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    "# Scipy\n",
    "\n",
    "## Scipy特征\n",
    "\n",
    "1. 内置了图像处理， 优化，统计等等相关问题的子模块\n",
    "2. scipy 是Python科学计算环境的核心。 它被设计为利用 numpy 数组进行高效的运行。从这个角度来讲，scipy和numpy是密不可分的。\n",
    "\n",
    "## 文件操作io\n",
    "\n",
    "1. 导包：`from scipy import io as spio`\n",
    "2. 保存mat格式文件`spio.savemat(\"test.mat\", {'a':a})`\n",
    "3. 加载mat文件`data = spio.loadmat(\"test.mat\")`\n",
    "  访问值：data[‘a’]–>相当于map\n",
    "4. 读取图片文件\n",
    "    导包：`from scipy import misc`\n",
    "    读取：`data = misc.imread(\"123.png\")`\n",
    "\n",
    "[注1]：与`matplotlib中plt.imread('fname.png')`类似\n",
    "\n",
    "[注2]：执行misc.imread时可能提醒不存在这个模块，那就安装pillow的包\n",
    "\n",
    "## 线性代数操作linalg\n",
    "\n",
    "1. 求行列式det`res = linalg.det(a)`\n",
    "2. 求逆矩阵inv`res = linalg.inv(a)`\n",
    "    若是矩阵不可逆，则会抛异常LinAlgError: singular matrix\n",
    "3. 奇异值分解svd`u,s,v = linalg.svd(a)`\n",
    "\n",
    "[注1]：s为a的特征值（一维），降序排列，\n",
    "\n",
    "[注2]：a = u*s*v’（需要将s转换一下才能相乘）\n",
    "\n",
    "```\n",
    "t = np.diag(s)\n",
    "print u.dot(t).dot(v)\n",
    "```\n",
    "\n",
    "## 梯度下降优化算法\n",
    "\n",
    "1. fmin_bfgs\n",
    "```\n",
    "def f(x):\n",
    "    return x**2-2*x\n",
    "initial_x = 0\n",
    "optimize.fmin_bfgs(f,initial_x)\n",
    "```\n",
    "[注]：initial_x为初始点（此方法可能会得到局部最小值）\n",
    "\n",
    "2. fmin()、fmin_cg等等方法\n",
    "\n",
    "## 拟合（最小二乘法）\n",
    "\n",
    "1. `curve_fit`\n",
    "```\n",
    "#产生数据\n",
    "def f(x):\n",
    "    return x**2 + 10*np.sin(x)\n",
    "xdata = np.linspace(-10, 10, num=20)\n",
    "ydata = f(xdata)+np.random.randn(xdata.size)\n",
    "plt.scatter(xdata, ydata, linewidths=3.0, \n",
    "           edgecolors=\"red\")\n",
    "#plt.show()\n",
    "#拟合\n",
    "def f2(x,a,b):\n",
    "    return a*x**2 + b*np.sin(x)\n",
    "guess = [2,2]\n",
    "params, params_covariance = optimize.curve_fit(f2, xdata, ydata, guess)\n",
    "#画出拟合的曲线\n",
    "x1 = np.linspace(-10,10,256)\n",
    "y1 = f2(x1,params[0],params[1])\n",
    "plt.plot(x1,y1)\n",
    "plt.show()\n",
    "```\n",
    "\n",
    "## 统计检验\n",
    "\n",
    "1. T-检验stats.ttest_ind\n",
    "    ```\n",
    "    a = np.random.normal(0, 1, size=10)\n",
    "    b = np.random.normal(1, 1, size=10)\n",
    "    print stats.ttest_ind(a, b)\n",
    "    ```\n",
    "    输出：`(-2.6694785119868358, 0.015631342180817954)`\n",
    "    后面的是概率p: 两个过程相同的概率。如果其值接近1，那么两个过程几乎可以确定是相同的，如果其值接近0，那么它们很可能拥有不同的均值。\n",
    "\n",
    "## 插值\n",
    "\n",
    "1. 导入包：from scipy.interpolate import interp1d\n",
    "```\n",
    "#产生一些数据\n",
    "x = np.linspace(0, 1, 10)\n",
    "y = np.sin(2 * np.pi * x)\n",
    "computed_time = np.linspace(0, 1, 50)\n",
    "#线性插值\n",
    "linear_interp = interp1d(x, y)\n",
    "linear_results = linear_interp(computed_time)\n",
    "#三次方插值\n",
    "cubic_interp = interp1d(x, y, kind='cubic')\n",
    "cubic_results = cubic_interp(computed_time)\n",
    "#作图\n",
    "plt.plot(x, y, 'o', ms=6, label='y')\n",
    "plt.plot(computed_time, linear_results, label='linear interp')\n",
    "plt.plot(computed_time, cubic_results, label='cubic interp')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "```\n",
    "\n",
    "## 求解非线性方程组\n",
    "\n",
    "1. optimize中的fsolve\n",
    "```\n",
    "from scipy.optimize import fsolve\n",
    "def func(x):\n",
    "    x0,x1,x2 = x.tolist()\n",
    "    return [5*x1-25,5*x0*x0-x1*x2,x2*x0-27]\n",
    "initial_x = [1,1,1]\n",
    "result = fsolve(func, initial_x)\n",
    "print result\n",
    "```"
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