The ndarray
is the underlying container of numerical data. It can be thought of as micropython’s own array
object, but has a great number of extra features starting with how it can be initialised, which operations can be done on it, and which functions can accept it as an argument. One important property of an ndarray
is that it is also a proper micropython
iterable.
The ndarray
consists of a short header, and a pointer that holds the data. The pointer always points to a contiguous segment in memory (numpy
is more flexible in this regard), and the header tells the interpreter, how the data from this segment is to be read out, and what the bytes mean. Some operations, e.g., reshape
, are fast, because they do not operate on the data, they work on the header, and therefore, only a couple of bytes are manipulated, even if there are a million data entries. A more detailed exposition of how operators are implemented can be found in the section titled Programming ulab.
Since the ndarray
is a binary container, it is also compact, meaning that it takes only a couple of bytes of extra RAM in addition to what is required for storing the numbers themselves. ndarray
s are also type-aware, i.e., one can save RAM by specifying a data type, and using the smallest reasonable one. Five such types are defined, namely uint8
, int8
, which occupy a single byte of memory per datum, uint16
, and int16
, which occupy two bytes per datum, and float
, which occupies four or eight bytes per datum. The precision/size of the float
type depends on the definition of mp_float_t
. Some platforms, e.g., the PYBD, implement double
s, but some, e.g., the pyboard.v.11, do not. You can find out, what type of float your particular platform implements by looking at the output of the .itemsize class property, or looking at the exact dtype
, when you print out an array.
In addition to the five above-mentioned numerical types, it is also possible to define Boolean arrays, which can be used in the indexing of data. However, Boolean arrays are really nothing but arrays of type uint8
with an extra flag.
On the following pages, we will see how one can work with ndarray
s. Those familiar with numpy
should find that the nomenclature and naming conventions of numpy
are adhered to as closely as possible. We will point out the few differences, where necessary.
For the sake of comparison, in addition to the ulab
code snippets, sometimes the equivalent numpy
code is also presented. You can find out, where the snippet is supposed to run by looking at its first line, the header of the code block.
A concise summary of a couple of the properties of an ndarray
can be printed out by calling the ndinfo
function. In addition to finding out what the shape and strides of the array array, we also get the itemsize
, as well as the type. An interesting piece of information is the data pointer, which tells us, what the address of the data segment of the ndarray
is. We will see the significance of this in the section Slicing and indexing.
Note that this function simply prints some information, but does not return anything. If you need to get a handle of the data contained in the printout, you should call the dedicated shape
, strides
, or itemsize
functions directly.
# code to be run in micropython
from ulab import numpy as np
a = np.array(range(5), dtype=np.float)
b = np.array(range(25), dtype=np.uint8).reshape((5, 5))
np.ndinfo(a)
print('\n')
np.ndinfo(b)
class: ndarray shape: (5,) strides: (8,) itemsize: 8 data pointer: 0x7f8f6fa2e240 type: float
class: ndarray shape: (5, 5) strides: (5, 1) itemsize: 1 data pointer: 0x7f8f6fa2e2e0 type: uint8
A new array can be created by passing either a standard micropython iterable, or another ndarray
into the constructor.
If the iterable is one-dimensional, i.e., one whose elements are numbers, then a row vector will be created and returned. If the iterable is two-dimensional, i.e., one whose elements are again iterables, a matrix will be created. If the lengths of the iterables are not consistent, a ValueError
will be raised. Iterables of different types can be mixed in the initialisation function.
If the dtype
keyword with the possible uint8/int8/uint16/int16/float
values is supplied, the new ndarray
will have that type, otherwise, it assumes float
as default.
# code to be run in micropython
from ulab import numpy as np
a = [1, 2, 3, 4, 5, 6, 7, 8]
b = np.array(a)
print("a:\t", a)
print("b:\t", b)
# a two-dimensional array with mixed-type initialisers
c = np.array([range(5), range(20, 25, 1), [44, 55, 66, 77, 88]], dtype=np.uint8)
print("\nc:\t", c)
# and now we throw an exception
d = np.array([range(5), range(10), [44, 55, 66, 77, 88]], dtype=np.uint8)
print("\nd:\t", d)
a: [1, 2, 3, 4, 5, 6, 7, 8] b: array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float64)
- c: array([[0, 1, 2, 3, 4],
[20, 21, 22, 23, 24], [44, 55, 66, 77, 88]], dtype=uint8)
- Traceback (most recent call last):
File "/dev/shm/micropython.py", line 15, in <module>
ValueError: iterables are not of the same length
An ndarray
can be initialised by supplying another array. This statement is almost trivial, since ndarray
s are iterables themselves, though it should be pointed out that initialising through arrays is a bit faster. This statement is especially true, if the dtype
s of the source and output arrays are the same, because then the contents can simply be copied without further ado. While type conversion is also possible, it will always be slower than straight copying.
# code to be run in micropython
from ulab import numpy as np
a = [1, 2, 3, 4, 5, 6, 7, 8]
b = np.array(a)
c = np.array(b)
d = np.array(b, dtype=np.uint8)
print("a:\t", a)
print("\nb:\t", b)
print("\nc:\t", c)
print("\nd:\t", d)
a: [1, 2, 3, 4, 5, 6, 7, 8]
b: array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float64)
c: array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float64)
d: array([1, 2, 3, 4, 5, 6, 7, 8], dtype=uint8)
Note that the default type of the ndarray
is float
. Hence, if the array is initialised from another array, type conversion will always take place, except, when the output type is specifically supplied. I.e.,
# code to be run in micropython
from ulab import numpy as np
a = np.array(range(5), dtype=np.uint8)
b = np.array(a)
print("a:\t", a)
print("\nb:\t", b)
a: array([0, 1, 2, 3, 4], dtype=uint8)
b: array([0.0, 1.0, 2.0, 3.0, 4.0], dtype=float64)
will iterate over the elements in a
, since in the assignment b = np.array(a)
, no output type was given, therefore, float
was assumed. On the other hand,
# code to be run in micropython
from ulab import numpy as np
a = np.array(range(5), dtype=np.uint8)
b = np.array(a, dtype=np.uint8)
print("a:\t", a)
print("\nb:\t", b)
a: array([0, 1, 2, 3, 4], dtype=uint8)
b: array([0, 1, 2, 3, 4], dtype=uint8)
will simply copy the content of a
into b
without any iteration, and will, therefore, be faster. Keep this in mind, whenever the output type, or performance is important.
There are nine functions that can be used for initialising an array.
