From 73cc328c815f30c8fbe1d0c1354b827b797568f3 Mon Sep 17 00:00:00 2001
From: estomm <yinkanglong@163.com>
Date: Fri, 25 Sep 2020 22:01:28 +0800
Subject: [PATCH] scipy

---
 Python/numpy/19多项式.md        |  54 +++++++++++++++++
 Python/numpy/1概述.md           |   2 +
 Python/readme.md                |   6 ++
 Python/scipy/0introduction.md   |  35 +++++++++++
 Python/scipy/10spatial.md       |   0
 Python/scipy/11stats.md         |   4 ++
 Python/scipy/12ndimage.md       |  92 +++++++++++++++++++++++++++++
 Python/scipy/13io.md            |  22 +++++++
 Python/scipy/1basicfunction.md  |  10 ++++
 Python/scipy/2special.md        |   6 ++
 Python/scipy/3integrate.md      | 101 ++++++++++++++++++++++++++++++++
 Python/scipy/4optimize.md       |  12 ++++
 Python/scipy/5interpolate.md    |  28 +++++++++
 Python/scipy/6fft.md            |  27 +++++++++
 Python/scipy/7signal.md         |   0
 Python/scipy/8linalg.md         |  13 ++++
 Python/scipy/9sparse.csgraph.md |   0
 17 files changed, 412 insertions(+)
 create mode 100644 Python/numpy/19多项式.md
 create mode 100644 Python/readme.md
 create mode 100644 Python/scipy/0introduction.md
 create mode 100644 Python/scipy/10spatial.md
 create mode 100644 Python/scipy/11stats.md
 create mode 100644 Python/scipy/12ndimage.md
 create mode 100644 Python/scipy/13io.md
 create mode 100644 Python/scipy/1basicfunction.md
 create mode 100644 Python/scipy/2special.md
 create mode 100644 Python/scipy/3integrate.md
 create mode 100644 Python/scipy/4optimize.md
 create mode 100644 Python/scipy/5interpolate.md
 create mode 100644 Python/scipy/6fft.md
 create mode 100644 Python/scipy/7signal.md
 create mode 100644 Python/scipy/8linalg.md
 create mode 100644 Python/scipy/9sparse.csgraph.md

diff --git a/Python/numpy/19多项式.md b/Python/numpy/19多项式.md
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+
+## basic API 
+
+| poly1d\(c\_or\_r\[, r, variable\]\) | A one\-dimensional polynomial class\.                                    |
+|-------------------------------------|--------------------------------------------------------------------------|
+| polyval\(p, x\)                     | Evaluate a polynomial at specific values\.                               |
+| poly\(seq\_of\_zeros\)              | Find the coefficients of a polynomial with the given sequence of roots\. |
+| roots\(p\)                          | Return the roots of a polynomial with coefficients given in p\.          |
+
+## filter
+
+| polyfit\(x, y, deg\[, rcond, full, w, cov\]\) | Least squares polynomial fit\. |
+|-----------------------------------------------|--------------------------------|
+
+
+## calculus
+
+| polyder\(p\[, m\]\)    | Return the derivative of the specified order of a polynomial\.     |
+|------------------------|--------------------------------------------------------------------|
+| polyint\(p\[, m, k\]\) | Return an antiderivative \(indefinite integral\) of a polynomial\. |
+
+## Arithmetic
+
+| polyadd\(a1, a2\) | Find the sum of two polynomials\.                           |
+|-------------------|-------------------------------------------------------------|
+| polydiv\(u, v\)   | Returns the quotient and remainder of polynomial division\. |
+| polymul\(a1, a2\) | Find the product of two polynomials\.                       |
+| polysub\(a1, a2\) | Difference \(subtraction\) of two polynomials\.             |
+
+
+## 创建多项式
+
+* f = np.poly1d(a)
+## 求微分和积分
+* f.deriv()
+* f.integ()
+
+```py
+from numpy import poly1d
+p = poly1d([3,4,5])
+print(p)
+   2
+3 x + 4 x + 5
+print(p*p)
+   4      3      2
+9 x + 24 x + 46 x + 40 x + 25
+print(p.integ(k=6))
+   3     2
+1 x + 2 x + 5 x + 6
+print(p.deriv())
+6 x + 4
+p([4, 5])
+array([ 69, 100])
+```
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diff --git a/Python/numpy/1概述.md b/Python/numpy/1概述.md
index f5c7d6fd..6003de1f 100644
--- a/Python/numpy/1概述.md
+++ b/Python/numpy/1概述.md
@@ -1,4 +1,6 @@
 # 量的定义
+> 定义n维数组，并且在数组上进行简单的变换与操作。
+
 
 ## 名称
 
diff --git a/Python/readme.md b/Python/readme.md
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+## numpy
+
+## scipy
+
+> 内容涉及大量的数学知识，不应该代码驱动学习，应该在学习或者使用相关的数学知识的时候，进行代码实现。
+
diff --git a/Python/scipy/0introduction.md b/Python/scipy/0introduction.md
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+## 功能概述
+SciPy is a collection of mathematical algorithms and convenience functions built on the NumPy extension of Python.
+
+Scipy是一个高级的科学计算库，建立在低一级的numpy的多维数组之上。Scipy有很多子模块可以完成不同的操作，如傅里叶变换、插值运算、优化算法和数学统计等。Scipy的常用的子模块如下：
+```py
+scipy.cluster	        向量量化
+scipy.constants	        数学常量
+scipy.fftpack	        快速傅里叶变换
+scipy.integrate	        积分
+scipy.interpolate	    插值
+scipy.io	            数据输入输出
+scipy.linalg	        线性代数
+scipy.ndimage	        N维图像
+scipy.odr	            正交距离回归
+scipy.optimize	        优化算法
+scipy.signal	        信号处理
+scipy.sparse	        稀疏矩阵
+scipy.spatial	        空间数据结构和算法
+scipy.special	        特殊数学函数
+scipy.stats	            统计函数
+
+>>> from scipy import linalg, optimize
+```
+
+
+> numpy提供了ndarray对象和关于该对象的基本操作和基本运算。scipy提供了ndarray的科学计算。
+
+
+## 查看帮助
+
+```py
+help(optimize.fmin)
+
+np.info(optimize.fmin)
+```
\ No newline at end of file
diff --git a/Python/scipy/10spatial.md b/Python/scipy/10spatial.md
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diff --git a/Python/scipy/11stats.md b/Python/scipy/11stats.md
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+# 统计函数
+
+> 实现概率论和数理统计相关的功能
+
diff --git a/Python/scipy/12ndimage.md b/Python/scipy/12ndimage.md
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+
+## ndimage用途
+SciPy的ndimage子模块专用于图像处理。这里，ndimage表示一个n维图像。
+图像处理中一些最常见的任务如下:
+
+* 输入/输出/显示图像
+* 基本操作:裁剪，翻转，旋转等图像过滤
+* 去噪，锐化等图像分割 
+* 标记对应于不同对象的像素
+* 分类
+* 特征提取
+* 注册/配准
+
+
+## 示例
+```
+# 导入图像
+from scipy import misc
+f = misc.face()
+misc.imsave('face.png', f) # uses the Image module (PIL)
+
+import matplotlib.pyplot as plt
+plt.imshow(f)
+plt.show()
+
+# 基本信息
+
+from scipy import misc
+f = misc.face()
+misc.imsave('face.png', f) # uses the Image module (PIL)
+
+face = misc.face(gray = False)
+print (face.mean(), face.max(), face.min())
+
+## 几何裁剪
+
+from scipy import misc
+f = misc.face()
+misc.imsave('face.png', f) # uses the Image module (PIL)
+face = misc.face(gray = True)
+lx, ly = face.shape
+
+crop_face = face[int(lx/4): -int(lx/4), int(ly/4): -int(ly/4)]
+
+import matplotlib.pyplot as plt
+plt.imshow(crop_face)
+plt.show()
+
+# 倒置图像
+from scipy import misc
+
+face = misc.face()
+flip_ud_face = np.flipud(face)
+
+import matplotlib.pyplot as plt
+plt.imshow(flip_ud_face)
+plt.show()
+
+# 旋转图像
+# rotation
+from scipy import misc,ndimage
+face = misc.face()
+rotate_face = ndimage.rotate(face, 45)
+
+import matplotlib.pyplot as plt
+plt.imshow(rotate_face)
+plt.show()
+
+# 模糊滤镜
+
+from scipy import misc
+face = misc.face()
+blurred_face = ndimage.gaussian_filter(face, sigma=3)
+import matplotlib.pyplot as plt
+plt.imshow(blurred_face)
+plt.show()
+
+# 边缘检测
+import scipy.ndimage as nd
+import numpy as np
+
+im = np.zeros((256, 256))
+im[64:-64, 64:-64] = 1
+im[90:-90,90:-90] = 2
+im = ndimage.gaussian_filter(im, 8)
+
+import matplotlib.pyplot as plt
+plt.imshow(im)
+plt.show()
+
+```
+
diff --git a/Python/scipy/13io.md b/Python/scipy/13io.md
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+## IO
+
+* loadmat
+加载一个MATLAB文件
+
+* savemat
+保存为一个MATLAB文件
+* whosmat
+列出MATLAB文件中的变量
+
+```py
+import scipy.io as sio
