax_in:
            plt.show()

    def plot_n_mid_r(self, ax_in=None, ylim=None):
        # Cut Out Empty Bins
        n_mid_r = self.n_mid_r
        rbins_centers = self.rbins_centers
        n_mid_r[n_mid_r == 0.0] = np.nan
        rbins_centers = rbins_centers[~np.isnan(n_mid_r)]
        n_mid_r = n_mid_r[~np.isnan(n_mid_r)]
        # Plot
        if not ax_in:
            fig = plt.figure()
            ax = fig.add_subplot(1,1,1)
        else:
            ax = ax_in
        ax.plot(rbins_centers, n_mid_r, 'bs-')
        ax.set_yscale('log')
        ax.set_xlabel('R [AU]')
        ax.set_ylabel('Log10 n [1/cm^3]')
        ax.set_title('Log10 Midplane Number Density [1/cm^3]')
        ax.grid()
        ax.set_xlim([self.rbin_min, self.rbin_max])
        if ylim:
            ax.set_ylim(ylim)
        if not ax_in:
            plt.show()

    def plot_ReM_mid_r(self, ax_in=None, ylim=None):
        # Cut Out Empty Bins
        ReM_mid_r = self.ReM_mid_r
        rbins_centers = self.rbins_centers
        ReM_mid_r[ReM_mid_r == 0.0] = np.nan
        rbins_centers = rbins_centers[~np.isnan(ReM_mid_r)]
        ReM_mid_r = ReM_mid_r[~np.isnan(ReM_mid_r)]
        # Plot
        if not ax_in:
            fig = plt.figure()
            ax = fig.add_subplot(1,1,1)
        else:
            ax = ax_in
        ax.plot(rbins_centers, ReM_mid_r, 'bs-')
        ax.set_yscale('log')
        ax.set_xlabel('R [AU]')
        ax.set_ylabel('Log10 ReM [-]')
        ax.set_title('Log10 Magnetic Reynolds Number [-]')
        ax.grid()
        ax.set_xlim([self.rbin_min, self.rbin_max])
        if ylim:
            ax.set_ylim(ylim)
        if not ax_in:
            plt.show()

    def plot_rho_r(self, ax_in=None, ylim=None):
        # Cut Out Empty Bins
        rho_r = self.rho_r
        rbins_centers = self.rbins_centers
        rho_r[rho_r==0.] = np.nan
        rbins_centers = rbins_centers[~np.isnan(rho_r)]
        rho_r = rho_r[~np.isnan(rho_r)]
        # Plot
        if not ax_in:
            fig = plt.figure()
            ax = fig.add_subplot(1,1,1)
        else:
            ax = ax_in
        ax.plot(rbins_centers, rho_r, 'bs-')
        ax.set_yscale('log')
        ax.set_xlabel('R [AU]')
        ax.set_ylabel('Log10 Surface Density [Mstar/AU^2]')
        ax.set_title('Log10 Surface Density [Mstar/AU^2]')
        ax.grid()
        ax.set_xlim([self.rbin_min, self.rbin_max])
        if ylim:
            ax.set_ylim(ylim)
        if not ax_in:
            plt.show()

    def plot_Q_xy(self, ax_in=None):
        ext = [np.min(self.xy0["x"]), np.max(self.xy0["x"]), \
               np.min(self.xy0["y"]), np.max(self.xy0["y"])]
        Q_xy = self.Q_xy
        Q_xy[Q_xy>10] = np.nan
        Q_xy[Q_xy<=0] = np.nan
        if not ax_in:
            fig = plt.figure()
            ax = fig.add_subplot(1,1,1)
        else:
            ax = ax_in
        im = ax.imshow(np.rot90(Q_xy.reshape(self.nx, self.ny)),\
                       extent=ext, interpolation='none')
        im.set_clim([0, 10])
        ax.set_xlabel('X [AU]')
        ax.set_ylabel('Y [AU]')
        ax.set_title('Toomre-Q')
        ax.grid()
        plt.colorbar(im, ax=ax)
        if not ax_in:
            plt.show()

    def plot_Q_r(self, ax_in=None):
        # Cut Out Empty Bins and Useless Values
        Q_r = self.Q_r
        rbins_centers = self.rbins_centers
        Q_r[Q_r>10] = np.nan
        Q_r[Q_r<=0] = np.nan
        Q_r[Q_r<0.0001] = np.nan
        rbins_centers = rbins_centers[~np.isnan(Q_r)]
        Q_r = Q_r[~np.isnan(Q_r)]
        if not ax_in:
            fig = plt.figure()
            ax = fig.add_subplot(1,1,1)
        else:
            ax = ax_in
        # Plot
        ax.hold(True)
        ax.plot(rbins_centers, Q_r, 'bs-')
        ax.plot([self.rbin_min, self.rbin_max], [1.5, 1.5], 'y-', \
                label='Q=1.5')
        ax.plot([self.rbin_min, self.rbin_max], [1.0, 1.0], 'r-', \
                label='Q=1.0')
        ax.hold(False)
        ax.grid()
        ax.set_xlabel('Radius [AU]')
        ax.set_ylabel('Toomre-Q')
        ax.set_title('Toomre-Q')
        ax.set_xlim([self.rbin_min, self.rbin_max])
        ax.set_ylim([0, 10])
        ax.legend(loc='best')
        if not ax_in:
            plt.show()

    def plot_mdot_r(self, ax_in=None, ylim=None):
        # Cut 0.0 and NaN
        mdot_r = self.mdot_r; rbins_centers = self.rbins_centers
        mdot_r[mdot_r==0] = np.nan
        rbins_centers = rbins_centers[~np.isnan(mdot_r)]
        mdot_r = mdot_r[~np.isnan(mdot_r)]
        # Plot
        if not ax_in:
            fig = plt.figure()
            ax = fig.add_subplot(1,1,1)
        else:
            ax = ax_in
        ax.plot(rbins_centers, np.abs(mdot_r)*2.*pi, 'bs-')
        ax.grid()
        ax.set_xlabel('Radius [AU]')
        ax.set_ylabel('Mass Flow [Mstar/yr]')
        ax.set_title('Absolute Mass Flow [Mstar/yr]')
        ax.set_yscale('log')
        ax.set_xlim([self.rbin_min, self.rbin_max])
        if ylim:
            ylim = [ylim[0]*2.*pi, ylim[1]*2.*pi]
            ax.set_ylim(ylim)
        if not ax_in:
            plt.show()

class Disk(DiskPlots):
    """Wrapper."""
    pass