objective.py

"""Handling of objective functions and objective quantities."""

from abc import ABC, abstractmethod
import numpy as np
import meep as mp
from .filter_source import FilteredSource
from .optimization_problem import atleast_3d, Grid

class ObjectiveQuantitiy(ABC):
    @abstractmethod
    def __init__(self):
        return
    @abstractmethod
    def register_monitors(self):
        return
    @abstractmethod
    def place_adjoint_source(self):
        return
    @abstractmethod
    def __call__(self):
        return
    @abstractmethod
    def get_evaluation(self):
        return

class EigenmodeCoefficient(ObjectiveQuantitiy):
    def __init__(self,sim,volume,mode,forward=True,kpoint_func=None,**kwargs):
        '''
        '''
        self.sim = sim
        self.volume=volume
        self.mode=mode
        self.forward = 0 if forward else 1
        self.normal_direction = None
        self.kpoint_func = kpoint_func
        self.eval = None
        self.EigenMode_kwargs = kwargs
        return

    def register_monitors(self,frequencies):
        self.frequencies = np.asarray(frequencies)
        self.monitor = self.sim.add_mode_monitor(frequencies,mp.ModeRegion(center=self.volume.center,size=self.volume.size),yee_grid=True)
        self.normal_direction = self.monitor.normal_direction
        return self.monitor

    def place_adjoint_source(self,dJ):
        '''Places an equivalent eigenmode monitor facing the opposite direction. Calculates the
        correct scaling/time profile.
        dJ ........ the user needs to pass the dJ/dMonitor evaluation
        '''
        dJ = np.atleast_1d(dJ)
        dt = self.sim.fields.dt # the timestep size from sim.fields.dt of the forward sim
        # determine starting kpoint for reverse mode eigenmode source
        direction_scalar = 1 if self.forward else -1
        if self.kpoint_func is None:
            if self.normal_direction == 0:
                k0 = direction_scalar * mp.Vector3(x=1)
            elif self.normal_direction == 1:
                k0 = direction_scalar * mp.Vector3(y=1)
            elif self.normal_direction == 2:
                k0 == direction_scalar * mp.Vector3(z=1)
        else:
            k0 = direction_scalar * self.kpoint_func(self.time_src.frequency,1)
        if dJ.ndim == 2:
            dJ = np.sum(dJ,axis=1)
        da_dE = 0.5 * self.cscale # scalar popping out of derivative

        scale = adj_src_scale(self, dt)

        if self.frequencies.size == 1:
            # Single frequency simulations. We need to drive it with a time profile.
            amp = da_dE * dJ * scale # final scale factor
            src = self.time_src
        else:
            # multi frequency simulations
            scale = da_dE * dJ * scale
            src = FilteredSource(self.time_src.frequency,self.frequencies,scale,dt) # generate source from broadband response
            amp = 1

        # generate source object
        self.source = [mp.EigenModeSource(src,
                    eig_band=self.mode,
                    direction=mp.NO_DIRECTION,
                    eig_kpoint=k0,
                    amplitude=amp,
                    eig_match_freq=True,
                    size=self.volume.size,
                    center=self.volume.center,
                    **self.EigenMode_kwargs)]
        
        return self.source

    def __call__(self):
        # We just need a workable time profile, so just grab the first available time profile and use that.
        self.time_src = self.sim.sources[0].src

        # Eigenmode data
        direction = mp.NO_DIRECTION if self.kpoint_func else mp.AUTOMATIC
        ob = self.sim.get_eigenmode_coefficients(self.monitor,[self.mode],direction=direction,kpoint_func=self.kpoint_func,**self.EigenMode_kwargs)
        self.eval = np.squeeze(ob.alpha[:,:,self.forward]) # record eigenmode coefficients for scaling
        self.cscale = ob.cscale # pull scaling factor

        return self.eval
    def get_evaluation(self):
        '''Returns the requested eigenmode coefficient.
        '''
        try:
            return self.eval
        except AttributeError:
            raise RuntimeError("You must first run a forward simulation before resquesting an eigenmode coefficient.")


class FourierFields(ObjectiveQuantitiy):
    def __init__(self,sim,volume, component):
        self.sim = sim
        self.volume=volume
        self.eval = None
        self.component = component
        return

    def register_monitors(self,frequencies):
        self.frequencies = np.asarray(frequencies)
        self.num_freq = len(self.frequencies)
        self.monitor = self.sim.add_dft_fields([self.component], self.frequencies, where=self.volume, yee_grid=False)
        return self.monitor

    def place_adjoint_source(self,dJ):
        dt = self.sim.fields.dt # the timestep size from sim.fields.dt of the forward sim
        self.sources = []
        scale = adj_src_scale(self, dt)

