10 minutes to xorbits.numpy#
This is a short introduction to xorbits.numpy which is originated from NumPy’s quickstart.
Array Creation#
Popular mechanisms for creating arrays in NumPy are supported in xorbits.numpy.
For example, you can create an array from a regular Python list or tuple using the array
function. The type of the resulting array is deduced from the type of the elements in the sequences.
>>> import xorbits.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')
In addition, creating an array from existing NumPy ndarray is supported.
>>> import numpy as np
>>> import xorbits.numpy as xnp
>>> a = np.arange(6)
>>> b = xnp.array(a)
>>> print(b)
array([0 1 2 3 4 5])
A frequent error consists in calling array with multiple arguments,
rather than providing a single sequence as an argument.
>>> a = np.array(1, 2, 3, 4) # WRONG
Traceback (most recent call last):
...
TypeError: array() takes from 1 to 2 positional arguments but 4 were given
>>> a = np.array([1, 2, 3, 4]) # RIGHT
array transforms sequences of sequences into two-dimensional arrays, sequences of sequences
of sequences into three-dimensional arrays, and so on.
>>> b = np.array([(1.5, 2, 3), (4, 5, 6)])
>>> b
array([[1.5, 2. , 3. ],
[4. , 5. , 6. ]])
The type of the array can also be explicitly specified at creation time:
>>> c = np.array([[1, 2], [3, 4]], dtype=complex)
>>> c
array([[1.+0.j, 2.+0.j],
[3.+0.j, 4.+0.j]])
Often, the elements of an array are originally unknown, but its size is known. Hence, several functions are offered to create arrays with initial placeholder content. These minimize the necessity of growing arrays, an expensive operation.
The function zeros creates an array full of zeros, the function ones creates an array full
of ones, and the function empty creates an array whose initial content is random and depends on the
state of the memory. By default, the dtype of the created array is float64, but it can be
specified via the key word argument dtype.
>>> 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)
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))
array([[3.73603959e-262, 6.02658058e-154, 6.55490914e-260], # may vary
[5.30498948e-313, 3.14673309e-307, 1.00000000e+000]])
To create sequences of numbers, use arange function which is analogous to the Python built-in
range, but returns an array.
>>> 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])
When arange is used with floating point arguments, it is generally not possible to predict the
number of elements obtained, due to the finite floating point precision. For this reason, it is
usually better to use the function linspace that receives as an argument the number of
elements that we want, instead of the step:
>>> from xorbits.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)
However, the way of loading and saving arrays is quite different. Please see io for detailed info. Here’s an example of creating and loading an HDF5 file:
>>> import h5py # if you don't have h5py installed, run "pip install h5py" first
>>> arr = np.random.randn(1000)
>>> with h5py.File('t.hdf5', 'w') as f:
>>> dset = f.create_dataset("t", data=arr)
>>>
>>> a = np.from_hdf5("t.hdf5", dataset="t")
Once an ndarray is created, use to_numpy to convert it to a local NumPy ndarray:
>>> a = np.array([1, 2, 3, 4])
>>> a.to_numpy()
array([1, 2, 3, 4])
Printing Arrays#
Xorbits displays an array in a similar way to NumPy:
the last axis is printed from left to right,
the second-to-last is printed from top to bottom,
the rest are also printed from top to bottom, with each slice separated from the next by an empty line.
One-dimensional arrays are then printed as rows, bidimensionals as matrices and tridimensionals as lists of matrices.
>>> a = np.arange(6) # 1d array
>>> print(a)
[0 1 2 3 4 5]
>>>
>>> b = np.arange(12).reshape(4, 3) # 2d array
>>> print(b)
[[ 0 1 2]
[ 3 4 5]
[ 6 7 8]
[ 9 10 11]]
>>>
>>> c = np.arange(24).reshape(2, 3, 4) # 3d array
>>> print(c)
[[[ 0 1 2 3]
[ 4 5 6 7]
[ 8 9 10 11]]
[[12 13 14 15]
[16 17 18 19]
[20 21 22 23]]]
If an array is too large to be printed, the central part of the array will be automatically skipped and only prints the corners:
>>> print(np.arange(10000))
[ 0 1 2 ... 9997 9998 9999]
>>>
>>> print(np.arange(10000).reshape(100, 100))
[[ 0 1 2 ... 97 98 99]
[ 100 101 102 ... 197 198 199]
[ 200 201 202 ... 297 298 299]
...
[9700 9701 9702 ... 9797 9798 9799]
[9800 9801 9802 ... 9897 9898 9899]
[9900 9901 9902 ... 9997 9998 9999]]
Basic Operations#
Arithmetic operators on arrays apply elementwise. A new array is created and filled with the result.
>>> 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])
Unlike in many matrix languages, the product operator * operates elementwise in
xorbits.numpy arrays. The matrix product can be performed using the @ operator (in
python >=3.5) or the dot function or method:
>>> A = np.array([[1, 1],
... [0, 1]])
>>> B = np.array([[2, 0],
... [3, 4]])
>>> A * B # elementwise product
array([[2, 0],
[0, 4]])
>>> A @ B # matrix product
array([[5, 4],
[3, 4]])
>>> A.dot(B) # another matrix product
array([[5, 4],
[3, 4]])
Some operations, such as += and *=, act in place to modify an existing array rather than
create a new one.