- numpy.arange
- numpy.concatenate
- numpy.eye
- numpy.frombuffer
- numpy.full
- numpy.linspace
- numpy.logspace
- numpy.ones
- numpy.zeros
numpy
: https://numpy.org/doc/stable/reference/generated/numpy.arange.html
The function returns a one-dimensional array with evenly spaced values. Takes 3 positional arguments (two are optional), and the dtype
keyword argument.
# code to be run in micropython
from ulab import numpy as np
print(np.arange(10))
print(np.arange(2, 10))
print(np.arange(2, 10, 3))
print(np.arange(2, 10, 3, dtype=np.float))
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=int16) array([2, 3, 4, 5, 6, 7, 8, 9], dtype=int16) array([2, 5, 8], dtype=int16) array([2.0, 5.0, 8.0], dtype=float64)
numpy
: https://numpy.org/doc/stable/reference/generated/numpy.concatenate.html
The function joins a sequence of arrays, if they are compatible in shape, i.e., if all shapes except the one along the joining axis are equal.
# code to be run in micropython
from ulab import numpy as np
a = np.array(range(25), dtype=np.uint8).reshape((5, 5))
b = np.array(range(15), dtype=np.uint8).reshape((3, 5))
c = np.concatenate((a, b), axis=0)
print(c)
- 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], [0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13, 14]], dtype=uint8)
WARNING: numpy
accepts arbitrary dtype
s in the sequence of arrays, in ulab
the dtype
s must be identical. If you want to concatenate different types, you have to convert all arrays to the same type first. Here b
is of float
type, so it cannot directly be concatenated to a
. However, if we cast the dtype
of b
, the concatenation works:
# code to be run in micropython
from ulab import numpy as np
a = np.array(range(25), dtype=np.uint8).reshape((5, 5))
b = np.array(range(15), dtype=np.float).reshape((5, 3))
d = np.array(b+1, dtype=np.uint8)
print('a: ', a)
print('='*20 + '\nd: ', d)
c = np.concatenate((d, a), axis=1)
print('='*20 + '\nc: ', c)
- 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]], dtype=uint8)
==================== d: array([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12], [13, 14, 15]], dtype=uint8) ==================== c: array([[1, 2, 3, 0, 1, 2, 3, 4], [4, 5, 6, 5, 6, 7, 8, 9], [7, 8, 9, 10, 11, 12, 13, 14], [10, 11, 12, 15, 16, 17, 18, 19], [13, 14, 15, 20, 21, 22, 23, 24]], dtype=uint8)
numpy
: https://docs.scipy.org/doc/numpy/reference/generated/numpy.eye.html
Another special array method is the eye
function, whose call signature is
eye(N, M, k=0, dtype=float)
where N
(M
) specify the dimensions of the matrix (if only N
is supplied, then we get a square matrix, otherwise one with M
rows, and N
columns), and k
is the shift of the ones (the main diagonal corresponds to k=0
). Here are a couple of examples.
# code to be run in micropython
from ulab import numpy as np
print(np.eye(5))
- array([[1.0, 0.0, 0.0, 0.0, 0.0],
[0.0, 1.0, 0.0, 0.0, 0.0], [0.0, 0.0, 1.0, 0.0, 0.0], [0.0, 0.0, 0.0, 1.0, 0.0], [0.0, 0.0, 0.0, 0.0, 1.0]], dtype=float64)
# code to be run in micropython
from ulab import numpy as np
print(np.eye(4, M=6, k=-1, dtype=np.int16))
- array([[0, 0, 0, 0, 0, 0],
[1, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0]], dtype=int16)
# code to be run in micropython
from ulab import numpy as np
print(np.eye(4, M=6, dtype=np.int8))
- array([[1, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0]], dtype=int8)
numpy
: https://numpy.org/doc/stable/reference/generated/numpy.frombuffer.html
The function interprets a contiguous buffer as a one-dimensional array, and thus can be used for piping buffered data directly into an array. This method of analysing, e.g., ADC data is much more efficient than passing the ADC buffer into the array
constructor, because frombuffer
simply creates the ndarray
header and blindly copies the memory segment, without inspecting the underlying data.
The function takes a single positional argument, the buffer, and three keyword arguments. These are the dtype
with a default value of float
, the offset
, with a default of 0, and the count
, with a default of -1, meaning that all data are taken in.
# code to be run in micropython
from ulab import numpy as np
buffer = b'\x01\x02\x03\x04\x05\x06\x07\x08'
print('buffer: ', buffer)
a = np.frombuffer(buffer, dtype=np.uint8)
print('a, all data read: ', a)
b = np.frombuffer(buffer, dtype=np.uint8, offset=2)
print('b, all data with an offset: ', b)
c = np.frombuffer(buffer, dtype=np.uint8, offset=2, count=3)
print('c, only 3 items with an offset: ', c)
buffer: b'x01x02x03x04x05x06x07x08' a, all data read: array([1, 2, 3, 4, 5, 6, 7, 8], dtype=uint8) b, all data with an offset: array([3, 4, 5, 6, 7, 8], dtype=uint8) c, only 3 items with an offset: array([3, 4, 5], dtype=uint8)
numpy
: https://docs.scipy.org/doc/numpy/reference/generated/numpy.full.html
The function returns an array of arbitrary dimension, whose elements are all equal to the second positional argument. The first argument is a tuple describing the shape of the tensor. The dtype
keyword argument with a default value of float
can also be supplied.
# code to be run in micropython
from ulab import numpy as np
# create an array with the default type
print(np.full((2, 4), 3))
print('\n' + '='*20 + '\n')
# the array type is uint8 now
print(np.full((2, 4), 3, dtype=np.uint8))
- array([[3.0, 3.0, 3.0, 3.0],
[3.0, 3.0, 3.0, 3.0]], dtype=float64)
- array([[3, 3, 3, 3],
[3, 3, 3, 3]], dtype=uint8)
numpy
: https://docs.scipy.org/doc/numpy/reference/generated/numpy.linspace.html
This function returns an array, whose elements are uniformly spaced between the start
, and stop
points. The number of intervals is determined by the num
keyword argument, whose default value is 50. With the endpoint
keyword argument (defaults to True
) one can include stop
in the sequence. In addition, the dtype
keyword can be supplied to force type conversion of the output. The default is float
. Note that, when dtype
is of integer type, the sequence is not necessarily evenly spaced. This is not an error, rather a consequence of rounding. (This is also the numpy
behaviour.)
