Numpy 多维数据数组的实现

%matplotlib inline
import matplotlib.pyplot as plt
from numpy import *

v = array([1,2,3,4])
v

M = array([[1, 2], [3, 4]])
M

type(v), type(M)

v.shape

M.shape

M.size

shape(M)

size(M)

M.dtype

M[0,0] = "hello"

M = array([[1, 2], [3, 4]], dtype=complex)
M

x = arange(0, 10, 1) # arguments: start, stop, step
x

x = arange(-1, 1, 0.1)
x

linspace(0, 10, 25)

logspace(0, 10, 10, base=e)

x, y = mgrid[0:5, 0:5]
x
y

#导入所需模块
from numpy import random

#区间[0,1]内的均匀分布数。
random.rand(5,5)

#来自于正态分布的随机数
random.randn(5,5)

#对角矩阵
diag([1,2,3])

#偏移对角矩阵
diag([1,2,3], k=1)

zeros((3,3))

ones((3,3))

data = genfromtxt('stockholm_td_adj.dat')
data.shape

fig, ax = plt.subplots(figsize=(14,4))
ax.plot(data[:,0]+data[:,1]/12.0+data[:,2]/365, data[:,5])
ax.axis('tight')
ax.set_title('Температура в Стокгольме')
ax.set_xlabel('год')
ax.set_ylabel('температура (C)');

M = random.rand(3,3)
M

savetxt("random-matrix.csv", M)
savetxt("random-matrix.csv", M, fmt='%.5f') # fmt 指定格式

save("random-matrix.npy", M)
load("random-matrix.npy")

# v是一个只有一个维度的向量，所以一个索引就足以获得元素。
v[0]

# M是一个矩阵(二维数组)，所以需要两个索引(行，列)。
M[1,1]

M

M[1]

M[1,:]#第一行

M[:,1]#第一列

M[0,0] = 1
M

#也适用于行和列
M[1,:] = 0
M[:,2] = -1
M

A = array([1,2,3,4,5])
A

A[1:3]

A[1:3] = [-2,-3]
A

A[::]#下限、上限、默认步数

A = array([1,2,3,4,5])
A[-1]#最后一个元素
A[-3:]#最后三个元素

A = array([[n+m*10 for n in range(5)] for m in range(5)]) 
A

#方阵
A[1:4, 1:4]

#渐进，带有指定间隔数
A[::2, ::2]

row_indices = [1, 2, 3]
A[row_indices]

col_indices = [1, 2, -1]
A[row_indices, col_indices]

B = array([n for n in range(5)])
B

row_mask = array([True, False, True, False, False])
B[row_mask]

row_mask = array([1,0,1,0,0], dtype=bool)
B[row_mask]

x = arange(0, 10, 0.5)
x

mask = (5 < x) * (x < 7.5)
mask

x[mask]

indices = where(mask)
indices

x[indices]#这个索引相当于x[mask]的索引。

diag(A)

diag(A,-1)

v2 = arange(-3,3)
v2

row_indices = [1, 3, 5]
v2[row_indices]

v2.take(row_indices)

take([-3, -2, -1, 0, 1, 2], row_indices)

which = [1, 0, 1, 0]
choices = [[-2,-2,-2,-2], [5,5,5,5]]
 
choose(which, choices) # 0th elem of 0 array, 1st elem of 1 array, ...

v1 = arange(0, 5)
v1 * 2

v1 + 2

A * 2

A + 2

A * A

v1 * v1

A.shape, v1.shape

A * v1

dot(A, A)

dot(A, v1)

dot(v1, v1)

M = matrix(A)
v = matrix(v1).T#换位
v

M * M

M * v

v.T * v

v + M*v

shape(data)

#温度柱
mean(data[:,3])

std(data[:,3]), var(data[:,3])

d = arange(0, 10)
d

#求和
sum(d)

#所有元素的乘积
prod(d+1)
#累计总和
cumsum(d)

#累积乘积
cumprod(d+1)
#和diag(A).sum()一样
trace(A)

m = random.rand(3,3)
m

m.max()

#每列最大值 
m.max(axis=0)

#每行最大值 
m.max(axis=1)

A

n, m = A.shape
B = A.reshape((1,n*m))
B

B[0,0:5] = 5
B

A 

B = A.flatten()
B

B[0:5] = 10
B

#A没有改变，因为B是A的副本，不是同一个对象的引用。
A

v = array([1,2,3])
shape(v)

#向量 -> 单列矩阵
v[:, newaxis]

#尺寸
v[:,newaxis].shape

v[newaxis,:].shape

b = array([[5, 6]])
a = array([[5, 6]])
concatenate((a, b), axis=0)

concatenate((a, b), axis=1)

vstack((a,b))

hstack((a,b))

A = array([[1, 2], [3, 4]])
A

#B等同于A
B = A 
#改变B，将影响A
B[0,0] = 10
 
B

A

B = copy(A)
#现在改变B将不再影响A
B[0,0] = -5
B

A

v = array([1,2,3,4])
 
for element in v:
  print(element)

M = array([[1,2], [3,4]])
 
for row in M:
  print("row", row)
  
  for element in row:
    print(element)

for row_idx, row in enumerate(M):
  print("row_idx", row_idx, "row", row)
  
  for col_idx, element in enumerate(row):
    print("col_idx", col_idx, "element", element)
    
    # update the matrix M: square each element
    M[row_idx, col_idx] = element ** 2

#每个元素现在都是列表
M