>>> a = np.ones((2, 3), dtype=int)
>>> b = np.random.random((2, 3))
>>> a *= 3
>>> a
array([[3, 3, 3],
[3, 3, 3]])
>>> b += a
>>> b
array([[3.51182162, 3.9504637 , 3.14415961],
[3.94864945, 3.31183145, 3.42332645]])
When operating with arrays of different types, the type of the resulting array corresponds to the more general or precise one (a behavior known as upcasting).
>>> a = np.ones(3, dtype=np.int32)
>>> b = np.linspace(0, np.pi, 3)
>>> b.dtype.name
'float64'
>>> c = a + b
>>> c
array([1. , 2.57079633, 4.14159265])
>>> c.dtype.name
'float64'
>>> d = np.exp(c * 1j)
>>> d
array([ 0.54030231+0.84147098j, -0.84147098+0.54030231j,
-0.54030231-0.84147098j])
>>> d.dtype.name
'complex128'
Many unary operations, such as computing the sum of all the elements in the array, are implemented
as methods of the ndarray class.
>>> a = np.random.random((2, 3))
>>> a
array([[0.82770259, 0.40919914, 0.54959369],
[0.02755911, 0.75351311, 0.53814331]])
>>> a.sum()
3.1057109529998157
>>> a.min()
0.027559113243068367
>>> a.max()
0.8277025938204418
By default, these operations apply to the array as though it were a list of numbers, regardless of
its shape. However, by specifying the axis parameter you can apply an operation along the
specified axis of an array:
>>> b = np.arange(12).reshape(3, 4)
>>> b
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>>
>>> b.sum(axis=0) # sum of each column
array([12, 15, 18, 21])
>>>
>>> b.min(axis=1) # min of each row
array([0, 4, 8])
>>>
>>> b.cumsum(axis=1) # cumulative sum along each row
array([[ 0, 1, 3, 6],
[ 4, 9, 15, 22],
[ 8, 17, 27, 38]])
Universal Functions#
Mathematical functions such as sin, cos, and exp are provided. These are called “universal
functions” (ufunc). These functions operate elementwise on an array, producing an array as
output.
>>> 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.])
Indexing, Slicing and Iterating#
One-dimensional arrays can be indexed, sliced and iterated over, much like lists and other Python sequences.
>>> 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])
>>> # equivalent to a[0:6:2] = 1000;
>>> # from start to position 6, exclusive, set every 2nd element to 1000
>>> a[:6:2] = 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.))
...
9.999999999999998
1.0
9.999999999999998
3.0
9.999999999999998
4.999999999999999
5.999999999999999
6.999999999999999
7.999999999999999
8.999999999999998
Multidimensional arrays can have one index per axis. These indices are given in a tuple separated by commas:
>>> def f(x, y):
... return 10 * x + y
...
>>> b = np.arange(12).reshape(3, 4)
>>> b
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> b[2, 3]
11
>>> b[0:3, 1] # each row in the second column of b
array([1, 5, 9])
>>> b[:, 1] # equivalent to the previous example
array([1, 5, 9])
>>> b[1:3, :] # each column in the second and third row of b
array([[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
When fewer indices are provided than the number of axes, the missing
indices are considered complete slices:
>>> b[-1] # the last row. Equivalent to b[-1, :]
array([ 8, 9, 10, 11])
The expression within brackets in b[i] is treated as an i
followed by as many instances of : as needed to represent the
remaining axes. You can also write this using dots as
b[i, ...].
The dots (...) represent as many colons as needed to produce a
complete indexing tuple. For example, if x is an array with 5
axes, then
x[1, 2, ...]is equivalent tox[1, 2, :, :, :],x[..., 3]tox[:, :, :, :, 3]andx[4, ..., 5, :]tox[4, :, :, 5, :].
>>> c = np.array([[[ 0, 1, 2], # a 3D array (two stacked 2D arrays)
... [ 10, 12, 13]],
... [[100, 101, 102],
... [110, 112, 113]]])
>>> c.shape
(2, 2, 3)
>>> c[1, ...] # same as c[1, :, :] or c[1]
array([[100, 101, 102],
[110, 112, 113]])
>>> c[..., 2] # same as c[:, :, 2]
array([[ 2, 13],
[102, 113]])
Iterating over multidimensional arrays is done with respect to the first axis:
>>> for row in b:
... print(row)
...
[0 1 2 3]
[4 5 6 7]
[ 8 9 10 11]
However, if one wants to perform an operation on each element in the
array, one can use the flat attribute which is an
iterator
over all the elements of the array:
>>> for element in b.flat:
... print(element)
...
0
1
2
3
4
5
6
7
8
9
10
11
Changing the shape of an array#
An array has a shape given by the number of elements along each axis:
>>> a = np.floor(10 * np.random.random((3, 4)))
>>> a
array([[6., 9., 5., 2.],
[4., 9., 8., 9.],
[4., 7., 2., 8.]])
