grid-EPIC-wstack.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Standalone Mode\n",
      "See crocodile repo for more information!\n",
      "The optimal gridding code is from Sze-Tan Meng\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import sys\n",
    "\n",
    "\n",
    "from matplotlib import pylab as plt\n",
    "from mpl_toolkits.mplot3d import axes3d, Axes3D \n",
    "\n",
    "import itertools\n",
    "import numpy\n",
    "import scipy\n",
    "import scipy.special\n",
    "import time\n",
    "import random\n",
    "\n",
    "from ipywidgets import interact\n",
    "from IPython.display import display, Markdown, clear_output\n",
    "\n",
    "try:\n",
    "    sys.path.append('../..')\n",
    "   \n",
    "    from crocodile.synthesis import *\n",
    "    from crocodile.simulate import *\n",
    "    from crocodile.antialias import *\n",
    "    from util.visualize import *\n",
    "    print(\"Crocodile Mode\")\n",
    "except:\n",
    "    print(\"Standalone Mode\")\n",
    "    print(\"See crocodile repo for more information!\")\n",
    "    import numpy as np\n",
    "    from scipy.optimize import leastsq, brent\n",
    "    from json_tricks.np import load\n",
    "    def coordinateBounds(N):\n",
    "        r\"\"\"\n",
    "        Returns lowest and highest coordinates of an image/grid given:\n",
    "\n",
    "        1. Step size is :math:`1/N`:\n",
    "\n",
    "           .. math:: \\frac{high-low}{N-1} = \\frac{1}{N}\n",
    "\n",
    "        2. The coordinate :math:`\\lfloor N/2\\rfloor` falls exactly on zero:\n",
    "\n",
    "           .. math:: low + \\left\\lfloor\\frac{N}{2}\\right\\rfloor * (high-low) = 0\n",
    "\n",
    "        This is the coordinate system for shifted FFTs.\n",
    "        \"\"\"\n",
    "        if N % 2 == 0:\n",
    "            return -0.5, 0.5 * (N - 2) / N\n",
    "        else:\n",
    "            return -0.5 * (N - 1) / N, 0.5 * (N - 1) / N\n",
    "\n",
    "    def coordinates(N):\n",
    "        \"\"\"1D array which spans [-.5,.5[ with 0 at position N/2\"\"\"\n",
    "        N2 = N // 2\n",
    "        if N % 2 == 0:\n",
    "            return numpy.mgrid[-N2:N2] / N\n",
    "        else:\n",
    "            return numpy.mgrid[-N2:N2+1] / N\n",
    "\n",
    "\n",
    "    def coordinates2(N):\n",
    "        \"\"\"Two dimensional grids of coordinates spanning -1 to 1 in each\n",
    "        dimension, with\n",
    "\n",
    "        1. a step size of 2/N and\n",
    "        2. (0,0) at pixel (floor(n/2),floor(n/2))\n",
    "\n",
    "        :returns: pair (cx,cy) of 2D coordinate arrays\n",
    "        \"\"\"\n",
    "\n",
    "        N2 = N // 2\n",
    "        if N % 2 == 0:\n",
    "            return numpy.mgrid[-N2:N2, -N2:N2][::-1] / N\n",
    "        else:\n",
    "            return numpy.mgrid[-N2:N2+1, -N2:N2+1][::-1] / N\n",
    "\n",
    "\n",
    "    def fft(a):\n",
    "        \"\"\" Fourier transformation from image to grid space\n",
    "\n",
    "        :param a: image in `lm` coordinate space\n",
    "        :returns: `uv` grid\n",
    "        \"\"\"\n",
    "        if len(a.shape) == 1:\n",
    "            return numpy.fft.fftshift(numpy.fft.fft(numpy.fft.ifftshift(a)))\n",
    "        elif len(a.shape) == 2:\n",
    "            return numpy.fft.fftshift(numpy.fft.fft2(numpy.fft.ifftshift(a)))\n",
    "        assert False, \"Unsupported image shape for FFT!\"\n",
    "\n",
    "\n",
    "    def ifft(a):\n",
    "        \"\"\" Fourier transformation from grid to image space\n",
    "\n",
    "        :param a: `uv` grid to transform\n",
    "        :returns: an image in `lm` coordinate space\n",
    "        \"\"\"\n",
    "        if len(a.shape) == 1:\n",
    "            return numpy.fft.fftshift(numpy.fft.ifft(numpy.fft.ifftshift(a)))\n",
    "        elif len(a.shape) == 2:\n",
    "            return numpy.fft.fftshift(numpy.fft.ifft2(numpy.fft.ifftshift(a)))\n",
    "        assert False, \"Unsupported grid shape for iFFT!\"\n",
    "\n",
    "\n",
    "    def pad_mid(ff, N):\n",
    "        \"\"\"\n",
    "        Pad a far field image with zeroes to make it the given size.\n",
    "\n",
    "        Effectively as if we were multiplying with a box function of the\n",
    "        original field's size, which is equivalent to a convolution with a\n",
    "        sinc pattern in the uv-grid.\n",
    "\n",
    "        :param ff: The input far field. Should be smaller than NxN.\n",
    "        :param N:  The desired far field size\n",
    "\n",
    "        \"\"\"\n",
    "\n",
    "        N0 = ff.shape[0]\n",
    "        if N == N0: return ff\n",
    "        assert N > N0\n",
    "        pad = [(N//2-N0//2, (N+1)//2-(N0+1)//2)]\n",
    "        if len(ff.shape) == 2:\n",
    "            assert N0 == ff.shape[1]\n",
    "            pad = 2*pad # both dimensions\n",
    "        return numpy.pad(ff, pad, mode='constant', constant_values=0.0)\n",
    "\n",
    "    def extract_mid(a, N):\n",
    "        \"\"\"\n",
    "        Extract a section from middle of a map\n",
    "\n",
    "        Suitable for zero frequencies at N/2. This is the reverse\n",
    "        operation to pad.\n",
    "\n",
    "        :param a: grid from which to extract\n",
    "        :param s: size of section\n",
    "        \"\"\"\n",
    "\n",
    "        assert N <= a.shape[0]\n",
    "        cx = a.shape[0] // 2\n",
    "        s = N // 2\n",
    "        if len(a.shape) == 2:\n",
    "            assert N <= a.shape[1]\n",
    "            cy = a.shape[1] // 2\n",
    "            if N % 2 != 0:\n",
    "                return a[cx - s:cx + s + 1, cy - s:cy + s + 1]\n",
    "            else:\n",
    "                return a[cx - s:cx + s, cy - s:cy + s]\n",
    "        elif len(a.shape) == 1:\n",
    "            if N % 2 != 0:\n",
    "                return a[cx - s:cx + s + 1]\n",
    "            else:\n",
    "                return a[cx - s:cx + s]\n",
    "        else:\n",
    "            assert False, \"Unsupported grid shape for extract_mid!\"\n",
    "\n",
    "    def extract_oversampled(a, Qpx, N):\n",
    "        \"\"\"\n",
    "        Extract the (xf-th,yf-th) w-kernel from the oversampled parent\n",
    "\n",
    "        Offsets are suitable for correcting of fractional coordinates,\n",
    "        e.g. an offset of (xf,yf) results in the kernel for an (-xf,-yf)\n",
    "        sub-grid offset.\n",
    "\n",
    "        We do not want to make assumptions about the source grid's symetry\n",
    "        here, which means that the grid's side length must be at least\n",
    "        Qpx*(N+2) to contain enough information in all circumstances\n",
    "\n",
    "        :param a: grid from which to extract\n",
    "        :param Qpx: oversampling factor\n",
    "        :param N: size of section\n",
    "        \"\"\"\n",
    "\n",
    "        Na = a.shape[0]\n",
    "        if len(a.shape) == 1:\n",
    "            result = numpy.empty((Qpx, N), dtype=complex)\n",
    "            for xf in range(Qpx):\n",
    "                # Determine start offset.\n",
    "                mx = Na//2 - Qpx*(N//2) + xf\n",
    "                # Extract every Qpx-th pixel\n",
    "                result[xf] = a[mx : mx+Qpx*N : Qpx]\n",
    "            return result\n",
    "        elif len(a.shape) == 2:\n",
    "            result = numpy.empty((Qpx, Qpx, N, N), dtype=complex)\n",
    "            for yf in range(Qpx):\n",
    "                for xf in range(Qpx):\n",
    "                    # Determine start offset.\n",
    "                    my = Na//2 - Qpx*(N//2) + yf\n",
    "                    mx = Na//2 - Qpx*(N//2) + xf\n",
    "                    # Extract every Qpx-th pixel\n",
    "                    result[yf,xf] = a[my : my+Qpx*N : Qpx,\n",
    "                                      mx : mx+Qpx*N : Qpx]\n",
    "            return result\n",
    "        assert False, \"Unsupported grid shape for extract_oversampled!\"\n",
    "\n",
    "    def anti_aliasing_function(shape, m, c):\n",
    "        \"\"\"\n",
    "        Compute the prolate spheroidal anti-aliasing function\n",
    "\n",
    "        See VLA Scientific Memoranda 129, 131, 132\n",
    "        :param shape: (height, width) pair or just width\n",
    "        :param m: mode parameter\n",
    "        :param c: spheroidal parameter\n",
    "        \"\"\"\n",
    "\n",
    "        # One dimensional?\n",
    "        if len(numpy.array(shape).shape) == 0:\n",
    "\n",
    "            # Remove one pixel on either side to prevent zeroes.\n",
    "            mult = 2 - 1/shape/4\n",
    "            return scipy.special.pro_ang1(m, m, c, mult*coordinates(shape))[0]\n",
    "\n",
    "        # 2D Prolate spheroidal angular function is seperable\n",
    "        return numpy.outer(anti_aliasing_function(shape[0], m, c),\n",
    "                           anti_aliasing_function(shape[1], m, c))\n",
    "\n",
    "    def kernel_transform(dl, dm):\n",
    "        \"\"\"Determine linear transformation matrix for a given shift that\n",
    "        keeps w-kernel coordinates as constant as possible.\n",
    "\n",
    "        To be precise: This returns a transformation matrix such that with\n",
    "\n",
    "          (l',m') = T (l,m) + (dl,dm)\n",
    "\n",
    "        We still have:\n",
    "\n",
    "          sqrt(1-l'^2-m'^2) ~~ sqrt(1-l^2-m^2)\n",
    "\n",
    "        As well as leaving l' and m' roughly aligned to l and m. This\n",
    "        boils down to matching up the first-order terms of the series\n",
    "        expansions (which are clearly zero for the right-hand term, as it\n",
    "        is symmetric in both l and m).\n",
    "\n",
    "        :param dl: Horizontal shift (directional cosine)\n",
    "        :param dl: Vertical shift (directional cosine)\n",
    "        :returns: A 2x2 transformation matrix\n",
    "        \"\"\"\n",
    "\n",
    "        dn = numpy.sqrt(1-dl**2-dm**2)\n",
    "        if dl != 0 or dm != 0:\n",
    "            f = (dn-1) / (dl**2 + dm**2)\n",
    "        else:\n",
    "            f = 0\n",
    "        return numpy.array([[dn-dm*dm*f,    dl*dm*f],\n",
    "                            [   dl*dm*f, dn-dl*dl*f]])\n",
    "\n",
    "    def kernel_coordinates(N, theta, dl=0, dm=0, T=None):\n",
    "        \"\"\"\n",
    "        Returns (l,m) coordinates for generation of kernels\n",
    "        in a far-field of the given size.\n",
    "\n",
    "        If coordinate transformations are passed, they must be inverse to\n",
    "        the transformations applied to the visibilities using\n",
    "        visibility_shift/uvw_transform.\n",
    "\n",
    "        :param N: Desired far-field resolution\n",
    "        :param theta: Field of view size (directional cosines)\n",
    "        :param dl: Pattern horizontal shift (see visibility_shift)\n",
    "        :param dm: Pattern vertical shift (see visibility_shift)\n",
    "        :param T: Pattern transformation matrix (see uvw_transform)\n",
    "        :returns: Pair of (m,l) coordinates\n",
    "        \"\"\"\n",
    "\n",
    "        l,m = coordinates2(N) * theta\n",
    "        if not T is None:\n",
    "            l,m = T[0,0]*l+T[1,0]*m, T[0,1]*l+T[1,1]*m\n",
    "\n",
    "\n",
    "        return l+dl, m+dm\n",
    "\n",
    "\n",
    "    def w_kernel_function(l, m, w):\n",
    "        \"\"\"W beam, the fresnel diffraction pattern arising from non-coplanar baselines\n",
    "\n",
    "        For the w-kernel, shifting the kernel pattern happens to also\n",
    "        shift the kernel depending on w. Use `kernel_recentre` to counter\n",
    "        this effect and `visibility_recentre` to apply the reverse\n",
    "        correction to visibilities.\n",
    "\n",
    "        :param l: Horizontal image coordinates\n",
    "        :param m: Vertical image coordinates\n",
    "        :param N: Size of the grid in pixels\n",
    "        :param w: Baseline distance to the projection plane\n",
    "        :returns: N x N array with the far field\n",
    "\n",
    "        \"\"\"\n",
    "\n",
    "        r2 = l**2 + m**2\n",
    "        assert numpy.all(r2 < 1.0), \"Error in image coordinate system: l %s, m %s\" % (l, m)\n",
    "        ph = 1 - numpy.sqrt(1.0 - r2)\n",
    "        cp = numpy.exp(2j * numpy.pi * w * ph)\n",
    "        return cp\n",
    "\n",
    "\n",
    "    def kernel_recentre(cp, theta, w, dl, dm):\n",
    "        \"\"\"\n",
    "        Re-center the kernel in grid-space by multiplying it by a phase\n",
    "        ramp in image space, allowing us to reduce kernel support. Must be\n",
    "        paired with `visibility_recentre` so that we end up with the same\n",
    "        uv-grid in the end.\n",
    "\n",
    "        :param cp: Kernel pattern\n",
    "        :param w: w-plane of kernel\n",
    "        :param dl: Horizontal shift to add\n",
    "        :param dm: Vertical shift to add\n",
    "        :returns: Re-centered kernel\n",
    "        \"\"\"\n",
    "        N = cp.shape[0]\n",
    "        l,m = coordinates2(N) * theta\n",
    "        return cp * numpy.exp(-2j * numpy.pi * w * (dl * l + dm * m))\n",
    "\n",
    "\n",
    "    def visibility_recentre(uvw, dl, dm):\n",
    "        \"\"\"\n",
    "        Compensate for kernel re-centering - see `kernel_recentre`.\n",
    "\n",
    "        :param uvw: Visibility coordinates\n",
    "        :param dl: Horizontal shift to compensate for\n",
    "        :param dm: Vertical shift to compensate for\n",
    "        :returns: Visibility coordinates re-centred to the peak of their w-kernel\n",
    "        \"\"\"\n",
    "\n",
    "        u, v, w = numpy.hsplit(uvw, 3)\n",
    "        return numpy.hstack([u - w*dl,\n",
    "                             v - w*dm,\n",
    "                             w])\n",
    "\n",
    "\n",
    "    def kernel_oversample(ff, Qpx, s=None):\n",
    "        \"\"\"\n",
    "        Takes a farfield pattern and creates an oversampled convolution\n",
    "        function.\n",
    "\n",
    "        If the far field size is smaller than N*Qpx, we will pad it. This\n",
    "        essentially means we apply a sinc anti-aliasing kernel by default.\n",
    "\n",
    "        :param ff: Far field pattern\n",
    "        :param Qpx: Factor to oversample by -- there will be Qpx x Qpx convolution arl\n",
    "        :param s: Size of convolution function to extract\n",
    "        :returns: Numpy array of shape [ov, ou, v, u], e.g. with sub-pixel\n",
    "          offsets as the outer coordinates.\n",
    "        \"\"\"\n",
    "\n",
    "        # Pad the far field to the required pixel size\n",
    "        N = ff.shape[0]\n",
    "        if s is None: s = N\n",
    "        padff = pad_mid(ff, N*Qpx)\n",
    "\n",
    "        # Obtain oversampled uv-grid\n",
    "        af = fft(padff)\n",
    "\n",
    "        # Extract kernels\n",
    "        return extract_oversampled(af, Qpx, s)\n",
    "\n",
    "\n",
    "    def w_kernel(theta, w, NpixFF, NpixKern, Qpx, invert=True, **kwargs):\n",
    "        \"\"\"\n",
    "        The middle s pixels of W convolution kernel. (W-KERNel-Aperture-Function)\n",
    "\n",
    "        :param theta: Field of view (directional cosines)\n",
    "        :param w: Baseline distance to the projection plane\n",
    "        :param NpixFF: Far field size. Must be at least NpixKern+1 if Qpx > 1, otherwise NpixKern.\n",
    "        :param NpixKern: Size of convolution function to extract\n",
    "        :param Qpx: Oversampling, pixels will be Qpx smaller in aperture\n",
    "          plane than required to minimially sample theta.\n",
    "        :param invert: Produce an inverted kernel (as required for imaging)\n",
    "\n",
    "        :returns: [Qpx,Qpx,s,s] shaped oversampled convolution kernels\n",
    "        \"\"\"\n",
    "        assert NpixFF > NpixKern or (NpixFF == NpixKern and Qpx == 1)\n",
    "\n",
    "        l,m = kernel_coordinates(NpixFF, theta, **kwargs)\n",
    "        kern = w_kernel_function(l,m,w)\n",
    "        if invert:\n",
    "            kern = 1 / kern\n",
    "        return kernel_oversample(kern, Qpx, NpixKern)\n",
    "\n",
    "\n",
    "    def invert_kernel(a):\n",
    "        \"\"\"\n",
    "        Pseudo-Invert a kernel: element-wise inversion (see RauThesis2010:Eq4.6)\n",
    "\n",
    "        NOT USED\n",
    "        \"\"\"\n",
    "        return numpy.conj(a) / (numpy.abs(a) ** 2)\n",
    "\n",
    "\n",
    "    def grid(a, p, v):\n",
    "        \"\"\"Grid visibilities (v) at positions (p) into (a) without convolution\n",
    "\n",
    "        :param a:   The uv plane to grid to (updated in-place!)\n",
    "        :param p:   The coordinates to grid to (in fraction [-.5,.5[ of grid)\n",
    "        :param v:   Visibilities to grid\n",
    "        \"\"\"\n",
    "        assert numpy.max(p) < 0.5\n",
    "\n",
    "        N = a.shape[0]\n",
    "        xy = N//2 + numpy.floor(0.5 + N * p[:,0:2]).astype(int)\n",
    "        for (x, y), v in zip(xy, v):\n",
    "            a[y, x] += v\n",
    "\n",
    "\n",
    "    def degrid(a, p):\n",
    "        \"\"\"DeGrid visibilities (v) at positions (p) from (a) without convolution\n",
    "\n",
    "        :param a:   The uv plane to de-grid from\n",
    "        :param p:   The coordinates to degrid at (in fraction of grid)\n",
    "        :returns: Array of visibilities.\n",
    "        \"\"\"\n",
    "        assert numpy.max(p) < 0.5\n",
    "\n",
    "        N = a.shape[0]\n",
    "        xy = N//2 + numpy.floor(0.5 + p[:,0:2] * N).astype(int)\n",
    "        v = [ a[y,x] for x,y in xy ]\n",
    "        return numpy.array(v)\n",
    "\n",
    "\n",
    "    def frac_coord(N, Qpx, p):\n",
    "        \"\"\"\n",
    "        Compute whole and fractional parts of coordinates, rounded to\n",
    "        Qpx-th fraction of pixel size\n",
    "\n",
    "        The fractional values are rounded to nearest 1/Qpx pixel value. At\n",
    "        fractional values greater than (Qpx-0.5)/Qpx coordinates are\n",
    "        roundeded to next integer index.\n",
    "\n",
    "        :param N: Number of pixels in total\n",
    "        :param Qpx: Fractional values to round to\n",
    "        :param p: Coordinate in range [-.5,.5[\n",
    "        \"\"\"\n",
    "        assert (p >= -0.5).all() and (p < 0.5).all()\n",
    "        x = N//2 + p * N\n",
    "        fx = numpy.around(-x * Qpx).astype(int)\n",
    "        return -(fx // Qpx), fx % Qpx\n",
    "\n",
    "\n",
    "    def frac_coords(shape, Qpx, p):\n",
    "        \"\"\"Compute grid coordinates and fractional values for convolutional\n",
    "        gridding\n",
    "\n",
    "        :param shape: (height,width) grid shape\n",
    "        :param Qpx: Oversampling factor\n",
    "        :param p: array of (x,y) coordinates in range [-.5,.5[\n",
    "        \"\"\"\n",
    "        h, w = shape # NB order (height,width) to match numpy!\n",
    "        x, xf = frac_coord(w, Qpx, p[:,0])\n",
    "        y, yf = frac_coord(h, Qpx, p[:,1])\n",
    "        return x,xf, y,yf\n",
    "\n",
    "    def make_gcf(src, gcf):\n",
    "\n",
    "        src = numpy.array(src)\n",
    "        if len(gcf.shape) - src.shape[1] == 2:\n",
    "            Qpx, gw = gcf.shape[-2:]\n",
    "            return Qpx, gw, gw, lambda s, xf, yf: numpy.outer(gcf[(*s, yf)], gcf[(*s, xf)])\n",
    "        elif len(gcf.shape) - src.shape[1] == 4:\n",
    "            Qpx, gh, gw = gcf.shape[-3:]\n",
    "            return Qpx, gw, gh, lambda s, xf, yf: gcf[(*s, yf, xf)]\n",
    "        else:\n",
    "            assert False\n",
    "\n",
    "\n",
    "    def convgrid(gcf, a, p, src, v):\n",
    "        \"\"\"Grid after convolving with gcf\n",
    "\n",
    "        Takes into account fractional `uv` coordinate values where the GCF\n",
    "        is oversampled.\n",
    "\n",
    "        :param a: Grid to add to\n",
    "        :param p: UVW positions\n",
    "        :param v: Visibility values\n",
    "        :param gcf: Oversampled convolution kernel\n",
    "        \"\"\"\n",
    "\n",
    "        if src is None: src = numpy.zeros((p.shape[0], 0))\n",
    "        Qpx, gh, gw, mk_gcf = make_gcf(src, gcf)\n",
    "        coords = frac_coords(a.shape, Qpx, p)\n",
    "        for v, s, x,xf, y,yf in zip(v, src, *coords):\n",
    "            a[y-gh//2 : y+(gh+1)//2,\n",
    "              x-gw//2 : x+(gw+1)//2] += mk_gcf(s,xf,yf) * v\n",
    "\n",
    "\n",
