From 83e47e31735523e00b9fcb459426fe1213efb9ef Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E6=9D=8E=E4=B8=AD=E6=A2=81?= Date: Tue, 2 Jan 2018 19:57:38 +0800 Subject: [PATCH 1/9] ignore chinese code question --- python_visual.py | 17 +++++++++++------ 1 file changed, 11 insertions(+), 6 deletions(-) diff --git a/python_visual.py b/python_visual.py index 32661a4..c6dbb50 100644 --- a/python_visual.py +++ b/python_visual.py @@ -12,8 +12,8 @@ import matplotlib.font_manager as fm from mpl_toolkits.mplot3d import Axes3D # 解决中文乱码问题 -myfont = fm.FontProperties(fname="/Library/Fonts/Songti.ttc", size=14) -matplotlib.rcParams["axes.unicode_minus"] = False +# myfont = fm.FontProperties(fname="/Library/Fonts/Songti.ttc", size=14) +# matplotlib.rcParams["axes.unicode_minus"] = False def simple_plot(): @@ -26,16 +26,19 @@ def simple_plot(): # 生成画布，并设定标题 plt.figure(figsize=(8, 6), dpi=80) - plt.title("简单曲线图", fontproperties=myfont) + # plt.title("简单曲线图", fontproperties=myfont) + plt.title("简单曲线图") plt.grid(True) # 设置X轴 - plt.xlabel("X轴", fontproperties=myfont) + # plt.xlabel("X轴", fontproperties=myfont) + plt.xlabel("X轴") plt.xlim(-4.0, 4.0) plt.xticks(np.linspace(-4, 4, 9, endpoint=True)) # 设置Y轴 - plt.ylabel("Y轴", fontproperties=myfont) + # plt.ylabel("Y轴", fontproperties=myfont) + plt.ylabel("Y轴") plt.ylim(-1.0, 1.0) plt.yticks(np.linspace(-1, 1, 9, endpoint=True)) @@ -44,7 +47,7 @@ def simple_plot(): plt.plot(x, y_sin, "g-", linewidth=2.0, label="sin示例") # 设置图例位置,loc可以为[upper, lower, left, right, center] - plt.legend(loc="upper left", prop=myfont, shadow=True) + # plt.legend(loc="upper left", prop=myfont, shadow=True) # 图形显示 plt.show() @@ -500,3 +503,5 @@ def three_dimension_bar(): plt.show() return # three_dimension_bar() + +simple_plot() From cc16437b6b7392484591bd8996052d88e2678c47 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E6=9D=8E=E4=B8=AD=E6=A2=81?= Date: Tue, 2 Jan 2018 21:15:12 +0800 Subject: [PATCH 2/9] Update python_visual.py --- python_visual.py | 2 -- 1 file changed, 2 deletions(-) diff --git a/python_visual.py b/python_visual.py index c6dbb50..2c84908 100644 --- a/python_visual.py +++ b/python_visual.py @@ -503,5 +503,3 @@ def three_dimension_bar(): plt.show() return # three_dimension_bar() - -simple_plot() From 8e2ad8ffb63c13971dd4467405cf24ca50487ed2 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E6=9D=8E=E4=B8=AD=E6=A2=81?= Date: Wed, 21 Feb 2018 05:15:08 +0000 Subject: [PATCH 3/9] Update README.md --- README.