>>> a.shape
(3, 4)
The shape of an array can be changed with various commands. Note that the following three commands all return a modified array, but do not change the original array:
>>> a.ravel() # returns the array, flattened
array([6., 9., 5., 2., 4., 9., 8., 9., 4., 7., 2., 8.])
>>> a.reshape(6, 2) # returns the array with a modified shape
array([[6., 9.],
[5., 2.],
[4., 9.],
[8., 9.],
[4., 7.],
[2., 8.]])
>>> a.T # returns the array, transposed
array([[6., 4., 4.],
[9., 9., 7.],
[5., 8., 2.],
[2., 9., 8.]])
>>> a.T.shape
(4, 3)
>>> a.shape
(3, 4)
The order of the elements in the array resulting from ravel is normally “C-style”, that is, the
rightmost index “changes the fastest”, so the element after a[0, 0] is a[0, 1]. If the
array is reshaped to some other shape, again the array is treated as “C-style”. Normally arrays
are created stored in this order, so ravel will usually not need to copy its argument, but if
the array was made by taking slices of another array or created with unusual options, it may need
to be copied. The functions ravel and reshape can also be instructed, using an optional
argument, to use FORTRAN-style arrays, in which the leftmost index changes the fastest.
If a dimension is given as -1 in a reshaping operation, the other dimensions are automatically
calculated:
>>> a.reshape(3, -1)
array([[6., 9., 5., 2.],
[4., 9., 8., 9.],
[4., 7., 2., 8.]])
Stacking together different arrays#
Several arrays can be stacked together along different axes:
>>> a = np.floor(10 * np.random.random((2, 2)))
>>> a
array([[9., 7.],
[5., 2.]])
>>> b = np.floor(10 * np.random.random((2, 2)))
>>> b
array([[1., 9.],
[5., 1.]])
>>> np.vstack((a, b))
array([[9., 7.],
[5., 2.],
[1., 9.],
[5., 1.]])
>>> np.hstack((a, b))
array([[9., 7., 1., 9.],
[5., 2., 5., 1.]])
The function column_stack stacks 1D arrays as columns into a 2D array. It is equivalent to
hstack only for 2D arrays:
>>> from xorbits.numpy import newaxis
>>> np.column_stack((a, b)) # with 2D arrays
array([[9., 7., 1., 9.],
[5., 2., 5., 1.]])
>>> a = np.array([4., 2.])
>>> b = np.array([3., 8.])
>>> np.column_stack((a, b)) # returns a 2D array
array([[4., 3.],
[2., 8.]])
>>> np.hstack((a, b)) # the result is different
array([4., 2., 3., 8.])
>>> a[:, newaxis] # view `a` as a 2D column vector
array([[4.],
[2.]])
>>> np.column_stack((a[:, newaxis], b[:, newaxis]))
array([[4., 3.],
[2., 8.]])
>>> np.hstack((a[:, newaxis], b[:, newaxis])) # the result is the same
array([[4., 3.],
[2., 8.]])
On the other hand, the function row_stack is equivalent to vstack for any input arrays. In
fact, row_stack is an alias for vstack:
>>> np.column_stack is np.hstack
False
>>> np.row_stack is np.vstack
True
In general, for arrays with more than two dimensions, hstack stacks along their second axes,
vstack stacks along their first axes, and concatenate allows for an optional arguments giving
the number of the axis along which the concatenation should happen.
备注
In complex cases, r_ and c_ are useful for creating arrays by stacking numbers along one axis.
They allow the use of range literals :.
>>> np.r_[1:4, 0, 4]
array([1, 2, 3, 0, 4])
When used with arrays as arguments, r_ and c_ are similar to vstack and hstack in their
default behavior, but allow for an optional argument giving the number of the axis along which to
concatenate.
Splitting one array into several smaller ones#
Using hsplit, you can split an
array along its horizontal axis, either by specifying the number of
equally shaped arrays to return, or by specifying the columns after
which the division should occur:
>>> a = np.floor(10 * np.random.random((2, 12)))
>>> a
array([[6., 7., 6., 9., 0., 5., 4., 0., 6., 8., 5., 2.],
[8., 5., 5., 7., 1., 8., 6., 7., 1., 8., 1., 0.]])
>>> # Split `a` into 3
>>> np.hsplit(a, 3)
[array([[6., 7., 6., 9.],
[8., 5., 5., 7.]]), array([[0., 5., 4., 0.],
[1., 8., 6., 7.]]), array([[6., 8., 5., 2.],
[1., 8., 1., 0.]])]
>>> # Split `a` after the third and the fourth column
>>> np.hsplit(a, (3, 4))
[array([[6., 7., 6.],
[8., 5., 5.]]), array([[9.],
[7.]]), array([[0., 5., 4., 0., 6., 8., 5., 2.],
[1., 8., 6., 7., 1., 8., 1., 0.]])]
vsplit splits along the vertical
axis, and array_split allows
one to specify along which axis to split.