numpy_practice85-90.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "85.创建一个满足 Z[i,j] == Z[j,i]的二维数组子类"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  9  1 13  9]\n",
      " [ 9  2 14  9 10]\n",
      " [ 1 14  4  9  9]\n",
      " [13  9  9  4  9]\n",
      " [ 9 10  9  9  9]]\n",
      "[[ 0  9  1 13  9]\n",
      " [ 9  2 14  9 10]\n",
      " [ 1 14  4 42  9]\n",
      " [13  9 42  4  9]\n",
      " [ 9 10  9  9  9]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "class Symetric(np.ndarray):\n",
    "    def __setitem__(self,index,value):\n",
    "        i ,j=index\n",
    "        super(Symetric,self).__setitem__((i,j),value)\n",
    "        super(Symetric,self).__setitem__((j,i),value)\n",
    "def symetric(Z):\n",
    "    return np.asarray(Z+Z.T-np.diag(Z.diagonal())).view(Symetric)\n",
    "S=symetric(np.random.randint(0,10,(5,5)))\n",
    "print(S)\n",
    "S[2,3]=42\n",
    "print(S)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "86. 考虑p个 nxn 矩阵和一组形状为(n,1)的向量，如何直接计算p个矩阵的乘积(n,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[[1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  ...\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]]\n",
      "\n",
      " [[1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  ...\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]]\n",
      "\n",
      " [[1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  ...\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]]\n",
      "\n",
      " ...\n",
      "\n",
      " [[1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  ...\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]]\n",
      "\n",
      " [[1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  ...\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]]\n",
      "\n",
      " [[1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  ...\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]\n",
      "  [1. 1. 1. ... 1. 1. 1.]]]\n",
      "[[[1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]]\n",
      "\n",
      " [[1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]]\n",
      "\n",
      " [[1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]]\n",
      "\n",
      " [[1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]]\n",
      "\n",
      " [[1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]]\n",
      "\n",
      " [[1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]]\n",
      "\n",
      " [[1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]]\n",
      "\n",
      " [[1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]]\n",
      "\n",
      " [[1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]]\n",
      "\n",
      " [[1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]\n",
      "  [1.]]]\n",
      "[[200.]\n",
      " [200.]\n",
      " [200.]\n",
      " [200.]\n",
      " [200.]\n",
      " [200.]\n",
      " [200.]\n",
      " [200.]\n",
      " [200.]\n",
      " [200.]\n",
      " [200.]\n",
      " [200.]\n",
      " [200.]\n",
      " [200.]\n",
      " [200.]\n",
      " [200.]\n",
      " [200.]\n",
      " [200.]\n",
      " [200.]\n",
      " [200.]]\n"
     ]
    }
   ],
   "source": [
    "p,n=10,20\n",
    "M=np.ones((p,n,n))\n",
    "print(M)\n",
    "V=np.ones((p,n,1))\n",
    "print(V)\n",
    "S=np.tensordot(M,V,axes=[[0,2],[0,1]])\n",
    "print(S)"
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "对于一个16x16的数组，如何得到一个区域的和(区域大小为4x4)?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[16. 16. 16. 16.]\n",
      " [16. 16. 16. 16.]\n",
      " [16. 16. 16. 16.]\n",
      " [16. 16. 16. 16.]]\n"
     ]
    }
   ],
   "source": [
    "Z=np.ones((16,16))\n",
    "k=4\n",
    "S = np.add.reduceat(np.add.reduceat(Z, np.arange(0, Z.shape[0], k), axis=0), np.arange(0, Z.shape[1], k), axis=1)\n",
    "print(S)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "88. 如何利用numpy数组实现Game of Life?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 0 ... 0 0 0]\n",
      " [0 0 0 ... 0 0 0]\n",
      " [0 0 0 ... 0 0 0]\n",
      " ...\n",
      " [0 0 0 ... 0 0 0]\n",
      " [0 0 0 ... 0 0 0]\n",
      " [0 0 0 ... 0 0 0]]\n"
     ]
    }
   ],
   "source": [
    "def iterate(Z):\n",
    "    # Count neighbours\n",
    "    N = (Z[0:-2,0:-2] + Z[0:-2,1:-1] + Z[0:-2,2:] +\n",
    "         Z[1:-1,0:-2]                + Z[1:-1,2:] +\n",
    "         Z[2:  ,0:-2] + Z[2:  ,1:-1] + Z[2:  ,2:])\n",
    " \n",
    "    # Apply rules\n",
    "    birth = (N==3) & (Z[1:-1,1:-1]==0)\n",
    "    survive = ((N==2) | (N==3)) & (Z[1:-1,1:-1]==1)\n",
    "    Z[...] = 0\n",
    "    Z[1:-1,1:-1][birth | survive] = 1\n",
    "    return Z\n",
    " \n",
    "Z = np.random.randint(0,2,(50,50))\n",
    "for i in range(100): Z = iterate(Z)\n",
    "print(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "89. 如何找到一个数组的第n个最大值?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[9995 9996 9997 9998 9999]\n"
     ]
    }
   ],
   "source": [
    "Z = np.arange(10000)\n",
    "np.random.shuffle(Z)\n",
    "n = 5\n",
    "# Slow\n",
    "print (Z[np.argsort(Z)[-n:]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[9999 9998]\n"
     ]
    }
   ],
   "source": [
    "Z = np.arange(10000)\n",
    "np.random.shuffle(Z)\n",
    "n = 2\n",
    "print (Z[np.argpartition(-Z,n)[:n]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "90. 给定任意个数向量，创建笛卡尔积(每一个元素的每一种组合)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 4 6]\n",
      " [1 4 7]\n",
      " [1 5 6]\n",
      " [1 5 7]\n",
      " [2 4 6]\n",
      " [2 4 7]\n",
      " [2 5 6]\n",
      " [2 5 7]\n",
      " [3 4 6]\n",
      " [3 4 7]\n",
      " [3 5 6]\n",
      " [3 5 7]]\n"
     ]
    }
   ],
   "source": [
    "def cartesian(arrays):\n",
    "    arrays = [np.asarray(a) for a in arrays]\n",
    "    shape = (len(x) for x in arrays)\n",
    " \n",
    "    ix = np.indices(shape, dtype=int)\n",
    "    ix = ix.reshape(len(arrays), -1).T\n",
    " \n",
    "    for n, arr in enumerate(arrays):\n",
    "        ix[:, n] = arrays[n][ix[:, n]]\n",
    " \n",
    "    return ix\n",
    " \n",
    "print (cartesian(([1, 2, 3], [4, 5], [6, 7])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}