    "    def convdegrid(gcf, a, p, src=None):\n",
    "        \"\"\"Convolutional degridding\n",
    "\n",
    "        Takes into account fractional `uv` coordinate values where the GCF\n",
    "        is oversampled\n",
    "\n",
    "        :param gcf: Oversampled convolution kernel\n",
    "        :param a:   The uv plane to de-grid from\n",
    "        :param p:   The coordinates to degrid at.\n",
    "        :param src: Visibility source information\n",
    "        :returns:   Array of visibilities.\n",
    "        \"\"\"\n",
    "\n",
    "        if src is None: src = numpy.zeros((p.shape[0], 0))\n",
    "        Qpx, gw, gh, mk_gcf = make_gcf(src, gcf)\n",
    "        coords = frac_coords(a.shape, Qpx, p)\n",
    "        return numpy.array([\n",
    "           numpy.sum(a[y-gh//2 : y+(gh+1)//2,\n",
    "                       x-gw//2 : x+(gw+1)//2] * mk_gcf(s, xf, yf))\n",
    "           for s, x,xf, y,yf in zip(src, *coords)])\n",
    "\n",
    "\n",
    "    def sort_vis_w(p, v=None):\n",
    "        \"\"\"Sort visibilities on the w value.\n",
    "        :param p: uvw coordinates\n",
    "        :param v: Visibility values (optional)\n",
    "        \"\"\"\n",
    "        zs = numpy.argsort(p[:, 2])\n",
    "        if v is not None:\n",
    "            return p[zs], v[zs]\n",
    "        else:\n",
    "            return p[zs]\n",
    "\n",
    "\n",
    "    def slice_vis(step, uvw, v=None):\n",
    "        \"\"\" Slice visibilities into a number of chunks.\n",
    "\n",
    "        :param step: Maximum chunk size\n",
    "        :param uvw: uvw coordinates\n",
    "        :param src: visibility source\n",
    "        :param v: Visibility values (optional)\n",
    "        :returns: List of visibility chunk (pairs)\n",
    "        \"\"\"\n",
    "        nv = len(uvw)\n",
    "        ii = range(0, nv, step)\n",
    "        if v is None:\n",
    "            return [ uvw[i:i+step] for i in ii ]\n",
    "        else:\n",
    "            return [ (uvw[i:i+step], v[i:i+step]) for i in ii ]\n",
    "\n",
    "\n",
    "    def doweight(theta, lam, p, v):\n",
    "        \"\"\"Re-weight visibilities\n",
    "\n",
    "        Note that as is usual, convolution kernels are not taken into account\n",
    "        \"\"\"\n",
    "        N = int(round(theta * lam))\n",
    "        assert N > 1\n",
    "        gw = numpy.zeros([N, N])\n",
    "        x, xf, y, yf = frac_coords(gw.shape, 1, p / lam)\n",
    "        for i in range(len(x)):\n",
    "            gw[x[i], y[i]] += 1\n",
    "        v = v.copy()\n",
    "        for i in range(len(x)):\n",
    "            v[i] /= gw[x[i], y[i]]\n",
    "        return v\n",
    "\n",
    "\n",
    "    def simple_imaging(theta, lam, uvw, src, vis):\n",
    "        \"\"\"Trivial function for imaging\n",
    "\n",
    "        Does no convolution but simply puts the visibilities into a grid\n",
    "        cell i.e. boxcar gridding\n",
    "        \"\"\"\n",
    "        N = int(round(theta * lam))\n",
    "        assert N > 1\n",
    "        guv = numpy.zeros([N, N], dtype=complex)\n",
    "        grid(guv, uvw / lam, vis)\n",
    "        return guv\n",
    "\n",
    "\n",
    "    def simple_predict(theta, lam, uvw, src, guv):\n",
    "        \"\"\"Trivial function for degridding\n",
    "\n",
    "        Does no convolution but simply extracts the visibilities from a grid cell i.e. boxcar degridding\n",
    "\n",
    "        :param theta: Field of view (directional cosines)\n",
    "        :param lam: Maximum uv represented in the grid\n",
    "        :param uvw: UVWs of visibilities\n",
    "        :param src: Visibility source information (ignored)\n",
    "        :param guv: Input u/v grid\n",
    "        :returns: p, v\n",
    "        \"\"\"\n",
    "        N = int(round(theta * lam))\n",
    "        assert N > 1\n",
    "        v = degrid(guv, uvw / lam)\n",
    "        return v\n",
    "\n",
    "\n",
    "    def conv_imaging(theta, lam, uvw, src, vis, kv):\n",
    "        \"\"\"Convolve and grid with user-supplied kernels\n",
    "\n",
    "        :param theta: Field of view (directional cosines))\n",
    "        :param lam: UV grid range\n",
    "        :param uvw: UVWs of visibilities\n",
    "        :param src: Visibility source information\n",
    "        :param vis: Visibility values\n",
    "        :param kv: Gridding kernel\n",
    "        :returns: UV grid\n",
    "        \"\"\"\n",
    "        N = int(round(theta * lam))\n",
    "        assert N > 1\n",
    "        guv = numpy.zeros([N, N], dtype=complex)\n",
    "        convgrid(kv, guv, uvw / lam, src, vis)\n",
    "        return guv\n",
    "\n",
    "    def conv_predict(theta, lam, uvw, src, guv, kv):\n",
    "        \"\"\"Convolve and grid with user-supplied kernels\n",
    "\n",
    "        :param theta: Field of view (directional cosines))\n",
    "        :param lam: UV grid range\n",
    "        :param uvw: UVWs of visibilities\n",
    "        :param src: Visibility source information\n",
    "        :param guv: UV grid\n",
    "        :param kv: Gridding kernel\n",
    "        :returns: visibility values\n",
    "        \"\"\"\n",
    "\n",
    "        if src is None: src = numpy.ndarray((len(uvw), 0))\n",
    "        return convdegrid(kv, guv, uvw / lam, src)\n",
    "\n",
    "\n",
    "    def w_slice_imaging(theta, lam, uvw, src, vis,\n",
    "                        wstep=2000,\n",
    "                        kernel_fn=w_kernel,\n",
    "                        **kwargs):\n",
    "        \"\"\"Basic w-projection imaging using slices\n",
    "\n",
    "        Sorts visibility by w value and splits into equally sized slices.\n",
    "        W-value used for kernels is mean w per slice. Uses the same size\n",
    "        for all kernels irrespective of w.\n",
    "\n",
    "        :param theta: Field of view (directional cosines)\n",
    "        :param lam: UV grid range (wavelenghts)\n",
    "        :param uvw: UVWs of visibilities (wavelenghts)\n",
    "        :param src: Visibility source information\n",
    "        :param vis: Visibility values\n",
    "        :param wstep: Size of w-slices\n",
    "        :param kernel_fn: Function for generating the kernels. Parameters\n",
    "          `(theta, w, *ant, **kwargs)`. Default `w_kernel`.\n",
    "        :returns: UV grid\n",
    "        \"\"\"\n",
    "        N = int(round(theta * lam))\n",
    "        assert N > 1\n",
    "        slices = slice_vis(wstep, *sort_vis_w(p, v))\n",
    "        guv = numpy.zeros([N, N], dtype=complex)\n",
    "        for ps, vs in slices:\n",
    "            w = numpy.mean(ps[:, 2])\n",
    "            wg = kernel_fn(theta, w, **kwargs)\n",
    "            convgrid(wg, guv, ps / lam, src, vs)\n",
    "        return guv\n",
    "\n",
    "\n",
    "    def w_slice_predict(theta, lam, uvw, src, guv,\n",
    "                        wstep=2000,\n",
    "                        kernel_fn=w_kernel,\n",
    "                        **kwargs):\n",
    "        \"\"\"Basic w-projection predict using w-slices\n",
    "\n",
    "        Sorts visibility by w value and splits into equally sized slices.\n",
    "        W-value used for kernels is mean w per slice. Uses the same size\n",
    "        for all kernels irrespective of w.\n",
    "\n",
    "        :param theta: Field of view (directional cosines)\n",
    "        :param lam: UV grid range (wavelenghts)\n",
    "        :param uvw: UVWs of visiblities\n",
    "        :param src: Visibility source information\n",
    "        :param guv: Input uv grid to de-grid from\n",
    "        :param wstep: Size of w-slices\n",
    "        :param kernel_fn: Function for generating the kernels. Parameters\n",
    "          `(theta, w, **kwargs)`. Default `w_kernel`.\n",
    "        :returns: Visibilities, same order as p\n",
    "        \"\"\"\n",
    "        # Calculate number of pixels in the Image\n",
    "        N = int(round(theta * lam))\n",
    "        assert N > 1\n",
    "        # Sort the u,v,w coordinates. We cheat a little and also pass\n",
    "        # visibility indices so we can easily undo the sort later.\n",
    "        nv = len(p)\n",
    "        slices = slice_vis(wstep, *sort_vis_w(p, numpy.arange(nv)))\n",
    "        v = numpy.ndarray(nv, dtype=complex)\n",
    "        for ps, ixs in slices:\n",
    "            w = numpy.mean(ps[:, 2])\n",
    "            wg = kernel_fn(theta, w, **kwargs)\n",
    "            v[ixs] = convdegrid(wg, guv, ps / lam)\n",
    "        return v\n",
    "\n",
    "\n",
    "    def w_conj_kernel_fn(kernel_fn):\n",
    "        \"\"\"Wrap a kernel function for which we know that\n",
    "\n",
    "           kernel_fn(w) = conj(kernel_fn(-w))\n",
    "\n",
    "        Such that we only evaluate the function for positive w. This is\n",
    "        benificial when the underlying kernel function does caching, as it\n",
    "        improves the cache hit rate.\n",
    "\n",
    "        :param kernel_fn: Kernel function to wrap\n",
    "        :returns: Wrapped kernel function\n",
    "        \"\"\"\n",
    "\n",
    "        def fn(theta, w, *args, **kw):\n",
    "            if w < 0:\n",
    "                return numpy.conj(kernel_fn(theta, -w, *args, **kw))\n",
    "            return kernel_fn(theta, w, *args, **kw)\n",
    "        return fn\n",
    "\n",
    "    def aw_kernel_fn(a_kernel_fn, w_kernel_fn=w_kernel):\n",
    "        \"\"\"\n",
    "        Make a kernel function to generate AW kernels.\n",
    "\n",
    "        This convolves three kernels for every AW-kernel: Two A-kernels\n",
    "        for either antenna and the w-kernel.\n",
    "\n",
    "        We expect the two first columns of \"src\" to identify the two\n",
    "        antennas involved in a baseline.\n",
    "\n",
    "        :param akernel_fn: Function to generate A-kernels. Parameters\n",
    "          (theta, ant, time, freq)\n",
    "        :param wkernel_fn: Function to generate w-kernels. Parameters\n",
    "          (theta, w)\n",
    "        :returns: Kernel function to generate AW-kernels\n",
    "\n",
    "        \"\"\"\n",
    "\n",
    "        def fn(theta, w, a1, a2, *src):\n",
    "\n",
    "            # Convolve antenna A-kernels\n",
    "            a1kern = a_kernel_fn(theta, a1, *src)\n",
    "            a2kern = a_kernel_fn(theta, a2, *src)\n",
    "            akern = scipy.signal.convolve2d(a1kern, a2kern, mode='same')\n",
    "\n",
    "            # Convolve with all oversampling values to obtain Aw-kernel\n",
    "            # (note that most oversampling sub-grid values will end up unused!)\n",
    "            wkern = w_kernel_fn(theta, w)\n",
    "            awkern = [[scipy.signal.convolve2d(akern, wk, mode='same')\n",
    "                       for wk in wks]\n",
    "                      for wks in wkern]\n",
    "            return numpy.array(awkern)\n",
    "\n",
    "        return fn\n",
    "\n",
    "    def sample_image(image, x, y):\n",
    "        \"\"\" Sample image at given position(s), relative to middle of image.\n",
    "\n",
    "        Performs simple bilinear interpolation if positions are not even numbers.\n",
    "\n",
    "        :param image: Image to sample\n",
    "        :param x: Horizontal sampling coordinates\n",
    "        :param y: Vertical sampling coordinates\n",
    "        \"\"\"\n",
    "\n",
    "        # Make positions relative to image middle\n",
    "        x += image.shape[0]/2\n",
    "        y += image.shape[1]/2\n",
    "        # Crude linear sampling\n",
    "        ix = numpy.floor(x).astype(int); dx = x - ix\n",
    "        iy = numpy.floor(y).astype(int); dy = y - iy\n",
    "        return numpy.sum([image[iy,   ix]  *((1-dx)*(1-dy)),\n",
    "                          image[iy,   ix+1]*(   dx *(1-dy)),\n",
    "                          image[iy+1, ix]  *((1-dx)*   dy ),\n",
    "                          image[iy+1, ix+1]*(   dx *   dy )], axis=0)\n",
    "\n",
    "    def w_cache_imaging(theta, lam, uvw, src, vis,\n",
    "                        wstep=2000,\n",
    "                        kernel_cache=None,\n",
    "                        kernel_fn=w_kernel,\n",
    "                        **kwargs):\n",
    "        \"\"\"Basic w-projection by caching convolution arl in w\n",
    "\n",
    "        A simple cache can be constructed externally and passed in:\n",
    "\n",
    "          kernel_cache = pylru.FunctionCacheManager(w_kernel, cachesize)\n",
    "\n",
    "        If applicable, consider wrapping in `w_conj_kernel_fn` to improve\n",
    "        effectiveness further.\n",
    "\n",
    "        :param theta: Field of view (directional cosines)\n",
    "        :param lam: UV grid range (wavelenghts)\n",
    "        :param uvw: UVWs of visibilities (wavelengths)\n",
    "        :param src: Visibility source information (various)\n",
    "        :param vis: Visibilites to be imaged\n",
    "        :param wstep: Size of w-bins (wavelengths)\n",
    "        :param kernel_cache: Kernel cache. If not passed, we fall back\n",
    "           to `kernel_fn`.\n",
    "        :param kernel_fn: Function for generating the kernels. Parameters\n",
    "           `(theta, w, **kwargs)`. Default `w_kernel`.\n",
    "        :returns: UV grid\n",
    "\n",
    "        \"\"\"\n",
    "\n",
    "        # Construct default cache, if needed. As visibilities are\n",
    "        # traversed in w-order it only needs to hold the last w-kernel.\n",
    "        if kernel_cache is None:\n",
    "            kernel_cache = pylru.FunctionCacheManager(kernel_fn, 1)\n",
    "\n",
    "        N = int(round(theta * lam))\n",
    "        guv = numpy.zeros([N, N], dtype=complex)\n",
    "        for p, s, v in zip(uvw, src, vis):\n",
    "            wbin = wstep * numpy.round(p[2] / wstep)\n",
    "            wg = kernel_cache(theta, wbin, *s, **kwargs)\n",
    "            convgrid(wg, guv, numpy.array([p / lam]), [()], numpy.array([v]))\n",
    "        return guv\n",
    "\n",
    "\n",
    "    def w_cache_predict(theta, lam, uvw, src, guv,\n",
    "                        wstep=2000,\n",
    "                        kernel_cache=None,\n",
    "                        kernel_fn=w_kernel,\n",
    "                        **kwargs):\n",
    "        \"\"\"Predict visibilities using w-kernel cache\n",
    "\n",
    "        :param theta: Field of view (directional cosines)\n",
    "        :param lam: UV grid range (wavelenghts)\n",
    "        :param uvw: UVWs of visibilities  (wavelengths)\n",
    "        :param guv: Input uv grid to de-grid from\n",
    "        :param wstep: Size of w-bins (wavelengths)\n",
    "        :param kernel_cache: Kernel cache. If not passed, we fall back\n",
    "           to `kernel_fn`. See `w_cache_imaging` for details.\n",
    "        :param kernel_fn: Function for generating the kernels. Parameters\n",
    "           `(theta, w, **kwargs)`. Default `w_kernel`.\n",
    "        :returns: degridded visibilities\n",
    "        \"\"\"\n",
    "\n",
    "        if kernel_cache is None:\n",
    "            kernel_cache = pylru.FunctionCacheManager(kernel_fn, 1)\n",
    "        def kernel_binner(theta, w, **kw):\n",
    "            wbin = wstep * numpy.round(w / wstep)\n",
    "            return kernel_cache(theta, wbin, **kw)\n",
    "        v = numpy.ndarray(nv, dtype=complex)\n",
    "        for p, s in zip(uvw, src):\n",
    "            wbin = wstep * numpy.round(p[2] / wstep)\n",
    "            wg = kernel_cache(theta, wbin, *s, **kwargs)\n",
    "            v[ixs] = convdegrid(wg, guv, numpy.array([p / lam]))\n",
    "        return v\n",
    "\n",
    "\n",
    "    def mirror_uvw(uvw, vis):\n",
    "        \"\"\"Mirror uvw with v<0 such that all visibilities have v>=0\n",
    "\n",
    "        The result visibilities will be equivalent, as every baseline\n",
    "        `a->b` has a \"sister\" baseline `b->a` with a complex-conjugate\n",
    "        value. A dataset typically only contains one of the two, so here\n",
    "        we simply choose visibilities that lie in one half of the grid.\n",
    "\n",
    "        :param uvw: UVWs of visibilities\n",
    "        :param vis: Visibilities\n",
    "        :returns: new uvw, vis\n",
    "        \"\"\"\n",
    "\n",
    "        # Determine indices with v<1, make copies to update\n",
    "        vn = uvw[:,1] < 0\n",
    "        uvw = numpy.copy(uvw)\n",
    "        vis = numpy.copy(vis)\n",
    "\n",
    "        # Flip coordinates and conjugate visibilities\n",
    "        uvw[vn] = -uvw[vn]\n",
    "        vis[vn] = numpy.conj(vis[vn])\n",
    "        return uvw, vis\n",
    "\n",
    "\n",
    "    def make_grid_hermitian(guv):\n",
    "        \"\"\"\n",
    "        Make a grid \"hermitian\" by adding it to its own conjugated mirror\n",
    "        image.\n",
    "\n",
    "        Just as baselines can be seen from two sides, the grid is\n",
    "        \"hermitian\": Mirrored coordinates yield complex-conjugate\n",
    "        uv-cells. However in practice, it is less computationally\n",
    "        intensive to just grid one of each baseline pair, and then restore\n",
    "        the hermitian property afterwards.\n",
    "\n",
    "        :param guv: Input grid\n",
    "        :returns: Hermitian grid\n",
    "        \"\"\"\n",
    "\n",
    "        # Make mirror image, then add its conjugate to the original grid.\n",
    "        # This is not the same concept as hermitian matrices, as:\n",
    "        #  1) Not the same symetry as transposition\n",
    "        #  2) We mirror on the zero point, which is off-center if the grid\n",
    "        #     has even size\n",
    "        if guv.shape[0] % 2 == 0:\n",
    "            guv[1:,1:] += numpy.conj(guv[:0:-1,:0:-1])\n",
    "            # Note that we ignore the high frequencies here\n",
    "        else:\n",
    "            guv += numpy.conj(guv[::-1,::-1])\n",
    "        return guv\n",
    "\n",
    "\n",
    "    def do_imaging(theta, lam, uvw, src, vis, imgfn, **kwargs):\n",
    "\n",
    "        \"\"\"Do imaging with imaging function (imgfn)\n",
    "\n",
    "        :param theta: Field of view (directional cosines)\n",
    "        :param lam: UV grid range (wavelenghts)\n",
    "        :param uvw: UVWs of visibilities (wavelengths)\n",
    "        :param ant: Visibility source information (various)\n",
    "        :param vis: Visibilities to be imaged\n",
    "        :param imgfn: imaging function e.g. `simple_imaging`, `conv_imaging`,\n",
    "          `w_slice_imaging` or `w_cache_imaging`. All keyword parameters\n",
    "          are passed on to the imaging function.\n",
    "        :returns: dirty Image, psf\n",
    "        \"\"\"\n",
    "        if src is None: src = numpy.ndarray((len(vis), 0))\n",
    "        # Mirror baselines such that v>0\n",
    "        uvw,vis = mirror_uvw(uvw, vis)\n",
    "        # Determine weights\n",
    "        wt = doweight(theta, lam, uvw, numpy.ones(len(uvw)))\n",
    "        # Make image\n",
    "        cdrt = imgfn(theta, lam, uvw, src, wt * vis, **kwargs)\n",
    "        drt = numpy.real(ifft(make_grid_hermitian(cdrt)))\n",
    "        # Make point spread function\n",
    "        c = imgfn(theta, lam, uvw, src, wt, **kwargs)\n",
    "        psf = numpy.real(ifft(make_grid_hermitian(c)))\n",
    "        # Normalise\n",
    "        pmax = psf.max()\n",
    "        assert pmax > 0.0\n",
    "        return drt / pmax, psf / pmax, pmax\n",
    "\n",
    "\n",
    "    def do_predict(theta, lam, uvw, src, modelimage, predfn, **kwargs):\n",
    "        \"\"\"Predict visibilities for a model Image at the phase centre using the\n",
    "        specified degridding function.\n",
    "\n",
    "        :param theta: Field of view (directional cosines)\n",
    "        :param lam: UV grid range (wavelenghts)\n",
    "        :param uvw: UVWs of visiblities (wavelengths)\n",
    "        :param modelimage: model image as numpy.array (phase center at Nx/2,Ny/2)\n",
    "        :param predfn: prediction function e.g. `simple_predict`,\n",
    "          `w_slice_predict` or `w_cache_predict`.\n",
    "        :returns: predicted visibilities\n",
    "        \"\"\"\n",
    "        ximage = fft(modelimage.astype(complex))\n",
    "        return predfn(theta, lam, uvw, src, ximage, **kwargs)\n",
    "\n",
    "\n",
    "    \n",
    "    print(\"The optimal gridding code is from Sze-Tan Meng\")\n",
    "    # Load kernel cache\n",
    "    KERNEL_CACHE = {}\n",
