Using numpy¶
[1]:
import numpy as np
NDArray¶
shape
dtype
[2]:
x = np.arange(12).reshape(3,4)
[3]:
x
[3]:
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
[4]:
x.shape
[4]:
(3, 4)
[5]:
x.dtype
[5]:
dtype('int64')
Indexing and slices¶
Views and copies
[6]:
x[0]
[6]:
array([0, 1, 2, 3])
[7]:
x[0, :]
[7]:
array([0, 1, 2, 3])
[8]:
x[:, 1:3]
[8]:
array([[ 1, 2],
[ 5, 6],
[ 9, 10]])
[9]:
y = x[:]
[10]:
y
[10]:
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
[11]:
y[1] = np.ones(4)
[12]:
y
[12]:
array([[ 0, 1, 2, 3],
[ 1, 1, 1, 1],
[ 8, 9, 10, 11]])
[13]:
x
[13]:
array([[ 0, 1, 2, 3],
[ 1, 1, 1, 1],
[ 8, 9, 10, 11]])
Matrix multiplication¶
Row vectors, column vectors and 1d arrays
Changing shape - reshape, newaxis, ravel, squeeze, keepdims
[14]:
x1 = np.arange(5)
x1.shape
[14]:
(5,)
[15]:
x2 = x1.reshape(-1,1)
x2.shape
[15]:
(5, 1)
[16]:
x1 @ x1.T
[16]:
30
[17]:
x2 @ x2.T
[17]:
array([[ 0, 0, 0, 0, 0],
[ 0, 1, 2, 3, 4],
[ 0, 2, 4, 6, 8],
[ 0, 3, 6, 9, 12],
[ 0, 4, 8, 12, 16]])
Conditional replacement with where¶
[18]:
x
[18]:
array([[ 0, 1, 2, 3],
[ 1, 1, 1, 1],
[ 8, 9, 10, 11]])
[19]:
np.where(x % 2 == 0, 0, 1)
[19]:
array([[0, 1, 0, 1],
[1, 1, 1, 1],
[0, 1, 0, 1]])
Array creating functions¶
[20]:
np.zeros((2,3))
[20]:
array([[0., 0., 0.],
[0., 0., 0.]])
[21]:
np.ones((2,3))
[21]:
array([[1., 1., 1.],
[1., 1., 1.]])
[22]:
np.fromfunction(lambda i, j: i*3+j, (2, 3))
[22]:
array([[0., 1., 2.],
[3., 4., 5.]])
Reductions (margins)¶
[23]:
x
[23]:
array([[ 0, 1, 2, 3],
[ 1, 1, 1, 1],
[ 8, 9, 10, 11]])
[24]:
x.sum()
[24]:
48
[25]:
x.sum(axis=0)
[25]:
array([ 9, 11, 13, 15])
[26]:
x.sum(axis=1)
[26]:
array([ 6, 4, 38])
Broadcasting¶
[27]:
x.shape
[27]:
(3, 4)
[28]:
x.sum(axis=0).shape
[28]:
(4,)
[29]:
x / x.sum(axis=0)
[29]:
array([[0. , 0.09090909, 0.15384615, 0.2 ],
[0.11111111, 0.09090909, 0.07692308, 0.06666667],
[0.88888889, 0.81818182, 0.76923077, 0.73333333]])
[30]:
x.sum(axis=1).shape
[30]:
(3,)
[31]:
x.sum(axis=1, keepdims=True).shape
[31]:
(3, 1)
[32]:
x / x.sum(axis=1, keepdims=True)
[32]:
array([[0. , 0.16666667, 0.33333333, 0.5 ],
[0.25 , 0.25 , 0.25 , 0.25 ],
[0.21052632, 0.23684211, 0.26315789, 0.28947368]])
[33]:
x / x.sum(axis=1)[:, None]
[33]:
array([[0. , 0.16666667, 0.33333333, 0.5 ],
[0.25 , 0.25 , 0.25 , 0.25 ],
[0.21052632, 0.23684211, 0.26315789, 0.28947368]])
[34]:
x / x.sum(axis=1)[:, np.newaxis]
[34]:
array([[0. , 0.16666667, 0.33333333, 0.5 ],
[0.25 , 0.25 , 0.25 , 0.25 ],
[0.21052632, 0.23684211, 0.26315789, 0.28947368]])
Universal functions (ufunc)¶
[35]:
np.sqrt(x)
[35]:
array([[0. , 1. , 1.41421356, 1.73205081],
[1. , 1. , 1. , 1. ],
[2.82842712, 3. , 3.16227766, 3.31662479]])
Einstein summation notation¶
[36]:
a = np.array([[1,2], [3,4]])
b = np.array([[3,4], [5,6], [7,8]])
[37]:
a
[37]:
array([[1, 2],
[3, 4]])
[38]:
b
[38]:
array([[3, 4],
[5, 6],
[7, 8]])
[39]:
m = np.zeros((a.shape[0], b.shape[0]))
for i, u in enumerate(a):
for j, v in enumerate(b):
m[i, j] = u @ v
m
[39]:
array([[11., 17., 23.],
[25., 39., 53.]])