# code to be run in micropython
from ulab import numpy as np
# generate a sequence with defaults
print('default sequence:\t', np.linspace(0, 10))
# num=5
print('num=5:\t\t\t', np.linspace(0, 10, num=5))
# num=5, endpoint=False
print('num=5:\t\t\t', np.linspace(0, 10, num=5, endpoint=False))
# num=5, endpoint=False, dtype=uint8
print('num=5:\t\t\t', np.linspace(0, 5, num=7, endpoint=False, dtype=np.uint8))
default sequence: array([0.0, 0.2040816326530612, 0.4081632653061225, ..., 9.591836734693871, 9.795918367346932, 9.999999999999993], dtype=float64) num=5: array([0.0, 2.5, 5.0, 7.5, 10.0], dtype=float64) num=5: array([0.0, 2.0, 4.0, 6.0, 8.0], dtype=float64) num=5: array([0, 0, 1, 2, 2, 3, 4], dtype=uint8)
linspace
’ equivalent for logarithmically spaced data is logspace
. This function produces a sequence of numbers, in which the quotient of consecutive numbers is constant. This is a geometric sequence.
numpy
: https://docs.scipy.org/doc/numpy/reference/generated/numpy.logspace.html
This function returns an array, whose elements are uniformly spaced between the start
, and stop
points. The number of intervals is determined by the num
keyword argument, whose default value is 50. With the endpoint
keyword argument (defaults to True
) one can include stop
in the sequence. In addition, the dtype
keyword can be supplied to force type conversion of the output. The default is float
. Note that, exactly as in linspace
, when dtype
is of integer type, the sequence is not necessarily evenly spaced in log space.
In addition to the keyword arguments found in linspace
, logspace
also accepts the base
argument. The default value is 10.
# code to be run in micropython
from ulab import numpy as np
# generate a sequence with defaults
print('default sequence:\t', np.logspace(0, 3))
# num=5
print('num=5:\t\t\t', np.logspace(1, 10, num=5))
# num=5, endpoint=False
print('num=5:\t\t\t', np.logspace(1, 10, num=5, endpoint=False))
# num=5, endpoint=False
print('num=5:\t\t\t', np.logspace(1, 10, num=5, endpoint=False, base=2))
default sequence: array([1.0, 1.151395399326447, 1.325711365590109, ..., 754.3120063354646, 868.5113737513561, 1000.000000000004], dtype=float64) num=5: array([10.0, 1778.279410038923, 316227.766016838, 56234132.5190349, 10000000000.0], dtype=float64) num=5: array([10.0, 630.9573444801933, 39810.71705534974, 2511886.431509581, 158489319.2461114], dtype=float64) num=5: array([2.0, 6.964404506368993, 24.25146506416637, 84.44850628946524, 294.066778879241], dtype=float64)
numpy
: https://docs.scipy.org/doc/numpy/reference/generated/numpy.zeros.html
numpy
: https://docs.scipy.org/doc/numpy/reference/generated/numpy.ones.html
A couple of special arrays and matrices can easily be initialised by calling one of the ones
, or zeros
functions. ones
and zeros
follow the same pattern, and have the call signature
ones(shape, dtype=float)
zeros(shape, dtype=float)
where shape is either an integer, or a tuple specifying the shape.
# code to be run in micropython
from ulab import numpy as np
print(np.ones(6, dtype=np.uint8))
print(np.zeros((6, 4)))
array([1, 1, 1, 1, 1, 1], dtype=uint8) array([[0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0]], dtype=float64)
When specifying the shape, make sure that the length of the tuple is not larger than the maximum dimension of your firmware.
# code to be run in micropython
from ulab import numpy as np
import ulab
print('maximum number of dimensions: ', ulab.__version__)
print(np.zeros((2, 2, 2)))
maximum number of dimensions: 2.1.0-2D
- Traceback (most recent call last):
File "/dev/shm/micropython.py", line 7, in <module>
TypeError: too many dimensions
ndarray
s are pretty-printed, i.e., if the number of entries along the last axis is larger than 10 (default value), then only the first and last three entries will be printed. Also note that, as opposed to numpy
, the printout always contains the dtype
.
# code to be run in micropython
from ulab import numpy as np
a = np.array(range(200))
print("a:\t", a)
a: array([0.0, 1.0, 2.0, ..., 197.0, 198.0, 199.0], dtype=float64)
The default values can be overwritten by means of the set_printoptions
function numpy.set_printoptions, which accepts two keywords arguments, the threshold
, and the edgeitems
. The first of these arguments determines the length of the longest array that will be printed in full, while the second is the number of items that will be printed on the left and right hand side of the ellipsis, if the array is longer than threshold
.
# code to be run in micropython
from ulab import numpy as np
a = np.array(range(20))
print("a printed with defaults:\t", a)
np.set_printoptions(threshold=200)
print("\na printed in full:\t\t", a)
np.set_printoptions(threshold=10, edgeitems=2)
print("\na truncated with 2 edgeitems:\t", a)
a printed with defaults: array([0.0, 1.0, 2.0, ..., 17.0, 18.0, 19.0], dtype=float64)
a printed in full: array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0, 18.0, 19.0], dtype=float64)
a truncated with 2 edgeitems: array([0.0, 1.0, ..., 18.0, 19.0], dtype=float64)
The set value of the threshold
and edgeitems
can be retrieved by calling the get_printoptions
function with no arguments. The function returns a dictionary with two keys.
# code to be run in micropython
from ulab import numpy as np
np.set_printoptions(threshold=100, edgeitems=20)
print(np.get_printoptions())
{'threshold': 100, 'edgeitems': 20}
Arrays have several properties that can queried, and some methods that can be called. With the exception of the flatten and transpose operators, properties return an object that describe some feature of the array, while the methods return a new array-like object.
numpy
https://numpy.org/doc/stable/reference/generated/numpy.char.chararray.byteswap.html
The method takes a single keyword argument, inplace
, with values True
or False
, and swaps the bytes in the array. If inplace = False
, a new ndarray
is returned, otherwise the original values are overwritten.
The frombuffer
function is a convenient way of receiving data from peripheral devices that work with buffers. However, it is not guaranteed that the byte order (in other words, the endianness) of the peripheral device matches that of the microcontroller. The .byteswap
method makes it possible to change the endianness of the incoming data stream.
Obviously, byteswapping makes sense only for those cases, when a datum occupies more than one byte, i.e., for the uint16
, int16
, and float
dtype
s. When dtype
is either uint8
, or int8
, the method simply returns a view or copy of self, depending upon the value of inplace
.