+import numpy as np
+
+#Save a mat file
+vect = np.arange(10)
+sio.savemat('array.mat', {'vect':vect})
+
+#Now Load the File
+mat_file_content = sio.loadmat('array.mat')
+print (mat_file_content)
+```
\ No newline at end of file
diff --git a/Python/scipy/1basicfunction.md b/Python/scipy/1basicfunction.md
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+## index trics
+
+## shape manipulation
+
+## polynomials
+
+## vectorizing functions
+
+## type handling
+
diff --git a/Python/scipy/2special.md b/Python/scipy/2special.md
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--- /dev/null
+++ b/Python/scipy/2special.md
@@ -0,0 +1,6 @@
+
+
+## Bessel functions of real order
+> bassel函数
+
+## Cython Bindings for Special Functions 
\ No newline at end of file
diff --git a/Python/scipy/3integrate.md b/Python/scipy/3integrate.md
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+## Breif
+The scipy.integrate sub-package provides several integration techniques including an ordinary differential equation integrator.
+
+```py
+>>> help(integrate)
+ Methods for Integrating Functions given function object.
+
+   quad          -- General purpose integration.
+   dblquad       -- General purpose double integration.
+   tplquad       -- General purpose triple integration.
+   fixed_quad    -- Integrate func(x) using Gaussian quadrature of order n.
+   quadrature    -- Integrate with given tolerance using Gaussian quadrature.
+   romberg       -- Integrate func using Romberg integration.
+
+ Methods for Integrating Functions given fixed samples.
+
+   trapz         -- Use trapezoidal rule to compute integral from samples.
+   cumtrapz      -- Use trapezoidal rule to cumulatively compute integral.
+   simps         -- Use Simpson's rule to compute integral from samples.
+   romb          -- Use Romberg Integration to compute integral from
+                    (2**k + 1) evenly-spaced samples.
+
+   See the special module's orthogonal polynomials (special) for Gaussian
+      quadrature roots and weights for other weighting factors and regions.
+
+ Interface to numerical integrators of ODE systems.
+
+   odeint        -- General integration of ordinary differential equations.
+   ode           -- Integrate ODE using VODE and ZVODE routines.
+```
+
+
+## General integration (quad)
+$$
+I = \int_0^{4.5}f(x)dx
+$$
+
+```py
+def f(x,y):
+    pass
+# 可以用lambda函数补充其他参数。
+result = integrate.quad(lambda x:f(x,19), 0, 4.5)
+```
+
+## 带参数积分
+
+$$
+I(a,b)=\int_0^1ax^2+bxdx
+$$
+```
+from scipy.integrate import quad
+def integrand(x, a, b):
+    return a*x**2 + bx
+
+a = 2
+b = 1
+I = quad(integrand, 0, 1, args=(a,b))
+I
+(1.6666666666666667, 1.8503717077085944e-14)
+```
+## 使用单积分实现多重积分
+$$
+I_n=\int_0^{\infin}\int_1^{\infin}\frac{e^{-xt}}{t^n}dtdx=\frac{1}{n}
+$$
+
+```py
+# 内层积分
+from scipy.integrate import quad
+def integrand(t, n, x):
+    return np.exp(-x*t) / t**n
+
+>>>
+def expint(n, x):
+    return quad(integrand, 1, np.inf, args=(n, x))[0]
+# 外层积分
+
