第六课：numpy.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. 向量和矩阵操作"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**创建矩阵**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0, 1, 2],\n",
       "       [3, 4, 5]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.arange(6).reshape(2,3)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[ 0,  1,  2,  3],\n",
       "        [ 4,  5,  6,  7],\n",
       "        [ 8,  9, 10, 11]],\n",
       "\n",
       "       [[12, 13, 14, 15],\n",
       "        [16, 17, 18, 19],\n",
       "        [20, 21, 22, 23]]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 可以不指定某一个维度的值，给-1，系统自动计算维度\n",
    "b = np.arange(24).reshape(2,-1,4)\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 3, 4)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "cannot reshape array of size 6 into shape (4,newaxis)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-6-01e57720cecc>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m#  如果维度不匹配会报错\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[0mc\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m6\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m: cannot reshape array of size 6 into shape (4,newaxis)"
     ]
    }
   ],
   "source": [
    "#  如果维度不匹配会报错\n",
    "c = np.arange(6).reshape(4,-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 0矩阵\n",
    "np.zeros( (3,4) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.],\n",
       "       [1., 1., 1., 1.]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 1矩阵\n",
    "np.ones( (3,4) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 0., 1.]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 单位矩阵\n",
    "np.eye(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**矩阵运算**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([20, 29, 38, 47])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = np.array( [20,30,40,50] )\n",
    "b = np.arange( 4 )\n",
    "a-b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array( [[1,1],\n",
    "               [0,1]] )\n",
    "B = np.array( [[2,0],\n",
    "               [3,4]] )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 0],\n",
       "       [0, 4]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# element-wise乘法\n",
    "A * B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5, 4],\n",
       "       [3, 4]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 矩阵乘法\n",
    "A.dot(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 3],\n",
       "       [0, 4]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 转置\n",
    "B.transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.5  ,  0.   ],\n",
       "       [-0.375,  0.25 ]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.inv(B)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**统计**\n",
    "\n",
    "https://docs.scipy.org/doc/numpy/reference/arrays.ndarray.html\n",
    "\n",
    "\n",
    "ndarray.max([axis, out, keepdims, initial, …])\tReturn the maximum along a given axis.<br>\n",
    "ndarray.argmax([axis, out])\tReturn indices of the maximum values along the given axis.<br>\n",
    "ndarray.min([axis, out, keepdims, initial, …])\tReturn the minimum along a given axis.<br>\n",
    "ndarray.argmin([axis, out])\tReturn indices of the minimum values along the given axis of a.<br>\n",
    "ndarray.ptp([axis, out, keepdims])\tPeak to peak (maximum - minimum) value along a given axis.<br>\n",
    "ndarray.clip([min, max, out])\tReturn an array whose values are limited to [min, max].<br>\n",
    "ndarray.conj()\tComplex-conjugate all elements.<br>\n",
    "ndarray.round([decimals, out])\tReturn a with each element rounded to the given number of decimals.<br>\n",
    "ndarray.trace([offset, axis1, axis2, dtype, out])\tReturn the sum along diagonals of the array.<br>\n",
    "ndarray.sum([axis, dtype, out, keepdims, …])\tReturn the sum of the array elements over the given axis.<br>\n",
    "ndarray.cumsum([axis, dtype, out])\tReturn the cumulative sum of the elements along the given axis.<br>\n",
    "ndarray.mean([axis, dtype, out, keepdims])\tReturns the average of the array elements along given axis.<br>\n",
    "ndarray.var([axis, dtype, out, ddof, keepdims])\tReturns the variance of the array elements, along given axis.<br>\n",
    "ndarray.std([axis, dtype, out, ddof, keepdims])\tReturns the standard deviation of the array elements along given axis.<br>\n",
    "ndarray.prod([axis, dtype, out, keepdims, …])\tReturn the product of the array elements over the given axis<br>\n",
    "ndarray.cumprod([axis, dtype, out])\tReturn the cumulative product of the elements along the given axis.<br>\n",
    "ndarray.all([axis, out, keepdims])\tReturns True if all elements evaluate to True.<br>\n",
    "ndarray.any([axis, out, keepdims])\tReturns True if any of the elements of a evaluate to True.<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([20, 30, 40, 50])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 20,  50,  90, 140])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.cumsum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**拼接/分割**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([20, 30, 40, 50, 20, 30, 40, 50])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.concatenate([a,a], axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "ename": "AxisError",
     "evalue": "axis 1 is out of bounds for array of dimension 1",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAxisError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-20-d0a33c1acf4d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mconcatenate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maxis\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mAxisError\u001b[0m: axis 1 is out of bounds for array of dimension 1"
     ]
    }
   ],
   "source": [
    "np.concatenate([a,a], axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[20, 30, 40, 50]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a2 = np.expand_dims(a,axis=0)\n",
    "a2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[20, 30, 40, 50],\n",
       "       [20, 30, 40, 50]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.vstack([a2,a2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([20, 30]), array([40, 50])]"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.split(a,2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**广播**\n",
    "\n",
    "\n",
    "首先用下面的图直观感受一下：<br>\n",
    "![](http://www.astroml.org/_images/fig_broadcast_visual_1.png)\n",
    "\n",
    "规则总结：某一个维度是1，其他维度相同，数据复制（广播）"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 官方文档\n",
    "https://docs.scipy.org/doc/numpy/user/quickstart.html"
   ]
  }
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