>>> print('hello')
>>> clear
>>> # Intro to Numpy
>>> # Numpy provides multi-dim arrays and mathematical ops
>>> a = [1, 2, 3]
>>> b = [2, 4, 6]
>>> a + b
[1, 2, 3, 2, 4, 6]
>>> result = []
>>> for val_a, val_b in zip(a, b):
...     result.append(val_a + val_b)
...
>>> result
[3, 6, 9]
>>> [val_a + val_b for val_a, val_b in zip(a,b)]
[3, 6, 9]
>>> import numpy as np
>>> np_a = np.array(a)
>>> np_b = np.array(b)
>>> np_a + np_b
array([3, 6, 9])
>>> np_a.dtype
dtype('int64')
>>> np_A
>>> np_a
array([1, 2, 3])
>>> np_a[0] = 1.3456
>>> np_a
array([1, 2, 3])
>>> np_a[0] = 13.3456
>>> np_a
array([13,  2,  3])
>>> np.dtype
numpy.dtype
>>> np.dtype()
>>> np_a.dtype()
>>> np_a.dtype
dtype('int64')
>>> np_a
array([13,  2,  3])
>>> np_a = np.array([1, 2, 3], dtype='float')
>>> np_a.dtype
dtype('float64')
>>> np_a[0] = 13.3456
>>> np_a
array([13.3456,  2.    ,  3.    ])
>>> # Ufunc
>>> np.sin(np_a)
array([0.70273137, 0.90929743, 0.14112001])
>>> np.cos(np_a)
array([ 0.71145528, -0.41614684, -0.9899925 ])
>>> type(np_a)
numpy.ndarray
>>> lol = [[1,2,3], [4,5,6]]
>>> type(lol)
list
>>> np_array = np.array(lol)
>>> lol
[[1, 2, 3], [4, 5, 6]]
>>> np_array
array([[1, 2, 3],
       [4, 5, 6]])
>>> lol[1]
[4, 5, 6]
>>> lol[1][1]
5
>>> lol[1,1]
>>> np_array[1,1]
5
>>> np_array[1][1]
5
>>> np_array = np.array(lol)
>>> np_array.ndim
2
>>> np_array[1]
array([4, 5, 6])
>>> np_array[0]
array([1, 2, 3])
>>> np_array[0, :]
array([1, 2, 3])
>>> np_array[1, :]
array([4, 5, 6])
>>> clear
>>> a = np.array([1, 2, 3])
>>> a
array([1, 2, 3])
>>> type(a)
numpy.ndarray
>>> a = [1,2,3]
>>> np.array(a)
array([1, 2, 3])
>>> type(a)
list
>>> a = np.array([1, 2, 3])
>>> type(a)
numpy.ndarray
>>> a.dtype
dtype('int64')
>>> a = np.array([1.0, 2.0, 3.0])
>>> a
array([1., 2., 3.])
>>> a.dtype
dtype('float64')
>>> type(1.0)
float
>>> type(1)
int
>>> type(1.)
float
>>> a = np.array([1,2,3])
>>> a
array([1, 2, 3])
>>> b = np.array([1., 2., 3.])
>>> b
array([1., 2., 3.])
>>> c = np.array([1, 2.0, 3])
>>> c
array([1., 2., 3.])
>>> c.dtype
dtype('float64')
>>> # Numeric Tower
>>> # Hierarcy
>>> 1 + 1
2
>>> 1 + 2.0
3.0
>>> # Bool -> Int -> Float -> complex
>>> a = np.array([0,1,2,3])
>>> a
array([0, 1, 2, 3])
>>> a.dtype
dtype('int64')
>>> a.dim
>>> a.ndim
1
>>> a.shape
(4,)
>>> a
array([0, 1, 2, 3])
>>> a.itemsize
8
>>> a.dtype
dtype('int64')
>>> # 8bit = 1 byte
>>> # 64bit -> 8bytes
>>> a.nbytes
32
>>> # 4 items each 8 bytes = 32 bytes
>>> # slide 5
>>> a
array([0, 1, 2, 3])
>>> range(4)
range(0, 4)
>>> list(range(4))
[0, 1, 2, 3]
>>> np.array(range(4))
array([0, 1, 2, 3])
>>> np.arange(4)
array([0, 1, 2, 3])
>>> np.arange(10, 2)
array([], dtype=int64)
>>> np.arange(10, step=2)
array([0, 2, 4, 6, 8])
>>> np.arange(start=10,end=20, step=2)
>>> np.arange(start=10, stop=20, step=2)
array([10, 12, 14, 16, 18])
>>> np.arange(5)
array([0, 1, 2, 3, 4])
>>> np.arange(5.)
array([0., 1., 2., 3., 4.])
