第七课：scipy.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Basic functions<br>\n",
    "Special functions (scipy.special) 物理学数值计算<br>\n",
    "Integration (scipy.integrate)<br>\n",
    "Optimization (scipy.optimize)<br>\n",
    "Interpolation (scipy.interpolate)<br>\n",
    "Fourier Transforms (scipy.fftpack)<br>\n",
    "Signal Processing (scipy.signal)<br>\n",
    "Linear Algebra (scipy.linalg)<br>\n",
    "Sparse Eigenvalue Problems with ARPACK<br>\n",
    "Compressed Sparse Graph Routines (scipy.sparse.csgraph)<br>\n",
    "Spatial data structures and algorithms (scipy.spatial)<br>\n",
    "Statistics (scipy.stats)<br>\n",
    "Multidimensional image processing (scipy.ndimage)<br>\n",
    "File IO (scipy.io)<br>\n",
    "https://docs.scipy.org/doc/scipy/reference/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. 矩阵操作"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import linalg "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([[1,2,3],[4,5,6],[7,8,8]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.66666667,  2.66666667, -1.        ],\n",
       "       [ 3.33333333, -4.33333333,  2.        ],\n",
       "       [-1.        ,  2.        , -1.        ]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linalg.inv(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.00000000e+00,  8.88178420e-16,  2.22044605e-16],\n",
       "       [ 0.00000000e+00,  1.00000000e+00, -4.44089210e-16],\n",
       "       [ 0.00000000e+00,  0.00000000e+00,  1.00000000e+00]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.dot(linalg.inv(A))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'np' 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-1-7672cf7f7005>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mA\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m5\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m6\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m7\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m8\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[0m\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdet\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\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 'np' is not defined"
     ]
    }
   ],
   "source": [
    "linalg.det(A) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 8]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0. 1. 0.]\n",
      " [0. 0. 1.]\n",
      " [1. 0. 0.]]\n",
      "[[1.         0.         0.        ]\n",
      " [0.14285714 1.         0.        ]\n",
      " [0.57142857 0.5        1.        ]]\n",
      "[[7.         8.         8.        ]\n",
      " [0.         0.85714286 1.85714286]\n",
      " [0.         0.         0.5       ]]\n"
     ]
    }
   ],
   "source": [
    "P, L, U = linalg.lu(A) \n",
    "print(P) \n",
    "print(L) \n",
    "print(U) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. 稀疏矩阵\n",
    "https://docs.scipy.org/doc/scipy/reference/sparse.html#module-scipy.sparse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 0, 0, 0],\n",
       "       [0, 0, 0, 0],\n",
       "       [0, 0, 0, 0]], dtype=int8)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.sparse import csc_matrix\n",
    "csc_matrix((3, 4), dtype=np.int8).toarray()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 4],\n",
       "       [0, 0, 5],\n",
       "       [2, 3, 6]], dtype=int64)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row = np.array([0, 2, 2, 0, 1, 2])\n",
    "col = np.array([0, 0, 1, 2, 2, 2])\n",
    "data = np.array([1, 2, 3, 4, 5, 6])\n",
    "csc_matrix((data, (row, col)), shape=(3, 3)).toarray()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 4],\n",
       "       [0, 0, 5],\n",
       "       [2, 3, 6]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "indptr = np.array([0, 2, 3, 6]) # indices中第几个数再第几行，区间左开右闭\n",
    "indices = np.array([0, 2, 2, 0, 1, 2])\n",
    "data = np.array([1, 2, 3, 4, 5, 6])\n",
    "# indptr:0-2 indices:0,2 data:1,2\n",
    "# indptr:2-3 indices:2 data:3\n",
    "# indptr:3-6 indices:0,1,2 data:4,5,6\n",
    "csc_matrix((data, indices, indptr), shape=(3, 3)).toarray()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. 统计学"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**概率分布**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "n1 = norm(0,1)\n",
    "n2 = norm(2,0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11199c080>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(n1.rvs(1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x111a36cf8>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.kdeplot(n2.rvs(1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n2.cdf(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**假设检验**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "np.random.seed(7654567)  # fix seed to get the same result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "rvs = stats.norm.rvs(loc=5, scale=10, size=(50,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "单样本检验"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_1sampResult(statistic=array([-0.68014479, -0.04323899]), pvalue=array([0.49961383, 0.96568674]))"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_1samp(rvs,5.0) # p>0.05，不拒绝"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_1sampResult(statistic=array([2.77025808, 4.11038784]), pvalue=array([0.00789095, 0.00014999]))"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_1samp(rvs,0.0) # p<0.05，拒绝"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(12345678)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "双独立样本：相同方差"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=0.26833823296238857, pvalue=0.788494433695651)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rvs1 = stats.norm.rvs(loc=5,scale=10,size=500)\n",
    "rvs2 = stats.norm.rvs(loc=5,scale=10,size=500)\n",
    "stats.ttest_ind(rvs1,rvs2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "双独立样本：不同方差"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=-0.46580283298287956, pvalue=0.6414964624656874)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rvs3 = stats.norm.rvs(loc=5, scale=20, size=500)\n",
    "stats.ttest_ind(rvs1, rvs3, equal_var = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 官方文档\n",
    "https://docs.scipy.org/doc/scipy/reference/index.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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