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/README.md b/README.md index 38d43d4..02e31bb 100644 --- a/README.md +++ b/README.md @@ -1,5 +1,6 @@ # LearnPython -以撸代码的形式学习Python, 具体说明在[知乎专栏-撸代码,学知识](https://zhuanlan.zhihu.com/pythoner) +以撸代码的形式学习Python, 具体说明在[知乎专栏-撸代码,学知识](https://zhuanlan.zhihu.com/pythoner) +[Python知识点总结](https://www.jianshu.com/p/2aeee1ed59ec) =================================================================================================== ### python_base.py: 千行代码入门Python From 098c310b85dd1e3a95f6c7cf36fba972895596fd Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E6=9D=8E=E4=B8=AD=E6=A2=81?= Date: Fri, 23 Feb 2018 14:48:36 +0800 Subject: [PATCH 4/9] Create python_numpy.py --- python_numpy.py | 150 ++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 150 insertions(+) create mode 100644 python_numpy.py diff --git a/python_numpy.py b/python_numpy.py new file mode 100644 index 0000000..83864d8 --- /dev/null +++ b/python_numpy.py @@ -0,0 +1,150 @@ +# _*_coding:utf-8-*_ +import numpy as np +# 定义矩阵变量并输出变量的一些属性 +# 用np.array()生成矩阵 +arr=np.array([[1,2,3], + [4,5,6]]) + +print(arr) +print('number of arr dimensions: ',arr.ndim) +print('~ ~ ~ shape: ',arr.shape) +print('~ ~ ~ size: ', arr.size) + +# 输出结果： +[[1 2 3] + [4 5 6]] +number of arr dimensions: 2 +~ ~ ~ shape: (2, 3) +~ ~ ~ size: 6 + +# 定义一些特殊矩阵 +# 指定矩阵数据类型 +arr=np.array([[1,2,3], + [4,5,6]], + dtype=np.float64) # 我的电脑np.int是int32，还可以使用np.int32/np.int64/np.float32/np.float64 +print(arr.dtype) + +# 用np.zeros()生成全零矩阵 +arr_zeros=np.zeros( (2,3) ) +print(arr_zeros) + +# 用np.ones()生成全一矩阵 +arr_ones=np.ones( (2,3) ) +print(arr_ones) + +# 生成随机矩阵np.random.random() +arr_random=np.random.random((2,3)) +print(arr_random) + +# 用np.arange()生成数列 +arr=np.arange(6,12) +print(arr) + +# 用np.arange().reshape()将数列转成矩阵 +arr=np.arange(6,12).reshape( (2,3) ) +print(arr) + +# 用np.linspace(开始，结束，多少点划分线段)，同样也可以用reshape() +arr=np.linspace(1,5,3) +print(arr) + +# 矩阵运算 +arr1=np.array([1,2,3,6]) +arr2=np.arange(4) + +# 矩阵减法，加法同理 +arr_sub=arr1-arr2 +print(arr1) +print(arr2) +print(arr_sub) + +# 矩阵乘法 +arr_multi=arr1**3 # 求每个元素的立方，在python中幂运算用**来表示 +print(arr_multi) + +arr_multi=arr1*arr2 # 元素逐个相乘 +print(arr_multi) + +arr_multi=np.dot(arr1, arr2.reshape((4,1))) # 维度1*4和4*1矩阵相乘 +print(arr_multi) + +arr_multi=np.dot(arr1.reshape((4,1)), arr2.reshape((1,4))) # 维度4*1和1*4矩阵相乘 +print(arr_multi) + +arr_multi=arr1.dot(arr2.reshape((4,1))) # 也可以使用矩阵名.doc(矩阵名) +print(arr_multi) + +# 三角运算：np.sin()/np.cos()/np.tan() +arr_sin=np.sin(arr1) +print(arr_sin) + +# 逻辑运算 +print(arr1<3) # 查看arr1矩阵中哪些元素小于3，返回[ True True False False] + +# 矩阵求和，求矩阵最大最小值 +arr1=np.array([[1,2,3], + [4,5,6]]) +print(arr1) +print(np.sum(arr1)) # 矩阵求和 +print(np.sum(arr1,axis=0)) # 矩阵每列求和 +print(np.sum(arr1,axis=1).reshape(2,1)) # 矩阵每行求和 + +print(np.min(arr1)) # 求矩阵最小值 +print(np.min(arr1,axis=0)) +print(np.min(arr1,axis=1)) + +print(np.max(arr1)) # 