>>> # slide 6
>>> a = np.array([1,2,3,4])
>>> b = np.array([2,3,4,5])
>>> a
array([1, 2, 3, 4])
>>> b
array([2, 3, 4, 5])
>>> a + b
array([3, 5, 7, 9])
>>> a * b
array([ 2,  6, 12, 20])
>>> a ** b
array([   1,    8,   81, 1024])
>>> x = np.array(11.0)
>>> x
array(11.)
>>> x = np.arange(11.0)
>>> x
array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.])
>>> # python is zero based index; "up to but not including" the stop value
>>> x
array([ 0.,  1.,  2.,  3.,  4.,  5.,  6.,  7.,  8.,  9., 10.])
>>> np.pi
3.141592653589793
>>> np.e
2.718281828459045
>>> c = (2 * np.pi) / 10
>>> c
0.6283185307179586
>>> x * c
array([0.        , 0.62831853, 1.25663706, 1.88495559, 2.51327412,
       3.14159265, 3.76991118, 4.39822972, 5.02654825, 5.65486678,
       6.28318531])
>>> # augmentation operation
>>> # x = x * c
>>> x *= c  # same as above
>>> x
array([0.        , 0.62831853, 1.25663706, 1.88495559, 2.51327412,
       3.14159265, 3.76991118, 4.39822972, 5.02654825, 5.65486678,
       6.28318531])
>>> np.sin(x)
array([ 0.00000000e+00,  5.87785252e-01,  9.51056516e-01,  9.51056516e-01,
        5.87785252e-01,  1.22464680e-16, -5.87785252e-01, -9.51056516e-01,
       -9.51056516e-01, -5.87785252e-01, -2.44929360e-16])
>>> a = np.array([1,2,3])
>>> a.dtype
dtype('int64')
>>> b = a.astype('float')
>>> a.dtype
dtype('int64')
>>> b.dtype
dtype('float64')
>>> c = np.array([1, 2, 3], dtype='float')
>>> c.dtype
dtype('float64')
>>> c = np.array([1, 2, 3], dtype=np.int32)
>>> x
array([0.        , 0.62831853, 1.25663706, 1.88495559, 2.51327412,
       3.14159265, 3.76991118, 4.39822972, 5.02654825, 5.65486678,
       6.28318531])
>>> dc.dtype
>>> c.dtype
dtype('int32')
>>> np.int32
numpy.int32
>>> np.int64
numpy.int64
>>> np.float32
numpy.float32
>>> np.float64
numpy.float64
>>> c = np.array([1, 2, 3], dtype='float')
>>> c = np.array([1, 2, 3], dtype='float32')
>>> c.dtype
dtype('float32')
>>> c = np.array([1, 2, 3], dtype=np.float64)
>>> c.dtype
dtype('float64')
>>> clear
>>> a = np.array(25)
>>> a
array(25)
>>> a = np.arange(25)
>>> a
array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
       17, 18, 19, 20, 21, 22, 23, 24])
>>> a.ndim
1
>>> a = np.arange(24)
>>> a
array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
       17, 18, 19, 20, 21, 22, 23])
>>> a.ndim
1
>>> a.shape
(24,)
>>> b = a.reshape(6,4)
>>> b
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11],
       [12, 13, 14, 15],
       [16, 17, 18, 19],
       [20, 21, 22, 23]])
>>> b.ndim
2
>>> d.shape
>>> b.shape
(6, 4)
>>> a = np.aragne(5)
>>> a = np.arange(5)
>>> a
array([0, 1, 2, 3, 4])
>>> a.shape
(5,)
>>> a.reshape(1,5)
array([[0, 1, 2, 3, 4]])
>>> a
array([0, 1, 2, 3, 4])
>>> a.shape
(5,)
>>> a = a.reshape(1,5)
>>> a.shape
(1, 5)
>>> a.ndim
2
>>> a
array([[0, 1, 2, 3, 4]])
>>> a = np.arange(5)
>>> a
array([0, 1, 2, 3, 4])
>>> a.ndim
1
>>> a.sum(axis=0)
10
>>> a.sum(axis=1)
>>> a.shape
(5,)
>>> a = a.reshape(1,5)
>>> a.sum(axis=0)
array([0, 1, 2, 3, 4])
>>> a.sum(axis=1)
array([10])
>>> a
array([[0, 1, 2, 3, 4]])
>>> a.shape
(1, 5)
>>> clear
>>> a = np.arange(1.0, 3.0, 0.5)
>>> a
array([1. , 1.5, 2. , 2.5])
>>> a * np.pi
array([3.14159265, 4.71238898, 6.28318531, 7.85398163])
>>> a * np.pi * 1e8