# code to be run in micropython
from ulab import numpy as np
buffer = b'\x01\x02\x03\x04\x05\x06\x07\x08'
print('buffer: ', buffer)
a = np.frombuffer(buffer, dtype=np.uint16)
print('a: ', a)
b = a.byteswap()
print('b: ', b)
buffer: b'x01x02x03x04x05x06x07x08' a: array([513, 1027, 1541, 2055], dtype=uint16) b: array([258, 772, 1286, 1800], dtype=uint16)
The .copy
method creates a new deep copy of an array, i.e., the entries of the source array are copied into the target array.
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3, 4], dtype=np.int8)
b = a.copy()
print('a: ', a)
print('='*20)
print('b: ', b)
a: array([1, 2, 3, 4], dtype=int8) ==================== b: array([1, 2, 3, 4], dtype=int8)
numpy
: https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.dtype.htm
The .dtype
property returns the dtype
of an array. This can then be used for initialising another array with the matching type. ulab
implements two versions of dtype
; one that is numpy
-like, i.e., one, which returns a dtype
object, and one that is significantly cheaper in terms of flash space, but does not define a the dtype
object, and returns a single character (number) instead.
WARNING: in circuitpython
:
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3, 4], dtype=np.int8)
b = np.array([5, 6, 7], dtype=a.dtype)
print('a: ', a)
print('dtype of a: ', a.dtype)
print('\nb: ', b)
a: array([1, 2, 3, 4], dtype=int8) dtype of a: dtype('int8')
b: array([5, 6, 7], dtype=int8)
WARNING: in micropython
:
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3, 4], dtype=np.int8)
b = np.array([5, 6, 7], dtype=a.dtype())
print('a: ', a)
print('dtype of a: ', a.dtype())
print('\nb: ', b)
a: array([1, 2, 3, 4], dtype=int8) dtype of a: dtype('int8')
b: array([5, 6, 7], dtype=int8)
If the ulab.h
header file sets the pre-processor constant ULAB_HAS_DTYPE_OBJECT
to 0 as
#define ULAB_HAS_DTYPE_OBJECT (0)
then the output of the previous snippet will be
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3, 4], dtype=np.int8)
b = np.array([5, 6, 7], dtype=a.dtype())
print('a: ', a)
print('dtype of a: ', a.dtype())
print('\nb: ', b)
a: array([1, 2, 3, 4], dtype=int8) dtype of a: 98
b: array([5, 6, 7], dtype=int8)
Here 98 is nothing but the ASCII value of the character b
, which is the type code for signed 8-bit integers. The object definition adds around 600 bytes to the firmware.
numpy
: https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.flatten.htm
.flatten
returns the flattened array. The array can be flattened in C
style (i.e., moving along the last axis in the tensor), or in fortran
style (i.e., moving along the first axis in the tensor).
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3, 4], dtype=np.int8)
print("a: \t\t", a)
print("a flattened: \t", a.flatten())
b = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.int8)
print("\nb:", b)
print("b flattened (C): \t", b.flatten())
print("b flattened (F): \t", b.flatten(order='F'))
a: array([1, 2, 3, 4], dtype=int8) a flattened: array([1, 2, 3, 4], dtype=int8)
- b: array([[1, 2, 3],
[4, 5, 6]], dtype=int8)
b flattened (C): array([1, 2, 3, 4, 5, 6], dtype=int8) b flattened (F): array([1, 4, 2, 5, 3, 6], dtype=int8)
numpy
: https://numpy.org/doc/stable/reference/generated/numpy.ndarray.itemsize.html
The .itemsize
method (property) returns an integer with the size of elements in the array.
WARNING: In circuitpython
:
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3], dtype=np.int8)
print("a:\n", a)
print("itemsize of a:", a.itemsize
b= np.array([[1, 2], [3, 4]], dtype=np.float)
print("\nb:\n", b)
print("itemsize of b:", b.itemsize
- a:
array([1, 2, 3], dtype=int8)
itemsize of a: 1
- b:
- array([[1.0, 2.0],
[3.0, 4.0]], dtype=float64)
itemsize of b: 8
WARNING: In micropython
:
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3], dtype=np.int8)
print("a:\n", a)
print("itemsize of a:", a.itemsize)
b= np.array([[1, 2], [3, 4]], dtype=np.float)
print("\nb:\n", b)
print("itemsize of b:", b.itemsize())
- a:
array([1, 2, 3], dtype=int8)
itemsize of a: <bound_method 7fdc008692c0 array([1, 2, 3], dtype=int8).<function>>
- b:
- array([[1.0, 2.0],
[3.0, 4.0]], dtype=float64)
itemsize of b: 8
numpy
: https://docs.scipy.org/doc/numpy/reference/generated/numpy.reshape.html
reshape
re-writes the shape properties of an ndarray
, but the array will not be modified in any other way. The function takes a single 2-tuple with two integers as its argument. The 2-tuple should specify the desired number of rows and columns. If the new shape is not consistent with the old, a ValueError
exception will be raised.
# code to be run in micropython
from ulab import numpy as np
a = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]], dtype=np.uint8)
print('a (4 by 4):', a)
print('a (2 by 8):', a.reshape((2, 8)))
print('a (1 by 16):', a.reshape((1, 16)))
- a (4 by 4): array([[1, 2, 3, 4],
[5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]], dtype=uint8)
- a (2 by 8): array([[1, 2, 3, 4, 5, 6, 7, 8],
[9, 10, 11, 12, 13, 14, 15, 16]], dtype=uint8)
a (1 by 16): array([[1, 2, 3, ..., 14, 15, 16]], dtype=uint8)
numpy
: https://numpy.org/doc/stable/reference/generated/numpy.ndarray.shape.html
The .shape
method (property) returns a tuple with the length of the array in along each dimension.
WARNING: In circuitpython
, you can call the method as a property, i.e.,
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3, 4], dtype=np.int8)
print("a:\n", a)
print("shape of a:", a.shape)
b= np.array([[1, 2], [3, 4]], dtype=np.int8)
print("\nb:\n", b)
print("shape of b:", b.shape
- a:
array([1, 2, 3, 4], dtype=int8)
shape of a: (4,)
- b:
- array([[1, 2],
[3, 4]], dtype=int8)
shape of b: (2, 2)
WARNING: On the other hand, since properties are not implemented in micropython
, there you would call the method as a function, i.e.,
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3, 4], dtype=np.int8)
print("a:\n", a)
print("shape of a:", a.shape())
b= np.array([[1, 2], [3, 4]], dtype=np.int8)
print("\nb:\n", b)
print("shape of b:", b.shape())
- a:
array([1, 2, 3, 4], dtype=int8)
shape of a: (4,)
- b:
- array([[1, 2],
[3, 4]], dtype=int8)
shape of b: (2, 2)
numpy
: https://numpy.org/doc/stable/reference/generated/numpy.ndarray.size.html
The .size
method (property) returns an integer with the number of elements in the array.
