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numpy

numpy. Numpy objects. >>> import numpy as np >>> np.array([1,2,3]) ‏ array([1, 2, 3]) ‏ >>> np.array([1,2,3.0]) ‏ array([ 1., 2., 3.]) ‏ >>> np.array([1,2,3],np.float64) ‏ array([ 1., 2., 3.]) ‏ >>> np.array([range(3) for x in range(4)],np.float64) ‏ array([[ 0., 1., 2.],

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numpy

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  1. numpy

  2. Numpy objects >>> import numpy as np >>> np.array([1,2,3])‏ array([1, 2, 3])‏ >>> np.array([1,2,3.0])‏ array([ 1., 2., 3.])‏ >>> np.array([1,2,3],np.float64)‏ array([ 1., 2., 3.])‏ >>> np.array([range(3) for x in range(4)],np.float64)‏ array([[ 0., 1., 2.], [ 0., 1., 2.], [ 0., 1., 2.], [ 0., 1., 2.]])‏ >>>

  3. Numpy objects >>> A= np.array([range(3) for x in range(4)],np.float64)‏ >>> np.matrix([range(3) for x in range(4)],np.float64)‏ matrix([[ 0., 1., 2.], [ 0., 1., 2.], [ 0., 1., 2.], [ 0., 1., 2.]])‏ >>> M= np.matrix([range(3) for x in range(4)],np.float64)‏ >>> type(A), type(M)‏ (<type 'numpy.ndarray'>, <class 'numpy.core.defmatrix.matrix'>)‏ >>> np.matrix(range(3),np.float64)‏ matrix([[ 0., 1., 2.]])‏ >>> np.array(range(3),np.float64)‏ array([ 0., 1., 2.])‏ >>> M=np.matrix(range(3),np.float64)‏ >>> A=np.array(range(3),np.float64)‏ >>> A.shape (3,)‏ >>> M.shape (1, 3)‏

  4. Numpy objects >>> M=np.matrix(range(3),np.float64)‏ >>> A=np.array(range(3),np.float64)‏ >>> A.T array([ 0., 1., 2.])‏ >>> M.T matrix([[ 0.], [ 1.], [ 2.]])‏ >>> A=np.array([[1,2],[2,-2]],np.float64)‏ >>> M=np.matrix([[1,2],[2,-2]],np.float64)‏ >>> M.T matrix([[ 1., 2.], [ 2., -2.]])‏ >>> A.T array([[ 1., 2.], [ 2., -2.]])‏ >>> A.I Traceback (most recent call last): File "<stdin>", line 1, in <module> AttributeError: 'numpy.ndarray' object has no attribute 'I' >>> M.I matrix([[ 0.33333333, 0.33333333], [ 0.33333333, -0.16666667]])‏ >>>

  5. Numpy objects >>> M matrix([[ 1., 2.], [ 2., -2.]])‏ >>> M.I matrix([[ 0.33333333, 0.33333333], [ 0.33333333, -0.16666667]])‏ >>>np.linalg.inv(A)‏ array([[ 0.33333333, 0.33333333], [ 0.33333333, -0.16666667]])‏ >>> >>> M2=np.matrix([[1,1],[0,0]],np.float64)‏ >>> A2=np.array([[1,1],[0,0]],np.float64)‏ >>> M*M2 matrix([[ 1., 1.], [ 2., 2.]])‏ >>> A*A2 array([[ 1., 2.], [ 0., -0.]])‏ >>> A2*A array([[ 1., 2.], [ 0., -0.]])‏ >>> M2*M matrix([[ 3., 0.], [ 0., 0.]])‏

  6. Numpy objects >>> A == M matrix([[ True, True], [ True, True]], dtype=bool)‏ >>> Ai=np.linalg.inv(A)‏ >>> np.dot(A,Ai)‏ array([[ 1.00000000e+00, 5.55111512e-17], [ 0.00000000e+00, 1.00000000e+00]])‏ >>> np.dot(Ai,A)‏ array([[ 1.00000000e+00, -1.11022302e-16], [ 0.00000000e+00, 1.00000000e+00]])‏ >>> M*M.I matrix([[ 1.00000000e+00, 5.55111512e-17], [ 0.00000000e+00, 1.00000000e+00]])‏ >>> M.I*M matrix([[ 1.00000000e+00, -1.11022302e-16], [ 0.00000000e+00, 1.00000000e+00]])‏

  7. Numpy objects >>> np.random.uniform()‏ 0.70420105296872415 >>> np.random.uniform(-0.1,0.1)‏ -0.059314492060574403 >>> np.random.uniform(-0.1,0.1,4)‏ array([ 0.06606591, 0.07766084, 0.08635536, 0.08010191])‏ >>> np.random.uniform(-0.1,0.1,(2,2))‏ array([[-0.06448909, 0.07906606], [-0.04752628, -0.02955906]])‏ >>> np.random.normal(-1,1,(3,2))‏ array([[-0.32922971, -0.05700329], [-2.81944081, 0.43708656], [-1.4274894 , -0.61651697]])‏ >>> >>> np.sort([1,5.9,2,-1])‏ array([-1. , 1. , 2. , 5.9])‏ >>> np.argsort([1,5.9,2,-1])‏ array([3, 0, 2, 1])‏ >>>