array([3.14159265e+08, 4.71238898e+08, 6.28318531e+08, 7.85398163e+08])
>>> a * np.pi * 1e-6
array([3.14159265e-06, 4.71238898e-06, 6.28318531e-06, 7.85398163e-06])
>>> np.get_printoptions()
{'edgeitems': 3,
 'threshold': 1000,
 'floatmode': 'maxprec',
 'precision': 8,
 'suppress': False,
 'linewidth': 75,
 'nanstr': 'nan',
 'infstr': 'inf',
 'sign': '-',
 'formatter': None,
 'legacy': False}
>>> np.set_options(precision=2)
>>> np.set_printoptions(precision=2)
>>> a
array([1. , 1.5, 2. , 2.5])
>>> a * np.pi
array([3.14, 4.71, 6.28, 7.85])
>>> a * np.pi * 1e8
array([3.14e+08, 4.71e+08, 6.28e+08, 7.85e+08])
>>> a * np.pi * 1e-6
array([3.14e-06, 4.71e-06, 6.28e-06, 7.85e-06])
>>> np.set_printoptions(supress=True)
>>> np.set_printoptions(suppress=True)
>>> a * np.pi * 1e-6
array([0., 0., 0., 0.])
>>> np.set_printoptions(suppress=False)
>>> np.set_printoptions(precision=8)
>>> a * np.pi
array([3.14159265, 4.71238898, 6.28318531, 7.85398163])
>>> a * np.pi * 1e-6
array([3.14159265e-06, 4.71238898e-06, 6.28318531e-06, 7.85398163e-06])
>>> a
array([1. , 1.5, 2. , 2.5])
>>> a * np.pi * 1e-6
array([3.14159265e-06, 4.71238898e-06, 6.28318531e-06, 7.85398163e-06])
>>> with np.printoptions(precision=2):
...     a * np.pi
...
>>> with np.printoptions(precision=2):
...     print(a * np.pi)
...
>>> a * np.pi
array([3.14159265, 4.71238898, 6.28318531, 7.85398163])
>>> np.get_printoptions()
{'edgeitems': 3,
 'threshold': 1000,
 'floatmode': 'maxprec',
 'precision': 8,
 'suppress': False,
 'linewidth': 75,
 'nanstr': 'nan',
 'infstr': 'inf',
 'sign': '-',
 'formatter': None,
 'legacy': False}
>>> d = {'a': 1, 'b': 2, 'c':3 }
>>> np.array(d)
array({'a': 1, 'b': 2, 'c': 3}, dtype=object)
>>> a = np.array(d)
>>> a
array({'a': 1, 'b': 2, 'c': 3}, dtype=object)
>>> a.shape
()
>>> a[0]
>>> a
array({'a': 1, 'b': 2, 'c': 3}, dtype=object)
>>> a[0]
>>> a = np.array(d.keys())
>>> a
array(dict_keys(['a', 'b', 'c']), dtype=object)
>>> a = np.array(d.values())
>>> a
array(dict_values([1, 2, 3]), dtype=object)
>>> a = np.array(list(d.values()))
>>> a
array([1, 2, 3])
>>> # slide 11
>>> a = np.array([10, 11, 12, 13, 14])
>>> a
array([10, 11, 12, 13, 14])
>>> #      0,  1,   2,  3,  4
>>> a[4]
14
>>> a[2]
12
>>> a
array([10, 11, 12, 13, 14])
>>> #     -5, -4, -3, -2, -1
>>> a[-1]
14
>>> a[-2]
13
>>> a[-3]
12
>>> a
array([10, 11, 12, 13, 14])
>>> clear
>>> a
array([10, 11, 12, 13, 14])
>>> a[3]
13
>>> a[-2]
13
>>> a[-1]
14
>>> a[4]
14
>>> a
array([10, 11, 12, 13, 14])
>>> a[::-1]
array([14, 13, 12, 11, 10])
>>> clear
>>> a
array([10, 11, 12, 13, 14])
>>> a[::-1]
array([14, 13, 12, 11, 10])
>>> a[1:3]
array([11, 12])
>>> a[1:-2]
array([11, 12])
>>> a[-4:3]
array([11, 12])
>>> a[-3:4]
array([12, 13])
>>> a[-3:-4]
array([], dtype=int64)
>>> a[-3:-4:-1]
array([12])
>>> a
array([10, 11, 12, 13, 14])
>>> a[2:]
array([12, 13, 14])
>>> a
array([10, 11, 12, 13, 14])
>>> a[::2]
array([10, 12, 14])
>>> a = np.arange(5)
>>> a
array([0, 1, 2, 3, 4])
>>> a[-2:]
array([3, 4])
>>> a[-2:] = [-42, -42]
>>> a
array([  0,   1,   2, -42, -42])
>>> a[-2:] = [1, 2, 3]
>>> a
array([  0,   1,   2, -42, -42])
>>> a[-2:] = 99
>>> a
array([ 0,  1,  2, 99, 99])
>>> a = np.arange(25)
>>> a
array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