WARNING: In circuitpython
, the numpy
nomenclature applies, i.e.,
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3], dtype=np.int8)
print("a:\n", a)
print("size of a:", a.size)
b= np.array([[1, 2], [3, 4]], dtype=np.int8)
print("\nb:\n", b)
print("size of b:", b.size)
- a:
array([1, 2, 3], dtype=int8)
size of a: 3
- b:
- array([[1, 2],
[3, 4]], dtype=int8)
size of b: 4
WARNING: In micropython
, size
is a method, i.e.,
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3], dtype=np.int8)
print("a:\n", a)
print("size of a:", a.size())
b= np.array([[1, 2], [3, 4]], dtype=np.int8)
print("\nb:\n", b)
print("size of b:", b.size())
- a:
array([1, 2, 3], dtype=int8)
size of a: 3
- b:
- array([[1, 2],
[3, 4]], dtype=int8)
size of b: 4
numpy
: https://numpy.org/doc/stable/reference/generated/numpy.ndarray.tobytes.html
The .tobytes
method can be used for acquiring a handle of the underlying data pointer of an array, and it returns a new bytearray
that can be fed into any method that can accep a bytearray
, e.g., ADC data can be buffered into this bytearray
, or the bytearray
can be fed into a DAC. Since the bytearray
is really nothing but the bare data container of the array, any manipulation on the bytearray
automatically modifies the array itself.
Note that the method raises a ValueError
exception, if the array is not dense (i.e., it has already been sliced).
# code to be run in micropython
from ulab import numpy as np
a = np.array(range(8), dtype=np.uint8)
print('a: ', a)
b = a.tobytes()
print('b: ', b)
# modify b
b[0] = 13
print('='*20)
print('b: ', b)
print('a: ', a)
a: array([0, 1, 2, 3, 4, 5, 6, 7], dtype=uint8) b: bytearray(b'x00x01x02x03x04x05x06x07') ==================== b: bytearray(b'rx01x02x03x04x05x06x07') a: array([13, 1, 2, 3, 4, 5, 6, 7], dtype=uint8)
numpy
: https://docs.scipy.org/doc/numpy/reference/generated/numpy.transpose.html
Returns the transposed array. Only defined, if the number of maximum dimensions is larger than 1.
# code to be run in micropython
from ulab import numpy as np
a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]], dtype=np.uint8)
print('a:\n', a)
print('shape of a:', a.shape())
a.transpose()
print('\ntranspose of a:\n', a)
print('shape of a:', a.shape())
- a:
- array([[1, 2, 3],
[4, 5, 6], [7, 8, 9], [10, 11, 12]], dtype=uint8)
shape of a: (4, 3)
- transpose of a:
- array([[1, 4, 7, 10],
[2, 5, 8, 11], [3, 6, 9, 12]], dtype=uint8)
shape of a: (3, 4)
numpy
: https://docs.scipy.org/doc/numpy/reference/generated/numpy.sort.html
In-place sorting of an ndarray
. For a more detailed exposition, see sort.
# code to be run in micropython
from ulab import numpy as np
a = np.array([[1, 12, 3, 0], [5, 3, 4, 1], [9, 11, 1, 8], [7, 10, 0, 1]], dtype=np.uint8)
print('\na:\n', a)
a.sort(axis=0)
print('\na sorted along vertical axis:\n', a)
a = np.array([[1, 12, 3, 0], [5, 3, 4, 1], [9, 11, 1, 8], [7, 10, 0, 1]], dtype=np.uint8)
a.sort(axis=1)
print('\na sorted along horizontal axis:\n', a)
a = np.array([[1, 12, 3, 0], [5, 3, 4, 1], [9, 11, 1, 8], [7, 10, 0, 1]], dtype=np.uint8)
a.sort(axis=None)
print('\nflattened a sorted:\n', a)
- a:
- array([[1, 12, 3, 0],
[5, 3, 4, 1], [9, 11, 1, 8], [7, 10, 0, 1]], dtype=uint8)
- a sorted along vertical axis:
- array([[1, 3, 0, 0],
[5, 10, 1, 1], [7, 11, 3, 1], [9, 12, 4, 8]], dtype=uint8)
- a sorted along horizontal axis:
- array([[0, 1, 3, 12],
[1, 3, 4, 5], [1, 8, 9, 11], [0, 1, 7, 10]], dtype=uint8)
- flattened a sorted:
array([0, 0, 1, ..., 10, 11, 12], dtype=uint8)
With the exception of len
, which returns a single number, all unary operators manipulate the underlying data element-wise.
This operator takes a single argument, the array, and returns either the length of the first axis.
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3, 4, 5], dtype=np.uint8)
b = np.array([range(5), range(5), range(5), range(5)], dtype=np.uint8)
print("a:\t", a)
print("length of a: ", len(a))
print("shape of a: ", a.shape())
print("\nb:\t", b)
print("length of b: ", len(b))
print("shape of b: ", b.shape())
a: array([1, 2, 3, 4, 5], dtype=uint8) length of a: 5 shape of a: (5,)
- b: array([[0, 1, 2, 3, 4],
[0, 1, 2, 3, 4], [0, 1, 2, 3, 4], [0, 1, 2, 3, 4]], dtype=uint8)
length of b: 2 shape of b: (4, 5)
The number returned by len
is also the length of the iterations, when the array supplies the elements for an iteration (see later).
The function is defined for integer data types (uint8
, int8
, uint16
, and int16
) only, takes a single argument, and returns the element-by-element, bit-wise inverse of the array. If a float
is supplied, the function raises a ValueError
exception.
With signed integers (int8
, and int16
), the results might be unexpected, as in the example below:
# code to be run in micropython
from ulab import numpy as np
a = np.array([0, -1, -100], dtype=np.int8)
print("a:\t\t", a)
print("inverse of a:\t", ~a)
a = np.array([0, 1, 254, 255], dtype=np.uint8)
print("\na:\t\t", a)
print("inverse of a:\t", ~a)
a: array([0, -1, -100], dtype=int8) inverse of a: array([-1, 0, 99], dtype=int8)
a: array([0, 1, 254, 255], dtype=uint8) inverse of a: array([255, 254, 1, 0], dtype=uint8)
This function takes a single argument, and returns the element-by-element absolute value of the array. When the data type is unsigned (uint8
, or uint16
), a copy of the array will be returned immediately, and no calculation takes place.
