NumPy (numerical python) provides Python support for multidimensional array objects: Ndarray, with vector computing power, fast and space-saving. NumPy supports advanced large number of dimension and matrix operations, and also provides a large number of mathematical libraries for array operations.
Ii. creating an array of Ndarrayndarray:n-dimensional array objects (matrices), all elements must be of the same type.
Ndarray Property: The Ndim property, which represents the number of dimensions; the Shape property, which represents the size of each dimension; The Dtype property that represents the data type.
To create an Ndarray array function:
code example:
#-*-coding:utf-8-*-import numpy;print ' use list to generate one-dimensional array ' data = [ 1,2,3,4,5,6]x = Numpy.array (data) print x #打印数组print x.dtype #打印数组元素的类型print ' use list to generate a two-dimensional array ' data = [[1,2],[3,4],[5,6]]x = num Py.array (data) print x #打印数组print x.ndim #打印数组的维度print x.shape #打印数组各个维度的长度. Shape is a tuple print ' Create an array using Zero/ones/empty: Create ' x = Numpy.zeros (6) #创建一维长度为6的 from shape, elements are 1-dimensional arrays print xx = Numpy.zeros ((2,3) ) #创建一维长度为2 a two-dimensional 0 array with a two-dimensional length of 3 print xx = Numpy.ones ((2,3)) #创建一维长度为2, a two-dimensional 1 array with a two-dimensional length of 3, print xx = Numpy.empty ((3,3)) #创建一维长度为2, Two-dimensional length 3, uninitialized two-dimensional array print xprint ' using arrange to generate continuous elements ' print Numpy.arange (6) # [0,1,2,3,4,5,] open interval print numpy.arange (0,6,2) # [0, 2,4]
NumPy Data type:
code example:
print ' generates an array of the specified element type: Set Dtype property ' x = Numpy.array ([1,2.6,3],dtype = Numpy.int64) Print x # element type Int64print X.dtypex = Numpy.array ([1,2,3],dtype = Numpy.float64) Print x # element type = Float64print x . dtypeprint ' Copy array with Astype and convert type ' x = Numpy.array ([1,2.6,3],dtype = numpy.float64) y = X.astype (numpy.int32) Print y # [1 2 3] Print x # [1. 2.6 3. ]z = Y.astype (numpy.float64) Print Z # [1. 2.3.] print ' converts a string element to a numeric element ' x = Numpy.array ([' 1 ', ' 2 ', ' 3 '],dtype = numpy.string_) y = X.astype (numpy.int32) print x # [' 1 ' 2 ' 3 ']p Rint y # [1 2 3] If the conversion failure throws an exception, print ' uses the data type of the other array as parameter ' x = Numpy.array ([1., 2.6,3.],dtype = numpy.float32); y = Numpy.arange (3 , Dtype=numpy.int32);p rint y # [0 1 2]print y.astype (x.dtype) # [0. 1.2.]
Vector operations: An operation between an array key of the same size applied to an element
Vector and scalar operations: "Broadcast"-scalar "broadcast" to individual elements
code example:
print ‘ndarray数组与标量/数组的运算‘x = numpy.array([1,2,3]) print x*2 # [2 4 6]print x>2 # [False False True]y = numpy.array([3,4,5])print x+y # [4 6 8]print x>y # [False False False]
Index of one-dimensional array: Similar to Python's list index function
Index of multidimensional arrays:
code example:
print ' Ndarray ' basic index ' x = Numpy.array ([[1,2],[3,4],[5,6]]) Print X[0] # [1,2]print x[0][1] # 2, index of normal python array print x[0,1] # Index of the x[0][1],ndarray array x = Numpy.array ([[[1, 2], [3,4]], [[5 , 6], [7,8]]) print x[0] # [[1 2],[3 4]]y = x[0].copy () # generate a copy z = x[0] # does not generate a copy print y # [[1 2],[3 4]]print y[0,0] # 1 y[0,0] = 0 z[0,0] = -1print y # [[0 2],[3 4]]print x[0] # [[-1 2],[3 4]]print z # [[-1 2],[3 4]]print ' ndarray slice ' x = nump Y.array ([1,2,3,4,5]) print X[1:3] # [2,3] right open interval print x[:3] # [0print] The left default is:] # [x[1] The right default is the number of elements print 2,3,4,5] # [1,3] subscript increment 2x = Numpy.array ([[[1,2],[3,4],[5,6]]) print X[:2] # [[1 2],[3 4]]print x[:2,:1] # [[1],[3]]x[:2,:1] = 0 # with scalar Value print x # [[0,2],[0,4],[5,6]]x[:2,:1] = [[8],[6]] # Assign a value in an array print x # [[8,2],[6,4],[5,6]]
Boolean index: Uses a Boolean array as the index. Arr[condition],condition is a Boolean array that consists of one condition/multiple conditions.
