{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x:\n",
      " [[ 1  0  0  0]\n",
      " [ 0 -1  0  0]\n",
      " [ 0  0  3  0]\n",
      " [ 0  0  0  1]\n",
      " [ 0  0  2  0]]\n",
      "y:\n",
      " [[4 5]\n",
      " [3 4]]\n",
      "conv:\n",
      " [[ 4  5  0  0  0]\n",
      " [ 3  0 -5  0  0]\n",
      " [ 0 -3  8 15  0]\n",
      " [ 0  0  9 16  5]\n",
      " [ 0  0  8 13  4]\n",
      " [ 0  0  6  8  0]]\n",
      "fft for my method:\n",
      " [[ 4  5  0  0  0]\n",
      " [ 3  0 -5  0  0]\n",
      " [ 0 -3  7 15  0]\n",
      " [ 0  0  9 16  5]\n",
      " [ 0  0  8 13  4]\n",
      " [ 0  0  6  8  0]]\n",
      "fft:\n",
      " [[ 3  5  0  0  0]\n",
      " [ 2  0 -4  0  0]\n",
      " [ 0 -2  7 14  0]\n",
      " [ 0  0  9 16  5]\n",
      " [ 0  0  8 13  3]\n",
      " [ 0  0  6  8  0]]\n",
      "openpiv:\n",
      " [[ 4  5  0  0  0]\n",
      " [ 3  0 -5  0  0]\n",
      " [ 0 -3  7 15  0]\n",
      " [ 0  0  9 16  5]\n",
      " [ 0  0  8 13  4]\n",
      " [ 0  0  6  8  0]]\n",
      "circular: \n",
      "  [[ 5  4  0  0]\n",
      " [ 3 -2 -3  0]\n",
      " [-2  0 17  6]\n",
      " [ 0  2 17 11]\n",
      " [ 0  2 14  8]\n",
      " [-1  1 10  3]]\n"
     ]
    }
   ],
   "source": [
    "from scipy import signal\n",
    "\n",
    "from scipy import linalg\n",
    "import numpy as np\n",
    "from openpiv.pyprocess import fft_correlate\n",
    "\n",
    "x = [[1 , 0 , 0 , 0] , [0 , -1 , 0 , 0] , [0 , 0 , 3 , 0] , [0 , 0 , 0 , 1],[0,0,2,0]]\n",
    "x = np.array(x)\n",
    "y = [[4 , 5] , [3 , 4]]\n",
    "y = np.array(y)\n",
    "\n",
    "# x = np.random.rand(2,3)\n",
    "# y = np.random.rand(4,6)\n",
    "\n",
    "print(\"x:\\n\", x)\n",
    "print(\"y:\\n\", y)\n",
    "\n",
    "print (\"conv:\\n\" ,  signal.convolve2d(x , y , 'full'))\n",
    "\n",
    "s1 = np.array(x.shape)\n",
    "s2 = np.array(y.shape)\n",
    "\n",
    "size = s1 + s2 - 1\n",
    "\n",
    "\n",
    "fsize = 2 ** np.ceil(np.log2(size)).astype(int)\n",
    "fslice = tuple([slice(0, int(sz)) for sz in size])\n",
    "\n",
    "\n",
    "new_x = np.fft.rfft2(x , fsize)\n",
    "\n",
    "\n",
    "new_y = np.fft.rfft2(y , fsize)\n",
    "result = np.fft.irfft2(new_x*new_y)[fslice].copy()\n",
    "\n",
    "print(\"fft for my method:\\n\" , np.array(result.real, np.int32))\n",
    "\n",
    "print(\"fft:\\n\" , np.array(signal.fftconvolve(x ,y,'full'), np.int32 ))\n",
    "\n",
    "print(\"openpiv:\\n\", fft_correlate(x,y[::-1,::-1]).astype(np.int32))\n",
    "\n",
    "print(\"circular: \\n \" ,np.array(np.fft.irfft2(np.fft.rfft2(x,size)*np.fft.rfft2(y,size))).astype(np.int32))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0.],\n",
       "       [0., 1., 1., 0.],\n",
       "       [0., 1., 1., 0.],\n",
       "       [0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = np.ones((2,2))\n",
    "np.pad(x,np.round(np.array(x.shape)/2).astype(np.int))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2., 2.])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.round(np.array(x.shape)/2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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