NumPy is an open source numerical computing extension for Python. This tool can be used to store and process large matrices and is much more efficient than Python's own nested list structure (which can also be used to represent matrices). NumPy (Numeric Python) provides many advanced numerical programming tools, such as: matrixdata type, vector processing, and sophisticated operation libraries. Built for rigorous number crunching. It is mostly used by many large financial companies, as well as core scientific computing organizations such as Lawrence Livermore, and NASA uses it to handle some tasks that were originally done using C++, Fortran or Matlab.
The data type in numpy, ndarray type, is different from array.array in the standard library.
>>> import numpy as np >>> a = np.array([2,3,4]) >>> a array([2, 3, 4]) >>> a.dtype dtype('int64') >>> b = np.array([1.2, 3.5, 5.1]) >>> b.dtype dtype('float64')
>>> b = np.array([(1.5,2,3), (4,5,6)]) >>> b array([[ 1.5, 2. , 3. ], [ 4. , 5. , 6. ]])
>>> c = np.array( [ [1,2], [3,4] ], dtype=complex ) >>> c array([[ 1.+0.j, 2.+0.j], [ 3.+0.j, 4.+0.j]])
>>> np.zeros( (3,4) ) array([[ 0., 0., 0., 0.], [ 0., 0., 0., 0.], [ 0., 0., 0., 0.]]) >>> np.ones( (2,3,4), dtype=np.int16 ) # dtype can also be specified array([[[ 1, 1, 1, 1], [ 1, 1, 1, 1], [ 1, 1, 1, 1]], [[ 1, 1, 1, 1], [ 1, 1, 1, 1], [ 1, 1, 1, 1]]], dtype=int16) >>> np.empty( (2,3) ) # uninitialized, output may vary array([[ 3.73603959e-262, 6.02658058e-154, 6.55490914e-260], [ 5.30498948e-313, 3.14673309e-307, 1.00000000e+000]])
>>> np.arange( 10, 30, 5 ) array([10, 15, 20, 25]) >>> np.arange( 0, 2, 0.3 ) # it accepts float arguments array([ 0. , 0.3, 0.6, 0.9, 1.2, 1.5, 1.8]) >>> from numpy import pi >>> np.linspace( 0, 2, 9 ) # 9 numbers from 0 to 2 array([ 0. , 0.25, 0.5 , 0.75, 1. , 1.25, 1.5 , 1.75, 2. ]) >>> x = np.linspace( 0, 2*pi, 100 ) # useful to evaluate function at lots of points >>> f = np.sin(x)
>>> a = np.array( [20,30,40,50] ) >>> b = np.arange( 4 ) >>> b array([0, 1, 2, 3]) >>> c = a-b >>> c array([20, 29, 38, 47]) >>> b**2 array([0, 1, 4, 9]) >>> 10*np.sin(a) array([ 9.12945251, -9.88031624, 7.4511316 , -2.62374854]) >>> a<35 array([ True, True, False, False], dtype=bool)
In matlab, there are .*,./, etc.
But in numpy, if you use +, -, ×,/, the priority is to perform addition, subtraction, multiplication and division between each point. Method
If two matrices (square matrices) can both perform operations between elements and perform matrix operations, the operations between elements will be performed first.
>>> import numpy as np >>> A = np.arange(10,20) >>> B = np.arange(20,30) >>> A + B array([30, 32, 34, 36, 38, 40, 42, 44, 46, 48]) >>> A * B array([200, 231, 264, 299, 336, 375, 416, 459, 504, 551]) >>> A / B array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) >>> B / A array([2, 1, 1, 1, 1, 1, 1, 1, 1, 1])
If matrix operations need to be performed, Generally, it is matrix multiplication operation
>>> A = np.array([1,1,1,1]) >>> B = np.array([2,2,2,2]) >>> A.reshape(2,2) array([[1, 1], [1, 1]]) >>> B.reshape(2,2) array([[2, 2], [2, 2]]) >>> A * B array([2, 2, 2, 2]) >>> np.dot(A,B) 8 >>> A.dot(B) 8
>>> B = np.arange(3) >>> B array([0, 1, 2]) >>> np.exp(B) array([ 1. , 2.71828183, 7.3890561 ]) >>> np.sqrt(B) array([ 0. , 1. , 1.41421356]) >>> C = np.array([2., -1., 4.]) >>> np.add(B, C) array([ 2., 0., 6.])
>>> a = np.arange(10)**3 >>> a array([ 0, 1, 8, 27, 64, 125, 216, 343, 512, 729]) >>> a[2] 8 >>> a[2:5] array([ 8, 27, 64]) >>> a[:6:2] = -1000 # equivalent to a[0:6:2] = -1000; from start to position 6, exclusive, set every 2nd element to -1000 >>> a array([-1000, 1, -1000, 27, -1000, 125, 216, 343, 512, 729]) >>> a[ : :-1] # reversed a array([ 729, 512, 343, 216, 125, -1000, 27, -1000, 1, -1000]) >>> for i in a: ... print(i**(1/3.)) ... nan 1.0 nan 3.0 nan 5.0 6.0 7.0 8.0 9.0
>>> import numpy as np >>> b = np.arange(16).reshape(4, 4) >>> for row in b: ... print(row) ... [0 1 2 3] [4 5 6 7] [ 8 9 10 11] [12 13 14 15] >>> for node in b.flat: ... print(node) ... 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
>>> a = np.floor(10 * np.random.random((3,4))) >>> a array([[ 6., 5., 1., 5.], [ 5., 5., 8., 9.], [ 5., 5., 9., 7.]]) >>> a.ravel() array([ 6., 5., 1., 5., 5., 5., 8., 9., 5., 5., 9., 7.]) >>> a array([[ 6., 5., 1., 5.], [ 5., 5., 8., 9.], [ 5., 5., 9., 7.]])
The difference between resize and reshape
resize will change the original matrix, but reshape will not
>>> a array([[ 6., 5., 1., 5.], [ 5., 5., 8., 9.], [ 5., 5., 9., 7.]]) >>> a.reshape(2,-1) array([[ 6., 5., 1., 5., 5., 5.], [ 8., 9., 5., 5., 9., 7.]]) >>> a array([[ 6., 5., 1., 5.], [ 5., 5., 8., 9.], [ 5., 5., 9., 7.]]) >>> a.resize(2,6) >>> a array([[ 6., 5., 1., 5., 5., 5.], [ 8., 9., 5., 5., 9., 7.]])
>>> a = np.floor(10*np.random.random((2,2))) >>> a array([[ 8., 8.], [ 0., 0.]]) >>> b = np.floor(10*np.random.random((2,2))) >>> b array([[ 1., 8.], [ 0., 4.]]) >>> np.vstack((a,b)) array([[ 8., 8.], [ 0., 0.], [ 1., 8.], [ 0., 4.]]) >>> np.hstack((a,b)) array([[ 8., 8., 1., 8.], [ 0., 0., 0., 4.]])
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