Example of a Boolean index code:
print ‘ndarray的布尔型索引‘x = numpy.array([3,2,3,1,3,0])# 布尔型数组的长度必须跟被索引的轴长度一致y = numpy.array([True,False,True,False,True,False]) print x[y] # [3,3,3] print x[y==False] # [2,1,0]print x>=3 # [ True False True False True False]print x[~(x>=3)] # [2,1,0]print (x==2)|(x==1) # [False True False True False False]print x[(x==2)|(x==1)] # [2 1]x[(x==2)|(x==1)] = 0print x # [3 0 3 0 3 0]
Fancy index: Use an integer array as the index.
Fancy Index code example:
print ‘ndarray的花式索引:使用整型数组作为索引‘x = numpy.array([1,2,3,4,5,6])print x[[0,1,2]] # [1 2 3]print x[[-1,-2,-3]] # [6,5,4]x = numpy.array([[1,2],[3,4],[5,6]])print x[[0,1]] # [[1,2],[3,4]]print x[[0,1],[0,1]] # [1,4] 打印x[0][0]和x[1][1]print x[[0,1]][:,[0,1]] # 打印01行的01列 [[1,2],[3,4]]# 使用numpy.ix_()函数增强可读性print x[numpy.ix_([0,1],[0,1])] #同上 打印01行的01列 [[1,2],[3,4]]x[[0,1],[0,1]] = [0,0]print x # [[0,2],[3,0],[5,6]]
The transpose/pivot of an array returns only one view of the source data and does not modify the source data.
code example:
print ' Ndarray ' the transpose and axes of the array ' k = Numpy.arange (9) #[0,1,.... 8]m = K.reshape ((3,3)) # Change the shape copy of the array to generate 2-dimensional, 3-dimensional array for each dimension, print K # [0 1 2 3 4 5 6 7 8]print m # [[0 1 2] [3 4 5] [6 7 8]]# Transpose (matrix) Array: T property: mt[x][y] = m[y][x]print m.t # [[0 3 6] [1 4 7] [2 5 8]]# compute the inner product of the matrix Xtxprint Numpy.dot (m,m.t) # Numpy.dot dot Multiply # high dimension Axis object of the Group K = Numpy.arange (8). Reshape (2,2,2) print k # [[[0 1],[2 3]],[[4 5],[6 7]]]print k[1][0][0]# Axis transform transpose parameter: A tuple of axis numbers m = K.transpose ((1,0,2)) # M[y][x][z] = k[x][y][z]print m # [[[0 1],[4 5]],[[2 3],[6 7]]]print m[0][1][0]# axis swap swapaxes (a Xes: Axis), parameter: Pair of axes number M = k.swapaxes (0,1) # switch first and second axes m[y][x][z] = k[x][y][z]print m # [[[0 1],[4 5]],[[2 3],[6 7]]]print m[0] [1] [0]# uses an axis interchange for array matrix transpose m = Numpy.arange (9). Reshape ((3,3)) Print M # [[0 1 2] [3 4 5] [6 7 8]]print m.swapaxes (1,0) # [[0 3 6] [1 4 7] [2 5 8]]
A general function (UFUNC) is a function that performs an element-level operation on data in Ndarray.
One dollar Ufunc:
One-dollar Ufunc code example:
print ‘一元ufunc示例‘x = numpy.arange(6)print x # [0 1 2 3 4 5]print numpy.square(x) # [ 0 1 4 9 16 25]x = numpy.array([1.5,1.6,1.7,1.8])y,z = numpy.modf(x)print y # [ 0.5 0.6 0.7 0.8]print z # [ 1. 1. 1. 1.]
Dual Ufunc:
Binary Ufunc code example:
print ‘二元ufunc示例‘x = numpy.array([[1,4],[6,7]])y = numpy.array([[2,3],[5,8]])print numpy.maximum(x,y) # [[2,4],[6,8]]print numpy.minimum(x,y) # [[1,3],[5,7]]
Np.where (condition, x, y), the first parameter is a Boolean array, the second argument and the third parameter can be scalar or an array.
code example:
print ‘where函数的使用‘cond = numpy.array([True,False,True,False])x = numpy.where(cond,-2,2)print x # [-2 2 -2 2]cond = numpy.array([1,2,3,4])x = numpy.where(cond>2,-2,2)print x # [ 2 2 -2 -2]y1 = numpy.array([-1,-2,-3,-4])y2 = numpy.array([1,2,3,4])x = numpy.where(cond>2,y1,y2) # 长度须匹配print x # [1,2,-3,-4]print ‘where函数的嵌套使用‘y1 = numpy.array([-1,-2,-3,-4,-5,-6])y2 = numpy.array([1,2,3,4,5,6])y3 = numpy.zeros(6)cond = numpy.array([1,2,3,4,5,6])x = numpy.where(cond>5,y3,numpy.where(cond>2,y1,y2))print x # [ 1. 2. -3. -4. -5. 0.]