       17, 18, 19, 20, 21, 22, 23, 24])
>>> a = np.arange(25).reshape(5,5)
>>> a
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14],
       [15, 16, 17, 18, 19],
       [20, 21, 22, 23, 24]])
>>> clear
>>> # orange
>>> a
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14],
       [15, 16, 17, 18, 19],
       [20, 21, 22, 23, 24]])
>>> a.shape
(5, 5)
>>> a[4]
array([20, 21, 22, 23, 24])
>>> a[-1]
array([20, 21, 22, 23, 24])
>>> a[-1, :]
array([20, 21, 22, 23, 24])
>>> a[4, :]
array([20, 21, 22, 23, 24])
>>> a.ndim
2
>>> clear
>>> a[-1, :]
array([20, 21, 22, 23, 24])
>>> a = np.arange(10)
>>> a[-1]
9
>>> a = np.arange(25).reshape(5,5)
>>> a[-1]
array([20, 21, 22, 23, 24])
>>> # red
>>> clear
>>> a
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14],
       [15, 16, 17, 18, 19],
       [20, 21, 22, 23, 24]])
>>> a[  :  , ::2  ]
array([[ 0,  2,  4],
       [ 5,  7,  9],
       [10, 12, 14],
       [15, 17, 19],
       [20, 22, 24]])
>>> a[  :  , 1::2  ]
array([[ 1,  3],
       [ 6,  8],
       [11, 13],
       [16, 18],
       [21, 23]])
>>> a[  :  , 1:4:2  ]
array([[ 1,  3],
       [ 6,  8],
       [11, 13],
       [16, 18],
       [21, 23]])
>>> a[  :  , 1::2  ]
array([[ 1,  3],
       [ 6,  8],
       [11, 13],
       [16, 18],
       [21, 23]])
>>> a[ ::2  ,    ]
array([[ 0,  1,  2,  3,  4],
       [10, 11, 12, 13, 14],
       [20, 21, 22, 23, 24]])
>>> a[ 1::2  ,    ]
array([[ 5,  6,  7,  8,  9],
       [15, 16, 17, 18, 19]])
>>> a[ 1::2  , ::2   ]
array([[ 5,  7,  9],
       [15, 17, 19]])
>>> a[ 1::2  , :-1:2   ]
array([[ 5,  7],
       [15, 17]])
>>> a[ 1::2  , :4:2   ]
array([[ 5,  7],
       [15, 17]])
>>> a[ 1::2  , 0:4:2   ]
array([[ 5,  7],
       [15, 17]])
>>> clear
>>> # Slide 15
>>> a = np.array([1,2,3,4])
>>> a
array([1, 2, 3, 4])
>>> b = a[2:4]
>>> b
array([3, 4])
>>> b[0] = 99
>>> b
array([99,  4])
>>> a
array([ 1,  2, 99,  4])
>>> np.shares_memory(a, b)
True
>>> c = a[2:4].copy()
>>> c
array([99,  4])
>>> a = np.array([1,2,3,4])
>>> c = a[2:4].copy()
>>> c
array([3, 4])
>>> a
array([1, 2, 3, 4])
>>> c[0] == 9
False
>>> c[0] = 99
>>> c
array([99,  4])
>>> a
array([1, 2, 3, 4])
>>> np.shares_memory(a, c)
False
>>> # facny indexing will always create a copy
>>> a
array([1, 2, 3, 4])
>>> a>3
array([False, False, False,  True])
>>> a[a>3]
array([4])
>>> a
array([1, 2, 3, 4])
>>> a[[1,2]]
array([2, 3])
>>> d = a[[1,2]]
>>> d
array([2, 3])
>>> a
array([1, 2, 3, 4])
>>> np.shares_memory(a, d)
False
>>> e = a[a>3]
>>> e
array([4])
>>> np.shares_memory(a, e)
False
>>> #slide 16
>>> a  = np.arange(0,80,10)
>>> a
array([ 0, 10, 20, 30, 40, 50, 60, 70])
>>> indices = [1, 2, -3]
>>> a[indices]
array([10, 20, 50])
>>> a[::2]
array([ 0, 20, 40, 60])
>>> a[1::2]
array([10, 30, 50, 70])
>>> a[[1, 2, -3]]
array([10, 20, 50])
>>> a
array([ 0, 10, 20, 30, 40, 50, 60, 70])
>>> a[[1, 2, -3]] = 99
>>> a
array([ 0, 99, 99, 30, 40, 99, 60, 70])
>>> # fancy indexing (1) indices as a list
>>> mask = np.array([1,0,1,0], dtype=bool)
>>> mask
array([ True, False,  True, False])
>>> a[mask]
>>> mask = np.array([1,0,1,0,1], dtype=bool)
>>> mask
array([ True, False,  True, False,  True])
>>> a[mask]
>>> a
array([ 0, 99, 99, 30, 40, 99, 60, 70])