[40]:
np.einsum('in,jn -> ij', a, b)
[40]:
array([[11, 17, 23],
[25, 39, 53]])
Random moudle (c.f. Scipy)¶
[41]:
np.random.poisson(3, (2,3))
[41]:
array([[2, 4, 2],
[4, 5, 2]])
[42]:
np.random.normal(0, 1, (2,3))
[42]:
array([[ 0.30178899, -0.2008874 , 0.9557239 ],
[ 0.35686771, 0.56554302, -0.42485798]])
[43]:
np.random.permutation(10)
[43]:
array([2, 8, 9, 1, 3, 7, 4, 5, 6, 0])
[44]:
np.random.choice(list('abc'), (4,5))
[44]:
array([['b', 'b', 'a', 'c', 'a'],
['b', 'a', 'b', 'c', 'c'],
['c', 'c', 'c', 'b', 'a'],
['c', 'b', 'c', 'a', 'b']], dtype='<U1')
Linear algebra submodule (c.f. Scipy)¶
[45]:
x
[45]:
array([[ 0, 1, 2, 3],
[ 1, 1, 1, 1],
[ 8, 9, 10, 11]])
[46]:
np.linalg.svd(x)
[46]:
(array([[-0.16753774, -0.97815111, -0.12309149],
[-0.10163439, 0.14132757, -0.98473193],
[-0.98061285, 0.15246943, 0.12309149]]),
array([1.95072080e+01, 1.86248100e+00, 3.47460824e-16]),
array([[-0.40736415, -0.46622191, -0.52507967, -0.58393743],
[ 0.73079029, 0.28746675, -0.15585679, -0.59918034],
[-0.10532429, -0.26019684, 0.83636654, -0.47084542],
[-0.53750051, 0.79517143, 0.02215866, -0.27982958]]))
[47]:
np.linalg.lstsq(x, np.arange(3), rcond=None)
[47]:
(array([ 0.21818182, 0.11818182, 0.01818182, -0.08181818]),
array([], dtype=float64),
2,
array([1.95072080e+01, 1.86248100e+00, 2.73318015e-16]))
Masked array¶
[48]:
a = np.arange(20).reshape((4,5))
a
[48]:
array([[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14],
[15, 16, 17, 18, 19]])
[49]:
mask = np.ma.make_mask(a % 2 == 0)
mask
[49]:
array([[ True, False, True, False, True],
[False, True, False, True, False],
[ True, False, True, False, True],
[False, True, False, True, False]])
[50]:
a = np.where(a % 2 != 0, np.nan, a)
[51]:
a
[51]:
array([[ 0., nan, 2., nan, 4.],
[nan, 6., nan, 8., nan],
[10., nan, 12., nan, 14.],
[nan, 16., nan, 18., nan]])
[52]:
np.sum(a)
[52]:
nan
[53]:
np.sum(a[mask])
[53]:
90.0
Memory mapping¶
When you are working with arrays that are too large to fit in memory, you can use memmap to map an array on disk.
[54]:
fp = np.memmap('foo.dat', dtype=np.float64, mode='w+', shape=(10,10))
[55]:
fp[:] = np.arange(100).reshape((10,10))
[56]:
fp
[56]:
memmap([[ 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., 25., 26., 27., 28., 29.],
[30., 31., 32., 33., 34., 35., 36., 37., 38., 39.],
[40., 41., 42., 43., 44., 45., 46., 47., 48., 49.],
[50., 51., 52., 53., 54., 55., 56., 57., 58., 59.],
[60., 61., 62., 63., 64., 65., 66., 67., 68., 69.],
[70., 71., 72., 73., 74., 75., 76., 77., 78., 79.],
[80., 81., 82., 83., 84., 85., 86., 87., 88., 89.],
[90., 91., 92., 93., 94., 95., 96., 97., 98., 99.]])
[57]:
del fp
[58]:
fp1 = np.memmap('foo.dat', dtype=np.float64, shape=(10,10))
[59]:
fp1[:5, :5]
[59]:
memmap([[ 0., 1., 2., 3., 4.],
[10., 11., 12., 13., 14.],
[20., 21., 22., 23., 24.],
[30., 31., 32., 33., 34.],
[40., 41., 42., 43., 44.]])
[60]:
fp2 = np.memmap('foo.dat', dtype=np.float64, offset=75*8, shape=(5,5))
[61]:
fp2
[61]:
memmap([[75., 76., 77., 78., 79.],
[80., 81., 82., 83., 84.],
[85., 86., 87., 88., 89.],
[90., 91., 92., 93., 94.],
[95., 96., 97., 98., 99.]])
[ ]: