python numpy基础
numpy基础用法的代码，以后自己可以查的笔记
# -*- coding: utf-8 -*-
import numpy as np
#1、数组（ndarray) 创建
aa=[1,2,3,4]
a_=np.array(aa)
print a_
aaa=np.arange(6)
bbb=np.arange(0,6,2)
print aaa
print bbb
a=np.array([1,2,3,4,5,6,7],dtype=np.float32)
print a.shape
print a.ndim
print a.dtype
am=a.astype(np.int32) #改变数组的数据类型
print am.dtype
print type(a)
print a
b=np.array([[1.0,2.0,3.0],[4.0,5.0,6.0]],dtype=np.float64)
print b.shape
print b.dtype
print type(b)
print b
c=np.zeros((2,2))
print c
d=np.ones((3,3))
print d
e=np.full((3,3),6)
print e
f=np.eye(5)
print f
g=np.random.random((6,6))
print g
h=np.random.randn(3,4)
print h
j=np.empty((3,3))
print j
a = np.linspace(0,10,7) # 生成首位是0，末位是10，含7个数的等差数列
print(a)
# 2、ndarray的矢量化计算
#矢量运算：相同大小的数组间的运算应用在元素上
#矢量和标量运算：“广播”— 将标量“广播”到各个元素
# 运算符 说明
# + 矩阵对应元素相加
# - 矩阵对应元素相减
# * 矩阵对应元素相乘
# / 矩阵对应元素相除，如果都是整数则取商
# % 矩阵对应元素相除后取余数
# ** 矩阵每个元素都取n次方，如**2：每个元素都取平方
a1 = np.array([[4,5,6],[1,2,3]])
a2 = np.array([[6,5,4],[3,2,1]])
print(a1+a2) #+
print(a1/a2) #-
print(a1%a2) #%
print(a1*a2) #*
print (a1**2)# **平方
print(a1*2)
x=np.array([1,2,3])
print x>2
y = np.array([3,4,5])
print x>y
# 3、 数组切片 重要！！！！
#切片：和Python列表类似，numpy数组可以使用切片语法。因为数组可以是多维的，所以你必须为每个维度指定好切片。
qAq = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])
qBq=qAq[:2, 1:3]
print qBq
print qBq.shape
qbq1=qAq[2,3] #get the value of element
qbq2=qAq[0]
qbq3=qAq[2][3]
print qbq1
print qbq2
print qbq3
# 你可以同时使用整型和切片语法来访问数组。但是，这样做会产生一个比原数组低阶的新数组
abc = np.array([[1,2,3,4], [5,6,7,8], [9,10,11,12]])
# Two ways of accessing the data in the middle row of the array.
# Mixing integer indexing with slices yields an array of lower rank,
# while using only slices yields an array of the same rank as the
# original array:
row_r1 = abc[1, :] # Rank 1 view of the second row of a
row_r2 = abc[1:2, :] # Rank 2 view of the second row of a
print row_r1, row_r1.shape # Prints "[5 6 7 8] (4,)"
print row_r2, row_r2.shape # Prints "[[5 6 7 8]] (1, 4)"
# We can make the same distinction when accessing columns of an array:
col_r1 = abc[:, 1]
col_r2 = abc[:, 1:2]
print col_r1, col_r1.shape # Prints "[ 2 6 10] (3,)"
print col_r2, col_r2.shape # Prints "[[ 2]
# [ 6]
# [10]] (3, 1)"
# 一个小技巧，没想到还有这种操作呢
ab = np.array([[1,2,3], [4,5,6], [7,8,9], [10, 11, 12]])
# Create an array of indices
ba = np.array([0, 2, 0, 1])
# Select one element from each row of a using the indices in b
print ab[np.arange(4), ba] # Prints "[ 1 6 7 11]"
# Mutate one element from each row of a using the indices in b
ab[np.arange(4), ba] += 10
print ab # prints "array([[11, 2, 3],
# [ 4, 5, 16],
# [17, 8, 9],
# [10, 21, 12]])
#一维数组也可以哦~~~
abcd=np.array([1,2,3,4,5,6])
print abcd[[0,2,3,1]]
# 4、布尔索引
ap = np.array([[1,2], [3, 4], [5, 6]])
bool_idx = (ap > 2) # Find the elements of a that are bigger than 2;
# this returns a numpy array of Booleans of the same
# shape as a, where each slot of bool_idx tells
# whether that element of a is > 2.
print bool_idx # Prints "[[False False]
# [ True True]
# [ True True]]"
# We use boolean array indexing to construct a rank 1 array
# consisting of the elements of a corresponding to the True values
# of bool_idx
print ap[bool_idx] # Prints "[3 4 5 6]"
# We can do all of the above in a single concise statement:
print ap[ap > 2] # Prints "[3 4 5 6]"
#5、矩阵运算
#1） 元素级别
x = np.array([[1,2],[3,4]], dtype=np.float64)
y = np.array([[5,6],[7,8]], dtype=np.float64)
print x + y #（1）
print np.add(x, y) #（2）
print x - y
print np.subtract(x, y)
print x * y #不是矩阵乘法，对应元素相乘
print np.multiply(x, y)
print x / y #对应元素相除
print np.divide(x, y)
print np.sqrt(x) #通用函数（ufunc）是一种对ndarray中的数据执行元素级运算的函数。更多函数可查询：https://blog.csdn.net/cxmscb/article/details/54583415
# 2） 在Numpy中使用dot来进行矩阵乘法：
x = np.array([[1,2],[3,4]])
y = np.array([[5,6],[7,8]])
v = np.array([9,10])
w = np.array([11, 12])
# Inner product of vectors; both produce 219
print v.dot(w)
print np.dot(v, w)
# Matrix / vector product; both produce the rank 1 array [29 67]
print x.dot(v)
print np.dot(x, v)
# Matrix / matrix product; both produce the rank 2 array
# [[19 22]
# [43 50]]
print x.dot(y)
print np.dot(x, y)
#3） 用于统计的函数sum mean
x = np.array([[1,2],[3,4]])
print np.sum(x) # Compute sum of all elements; prints "10"
print np.sum(x, axis=0) # Compute sum of each column; prints "[4 6]"
print np.sum(x, axis=1) # Compute sum of each row; prints "[3 7]"
print np.mean(x) # Compute mean of all elements;
print np.mean(x, axis=0) # Compute mean of each column;
print np.mean(x, axis=1) # Compute mean of each row;
print np.max(x) # Compute max of all elements;
print np.max(x, axis=0) # Compute max of each column;
print np.max(x, axis=1) # Compute max of each row;
print np.min(x) # Compute min of all elements;
print np.min(x, axis=0) # Compute min of each column;
print np.min(x, axis=1) # Compute min of each row;
print np.argmax(x) # Compute argmax of all elements;
print np.argmax(x, axis=0) # Compute argmax of each column;
print np.argmax(x, axis=1) # Compute argmax of each row;
print np.argmin(x) # Compute argmin of all elements;
print np.argmin(x, axis=0) # Compute argmin of each column;
print np.argmin(x, axis=1) # Compute argmin of each row;
print np.std(x) #标准差
print np.std(x,0)
print np.std(x,1)
print np.var(x) #方差
print np.var(x,0)
print np.var(x,1)
y=np.array([1,2,3,4,5])
print np.cumsum(y) #所有元素累积和
print np.cumprod(y) #所有元素累积积
# 4） 矩阵转置和轴对换
print x.T #easy
k = np.arange(8).reshape(2,2,2)
print k
m=k.transpose((1,0,2)) # m[y][x][z] = k[x][y][z] # 轴变换 transpose 参数:由轴编号组成的元组
print m
m = k.swapaxes(0,1) # 将第一个轴和第二个轴交换 m[y][x][z] = k[x][y][z] # 轴交换 swapaxes (axes：轴)，参数:一对轴编号
print m
# 5) ndarray 去重复计算
print 'ndarray的唯一化和集合运算'
x =np.array([[1,6,2],[6,1,3],[1,5,2]])
print np.unique(x) # [1,2,3,5,6]
y = np.array([1,6,5])
print np.in1d(x,y) # [ True True False True True False True True False]
print np.setdiff1d(x,y) # [2 3]
print np.intersect1d(x,y) # [1 5 6]
# 6 numpy的线性代数
#import numpy.linalg 模块。线性代数（linear algebra） 常用的numpy.linalg模块函数：更多函数查询文档
x = np.array([[1,2],[3,4]])
y = np.array([[1,3],[2,4]])
z=np.linalg.inv(x)
z1=np.linalg.det(x)
U,S,V=np.linalg.svd(x)
# 7 numpy数组的reshape 数组重塑
print 'ndarray数组重塑'
x = np.arange(0,6) #[0 1 2 3 4]
print x #[0 1 2 3 4]
print x.reshape((2,3)) # [[0 1 2][3 4 5]] ###重要 返回的是副本，不改变数组本身
print x #[0 1 2 3 4]
print x.reshape((2,3)).reshape((3,2)) # [[0 1][2 3][4 5]]
yy = np.array([[1,1,1],[1,1,1]])
x = x.reshape(y.shape)
print x # [[0 1 2][3 4 5]]
print x.flatten() # [0 1 2 3 4 5] ########重要 展开矩阵为一维数组
x.flatten()[0] = -1 # flatten返回的是拷贝
print x # [[0 1 2][3 4 5]]
print x.ravel() # [0 1 2 3 4 5]
x.ravel()[0] = -1 # ravel返回的是视图（引用）
print x # [[-1 1 2][3 4 5]]
print "维度大小自动推导"
arr = np.arange(15)
print arr.reshape((5, -1)) # 15 / 5 = 3 列
print arr.reshape((-1, 5)) # 15 / 5 = 3 行
# 8、矩阵合并
a1=np.array([[1,2],[3,4]])
a2=np.array([[5,6],[7,8]])
# #方式1：
print np.hstack([a1,a2]) #行合并
print np.vstack([a1,a2]) #列合并
# #方式2：
np.concatenate((a1,a2),axis=0) #行
np.concatenate((a1,a2),axis=1) #列