>>> mask = np.array([1,0,1,0,1,0,0,0], dtype=bool)
>>> a[mask]
array([ 0, 99, 40])
>>> clear
>>> a
array([ 0, 99, 99, 30, 40, 99, 60, 70])
>>> mask
array([ True, False,  True, False,  True, False, False, False])
>>> a[mask]
array([ 0, 99, 40])
>>> mask = np.array([1,0,1,0,1,0,0,0], dtype=bool)
>>> mask
array([ True, False,  True, False,  True, False, False, False])
>>> a
array([ 0, 99, 99, 30, 40, 99, 60, 70])
>>> a > 20
array([False,  True,  True,  True,  True,  True,  True,  True])
>>> mask = a > 20
>>> a[ask]
>>> a[mask]
array([99, 99, 30, 40, 99, 60, 70])
>>> a[a>20]
array([99, 99, 30, 40, 99, 60, 70])
>>> a
array([ 0, 99, 99, 30, 40, 99, 60, 70])
>>> a > 20
array([False,  True,  True,  True,  True,  True,  True,  True])
>>> mask = _
>>> mask
array([False,  True,  True,  True,  True,  True,  True,  True])
>>> a[mask]
array([99, 99, 30, 40, 99, 60, 70])
>>> a[ a > 20 ]
array([99, 99, 30, 40, 99, 60, 70])
>>> 5
5
>>> _
5
>>> _ + 5
10
>>> _ + 5
15
>>> _ + 5
20
>>> _ + 5
25
>>> a > 20
array([False,  True,  True,  True,  True,  True,  True,  True])
>>> mask = _
>>> mask = a > 20
>>> a
array([ 0, 99, 99, 30, 40, 99, 60, 70])
>>> a == 0
array([ True, False, False, False, False, False, False, False])
>>> a
array([ 0, 99, 99, 30, 40, 99, 60, 70])
>>> b = np.array([0])
>>> a == b
array([ True, False, False, False, False, False, False, False])
>>> a
array([ 0, 99, 99, 30, 40, 99, 60, 70])
>>> b
array([0])
>>> a == 0
array([ True, False, False, False, False, False, False, False])
>>> a
array([ 0, 99, 99, 30, 40, 99, 60, 70])
>>> a > 5-
>>> a > 50
array([False,  True,  True, False, False,  True,  True,  True])
>>> 20 < a < 50
>>> (20 < a) & (a< 50)
array([False, False, False,  True,  True, False, False, False])
>>> (20 < a) and (a< 50)
>>> a = np.arange(6).reshape(1,6) + np.arange(60, step=10)
>>> a
array([[ 0, 11, 22, 33, 44, 55]])
>>> np.arange(6)
array([0, 1, 2, 3, 4, 5])
>>> np.arange(6) + np.arange(0,60,step=10)
array([ 0, 11, 22, 33, 44, 55])
>>> np.arange(6).reshape(6,1) + np.arange(0,60,step=10)
array([[ 0, 10, 20, 30, 40, 50],
       [ 1, 11, 21, 31, 41, 51],
       [ 2, 12, 22, 32, 42, 52],
       [ 3, 13, 23, 33, 43, 53],
       [ 4, 14, 24, 34, 44, 54],
       [ 5, 15, 25, 35, 45, 55]])
>>> np.arange(6) + np.arange(0,60,step=10).reshape(-1,1)
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 = np.arange(6) + np.arange(0,60,step=10).reshape(-1,1)
>>> 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]])
>>> rows = [0, 1, 2, 3, 4]
>>> cols = [1, 2, 3, 4, 5]
>>> list(zip(row, cols))
>>> list(zip(rows, cols))
[(0, 1), (1, 2), (2, 3), (3, 4), (4, 5)]
>>> 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]])
>>> row
>>> rows
[0, 1, 2, 3, 4]
>>> cols
[1, 2, 3, 4, 5]
>>> list(zip(rows, cols))
[(0, 1), (1, 2), (2, 3), (3, 4), (4, 5)]
>>> zz
>>> 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]])
>>> clear
>>> rows
[0, 1, 2, 3, 4]
>>> cols
[1, 2, 3, 4, 5]
>>> list(zip(rows, cols))
[(0, 1), (1, 2), (2, 3), (3, 4), (4, 5)]
>>> 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]])
>>> np.diagonal(a)
array([ 0, 11, 22, 33, 44, 55])
>>> np.diagonal(a, offset=1)
array([ 1, 12, 23, 34, 45])
>>> #  modulo
>>> 25%5
0
>>> 25$4
>>> 25%4
1
>>> divmod(25,4)
(6, 1)
>>> a[rows, cols]
array([ 1, 12, 23, 34, 45])