求矩阵最大值 + +print(np.mean(arr1)) # 输出矩阵平均值，也可以用arr1.mean() +print(np.median(arr1)) # 输出矩阵中位数 + +# 输出矩阵某些值的位置 +arr1=np.arange(2,14).reshape((3,4)) +print(arr1) + +print(np.argmin(arr1)) # 输出矩阵最小值的位置，0 +print(np.argmax(arr1)) # 输出矩阵最大值的位置，11 + +print(np.cumsum(arr1)) # 输出前一个数的和，前两个数的和，等等 +print(np.diff(arr1)) # 输出相邻两个数的差值 + +arr_zeros=np.zeros((3,4)) +print(np.nonzero(arr_zeros)) #输出矩阵非零元素位置，返回多个行向量，第i个行向量表示第i个维度 +print(np.nonzero(arr1)) + +print(np.sort(arr1)) # 矩阵逐行排序 +print(np.transpose(arr1)) # 矩阵转置，也可以用arr1.T + +print(np.clip(arr1,5,9)) #将矩阵中小于5的数置5，大于9的数置9 + +# numpy索引 +arr1=np.array([1,2,3,6]) +arr2=np.arange(2,8).reshape(2,3) + +print(arr1) +print(arr1[0]) # 索引从0开始计数 + +print(arr2) +print(arr2[0][2]) # arr[行][列]，也可以用arr[行,列] +print(arr2[0,:]) # 用:来代表所有元素的意思 +print(arr2[0,0:3]) # 表示输出第0行，从第0列到第2列所有元素 + # 注意python索引一般是左闭右开 + +# 通过for循环每次输出矩阵的一行 +for row in arr2: + print(row) + +# 如果要每次输出矩阵的一列，就先将矩阵转置 +arr2_T=arr2.T +print(arr2_T) +for row in arr2_T: + print(row) + +# 将矩阵压成一行逐个输出元素 +arr2_flat=arr2.flatten() +print(arr2_flat) + +for i in arr2.flat: # 也可以用arr2.flatten() + print(i) + + From 7337fa7dc94f68df0ea3876f05866a9b989232fd Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E6=9D=8E=E4=B8=AD=E6=A2=81?= Date: Fri, 23 Feb 2018 16:35:08 +0800 Subject: [PATCH 5/9] Update python_numpy.py --- python_numpy.py | 56 +++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 56 insertions(+) diff --git a/python_numpy.py b/python_numpy.py index 83864d8..9d32a4f 100644 --- a/python_numpy.py +++ b/python_numpy.py @@ -147,4 +147,60 @@ print(arr2_flat) for i in arr2.flat: # 也可以用arr2.flatten() print(i) +# 矩阵合并与分割 +# 矩阵合并 +arr1=np.array([1,2,3,6]) +arr2=np.arange(4) +arr3=np.arange(2,16+1,2).reshape(2,4) +print(arr1) +print(arr2) +print(arr3) +arr_hor=np.hstack((arr1,arr2)) # 水平合并，horizontal +arr_ver=np.vstack((arr1,arr3)) # 垂直合并，vertical +print(arr_hor) +print(arr_ver) + +# 矩阵分割 +print('arr3: ',arr3) +print(np.split(arr3,4,axis=1)) # 将矩阵按列均分成4块 +print(np.split(arr3,2,axis=0)) # 将矩阵按行均分成2块 +print(np.hsplit(arr3,4)) # 将矩阵按列均分成4块 +print(np.vsplit(arr3,2)) # 将矩阵按行均分成2块 +print(np.array_split(arr3,3,axis=1)) # 将矩阵进行不均等划分 + +# numpy复制：浅复制，深复制 +# 浅复制 +arr1=np.array([3,1,2,3]) +print(arr1) +a1=arr1 +b1=a1 +# 通过上述赋值运算，arr1,a1,b1都指向了同一个地址（浅复制） +print(a1 is arr1) +print(b1 is arr1) +print(id(a1)) +print(id(b1)) +print(id(arr1)) + +# 会发现通过b1[0]改变内容，arr1,a1,b1的内容都改变了 +b1[0]=6 +print(b1) +print(a1) +print(arr1) + +# 深复制 +arr2=np.array([3,1,2,3]) +print('\n') +print(arr2) +b2=arr2.copy() # 深复制，此时b2拥有不同于arr2的空间 +a2=b2.copy() +# 通过上述赋值运算，arr1,a1,b1都指向了不同的地址（深复制） +print(id(arr2)) +print(id(a2)) +print(id(b2)) +# 此时改变b2,a2的值，互不影响 +b2[0]=1 +a2[0]=2 +print(b2) +print(a2) +print(arr2) From efa1485416d6d9be370ed1c0b045801633dff092 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E6=9D=8E=E4=B8=AD=E6=A2=81?