  8. Numpy objects >>>np.ones((4,4))‏ array([[ 1., 1., 1., 1.], [ 1., 1., 1., 1.], [ 1., 1., 1., 1.], [ 1., 1., 1., 1.]])‏ >>> np.zeros((4,4))‏ array([[ 0., 0., 0., 0.], [ 0., 0., 0., 0.], [ 0., 0., 0., 0.], [ 0., 0., 0., 0.]])‏ >>> A=np.zeros((4,4))‏ >>> for i in range(len(A)): ... A[i][:]=np.random.uniform(-10,10,len(A))‏ ... >>> A array([[-2.74761648, -3.81873152, 8.5612057 , -6.50432488], [ 4.04987279, -9.37231031, -7.96381121, 0.4987925 ], [-5.86088041, 7.90005728, 7.30370647, 8.57564479], [ 9.09765827, 2.85531062, 9.41611209, -8.07463238]])‏ >>> for i in range(len(A)): ... A[i,:]=np.random.uniform(-10,10,len(A))‏ ...

  9. Numpy objects >>> B array([[ 0., 1.], [ 1., 0.]])‏ >>> evals,evecs=np.linalg.eig(B)‏ >>> evals array([ 1., -1.])‏ >>> for i in range(len(B)): ... print evals[i],evecs[i] ... 1.0 [ 0.70710678 -0.70710678] -1.0 [ 0.70710678 0.70710678] >>>

  10. Numpy objects >>> A+A.T array([[ -9.87072296, -8.6819582 , 1.05438839, 0.77621665], [ -8.6819582 , -6.20131579, 12.1133606 , -4.29184743], [ 1.05438839, 12.1133606 , 13.24488407, -7.21060701], [ 0.77621665, -4.29184743, -7.21060701, 19.57503177]])‏ >>> A=A+A.T >>> evals,evecs=np.linalg.eig(A)‏ >>> evals array([-19.38912856, -2.79317213, 27.87492659, 11.05525118])‏

  11. Numpy objects >>> inputs=np.array([[ 1.],[ 2.],[ 3.],[ 4.],[ 5.]])‏ >>> targets=np.array([[ 3.],[ 5.],[ 7.],[ 9.],[ 11.]])‏ >>> np.concatenate((inputs,targets))‏ array([[ 1.], [ 2.], [ 3.], [ 4.], [ 5.], [ 3.], [ 5.], [ 7.], [ 9.], [ 11.]])‏ >>> np.concatenate((inputs,targets),axis=1)‏ array([[ 1., 3.], [ 2., 5.], [ 3., 7.], [ 4., 9.], [ 5., 11.]])‏ >>> it=np.concatenate((inputs,targets),axis=1)‏

  12. Numpy objects >>> print np.sum(it), it.size 50.0 10 >>> print np.mean(it), np.sum(it)/it.size 5.0 5.0 >>> np.sum(it,axis=0), np.sum(it,axis=1)‏ (array([ 15., 35.]), array([ 4., 7., 10., 13., 16.]))‏ >>> len(it), len(it[0])‏ (5, 2)‏ >>> np.mean(it,axis=0),np.mean(it,axis=1)‏ (array([ 3., 7.]), array([ 2. , 3.5, 5. , 6.5, 8. ]))‏ >>>

  13. Numpy objects >>> D=np.zeros((20,3))‏ >>> for i in range(len(D)): ... D[i,:]=np.random.uniform(-10,10,len(D[i]))‏ >>> D.mean(axis=0)‏ array([-1.02909335, 2.77430392, -1.00094332])‏ >>> >>> np.std(D)‏ 5.8341355973553766 >>> np.std(D,axis=0)‏ array([ 6.37529467, 5.64920856, 4.46994818])‏ >>> np.var(D,axis=0)‏ array([ 40.64438211, 31.91355732, 19.98043675])‏ >>> np.sqrt(np.var(D,axis=0))‏ array([ 6.37529467, 5.64920856, 4.46994818])‏ >>>

  14. Numpy objects >>> r=0.1 >>> a=np.array(range(4),np.float)+np.random.uniform(-r,r)‏ >>> b=np.array(range(4),np.float)+np.random.uniform(-r,r) -5 >>> c=np.array(range(4,0,-1),np.float)+np.random.uniform(-r,r) -5 >>> d=np.matrix([np.random.uniform(-r,r) for i in range(4)],np.float)‏ >>> np.cov(a,a)‏ array([[ 1.66666667, 1.66666667], [ 1.66666667, 1.66666667]])‏ >>> np.cov(a,b)‏ array([[ 1.66666667, 1.66666667], [ 1.66666667, 1.66666667]])‏ >>> np.cov(a,c)‏ array([[ 1.66666667, -1.66666667], [-1.66666667, 1.66666667]])‏ >>> np.cov(a,d)‏ array([[ 1.66666667, -0.01641726], [-0.01641726, 0.0033877 ]])‏

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