>>> clear
>>> # slide 18 review
>>> a = np.arange(25).reshape(5,5)
>>> a
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14],
       [15, 16, 17, 18, 19],
       [20, 21, 22, 23, 24]])
>>> # Blue left to right (10, 6, 3, 19)
>>> rows = [2, 1, 0, 3]
>>> cols = [0,1, 3,4]
>>> a[row, cols]
>>> a[rows, cols]
array([10,  6,  3, 19])
>>> a%3
array([[0, 1, 2, 0, 1],
       [2, 0, 1, 2, 0],
       [1, 2, 0, 1, 2],
       [0, 1, 2, 0, 1],
       [2, 0, 1, 2, 0]])
>>> mask = a%3 == 0
>>> a[mask]
array([ 0,  3,  6,  9, 12, 15, 18, 21, 24])
>>> a[a%3==0]
array([ 0,  3,  6,  9, 12, 15, 18, 21, 24])
>>> np.where(a%3==0)
(array([0, 0, 1, 1, 2, 3, 3, 4, 4]), array([0, 3, 1, 4, 2, 0, 3, 1, 4]))
>>> np.where(a%3==0, 1, 0)
array([[1, 0, 0, 1, 0],
       [0, 1, 0, 0, 1],
       [0, 0, 1, 0, 0],
       [1, 0, 0, 1, 0],
       [0, 1, 0, 0, 1]])
>>> np.where(a%3==0, 99, 13)
array([[99, 13, 13, 99, 13],
       [13, 99, 13, 13, 99],
       [13, 13, 99, 13, 13],
       [99, 13, 13, 99, 13],
       [13, 99, 13, 13, 99]])
>>> a[a%3==0]
array([ 0,  3,  6,  9, 12, 15, 18, 21, 24])
>>> a
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14],
       [15, 16, 17, 18, 19],
       [20, 21, 22, 23, 24]])
>>> # Blue left to right (10, 6, 3, 19)
>>> a in [10, 6, 3, 19]
>>> a in np.array([10, 6, 3, 19])
False
>>> a
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14],
       [15, 16, 17, 18, 19],
       [20, 21, 22, 23, 24]])
>>> a
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14],
       [15, 16, 17, 18, 19],
       [20, 21, 22, 23, 24]])
>>> a == 10
array([[False, False, False, False, False],
       [False, False, False, False, False],
       [ True, False, False, False, False],
       [False, False, False, False, False],
       [False, False, False, False, False]])
>>> np.any(a == [10, 6, 9])
False
>>> a
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14],
       [15, 16, 17, 18, 19],
       [20, 21, 22, 23, 24]])
>>> (a==9) | (a==10)
array([[False, False, False, False, False],
       [False, False, False, False,  True],
       [ True, False, False, False, False],
       [False, False, False, False, False],
       [False, False, False, False, False]])
>>> # Blue left to right (10, 6, 3, 19)
>>> a in [10, 6, 3, 19]
>>> (a==10) | (a==6)
array([[False, False, False, False, False],
       [False,  True, False, False, False],
       [ True, False, False, False, False],
       [False, False, False, False, False],
       [False, False, False, False, False]])
>>> a
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14],
       [15, 16, 17, 18, 19],
       [20, 21, 22, 23, 24]])
>>> a.__contains__
<method-wrapper '__contains__' of numpy.ndarray object at 0x7f92c799bab0>
>>> a.__contains__()
>>> a.__contains__(10)
True
>>> a.__contains__((10,6))
False
>>> a
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14],
       [15, 16, 17, 18, 19],
       [20, 21, 22, 23, 24]])
>>> (a==10) | (a==6)
array([[False, False, False, False, False],
       [False,  True, False, False, False],
       [ True, False, False, False, False],
       [False, False, False, False, False],
       [False, False, False, False, False]])
>>> np.any(a[:, 0] == 10)
True
>>> np.searchsorted>
>>> np.searchsorted?
