numpy - Arrays (9) (Vector and matrix mathematics)

Vector and matrix mathematics

벡터의 내적(dot product) 계산

>>> a = np.array([[0,1],[2,3]], float) >>> b = np.array([2,3], float) >>> c = np.array([[1,1],[4,0]], float) >>> a array([[ 0.,  1.],        [ 2.,  3.]]) >>> np.dot(b,a) array([  6.,  11.]) >>> np.dot(a,b) array([  3.,  13.]) >>> np.dot(a,c) array([[  4.,   0.],        [ 14.,   2.]]) >>> np.dot(c,a) array([[ 2.,  4.],        [ 0.,  4.]]) >>>

inner product, outer product, cross product 의 계산

>>> a = np.array([1,4,2], float) >>> b = np.array([2,2,1], float) >>> np.outer(a,b) array([[ 2.,  2.,  1.],        [ 8.,  8.,  4.],        [ 4.,  4.,  2.]]) >>> np.inner(a,b) 12.0 >>> np.cross(a,b) array([ 0.,  3., -6.]) >>>

linalg 라는 서브 모듈이 선형대수연산을 위한 내장 루틴. 

>>> a = np.array([[4, 2, 0], [9, 3, 7], [1, 2, 1]], float) >>> a array([[ 4.,  2.,  0.],        [ 9.,  3.,  7.],        [ 1.,  2.,  1.]]) >>> np.linalg.det(a) -48.000000000000028 >>>

eigenvalues(고유값)과 eigenvectors(고유벡터) 조회

>>> vals, vecs = np.linalg.eig(a) >>> vals array([ 8.85591316,  1.9391628 , -2.79507597]) >>> vecs array([[-0.3663565 , -0.54736745,  0.25928158],        [-0.88949768,  0.5640176 , -0.88091903],        [-0.27308752,  0.61828231,  0.39592263]]) >>>

inverse of a matrix(역행렬)

>>> b = np.linalg.inv(a) >>> b array([[ 0.22916667,  0.04166667, -0.29166667],        [ 0.04166667, -0.08333333,  0.58333333],        [-0.3125    ,  0.125     ,  0.125     ]]) >>> np.dot(a,b) array([[  1.00000000e+00,   0.00000000e+00,  -2.22044605e-16],        [  0.00000000e+00,   1.00000000e+00,   0.00000000e+00],        [  0.00000000e+00,   0.00000000e+00,   1.00000000e+00]]) >>>

Singular value decomposition(SVD, 특이값분해)

>>> a = np.array([[1, 3, 4], [5, 2, 3]], float) >>> U, s, Vh = np.linalg.svd(a) >>> U array([[-0.6113829 , -0.79133492],        [-0.79133492,  0.6113829 ]]) >>> s array([ 7.46791327,  2.86884495]) >>>Vh array([[-0.61169129, -0.45753324, -0.64536587],        [ 0.78971838, -0.40129005, -0.46401635],        [-0.046676  , -0.79349205,  0.60678804]])   >>>