# code to be run in micropython
from ulab import numpy as np
a = np.array([0, -1, -100], dtype=np.int8)
print("a:\t\t\t ", a)
print("absolute value of a:\t ", abs(a))
a: array([0, -1, -100], dtype=int8) absolute value of a: array([0, 1, 100], dtype=int8)
This operator takes a single argument, and changes the sign of each element in the array. Unsigned values are wrapped.
# code to be run in micropython
from ulab import numpy as np
a = np.array([10, -1, 1], dtype=np.int8)
print("a:\t\t", a)
print("negative of a:\t", -a)
b = np.array([0, 100, 200], dtype=np.uint8)
print("\nb:\t\t", b)
print("negative of b:\t", -b)
a: array([10, -1, 1], dtype=int8) negative of a: array([-10, 1, -1], dtype=int8)
b: array([0, 100, 200], dtype=uint8) negative of b: array([0, 156, 56], dtype=uint8)
This function takes a single argument, and simply returns a copy of the array.
# code to be run in micropython
from ulab import numpy as np
a = np.array([10, -1, 1], dtype=np.int8)
print("a:\t\t", a)
print("positive of a:\t", +a)
a: array([10, -1, 1], dtype=int8) positive of a: array([10, -1, 1], dtype=int8)
ulab
implements the +
, -
, *
, /
, **
, <
, >
, <=
, >=
, ==
, !=
, +=
, -=
, *=
, /=
, **=
binary operators that work element-wise. Broadcasting is available, meaning that the two operands do not even have to have the same shape. If the lengths along the respective axes are equal, or one of them is 1, or the axis is missing, the element-wise operation can still be carried out. A thorough explanation of broadcasting can be found under https://numpy.org/doc/stable/user/basics.broadcasting.html.
WARNING: note that relational operators (<
, >
, <=
, >=
, ==
, !=
) should have the ndarray
on their left hand side, when compared to scalars. This means that the following works
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3])
print(a > 2)
array([False, False, True], dtype=bool)
while the equivalent statement, 2 < a
, will raise a TypeError
exception:
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3])
print(2 < a)
- Traceback (most recent call last):
File "/dev/shm/micropython.py", line 5, in <module>
TypeError: unsupported types for __lt__: 'int', 'ndarray'
WARNING: circuitpython
users should use the equal
, and not_equal
operators instead of ==
, and !=
. See the section on array comparison for details.
Binary operations require special attention, because two arrays with different typecodes can be the operands of an operation, in which case it is not trivial, what the typecode of the result is. This decision on the result’s typecode is called upcasting. Since the number of typecodes in ulab
is significantly smaller than in numpy
, we have to define new upcasting rules. Where possible, I followed numpy
’s conventions.
ulab
observes the following upcasting rules:
- Operations on two
ndarray
s of the samedtype
preserve theirdtype
, even when the results overflow. - if either of the operands is a float, the result is automatically a float
- When one of the operands is a scalar, it will internally be turned into a single-element
ndarray
with the smallest possibledtype
. Thus, e.g., if the scalar is 123, it will be converted into an array ofdtype
uint8
, while -1000 will be converted intoint16
. Anmp_obj_float
, will always be promoted todtype
float
. Other micropython types (e.g., lists, tuples, etc.) raise aTypeError
exception.
left hand side | right hand side | ulab result | numpy result |
---|---|---|---|
uint8 |
int8 |
int16 |
int16 |
uint8 |
int16 |
int16 |
int16 |
uint8 |
uint16 |
uint16 |
uint16 |
int8 |
int16 |
int16 |
int16 |
int8 |
uint16 |
uint16 |
int32 |
uint16 |
int16 |
float |
int32 |
Note that the last two operations are promoted to int32
in numpy
.
WARNING: Due to the lower number of available data types, the upcasting rules of ulab
are slightly different to those of numpy
. Watch out for this, when porting code!
Upcasting can be seen in action in the following snippet:
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3, 4], dtype=np.uint8)
b = np.array([1, 2, 3, 4], dtype=np.int8)
print("a:\t", a)
print("b:\t", b)
print("a+b:\t", a+b)
c = np.array([1, 2, 3, 4], dtype=np.float)
print("\na:\t", a)
print("c:\t", c)
print("a*c:\t", a*c)
a: array([1, 2, 3, 4], dtype=uint8) b: array([1, 2, 3, 4], dtype=int8) a+b: array([2, 4, 6, 8], dtype=int16)
a: array([1, 2, 3, 4], dtype=uint8) c: array([1.0, 2.0, 3.0, 4.0], dtype=float64) a*c: array([1.0, 4.0, 9.0, 16.0], dtype=float64)
The following snippet compares the performance of binary operations to a possible implementation in python. For the time measurement, we will take the following snippet from the micropython manual:
# code to be run in micropython
import utime
def timeit(f, *args, **kwargs):
func_name = str(f).split(' ')[1]
def new_func(*args, **kwargs):
t = utime.ticks_us()
result = f(*args, **kwargs)
print('execution time: ', utime.ticks_diff(utime.ticks_us(), t), ' us')
return result
return new_func
# code to be run in micropython
from ulab import numpy as np
@timeit
def py_add(a, b):
return [a[i]+b[i] for i in range(1000)]
@timeit
def py_multiply(a, b):
return [a[i]*b[i] for i in range(1000)]
@timeit
def ulab_add(a, b):
return a + b
@timeit
def ulab_multiply(a, b):
return a * b
a = [0.0]*1000
b = range(1000)
print('python add:')
py_add(a, b)
print('\npython multiply:')
py_multiply(a, b)
a = np.linspace(0, 10, num=1000)
b = np.ones(1000)
print('\nulab add:')
ulab_add(a, b)
print('\nulab multiply:')
ulab_multiply(a, b)
python add: execution time: 10051 us
python multiply: execution time: 14175 us
ulab add: execution time: 222 us
ulab multiply: execution time: 213 us
The python implementation above is not perfect, and certainly, there is much room for improvement. However, the factor of 50 difference in execution time is very spectacular. This is nothing but a consequence of the fact that the ulab
functions run C
code, with very little python overhead. The factor of 50 appears to be quite universal: the FFT routine obeys similar scaling (see Speed of FFTs), and this number came up with font rendering, too: fast font rendering on graphical displays.