>>> a.searchsorted(10)
>>> np.searchsorted(a,10)
>>> np.searchsorted(a,np.array([10]))
>>> a
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14],
       [15, 16, 17, 18, 19],
       [20, 21, 22, 23, 24]])
>>> b=a.flatten()
>>> b
array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
       17, 18, 19, 20, 21, 22, 23, 24])
>>> b.searchsorted([3,5,7])
array([3, 5, 7])
>>> b[b.searchsorted([3,5,7])]
array([3, 5, 7])
>>> b[b.searchsorted([3,5,7])] == [3, 5, 7]
array([ True,  True,  True])
>>> a = np.arange(24).reshape(6,4)
>>> clear
>>> a
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11],
       [12, 13, 14, 15],
       [16, 17, 18, 19],
       [20, 21, 22, 23]])
>>> a.sum()
276
>>> np.sum(a)
276
>>> a.sum(axis=0)
array([60, 66, 72, 78])
>>> a.sum(axis=1)
array([ 6, 22, 38, 54, 70, 86])
>>> a.shape
(6, 4)
>>> # the axis that you specify will "disappear" in the reduction
>>> a.sum(axis=0).shape
(4,)
>>> a.sum(axis=1).shape
(6,)
>>> a = np.array([1, 2, np.nan, 4])
>>> a.sum()
nan
>>> a.mean()
nan
>>> np.nansum(a)
7.0
>>> np.nanmean(a)
2.3333333333333335
>>> (1+2+4) / 3
2.3333333333333335
>>> (1+2+4) / 4
1.75
>>> a
array([ 1.,  2., nan,  4.])
>>> a.sum()
nan
>>> a.nansum()
>>> np.nansum(a)
7.0
>>> clear
>>> # slide 29
>>> a = np.array([[2,3],[0,1]])
>>> a
array([[2, 3],
       [0, 1]])
>>> a.min()
0
>>> a.min(axis=1)
array([2, 0])
>>> a.min(axis=0)
array([0, 1])
>>> a.argmax()
1
>>> a.flatten()
array([2, 3, 0, 1])
>>> np.unravel_index(a.argmax(), a.shape)
(0, 1)
>>> a
array([[2, 3],
       [0, 1]])
>>> a
array([[2, 3],
       [0, 1]])
>>> a = np.arange(-2, 2) **2
>>> # slide 30
>>> a
array([4, 1, 0, 1])
>>> mask = a %2 ==0
>>> mask
array([ True, False,  True, False])
>>> a.where(mask)
>>> np.where(mask)
(array([0, 2]),)
>>> a
array([4, 1, 0, 1])
>>> mask
array([ True, False,  True, False])
>>> clear
>>> mask
array([ True, False,  True, False])
>>> np.where(mask)
(array([0, 2]),)
>>> a
array([4, 1, 0, 1])
>>> a = np.array([[2,3],[0,1]])
>>> a
array([[2, 3],
       [0, 1]])
>>> np.where(a<2)
(array([1, 1]), array([0, 1]))
>>> a = np.arange(25).reshap(5,5)
>>> a = np.arange(25).reshape(5,5)
>>> a
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14],
       [15, 16, 17, 18, 19],
       [20, 21, 22, 23, 24]])
>>> np.where(a%5==0)
(array([0, 1, 2, 3, 4]), array([0, 0, 0, 0, 0]))
>>> np.where(a%5==0, 1, 0)
array([[1, 0, 0, 0, 0],
       [1, 0, 0, 0, 0],
       [1, 0, 0, 0, 0],
       [1, 0, 0, 0, 0],
       [1, 0, 0, 0, 0]])
>>> a = np.array([[1,2,3],[4,5,6]])
>>> a
array([[1, 2, 3],
       [4, 5, 6]])
>>> a.mean(axis=0)
array([2.5, 3.5, 4.5])
>>> a.mean(axis=1)
array([2., 5.])
>>> a.std(axis=1)
array([0.81649658, 0.81649658])
>>> a.var(axis=1)
array([0.66666667, 0.66666667])
>>> a.std(axis=1) ** 2
array([0.66666667, 0.66666667])
>>> a.var?
