Numpy

Python

import

import numpy as np

arange

# array arange(include, exclude, step)
np.arange(1, 5)     # [1 2 3 4]
np.arange(1, 15, 2) # [ 1  3  5  7  9 11 13]
np.arange(5)        # [0 1 2 3 4]

linspace

# 在0到2PI之间均匀的生成50个数字
np.linspace(0, 2 * np.pi, 50)

array

tuple1 = (1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
arr1 = np.array(tuple1) # [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
# reshape(row, col)
# [[ 1  2  3  4  5]
#  [ 6  7  8  9 10]]
arr2 = arr1.reshape(2, 5)
# shape
arr2.shape;         # (2,5)
# 各种运算
arr2.max()          # 10
np.max(arr2[1])     # 10
np.min(arr2[0])     # 1
np.max(arr2[1, :3]) # 8 第二行，前3个数中的最大值
np.mean(arr2[0])    # 3.0 第一行平均值
np.sum(arr2[1])     # 40，第二行相加
np.sum(arr2[:,2])   # 11，第三列相加，即 3 + 8
np.sum(arr2, 0)     # [ 7  9 11 13 15] 求各列的和
np.sum(arr2, 1)     # [15 40]   各行的和
# [[0 0 0]
#  [0 0 0]
#  [0 0 0]]
mat_o = np.zeros((3, 3), dtype=np.int32) # 参数2可选，默认float
# [[1 0 0]
#  [0 1 0]
#  [0 0 1]]
mat_i = np.eye(3, dtype=np.int32) # 注意eye只有一个参数，即方阵的阶，如eye(3)代表3阶单位矩阵
# [[1 1 1]
#  [1 1 1]
#  [1 1 1]]
mat_1 = np.ones((3, 3), dtype=np.int32)
# type
type(mat_1) # <type 'numpy.ndarray'>
# size
print mat_1.size;   # 9
# [[1 2 3]
#  [4 5 6]
#  [7 8 9]]
mat = np.array([1,2,3,4,5,6,7,8,9]).reshape((3,3))
print mat[1, 1] # 5，代表第二行第二列，从0开始
print mat[0]    # [1 2 3]
print mat[1]    # [4 5 6]
print mat[2]    # [7 8 9] 
print mat[:1]   # [[1 2 3]]
print mat[1:2]  # [[4 5 6]]
print mat[2:]   # [[7 8 9]]
print mat[1,:2] # [4 5]
# 运算
# [[2 1 1]
#  [1 2 1]
#  [1 1 2]]
print mat_i + mat_1
# 矩阵乘法 np.dot(mat1, mat2)
# [[ 6  6  6]
#  [15 15 15]
#  [24 24 24]]
print np.dot(mat, mat_1)
# [[1 2 3]
#  [4 5 6]
#  [7 8 9]]
print np.dot(mat, mat_i)
# 逐项乘，即 *
# [[1 0 0]
#  [0 5 0]
#  [0 0 9]]
print mat * mat_i
# 逆矩阵
# [[ 1.  0.  0.]
#  [ 0.  1.  0.]
#  [ 0.  0.  1.]]
np.linalg.inv(mat_i)
# 转置矩阵
# [[1 4 7]
#  [2 5 8]
#  [3 6 9]]
mat.transpose()

SymPy，可以输出符号公式的包

import numpy as np
import sympy as sp
a,b,c,d,e,f,g,h,i = sp.symbols('a b c d e f g h i')
mat = np.array([a,b,c,d,e,f,g,h,i]).reshape((3,3))
M = sp.Matrix(mat)
print M         # Matrix([[a, b, c], [d, e, f], [g, h, i]])
print M.det()   # a*e*i - a*f*h - b*d*i + b*f*g + c*d*h - c*e*g

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