    "    with open('gridder.json', 'r') as f:\n",
    "        for key, val in load(f):\n",
    "            KERNEL_CACHE[tuple(key[0])] = val\n",
    "\n",
    "    def trap(vec, dx):\n",
    "        # Perform trapezoidal integration\n",
    "        return dx * (numpy.sum(vec) - 0.5 * (vec[0] + vec[-1]))\n",
    "\n",
    "    def func_to_min(h, x0, M, R):\n",
    "        N = len(h)\n",
    "        nu = (np.arange(M, dtype=float) + 0.5) / (2 * M)\n",
    "        x = x0 * np.arange(N+1, dtype=float)/N\n",
    "        C = calc_gridder_as_C(h, x0, nu, R)\n",
    "        dnu = nu[1] - nu[0]\n",
    "        dx = x[1] - x[0]\n",
    "        h_ext = np.concatenate(([1.0], h))\n",
    "        loss = np.zeros((len(h_ext), 2, M), dtype=float)\n",
    "        for n, x_val in enumerate(x):\n",
    "            one_app = 0\n",
    "            for r in range(0, 2 * R):\n",
    "                l = r - R + 1\n",
    "                one_app += h_ext[n] * C[r, :] * np.exp(2j * np.pi * (l - nu) * x_val)\n",
    "            loss[n, 0, :] = 1.0 - np.real(one_app)\n",
    "            loss[n, 1, :] = np.imag(one_app)\n",
    "            if n in [0, N]:\n",
    "                loss[n, :, :] /= np.sqrt(2)\n",
    "        loss = loss.reshape(2 * M * (N + 1))\n",
    "        return loss\n",
    "\n",
    "    def optimal_grid(R, x0, N, M, h_initial=None):\n",
    "        if h_initial is None:\n",
    "            h_initial = np.ones(N, dtype=float)\n",
    "        return leastsq(func_to_min, h_initial, args=(x0, M, R), full_output=True)\n",
    "\n",
    "    def find_cached_kernel(R, x0,  N=32, M=64, max_dx0=1/16):\n",
    "        \"\"\" Returns the key for a cached gridder with th given parameters\n",
    "\n",
    "        :param R: Half support in pixels\n",
    "        :param x0: Image plane coordinates up to which coordinates are optimised\n",
    "        :param N: Number of points to evaluate in image space\n",
    "        :param M: Number of sub-grid points to evaluate in grid space (oversampling)\n",
    "        :param max_dx0: Difference in x0 to accept when using cached kernel\n",
    "        \"\"\"\n",
    "\n",
    "        # First try to look up directly\n",
    "        key = (R, x0, N, M)\n",
    "        if key in KERNEL_CACHE:\n",
    "            return key\n",
    "\n",
    "        # Then try to find next best one\n",
    "        best = None\n",
    "        dx0 = 1e15\n",
    "        for kp in KERNEL_CACHE.keys():\n",
    "            Rp, x0p, Np, Mp = kp\n",
    "\n",
    "            # R must match, x0 difference must be at least as good\n",
    "            if Rp != R: continue\n",
    "            if abs(x0p - x0) > dx0: continue\n",
    "\n",
    "            # Otherwise select by quality of optimisation\n",
    "            if abs(x0p - x0) == dx0:\n",
    "                if Np < best[2] or Mp < best[3]:\n",
    "                    continue\n",
    "            best = kp\n",
    "            dx0 = abs(x0p - x0)\n",
    "\n",
    "        return best\n",
    "\n",
    "    def optimal_grid_cached(R, x0, N=32, M=64, max_dx0=1/16, h_initial=None):\n",
    "        \"\"\" Returns an optimal gridder for the given parameters.\n",
    "\n",
    "        :param R: Half support in pixels\n",
    "        :param x0: Image plane coordinates up to which coordinates are optimised\n",
    "        :param N: Number of points to evaluate in image space\n",
    "        :param M: Number of sub-grid points to evaluate in grid space (oversampling)\n",
    "        :param max_dx0: Difference in x0 to accept when using cached kernel\n",
    "        \"\"\"\n",
    "        assert R >= 1\n",
    "        assert x0 < 0.5\n",
    "\n",
    "        # Best one good enough?\n",
    "        best = find_cached_kernel(R, x0, N, M, max_dx0)\n",
    "        if best is not None:\n",
    "            Rp, x0p, Np, Mp = best\n",
    "            if x0p >= x0 and x0p - x0 <= max_dx0 and Np >= N and Mp >= M:\n",
    "                return KERNEL_CACHE[best]\n",
    "\n",
    "        # Have one that is at least close enough for an initial solution?\n",
    "        h_initial = None\n",
    "        if best is not None:\n",
    "            Rp, x0p, Np, Mp = best\n",
    "            if abs(x0p - x0) <= max_dx0:\n",
    "                x = x0 * (1 + np.arange(0, N, dtype=float))/N\n",
    "                h_initial = calc_gridding_correction_fine(x, KERNEL_CACHE[best]['h'], x0p, M, Rp)\n",
    "\n",
    "        # As last resort, use one with less support\n",
    "        if h_initial is None:\n",
    "            if R == 3:\n",
    "                h_initial = optimal_grid_cached(R-1,x0,N,M, max_dx0)['h']\n",
    "            elif R >= 4:\n",
    "                h0 = optimal_grid_cached(R-2,x0,N,M, max_dx0)['h']\n",
    "                h1 = optimal_grid_cached(R-1,x0,N,M, max_dx0)['h']\n",
    "                h_initial = h1 * (h1/h0)\n",
    "\n",
    "        # Run optimisation\n",
    "        key = (R, x0, N, M)\n",
    "        print(\"Calculating\", key)\n",
    "        h, cov_h, infodict, mesg, ler = optimal_grid(R, x0, N, M, h_initial)\n",
    "        if ler == 0:\n",
    "            return None\n",
    "\n",
    "        # Determine error\n",
    "        mean_map_err = calc_mean_map_error(x0, N, M, R, h)\n",
    "        print(\"Mean map error: %g\" % mean_map_err)\n",
    "\n",
    "        # Make & cache result\n",
    "        result = {\"R\": R, \"x0\":x0, \"h\":h, \"err\":mean_map_err}\n",
    "        KERNEL_CACHE[key] = result\n",
    "        return result\n",
    "\n",
    "    def calc_gridder_as_C(h, x0, nu, R):\n",
    "        # Calculate gridding function C(l,nu) from gridding correction h(x) evaluated at (n+1) x_0/N where n is in range 0,...,N-1. \n",
    "        #  We assume that h(0)=1 for normalization, and use the trapezium rule for integration.\n",
    "        # The gridding function is calculated for l=-R+1 to R at points nu\n",
    "        M = len(nu)\n",
    "        C = np.zeros((2*R, M), dtype=float)\n",
    "        K = np.zeros((2*R, 2*R))\n",
    "        N = len(h)\n",
    "        x = x0 * np.arange(0, N+1, dtype=float)/N\n",
    "        dx = x0 / N\n",
    "        h_ext = np.concatenate(([1.0], h))\n",
    "\n",
    "        for rp in range(0, 2 * R):\n",
    "            lp = rp - R + 1\n",
    "            for r in range(2 * R):\n",
    "                l = r - R + 1\n",
    "                K[rp, r] = trap((h_ext**2) * np.cos(2 * np.pi * (lp - l) * x), dx)\n",
    "        #Kinv = np.linalg.pinv(K)\n",
    "\n",
    "        rhs = np.zeros(2*R, dtype=float)\n",
    "        for m, nu_val in enumerate(nu):\n",
    "            for rp in range(0, 2 * R):\n",
    "                lp = rp - R + 1\n",
    "                rhs[rp] = trap(h_ext * np.cos(2 * np.pi * (lp - nu_val) * x), dx)\n",
    "            C[:,m] = np.linalg.lstsq(K, rhs, 1e-14)[0]\n",
    "            # C[:,m] = np.dot(Kinv, rhs)\n",
    "        return C\n",
    "\n",
    "    def make_evaluation_grids(R, M, N):\n",
    "        \"\"\"Generate vectors nu and x on which the gridder and gridding correction functions need to be evaluated.\n",
    "            R is the number of integer gridpoints on each side of the data point\n",
    "            M determines the sampling of the nu grid, dnu = 1/(2*M)\n",
    "            N determines the sampling of the x grid, dx = 1/(2*N)\n",
    "        \"\"\"\n",
    "        nu = (numpy.arange(2 * R * M, dtype=float) + 0.5) / (2 * M)\n",
    "        x = numpy.arange(N+1, dtype=float)/(2*N)\n",
    "        return nu, x\n",
    "\n",
    "    def calc_gridder(h, x0, nu, M, R):\n",
    "        # Calculate gridder function on a grid nu which should have been generated using make_evaluation_grids\n",
    "        #  The array h is the result of an optimization process for the gridding correction function evaluated\n",
    "        #  on a relatively coarse grid extending from 0 to x0\n",
    "        C = calc_gridder_as_C(h, x0, nu, R)\n",
    "        gridder = np.zeros(2*M*R, dtype=float)\n",
    "        for m in range(M):\n",
    "            for rp in range(0, 2 * R):\n",
    "                lp = rp - R + 1\n",
    "                indx = m - 2*lp*M\n",
    "                if indx >= 0:\n",
    "                    gridder[indx] = C[rp, m]\n",
    "                else:\n",
    "                    gridder[-indx-1] = C[rp, m]\n",
    "        return gridder\n",
    "\n",
    "    # The functions with the \"_fine\" suffix allow the convolution function\n",
    "    # C and the gridding correction function h to be evaluated at\n",
    "    # arbitrary points, rather than at only the points which were used in\n",
    "    # performing the optimization\n",
    "\n",
    "    def calc_gridding_fine(h, x0, nu, R):\n",
    "        # Calculate gridding function C(l,nu) from gridding correction h(x) evaluated at (n+1) x_0/N where n is in range 0,...,N-1.\n",
    "        #  We assume that h(0)=1 for normalization, and use the trapezium rule for integration.\n",
    "        # The gridding function is calculated for l=-R+1 to R at points nu\n",
    "        M = len(nu)\n",
    "        C = numpy.zeros((2*R, M), dtype=float)\n",
    "        K = numpy.zeros((2*R, 2*R))\n",
    "        N = len(h)\n",
    "        x = x0 * numpy.arange(0, N+1, dtype=float)/N\n",
    "        dx = x0 / N\n",
    "        h_ext = numpy.concatenate(([1.0], h))\n",
    "\n",
    "        for rp in range(0, 2 * R):\n",
    "            lp = rp - R + 1\n",
    "            for r in range(2 * R):\n",
    "                l = r - R + 1\n",
    "                K[rp, r] = trap((h_ext**2) * numpy.cos(2 * numpy.pi * (lp - l) * x), dx)\n",
    "        Kinv = numpy.linalg.inv(K)\n",
    "\n",
    "        rhs = numpy.zeros(2*R, dtype=float)\n",
    "        for m, nu_val in enumerate(nu):\n",
    "            for rp in range(0, 2 * R):\n",
    "                lp = rp - R + 1\n",
    "                rhs[rp] = trap(h_ext * numpy.cos(2 * numpy.pi * (lp - nu_val) * x), dx)\n",
    "            C[:,m] = numpy.dot(Kinv, rhs)\n",
    "        return C\n",
    "\n",
    "    def gridder_to_C(gridder, R):\n",
    "        \"\"\"Reformat gridder evaluated on the nu grid returned by make_evaluation_grids into the sampled C function\n",
    "           which has an index for the closest gridpoint and an index for the fractional distance from that gridpoint\n",
    "        \"\"\"\n",
    "        M = len(gridder) // (2 * R)\n",
    "        C = np.zeros((2 * R, M), dtype=float)\n",
    "        for r in range(0, 2 * R):\n",
    "            l = r - R + 1\n",
    "            indx = np.arange(M) - 2 * M * l\n",
    "            # Use symmetry to deal with negative indices\n",
    "            indx[indx<0] = -indx[indx<0] - 1\n",
    "            C[r, :] = gridder[indx]\n",
    "        return C\n",
    "\n",
    "    def calc_gridding_correction_fine(x, h, x0, M, R):\n",
    "        nu = (numpy.arange(M, dtype=float) + 0.5) / (2 * M)\n",
    "        C = calc_gridding_fine(h, x0, nu, R)\n",
    "        nu = (numpy.arange(M, dtype=float) + 0.5) / (2 * M)\n",
    "        dnu = 1.0 / (2 * M)\n",
    "        c = numpy.zeros(x.shape, dtype=float)\n",
    "        d = numpy.zeros(x.shape, dtype=float)\n",
    "        for n, x_val in enumerate(x):\n",
    "            for rp in range(0, 2 * R):\n",
    "                lp = rp - R + 1\n",
    "                for r in range(2 * R):\n",
    "                    l = r - R + 1\n",
    "                    d[n] += numpy.sum(C[rp, :] * C[r, :] * numpy.cos(2 * numpy.pi * (lp - l) * x_val)) * dnu\n",
    "                c[n] += numpy.sum(C[rp, :] * numpy.cos(2 * numpy.pi * (lp - nu) * x_val)) * dnu\n",
    "        hfine = c/d\n",
    "        return hfine\n",
    "\n",
    "    def calc_map_error(gridder, grid_correction, nu, x, R):\n",
    "        M = len(nu) // (2 * R)\n",
    "        N = len(x) - 1\n",
    "        dnu = nu[1] - nu[0]\n",
    "        C = gridder_to_C(gridder, R)\n",
    "        loss = np.zeros((len(x), 2, M), dtype=float)\n",
    "        for n, x_val in enumerate(x):\n",
    "            one_app = 0\n",
    "            for r in range(0, 2 * R):\n",
    "                l = r - R + 1\n",
    "                one_app += grid_correction[n] * C[r, :] * np.exp(2j * np.pi * (l - nu[:M]) * x_val)\n",
    "            loss[n, 0, :] = 1.0 - np.real(one_app)\n",
    "            loss[n, 1, :] = np.imag(one_app)\n",
    "        map_error = np.zeros(len(x), dtype=float)\n",
    "        for i in range(len(x)):\n",
    "            map_error[i] = 2 * np.sum((loss[i, :, :].flatten())**2) * dnu\n",
    "        return map_error\n",
    "\n",
    "    def calc_mean_map_error(x0, N, M, R, h):\n",
    "        nu, x = make_evaluation_grids(R, M, N)\n",
    "        gridder = calc_gridder(h, x0, nu, M, R)\n",
    "        grid_correction = calc_gridding_correction_fine(x, h, x0, M, R)\n",
    "        map_err = calc_map_error(gridder, grid_correction, nu, x, R)\n",
    "        which = np.digitize(x0, x)\n",
    "        return numpy.sqrt( trap(map_err[:which], 1.0/(2*N)) / x[which] )\n",
    "\n",
    "    def sze_tan_grid_correction(R, x0, image_size, Nopt=64, Mopt=32, max_dx0=1/16):\n",
    "        \"\"\" Generate a Sze-Tan grid correction pattern in crocodile coordinate system\n",
    "        :param R: Half-support of kernel\n",
    "        :param x0: Significant part of image\n",
    "        :param grid_size: Size of pattern to create\n",
    "        :param Nopt: Number of points to evaluate in image space\n",
    "        :param Mopt: Number of sub-grid points to evaluate in grid space (oversampling)\n",
    "        :param max_dx0: Difference in x0 to accept when using cached kernel\n",
    "        \"\"\"\n",
    "        grid = optimal_grid_cached(R, x0, Nopt, Mopt, max_dx0)\n",
    "        return sze_tan_grid_correction_gen(R, x0, coordinates(image_size), Nopt, Mopt, max_dx0)\n",
    "\n",
    "    def sze_tan_grid_correction_gen(R, x0, x, Nopt=64, Mopt=32, max_dx0=1/16):\n",
    "        \"\"\" Generate a Sze-Tan grid correction pattern for arbitrary image coordinates\n",
    "        :param R: Half-support of kernel\n",
    "        :param x0: Significant part of image\n",
    "        :param x: Image coordinates\n",
    "        :param Nopt: Number of points to evaluate in image space\n",
    "        :param Mopt: Number of sub-grid points to evaluate in grid space (oversampling)\n",
    "        :param max_dx0: Difference in x0 to accept when using cached kernel\n",
    "        \"\"\"\n",
    "        grid = optimal_grid_cached(R, x0, Nopt, Mopt, max_dx0)\n",
    "        grid_correction = calc_gridding_correction_fine(numpy.array(x), grid['h'], grid['x0'], len(x), R)\n",
    "        return 1 / grid_correction\n",
    "\n",
    "    def sze_tan_gridder(R, x0, over, Nopt=64, Mopt=32, max_dx0=1/16):\n",
    "        grid = optimal_grid_cached(R, x0, Nopt, Mopt, max_dx0)\n",
    "\n",
    "        # Generate gridder in crocodile coordinate system\n",
    "        nu = numpy.arange(over, dtype=float) / over\n",
    "        gridding = calc_gridding_fine(grid['h'], grid['x0'], nu, R)\n",
    "        return numpy.transpose(gridding[::-1])\n",
    "\n",
    "    def sze_tan_mean_error(R, x0, Nopt=64, Mopt=32, max_dx0=1/16):\n",
    "        grid = optimal_grid_cached(R, x0, Nopt, Mopt, max_dx0)\n",
    "        return calc_mean_map_error(x0, Nopt, Mopt, R, grid['h'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "theta = 2.0\n",
    "lam = 32\n",
    "grid_size = int(theta*lam)\n",
    "\n",
    "# Convert Locations to u/v/w from metres\n",
    "cfreq = 74029999.9919\n",
    "wl = 3e8/cfreq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#print(locations_uvw)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulate Electric Field\n",
    "\n",
    "We really want to simulate instead of use real data here, so we can generate the absolute worst possible antenna distribution and show we are able to recover an image by the FFT algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate_electric_fields_coplanar(locations_uvw,points):\n",
    "    elec_ss = numpy.zeros(shape=(locations_uvw.shape[0]),dtype=numpy.complex128)\n",
    "    \n",
    "    for i in numpy.arange(locations_uvw.shape[0]):\n",
    "        for point in points:\n",
    "            elec_ss[i] += point[2]*numpy.exp(2j*numpy.pi*(locations_uvw[i,0]*point[0]+locations_uvw[i,1]*point[1]))\n",
    "    return elec_ss\n",
    "\n",
    "def simulate_electric_fields(locations_uvw,points):\n",
    "    elec_ss = numpy.zeros(shape=(locations_uvw.shape[0]),dtype=numpy.complex128)\n",
    "    \n",
    "    for i in numpy.arange(locations_uvw.shape[0]):\n",
    "        for point in points:\n",
    "            l = point[0]\n",
    "            m = point[1]\n",
    "            n = numpy.sqrt(1.0-l**2-m**2) - 1.0\n",
    "            amp = point[2]\n",
    "            u = locations_uvw[i,0]\n",
    "            v = locations_uvw[i,1]\n",
    "            w = locations_uvw[i,2]\n",
    "            elec_ss[i] += amp*numpy.exp(2j*numpy.pi*(u*l+v*m+w*n))\n",
    "    return elec_ss\n",
    "\n",
    "def calculate_gaussian_volume_of_points(antenna_number):   \n",
    "    return (numpy.random.standard_normal((antenna_number,3))-0.5)*6\n",
    "    \n",
    "def epic_image_snapshot(efield,locations):\n",
    "    grid = numpy.zeros(shape=(grid_size,grid_size),dtype=numpy.complex128)\n",
    "    image = numpy.zeros(shape=(grid_size,grid_size),dtype=numpy.complex128)    \n",
    "    location_grid_points = locations\n",
    "\n",
    "    for j,efieldd in enumerate(efield):\n",
    "            grid[location_grid_points[j,0],location_grid_points[j,1]] += efieldd\n",
    "\n",
    "    imaged = numpy.fft.fftshift(numpy.fft.ifft2(numpy.fft.fftshift(grid),s=(grid_size,grid_size)))\n",
    "    imaged = imaged * imaged.conj()\n",
    "    image += imaged\n",
    "    grid[...] = 0.0\n",
    "        \n",
    "    #plt.imshow(grid.real)\n",
    "    #plt.show()\n",
    "    #image = numpy.fft.fftshift(numpy.fft.ifft2(numpy.fft.fftshift(grid)))\n",
    "    #imsq = image * image.conj()\n",
    "    return image\n",
    "\n",
    "def normalise_image(image):\n",
    "\n",
    "    im_max = numpy.max(image)\n",
    "    im_min = numpy.min(image)\n",
    "    \n",
    "    im_n = (image - im_min)/(im_max-im_min)\n",
    "    return im_n\n",
    "     \n",
    "def plot_celestial_sphere(image,title='Celestial Sphere',norm=None,l_max_min=1,m_max_min=1,cmap=None,save=None,contour=False,levels=None):\n",
    "    \n",
    "    xticks = (numpy.arange(image.shape[0])/image.shape[0]  * theta) - theta/2\n",
    "    yticks = xticks.copy()\n",
    "    \n",
    "    lm_coord = [0,image.shape[0]//2,image.shape[0]]\n",
    "    \n",
    "    \n",
    "    fig,ax = plt.subplots(figsize=(5,5))\n",
    "    s= ax.imshow(numpy.abs(image),norm=norm,cmap=cmap,origin='lower')\n",
    "    if contour:\n",
    "        ax.contour(numpy.abs(image),colors='k',origin='lower',levels=levels)\n",
    "    ax.set_xticks(lm_coord)\n",
    "    ax.set_xticklabels([-l_max_min,0,l_max_min])\n",
    "    ax.set_yticks(lm_coord)\n",
    "    ax.set_yticklabels([-m_max_min,0,m_max_min])\n",
    "    fig.colorbar(s,ax=ax)\n",
    "    ax.set_title(title)\n",
    "    ax.set_xlabel(\"l\")\n",
    "    ax.set_ylabel(\"m\")\n",
    "    if save is not None:\n",
    "        plt.savefig(save)\n",
    "    \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Now let us try with a gaussian cube of electric field locations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Generate a gaussian cube\n",
    "locations_gaussian = calculate_gaussian_volume_of_points(1024)\n",
    "\n",
    "us = locations_gaussian[:,0]\n",
    "vs = locations_gaussian[:,1]\n",
    "ws = locations_gaussian[:,2]\n",
    "fig = plt.figure(figsize=(6,6))\n",
    "ax = fig.add_subplot(111,projection='3d')\n",
    "#ax = plt.subplot(111, projection='3d')\n",
    "ax.scatter(us,vs,ws, color='red',marker='x',alpha=0.3)\n",
    "ax.set_title('Electric Field Locations')\n",
    "ax.set_xlabel('u'); ax.set_ylabel('v'); ax.set_zlabel('w')\n",
    "plt.savefig('efield_locs.pdf')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[124.50028736  94.81461139  92.988958  ]\n",
      "U Range: 20.520006\n",
      "V Range: 20.269554\n",
      "W Range: 17.962194\n"
     ]
    }
   ],
   "source": [
    "locations_uvw = locations_gaussian/(wl/2)\n",
    "\n",
    "u,s,vh = numpy.linalg.svd(locations_uvw)\n",
    "\n",
    "print(s)\n",
    "\n",