        if self.num_freq == 1:
            amp = -atleast_3d(dJ[0]) * scale
            src = self.time_src
            if self.component in [mp.Hx, mp.Hy, mp.Hz]:
                amp = -amp
            for zi in range(len(self.dg.z)):
                for yi in range(len(self.dg.y)):
                    for xi in range(len(self.dg.x)):
                        if amp[xi, yi, zi] != 0:
                            self.sources += [mp.Source(src, component=self.component, amplitude=amp[xi, yi, zi],
                            center=mp.Vector3(self.dg.x[xi], self.dg.y[yi], self.dg.z[zi]))]
        else:
            dJ_4d = np.array([atleast_3d(dJ[f]) for f in range(self.num_freq)])
            if self.component in [mp.Hx, mp.Hy, mp.Hz]:
                dJ_4d = -dJ_4d
            for zi in range(len(self.dg.z)):
                for yi in range(len(self.dg.y)):
                    for xi in range(len(self.dg.x)):
                        final_scale = -dJ_4d[:,xi,yi,zi] * scale
                        src = FilteredSource(self.time_src.frequency,self.frequencies,final_scale,dt)
                        self.sources += [mp.Source(src, component=self.component, amplitude=1,
                                center=mp.Vector3(self.dg.x[xi], self.dg.y[yi], self.dg.z[zi]))]

        return self.sources

    def __call__(self):
        self.time_src = self.sim.sources[0].src
        self.dg = Grid(*self.sim.get_array_metadata(dft_cell=self.monitor))
        self.eval = np.array([self.sim.get_dft_array(self.monitor, self.component, i) for i in range(self.num_freq)]) #Shape = (num_freq, [pts])
        return self.eval

    def get_evaluation(self):
        try:
            return self.eval
        except AttributeError:
            raise RuntimeError("You must first run a forward simulation.")


class Near2FarFields(ObjectiveQuantitiy):
    def __init__(self,sim,Near2FarRegions, far_pt):
        self.sim = sim
        self.Near2FarRegions=Near2FarRegions
        self.eval = None
        self.far_pt = far_pt
        return

    def register_monitors(self,frequencies):
        self.frequencies = np.asarray(frequencies)
        self.num_freq = len(self.frequencies)
        self.monitor = self.sim.add_near2far(self.frequencies, *self.Near2FarRegions, yee_grid=True)
        return self.monitor

    def place_adjoint_source(self,dJ):
        dt = self.sim.fields.dt # the timestep size from sim.fields.dt of the forward sim
        self.sources = []
        dJ = dJ.flatten()

        #TODO far_pts in 3d or cylindrical, perhaps py_v3_to_vec from simulation.py
        self.all_nearsrcdata = self.monitor.swigobj.near_sourcedata(mp.vec(self.far_pt.x, self.far_pt.y), dJ)
        for near_data in self.all_nearsrcdata:
            cur_comp = near_data.near_fd_comp
            amp_arr = np.array(near_data.amp_arr).reshape(-1, self.num_freq)
            scale = amp_arr * adj_src_scale(self, dt, include_resolution=False)

            if self.num_freq == 1:
                self.sources += [mp.IndexedSource(self.time_src, near_data, scale[:,0])]
            else:
                src = FilteredSource(self.time_src.frequency,self.frequencies,scale,dt)
                (num_basis, num_pts) = src.nodes.shape
                for basis_i in range(num_basis):
                    self.sources += [mp.IndexedSource(src.time_src_bf[basis_i], near_data, src.nodes[basis_i])]

        return self.sources

    def __call__(self):
        self.time_src = self.sim.sources[0].src
        self.eval = np.array(self.sim.get_farfield(self.monitor, self.far_pt))
        self.eval = self.eval.reshape((self.num_freq, 6))
        return self.eval

    def get_evaluation(self):
        try:
            return self.eval
        except AttributeError:
            raise RuntimeError("You must first run a forward simulation.")


def adj_src_scale(obj_quantity, dt, include_resolution=True):
    # -------------------------------------- #
    # Get scaling factor
    # -------------------------------------- #
    # leverage linearity and combine source for multiple frequencies
    T = obj_quantity.sim.meep_time()

    if not include_resolution:
        dV = 1
    elif obj_quantity.sim.cell_size.y == 0:
        dV = 1/obj_quantity.sim.resolution
    elif obj_quantity.sim.cell_size.z == 0:
        dV = 1/obj_quantity.sim.resolution * 1/obj_quantity.sim.resolution
    else:
        dV = 1/obj_quantity.sim.resolution * 1/obj_quantity.sim.resolution * 1/obj_quantity.sim.resolution

    iomega = (1.0 - np.exp(-1j * (2 * np.pi * obj_quantity.frequencies) * dt)) * (1.0 / dt) # scaled frequency factor with discrete time derivative fix

    src = obj_quantity.time_src

    # an ugly way to calcuate the scaled dtft of the forward source
    y = np.array([src.swigobj.current(t,dt) for t in np.arange(0,T,dt)]) # time domain signal
    fwd_dtft = np.matmul(np.exp(1j*2*np.pi*obj_quantity.frequencies[:,np.newaxis]*np.arange(y.size)*dt), y)*dt/np.sqrt(2*np.pi) # dtft

    # we need to compensate for the phase added by the time envelope at our freq of interest
    src_center_dtft = np.matmul(np.exp(1j*2*np.pi*np.array([src.frequency])[:,np.newaxis]*np.arange(y.size)*dt), y)*dt/np.sqrt(2*np.pi)
    adj_src_phase = np.exp(1j*np.angle(src_center_dtft))

    if obj_quantity.frequencies.size == 1:
        # Single frequency simulations. We need to drive it with a time profile.
        scale = dV * iomega / fwd_dtft / adj_src_phase # final scale factor
    else:
        # multi frequency simulations
        scale = dV * iomega / adj_src_phase
    return scale