The smaller than, greater than, smaller or equal, and greater or equal operators return a vector of Booleans indicating the positions (True
), where the condition is satisfied.
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3, 4, 5, 6, 7, 8], dtype=np.uint8)
print(a < 5)
array([True, True, True, True, False, False, False, False], dtype=bool)
WARNING: at the moment, due to micropython
’s implementation details, the ndarray
must be on the left hand side of the relational operators.
That is, while a < 5
and 5 > a
have the same meaning, the following code will not work:
# code to be run in micropython
import ulab as np
a = np.array([1, 2, 3, 4, 5, 6, 7, 8], dtype=np.uint8)
print(5 > a)
- Traceback (most recent call last):
File "/dev/shm/micropython.py", line 5, in <module>
TypeError: unsupported types for __gt__: 'int', 'ndarray'
ndarray
s are iterable, which means that their elements can also be accessed as can the elements of a list, tuple, etc. If the array is one-dimensional, the iterator returns scalars, otherwise a new reduced-dimensional view is created and returned.
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3, 4, 5], dtype=np.uint8)
b = np.array([range(5), range(10, 15, 1), range(20, 25, 1), range(30, 35, 1)], dtype=np.uint8)
print("a:\t", a)
for i, _a in enumerate(a):
print("element %d in a:"%i, _a)
print("\nb:\t", b)
for i, _b in enumerate(b):
print("element %d in b:"%i, _b)
a: array([1, 2, 3, 4, 5], dtype=uint8) element 0 in a: 1 element 1 in a: 2 element 2 in a: 3 element 3 in a: 4 element 4 in a: 5
- b: array([[0, 1, 2, 3, 4],
[10, 11, 12, 13, 14], [20, 21, 22, 23, 24], [30, 31, 32, 33, 34]], dtype=uint8)
element 0 in b: array([0, 1, 2, 3, 4], dtype=uint8) element 1 in b: array([10, 11, 12, 13, 14], dtype=uint8) element 2 in b: array([20, 21, 22, 23, 24], dtype=uint8) element 3 in b: array([30, 31, 32, 33, 34], dtype=uint8)
numpy
has a very important concept called views, which is a powerful extension of python
’s own notion of slicing. Slices are special python objects of the form
slice = start:end:stop
where start
, end
, and stop
are (not necessarily non-negative) integers. Not all of these three numbers must be specified in an index, in fact, all three of them can be missing. The interpreter takes care of filling in the missing values. (Note that slices cannot be defined in this way, only there, where an index is expected.) For a good explanation on how slices work in python, you can read the stackoverflow question https://stackoverflow.com/questions/509211/understanding-slice-notation.
In order to see what slicing does, let us take the string a = '012345679'
! We can extract every second character by creating the slice ::2
, which is equivalent to 0:len(a):2
, i.e., increments the character pointer by 2 starting from 0, and traversing the string up to the very end.
# code to be run in CPython
string = '0123456789'
string[::2]
'02468'
Now, we can do the same with numerical arrays.
# code to be run in micropython
from ulab import numpy as np
a = np.array(range(10), dtype=np.uint8)
print('a:\t', a)
print('a[::2]:\t', a[::2])
a: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8) a[::2]: array([0, 2, 4, 6, 8], dtype=uint8)
This looks similar to string
above, but there is a very important difference that is not so obvious. Namely, string[::2]
produces a partial copy of string
, while a[::2]
only produces a view of a
. What this means is that a
, and a[::2]
share their data, and the only difference between the two is, how the data are read out. In other words, internally, a[::2]
has the same data pointer as a
. We can easily convince ourselves that this is indeed the case by calling the ndinfo function: the data pointer entry is the same in the two printouts.
# code to be run in micropython
from ulab import numpy as np
a = np.array(range(10), dtype=np.uint8)
print('a: ', a, '\n')
np.ndinfo(a)
print('\n' + '='*20)
print('a[::2]: ', a[::2], '\n')
np.ndinfo(a[::2])
a: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8)
class: ndarray shape: (10,) strides: (1,) itemsize: 1 data pointer: 0x7ff6c6193220 type: uint8
==================== a[::2]: array([0, 2, 4, 6, 8], dtype=uint8)
class: ndarray shape: (5,) strides: (2,) itemsize: 1 data pointer: 0x7ff6c6193220 type: uint8
If you are still a bit confused about the meaning of views, the section Slicing and assigning to slices should clarify the issue.
The simplest form of indexing is specifying a single integer between the square brackets as in
# code to be run in micropython
from ulab import numpy as np
a = np.array(range(10), dtype=np.uint8)
print("a: ", a)
print("the first, and last element of a:\n", a[0], a[-1])
print("the second, and last but one element of a:\n", a[1], a[-2])
a: array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], dtype=uint8) the first, and last element of a: 0 9 the second, and last but one element of a: 1 8
Indexing can be applied to higher-dimensional tensors, too. When the length of the indexing sequences is smaller than the number of dimensions, a new view is returned, otherwise, we get a single number.
# code to be run in micropython
from ulab import numpy as np
a = np.array(range(9), dtype=np.uint8).reshape((3, 3))
print("a:\n", a)
print("a[0]:\n", a[0])
print("a[1,1]: ", a[1,1])
- a:
- array([[0, 1, 2],
[3, 4, 5], [6, 7, 8]], dtype=uint8)
- a[0]:
array([[0, 1, 2]], dtype=uint8)
a[1,1]: 4
Indices can also be a list of Booleans. By using a Boolean list, we can select those elements of an array that satisfy a specific condition. At the moment, such indexing is defined for row vectors only; when the rank of the tensor is higher than 1, the function raises a NotImplementedError
exception, though this will be rectified in a future version of ulab
.
# code to be run in micropython
from ulab import numpy as np
a = np.array(range(9), dtype=np.float)
print("a:\t", a)
print("a < 5:\t", a[a < 5])
a: array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0], dtype=float) a < 5: array([0.0, 1.0, 2.0, 3.0, 4.0], dtype=float)
Indexing with Boolean arrays can take more complicated expressions. This is a very concise way of comparing two vectors, e.g.:
# code to be run in micropython
from ulab import numpy as np
a = np.array(range(9), dtype=np.uint8)
b = np.array([4, 4, 4, 3, 3, 3, 13, 13, 13], dtype=np.uint8)
print("a:\t", a)
print("\na**2:\t", a*a)
print("\nb:\t", b)
print("\n100*sin(b):\t", np.sin(b)*100.0)
print("\na[a*a > np.sin(b)*100.0]:\t", a[a*a > np.sin(b)*100.0])
a: array([0, 1, 2, 3, 4, 5, 6, 7, 8], dtype=uint8)
a**2: array([0, 1, 4, 9, 16, 25, 36, 49, 64], dtype=uint16)
b: array([4, 4, 4, 3, 3, 3, 13, 13, 13], dtype=uint8)
100*sin(b): array([-75.68024953079282, -75.68024953079282, -75.68024953079282, 14.11200080598672, 14.11200080598672, 14.11200080598672, 42.01670368266409, 42.01670368266409, 42.01670368266409], dtype=float)
a[a*a > np.sin(b)*100.0]: array([0, 1, 2, 4, 5, 7, 8], dtype=uint8)
Boolean indices can also be used in assignments, if the array is one-dimensional. The following example replaces the data in an array, wherever some condition is fulfilled.