    "\n",
    "urange = numpy.max(locations_uvw[:,0]) - numpy.min(locations_uvw[:,0])\n",
    "vrange = numpy.max(locations_uvw[:,1]) - numpy.min(locations_uvw[:,1])\n",
    "wrange = numpy.max(locations_uvw[:,2]) - numpy.min(locations_uvw[:,2])\n",
    "print(\"U Range: %f\"%(urange))\n",
    "print(\"V Range: %f\"%(vrange))\n",
    "print(\"W Range: %f\"%(wrange))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot locations\n",
    "\n",
    "grid_locs = numpy.zeros(shape=(grid_size,grid_size))\n",
    "location_grid_points = (2*locations_uvw + grid_size/2).astype(int)\n",
    "location_grid_points[:,0] = location_grid_points[:,0] +4\n",
    "location_grid_points[:,1] = location_grid_points[:,1] +4\n",
    "#print(location_grid_points)\n",
    "for i in numpy.arange(location_grid_points.shape[0]):\n",
    "    grid_locs[location_grid_points[i,0],location_grid_points[i,1]] += 1.0\n",
    "    \n",
    "plt.imshow(grid_locs)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "points = [[-0.45,0.45,1],[0.45,0.45,1],[0.45,-0.45,1],[-0.45,-0.45,1],[0.5,0.0,1],[0.0,0.5,1],[-0.5,0.0,1],[-0.5,-0.5,1],[-0.8,0.0,1],[0.8,0.0,1]]\n",
    "ee_gaussian_s = simulate_electric_fields(locations_uvw,numpy.asarray(points))\n",
    "ee_gaussian_sc = simulate_electric_fields_coplanar(locations_uvw,numpy.asarray(points))\n",
    "#ee_gaussian_s = simulate_electric_fields(locations_uvw,numpy.asarray([[-0.1,-0.1,100],[-0.1,-0.4,100]]))\n",
    "#ee_gaussian_sc = simulate_electric_fields_coplanar(locations_uvw,numpy.asarray([[-0.1,-0.1,100],[-0.1,-0.4,100]]))\n",
    "image3d = epic_image_snapshot(ee_gaussian_s,location_grid_points) # 3D \n",
    "plot_celestial_sphere(image3d,save='nocorrection.pdf',cmap=plt.get_cmap('cubehelix'))\n",
    "image2d = epic_image_snapshot(ee_gaussian_sc,location_grid_points) # Coplanar Array\n",
    "plot_celestial_sphere(image2d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Try computing with the DFT to make sure we're still on the right line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [],
   "source": [
    "def epic_image_dft(theta,lam,efield,locations):\n",
    "    grid_size = int(theta*lam)\n",
    "    image = numpy.zeros(shape=(grid_size,grid_size),dtype=numpy.complex128)\n",
    "    \n",
    "    for lg in numpy.arange(grid_size):\n",
    "        \n",
    "        lv = (1.0 / (0.5*grid_size)) * (lg - grid_size/2)\n",
    "        #print(lv)\n",
    "        for mg in numpy.arange(grid_size):\n",
    "            mv = (1.0/ (0.5*grid_size)) * (mg - grid_size/2)\n",
    "            if (lv**2 + mv**2 > 1.0):\n",
    "                nv = 0\n",
    "            else:\n",
    "                nv = 1.0 - numpy.sqrt(1.0 - lv**2 - mv**2)\n",
    "            #print(nv)\n",
    "            for j,efieldd in enumerate(efield):\n",
    "                u = locations[j,0]\n",
    "                v = locations[j,1]\n",
    "                w = locations[j,2]\n",
    "                #w = 0\n",
    "                image[lg,mg] += efieldd * numpy.exp(2j*numpy.pi*(u*lv + v*mv + w*nv))\n",
    "    return image / (grid_size**2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "im = epic_image_dft(theta,lam,ee_gaussian_s,locations_uvw)\n",
    "imcg = im * im.conj()\n",
    "plot_celestial_sphere(imcg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "locations_uvwc = locations_uvw.copy()\n",
    "locations_uvwc[:,2] = 0.0\n",
    "im = epic_image_dft(theta,lam,ee_gaussian_sc,locations_uvwc)\n",
    "imc = im * im.conj()\n",
    "plot_celestial_sphere(imc)\n",
    "plot_celestial_sphere(imcg-imc,title='diff')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "DFT Looks good, let's do this the easy way with W-Stacking (or W-Projection kernels get ridiculous)\n",
    "\n",
    "(Sorry Steve)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w range:        -0.500 - 0.500 lambda\n",
      "Kernel size:    5 px (> 13.567 recommended)\n",
      "Expected error: 8.574441 %\n"
     ]
    }
   ],
   "source": [
    "wstack_delta = 1.0\n",
    "wmax = wstack_delta/2\n",
    "size=5\n",
    "# Stealing Peter's code makes life easier.\n",
    "def recommended_size(eps=0.01):\n",
    "    usupp = numpy.sqrt((wmax*theta/2)**2 + (wmax**1.5 * theta / 2 / numpy.pi / eps))\n",
    "    return 2 * theta * usupp\n",
    "def recommended_diff(eps):\n",
    "    return abs(recommended_size(eps) - size)\n",
    "\n",
    "print(\"w range:        %.3f - %.3f lambda\" % (-wmax, wmax))\n",
    "print(\"Kernel size:    %d px (> %.3f recommended)\" % (size, recommended_size()))\n",
    "print(\"Expected error: %f %%\" % (100 * scipy.optimize.minimize(recommended_diff, 0.0001, bounds=[(1e-10,1)]).x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define our wide field correction functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Write our versions of these. I guess Bojan never thought people would be crazy enough to do horizon-to-horizon images!\n",
    "def my_w_kernel_function(l, m, w):\n",
    "    \n",
    "    r2 = l**2 + m**2\n",
    "    r2v = r2 > 1\n",
    "    #print(r2v)\n",
    "    r2[r2v] = 0.0\n",
    "    \n",
    "    ph = 1.0 - numpy.sqrt(1.0 - r2)\n",
    "    cp = numpy.exp(2j * numpy.pi * w * ph)\n",
    "    #cp[r2v] = numpy.exp(2j*numpy.pi * w)\n",
    "    return cp\n",
    "\n",
    "def w_kern(theta, w, NpixFF, NpixKern, Qpx, invert=True,**kwargs):\n",
    "    assert NpixFF > NpixKern or (NpixFF == NpixKern and Qpx == 1)\n",
    "\n",
    "    l,m = kernel_coordinates(NpixFF, theta, **kwargs)\n",
    "    #l,m = theta * coordinates2(NpixFF)\n",
    "    kern = my_w_kernel_function(l,m,w)\n",
    "    if invert:\n",
    "        kern = 1 / kern\n",
    "    krn = kernel_oversample(kern, Qpx, NpixKern)\n",
    "    return krn\n",
    "    \n",
    "def generate_fresnel(theta,lam,dw):\n",
    "    grid_size = int(theta * lam)\n",
    "    ls,ms = theta*coordinates2(grid_size) \n",
    "    \n",
    "    return my_w_kernel_function(ls,ms,dw)\n",
    "\n",
    "def wide_field_wkernel(theta,lam,dw):\n",
    "    grid_size = int(theta * lam)\n",
    "    frnl = generate_fresnel(theta,lam,dw)\n",
    "    plt.imshow(frnl.real)\n",
    "    plt.colorbar()\n",
    "    plt.show()\n",
    "    plt.imshow(frnl.imag)\n",
    "    plt.colorbar()\n",
    "    plt.show()\n",
    "    frnl_f = numpy.fft.fftshift(numpy.fft.fft2(numpy.fft.fftshift(frnl)))\n",
    "    frnl_f = frnl_f/numpy.max(frnl_f)\n",
    "    plt.imshow(frnl_f.real)\n",
    "    \n",
    "    plt.colorbar()\n",
    "    plt.show()\n",
    "    \n",
    "\n",
    "def kernel_correction(theta,lam,size):\n",
    "    grid_size = int(theta*lam)\n",
    "    grid = numpy.zeros(shape=(grid_size,grid_size),dtype=numpy.complex128)\n",
    "    \n",
    "    gc = grid_size//2\n",
    "    gclb = int(gc - size//2)\n",
    "    gcub = int(gc + size//2)+1\n",
    "\n",
    "    grid[gclb:gcub,gclb:gcub] = 1.0\n",
    "    grid = numpy.fft.fftshift(numpy.fft.fft2(numpy.fft.fftshift(grid)))\n",
    "    return grid\n",
    "\n",
    "# This is a helpful blugeoning function for when I care not for normalising correctly...\n",
    "def normalise_image(image):\n",
    "    \n",
    "    im_min = numpy.min(image)\n",
    "    im_max = numpy.max(image)\n",
    "    \n",
    "    im_n = (image - im_min)/(im_max-im_min)\n",
    "    return im_n\n",
    "\n",
    "#wide_field_wkernel(theta,lam,0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our anti-aliasing function. Here we use a Prolate Spheroidal Wave Function (PSWF) which is very near to optimal.\n",
    "\n",
    "You can also use a sinc or a sinc modulated by a wide gaussian, but PSWF gives the best performance without optimising versus the DFT (which is what Sze-Tan promoted in his 1986 PhD Thesis). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(128, 12)\n"
     ]
    }
   ],
   "source": [
    "# Generate a prolate spheroidal wave function anti-aliasing function.\n",
    "# For electric fields you need to apply it twice! (or square it and apply after multiplying image by its conjugate!)\n",
    "support = 12\n",
    "aa = anti_aliasing_function(int(theta*lam), 0, support)\n",
    "aa2 = numpy.outer(aa, aa)\n",
    "plt.rcParams['figure.figsize'] = 7, 5\n",
    "plt.plot(theta*coordinates(int(theta*lam)), aa)\n",
    "plt.title(\"Anti Aliasing Function (Image Space)\")\n",
    "plt.show()\n",
    "#show_image(aa2, \"aa2\", theta)\n",
    "\n",
    "#aa_grid = numpy.fft.fft(aa)\n",
    "oversample = 128\n",
    "r = numpy.arange(-oversample*(support//2), oversample*((support+1)//2)) / oversample\n",
    "kv=kernel_oversample(aa, oversample, support)/64\n",
    "plt.plot(r, numpy.transpose(kv).flatten().real);\n",
    "plt.title(\"Anti Aliasing Function (Grid Space)\")\n",
    "plt.show()\n",
    "\n",
    "aaf_2D = numpy.outer(aa.T.flatten(),aa.T.flatten().T)\n",
    "plt.imshow(aaf_2D.real,cmap=plt.get_cmap('jet'))\n",
    "plt.colorbar()\n",
    "plt.title(\"2D Anti Aliasing Function(Image Space)\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "kv_2D = numpy.outer(kv[0,:].T.flatten(),kv[0,:].T.flatten().T)\n",
    "plt.imshow(kv_2D.real,cmap=plt.get_cmap('jet'))\n",
    "plt.colorbar()\n",
    "plt.title(\"2D Anti Aliasing Function(Grid Space)\")\n",
    "plt.show()\n",
    "\n",
    "\n",
    "print(kv.shape)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's W-Stack and just to hammer the point home about anti-aliasing we compute a  W-Stack with an anti-aliasing kernel and also compute a w-stack without any AA to show how important it is! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AA Support:  12\n",
      "AA Oversampling:  128\n",
      "Max W:  7.620837651365984\n",
      "Min W:  -10.341356347721634\n",
      "W Range:  17.962193999087617\n",
      "Number of W Planes:  36.0\n",
      "Max W:  7.620837651365984\n",
      "Min W:  -10.341356347721634\n",
      "W Range:  17.962193999087617\n",
      "Number of W Planes:  36.0\n",
      "0.06839650866239202\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total Error: 0.000077\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total Error: 0.000812\n"
     ]
    }
   ],
   "source": [
    "## Notes:\n",
    "# W-Kernel is definitely not right. Understand why.\n",
    "def epic_wstacking(theta,lam,locations, efieldf,dw,use_aaf=False,aaf=None,gridcor=None):\n",
    "    #print(w_kernel[0,0,:,:])\n",
    "    grid_size = int(theta*lam)\n",
    "    #w_kernel = w_kern(theta,dw,NpixFF=256,NpixKern=size,Qpx=8, invert=True)\n",
    "    #wkh = w_kernel.shape[2]//2\n",
    "    max_w = numpy.max(locations[:,2])\n",
    "    min_w = numpy.min(locations[:,2]) \n",
    "    w_range = max_w - min_w\n",
    "    w_planes = numpy.ceil(w_range/(dw)) \n",
    "    \n",
    "    if use_aaf == True:\n",
    "        if aaf is None:\n",
    "            raise ValueError(\"No anti-aliasing function provided!\")\n",
    "        if gridcor is None:\n",
    "            raise ValueError(\"No Gridding Correction provided!\")\n",
    "        support_aa = aaf.shape[0]\n",
    "        oversampling_aa = aaf.shape[-1]\n",
    "        print(\"AA Support: \",support_aa)\n",
    "        print(\"AA Oversampling: \",oversampling_aa)\n",
    "        \n",
    "    \n",
    "    print(\"Max W: \",max_w)\n",
    "    print(\"Min W: \",min_w)\n",
    "    print(\"W Range: \",w_range)\n",
    "    print(\"Number of W Planes: \",w_planes)\n",
    "    \n",
    "    \n",
    "    #Fresnel Pattern\n",
    "    fresnel_pattern = numpy.fft.fftshift(generate_fresnel(theta,lam,dw))\n",
    "\n",
    "    #Setup W-Stacks\n",
    "    image = numpy.zeros(shape=(grid_size,grid_size),dtype=numpy.complex128)\n",
    "    grid = numpy.zeros(shape=(grid_size,grid_size),dtype=numpy.complex128)\n",
    "    conti = 0\n",
    "    for i in numpy.arange(0,w_planes):\n",
    "        if(i == 0):\n",
    "            pass\n",
    "        else:\n",
    "            grid = numpy.fft.fftshift(numpy.fft.fft2(image))\n",
    "        wpi = i - w_planes//2 \n",
    "        wc = wpi*dw # Gives us our central w-value, so we know which electric field contributions belong to us.\n",
    "        w_ub = wc + dw/2\n",
    "        w_lb = wc - dw/2\n",
    "\n",
    "        # Let's work out which contributions to put on each plane of the W-Stack.\n",
    "        for j,efield in enumerate(efieldf):\n",
    "            #print(efield)\n",
    "            u = locations[j,0]\n",
    "            v = locations[j,1]\n",
    "            w = locations[j,2]\n",
    "            #print(grid)\n",
    "            if ((w > w_lb) and (w < w_ub)):\n",
    "                #print(\"Cont: \",conti)\n",
    "                #conti += 1\n",
    "                ulo = 2*u + grid_size/2\n",
    "                vlo = 2*v + grid_size/2\n",
    "                u_loc = int(numpy.ceil(ulo))\n",
    "                v_loc = int(numpy.ceil(vlo))\n",
    "                \n",
    "                #TODO: Oversample Kernels Correctly\n",
    "                \n",
    "                # Boxcar gridding so I can work out wtf is going on here.\n",
    "                if use_aaf is True:\n",
    "                    # This is where we convolve with our anti-aliasing function\n",
    "                    u_os = int(oversampling_aa*abs(ulo-u_loc))\n",
    "                    v_os = int(oversampling_aa*abs(vlo-v_loc))\n",
    "                    \n",
    "                    aaf_u = aaf[:,u_os]\n",
    "                    aaf_v = aaf[:,v_os]\n",
    "                    aaf_uv = numpy.outer(aaf_u,aaf_v.T).T\n",
    "                    grid[v_loc-support_aa//2:v_loc+support_aa//2,\n",
    "                         u_loc-support_aa//2:u_loc+support_aa//2] += efield * aaf_uv \n",
    "                else:\n",
    "                    grid[v_loc,u_loc] += efield\n",
    "        \n",
    "        image = numpy.fft.ifft2(numpy.fft.fftshift(grid))    \n",
    "        image /= fresnel_pattern\n",
    "\n",
    "    if use_aaf == True:      \n",
    "        return numpy.fft.fftshift(image*(fresnel_pattern**(w_planes//2)))/gridcor\n",
    "    else:\n",
    "        return numpy.fft.fftshift(image*(fresnel_pattern**(w_planes//2)))\n",
    "\n",
    "\n",
    "\n",
    "#for wval in numpy.arange(1.0,5.0,0.025):\n",
    "image_wsg = epic_wstacking(theta,lam,locations_uvw,ee_gaussian_s,0.5,use_aaf=True,aaf=kv.T,gridcor=aaf_2D)\n",
    "image_wsi = (image_wsg * image_wsg.conj())\n",
    "gc_im = image_wsi.T\n",
    "\n",
    "image_wsg_noaa = epic_wstacking(theta,lam,locations_uvw,ee_gaussian_s,0.5,use_aaf=False)\n",
    "image_wsi_noaa = (image_wsg_noaa * image_wsg_noaa.conj())\n",
    "gc_im_noaa = image_wsi_noaa.T\n",
    "\n",
    "from matplotlib.colors import LogNorm\n",
    "from matplotlib.colors import Normalize\n",
    "#plot_celestial_sphere(gc_im,title='W-Stacked Image',norm=Normalize(vmin=0.0, vmax=50.0))\n",
    "#plot_celestial_sphere(imcg,title='Direct Fourier Transform',norm=Normalize(vmin=0.0, vmax=50.0))\n",
    "\n",
    "#Normalise\n",
    "gc_im_n = normalise_image(gc_im)\n",
    "gc_im_noaa_n = normalise_image(gc_im_noaa)\n",
    "imcg_n = normalise_image(imcg)\n",
    "dft_peak = numpy.max(imcg).real\n",
    "print(dft_peak)\n",
    "plot_celestial_sphere(gc_im/numpy.max(gc_im).real,\n",
    "                      title='W-Stacked Image (Anti-Aliased)',\n",
    "                      save='corrected.pdf',\n",
    "                      norm=LogNorm(vmin=0.0001, vmax=0.1),\n",
    "                      cmap=plt.get_cmap('cubehelix'),\n",
    "                      contour=True,\n",
    "                     levels=numpy.arange(0.0,1.0,0.2))\n",
    "plot_celestial_sphere(gc_im_noaa,title='W-Stacked Image (No AA)')\n",
    "plot_celestial_sphere(imcg_n,title='Direct Fourier Transform')\n",
    "diff=numpy.abs(imcg-gc_im)/dft_peak\n",
    "diff_noaa = numpy.abs(gc_im_noaa - imcg)/dft_peak\n",
    "plot_celestial_sphere(diff,title='Diff (Anti-Aliasing)',norm=LogNorm(vmin=0.0001, vmax=0.01),cmap=plt.get_cmap('jet'),save='diffvsdft.pdf')\n",
    "print(\"Total Error: %f\"%(numpy.sum(numpy.square(diff))/(diff.shape[0]*diff.shape[1])))\n",
    "plot_celestial_sphere(diff_noaa,title='Diff (No Anti-Aliasing)',norm=LogNorm(vmin=0.0001, vmax=1),cmap=plt.get_cmap('jet'))\n",
    "print(\"Total Error: %f\"%(numpy.sum(numpy.square(diff_noaa))/(diff_noaa.shape[0]*diff_noaa.shape[1])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 360x864 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "diff=numpy.abs(imcg-gc_im)/dft_peak\n",
    "diff_noaa = numpy.abs(gc_im_noaa - imcg)/dft_peak\n",
    "\n",
    "tick_locs = [0,31,63]\n",
    "tick_names = [-1,0,1]\n",
    "\n",
    "levels = np.arange(0.0, 1.0, 0.05)\n",
    "\n",
    "fig = plt.figure(figsize=(5,12))\n",
    "ax1 = fig.add_subplot(211)\n",
    "ax2 = fig.add_subplot(212)\n",
    "s1 = ax1.imshow(diff,norm=LogNorm(vmin=0.0001, vmax=0.1),cmap=plt.get_cmap('cubehelix'),origin='lower')\n",
    "ax1.contour(diff, levels=levels,colors='k', origin='lower')\n",
    "ax1.set_xticks(tick_locs)\n",
    "ax1.set_xlabel('l')\n",
    "ax1.set_yticks(tick_locs)\n",
    "ax1.set_ylabel('m')\n",
    "ax1.set_xticklabels(tick_names)\n",
    "ax1.set_yticklabels(tick_names)\n",
    "ax1.set_title(\"Anti-Aliased\")\n",
    "s2 = ax2.imshow(diff_noaa,norm=LogNorm(vmin=0.0001, vmax=0.1),cmap=plt.get_cmap('cubehelix'),origin='lower')\n",
    "ax2.contour(diff_noaa, levels=levels,colors='k', origin='lower')\n",
    "ax2.set_xticks(tick_locs)\n",
    "ax2.set_xlabel('l')\n",
    "ax2.set_yticks(tick_locs)\n",
    "ax2.set_ylabel('m')\n",
    "ax2.set_xticklabels(tick_names)\n",
    "ax2.set_yticklabels(tick_names)\n",
    "ax2.set_title(\"No Anti-Aliasing\")\n",
    "cax = fig.add_axes([0.21, 0.03, 0.6, 0.05])\n",
    "fig.colorbar(s1, cax=cax, orientation='horizontal')\n",
    "\n",
    "plt.savefig('diffvsdft.pdf')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Error down to four parts in 10^6? Seems okay. But the sky does start to distort horribly if we don't use lots of w-planes. (Or use less and w-project).\n",
    "\n",
    "Also important to point out we can halve the number of W-Planes by reversing the signs of all the electric field contributions that sit in the negative half of our W-Space. We need to conjugate those electric fields after doing that, but it's an easy optimisation! (Think Mike Hobson originally told me this in my first year PhD viva)\n",
    "\n",
    "## Visibility Comparison\n",
    "\n",
    "Right let's generate some visibilities to show that the two methods are similar, and vanquish the prophets of doom."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(ee_gaussian_s.shape)\n",
    "vis_efield = numpy.outer(ee_gaussian_s,ee_gaussian_s.T.conj())/1000\n",
    "\n",
    "\n",
    "def generate_baseline_vectors(locations):\n",
    "    \n",
    "    loc_no = locations.shape[0]\n",
    "    baseline_vectors = numpy.zeros(shape=(loc_no, loc_no,3))\n",
    "    \n",
    "    for i in numpy.arange(loc_no):\n",
    "        for j in numpy.arange(loc_no):\n",
    "            baseline_vectors[i,j,0] = (locations[i,0] - locations[j,0])#/2\n",
    "            baseline_vectors[i,j,1] = (locations[i,1] - locations[j,1])#/2\n",
    "            baseline_vectors[i,j,2] = (locations[i,2] - locations[j,2])#/2\n",
    "            \n",
    "    return baseline_vectors\n",
    "\n",
    "\n",
    "def plot_baselines(baselines):\n",
    "    \n",
    "    us = baselines[:,0]\n",
    "    vs = baselines[:,1]\n",
    "    ws = baselines[:,2]\n",
    "    ax = plt.subplot(121, projection='3d')\n",
    "    ax.scatter(us,vs,ws, color='red')\n",
    "    ax.set_title('Electric Field Locations')\n",
    "    ax.set_xlabel('u'); ax.set_ylabel('v'); ax.set_zlabel('w')\n",
    "    \n",
    "\n",
    "baselines = generate_baseline_vectors(locations_uvw)\n",
    "\n",
    "# No reason to do more work than necessary\n",
    "\n",
    "#baseline_triu = numpy.triu(baselines)\n",
    "vis_triu = vis_efield\n",
    "#vis_triu = numpy.triu(vis_efield)\n",
    "#baselines = numpy.transpose(baselines,axes=(1,0,2))\n",
    "baselines_uvw = numpy.reshape(baselines,(baselines.shape[0]**2,3))\n",
    "\n",
    "numpy.fill_diagonal(vis_triu,0.0)\n",
    "visibilities = numpy.reshape(vis_triu,(vis_triu.shape[0]**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "#plot_baselines(baselines.reshape(baselines.shape[0]**2,3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(128, 128)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "support_vis = 6\n",
    "oversample_vis = 128\n",
    "\n",