= Date: Fri, 23 Feb 2018 16:40:44 +0800 Subject: [PATCH 6/9] Update README.md --- README.md | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/README.md b/README.md index 02e31bb..f6d1878 100644 --- a/README.md +++ b/README.md @@ -53,7 +53,9 @@ ### python_wechat.py: 玩点好玩的--自己写一个微信小助手 -### python_csv.py: Python中CSV文件的简单读写 +### python_csv.py: Python中CSV文件的简单读写 + +### python_numpy.py: 使用numpy进行矩阵操作 =================================================================================================== ### 您可以fork该项目, 并在修改后提交Pull request From 88b2242fe8789f21d658508b329b1d556af88c16 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E6=9D=8E=E4=B8=AD=E6=A2=81?= Date: Sat, 24 Feb 2018 18:06:48 +0800 Subject: [PATCH 7/9] Update python_numpy.py --- python_numpy.py | 112 ++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 112 insertions(+) diff --git a/python_numpy.py b/python_numpy.py index 9d32a4f..ce48d1f 100644 --- a/python_numpy.py +++ b/python_numpy.py @@ -204,3 +204,115 @@ a2[0]=2 print(b2) print(a2) print(arr2) + +# 线性代数模块（linalg） +# 求范数 +a=np.array([5,12]) +print(a) +b=np.linalg.norm(a) # norm表示范数，默认求2范数，ord=1求1范数，ord=np.inf求无穷范数 +print(b) + +# 求矩阵的迹、行列式、秩、特征值、特征向量 +b = np.array([ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9] +]) + +print(np.trace(b)) # 15，求矩阵的迹（主对角线上各个元素的总和） + +c=np.linalg.det(b) +print(c) # 输出一个很小的值6.66133814775e-16，求矩阵的行列式值 + # 如果希望输出为0，使用round(c, 2)，四舍五入保留小数点后两位 + # 不过对精度要求高可以使用decimal模块 + +c=np.linalg.matrix_rank(b) +print(c) # 2，求矩阵的秩 + +u,v=np.linalg.eig(b) # u为特征值 +print(u) +print(v) + +# 矩阵分解 +# Cholesky分解并重建 +d = np.array([ + [2, 1], + [1, 2] +]) + +l = np.linalg.cholesky(d) +print(l) # 得到下三角矩阵 +e=np.dot(l, l.T) +print(e) # 重建得到矩阵d + + +# 对不正定矩阵，进行SVD分解并重建 +U, s, V = np.linalg.svd(d) + +S = np.array([ + [s[0], 0], + [0, s[1]] +]) + +print(np.dot(U, np.dot(S, V))) # 重建得到矩阵d + +# 矩阵乘法 +# https://docs.scipy.org/doc/numpy/reference/generated/numpy.dot.html#numpy.dot +print(np.dot(3, 4)) # 12，0-D矩阵相乘（也就是标量相乘） + +print(np.dot([2j, 3j], [2j, 3j])) # (-13+0j)，1-D矩阵相乘（实际上是向量做点积） + +a=[[1, 0], [0, 1]] +b=[[4, 1, 0], [2, 2, 0]] +print(np.dot(a, b)) +''' +array([[4, 1], + [2, 2]]) +2-D矩阵相乘 +这里是2*2矩阵和2*3矩阵相乘，结果为2*3矩阵 +''' + +a=[[1, 0], [1, 2]] +b=[2,2] +c=np.dot(a,b) +print(c) +''' +[2 6] +注意这里b是向量 +numpy处理时并不是按照矩阵乘法规则计算 +而是向量点积 +也就是np.dot([1, 0],[1, 2])和np.dot([1, 2],[2,2]) +''' + +# 再做个实验来区别向量乘法和矩阵乘法 +b=np.array([ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9] +]) + +# 这里插播一下，np.array([1,0,1])是3维向量，而不是1*3的矩阵 +c1=np.array([[1,0,2]]) +print(c1.shape) # (1, 3)，这是一个1*3的矩阵 +c2=np.array([1,0,2]) +print(c2.shape) # (3,)，这是一个3维向量 + +# print(np.dot(b,c1)) # 报错，不符合矩阵乘法规则 +print(np.dot(b,c2)) # [ 7 16 25]，点积运算 + +print(np.dot(c1,b)) # [[15 18 21]]，矩阵乘法运算规则 +print(np.dot(c2,b)) # [15 18 21]，点积运算 + +# 还要补充一下，如果是用python自带的*运算符计算则是广播机制 +print(b*c1) # print(b*c2)结果一样 +''' +[[ 1 0 6] + [ 4 0 12] + [ 7 0 18]] +''' +print(b+c1) # print(b*c2)结果一样 +''' +[[ 2 2 5] + [ 5 5 8] + [ 8 8 11]] +''' From 967c2b4e45d74c2d93e444cc4ca5f9f86865788b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E6=9D=8E=E4=B8=AD=E6=A2=81?= Date: Sat, 24 Feb 2018 18:37:06 +0800 Subject: [PATCH 8/9] Update README.md --- README.md | 1 - 1 file changed, 1 deletion(-) diff --git a/README.md b/README.md index f6d1878..258714c 100644 --- a/README.md +++ b/README.md @@ -1,6 +1,5 @@ # LearnPython 以撸代码的形式学习Python, 具体说明在[知乎专栏-撸代码,学知识](https://zhuanlan.zhihu.com/pythoner) -[Python知识点总结](https://www.jianshu.com/p/2aeee1ed59ec) =================================================================================================== ### python_base.py: 千行代码入门Python From 1b7d754590fa294a0de07a2e3cf39c8d91fb9ed1 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=E6=9D=8E=E4=B8=AD=E6=A2=81?= Date: Sat, 24 Feb 2018 19:14:59 +0800 Subject: [PATCH 9/9] Update python_visual.py --- python_visual.py | 15 ++++++--------- 1 file changed, 6 insertions(+), 9 deletions(-) diff --git a/python_visual.py b/python_visual.py index 2c84908..32661a4 100644 --- a/python_visual.py +++ b/python_visual.py @@ -12,8 +12,8 @@ import matplotlib.font_manager as fm from mpl_toolkits.mplot3d import Axes3D # 解决中文乱码问题 -# myfont = fm.FontProperties(fname="/Library/Fonts/Songti.ttc", size=14) -# matplotlib.rcParams["axes.unicode_minus"] = False +myfont = fm.FontProperties(fname="/Library/Fonts/Songti.ttc", size=14) +matplotlib.rcParams["axes.unicode_minus"] = False def simple_plot(): @@ -26,19 +26,16 @@ def simple_plot(): # 生成画布，并设定标题 plt.figure(figsize=(8, 6), dpi=80) - # plt.title("简单曲线图", fontproperties=myfont) - plt.title("简单曲线图") + plt.title("简单曲线图", fontproperties=myfont) plt.grid(True) # 设置X轴 - # plt.xlabel("X轴", fontproperties=myfont) - plt.xlabel("X轴") + plt.xlabel("X轴", fontproperties=myfont) plt.xlim(-4.0, 4.0) plt.xticks(np.linspace(-4, 4, 9, endpoint=True)) # 设置Y轴 - # plt.ylabel("Y轴", fontproperties=myfont) - plt.ylabel("Y轴") + plt.ylabel("Y轴", fontproperties=myfont) plt.ylim(-1.0, 1.0) plt.yticks(np.linspace(-1, 1, 9, endpoint=True)) @@ -47,7 +44,7 @@ def simple_plot(): plt.plot(x, y_sin, "g-", linewidth=2.0, label="sin示例") # 设置图例位置,loc可以为[upper, lower, left, right, center] - # plt.legend(loc="upper left", prop=myfont, shadow=True) + plt.legend(loc="upper left", prop=myfont, shadow=True) # 图形显示 plt.show()