>>> a = np.arange(-15, 15).reshape(5, 6) ** 2
>>> a
array([[225, 196, 169, 144, 121, 100],
       [ 81,  64,  49,  36,  25,  16],
       [  9,   4,   1,   0,   1,   4],
       [  9,  16,  25,  36,  49,  64],
       [ 81, 100, 121, 144, 169, 196]])
>>> clear
>>> a
array([[225, 196, 169, 144, 121, 100],
       [ 81,  64,  49,  36,  25,  16],
       [  9,   4,   1,   0,   1,   4],
       [  9,  16,  25,  36,  49,  64],
       [ 81, 100, 121, 144, 169, 196]])
>>> a.shape
(5, 6)
>>> a.max(axis=1)
array([225,  81,   9,  64, 196])
>>> a.max(axis=0).shape
(6,)
>>> a.max(axis=1).shape
(5,)
>>> a.mean(axis=0)
array([81., 76., 73., 72., 73., 76.])
>>> # option 1
>>> np.argmin(a)
15
>>> a.flatten()
array([225, 196, 169, 144, 121, 100,  81,  64,  49,  36,  25,  16,   9,
         4,   1,   0,   1,   4,   9,  16,  25,  36,  49,  64,  81, 100,
       121, 144, 169, 196])
>>> np.unravel_index(a.argmin(), a.shape)
(2, 3)
>>> a
array([[225, 196, 169, 144, 121, 100],
       [ 81,  64,  49,  36,  25,  16],
       [  9,   4,   1,   0,   1,   4],
       [  9,  16,  25,  36,  49,  64],
       [ 81, 100, 121, 144, 169, 196]])
>>> # option 2
>>> np.where(a == 0)
(array([2]), array([3]))
>>> np.where(a == np.min())
>>> np.where(a == a.min())
(array([2]), array([3]))
>>> a
array([[225, 196, 169, 144, 121, 100],
       [ 81,  64,  49,  36,  25,  16],
       [  9,   4,   1,   0,   1,   4],
       [  9,  16,  25,  36,  49,  64],
       [ 81, 100, 121, 144, 169, 196]])
>>> a.min(axis=1)
array([100,  16,   0,   9,  81])
>>> a.min(axis=1).argmin()
2
>>> a.min(axis=0).argmin()
3
>>> a[0,0] = 0
>>> a
array([[  0, 196, 169, 144, 121, 100],
       [ 81,  64,  49,  36,  25,  16],
       [  9,   4,   1,   0,   1,   4],
       [  9,  16,  25,  36,  49,  64],
       [ 81, 100, 121, 144, 169, 196]])
>>> np.unravel_index(a.argmin(), a.shape)
(0, 0)
>>> np.where(a == a.min())
(array([0, 2]), array([0, 3]))
>>> a.min(axis=0).argmin()
0
>>> a.min(axis=1).argmin()
0
>>> # slide 37
>>> a = np.array([0, 10, 20, 30])
>>> b = np.array([0, 1, 2])
>>> a.shape
(4,)
>>> b.shape
(3,)
>>> b.reshape(1,3)
array([[0, 1, 2]])
>>> b[np.newaxis, :]
array([[0, 1, 2]])
>>> a + b
>>> a.shape
(4,)
>>> b.shape
(3,)
>>> b = b[np.newaxis, :]
>>> b.shape
(1, 3)
>>> a + b
>>> b = b[:, np.newaxis]
>>> a
array([ 0, 10, 20, 30])
>>> b
array([[[0, 1, 2]]])
>>> a+b
>>> b = np.array([0, 1, 2])
>>> b = b[:, np.newaxis]
>>> a + b
array([[ 0, 10, 20, 30],
       [ 1, 11, 21, 31],
       [ 2, 12, 22, 32]])
>>> a
array([ 0, 10, 20, 30])
>>> b
array([[0],
       [1],
       [2]])
>>> a+b
array([[ 0, 10, 20, 30],
       [ 1, 11, 21, 31],
       [ 2, 12, 22, 32]])
>>> c = a+b
>>> c.shape
(3, 4)
>>> a.shape
(4,)
>>> b.shape
(3, 1)
>>> a = np.array([0, 10, 20, 30])
>>> b = np.array([0, 1, 2])
>>> y = a[np.newaxis, :] + b
>>> y = a[:, np.newaxis] + b
>>> y
array([[ 0,  1,  2],
       [10, 11, 12],
       [20, 21, 22],
       [30, 31, 32]])
>>> a[:, np.newaxis]
array([[ 0],
       [10],
       [20],
       [30]])
>>> a
array([ 0, 10, 20, 30])
>>> ls
>>> %history -pof ipython_out.txt