+result = quad(lambda x: expint(3, x), 0, np.inf)
+print(result)
+(0.33333333324560266, 2.8548934485373678e-09)
+```
+## General multiple integration (dblquad, tplquad, nquad)¶
+
+$$
+I_n=\int_0^{\infin}\int_1^{\infin}\frac{e^{-xt}}{t^n}dtdx=\frac{1}{n}
+$$
+```
+from scipy.integrate import quad, dblquad
+def I(n):
+    return dblquad(lambda t, x: np.exp(-x*t)/t**n, 0, np.inf, lambda x: 1, lambda x: np.inf)
+```
+
+## Gaussian quadrature
+
+## Romberg Integration
+
+## Integrating using Samples
+
+## Faster integration using low-level callback functions
+
+## Ordinary differential equations (solve_ivp)
+
diff --git a/Python/scipy/4optimize.md b/Python/scipy/4optimize.md
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+## 优化算法
+
+scipy.optimize包提供了几种常用的优化算法。
+
+* 使用各种算法(例如BFGS，Nelder-Mead单纯形，牛顿共轭梯度，COBYLA或SLSQP)的无约束和约束最小化多元标量函数(minimize())
+* 全局(蛮力)优化程序(例如，anneal()，basinhopping())
+* 最小二乘最小化(leastsq())和曲线拟合(curve_fit())算法
+* 标量单变量函数最小化(minim_scalar())和根查找(newton())
+* 使用多种算法(例如，Powell，Levenberg-Marquardt混合或Newton-Krylov等大规模方法)的多元方程系统求解(root)
+
+
+
diff --git a/Python/scipy/5interpolate.md b/Python/scipy/5interpolate.md
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@@ -0,0 +1,28 @@
+
+## 定义
+
+插值是在直线或曲线上的两点之间找到值的过程。 为了帮助记住它的含义，我们应该将“inter”这个词的第一部分想象为“输入”，表示要查看原来数据的“内部”。 这种插值工具不仅适用于统计学，而且在科学，商业或需要预测两个现有数据点内的值时也很有用。
+
+```py
+import numpy as np
+from scipy import interpolate
+import matplotlib.pyplot as plt
+x = np.linspace(0, 4, 12)
+y = np.cos(x**2/3+4)
+
+
+plt.plot(x, y,’o’)
+plt.show()
+```
+
+## 一维插值
+
+一维插值scipy.interpolate中的interp1d类是一种创建基于固定数据点的函数的便捷方法，可以使用线性插值在给定数据定义的域内的任意位置评估该函数。
+通过使用上述数据，创建一个插值函数并绘制一个新的插值图。
+```
+f1 = interp1d(x, y,kind = 'linear')
+
+f2 = interp1d(x, y, kind = 'cubic'
+
+
+```
\ No newline at end of file
diff --git a/Python/scipy/6fft.md b/Python/scipy/6fft.md
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+
+## 傅里叶变换
+
+对时域信号计算傅里叶变换以检查其在频域中的行为。 傅里叶变换可用于信号和噪声处理，图像处理，音频信号处理等领域。SciPy提供fftpack模块，可让用户计算快速傅立叶变换。
+以下是一个正弦函数的例子，它将用于使用fftpack模块计算傅里叶变换。
+
+## 一维傅里叶变换
+
+```py
+#Importing the fft and inverse fft functions from fftpackage
+from scipy.fftpack import fft
+
+#create an array with random n numbers
+x = np.array([1.0, 2.0, 1.0, -1.0, 1.5])
+
+#Applying the fft function
+y = fft(x)
+print (y)
+```
+
+## 离散余弦变换
+
+```py
+from scipy.fftpack import dct
+mydict = dct(np.array([4., 3., 5., 10., 5., 3.]))
+print(mydict)
+```
\ No newline at end of file
diff --git a/Python/scipy/7signal.md b/Python/scipy/7signal.md
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diff --git a/Python/scipy/8linalg.md b/Python/scipy/8linalg.md
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@@ -0,0 +1,13 @@
+## 线性代数
+> 主要修改二维数组
+SciPy是使用优化的ATLAS LAPACK和BLAS库构建的。 它具有非常快的线性代数能力。 所有这些线性代数例程都需要一个可以转换为二维数组的对象。 这些例程的输出也是一个二维数组。
+
+
+## 线性方程组
+
+## 行列式
+
+## 特征值特征向量
+
+## 奇异值分解
+
diff --git a/Python/scipy/9sparse.csgraph.md b/Python/scipy/9sparse.csgraph.md
new file mode 100644
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