# code to be run in micropython
from ulab import numpy as np
a = np.array(range(9), dtype=np.uint8)
b = np.array(range(9)) + 12
print(a[b < 15])
a[b < 15] = 123
print(a)
array([0, 1, 2], dtype=uint8) array([123, 123, 123, 3, 4, 5, 6, 7, 8], dtype=uint8)
On the right hand side of the assignment we can even have another array.
# code to be run in micropython
from ulab import numpy as np
a = np.array(range(9), dtype=np.uint8)
b = np.array(range(9)) + 12
print(a[b < 15], b[b < 15])
a[b < 15] = b[b < 15]
print(a)
array([0, 1, 2], dtype=uint8) array([12.0, 13.0, 14.0], dtype=float) array([12, 13, 14, 3, 4, 5, 6, 7, 8], dtype=uint8)
You can also generate sub-arrays by specifying slices as the index of an array. Slices are special python objects of the form
# code to be run in micropython
from ulab import numpy as np
a = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]], dtype=np.uint8)
print('a:\n', a)
# the first row
print('\na[0]:\n', a[0])
# the first two elements of the first row
print('\na[0,:2]:\n', a[0,:2])
# the zeroth element in each row (also known as the zeroth column)
print('\na[:,0]:\n', a[:,0])
# the last row
print('\na[-1]:\n', a[-1])
# the last two rows backwards
print('\na[-1:-3:-1]:\n', a[-1:-3:-1])
- a:
- array([[1, 2, 3],
[4, 5, 6], [7, 8, 9]], dtype=uint8)
- a[0]:
array([[1, 2, 3]], dtype=uint8)
- a[0,:2]:
array([[1, 2]], dtype=uint8)
- a[:,0]:
- array([[1],
[4], [7]], dtype=uint8)
- a[-1]:
array([[7, 8, 9]], dtype=uint8)
- a[-1:-3:-1]:
- array([[7, 8, 9],
[4, 5, 6]], dtype=uint8)
Assignment to slices can be done for the whole slice, per row, and per column. A couple of examples should make these statements clearer:
# code to be run in micropython
from ulab import numpy as np
a = np.zeros((3, 3), dtype=np.uint8)
print('a:\n', a)
# assigning to the whole row
a[0] = 1
print('\na[0] = 1\n', a)
a = np.zeros((3, 3), dtype=np.uint8)
# assigning to a column
a[:,2] = 3.0
print('\na[:,0]:\n', a)
- a:
- array([[0, 0, 0],
[0, 0, 0], [0, 0, 0]], dtype=uint8)
- a[0] = 1
- array([[1, 1, 1],
[0, 0, 0], [0, 0, 0]], dtype=uint8)
- a[:,0]:
- array([[0, 0, 3],
[0, 0, 3], [0, 0, 3]], dtype=uint8)
Now, you should notice that we re-set the array a
after the first assignment. Do you care to see what happens, if we do not do that? Well, here are the results:
# code to be run in micropython
from ulab import numpy as np
a = np.zeros((3, 3), dtype=np.uint8)
b = a[:,:]
# assign 1 to the first row
b[0] = 1
# assigning to the last column
b[:,2] = 3
print('a: ', a)
- a: array([[1, 1, 3],
[0, 0, 3], [0, 0, 3]], dtype=uint8)
Note that both assignments involved b
, and not a
, yet, when we print out a
, its entries are updated. This proves our earlier statement about the behaviour of views: in the statement b = a[:,:]
we simply created a view of a
, and not a deep copy of it, meaning that whenever we modify b
, we actually modify a
, because the underlying data container of a
and b
are shared between the two object. Having a single data container for two seemingly different objects provides an extremely powerful way of manipulating sub-sets of numerical data.
If you want to work on a copy of your data, you can use the .copy
method of the ndarray
. The following snippet should drive the point home:
# code to be run in micropython
from ulab import numpy as np
a = np.zeros((3, 3), dtype=np.uint8)
b = a.copy()
# get the address of the underlying data pointer
np.ndinfo(a)
print()
np.ndinfo(b)
# assign 1 to the first row of b, and do not touch a
b[0] = 1
print()
print('a: ', a)
print('='*20)
print('b: ', b)
class: ndarray shape: (3, 3) strides: (3, 1) itemsize: 1 data pointer: 0x7ff737ea3220 type: uint8
class: ndarray shape: (3, 3) strides: (3, 1) itemsize: 1 data pointer: 0x7ff737ea3340 type: uint8
- a: array([[0, 0, 0],
[0, 0, 0], [0, 0, 0]], dtype=uint8)
==================== b: array([[1, 1, 1], [0, 0, 0], [0, 0, 0]], dtype=uint8)
The .copy
method can also be applied to views: below, a[0]
is a view of a
, out of which we create a deep copy called b
. This is a row vector now. We can then do whatever we want to with b
, and that leaves a
unchanged.
# code to be run in micropython
from ulab import numpy as np
a = np.zeros((3, 3), dtype=np.uint8)
b = a[0].copy()
print('b: ', b)
print('='*20)
# assign 1 to the first entry of b, and do not touch a
b[0] = 1
print('a: ', a)
print('='*20)
print('b: ', b)
b: array([0, 0, 0], dtype=uint8) ==================== a: array([[0, 0, 0], [0, 0, 0], [0, 0, 0]], dtype=uint8) ==================== b: array([1, 0, 0], dtype=uint8)
The fact that the underlying data of a view is the same as that of the original array has another important consequence, namely, that the creation of a view is cheap. Both in terms of RAM, and execution time. A view is really nothing but a short header with a data array that already exists, and is filled up. Hence, creating the view requires only the creation of its header. This operation is fast, and uses virtually no RAM.