【Python】【numpy-汇总10】numpy.linalg函数的示例代码_python中linalg函数

1.np.linalg所有函数

2.使用示例

det计算方阵的行列式

#det(ndarray)	计算方阵的矩阵列式
a = np.array([[1,6,7],
              [2,5,3],
              [3,4,1]])
ret = np.linalg.det(a) #-14

eig计算方阵的本征值和本征向量

a = np.array([[1,2,3],
              [6,5,4],
              [7,6,5]])
ret = np.linalg.eig(a) #本征值,本征向量
print(ret[0]) #[  1.27284161e+01  -1.72841615e+00   1.90757877e-16]
print(ret[1]) #[[ 0.29245036  0.78800111  0.40824829]
              # [ 0.60875015 -0.45826232 -0.81649658]
              # [ 0.73749308 -0.41115678  0.40824829]]

inv 计算方阵的逆

a = np.array([[1,2,3],
              [4,5,6],
              [7,8,9]])
ai = np.linalg.inv(a)
print(ai)
print(ai.shape)
'''
[[ -4.50359963e+15   9.00719925e+15  -4.50359963e+15]
 [  9.00719925e+15  -1.80143985e+16   9.00719925e+15]
 [ -4.50359963e+15   9.00719925e+15  -4.50359963e+15]]
(3, 3)
'''

pinv 计算方阵的Moore-Penrose伪逆

api = np.linalg.pinv(a)
print(api)
print(api.shape)
'''
[[ -6.38888889e-01  -1.66666667e-01   3.05555556e-01]
 [ -5.55555556e-02   3.46944695e-17   5.55555556e-02]
 [  5.27777778e-01   1.66666667e-01  -1.94444444e-01]]
(3, 3)
'''

qr计算qr分解 

a = np.array([[1,2,3],
              [4,5,6],
              [7,8,9]])
aqr = np.linalg.qr(a)  
print(aqr)
'''
(array([[-0.12309149,  0.90453403,  0.40824829],
       [-0.49236596,  0.30151134, -0.81649658],
       [-0.86164044, -0.30151134,  0.40824829]]), 
array([[ -8.12403840e+00,  -9.60113630e+00,  -1.10782342e+01],
       [  0.00000000e+00,   9.04534034e-01,   1.80906807e+00],
       [  0.00000000e+00,   0.00000000e+00,  -7.58790979e-16]]))
'''

svd计算奇异值分解svd

asvd = np.linalg.svd(a)
print(asvd)
'''
(array([[-0.21483724,  0.88723069,  0.40824829],
       [-0.52058739,  0.24964395, -0.81649658],
       [-0.82633754, -0.38794278,  0.40824829]]), 
 array([  1.68481034e+01,   1.06836951e+00,   4.41842475e-16]), 
 array([[-0.47967118, -0.57236779, -0.66506441],
       [-0.77669099, -0.07568647,  0.62531805],
       [-0.40824829,  0.81649658, -0.40824829]]))
'''

solve解线性方程组Ax = b，其中A为方阵 

a = np.array([[1,2,3],
              [4,5,6],
              [7,8,9]])
b = np.array([0,2,6])
ret = np.linalg.solve(a,b)
print(ret)
'''
(array([[-0.21483724,  0.88723069,  0.40824829],
       [-0.52058739,  0.24964395, -0.81649658],
       [-0.82633754, -0.38794278,  0.40824829]]), 
array([  1.68481034e+01,   1.06836951e+00,   4.41842475e-16]), 
array([[-0.47967118, -0.57236779, -0.66506441],
       [-0.77669099, -0.07568647,  0.62531805],
       [-0.40824829,  0.81649658, -0.40824829]]))
[ -9.00719925e+15   1.80143985e+16  -9.00719925e+15]
'''

lstsq计算Ax=b的最小二乘解 

a = np.array([[1,2,3],
              [4,5,6],
              [7,8,9]])
b = np.array([0,2,6])
ret = np.linalg.lstsq(a,b)
print('lstsq:\n',ret)
'''
lstsq:
 (array([ 1.5       ,  0.33333333, -0.83333333]), 
 array([], dtype=float64), 2, 
 array([  1.68481034e+01,   1.06836951e+00,   4.41842475e-16]))
'''

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