    "aa_vis = anti_aliasing_function(int(theta*2*lam), 0, support_vis)\n",
    "\n",
    "kv_vis=kernel_oversample(aa_vis, oversample_vis, support)/64\n",
    "aaf_2D_vis = numpy.outer(aa_vis,aa_vis.T)\n",
    "print(aaf_2D_vis.shape)\n",
    "plt.imshow(aaf_2D_vis.real,norm=LogNorm(vmin=0.0001, vmax=1),cmap=plt.get_cmap('jet'))\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "imv = epic_image_dft(theta,2*lam,ee_gaussian_s,locations_uvw)\n",
    "imvc = imv * imv.conj()\n",
    "plot_celestial_sphere(imvc)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "imvc_n = normalise_image(imvc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AA Support:  12\n",
      "AA Oversampling:  128\n",
      "Max W:  17.962193999087617\n",
      "Min W:  -17.962193999087617\n",
      "W Range:  35.924387998175234\n",
      "Number of W Planes:  360.0\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-114-265ae705f2c5>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m    112\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    113\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 114\u001b[0;31m \u001b[0mimage_vis\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvisibility_wstacking\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtheta\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mlam\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mbaselines_uvw\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mvisibilities\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0.1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0muse_aaf\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0maaf\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mkv_vis\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mT\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mgridcor\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0maaf_2D_vis\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    115\u001b[0m \u001b[0mimage_vis_noaa\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvisibility_wstacking\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtheta\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mlam\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mbaselines_uvw\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mvisibilities\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0.1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0muse_aaf\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-114-265ae705f2c5>\u001b[0m in \u001b[0;36mvisibility_wstacking\u001b[0;34m(theta, lam, locations, efieldf, dw, use_aaf, aaf, gridcor)\u001b[0m\n\u001b[1;32m     44\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     45\u001b[0m         \u001b[0;31m# Let's work out which contributions to put on each plane of the W-Stack.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 46\u001b[0;31m         \u001b[0;32mfor\u001b[0m \u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mefield\u001b[0m \u001b[0;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mefieldf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     47\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     48\u001b[0m             \u001b[0mu\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlocations\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mj\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "def visibility_wstacking(theta,lam,locations, efieldf,dw,use_aaf=False,aaf=None,gridcor=None):\n",
    "    #print(w_kernel[0,0,:,:])\n",
    "    grid_size = int(theta*lam)\n",
    "    #w_kernel = w_kern(theta,dw,NpixFF=256,NpixKern=size,Qpx=8, invert=True)\n",
    "    #wkh = w_kernel.shape[2]//2\n",
    "    max_w = numpy.max(locations[:,2])\n",
    "    min_w = numpy.min(locations[:,2]) \n",
    "    w_range = max_w - min_w\n",
    "    w_planes = numpy.ceil(w_range/(dw)) \n",
    "    \n",
    "    if use_aaf == True:\n",
    "        if aaf is None:\n",
    "            raise ValueError(\"No anti-aliasing function provided!\")\n",
    "        if gridcor is None:\n",
    "            raise ValueError(\"No Gridding Correction provided!\")\n",
    "        support_aa = aaf.shape[0]\n",
    "        oversampling_aa = aaf.shape[-1]\n",
    "        print(\"AA Support: \",support_aa)\n",
    "        print(\"AA Oversampling: \",oversampling_aa)\n",
    "\n",
    "    \n",
    "    print(\"Max W: \",max_w)\n",
    "    print(\"Min W: \",min_w)\n",
    "    print(\"W Range: \",w_range)\n",
    "    print(\"Number of W Planes: \",w_planes)\n",
    "    \n",
    "    \n",
    "    #Fresnel Pattern\n",
    "    fresnel_pattern = numpy.fft.fftshift(generate_fresnel(theta,lam,dw))\n",
    "\n",
    "    #Setup W-Stacks\n",
    "    image = numpy.zeros(shape=(grid_size,grid_size),dtype=numpy.complex128)\n",
    "    grid = numpy.zeros(shape=(grid_size,grid_size),dtype=numpy.complex128)\n",
    "    conti = 0\n",
    "    for i in numpy.arange(0,w_planes):\n",
    "        if(i == 0):\n",
    "            pass\n",
    "        else:\n",
    "            grid = numpy.fft.fftshift(numpy.fft.fft2(image))\n",
    "        wpi = i - w_planes//2 \n",
    "        wc = wpi*dw # Gives us our central w-value, so we know which electric field contributions belong to us.\n",
    "        w_ub = wc + dw/2\n",
    "        w_lb = wc - dw/2\n",
    "\n",
    "        # Let's work out which contributions to put on each plane of the W-Stack.\n",
    "        for j,efield in enumerate(efieldf):\n",
    "            \n",
    "            u = locations[j,0]\n",
    "            v = locations[j,1]\n",
    "            w = locations[j,2]\n",
    "            \n",
    "            \n",
    "                \n",
    "            #print(grid)\n",
    "            if ((w > w_lb) and (w < w_ub)):\n",
    "                conti += 1\n",
    "                #print(\"Cont: \",conti)\n",
    "                #conti += 1\n",
    "                ulo = 2*u + grid_size/2\n",
    "                vlo = 2*v + grid_size/2\n",
    "                u_loc = int(numpy.ceil(ulo))\n",
    "                v_loc = int(numpy.ceil(vlo))\n",
    "                #if use_aaf == True:\n",
    "                #    if u_loc > (grid_size -1-support_aa//2): \n",
    "                #        continue\n",
    "                #    if u_loc < support_aa//2: \n",
    "                #        continue\n",
    "                #    if v_loc > (grid_size-1-support_aa//2): \n",
    "                #\n",
    "                #        continue\n",
    "                #    if v_loc < support_aa//2: \n",
    "                #        continue\n",
    "                #else:  \n",
    "                #    if u_loc > (grid_size -1): \n",
    "                #        continue\n",
    "                #    if u_loc < 0: \n",
    "                #        continue\n",
    "                #    if v_loc > (grid_size-1): \n",
    "                #        continue\n",
    "                #    if v_loc < 0: \n",
    "                #        continue\n",
    "                #TODO: Oversample Kernels Correctly\n",
    "                \n",
    "                # Boxcar gridding so I can work out wtf is going on here.\n",
    "                 # Boxcar gridding so I can work out wtf is going on here.\n",
    "                if use_aaf is True:\n",
    "                    # This is where we convolve with our anti-aliasing function\n",
    "                    u_os = int(oversampling_aa*abs(ulo-u_loc))\n",
    "                    v_os = int(oversampling_aa*abs(vlo-v_loc))\n",
    "                    \n",
    "                    aaf_u = aaf[:,u_os]\n",
    "                    aaf_v = aaf[:,v_os]\n",
    "                    aaf_uv = numpy.outer(aaf_u,aaf_v.T).T\n",
    "                    \n",
    "\n",
    "                    grid[v_loc-support_aa//2:v_loc+support_aa//2,\n",
    "                         u_loc-support_aa//2:u_loc+support_aa//2] += efield * aaf_uv\n",
    "                    \n",
    "                else:\n",
    "                    grid[v_loc,u_loc] += efield\n",
    "        \n",
    "        image = numpy.fft.ifft2(numpy.fft.fftshift(grid))    \n",
    "        image /= fresnel_pattern\n",
    "    print(conti)\n",
    "    if use_aaf == True:      \n",
    "        return numpy.fft.fftshift(image*(fresnel_pattern**(w_planes//2)))/gridcor\n",
    "    else:\n",
    "        return numpy.fft.fftshift(image*(fresnel_pattern**(w_planes//2)))\n",
    "\n",
    "\n",
    "#for wval in numpy.arange(1.0,5.0,0.025):\n",
    "\n",
    "\n",
    "image_vis = visibility_wstacking(theta,2*lam,baselines_uvw,visibilities,0.1,use_aaf=True,aaf=kv_vis.T,gridcor=aaf_2D_vis)\n",
    "image_vis_noaa = visibility_wstacking(theta,2*lam,baselines_uvw,visibilities,0.1,use_aaf=False)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(visibilities.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Let's compare this to the DFT first"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "image_vis_n = normalise_image(numpy.abs(image_vis))\n",
    "image_vis_noaa_n = normalise_image(numpy.abs(image_vis_noaa))\n",
    "plot_celestial_sphere(image_vis_n.T,title='Anti Aliased')\n",
    "plot_celestial_sphere(image_vis_noaa_n.T,title='Nearest Neighbour')\n",
    "diff_vis = abs(imvc_n - image_vis_n.T)\n",
    "diff_vis_noaa = abs(imvc_n - image_vis_noaa_n.T)\n",
    "plot_celestial_sphere(diff_vis,title='Diff vs E-Field DFT (AA)',norm=LogNorm(vmin=0.0001, vmax=1),cmap=plt.get_cmap('jet'))\n",
    "print(\"Total Error: %f\"%(numpy.sum(numpy.square(diff_vis))/(diff_vis.shape[0]*diff_vis.shape[1])))\n",
    "plot_celestial_sphere(diff_vis_noaa,title='Diff vs E-Field DFT (No AA)',norm=LogNorm(vmin=0.0001, vmax=1),cmap=plt.get_cmap('jet'))\n",
    "print(\"Total Error: %f\"%(numpy.sum(numpy.square(diff_vis_noaa))/(diff_vis_noaa.shape[0]*diff_vis_noaa.shape[1])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Things look correct and what I expect. Let us add some noise.\n",
    "\n",
    "In there will be some system noise on the electric fields / visibilities, let us put some gaussian white noise on top of our random e-fields."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate_electric_fields_noise(locations_uvw,points):\n",
    "    elec_ss = numpy.zeros(shape=(locations_uvw.shape[0]),dtype=numpy.complex128)\n",
    "    noise = numpy.random.standard_normal((locations_uvw.shape[0]))*1000\n",
    "    for i in numpy.arange(locations_uvw.shape[0]):\n",
    "        for point in points:\n",
    "            l = point[0]\n",
    "            m = point[1]\n",
    "            n = numpy.sqrt(1.0-l**2-m**2) - 1.0\n",
    "            amp = point[2]\n",
    "            u = locations_uvw[i,0]\n",
    "            v = locations_uvw[i,1]\n",
    "            w = locations_uvw[i,2]\n",
    "            elec_ss[i] += amp*numpy.exp(2j*numpy.pi*(u*l+v*m+w*n))\n",
    "    elec_ss = elec_ss + noise\n",
    "    return elec_ss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AA Support:  12\n",
      "AA Oversampling:  128\n",
      "Max W:  7.620837651365984\n",
      "Min W:  -10.341356347721634\n",
      "W Range:  17.962193999087617\n",
      "Number of W Planes:  180.0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ee_gaussian_ns = simulate_electric_fields_noise(locations_uvw, points)\n",
    "image_wsg = epic_wstacking(theta,lam,locations_uvw,ee_gaussian_ns,0.1,use_aaf=True,aaf=kv.T,gridcor=aaf_2D)\n",
    "image_wsgi = image_wsg * image_wsg.conj()\n",
    "plot_celestial_sphere(image_wsgi.T)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compute Costs\n",
    "\n",
    "Let's do some cost calculations now for the various different methods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 221,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dft_cost(n_a,n_g,vis=False, n_t=1):\n",
    "    if vis == True:\n",
    "        return 6 * n_a*(n_a - 1)/2 * (2*n_g)**2 \n",
    "    else:\n",
    "        return 6 * n_a * n_g**2 * n_t\n",
    "    \n",
    "def wstack_cost(n_a, n_g, n_w, n_s,vis=False, n_t=1):\n",
    "    if vis == True:\n",
    "        return 6 * n_a*(n_a -1)/2 * n_s**2 + 6 * n_w * (2* n_g)**2 * numpy.log2((2* n_g)**2) + 6 * (n_w + 1) * (2*n_g)**2\n",
    "    else:\n",
    "        return (6 * n_a * n_s**2 + 4 * n_w * n_g**2 * numpy.log2(n_g**2) + 6 * (n_w + 1) * n_g**2)*n_t\n",
    "    \n",
    "def fft_romein_cost(n_a,n_g,n_s,vis=False, n_t=1):\n",
    "    if vis == True:\n",
    "        return 6 * (n_a*(n_a - 1) * n_s) + 4 * n_g**2 * numpy.log2(n_g**2) \n",
    "    else: \n",
    "        return (6 * (n_a * n_s) + 4 * n_g**2 * numpy.log2(n_g**2))*n_t\n",
    "    \n",
    "def sze_stack_cost(n_a, n_g, n_w, n_us, n_ws,vis=False):\n",
    "    if vis == True:\n",
    "        return n_a*(n_a - 1)/2 * n_ws * n_us**2 + 6 * n_wo * 2 * n_g * numpy.log2(2 * n_g) + 6 * n_wo * (2*n_g)**2\n",
    "    else:\n",
    "        return n_a * n_ws * n_us**2 + 6 * n_wo * n_g * numpy.log2(n_g) + 6 * n_wo * n_g**2\n",
    "        \n",
    "def wstack_wproj_cost(n_a, n_g, n_w, n_s, n_wp,vis=False):\n",
    "    if vis == True: \n",
    "        return n_a*(n_a - 1)/2 * (n_s + n_w) + 6 * n_w * n_g * numpy.log2(n_g) + 6 * n_w * n_g**2\n",
    "    else: \n",
    "        return n_a * (n_s + n_wp) + 6 * n_w * n_g * numpy.log2(n_g) + 6 * n_w * n_g**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 222,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Test set paramaters\n",
    "N_grid = 64\n",
    "N_time = 10\n",
    "N_ant = numpy.arange(10,10000,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [],
   "source": [
    "dft_cost_efield = dft_cost(N_ant,N_grid,vis=False,n_t=N_time)\n",
    "dft_cost_vis = dft_cost(N_ant,N_grid,vis=True,n_t=N_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "plt.plot(N_ant,dft_cost_efield,label='E-Field')\n",
    "plt.plot(N_ant,dft_cost_vis,label='Visibilities')\n",
    "plt.legend()\n",
    "plt.title(\"DFT Cost for E-Field vs Visibilities \\n Grid Size = 128, N_Times=10\")\n",
    "plt.xlabel(\"No. of Antennas\")\n",
    "plt.ylabel(\"Floating Point Operations(FLOPS)\")\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 225,
   "metadata": {},
   "outputs": [],
   "source": [
    "N_w = 10\n",
    "N_w_vis=N_w*2\n",
    "N_s = 12\n",
    "\n",
    "wstack_cost_efield = wstack_cost(N_ant,N_grid,N_w,N_s,vis=False,n_t=N_time)\n",
    "wstack_cost_vis = wstack_cost(N_ant,N_grid,N_w_vis,N_s,vis=True,n_t=N_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "plt.plot(N_ant,wstack_cost_efield,label='E-Field')\n",
    "plt.plot(N_ant,wstack_cost_vis,label='Visibilities')\n",
    "plt.legend()\n",
    "plt.title(\"W-Stack Cost for E-Field vs Visibilities \\n #W-Planes: 50, Grid Size = 128^2, No. of Time-Steps: 10\")\n",
    "plt.xlabel(\"No. of Antennas\")\n",
    "plt.ylabel(\"Floating Point Operations (FLOPs)\")\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.savefig(\"wstack_cost.pdf\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {},
   "outputs": [],
   "source": [
    "wstack_cost_efield_ht = wstack_cost(N_ant,N_grid,N_w,N_s,vis=False,n_t=100)\n",
    "wstack_cost_vis_ht = wstack_cost(N_ant,N_grid,N_w_vis,N_s,vis=True,n_t=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "plt.plot(N_ant,wstack_cost_efield_ht,label='E-Field')\n",
    "plt.plot(N_ant,wstack_cost_vis_ht,label='Visibilities')\n",
    "plt.legend()\n",
    "plt.title(\"W-Stack Cost for E-Field vs Visibilities \\n #W-Planes: 50, Grid Size = 128^2, No. of Time-Steps: 100\")\n",
    "plt.xlabel(\"No. of Antennas\")\n",
    "plt.ylabel(\"Floating Point Operations (FLOPS)\")\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "plt.savefig(\"wstack_cost_ht.pdf\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {},
   "outputs": [],
   "source": [
    "N_grid=64\n",
    "dft_cost_efield_ht = dft_cost(N_ant,N_grid,vis=False,n_t=4096)\n",
    "dft_cost_vis_ht = dft_cost(N_ant,N_grid,vis=True,n_t=4096)\n",
    "wstack_cost_efield_hht = wstack_cost(N_ant,N_grid,N_w,N_s,vis=False,n_t=4096)\n",
    "wstack_cost_vis_hht = wstack_cost(N_ant,N_grid,N_w_vis,N_s,vis=True,n_t=4096)\n",
    "\n",
    "romein_cost_efield_ht = fft_romein_cost(N_ant,N_grid,N_s,vis=False,n_t=4096)\n",
    "romein_cost_vis_ht = fft_romein_cost(N_ant,N_grid,N_s,vis=True,n_t=4096)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,10))\n",
    "ax1 = fig.add_subplot(211)\n",
    "ax2 = fig.add_subplot(212)\n",
    "\n",
    "#ax4 = fig.add_subplot(224)\n",
    "\n",
    "ax1.plot(N_ant,dft_cost_efield_ht,'r--',label='DFT E-Field')\n",
    "ax1.plot(N_ant,dft_cost_vis_ht,'r:',label='DFT Visibilities')\n",
    "ax1.plot(N_ant,wstack_cost_efield_hht,'b-.',label='W-Stack E-Field')\n",
    "ax1.plot(N_ant,wstack_cost_vis_hht,'b-',label='Wstack Visibilities')\n",
    "ax1.plot(N_ant,romein_cost_efield_ht,'g^',label='FFT E-Field')\n",
    "ax1.plot(N_ant,romein_cost_vis_ht,'gx',label='FFT Visibilities')\n",
    "ax1.legend()\n",
    "ax1.set_title(\"Floating Point Operations Cost for E-Field vs Visibilities \\n Grid Size = $64^2$, N_Timestamps=4096\")\n",
    "ax1.set_xlabel(\"No. of Antennas\")\n",
    "ax1.set_ylabel(\"Floating Point Operations(FLOPS)\")\n",
    "ax1.set_ylim((10e4,10e13))\n",
    "ax1.set_xscale('log')\n",
    "ax1.set_yscale('log')\n",
    "\n",
    "N_grid=128\n",
    "\n",
    "\n",
    "dft_cost_efield_ht = dft_cost(N_ant,N_grid,vis=False,n_t=4096)\n",
    "dft_cost_vis_ht = dft_cost(N_ant,N_grid,vis=True,n_t=4096)\n",
    "wstack_cost_efield_hht = wstack_cost(N_ant,N_grid,N_w,N_s,vis=False,n_t=4096)\n",
    "wstack_cost_vis_hht = wstack_cost(N_ant,N_grid,N_w_vis,N_s,vis=True,n_t=4096)\n",
    "romein_cost_efield_ht = fft_romein_cost(N_ant,N_grid,N_s,vis=False,n_t=4096)\n",
    "romein_cost_vis_ht = fft_romein_cost(N_ant,N_grid,N_s,vis=True,n_t=4096)\n",
    "\n",
    "ax2.plot(N_ant,dft_cost_efield_ht,'r--',label='DFT E-Field')\n",
    "ax2.plot(N_ant,dft_cost_vis_ht,'r:',label='DFT Visibilities')\n",
    "ax2.plot(N_ant,wstack_cost_efield_hht,'b-.',label='W-Stack E-Field')\n",
    "ax2.plot(N_ant,wstack_cost_vis_hht,'b-',label='Wstack Visibilities')\n",
    "ax2.plot(N_ant,romein_cost_efield_ht,'g^',label='FFT E-Field')\n",
    "ax2.plot(N_ant,romein_cost_vis_ht,'gx',label='FFT Visibilities')\n",
    "ax2.legend()\n",
    "ax2.set_title(\"Floating Point Operations Cost for E-Field vs Visibilities \\n Grid Size = $128^2$, N_Timestamps=4096\")\n",
    "ax2.set_xlabel(\"No. of Antennas\")\n",
    "ax2.set_ylabel(\"Floating Point Operations(FLOPS)\")\n",
    "ax2.set_ylim((10e4,10e13))\n",
    "ax2.set_xscale('log')\n",
    "ax2.set_yscale('log')\n",
    "\n",
    "plt.tight_layout()\n",
    "\n",
    "plt.savefig(\"costs.pdf\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So total floating point operations looks interesting. EPIC looks poor for wide field correction because of the time sampling. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Alternative metric where we divide each FLOPs contribution by their respective operational intensity. \n",
    "# FFT Operational Intensity based on Radix 2.\n",
    "\n",
    "def dft_cost_bytes(n_a,n_g,vis=False, n_t=1):\n",
    "    if vis == True:\n",
    "        return 4 * n_a*(n_a - 1)/2 * n_g**2\n",
    "    else:\n",
    "        return 4 * n_a * n_g**2 * n_t\n",
    "    \n",
    "def wstack_cost_bytes(n_a, n_g, n_w, n_s,vis=False, n_t=1):\n",
    "    if vis == True:\n",
    "        return (n_a*(n_a -1)/2 * n_s**2)/0.25 + (4 * n_w * n_g * numpy.log2(n_g))/200 + (6 * (n_w + 1) * n_g**2)/0.25\n",
    "    else:\n",
    "        return ((n_a * n_s**2)/0.25 + (4 * n_w * n_g * numpy.log2(n_g))/200 + (6 * (n_w + 1) * n_g**2)/0.25)*n_t\n",
    "    \n",
    "def sze_stack_cost_bytes(n_a, n_g, n_w, n_us, n_ws,vis=False):\n",
    "    if vis == True:\n",
    "        return n_a*(n_a - 1)/2 * n_ws * n_us**2 + 4 * n_wo * n_g * numpy.log2(n_g) + 6 * n_wo * n_g**2\n",
    "    else:\n",
    "        return n_a * n_ws * n_us**2 + 4 * n_wo * n_g * numpy.log2(n_g) + 6 * n_wo * n_g**2\n",
    "        \n",
    "def wstack_wproj_cost_bytes(n_a, n_g, n_w, n_s, n_wp,vis=False):\n",
    "    if vis == True: \n",
    "        return n_a*(n_a - 1)/2 * (n_s + n_w) + 4 * n_w * n_g * numpy.log2(n_g) + 6 * n_w * n_g**2\n",
    "    else: \n",