The data of an entire array/axis can be statistically calculated by these basic statistical methods.
code example:
print ‘numpy的基本统计方法‘x = numpy.array([[1,2],[3,3],[1,2]]) #同一维度上的数组长度须一致print x.mean() # 2print x.mean(axis=1) # 对每一行的元素求平均print x.mean(axis=0) # 对每一列的元素求平均print x.sum() #同理 12print x.sum(axis=1) # [3 6 3]print x.max() # 3print x.max(axis=1) # [2 3 2]print x.cumsum() # [ 1 3 6 9 10 12]print x.cumprod() # [ 1 2 6 18 18 36]
Statistical methods for Boolean arrays:
code example:
print ‘用于布尔数组的统计方法‘x = numpy.array([[True,False],[True,False]])print x.sum() # 2print x.sum(axis=1) # [1,1]print x.any(axis=0) # [True,False]print x.all(axis=1) # [False,False]
Use sort to sort the array/array in-place with a dimension (the arrays themselves are modified).
code example:
print ‘.sort的就地排序‘x = numpy.array([[1,6,2],[6,1,3],[1,5,2]])x.sort(axis=1) print x # [[1 2 6] [1 3 6] [1 2 5]]#非就地排序：numpy.sort()可产生数组的副本
code example: (Method return type is a one-dimensional array (1d))
print ‘ndarray的唯一化和集合运算‘x = numpy.array([[1,6,2],[6,1,3],[1,5,2]])print numpy.unique(x) # [1,2,3,5,6]y = numpy.array([1,6,5])print numpy.in1d(x,y) # [ True True False True True False True True False]print numpy.setdiff1d(x,y) # [2 3]print numpy.intersect1d(x,y) # [1 5 6]
Import Numpy.linalg module. Linear algebra (linear algebra)
Common NUMPY.LINALG Module functions:
code example:
print ‘线性代数‘import numpy.linalg as nlaprint ‘矩阵点乘‘x = numpy.array([[1,2],[3,4]])y = numpy.array([[1,3],[2,4]])print x.dot(y) # [[ 5 11][11 25]]print numpy.dot(x,y) # # [[ 5 11][11 25]]print ‘矩阵求逆‘x = numpy.array([[1,1],[1,2]])y = nla.inv(x) # 矩阵求逆（若矩阵的逆存在）print x.dot(y) # 单位矩阵 [[ 1. 0.][ 0. 1.]]print nla.det(x) # 求行列式
Import Numpy.random module.
Common Numpy.random Module functions:
code example:
print ‘numpy.random随机数生成‘import numpy.random as nprx = npr.randint(0,2,size=100000) #抛硬币print (x>0).sum() # 正面的结果print npr.normal(size=(2,2)) #正态分布随机数数组 shape = (2,2)
code example:
print ‘ndarray数组重塑‘x = numpy.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]]print x #[0 1 2 3 4]print x.reshape((2,3)).reshape((3,2)) # [[0 1][2 3][4 5]]y = numpy.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]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 = numpy.arange(15)print arr.reshape((5, -1)) # 15 / 5 = 3
code example:
The merge and split of print ' arrays ' x = Numpy.array ([[1, 2, 3], [4, 5, 6]]) y = Numpy.array ([[7, 8, 9], [Ten, One,]]) print numpy.concatenate ([ x, y], Axis = 0) # vertical combination [[1 2 3][4 5 6][7 8 9][10 one 12]]print numpy.concatenate ([x, y], Axis = 1) # horizontal combination [[1 2 3 7 8 9][4 5 6 12]]print ' vertical stack with horizontal stack ' Print numpy.vstack ((x, y)) # vertical stacking: With respect to the vertical combination of print numpy.hstack ((x, Y) # Horizontal stacking: In relation to horizontal combo # Dstack: Stacked by depth print numpy.split (x,2,axis=0) # Split by row [Array ([[[1, 2, 3]]), Array ([[[4, 5, 6])]print NUMPY.S Plit (X,3,axis=1) # Split by column [Array ([[[1],[4]]), Array ([[[2],[5]]), Array ([[[3],[6]])]# stack auxiliary class import numpy as Nparr = Np.arange (6) arr1 = Arr.reshape ((3, 2)) arr2 = Np.random.randn (3, 2) print ' R_ used to stack by rows ' Print np.r_[arr1, arr2] ' [[0. 1.] [2. 3.] [4. 5.] [0.22621904 0.39719794] [ -1.2201912-0.23623549] [ -0.83229114-0.72678578]] ' print ' c_ used to stack by column ' Print Np.c_[n P.R_[ARR1, arr2], arr] "[[0]. 1.0. ] [2. 3.1. ] [4. 5.2. ] [0.22621904 0.39719794 3. ] [ -1.2201912-0.23623549 4. ] [ -0.83229114-0.72678578 5. ] ' print ' Slice directly to array ' Print Np.c_[1:6, -10:-5] ' [[1-10] [2-9] [3-8] [4-7] [5-6]] 'code example:
print ‘数组的元素重复操作‘x = numpy.array([[1,2],[3,4]])print x.repeat(2) # 按元素重复 [1 1 2 2 3 3 4 4]print x.repeat(2,axis=0) # 按行重复 [[1 2][1 2][3 4][3 4]]print x.repeat(2,axis=1) # 按列重复 [[1 1 2 2][3 3 4 4]]x = numpy.array([1,2])print numpy.tile(x,2) # tile瓦片：[1 2 1 2]print numpy.tile(x, (2, 2)) # 指定从低维到高维依次复制的次数。 # [[1 2 1 2][1 2 1 2]]
Basic use of Python's numpy
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