construction_.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Defining the constants\n",
    "P = 6\n",
    "N = 2**P\n",
    "U0 = 0.1\n",
    "h = 1/N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Construction of \\hat{T}_h\n",
    "hat_Th = np.zeros((N+1,N+1), dtype=np.float32)\n",
    "hat_Th[0,0] = h**2\n",
    "hat_Th[-1,-1] = h**2\n",
    "Th = 4*np.eye(N-1)-np.eye(N-1, k=-1)-np.eye(N-1, k=1)\n",
    "\n",
    "hat_Th[1:-1,1:-1] = Th\n",
    "\n",
    "hatI = np.eye(N+1, dtype=np.int8)\n",
    "hatI[0,0] = 0\n",
    "hatI[-1,-1]=0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Ah = np.zeros((N+1)**2) #Initialise array of zeroes to fill\n",
    "\"\"\"\n",
    "If we make this complexer we can tactically use different array-types to make this more memory efficient\n",
    "\"\"\"\n",
    "\n",
    "main_diag = np.eye((N+1), k=0, dtype=np.int8)\n",
    "main_diag[0,0], main_diag[-1,-1] = 0, 0\n",
    "\n",
    "Ah_ = np.kron(main_diag, hat_Th)\n",
    "np.save(\"Ah_\"+str(N+1),Ah_)\n",
    "main_diag = None\n",
    "Ah_ = None\n",
    "\n",
    "off_diag = np.eye((N+1), k=1) + np.eye((N+1), k=-1, dtype=np.int8)\n",
    "off_diag[0,1], off_diag[1,0], off_diag[-1,-2], off_diag[-2,-1] = 0, 0, 0, 0\n",
    "\n",
    "tmp = - np.kron(off_diag, hatI)\n",
    "off_diag = None\n",
    "Ah_ = np.load(\"Ah_\"+str(N+1)+\".npy\")\n",
    "Ah_ += tmp\n",
    "\n",
    "tmp = None\n",
    "\n",
    "Ah_[0:N+1,0:N+1], Ah_[-(N+1):,-(N+1):] = h**2 * np.eye(N+1), h**2 * np.eye(N+1)\n",
    "\n",
    "Ah = Ah_/(h**2)\n",
    "Ah_ = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x238effea430>"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(Ah)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Creating the forcing function\n",
    "x, y = np.linspace(0,1,N+1), np.linspace(0,1,N+1)\n",
    "X, Y = np.meshgrid(x, y)\n",
    "\n",
    "arrayF_i = (X**2 +Y**2)*np.sin(X*Y) #This array has the wrong ordering with (0,0) top left\n",
    "arrayF_b = U0 * np.ones(arrayF_i.shape)\n",
    "arrayF_b[1:-1,1:-1] = arrayF_i[1:-1,1:-1]\n",
    "arrayF = arrayF_b\n",
    "vecF = arrayF.flatten()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.1 0.1 0.1 ... 0.1 0.1 0.1]\n"
     ]
    }
   ],
   "source": [
    "print(vecF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x2388889e5e0>"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(arrayF_b)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Cholesky decomposition of Ah\n",
    "C = np.linalg.cholesky(Ah)\n",
    "L = C\n",
    "U = C.T\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [],
   "source": [
    "u_prime\t= np.linalg.solve(U, vecF)\n",
    "u\t= np.linalg.solve(L, u_prime)\n",
    "test\t= np.linalg.solve(Ah, vecF)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "array_u = u.reshape((N+1,N+1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x23888972880>"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u_ex = np.sin(X*Y)\n",
    "u_ex_b = U0+0*u_ex\n",
    "u_ex_b[1:-1,1:-1] = u_ex[1:-1,1:-1]\n",
    "vec_u_ex = u_ex_b.flatten()\n",
    "plt.imshow(u_ex)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x2388cdce580>"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(test.reshape((N+1,N+1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x2388ce38370>"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(array_u)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x2388ced2790>"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(u_ex_b)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x2388cf68160>"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "error = np.abs(array_u-u_ex_b)\n",
    "plt.imshow(error)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x238eedefe50>"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "solution = np.linalg.solve(Ah, vecF).reshape((N+1,N+1))[::-1,:]\n",
    "plt.imshow(solution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [],
   "source": [
    "solF = Ah.dot(vec_u_ex)\n",
    "arr_solF = solF.reshape((N+1,N+1))[::-1,:]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.colorbar.Colorbar at 0x2388ced0c70>"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(arr_solF)\n",
    "plt.colorbar()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [],
   "source": [
    "Ah_inv = np.linalg.inv(Ah)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x2388d112a00>"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(Ah_inv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x238959d3070>"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "test = Ah_inv.dot(vecF)\n",
    "test = test.reshape((N+1,N+1))[::-1,:]\n",
    "plt.imshow(test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "2ea1d2d7f4049888098689028c10f21718f9dd1594b80595dd2baeb3be943db3"
  },
  "kernelspec": {
   "display_name": "Python 3.9.5 64-bit",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.0"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}