    "        return n_a * (n_s + n_wp) + 4 * n_w * n_g * numpy.log2(n_g) + 6 * n_w * n_g**2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'N_ant' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-145-3adfa0b238ad>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mwstack_cost_efield_bytes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mwstack_cost_bytes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mN_ant\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mN_grid\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mN_w\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mN_s\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mvis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mn_t\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mN_time\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mwstack_cost_vis_bytes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mwstack_cost_bytes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mN_ant\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mN_grid\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mN_w_vis\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mN_s\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mvis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mn_t\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mN_time\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'N_ant' is not defined"
     ]
    }
   ],
   "source": [
    "wstack_cost_efield_bytes = wstack_cost_bytes(N_ant,N_grid,N_w,N_s,vis=False,n_t=N_time)\n",
    "wstack_cost_vis_bytes = wstack_cost_bytes(N_ant,N_grid,N_w_vis,N_s,vis=True,n_t=N_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'N_ant' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-146-8556f68874cc>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mfig\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfigure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mN_ant\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mwstack_cost_efield_bytes\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'E-Field'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mN_ant\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mwstack_cost_vis_bytes\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Visibilities'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlegend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtitle\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"W-Stack Cost for E-Field vs Visibilities \\n #W-Planes: 50, Grid Size = 128^2, No. of Time-Steps: 10\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'N_ant' is not defined"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 504x360 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "plt.plot(N_ant,wstack_cost_efield_bytes,label='E-Field')\n",
    "plt.plot(N_ant,wstack_cost_vis_bytes,label='Visibilities')\n",
    "plt.legend()\n",
    "plt.title(\"W-Stack Cost for E-Field vs Visibilities \\n #W-Planes: 50, Grid Size = 128^2, No. of Time-Steps: 10\")\n",
    "plt.xlabel(\"No. of Antennas\")\n",
    "plt.ylabel(\"Floating Point Operations (FLOPS)\")\n",
    "plt.xscale('log')\n",
    "plt.yscale('log')\n",
    "#plt.savefig(\"wstack_cost.pdf\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#Image directly from image routines using the EPIC formalism.\n",
    "\n",
    "def epic_image(efield,locations):\n",
    "    grid = numpy.zeros(shape=(grid_size,grid_size),dtype=numpy.complex64)\n",
    "    image = numpy.zeros(shape=(grid_size,grid_size),dtype=numpy.complex64)    \n",
    "    location_grid_points = locations\n",
    " \n",
    "    for j,efieldd in enumerate(efield):\n",
    "        for i,e_sample in enumerate(efieldd[:,0]):\n",
    "            #print(\"Sample: %d\"%i)\n",
    "            grid[location_grid_points[i,0],location_grid_points[i,1]] += e_sample\n",
    "\n",
    "        imaged = numpy.fft.fftshift(numpy.fft.ifft2(numpy.fft.fftshift(grid),s=(grid_size,grid_size)))\n",
    "        imaged = imaged * imaged.conj()\n",
    "        #plt.imshow(numpy.abs(imaged))\n",
    "        #plt.colorbar()\n",
    "        #plt.show()\n",
    "        \n",
    "        \n",
    "        \n",
    "        image += imaged\n",
    "        grid[...] = 0.0\n",
    "            \n",
    "    #plt.imshow(grid.real)\n",
    "    #plt.show()\n",
    "    #image = numpy.fft.fftshift(numpy.fft.ifft2(numpy.fft.fftshift(grid)))\n",
    "    #imsq = image * image.conj()\n",
    "    #print(\"Aah\")\n",
    "    plt.imshow(numpy.abs(image/efield.shape[0]))\n",
    "    plt.colorbar()\n",
    "    plt.show()\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Time dependence\n",
    "\n",
    "Due to the noise dominating a real measurement, now that I have shown the mathematical equivalence, it is time to add time dependence and some noise to the electric field amplitudes calculated previously.\n",
    "\n",
    "This experiment is setup as follows:\n",
    "\n",
    "1) Generate M Time Samples of N Electric Field measurements.\n",
    "\n",
    "2) Correct their non-coplanarity and accumulate the image.\n",
    "\n",
    "3) Generate Visibilities from 1), and accumulate the visibilities over M Times, so that you are left with N(N-1)/2 visibilities. \n",
    "\n",
    "4) Image Visibilities in same way.\n",
    "\n",
    "Observe how the images differ. By induction they should not differ that much."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# We assume the sky doesn't move during this time for simplicity.\n",
    "def generate_n_time_samples(n_time,locations_uvw,points):\n",
    "    elec_field_samples = numpy.zeros(shape=(n_time,locations_uvw.shape[0]),dtype=numpy.complex128)\n",
    "    for i in numpy.arange(n_time):\n",
    "        elec_field_samples[i,:] = simulate_electric_fields_noise(locations_uvw,points)\n",
    "    \n",
    "    return elec_field_samples\n",
    "\n",
    "def accumulate_efield_image(efield_samples):\n",
    "    grid_size = int(theta * lam)\n",
    "    image_accum = numpy.zeros(shape=(grid_size,grid_size),dtype=numpy.complex128)\n",
    "    for i in numpy.arange(efield_samples.shape[0]):\n",
    "        image = epic_wstacking(theta,lam,locations_uvw,efield_samples[i,:],0.1,use_aaf=True,aaf=kv.T,gridcor=aaf_2D)\n",
    "        image_accum += (image * image.conj())\n",
    "    return image_accum/efield_samples.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "generate_nts = generate_n_time_samples(20,locations_uvw,points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "image_noisy = accumulate_efield_image(generate_nts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_celestial_sphere(image_noisy.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now for visibilities:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def accumulate_visibilities(efield_samples):\n",
    "    # efield_samples - [N_time,N_Ant]\n",
    "    vis_matrix_acc = numpy.zeros(shape=(efield_samples.shape[1],efield_samples.shape[1]),dtype=numpy.complex128)\n",
    "    for i in numpy.arange(efield_samples.shape[0]):\n",
    "        vis_matrix_acc += numpy.outer(efield_samples[i,:],efield_samples[i,:].T.conj())/efield_samples.shape[1]\n",
    "    return vis_matrix_acc/efield_samples.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "vis_accum = accumulate_visibilities(generate_nts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "print(vis_accum.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "image_vis_noisy = visibility_wstacking(theta,2*lam,baselines_uvw,vis_accum.flatten(),0.1,use_aaf=True,aaf=kv_vis.T,gridcor=aaf_2D_vis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plot_celestial_sphere(image_vis_noisy.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Apart from resolution and scaling, images look the same."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Remove Auto-Correlations\n",
    "\n",
    "1) Grid everything at origin of each plane where they contribute.\n",
    "2) Subtract from final image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def efield_dft_minus_autocorrs(theta,lam,efield,locations):\n",
    "    grid_size = int(theta*lam)\n",
    "    image = numpy.zeros(shape=(grid_size,grid_size), dtype=numpy.complex128)\n",
    "    autocorrs = numpy.zeros(shape=(grid_size,grid_size), dtype=numpy.complex128)\n",
    "    \n",
    "    for lg in numpy.arange(grid_size):\n",
    "        \n",
    "        lv = (1.0 / (0.5*grid_size)) * (lg - grid_size/2)\n",
    "        #print(lv)\n",
    "        for mg in numpy.arange(grid_size):\n",
    "            mv = (1.0/ (0.5*grid_size)) * (mg - grid_size/2)\n",
    "            if (lv**2 + mv**2 > 1.0):\n",
    "                nv = 0\n",
    "            else:\n",
    "                nv = 1.0 - numpy.sqrt(1.0 - lv**2 - mv**2)\n",
    "            #print(nv)\n",
    "            for j,efieldd in enumerate(efield):\n",
    "                u = locations[j,0]\n",
    "                v = locations[j,1]\n",
    "                w = locations[j,2]\n",
    "                #w = 0\n",
    "                image[lg,mg] += efieldd * numpy.exp(2j*numpy.pi*(u*lv + v*mv + w*nv))\n",
    "    return image / (grid_size**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## Notes:\n",
    "# W-Kernel is definitely not right. Understand why.\n",
    "def epic_wstacking_autocors(theta,lam,locations, efieldf,dw,use_aaf=False,aaf=None,gridcor=None):\n",
    "    #print(w_kernel[0,0,:,:])\n",
    "    grid_size = int(theta*lam)\n",
    "    gs2 = grid_size//2\n",
    "    #w_kernel = w_kern(theta,dw,NpixFF=256,NpixKern=size,Qpx=8, invert=True)\n",
    "    #wkh = w_kernel.shape[2]//2\n",
    "    max_w = numpy.max(locations[:,2])\n",
    "    min_w = numpy.min(locations[:,2]) \n",
    "    w_range = max_w - min_w\n",
    "    w_planes = numpy.ceil(w_range/(dw)) \n",
    "    \n",
    "    if use_aaf == True:\n",
    "        if aaf is None:\n",
    "            raise ValueError(\"No anti-aliasing function provided!\")\n",
    "        if gridcor is None:\n",
    "            raise ValueError(\"No Gridding Correction provided!\")\n",
    "        support_aa = aaf.shape[0]\n",
    "        oversampling_aa = aaf.shape[-1]\n",
    "        print(\"AA Support: \",support_aa)\n",
    "        print(\"AA Oversampling: \",oversampling_aa)\n",
    "        \n",
    "    \n",
    "    print(\"Max W: \",max_w)\n",
    "    print(\"Min W: \",min_w)\n",
    "    print(\"W Range: \",w_range)\n",
    "    print(\"Number of W Planes: \",w_planes)\n",
    "    \n",
    "    \n",
    "    #Fresnel Pattern\n",
    "    fresnel_pattern = numpy.fft.fftshift(generate_fresnel(theta,lam,dw))\n",
    "\n",
    "    #Auto-Correlations\n",
    "    efield_autocorrs = efieldf * efieldf.conj()\n",
    "    \n",
    "    #Setup W-Stacks\n",
    "    image = numpy.zeros(shape=(grid_size,grid_size),dtype=numpy.complex128)\n",
    "    image_autocorr = numpy.zeros(shape=(grid_size,grid_size),dtype=numpy.complex128)\n",
    "    grid = numpy.zeros(shape=(grid_size,grid_size),dtype=numpy.complex128)\n",
    "    grid_autocorr = numpy.zeros(shape=(grid_size,grid_size),dtype=numpy.complex128)\n",
    "    conti = 0\n",
    "    for i in numpy.arange(0,w_planes):\n",
    "        if(i == 0):\n",
    "            pass\n",
    "        else:\n",
    "            grid = numpy.fft.fftshift(numpy.fft.fft2(image))\n",
    "            #grid_autocorr = numpy.fft.fftshift(numpy.fft.fft2(image_autocorr))\n",
    "        wpi = i - w_planes//2 \n",
    "        wc = wpi*dw # Gives us our central w-value, so we know which electric field contributions belong to us.\n",
    "        w_ub = wc + dw/2\n",
    "        w_lb = wc - dw/2\n",
    "\n",
    "        # Let's work out which contributions to put on each plane of the W-Stack.\n",
    "        for j,efield in enumerate(efieldf):\n",
    "            #print(efield)\n",
    "            u = locations[j,0]\n",
    "            v = locations[j,1]\n",
    "            w = locations[j,2]\n",
    "            #print(grid)\n",
    "            if ((w > w_lb) and (w < w_ub)):\n",
    "                #print(\"Cont: \",conti)\n",
    "                #conti += 1\n",
    "                ulo = 2*u + grid_size/2\n",
    "                vlo = 2*v + grid_size/2\n",
    "                u_loc = int(numpy.ceil(ulo))\n",
    "                v_loc = int(numpy.ceil(vlo))\n",
    "                \n",
    "                #TODO: Oversample Kernels Correctly\n",
    "                \n",
    "                # Boxcar gridding so I can work out wtf is going on here.\n",
    "                if use_aaf is True:\n",
    "                    # This is where we convolve with our anti-aliasing function\n",
    "                    u_os = int(oversampling_aa*abs(ulo-u_loc))\n",
    "                    v_os = int(oversampling_aa*abs(vlo-v_loc))\n",
    "                    \n",
    "                    aaf_u = aaf[:,u_os]\n",
    "                    aaf_v = aaf[:,v_os]\n",
    "                    aaf_uv = numpy.outer(aaf_u,aaf_v.T).T\n",
    "                    grid[v_loc-support_aa//2:v_loc+support_aa//2,\n",
    "                         u_loc-support_aa//2:u_loc+support_aa//2] += efield * aaf_uv \n",
    "                    grid_autocorr[gs2,gs2] += efield_autocorrs[j]\n",
    "                #    # Process autocorrelations\n",
    "                #    grid_autocorr[gs2 - support_aa//2:gs2 + support_aa//2,\n",
    "                #                  gs2 - support_aa//2:gs2 + support_aa//2] += efield_autocorrs[j] * aaf_uv\n",
    "                else:\n",
    "                    grid[v_loc,u_loc] += efield\n",
    "                    grid_autocorr[gs2,gs2] += efield_autocorrs[j]\n",
    "                    \n",
    "        image = numpy.fft.ifft2(numpy.fft.fftshift(grid))    \n",
    "        \n",
    "        image /= fresnel_pattern\n",
    "        #image_autocorr /= fresnel_pattern\n",
    "    print(efield_autocorrs)\n",
    "    plt.imshow(numpy.abs(grid_autocorr))\n",
    "    plt.colorbar()\n",
    "    plt.show()\n",
    "    image_autocorr = numpy.fft.ifft2(numpy.fft.fftshift(grid_autocorr/efield_autocorrs.shape[0]))\n",
    "    if use_aaf == True:      \n",
    "        \n",
    "        imcor = numpy.fft.fftshift(image*(fresnel_pattern**(w_planes//2)))\n",
    "        imcor = (imcor * imcor.conj())/gridcor\n",
    "        autocor = numpy.fft.fftshift(image_autocorr)#/gridcor\n",
    "        #autocor = numpy.fft.fftshift(image_autocorr*(fresnel_pattern**(w_planes//2)))/gridcor     \n",
    "        plt.imshow(autocor.real)\n",
    "        plt.colorbar()\n",
    "        plt.show()\n",
    "        plt.imshow(imcor.real)\n",
    "        plt.colorbar()\n",
    "        plt.show()\n",
    "        return (imcor-autocor)\n",
    "\n",
    "    else:\n",
    "        imcor = numpy.fft.fftshift(image*(fresnel_pattern**(w_planes//2)))\n",
    "        imcor = imcor * imcor.conj()\n",
    "        autocor = numpy.fft.fftshift(image_autocorr)\n",
    "        plt.imshow(autocor.real)\n",
    "        plt.colorbar()\n",
    "        plt.show()\n",
    "        return imcor - autocor\n",
    "\n",
    "\n",
    "\n",
    "#for wval in numpy.arange(1.0,5.0,0.025):\n",
    "image_wsg = epic_wstacking_autocors(theta,lam,locations_uvw,ee_gaussian_s,0.1,use_aaf=True,aaf=kv.T,gridcor=aaf_2D)\n",
    "image_wsi = (image_wsg * image_wsg.conj())\n",
    "gc_im = image_wsi.T\n",
    "\n",
    "image_wsg_noaa = epic_wstacking_autocors(theta,lam,locations_uvw,ee_gaussian_s,0.1,use_aaf=False)\n",
    "image_wsi_noaa = (image_wsg_noaa * image_wsg_noaa.conj())\n",
    "gc_im_noaa = image_wsi_noaa.T\n",
    "\n",
    "from matplotlib.colors import LogNorm\n",
    "from matplotlib.colors import Normalize\n",
    "#plot_celestial_sphere(gc_im,title='W-Stacked Image',norm=Normalize(vmin=0.0, vmax=50.0))\n",
    "#plot_celestial_sphere(imcg,title='Direct Fourier Transform',norm=Normalize(vmin=0.0, vmax=50.0))\n",
    "\n",
    "#Normalise\n",
    "gc_im_n = normalise_image(gc_im)\n",
    "gc_im_noaa_n = normalise_image(gc_im_noaa)\n",
    "imcg_n = normalise_image(imcg)\n",
    "\n",
    "plot_celestial_sphere(gc_im_n,title='W-Stacked Image (Anti-Aliased)')\n",
    "plot_celestial_sphere(gc_im_noaa_n,title='W-Stacked Image (No AA)')\n",
    "plot_celestial_sphere(imcg_n,title='Direct Fourier Transform')\n",
    "diff=numpy.abs(imcg_n-gc_im_n)\n",
    "diff_noaa = numpy.abs(gc_im_noaa_n - imcg_n)\n",
    "plot_celestial_sphere(diff,title='Diff (Anti-Aliasing)',norm=LogNorm(vmin=0.0001, vmax=1),cmap=plt.get_cmap('jet'))\n",
    "print(\"Total Error: %f\"%(numpy.sum(numpy.square(diff))/(diff.shape[0]*diff.shape[1])))\n",
    "plot_celestial_sphere(diff_noaa,title='Diff (No Anti-Aliasing)',norm=LogNorm(vmin=0.0001, vmax=1),cmap=plt.get_cmap('jet'))\n",
    "print(\"Total Error: %f\"%(numpy.sum(numpy.square(diff_noaa))/(diff_noaa.shape[0]*diff_noaa.shape[1])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Real Dataset\n",
    "\n",
    "This is a Cygnus A Snapshot, which was done by Jayce Dowell at University of New Mexico on the LWA. We compare the effects on the images for the small non-coplanarity of the LWA Seviletta Site. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimal Gridding\n",
    "\n",
    "Let's do things a la Sze Tan and co. Optimal kernels are already generated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using Sze-Tan's gridder with R=2, x_0=0.25\n",
      "Mean error: 0.00019152018327907744\n",
      "Optimal du = 0.25\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-125-653b08f44045>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     37\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcoordinates\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m10001\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     38\u001b[0m \u001b[0;31m#print(x)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 39\u001b[0;31m \u001b[0msze_aa_im\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0maa\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     40\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msze_aa_im\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     41\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtheta\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0maa_x0\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maa\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m;\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-125-653b08f44045>\u001b[0m in \u001b[0;36maa\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m     12\u001b[0m     \u001b[0maa_gcf\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msze_tan_gridder\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maa_support\u001b[0m\u001b[0;34m//\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maa_x0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maa_over\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     13\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0maa\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 14\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0msze_tan_grid_correction_gen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maa_support\u001b[0m\u001b[0;34m//\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maa_x0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     15\u001b[0m     \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Mean error:\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msze_tan_mean_error\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0maa_support\u001b[0m\u001b[0;34m//\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maa_x0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     16\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-5-45d36502b80b>\u001b[0m in \u001b[0;36msze_tan_grid_correction_gen\u001b[0;34m(R, x0, x, Nopt, Mopt, max_dx0)\u001b[0m\n\u001b[1;32m   1214\u001b[0m         \"\"\"\n\u001b[1;32m   1215\u001b[0m         \u001b[0mgrid\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0moptimal_grid_cached\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mR\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mNopt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mMopt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmax_dx0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1216\u001b[0;31m         \u001b[0mgrid_correction\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcalc_gridding_correction_fine\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnumpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrid\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'h'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrid\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'x0'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mR\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1217\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0;36m1\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0mgrid_correction\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1218\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m<ipython-input-5-45d36502b80b>\u001b[0m in \u001b[0;36mcalc_gridding_correction_fine\u001b[0;34m(x, h, x0, M, R)\u001b[0m\n\u001b[1;32m   1162\u001b[0m                     \u001b[0ml\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mr\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mR\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1163\u001b[0m                     \u001b[0md\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mC\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mrp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mC\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcos\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpi\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mlp\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0ml\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mx_val\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mdnu\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1164\u001b[0;31m                 \u001b[0mc\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mC\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mrp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcos\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m2\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mnumpy\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpi\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mlp\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mnu\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mx_val\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mdnu\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1165\u001b[0m         \u001b[0mhfine\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1166\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mhfine\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "aa_over = 4096\n",
