5  Numpy

import numpy as np

a=np.array([np.arange(6)]*6)+np.arange(0,51,10).reshape(6,1)
a

array([[ 0,  1,  2,  3,  4,  5],
       [10, 11, 12, 13, 14, 15],
       [20, 21, 22, 23, 24, 25],
       [30, 31, 32, 33, 34, 35],
       [40, 41, 42, 43, 44, 45],
       [50, 51, 52, 53, 54, 55]])

a[0,3:5]

array([3, 4])

a[4:,4:]

array([[44, 45],
       [54, 55]])

a[0:,2]

array([ 2, 12, 22, 32, 42, 52])

a[0:,2:3]

array([[ 2],
       [12],
       [22],
       [32],
       [42],
       [52]])

a[0:,2]=[1,2,3,4,5,6]
a

array([[ 0,  1,  1,  3,  4,  5],
       [10, 11,  2, 13, 14, 15],
       [20, 21,  3, 23, 24, 25],
       [30, 31,  4, 33, 34, 35],
       [40, 41,  5, 43, 44, 45],
       [50, 51,  6, 53, 54, 55]])

a[2::2,0:6:2]

array([[20,  3, 24],
       [40,  5, 44]])

# Operations on Arrays
# Numpy aggregates

# Exercise 4
# F=9/5C+32

c=np.arange(20,31)
c*9/5+32

array([68. , 69.8, 71.6, 73.4, 75.2, 77. , 78.8, 80.6, 82.4, 84.2, 86. ])

# Exercise 5
np.random.seed(1)
Z=np.random.rand(5)
print(Z,(Z-Z.min())/(Z.max()-Z.min()),sep="\n")

[4.17022005e-01 7.20324493e-01 1.14374817e-04 3.02332573e-01
 1.46755891e-01]
[0.57886944 1.         0.         0.41962504 0.20360935]

# Exercise 6
Z=np.random.uniform(0,10,10)
np.floor(Z)

array([6., 4., 5., 1., 1., 8., 9., 3., 6., 8.])

np.ceil(Z)-1

array([6., 4., 5., 1., 1., 8., 9., 3., 6., 8.])

Z-Z%1

array([6., 4., 5., 1., 1., 8., 9., 3., 6., 8.])

# Exercise 7
x=np.zeros((6,6))
y=np.arange(0,6)

x+y

array([[0., 1., 2., 3., 4., 5.],
       [0., 1., 2., 3., 4., 5.],
       [0., 1., 2., 3., 4., 5.],
       [0., 1., 2., 3., 4., 5.],
       [0., 1., 2., 3., 4., 5.],
       [0., 1., 2., 3., 4., 5.]])

x+y[:,np.newaxis]

array([[0., 0., 0., 0., 0., 0.],
       [1., 1., 1., 1., 1., 1.],
       [2., 2., 2., 2., 2., 2.],
       [3., 3., 3., 3., 3., 3.],
       [4., 4., 4., 4., 4., 4.],
       [5., 5., 5., 5., 5., 5.]])

x+y.reshape(6,1)

array([[0., 0., 0., 0., 0., 0.],
       [1., 1., 1., 1., 1., 1.],
       [2., 2., 2., 2., 2., 2.],
       [3., 3., 3., 3., 3., 3.],
       [4., 4., 4., 4., 4., 4.],
       [5., 5., 5., 5., 5., 5.]])

# Exercise 9
np.random.seed(123)
mat = np.random.randn(6, 4); mat

array([[-1.0856306 ,  0.99734545,  0.2829785 , -1.50629471],
       [-0.57860025,  1.65143654, -2.42667924, -0.42891263],
       [ 1.26593626, -0.8667404 , -0.67888615, -0.09470897],
       [ 1.49138963, -0.638902  , -0.44398196, -0.43435128],
       [ 2.20593008,  2.18678609,  1.0040539 ,  0.3861864 ],
       [ 0.73736858,  1.49073203, -0.93583387,  1.17582904]])

mat=np.concatenate([mat,np.exp(mat[:,0])[:,np.newaxis]],axis=1)
mat

array([[-1.0856306 ,  0.99734545,  0.2829785 , -1.50629471,  0.33768877],
       [-0.57860025,  1.65143654, -2.42667924, -0.42891263,  0.56068263],
       [ 1.26593626, -0.8667404 , -0.67888615, -0.09470897,  3.54641154],
       [ 1.49138963, -0.638902  , -0.44398196, -0.43435128,  4.44326571],
       [ 2.20593008,  2.18678609,  1.0040539 ,  0.3861864 ,  9.07869158],
       [ 0.73736858,  1.49073203, -0.93583387,  1.17582904,  2.09042747]])

mat=mat+[1,-1,1,-1,1]; mat

array([[-8.56306033e-02, -2.65455342e-03,  1.28297850e+00,
        -2.50629471e+00,  1.33768877e+00],
       [ 4.21399748e-01,  6.51436537e-01, -1.42667924e+00,
        -1.42891263e+00,  1.56068263e+00],
       [ 2.26593626e+00, -1.86674040e+00,  3.21113848e-01,
        -1.09470897e+00,  4.54641154e+00],
       [ 2.49138963e+00, -1.63890200e+00,  5.56018040e-01,
        -1.43435128e+00,  5.44326571e+00],
       [ 3.20593008e+00,  1.18678609e+00,  2.00405390e+00,
        -6.13813601e-01,  1.00786916e+01],
       [ 1.73736858e+00,  4.90732028e-01,  6.41661316e-02,
         1.75829045e-01,  3.09042747e+00]])

mat=mat*np.array([1/10,1/10,1/10,10,10,10]).reshape(6,1)
mat

array([[-8.56306033e-03, -2.65455342e-04,  1.28297850e-01,
        -2.50629471e-01,  1.33768877e-01],
       [ 4.21399748e-02,  6.51436537e-02, -1.42667924e-01,
        -1.42891263e-01,  1.56068263e-01],
       [ 2.26593626e-01, -1.86674040e-01,  3.21113848e-02,
        -1.09470897e-01,  4.54641154e-01],
       [ 2.49138963e+01, -1.63890200e+01,  5.56018040e+00,
        -1.43435128e+01,  5.44326571e+01],
       [ 3.20593008e+01,  1.18678609e+01,  2.00405390e+01,
        -6.13813601e+00,  1.00786916e+02],
       [ 1.73736858e+01,  4.90732028e+00,  6.41661316e-01,
         1.75829045e+00,  3.09042747e+01]])

np.median(mat,axis=0)

array([ 8.80013969,  0.0324391 ,  0.38497958, -0.19676037, 15.67945792])

np.percentile(mat,70,axis=0)

array([21.14379101,  2.48623197,  3.10092086, -0.12618108, 42.66846589])

np.sort(mat[2,:])[::-1]

array([ 0.45464115,  0.22659363,  0.03211138, -0.1094709 , -0.18667404])

np.argsort(mat[2,:])[::-1]

array([4, 0, 2, 3, 1])

np.sum(np.where(np.exp(mat)>3,1,0),axis=1)

array([0, 0, 0, 3, 4, 4])

# or
np.sum(np.exp(mat)>3,axis=1)

array([0, 0, 0, 3, 4, 4])

np.nonzero(mat>np.mean(mat,axis=0))

(array([0, 1, 1, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5]),
 array([3, 1, 3, 3, 0, 2, 4, 0, 1, 2, 4, 0, 1, 3]))