    "aa_support = 4\n",
    "aa_x0 = 0.25\n",
    "aa_mode = 0\n",
    "aa_szetan = True\n",
    "if aa_support == 1:\n",
    "    print(\"Using trivial gridder\")\n",
    "    aa_gcf = numpy.ones((aa_over, aa_support))\n",
    "    def aa(x): return numpy.ones_like(x)\n",
    "elif aa_szetan:\n",
    "    print(\"Using Sze-Tan's gridder with R=%d, x_0=%g\" % (aa_support//2, aa_x0))\n",
    "    aa_gcf = sze_tan_gridder(aa_support//2, aa_x0, aa_over)\n",
    "    def aa(x):\n",
    "        return sze_tan_grid_correction_gen(aa_support//2, aa_x0, x)\n",
    "    print(\"Mean error:\", sze_tan_mean_error(aa_support//2, aa_x0))\n",
    "else:\n",
    "    aa_parameter = aa_support\n",
    "    print(\"Using PSWF with mode %d and parameter %g\" % (aa_mode, aa_parameter))\n",
    "    aa_gcf = kernel_oversample(anti_aliasing_function(grid_size, aa_mode, aa_parameter), aa_over, aa_support)\n",
    "    aa_gcf /= numpy.sum(aa_gcf[0])\n",
    "    def aa(x):\n",
    "        return scipy.special.pro_ang1(aa_mode, aa_mode, aa_parameter, 2*x)[0]\n",
    "    \n",
    "# Calculate appropriate step length to give us full accuracy for a field of view of size theta\n",
    "du = du_opt = aa_x0/(theta/2)\n",
    "print(\"Optimal du =\", du)\n",
    "\n",
    "# Plot gridding function\n",
    "plt.rcParams['figure.figsize'] = 10, 5\n",
    "r = numpy.arange(-aa_over*(aa_support//2), aa_over*((aa_support+1)//2)) / aa_over\n",
    "plt.plot(du_opt*r, numpy.transpose(aa_gcf).flatten().real);\n",
    "plt.xticks(du_opt*numpy.arange(-(aa_support//2), ((aa_support+1)//2)+1))\n",
    "plt.grid(True);plt.xlabel('u/v [$\\lambda$]');plt.title('$u/v$ Gridder');plt.show()\n",
    "\n",
    "# Plot grid correction function\n",
    "theta_x0 = theta/aa_x0/2\n",
    "x = coordinates(10001)\n",
    "#print(x)\n",
    "sze_aa_im = aa(x)\n",
    "print(sze_aa_im.shape)\n",
    "plt.plot(theta*x/aa_x0/2, aa(x));\n",
    "plt.title('$u/v$ Grid correction');plt.grid(True);plt.xlabel('l [1]')\n",
    "plt.axvspan(theta/2, theta_x0/2, color='lightgray', hatch='x', alpha=0.5)\n",
    "plt.axvspan(-theta/2, -theta_x0/2, color='lightgray', hatch='x', alpha=0.5)\n",
    "plt.annotate('(unused)', xy=((theta+theta_x0)/4,0.9), ha='center', color='gray')\n",
    "plt.annotate('(unused)', xy=(-(theta+theta_x0)/4,0.9), ha='center', color='gray');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using Sze-Tan's gridder with R=2, x_0=0.25\n",
      "Mean error: 0.00019152018327907744\n",
      "max_n = 1.0\n",
      "Optimal dw = 0.25\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.49995    -0.49985001 -0.49975002 ...  0.49975002  0.49985001\n",
      "  0.49995   ]\n",
      "[0.18980086 0.18959281 0.18938583 ... 0.18938583 0.18959281 0.18980086]\n"
     ]
    },
    {
     "data": {
      "image/png": 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vgYU0cOPfEGtLU+Gwm/H80fZLvw/3jRfoKgbyK/eLdgkqQRDawjkXpv6Qf9T//LF2MADXlaeF7Y+1APOy47CvsV/Io0vjMUTT5OUcbzc5sWSaI6RzuBPfEDaLCVtmpWFXXTd6XO5Ltwv1jaH0sk/yK/MTBBF9iFJ/yA94vBwvHGvHsiIHsh0xqviXFyfjTIcLHf1iX4RliKbpdNsgel0eLMp3BD1w/t5w189Jx7CHY/vJzstur5bfH+QP7CcIIvoQpf6QH9jX0IuLfSO4Ye7le7uG418ybXTf17ebnAHvpyeGaJoOjs09WlQwOp9J6cBN9YabmRmHssw4vHCs/Yr7qeGfCvJPjWjnuAmC0JZgPvOy1zcZ/C+f7IDDbsbq6VducB+qf2ZmHOJtZhxqpKZJcw41OlGQHIOsxPdWIw00cErecO+bnYaTFwfQ0HnlAltq+KeC/ARBEKEhe30T2T844sHO093YMCMVVvPkLUQofouJYUFeAg419Qb9fCKJ9E2T28vxzvm+S0eZxuNv4JS+4a6ZmQIGYMepzkl/H64/EP78gSZFhuvXOj81TARBaI3s9c3fxS965999pgcutxebZqWq7l9UkIhzXUNo6xsO+XlpjfRN0+m2AfQPe3BV/uRLDUwcuGDecBkJNlxVkIjtpzr9XrEVjl8Jk/k555r6tc5PDRNBEJFA9vrm83POhcm//WQnMhKsWJCXoLp/0dj3uMjzmqRvmo609AMA5uX6H0DfwIWyF8/Gmalo6HKhpm1QE78SJvoZY5r6tc5PDRNBEJFC9vpmNpvBGBMif4/LjT31PdhYlgqTwnlmwfhLM+Jgt5hwdOx7XUSkb5qOtvQhLc6K7MTgdldWyvoZKTCbGLaf7NDETxAEQRAyUFXbBbeXY1PZ1KfmQsViYijPjsPRlj5N/Gogf9N0oR8VufFTXl3hOyQYyl48SbEWLCt0YEdNF7x+TtGF41fCRL/vUK1Wfq3zq+0nCILwh+z1zTclQ4T82051YlpKDGZlKt+cN9jXZ252Ak61DcLl9gb9XCKB1E1T9+AImrqHMDc73u9tJp5DDWUBro1lqWh1DqO6+cruVw3/VEzmZ4xp6tc6v5p+giAIf8he33x+35QMPfO39w3j7UYnNpWlKl4CIpTXZ25uPDxejpqLA2E/Py2QumnynfecmzP5fCZ/k86CfeOtKUmGzczwWm2XJn5/+PMzxjT1a52fGieCILRG9vo23j9xr1U98u+q6wYHsGGGslNzob4+c7NHv89FPUUnfdNkZsDsrCsPFQaapR/MGy/eZsbVhUmoOt196So6Nf2TQX6CIIjQkL2+iejfWdeNguQYFKfZNc2fFm9FjsN26SIv0ZC8aeobnW1vvXxQlF6WGcwbb/2MZLQ6h3GidUATv9b5jeSnDXsJIroI5jMve30T0d8zMIyDjU6sLUkOeGpOjfwVOQl0pEltOOc4cXEAcybMZwp2HQulb7xV05NhNjG8WtOhiV/r/EbyEwQRfYhSf6LRv/t0B9xejrWlKRHJPysrDhf7RtA1IN7mvdI2Te0uoG/Ig5kZ752aC3XhLyVvPIfdgkX5CXi9ths2m011v9b5jeQnCCL6EKX+RKN/T2M/UmLNmJXh/9ScmvnLxq7OO9Um3mRwaZumc87Rw7W+FzfUAfMR6I3n8XiwsjAB53uHUd8d/BLvSvxa5zeKnzbsJYjoItDFL0aqb6L5h91evFXfi9XTk+EeGY5I/rKxgyGnWqlpUo1zvV6YGVCSHhv2gPnw98bz+TeUpYEBqKrt1sSvdf5o9xMEIS+y1x9Z/W83OTEw7MXa0pSI5Y+zMuQ6bKhpGxBuDqu8TVMfR1GqHRamzua1Pia+8ca/ITIS7Zifl4DXT3cFFoXg1zo/+QmCkBnZ64+M/p113Yi1mrBkmiOi+WdmxOEkHWlSj0YnR0lqTMT34llXmoLT7YM41+XSxK8G5CcIwqjIXn9k8ns5x666biwvSkKMxRTR/NNTrGjqGcKAm440hU2bcwg9w0BpeuD1ItSmsjQZAFAVxtEmgiAIghCd4xf60d4/grUlyRF/7Blj3+9NTmqawuZYcw8AYE5OYsT34sl2xKA8Kw5Vp0Ob1xTIrwbkJwjCqMhef2Ty76zrhtnEsKI4SRP/ZPj8Ffmjj3muj5qmsDnW3AsAmJWdEPICX/6YeI52Mv+akmQcu9CP9r7gr6JT4tc6fzT7CYKQF9nrj2z+XXXdWJSfAIfdEvH8GYl2pMdbL10pLwpSNk3Hm3uREQskxIwOpFoD529S20T/mpLRBb52n+nRxK91/mj1EwQhL7LXH9n8DZ0u1He6Ln3f6ZF/RkYsmgRbGFzKpumi04WChMvX6gl34AJdBTDeX5hsRa7Dhl1nlJ+iC8avdX7Z/aJdgkoQhLZwPvVV0kaqb6L4d9WNzttdU5KsW/4ZGXFwDnN4vOLUfCmbpic+twJ3zLVc8fNQB07pZZM+//DwMFZPT8LBc70YGFZv6fpI5ZfdTxBE9CFK/YkW/866bszKjEN6nFm3/J9dlouHVllhNomzoLGUTRMAWP28iMEOXLDrTPj8ywriMOzh2NfQq4lf6/wy+wmCiD5EqT/R4G/vG8bRln6snp6ka36bxSTcDhDSNk1ToXTgQl2Yy2w2Y1FhChJjTNg5xdID4fi1zi+zX7QPEUEQ2hLMZ172+iaCf/eZHnAAywtihcuvN4ZsmgDt9/qJsVqwoigJb57twdCIW3W/1vll9xMEQfhD9vqmt3/n6S7kOqwoy3YImV9PDNs0Adrv9bO2NAW9Qx4caujSxO8vf6BJkeH6tc4v8weGIAg5kL2++bv4Rev8vQPDONjoxNqSFFgsV84dDtcve/03dNMEaLvXz7KiJFjNDHsbBzTx+8vPOdfUr3V+mT8wBEHIg+z1zefnnEcs/+66Dox4OdaWpmjil73+h95GSoRv4Fyu0f3i7Ha7KgMWbzNjcUEi3jzbi39bnae638fE/IwxTf1a51fbTxAE4Q/Z65vZbAZjLGL595wbQHKsBfNyEzTxy17/DX+kSWvWlKSgqWcIZztD38CXIAiCIPRmxMPxVn0PVk9PFuoyf5FQ1DQxxuoZY0cYY4cZYwe1DqU2vkOCWuyVs3r66P44r9d0RGwvId+hWq38WudX208QBOEP2eubb0pGJPKf6BhB/7AXq4sdmviNUP+DOdK0jnO+gHO+WLM0GjDxHGqoC3D5IzXWjFkZduw516+Jf7L8jDFN/VrnV9NPEAThD9nrm8/vm5Khdf7dZ3tht5gwL8smxeujB4Y+Pedv0plaA+fzrylNwfHWAbSNbeCrtn9ifsaYpn6t8xvhg0MQhNjIXt/G+8evU6VVfi/n2FXXjWVFDjjiY4V/ffRCadPEAWxnjB1ijN2pZSC1CDRLP9yBG++vLE0FALwxbgNfNf1a55fRTxAE4Q/Z65se/pOtA2jrG8HakhTh8+sJU7L5KWMsj3N+njGWCWAHgHs457sm3OZOAHcCQFZW1qKtW7dqkfcSTqcTsbGxk/6Ocw7OORhjAVeSDea2/u7DOcdX3hpGTpwJ9y60qu6fyODg4KXnroVf6/zh+gcGBuBwqHfOXSb6+vqQkKDOVS0yEs3PP5qfe29vL+Li4hTdVvb6Ntl9xtd8rfI/fdqNlxs8+OkaGxKsTHV/qLcdHBxEYmKioscOh3Xr1h1SMv1I0ZIDnPPzY/+9yBh7BsBSALsm3OYRAI8AwOLFi3llZWWwmYNix44dqKiouOLnoawDEcx9/N32ms5zeLq6DSVl5YizmRXdJ9QsR44cuey5q+0P5z6R8B89ehRav79EpaqqKmqfOxDdzz+an/v27dtRXl4uRP3Rwz+x5muR/7tvH8XC/Dgsv6pME3+o96murhbqfR/w9BxjLJ4xluj7O4BNAI5qHSwUQl04S+mhwqn8a0qSMezh2DvJBr5q+LXOL5OfIIjoQ5T6Y0T/uS4Xzna6sLYkWdj8oqBkTlMWgDcYY+8C2A/gRc75y9rGCp5wVxoNNHCB/PPzEuGIMWNXXbcmfq3zy+SnDXsJIroIdPGLkeqbHv6dY99bayZpmkTILxIBmybO+RnO+fyxP3M459+NRLBARHIvHiV+i4lh5fRkvHmmG27v5PPEwvFrnT8a/ARByIvs9Udk/67TXSjLjEOOI0a4/ErmXUcSqZcc8HjE2ktobUkyeoc8OHzeqYlf6/zR4CcIQl5krz8i+jv6R3Ckpd/vUSa984uG1HvPibaX0LIiB2LMDLvqurG4wP/VXaH6lUJ+giCMiuz1RzT/G2e6weH/1Fy4/mCZ6BcNqY80iUas1YylhQ7squsW7pAiQRAEQUxkZ103chw2zEiffAkf4nKkbppE3EtoTUkKWnqHUds2qIlfCeQnCMKoyF5/RPL3D3tw4Fwv1pYkK77AJtL5RUPqpslsFm8vodXTk2BiwM66Lk38Wuc3up8gCHmRvf6I5t9b34NhD8fa0hRh84uGtE1TJPbiCcWfEmfFvNyES5dwqu3XOr+R/QRByIvs9UdE/866biTZLZiXG3ileb3yi7bEjLRN00TCHbhAVwEE419bkozatkE097y3EKOafq3zi+6n+WIEEV1wzoWpP0bxj3i8ePNsD1ZNT4LFNHVjond+kTBM0wSEPnBKB0yp33cVgu9ok9p+rfOL7icIIvoQpf4YxX+oyYm+IQ8qA5yaEyW/KBiqaQKCH7hgB0yJPz/ZjpK0WOyq69LEr3V+0f0EQUQfotQfo/irartgt5iwtND/8jii5RcBwzVNgBh75awpTcbh83242N2viV/r/CL7RTvHTRCEtgTzmZe9vkXCb7XZsKuuG8sKE2G3TN4GiJpfbwzZNAH675WzutgBLwcONLs08WudX3Q/QRCEP2Svb1r7T7a50DHgxopp8VLm1xPDNk2Avnv9FDlMyEywYvfZXtX9gSZFqpFfBj9BEIQ/ZK9v/i5+UcO/63Q3zCaGNTPSpH199MLQTROg314/drsda0tTsK+hF66R0C/DnMzPOdc8vyx+giAIf8he33x+zrlqfs45quq6sCg/ASnxMVK/Pnpg+KYJuHwvG5fLpfqA+fOvLUnGkNuLfedCP9o0mZ8xFpH8svgJgiD8IXt9M5vNYIyp5q/vdOFc19ClBS1lf30iTVQ0TXqxMC8BiTFm7Dx95UKXBEEQBBFpfEvhKN2gl7gci94BIsH4U2YAVD886M9vMZuxsjgJb5zpgdvLAy4gptTvO1SrdX5Z/ARBEP6Qvb75pmSo5a863YU52fHITLBFLL+R6r/hjzRNPIca7DoS4frXlqagx+VGdXOfan7GWMTyi+4nCILwh+z1zef3TckI19/qHMaJ1gGsHTvKJPvroweGbpr8TTpTa+CU+Jfkx8NmZth5evINfEPxM8Yill9kP0EQhD9kr2/j/Wrttbpr7NTc2tJk6V8fvTBs0xRoln64A6fUb+ZuLClIxM667qD2TBMlv6h+giAIf8he37TyV53uQlGqHQVJNinzi4AhmyallzWGOnDB+lcUxqOldxg1bYNS5hfNTxv2EkR0oeb/cPoQtb5p5e9xufFOkxOri5OkzC8Khmuagl0HItiBC8W/fmY6TAx45VSHlPlF8xMEEX2IUn9k9b95phseDiyfFidlflEwVNMU6sJZSgcuVH9qQgwW5Sfi1ZouuN1u6fKL5icIIvoQpf7I6n/lVCcyEyyYn58kZX5RMEzTFO5Ko4EGLlz/hpmpON87jOMtvZr4tc4vkp827CWI6CLQxS9Gqm9a+HsGhrH/nBPrSlNgsQS/0pDe+UVC2qZJ7b14AG33yllbmgwTA95s6NfEr3V+I/gJgpAX2euPnv7Xa9ox4uXYWJYmXX7R5rBK2zQBo4Ol9hfqxIFTy58aZ8VV+Yl4/XQPbDab6n6t8xvFTxCEvMhef/Ty767vR2aCFXNy4qXLLxpSrwjucrkAAHa7XdUvVN/Aqe1fPyMFP3rtHBq6R1CUor7fh1b5jeInCEJeZK8/kfZ7mBX7z/XiA/MyYFJhakOk84uG1EeaZKOyNAUMwGu1nXpHIQiCIKKAN872YNjDsWFGit5RDIHUTZPdbofdbld98pjvkKPa/rR4KxbmJ+DVmi5N/D60ym8UP0F01rQlAAAgAElEQVQQ8iJ7/Ym0/9WaTqTHW1GRm6CJX+v8oiF102Q2y7dXTmVJMs52utDSz6XML7ufIAh5kb3+RNrv8gD7G/uwujgR3OuVLr+I0zKkbZrU2otnPP4mtanpX14QCwagqq5Hyvwy+wmCkBfZ648e/jfOdGPYM3rVnIz5AQi3xIy0TdNEwh24QFcBqOXPS03AvNwEvFZ7+Qa+suQXwS/aJagEQWgL51yY+iOT/7XaLqTHW7GwwCFlfhExTNMEiLtXzkT/+hkpON0+iHNdl18dIEt+vf0EQUQfotQfWfwDwx7sOduDdTNSYGJMuvyiYqimCRBvr5zJ/OvGrmJ4pebKq+hkyK+3nyCI6EOU+iOL/82zPRjycKwfd9WcTPlFxXBNEyDOXjn+/FmJNszPTcD2k52TnmoSPb/eftHOcRMEoS3BfOZlr29q+V+p6URanBXzJ1w1J0t+UTFk0wTov1dOIP/mWak42+nC6fZBKfPr7ScIgvCH7PUtXL/T5cabZ3twTVkKzKYrG07R84uMYZsmQOy9hNbPSIGZAdtP+l/o0p8/0KTISOQXwU8QBOEP2eubv4tflPir6rox4uHYPCtViPxGqv+GbpoAcfcSSomzYmmhAztqOuGd4mqwyfycc93zi+InCILwh+z1zefnnAfl336yA/lJMSjPmnqvOdlfHz0wfNMEXL6XjcvlUn3AQvVvKktDS+8wjjT3BeVnY1dCqIWorw9BEES4yF7fzGYzGGOK/R39IzjY6MTGWamK5oLJ/vpEmqhomkRlbWkyYswM20/RXnQEQRBE+LxS0wkvBzaX+T81R4ROVDRNvkOCou0lFG8zY9X0ZLxa0wW31/8puol+36FavfOL4icIgvCH7PXNNyVDqX/byU7MzIhFcVqsYr/Mr0+kUdw0McbMjLF3GGMvaBlIbSaeQw11AS6t/JtnpaJr0I2D53oV+xljwuTX208QBOEP2eubz++bkhHIf757CMcu9GOTwqNMsr8+ehDMkaZ7AZzQKogW+Jt0ptbAqeFfXpSEhBgztk1yFZ0/P2NMmPx6+gmCIPwhe30b71e61+r2Ux0AgI0KmibZXx+9UNQ0McbyAbwfwO+0jaMegWbphztwavltFhPWlaagqq4LLvd7u1DLkl8vP0EQhD9kr2+h+Dnn2HayEwvyEpDtmHq7KRHzy4LSI00/A/BlAN5ANxQBpZc1hjpwavs3laViYNiLN890S5k/0n7asJcgootgPvOy17dQ/afbB3G20xXw1Jyo+WWBBXozMsauA3At5/xuxlglgC9xzq+b5HZ3ArgTALKyshZt3bpVg7jv4XQ6ERt75UQ3zjk452CMKV56P5j7aOH3co4Hdg+jyGHCv863BPQPDg5e9tz1zh9p/+DgIBwOhyK30ejr60NCQkLgGxqUaH7+0fzce3t7ERsbK0T90cM/seZPdp8nT3vwaqMXP15tQ6Jt8seR8fUZHBxEYmKiIlc4rFu37hDnfHGg21kUuFYCuIExdi0AOwAHY+wxzvnHx9+Ic/4IgEcAYPHixbyysjL41EGwY8cOVFRUXPazcBbOUnJfLf3Xdzfib++0Ii2vCNnJ8VP6jxw5EtJzl/n1GX+b2tpaaP3+EpWqqqqofe5AdD//aH7u27dvR2lpqRD1Rw//ZDV/PEMjbhzYcwQri5OwYtEM4fKH46+urhbqfR/w9Bzn/Cuc83zOeRGAWwG8NrFhEoFwVxoNdKhQa/+WWSnweIGdZ/ulzB9JP23YSxDRRaCLX4xU30LxH2zqQ9egBxtLE6XML9OpOmnXaQp2Lx4l+Bu4SPjzEkyYlRmHf06xF53I+WXwEwQhL7LXHy39Lx7rQJLdgjUz0qTMP5VftDmsQTVNnPOqyeYz6YXHI99eOVP5r5uTjtq2QdS0DUiZXwY/QRDyInv90cLf63Jj15lubJ6VCrvNKl3+QH7RkPZIEwBp98rx599UlgqLieGfxzs08auF7H6CIORF9vqjtv+VU50Y8XC8vzxNE/9EIu0XDambJqORFGvBqulJePlEB9weKVZ3IAiCIHTkheMdKEmLRVlmnN5RogKpmyZZ98qZyn9deTq6Bt3YUz/5tirh+tVAdj9BEPIie/1R09/Q6cKxC/14/5y0SxfIyJRfiV80pG6azGb59soJ5F9e5EBKrAUvhniKTu/8ovsJgpAX2euP2v4Xj7fDzIAts9KkzK/ELxrSNk1K9+IJBn+T2iLpZ+DYPCsVu890o2fQLV1+kf0EQciL7PVHbb/Hy/HPEx24uigJafFW6fIr9Yu2xIy0TdNEwh24QFcBRNJ/7exUuL0cL59UfrRJpPxa+0W7BJUgCG3hnAtTf0Tx72voRVvfCK4rT5MyfzB+kTBM0wSIu1dOsP6CRBPKs+LwjyNtihoE0fJr7ScIIvoQpf6I4v/HkTakxFqwsihRyvzB+kXBUE0TEPzABTtgkfJfW5aEMx0uHG3plzK/ln6CIKIPUeqPCP72vmG8caYb15anwusekS5/qH4RMFzTBCgfuFAHLBL+LeUZiLWa8HT1RSnza+kX7Rw3QRDaEsxnXvb6psT/wvEOeDiwZUailPnD8euNIZsmQP+9csL1J8basLksBa/WdqF7YEi6/Fr7CYIg/CF7fZvK7+Uczx5pw8LcOJRkOqTLr4ZfTwzbNAFy7yUEADfNy8SQm+PFo22X+QNNihQlv9Z+giAIf8he3/xd/LKvvhvNvcO4sSJDmvxGqv+GbpoAOfcS8jE7Kx5lmXH456luuFyuS37OuRT5I+EnCILwh+z1zefnnF/yP1N9EUl2M9bPTJMmv5Hqv0XvAJHAN3C+fWzsdruqA6al/6aKDPzw1Qac6fZgevKonzEmTf5I+AmCIPwhe30zm81gjMHlcqFzwI036p24ZUEWYizqHPOQ/fWJNIY/0iQ7m8pSYbeY8OzR8DbxJQiCIORme00PPF7ghrnpekeJWqKiafIdEpRxL56EGDM2zkzBjppOjDAL7Hb7pUO1aiHz60MQBDEVstc335QMqy0GL5zsxrzsOExLtqnql/n1iTSGb5omnkMNdQEuPf3XzXLA5eZ46WT3pUO1MuXX0k8QBOEP2eubz88Yw/7GPjT3DuMjCzOly2+k+m/opsnfpDO1Bi5S/or8ZMzLiceT716El3MwxqTKr5WfIAjCH7LXt/F+xhieOHwRGfFWrJuRKl1+I9V/wzZNgWbphztwkfbfvDALTd1D2FPfI2V+tf0EQRD+kL2+TfRf6Pdib0MvPjAvAxazSbr8avv1xJBNk9LLGkMdOD3860uTkR5vxROH31shXKb8avppw16CiC6C+czLXt8m87/e5IXFxHBTRYaU+dX0643hmqZg14EIduD08lvMJnxgXgb21PeidcArXX41/QRBRB+i1J9I+/uHPXir2YNrZqYgLd4qXX41/SJgqKYp1IWzlA6c3v4PVGTAYmJ4vdF72c9lya+WnyCI6EOU+hNp/0snOjDoAW5ekCllfrX8omCYpinUAfMRaOBE8KfFW3HNzBS82ezBwPDlDhnyq+WnDXsJIroIdPGLkerbeD/nHE8cvogiB8Oc7Hjp8qvlFwlpm6bx57jDHTAf/gZOJP/NCzIx6AH+eeLKxS5lyK+nnyAIeZG9/oTi33+uF/WdLqzLNwf8n0UR86vhF20Oq7RNEzA6WGp/oU4cONH8c7LjUexg2Pp2KzzeK99MoufX208QhLzIXn+C9f/1UCvS4qxYmq3sq1q0/Gr4RUPqpsnlcsHlcqn+heobOBH9jDFsLjSjsXsIb5zpli6/CH6CIORF9vqj1F/bNoC9Db34yMJMWE3KpySIkl8tv2hI3TRFKwszTMh12PDYwQt6RyEIgiA04G9vtyLWOnrVNCEOUjdNsu6VE67fbGK47aosVLf0o7q5T7r8evsJgpAX2euPEn9b3zC2nezE9XPSkWS3SJdfTb9oSN00mc3y7ZWjlv/6uelwxJjxl0OXH22SJb9efoIg5EX2+qPU//fDo1tm3bowS8r8avpFQ9qmafyVBGoNnL9JbSL6Y61mfGh+Jnae7sa5Lpd0+fXwEwQhL7LXH6X+/mEPnqluw7rSFOQlx0iXX22/aEvMSNs0TSTcgQt0FYCI/psXZMJiZvjb261S5g/VL9olqARBaAvnXJj6o7X/2SMX4Rzy4KOLlB9lEim/Fn6RMEzTBIi7V45W/rR4K66dnYYXjrXjQne/dPlD9RMEEX2IUn+09JssVmx9+yLm58Zjbk6CdPm19IuCoZomQLy9crT237owAyMejn8c75Eyfyh+giCiD1Hqj5b+7TU9aO0bwUfnp0mZX2u/CBiuaQLE2SsnEv7sOIb1M5LxZHUbelxu6fKH4hftHDdBENoSzGde1vrm9nI8eqAFszLjsKo0Vbr8kfLrjSGbJkD/vXIi6b99WS4Ghr34+zutUuaX6QNDEIT4yFjfXq3pRFP3EG6/OgcWi0W6/JH064lhmybA2HvxjPeXpsdhbUkyHn/nIvqGgljvSfLXhyAIwh8y1Tcv5/jjvhaUpMVidUnyFf5o3WtVRAzdNAHG3IuHc36F/9NX58A55MGT714UPr/MHxiCIORBlvpWdbobZztd+NTVOTBNspwO51zo/Hr59SC4pUYlxTdwvn1s7Ha7qgMWaT9j7Ar/7Kx4rChOwl8PteIjCzIRZwv+HLSsrw9BEIQ/RK9vnHP8cV8zCpJjsGFGyqR+xpiw+fX2RxrDH2mKJm5fmoMelxvPHGnTOwpBEAShgDfO9KCmbRCfWpoDcxAb8xL6EBVNk++QoFH24vEdqp1IRW4ClhQk4s8HL2BwJPh1MmR9fQiCIPwhcn3zco7f7DmP/KQYbJmV6tfPORcyvwj+SBOwaWKM2Rlj+xlj7zLGjjHGvhmJYGox8RxqqAtwieRnjPn137UiD10Dbjz+jrK5TbK/PgRBEP4Qvb69XtuF2rZB3LE8FxbzlV/HPr9vSoZo+fX264GSI01DANZzzucDWABgC2Nsmbax1MHfpDO1Bk4vP2PMr78iNwGripPw2MEL6A2wbpPsrw9BEIQ/RK9vHi/HI3uaUZxqx6ayK48yjfdH+16rIhGwaeKj9I390zr2R/jNvwLN0g934ET237UyD84hD/5y6IKU+QmCIMJBhvr28okO1He6cNeKvCvmMsmQX0+/niia08QYMzPGDgO4CGAH53yftrHCQ+lljaEOnOj+mRlx2FiWisffuYiO/hHp8geCNuwliOgimM+8DPVtxOPFb/c2oywzDpWlydLl19OvNyyYNyNjLBnAMwDu4ZwfnfC7OwHcCQBZWVmLtm7dqmbOK3A6nYiNjb3i55xzcM7BGFO89H4w9xHBPzg4eNlzn+w+F/q9+NreEazPN+PWMsuUt410/nD9g4ODcDgcitxGo6+vDwkJyjbyNCLR/Pyj+bn39vYiNjZWiPqjhr+qyYPHTrpx7wILKtLNU94WuLLm650/kv7BwUEkJiYqcoXDunXrDnHOFwe6XVDrNHHOuxljrwPYAuDohN89AuARAFi8eDGvrKwMRh00O3bsQEVFxWU/C2fhLCX3FcV/5MiRgM+9AsABZz3+eaID92yaiWxHjDD5w/XX1tZC6/eXqFRVVUXtcwei+/lH83Pfvn07SktLhag/4fqHvcBX9hzFvNwE3FZZdqlRmMo/Wc3XK3+k/dXV1UK975VcPZcxdoQJjLFYABsBnNQ6WLCEu9JooEOFMvo/sywXDMAje5qlzO/PTxv2EkR0MdXFL4Bc9fkvBy+grX8E/7oqT1HDJFp+PfwioWROUw6A1xlj1QAOYHRO0wvaxgoM7cUT2J+VaMMtC7Pwz+MdONLULV1+tf0EQciL7PXHbDbD6TbhzwcvoLIkGfPzEqXLr4dftDmsSq6eq+acL+Scz+Ocz+WcfysSwZTg8ci3V06k/Z9YlAmH3Yzf7GuDyRT+Wqayvz4EQciL7PXn9/suwO0F7liSLmV+PfyiIfXec7LulRNJvwXAHcty8JOqJuw+04M1JckB7x+MH5Dv9SEIQl5krT917YN4/lg7PrIgE9MzE6XLr5dfNKJiG5Vo58a56ShKteOXuxvh9nj1jkMQBBF1/HJ3I+JtZtx+da7eUYgwkLppknWvnEj7PSPD+MLKXJzrGsLT1eFv5iv760MQhLzIWH/2NvRgT30vPn11DhJsTLr8evpFQ+qmyWyWb68cvfyLcmKwuCABv93bjJ4A26uImJ8aJ4IgZKw/Ix4v/qeqEXlJMfjg3DTp8uvtFw1pmybaiyc4v91ux+euzkT/kAe/efO8dPmpcSKI6EbW+vP3wxdR3+nCfWvywD0j0uXX2y/aEjPSNk0TCXfgAl0FYAR/eW4SbpqTiqer23CitV+6/D6/aJegEgShLZxzYepPMP62vmH8bk8zVhY5sDjXLl1+UfwiYZimCRB3rxyR/HetzEdyrBk/erUBXoXNh0j5Y2JiFHsJgjAOotSfYPy/2t0Et5fj88sypcwvkl8UDNU0AcEPXLADJrs/Kc6Ge1bn43jrAJ6tvihdfhk+VARBqI8o9Uep/50mJ14+2Ylb5qdhemaidPlF9IuA4ZomQPnAhTpgsvuvLU/H/Nx4/PqtZnT2DUmXX7Rz3ARBaEswn3kR6rPby/HQaw3ISrDi01fnCVU/ZffrjSGbJkD/vXJE9jPG8OUNhegf8uB/32iULj9BEMRU6F2f/3aoBXUdLty3Nh/xdqt0+UX364lhmybA2HvxhOsvTY/DLQuz8MKJbuw/2ynl60MQBOEPvepzQ8cAfru3BWumJ2HdjFRV/LTXqjgYumkCjLkXD+dcFf+dK3KR67DhJ7svoLd/UMrXhyAIwh+Rrs9utxs/eLUBFhPDAxsKw55K4PNzzqWsz0as/4ZvmoDL97JxuVyqD1ik/YwxVfyxVjO+ck0RGruH8JfDXdK+PgRBEP6IZH1+troVb5/vx7+uykdmgk01P2NM2vpstPofFU0T4Z+lhQ5cNycNf327FbXtYm6QSBAEITqdA248vLcV83PjcdO8DL3jEBoRFU2T75CgUfbi8R2qVYt/XZmLpFgLfrL7Aiw29Vfe1vr1IQiC8Eek6vPD+9rgGuH44qpscK96G6P7pmQY5ftL9vpv+KZp4jnUUBfgEsnPGFPVH8M8uL+yADVtg/jbO21SvT4EQRD+iFR93t0wgFdru3H7shzMyHao7vdNyTDC95fs9d/QTZO/SWdqDZxefsaY6v5rytKwfkYKfrunGXUdQ1K8PgRBEP6IVH12uk34cVUj5mTH45NLcjSp/7TXqjgYtmkKNEs/3IEzov8/NhQiOdaCr798Bm4eXmOmdX6CIAh/RKp+2mw2/OC1RgyNePH1zcWwmJiqfiN9v6jp1xNDNk1KL2sMdeCM6k+KteC/NhbhTIcL/++t88Lmpw17CSK6COYzH8n6+cKJLrx1tgf/ujofhal21f1G+n5Ry683hmuagl0HItiBM7p/RXESPjQvA3871IqDjb1C5icIIvoQpf74/BecbvxsZyOWFCTiwwsyVfcb8fslXL8IGKppCnXhLKUDFy3+e9bkIz85Bt/aVg+nyy1cfoIgog9R6k9MTAw4GL7+8hmYGMNXNxfDNMUilqLVT1n9omCYpinUAfMRaOCiyR9rNeMbW4rR3jeMH7zaAM65UPlpw16CiC4CXfwS6fr5mz3NONLSj69cU4isxMCLWIpUP2X0i4S0TRPtxaOtf25OAu5akYdXarrwTHWbdPkJgjAWotSfvQ09+L8DF3Dj3HRsLFO+t5wo+WXzizaHVdqmCRgdLLW/UCcOXDT7P7EkG8uLHPifnY2ouTggXX6CIIyF3vWno38E33j5LKan2fHFygLp8svoFw2pmyZZ98qRxW9iDF/fXIwkuwX/+WId+oc9UuUnCMJ46FV/PF6Or790BgPDXnz32hLYraE9puz1M9J+0ZC6aSK0JyXOim9fOx3ne4bwg1cahDtUShAEEQn+uL8FBxqduL+yANPTY/WOQ+iE1E2TrHvlyOZfmJ+Izy7PxfZTnXjy3Tbp8hMEYRz0qD+7Tnfid3ua8b7ZabhhbrrqfpnqZ6T9oiF102Q2y7dXjqz+Ty3NwariJPzPznPYf7ZTuvwEQciPHvXz4iDHN7bVY0ZGLP7jmsKwrt6Vtf7r6RcNaZsm2osnsn4TY/japkLkJtrwzVfOo33gPY8M+QmCkBs96ufAsAdfefEsLCaGb27Mg5WFPj1B5vqvp1+0JWakbZomEu7ABboKgPweWOHGD68vwZDHiwefPw2X26tLfppXRRDRBec84vWTc47v7qhHfacL37m2BIXpiULXZyP7RcIwTRMg7l45RvKXZMTjG1uKcaJ1AD969fKJ4ZHKTxBE9BHp+vnogQt4paYLd6/Mw9JChxT12ch+UTBU0wSIt1eOEf1rS1Lw2WW5ePF4Bx47eCHi+QmCiD4iWT93nOrEw2+ex5ZZqfj44mzV/VrnN6pfBAzXNAHi7JVjZP/ty3JwzcwU/OqN83jlVGdE84t2jpsgCG0J5jMfbv050tyHb207i/m5CfivjUVXPLYM9dnIfr0xZNME6L9XjtH9Jsbwtc3FmJebgG9uO4vq5r6I5icIgvBHqPWnuWcIDzx3GpkJNvzohhLYLJN/RYpen43u1xPDNk2AsffiESF/jMWEh24oQWaiDQ88dxqN3Zev3qr160MQBOGPYOuP0+XGF/9RC7eX46c3zUByrFVVfzj5aa9VcTB00wQYcy8ezrkw+ZNjrfifm2aAc+Dfn6lF18CIqn6CIIhQUVp/XG4vvvTcaTR2D+EH15egMFXZooqRqv+cc8N8f8le/w3fNAHG24uHMSZU/mkpdjx0QwkuOodx3zO16Bu6/HCs1q8PQRCEPwLVH7eX479frMO75/vwjS3FWFzgUNWvRn7GmGG+v2Sv/1HRNBHaMz8vEd+7rgS17YN44Lnay9ZwIgiCEBEv5/jejnrsPtODB9ZPw8ayVL0jEYITFU2T75CgUfbi8R2q1cofav5V05Px9c1FeKepD//9Yh3cHq+qfoIgiGDxV3845/jl7ia8eLwDn12eiw/Nz1TVr2Z+zrlhvr9kr/+Gb5omnkMNdQEukfyMMWHzb56VhvvXTcPuMz349vZ6jLjdmr4+BEEQ/piqvv1+bzP+eqgVNy/IxGeuzlHdr2Z99k3JMML3l+z1P2DTxBgrYIy9zhg7zhg7xhi7NxLB1MDfpDO1Bk4vP2NM6Pw3L8jEXSty8fLJTnx/Rz2sNpsmrw9BEIQ/pqpvf6vuwm/3tuB9s1LxxcqCkNZ+i2T9p71WxUHJkSY3gPs55+UAlgH4AmOsXNtY4RNoln64A0f+qfnkokx8fGE6XjzZjYdeb4J3wn5xsn9wCIIQl6nq26P7W/DInhZsLkvB/auzwL3Bz7+UvT7L7teTgE0T57yFc/722N+dAE4AyNM6WDgovawx1IEjf2D/8PAwPr8qH5++OgfPHm3HD15pUK1xog17CSK6COYzP1V9+/PBC/j1m+exeVYqvr5lOuJig59jY4T6LLNfb4Ka08QYKwKwEMA+LcKoQbDrQAQ7cORX7rdYLLhreS5uH2ucvq9C4yTTh4sgCPUIt77934EW/Gp3EzaWpeJrm4thNjGh6yf5xYQp7eAZYwkAdgL4Luf86Ul+fyeAOwEgKytr0datW9XMeQVOpxOxsbGX/YxzDs45GGNBn6NWcl9R/IODgyE9d73yc87x3BkPnj/rwdXZJny63AKLiSm672S3cblccDiCW0vFKPT19SEhIUHvGLoRzc8/mp97b28v7HZ7yPXn6ToPXqr3YGmWCZ+ZY4E5jPqjR/2frObLlD8c/+DgIBITE4PyhcK6desOcc4XB7qdoqaJMWYF8AKAbZzznwa6/eLFi/nBgwcVBQ2VHTt2YN68eZf+rcZKo1M5RPIfOXIEFRUV0uX/0/4WPPzmeawsTsL33j8ddqtyx/jfHTt2DBs3bgzpOchOVVUVKisr9Y6hG9H8/KP5ue/YsQNz5swJuv54OcdDr53D09Vt+OC8DHxp3bQrGqZAjkC/U0o4fn81X5b84firq6sjUu8ZY4qaJiVXzzEAvwdwQknDFCloLx75/J9amoMHNxTirbM9+Lena+F0uSOanyAIeQm2Prg9Xnzj5bN4uroNn1ycjS+v998wheLXOj/5RxFtDquSOU0rAXwCwHrG2OGxP9dqnEsRHo98e+VEu/+D8zLwnWun49iFfnz+yVPo6Ke96giCUIbS+jAw7MEDz9dh28lO3L0yD19Yna/olJHo9TMa/aJhCXQDzvkbAIJfxCICuFwuAIDdblf1C9U3cOTXxn9NWSoSYsx48Pk63LH1BH560wwUp713vl7r/ARByEug+tDWN4z7nz2N2rYBPLihEB+cl6GqX+v85L/cLxqGXxGcEJNlRUl4+OYyuNxe3PH4SRw416t3JIIgJKeufRCf2XoS57pc+PGNpUE3TAQRCKmbJln3yiH/KOXZ8fjDbbORlWDDvc/U4tkjbRHJTxCEvPirD/sbevHZx0/C4+X4zUdmYWVxsqp+rfOTf3K/aEjdNJnN8u2VQ/7LyXHE4JFbZmFJQSK+90oDfrHrHAYGXZrlJwhCXiarPzabDVsPteC+f9QgO9GGP9w2G2WZcar5Ra6f0eAXDWmbJtqLxzj+hBgzfnLTDHygIh1/OXQR/729CX0j710xQY0TQRCT1Z8htxfff60Rv3jzApbmJ+DhD89AVqJNNT8gfv00uj+UfQG1RNqmaSLhDlygqwDIr62fcS/uWZ6BL68vwMHGPnz6rydQ0zYwqV+0S1AJgtAWzvkV9afVOYzPP3EKLxzrwO1X5+ChG0thhVvI+kb+8PwiYZimCRB3rxzyK/Pb7XZ8aH4W/t9HyjDs9uKOrSex7WTHFX6CIKKP8fXnnSYnPvXX4zjbMYgfXV+Cu1bkwWqxCF3fyHuxAMkAAB7DSURBVB+eXxQM1TQB4u2VQ/7g/RU5CXj0Y+Uoz4rD1146ix+/fg5Dbu8lP0EQ0YfZbIbHy/GHfc24+8lTiLeZ8fvbZmNtacpltxG9vpE/dL8IGK5pApQPXKgDRn7t/WnxVvzqQzPx0auy8MThi/jM1hOo7xwEIN45boIgtIUxho7+Edz7dA1+81YzNpal4tGPlWN62pX7sclQ38gvZ8MEGLRpAgIPXLgDRn7t/RazCfeuLcBPbypFW98I/uUvJ/Dc0Taa00QQUcbxDi8+9tgxVLf04782FuGbW4oRbwv9VJEI9Y388jVMgIGbJsDYe/HInD9Y/8riZDz28XLMzYnHd3c04LdHPegZGAl4P4Ig5MY14sG3XziOnx12I9luwZ9um40b5qaHtCWKD9HqmxI/7bUqDoZumgBj7sXDOZc6fyj+jAQbfvHBmfj8yjwcavNi08924rWTrWHnIwhCTA43duPaX+zG7984i7V5Jvzpo7MxPf3K03FTIUt9C+TnnEudXyu/HgTce84I+AbOKHvxMMakzh+q32xi+NTSHKQNt+KJczbc/qeDuHlRPr56fTkcdqtqeQmC0I9htxe/fK0Wv66qQ2ZiDB77zNUYrH8HdmtoNUmW+jaVnzEmdX4t/ZHG8EeaCONR6DDhuXtW4gvrSvDU203Y/D+7sLOmTe9YBEGEybuN3bjxf9/EL187jZsW5OHl+9Zg1Yx0vWMRxCWi4kjT+HWAAKh+eDDSft+hWlnzq+GPsZjxwOZZ2FiejS898S7+5Q/7ceOCXPzX+2cjM1G8/YoIgvCP0zWCn2yvwf/tqUd6Qgx+84lF2DwnWxW3jPVtop9zLnV+Lf2RxvBHmiaeQw12HQkR/YwxqfOr6V9QkIwX7lmFezfMwEtHLmDDT3biz3sb4PHSFXYEIQPbjl3Axp/uwqN76vHxZYV45f61qjdMstY3n983JUPW/Fr59cDQTZO/SWdqDZxefsaY1PnV/uDYrWb8+8aZePm+1ZiXn4Sv/uMoPvjwWzh6vidsN0EQ2tDQ0Y87Hj2Iu/58CMlxVjz1+RX41o1zVZufKHt9G++nvVbFwbBNU6BZ+uEOHPn19U/G9IwEPPaZq/HzWxfgfNcArv/VG3jwyWpcdLpU8RMEET5O1wi+/9IJbPzpLrxV147/eN8sPH/PKlw1LSXwnRUie30jv7gYck6T0ssaxw9cMOdYya+vf6rFLRljuHFBHirLMvHLV2vx6J56vFDdjLvXleIzq4pDvgKHIIjw8Hg5njzUiIe21aC9bwgfXpSPL28uQ6Yj8BzEYBa0lb2+kV9sDHekKdh1IILteMmvv18JSbFW/Pd15dj+72uxsjQdD207hQ0/2YlnD5+Hl+Y7EUTE4JxjZ00bbvjVG3jwqSOYlhqLZ7+wEj++eb6ihsmHKPWH/Pr5RcBQTVOoC2cpHTjyi+EPhuL0eDzyycX462evRlKsFfduPYz3//INvHK8lbZjIQiNOdTQiVse2Yt/+cN+9AyO4Oe3LsBTn1+B+QXJQbtEqT/k18cvCoZpmsJdaTTQwJFfHH8oG/auKEnH8/esws9uWYCBYTfu+L+D+MCv38Ibte3UPBGEyhxv7sXtfzqADz28B2fa+vGtG+fgtfsrceOCvJA+v4EufjFSfSO/2I2TtHOatN6LZ7yL/AbxmxhuWpiH98/LwVOHmvCLV2vx8d/vw9XFqbh3wwwsL0kLqaATBDFKdVM3/vf109h2rBUOuwUPbC7Dp1cWIc4W/leN9PWH/CH5RfufWmmbJuC9c9xqTiSbOHDkN5YfAKxmE25dOg0fuCoPf9t3Dv9bVYeP/m4f5hck4/NrS7CpPAsmEzVPBKGUfWc68KvXT2N3bTscdgv+bX0pPrNqOpLi1N3eSPb6Q/7g/aIhddMk61455NfX7yPGYsanVhbj1qXT8OShJjyy6ww+99ghlGTE43NrS3DTwjxYzYY5g00QquL1clTVXMTDVXU4UN+F9AQbHtwyCx9fNg2JGu4FKXv9IX9wftGQumkiCDWwW834+LJC3LqkAC8eacHDVXV44Mlq/GR7DT6xfPTnaQli/l8PQUSaviE3njrUhD+9VY+z7f3ITbLjG9eX45Yl0xBrk+OycYIIFambJln3yiG/vn5/WMwm3LggDzfMz8Xrpy7iD2/U46Ftp/DzV2txw/xcfGpFEebmJWmagSBEpbFzAI++VY/HDzTCOeTGgoJk/OK2hXjf3OyIHpGVvf6QPzi/aEjdNPkGabLJY6Ey2aQ28hvHrwTGGNbPysL6WVmobXXi0T31eOrQeTx5qAmLC1Pw8WWF2DI3mxbKJAzPiMeL105exOMHGlF16iJMjOF9FTn49MoiVVfwVors9Yf8wftFQ9qmyd9ePOG82P4GjPxi+SPJjKxEfOemCjyweRaeONiI/9vTgPsePwzHsxbcuCAPtywpoKNPhOFo6OjH1gONePJQE9qcQ8hMjMHdlaX42LJpyEmK1SWTKPWH/JH1i3ZFs7RN00TCHbhg9sohv75+PS5BTYq14o7V03H7ymLsPdOBvx9sxN8PNuLPextQnuPALUsKcP38XKTG2yKejSDUwOkawbZjrXj67Sa8VdcBEwPWz8rELUumYV1ZBiw6XhTBORem/pA/8n6RMEzTBIi7Vw751fXricnEsKI0HStK0/HNgRE89+55PH6wEV9/7hi+/cJxrJqRjhvm52LTnGwkxBjq40UYkCG3B1Wn2vDc4Wa8cqIVQ24vClJjcf/Gmbh5cQGyk8SZVyJK/SG/Pn5RMFxVD3bgwtkrh/z6+EUhKc6KTywvwieWF+FESy+ePdyM599txhf//i5iLEewYXYmbpifi8qyTJr/RAjDsNuLvWc68M8jLfjnkRb0utxIi7fh1iUFuGFBHq6alizcKRFA2WffCPWN/GJjuKYJUD5wauyVQ/7I+0Us6LNzHJid48CDW8rw9rkuPHe4GS8eacE/j1xArNWMNTPTsak8G+tnZSKFTuEREaZ/yI2dNW3YduwCXjt5EU6XG/E2MzbPycYNC3KxqjRd19NvgQjmMy97fSO/2BiyaQICD5yae+WQP/J+UWGMYVFhKhYVpuKr15Vjz5kObD/Wih3HW7HtWCvMJobFhSnYNCcbG2dnYVpanN6RCYPS0jOIXTVt2HG8Fbtr2zHk9iIlzootc7KxeU42Vs1IN+wRUNnr20T/RGTLb6T6b9imCTD2Xjwy55f5AxMMFrMJq2dkYPWMDHzrxjk4cr7nUgP17ReO49svHEdhWhzWzMjA6hnpWF6SpulKyoSxcY14cLC+CztrLmJnTRtqWvsAALlJdty2dBo2z8nGkqIUoY8oqYns9W28n/ZaFQdDN02AMffi4ZxLnV/mD0yoMMYwLz8Z8/KT8aXNZWjo6EfVqTbsqmnDU2834c97G2AxMVw1LeVSA1WRn4QYS/S8RkRwuD1eHG/pxb4znXirrh17znTANeKFzWzCkuIUfHhRPtbOzMTMrAQhT2lHAtnrm8/POae9VgXB8E0TYLy9eBhjUufXai85mShMi8e/rIjHv6wowrDbi7fPdWFXTRt217bjJztqgB1AjMWEhdOSsbQ4DVcXp2LhtGS9YxM64vZyHGrowr6zHdh3phOHGrrQN+QGABSnx+OWxQVYW5aBZdPTEGeLitKuCNnrm9lsBmNM6vxGqv/0ySIInbFZTFg2PQ3Lpqfhy1uAzv5h7D/bOfqnvgO/eq0Wv+CAxcQwLZFhp/MYFhSMHrUqSouL2qMIRoZzjpYeFw43duPdxm6809iNw+cGMLz9LQBAaWYCbliQi6uLU3F1cZpQSwMQhJGJiqbJaHvx+A7Vyppf9sOzWpMab8OWudnYMjcbwOiig4caurD/bCdeefcs/rb/HP74Zj2A0UU35+UnYX5+MuYXJGNOrgM5SXZqpCSCc4425xBOXHDi6PkeHG7sxuHGbrQ5hwAANrMJs3MdWJNnwQdXz8PS4lSk0wbSipG9vnk8HnDOpc5vpPpv+KbJiHvxMMakzq+mPxpItFtRWZaJyrJMLLVfwKrVa1DT2ofqpm6829SNdxt78PDOOni8o5NFHXYLZmU7MCsnEWXZiZiV7UBZdiIttikAQ24PTl/sw4kWJ0629OLEhV6cbHGio3/40m2mp8djVWk6FhSMNsKzcxIRYzGjqqoKlRU5OqaXD9nrm88/fkqGjPmNVP8NXUWNvBePzPnV8kcrFrMJ5bkOlOc6cOvSaQCAwWEPjrf04PjYl/GpC048/fb5S3NeACAvORbTM+IxPT0exenxKM5IwPT0eOQmx8JsoiNTasE5x0XnEOra+nCmrR9n2vpxtr0PZ9r70dg5gLHeFjEWE8qyE7Fhdualdb5mZzuQFEdXUKqB7PVtvJ/2WhWHgE0TY+wPAK4DcJFzPlf7SOqg91455NfWT1xOrM18aX0oH5xzNHUN4tQFJ05e6EVNax/qO/rx1IRmymY2oTAtDtNS45CXEovc5FjkJcciL2X0vxkJMTBRU3UJzjm6BkZwvmsQTV0DON89iKau0T/nuwdxrqMf/cOeS7e3W00oTk/A3Lwk3DA/FzOzEjE7x4GitLioufw/0she38gvLkqONP0J+P/t3XtsW/d1wPHvEUVRkk1JViQ/KsmOZMuSMyuwEyNpnMdiuzYSZ3ETLEFWDFiDZciKYUCH/TEEKLA/hgFDN2ADhm4Ygq5YixSZsC5dsjztzHacpxy7lmQ1fkR2JMeqVFNmJFEPUnz89gevGErWg5JI3kvyfADCpHh1fM79kT8d3nt5Lz8CfpbZVNLHKdfKmYk/MTHB8ePHOXLkCEVFS0+Smc5/ZGSEt99+m6effpqRkRG6urrYv39/2uJnOn87Ltibi0SEhupyGqrL+dYdGxI/N8YwPD7NF8NfbwG56pvg+ldTfNrnZywYmRWnxFXEpqpS1ns91Ho91Kz1ULs26b7XQ43Xw7pyN2VuV84eTxUMRxmZDOOfmMY3HuLGWBDfeAhfIH67EQgxHAgxNBZkMqkpAlhT4qJ+XbzpvLex2tqit5bG2jVsqijVpnOVlvOet3v+j0QivPHGGzz++OOOmD/HxsZ46623eOaZZ7h58yadnZ3cd999jvn7mGuN05JNkzHmlIjcnvlU0sNp18pxuVz09fXR0NCQ0hs/G/lPT08n9pHfdtttTExMEAgE8Hq9aYmf6fzV6ogItVYDdE9j9S3PB4JhfjMSZGBkkoGRIAPWFhRfIMiloQAfBIZvaaxmuF1CZZmbijI3FaVuKsvc1uNivKXxpqrM7aLUXUSp20VZiSvxM4/bhatIcIlQVATFRUW4iqBIBFeRUCSCbzLGF8MTRGOGaMwQicWIxSASixGNGcJRQzAcZSocZXI6/m9w+uv7U9MRAsEIo1NhRqbCjCbdpiOxeWta6ymOr6+1HnZ8o4LfbamNN0hVZdSvi98qy9w52yzmilS+/OKE+f/ixYs0NjYmPiA7af6sqqoiEAgQDocpL1/6agROm/+dIK+OaXLqtXKuXLnCvn376O/v58KFCzz22GMAvP/++9TW1tLa2spLL73E9u3b6evrwxjDoUOHWLduHZ9++ilut5tdu3YB0N7eTlNTE+FwmGPHjjExMUEsFmP37t3U19czNjZGR0cH4XCY0tJS9u3bx5o1a/D5fJw4cQJjDA0NDbPy27JlC729vezevduW9bPc+CqzvKVuWja6adl4axM9IxSJMjw+zbC1FcY3HmJk8usGZCwYZmwqzFeT0/TdnGB0KsxEKEI4moathKdOrujXSlxFlLqL8FrNXFW5m+b1axONXWV5/N915SWs93pY7y2lxlui5zxyCKfMP0vF//zzzzlw4AADAwN0dXVx+PBhPB4Pp06dYuPGjezYsYOXXnqJlpYW+vv7icViHDx4kIqKCjo6OigrK0vMxe3t7Tz66KNEo1HefPPNxHx/9913s23bNnw+Hx999BHhcBi3283+/fvxer34fD5OnjwJQH19/az8GxsbuXr16oLzfabXz0rjO0XaZgMReR54HmDDhg2JAcuUYDDI+fPnE4+NMRhjEJEVf+JbLMZK48diMfx+P19++SUjIyMEAgG6u7sREW7evEkoFCIcDhMOh/H7/bS2tjI0NMSJEydobm7mxo0buFyuRK2hUIhgMMgHH3xAKBSitbUVgImJCS5fvkxPTw87duygpKQEn8/HO++8Q3NzM+fOnaOxsZHKykr6+voIhUKJmIFAgOvXr1NcvPjLIRPrZyXxQ6FQxl9fTjU+Pu642ouBTdaNMus2iwAlQAnRmGE6BtNRmI7O3DeJxzEgZua7GWIm/vovLyulSMAlUJR0cwm4RChxQYlL8LigxAUel1BSxJyD3aPWLTg71an4bfwmjANXM7C+VsqJY58toVCI3t5eR8w/i8Wfme/7+/sZHR0lEAgk5tnR0VEikcis+b6lpYXBwUFOnDjB1q1b8fv9FBcXz5rvL126hN/vnzXfBwIBurq6EvO92+3G5/Nx9OhRmpub6ezspKmpicrKSr744guCwSA9PT2ICOPj4ynN95lYPyuJHwwGHfW6T1vTZIx5EXgRYM+ePebhhx9OV+h5HT16lLa2NiC917KZL9Zq4k9MTHDhwgXa2toYGBhgbGyMbdu24fF4GBkZoba2NvEi37t3LxUVFWzYsIHTp0/T1tZGMBjE7XYnav3ss88oLS2lubmZ119/nYmJCbZs2cKmTZvw+/2cPXuW3t7exIuuvLycrVu3cu7cOfbu3YvL5aKuro533303EXNkZITBwcHE42yun5XE7+7uJtOvL6c6efJkwdYOhV1/Idd+7Ngx7rzzTkfMP4uZb75PnmdramrYsmUL3d3d3H///axdu5aamho6OjrYuXMn09PTt8z3LS0tXLx4EZ/Pd8t8f+bMGa5cuQLEm46ysjI2b95MV1cXDzzwABDfiHH8+HF27tyJy+Va1nyf7vWzkvhdXV2Oet3n9HbnXLgWT3FxMZFI/PiPufu4I5FI4uK7IoLbHf+qsYgQi8USvzP3Yo0Q3zf91FNPce3aNU6fPk1dXR2NjY1UV1dz5MiRWfkHAoFFL70SjUZT/tSR7vWT7fhKqdzl9Pln7nw/d+6eOV3MzBaVaDRKOBxOzM8LzfdlZWULzvdPPvnkrBwmJydnXasuOf5MzOVuZUrX+llJfKdZ8qtcIvIy8DHQIiLXReS5zKeVmmAwSDAYTPsf1JmBS0f8mTdIJBLB6/Xy1VdfJZ67fv064XB40ReH1+tleHgYAJ/PRyAQAOKfaIqLi9m+fTu7du1ieHiYqqoqpqam8Pl8eDweJicnGRoawuv14vF4GBwcBOL73JONjo5SXX3rAcELSef6sSO+Uip3OXn+mW++n9l6MjAwkIg/cy25YDBISUlJ4vcXmu9DodCC8/3Q0BAQb4b8fj/l5eWUlpZy7do1gsEg/f39s3Jc7nyfzvWzkvhOk8q3576TjUTyWUNDA0NDQ9TX17N161ba29vxer0pvXCbmpq4fPky7e3trF+/nsrKSgD8fj8ff/wxIkJRUREPPvggLpeLQ4cO8eGHHxIKhYhGo+zYsYONGzeyb9++Ww4MnDEwMMDmzZvTXrdSShWa+eb7iooKampqlvzdheb7yclJXnnllQXn++npaWKxGG1tbVRXV/PQQw/x3nvvJfJJpvP96kgmznmzZ88ec+bMmbTHTXb06FF27oyfazPdu2+S96umI77P56O7u5sDBw6kJf758+cX3R+9nPjRaJRXX32VJ554IqVzSKUj/9XG7+7u5uDBg2n5v3JNIR/XAoVdfyHXPnNME9g//yxl7nyfjvhLzfmpxl/JfJ+O/FcTv6enh0OHDqUl9mJE5KwxZs9Sy+X06WhdLtesfaDpOIfP3APR0hG/traWuro6YrFYRuKvJv9AIMC99967oobJCfkrpQpHLsw/yfO90/Jf7nzvhPydJmebpoWuxbOagUvlWjkrjd/a2po46DsT8Veaf1VVFXV1dRmLn+n8lVKFIZfmn9bW1lsaEyfk7/V6U57vVxI/E/k77aSxOds0zbXagVvOtXI0vr3x9TIqShWWhT5wzsin+U3jO2/rUrK8aZpg5QO3kmvlaHz74iulCo9T5h+Nb098p8irpgmWP3DLHTCNb398pVThccr8o/Hti+8Eedc0QeoDt9IB0/j2xnfaPm6lVGYt5z2f6/Obxne2jJxyQER8QP+SC65ODTCc4f/DqQq5dijs+gu5dijs+rX2wlXI9Wer9i3GmNqlFspI05QNInImlXMq5KNCrh0Ku/5Crh0Ku36tvTBrh8Ku32m15+XuOaWUUkqpdNOmSSmllFIqBbncNL1odwI2KuTaobDrL+TaobDr19oLVyHX76jac/aYJqWUUkqpbMrlLU1KKaWUUlmTM02TiPyDiFwUkW4R+aWIVC2w3CMicklEekXkhWznmQki8rSI/FpEYiKy4LcIRKRPRM6LSKeInMlmjpm0jPrzceyrReSYiHxu/btugeWi1rh3ishr2c4znZYaRxHxiEi79XyHiNye/SwzJ4X6nxURX9J4/4kdeWaCiPxERG6ISM8Cz4uI/LO1brpF5K5s55gpKdT+sIiMJo37X2c7x0wRkQYROSEin1lz/ffnWcYZY2+MyYkbcAgotu7/EPjhPMu4gCtAE1ACdAF32J17GmrfAbQAJ4E9iyzXB9TYna8d9efx2P898IJ1/4X5XvfWc+N255qmepccR+DPgH+z7v8B0G533lmu/1ngR3bnmqH6HwLuAnoWeP4w8BYgwDeBDrtzzmLtDwOv251nhmrfBNxl3fcCl+d53Tti7HNmS5Mx5qgxJmI9/ASon2exe4BeY8xVY8w08J/At7OVY6YYYy4YYy7ZnYddUqw/L8eeeA0/te7/FHjCxlyyIZVxTF4nvwAOSP6cJj5fX8cpMcacAvyLLPJt4Gcm7hOgSkQ2ZSe7zEqh9rxljBk0xvzKuh8ALgB1cxZzxNjnTNM0xx8T7zjnqgO+THp8nVtXfD4zwFEROSsiz9udTJbl69hvMMYMWveHgA0LLFcqImdE5BMRyeXGKpVxTCxjfZAaBW7LSnaZl+rr+PetXRS/EJGG7KTmCPn6Pk/VfSLSJSJvicjv2J1MJli723cDHXOecsTYF2f7P1yMiLwLbJznqR8YY161lvkBEAF+ns3cMi2V2lPwgDFmQETWA8dE5KL16cXx0lR/Tlqs9uQHxhgjIgt93XWLNfZNwHEROW+MuZLuXJUj/C/wsjEmJCJ/Snyr236bc1KZ9yvi7/NxETkM/A/QbHNOaSUia4H/Bv7CGDNmdz7zcVTTZIz51mLPi8izwO8BB4y1k3OOASD5U1e99TPHW6r2FGMMWP/eEJFfEt/UnxNNUxrqz8uxF5HfisgmY8ygtSn6xgIxZsb+qoicJP5JLRebplTGcWaZ6yJSDFQCN7OTXsYtWb8xJrnWHxM/7q1Q5Oz7fLWSmwhjzJsi8q8iUmOMyYtr0omIm3jD9HNjzCvzLOKIsc+Z3XMi8gjwV8ARY8zkAot9CjSLSKOIlBA/SDSnv0mUKhFZIyLemfvED5yf91sYeSpfx/414LvW/e8Ct2x1E5F1IuKx7tcA9wOfZS3D9EplHJPXyVPA8QU+ROWiJeufcxzHEeLHfxSK14A/sr5J9U1gNGn3dV4TkY0zx+6JyD3E/37nxYcFq65/By4YY/5xgcWcMfZ2HH2+khvQS3x/Zqd1m/n2zDeAN5OWO0z8yPsrxHft2J57Gmp/kvj+2xDwW+CdubUT/7ZNl3X7db7Unmr9eTz2twH/B3wOvAtUWz/fA/zYur8XOG+N/XngObvzXmXNt4wj8DfEPzABlAL/Zc0Jp4Emu3POcv1/Z73Hu4ATQKvdOaex9peBQSBsveefA74HfM96XoB/sdbNeRb5NnGu3VKo/c+Txv0TYK/dOaex9geIH5PbnfQ3/rATx17PCK6UUkoplYKc2T2nlFJKKWUnbZqUUkoppVKgTZNSSimlVAq0aVJKKaWUSoE2TUoppZRSKdCmSSmllFIqBdo0KaWUUkqlQJsmpZSjicjtIjIlIp1JP/uJiNwQkZ6kn5WJSKeITFtnRldKqbTSpkkplQuuGGN2JT3+D+CR5AWMMVPWMr/JZmJKqcKhTZNSylYi8oqI/K2InBKRayKy5MWbjTGnAH8W0lNKqQRtmpRSdmsDRowxDwHfB/7Q5nyUUmpe2jQppWwjIuVAJfBP1o/cwIh9GSml1MK0aVJK2ekO4KwxJmo9vhPoWWR5pZSyjTZNSik7tQGdSY/vBLptykUppRalTZNSyk5zm6adpLClSUReBj4GWkTkuog8l6H8lFIqodjuBJRShcsY85dzHjel+HvfyUxGSim1MN3SpJRyuihQmXxyy/nMnNyS+MHksaxkppQqKGKMsTsHpZRSSinH0y1NSimllFIp0KZJKaWUUioF2jQppZRSSqVAmyallFJKqRRo06SUUkoplQJtmpRSSimlUqBNk1JKKaVUCrRpUkoppZRKwf8DBv2ZQ089VQUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "aa_support_w = 4\n",
    "aa_x0_w = 0.25\n",
    "aa_parameter_w = aa_support_w\n",
    "aa_szetan_w = True\n",
    "if aa_support_w == 1:\n",
    "    print(\"Using trivial gridder\")\n",
    "    aa_gcf_w = numpy.ones((aa_over, aa_support_w))\n",
    "    def aa_w(x): return numpy.ones_like(x)\n",
    "elif aa_szetan_w:\n",
    "    print(\"Using Sze-Tan's gridder with R=%d, x_0=%g\" % (aa_support_w//2, aa_x0_w))\n",
    "    aa_gcf_w = sze_tan_gridder(aa_support_w//2, aa_x0_w, aa_over)\n",
    "    def aa_w(x):\n",
    "        return sze_tan_grid_correction_gen(aa_support_w//2, aa_x0_w, x)\n",
    "    print(\"Mean error:\", sze_tan_mean_error(aa_support_w//2, aa_x0_w))\n",
    "else:\n",
    "    aa_gcf_w = kernel_oversample(anti_aliasing_function(grid_size, 0, aa_parameter_w), aa_over, aa_support_w)\n",
    "    aa_gcf_w /= numpy.sum(aa_gcf_w[0])\n",
    "    def aa_w(x):\n",
    "        return scipy.special.pro_ang1(aa_mode, aa_mode, aa_parameter_w, 2*x)[0]\n",
    "\n",
    "# Calculate appropriate step length to give us full accuracy for a field of view of size theta\n",
    "max_n = 1.0\n",
    "print(\"max_n =\", max_n)\n",
    "dw = dw_opt = aa_x0_w / max_n\n",
    "print(\"Optimal dw =\", dw)\n",
    "\n",
    "# Plot gridding function\n",
    "plt.rcParams['figure.figsize'] = 10, 5\n",
    "r = numpy.arange(-aa_over*(aa_support_w//2), aa_over*((aa_support_w+1)//2)) / aa_over\n",
    "plt.plot(dw_opt*r, numpy.transpose(aa_gcf_w).flatten().real);\n",
    "plt.xticks(dw_opt*numpy.arange(-(aa_support_w//2), ((aa_support_w+1)//2)+1))\n",
    "plt.grid(True); plt.xlabel('w [$\\lambda$]'); plt.title('$w$ Gridder'); plt.show()\n",
    "\n",
    "x = coordinates(10001)\n",
    "print(x)\n",
    "sze_w_im = aa_w(x)\n",
    "print(sze_w_im)\n",
    "#plt.plot(max_n*x/aa_x0_w, aa_w(x));\n",
    "plt.plot(max_n*x/aa_x0_w, 1/aa_w(x));\n",
    "plt.title('$w$ Grid correction'); plt.grid(True); plt.xlabel('$n$ [1]');\n",
    "max_n_x0 = max_n/aa_x0_w/2\n",
    "plt.axvspan(max_n, max_n_x0, color='lightgray', hatch='x', alpha=0.5)\n",
    "plt.axvspan(-max_n, -max_n_x0, color='lightgray', hatch='x', alpha=0.5)\n",
    "plt.annotate('(unused)', xy=((max_n+max_n_x0)/2,0.9), ha='center', color='gray')\n",
    "plt.annotate('(unused)', xy=(-(max_n+max_n_x0)/2,0.9), ha='center', color='gray');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "max_w = numpy.sin(theta/2) * numpy.sqrt(grid_size**2 + grid_size**2)\n",
    "max_w = numpy.max(locations_uvw[:,2]) - numpy.min(locations_uvw[:,2])\n",
    "w_planes = 2*numpy.ceil(max_w/(2*dw)) + aa_support_w\n",
    "\n",
    "print(\"Stacking Parameters: \")\n",
    "print(max_w)\n",
    "print(w_planes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Generating a fresnel pattern for such a large field of view is problematic...\n",
    "def generate_fresnel_x0(theta,lam,dw,x0):\n",
    "    grid_size = int(theta*lam)\n",
    "    x0ih = 0.5/x0\n",
    "    oversampg = x0ih * grid_size\n",
    "    print(oversampg)\n",
    "    grid_size = int(theta * lam)\n",
    "    ls,ms = x0ih*theta*coordinates2(x0ih*grid_size)\n",
    "    r2 = ls**2 + ms**2\n",
    "    r2i = r2 > 1.0\n",
    "    r2[r2i] = 0.0\n",
    "    #ns = numpy.sqrt(1 - r2) - 1.0\n",
    "    #ns = numpy.nan_to_num(ns)\n",
    "    \n",
    "    #Fresnel Pattern\n",
    "    \n",
    "    ph = 1 - numpy.sqrt(1.0 -r2)\n",
    "    frnl = numpy.exp(2j * numpy.pi * dw * ph)\n",
    "    frnl[r2i] = 1.0\n",
    "    return(frnl)\n",
    "\n",
    "# Grid Correction Function\n",
    "def grid_correction(theta,lam,aa,aa_w):\n",
    "    grid_size=int(theta*lam)\n",
    "    ls,ms = 2*theta*coordinates2(2*grid_size)\n",
    "    ns = numpy.sqrt(1 - ls**2 - ms**2) - 1.0\n",
    "    aaf = aa(ls.flatten()) * aa(ms.flatten()) * aa_w(ns.flatten())\n",
    "    return numpy.reshape(aaf,(2*grid_size,2*grid_size))\n",
    "    \n",
    "    \n",
    "\n",
    "print(theta)\n",
    "frnl = generate_fresnel_x0(theta,lam,dw_opt,aa_x0)\n",
    "plt.imshow(frnl.real)\n",
    "plt.colorbar()\n",
    "plt.show()\n",
    "\n",
    "gridcor = grid_correction(theta,lam,aa,aa_w)\n",
    "plt.imshow(gridcor)\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Prove it for a snapshot first.\n",
    "# Also extend to Y polarisation too!\n",
    "def epic_wstack(theta,lam,efieldf,locations,x0,du=du_opt,dw=dw_opt,\n",
    "                aa_support=aa_support,aa_support_w=aa_support_w,gcf=aa_gcf,gcf_w=aa_gcf_w, aa=aa, aa_w=aa_w):\n",
    "    \n",
    "    locations[:,0] = 2 * locations[:,0]\n",
    "    locations[:,1] = 2 * locations[:,1]\n",
    "    grid_size = int(theta*lam)\n",
    "    #w_kernel = w_kern(theta,dw,NpixFF=256,NpixKern=size,Qpx=8, invert=True)\n",
    "    #wkh = w_kernel.shape[2]//2\n",
    "    \n",
    "    max_w = numpy.max(locations[:,2])\n",
    "    min_w = numpy.min(locations[:,2]) \n",
    "    w_range = max_w - min_w\n",
    "    w_planes = numpy.ceil(w_range/(dw)) + aa_support_w\n",
    "        \n",
    "    print(\"Max W: \",max_w)\n",
    "    print(\"Min W: \",min_w)\n",
    "    print(\"W Range: \",w_range)\n",
    "    print(\"Number of W Planes: \",w_planes)\n",
    "    #Fresnel Pattern\n",
    "    fresnel_pattern = numpy.fft.fftshift(generate_fresnel_x0(theta,lam,dw,x0))\n",
    "    \n",
    "    # W-Stacking\n",
    "    wstacks = numpy.zeros(shape=(int(w_planes),2*grid_size,2*grid_size),dtype=numpy.complex128)\n",
    "    image = numpy.zeros(shape=(2*grid_size,2*grid_size),dtype=numpy.complex128)\n",
    "    \n",
    "    \n",
    "    # 3D Convolution onto the correct grid points.\n",
    "    for j,efield in enumerate(efieldf):\n",
    "        \n",
    "        # Locations\n",
    "        u = locations[j,0]\n",
    "        v = locations[j,1]\n",
    "        w = locations[j,2]\n",
    "    \n",
    "        # Get grid co-ordinates\n",
    "        ulo = 2*u + grid_size\n",
    "        vlo = 2*v + grid_size\n",
    "        u_loc = int(ulo) # No anti-alising.\n",
    "        v_loc = int(vlo) \n",
    "        \n",
    "        # W Co-ordinates \n",
    "        wp = int((w + abs(min_w))//dw)\n",
    "        #print(wp)\n",
    "        \n",
    "        \n",
    "        # Oversampling\n",
    "        u_os = (u - numpy.ceil(u/du)*du)\n",
    "        v_os = (v - numpy.ceil(v/du)*du)\n",
    "        w_os = (w - numpy.ceil(w/dw)*dw)\n",
    "        \n",
    "        ovu = int(numpy.floor(abs(u_os)/du * aa_over))\n",
    "        ovv = int(numpy.floor(abs(v_os)/du * aa_over))\n",
    "        ovw = int(numpy.floor(abs(w_os)/dw * aa_over))\n",
    "        \n",
    "        for uc in numpy.arange(aa_support):\n",
    "            u_locc = int(u_loc - aa_support//2 + uc)\n",
    "            gcf_u = gcf[ovu,uc]\n",
    "            for vc in numpy.arange(aa_support):\n",
    "                v_locc = int(v_loc - aa_support//2 + vc)\n",
    "                gcf_v = gcf[ovv,vc]\n",
    "                for wc in numpy.arange(aa_support_w):\n",
    "                    w_locc = int(wp - aa_support_w//2 + wc)\n",
    "                    gcfw = gcf_w[ovw,wc]\n",
    "                    \n",
    "                    #Place contribution onto correct grid\n",
    "                    wstacks[w_locc,v_locc,u_locc] += efield * gcf_u * gcf_v * gcfw\n",
    "    \n",
    "    # Now to W-Stack\n",
    "    accum_image = numpy.zeros(shape=(2*grid_size,2*grid_size),dtype=numpy.complex128)\n",
    "    image_stack = numpy.fft.ifft2(numpy.fft.ifftshift(wstacks,axes=(1,2)))\n",
    "    print(image_stack.shape)\n",
    "    for i in numpy.arange(0,w_planes):         \n",
    "        accum_image += image_stack[int(i),:,:]\n",
    "        accum_image /= fresnel_pattern\n",
    "    \n",
    "    # Now Grid Correct a la Sze-Tan\n",
    "    \n",
    "    #gridcor = grid_correction(theta, lam, aa, aa_w)\n",
    "    #plt.imshow(gridcor)\n",
    "    #plt.colorbar()\n",
    "    #plt.show()\n",
    "    return numpy.fft.fftshift(accum_image)#/gridcor\n",
    "                    \n",
    "im_sze = epic_wstack(theta,lam,ee_gaussian_s,locations_uvw.copy(),aa_x0)    \n",
    "im_szea = im_sze * im_sze.conj()\n",
    "im_szeae = im_szea[32:-32,32:-32]\n",
    "plot_celestial_sphere(normalise_image(im_szeae),title='Sze Tan W-Stacker',norm=LogNorm(vmin=0.0001, vmax=10),cmap=plt.get_cmap('jet'))\n",
    "plot_celestial_sphere(imcg_n,title='Direct Fourier Transform',norm=LogNorm(vmin=0.0001, vmax=10),cmap=plt.get_cmap('jet'))\n",
    "plot_celestial_sphere(numpy.abs(imcg_n-im_szeae),title='Diff',norm=LogNorm(vmin=0.0001, vmax=10),cmap=plt.get_cmap('jet'))\n",
    "plot_celestial_sphere(gc_im_n,title='W-Stacked Image',norm=LogNorm(vmin=0.0001, vmax=10),cmap=plt.get_cmap('jet'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Work in progress / I have no idea why this doesn't work"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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