ndarray, the base class¶
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
typeaware, 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 abovementioned 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.
The ndinfo function¶
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
Initialising an array¶
A new array can be created by passing either a standard micropython
iterable, or another ndarray
into the constructor.
Initialising by passing iterables¶
If the iterable is onedimensional, i.e., one whose elements are
numbers, then a row vector will be created and returned. If the iterable
is twodimensional, 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. In addition, if ULAB_SUPPORTS_COMPLEX
is set to 1 in
ulab.h,
the dtype
can also take on the value of complex
.
# 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 twodimensional array with mixedtype 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
Initialising by passing arrays¶
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.
Array initialisation functions¶
There are nine functions that can be used for initialising an array.
Starred functions accept complex
as the value of the dtype
, if
the firmware was compiled with complex support.
arange¶
numpy
:
https://numpy.org/doc/stable/reference/generated/numpy.arange.html
The function returns a onedimensional 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)
concatenate¶
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)
diag¶
numpy
:
https://numpy.org/doc/stable/reference/generated/numpy.diag.html
Extract a diagonal, or construct a diagonal array.
The function takes two arguments, an ndarray
, and a shift. If the
first argument is a twodimensional array, the function returns a
onedimensional array containing the diagonal entries. The diagonal can
be shifted by an amount given in the second argument.
If the first argument is a onedimensional array, the function returns a twodimensional tensor with its diagonal elements given by the first argument.
The diag
function can accept a complex array, if the firmware was
compiled with complex support.
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3, 4])
print(np.diag(a))
array([[1.0, 0.0, 0.0, 0.0],
[0.0, 2.0, 0.0, 0.0],
[0.0, 0.0, 3.0, 0.0],
[0.0, 0.0, 0.0, 4.0]], dtype=float64)
# code to be run in micropython
from ulab import numpy as np
a = np.array(range(16)).reshape((4, 4))
print('a: ', a)
print()
print('diagonal of a: ', np.diag(a))
a: 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]], dtype=float64)
diagonal of a: array([0.0, 5.0, 10.0, 15.0], dtype=float64)
empty¶
numpy
:
https://numpy.org/doc/stable/reference/generated/numpy.empty.html
empty
is simply an alias for zeros
, i.e., as opposed to
numpy
, the entries of the tensor will be initialised to zero.
The empty
function can accept complex as the value of the dtype, if
the firmware was compiled with complex support.
eye¶
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.
The eye
function can accept complex
as the value of the
dtype
, if the firmware was compiled with complex support.
With a single argument¶
# 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)
Specifying the dimensions of the matrix¶
# 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)
frombuffer¶
numpy
:
https://numpy.org/doc/stable/reference/generated/numpy.frombuffer.html
The function interprets a contiguous buffer as a onedimensional 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)
full¶
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.
The full
function can accept a complex scalar, or complex
as the
value of dtype
, if the firmware was compiled with complex support.
# 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)
linspace¶
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.)
The linspace
function can accept complex
as the value of the
dtype
, if the firmware was compiled with complex support. The output
dtype
is automatically complex, if either of the endpoints is a
complex scalar.
# 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)
logspace¶
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)
ones, zeros¶
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.
The ones/zeros
functions can accept complex as the value of the
dtype, if the firmware was compiled with complex support.
# 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: 2.1.02D
Traceback (most recent call last):
File "/dev/shm/micropython.py", line 7, in <module>
TypeError: too many dimensions
Customising array printouts¶
ndarray
s are prettyprinted, 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)
set_printoptions¶
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)
get_printoptions¶
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}
Methods and properties of ndarrays¶
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 arraylike object. The imag
,
and real
properties are included in the firmware only, when it was
compiled with complex support.
.byteswap¶
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)
.copy¶
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)
.dtype¶
numpy
:
https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.dtype.htm
The .dtype
property is 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 dtype
object,
and holds a single character (number) instead.
# 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 preprocessor 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 8bit integers. The object definition adds
around 600 bytes to the firmware.
.flat¶
numpy: https://docs.scipy.org/doc/numpy/reference/generated/numpy.ndarray.flat.htm
.flat
returns the array’s flat iterator. For onedimensional objects
the flat iterator is equivalent to the standart iterator, while for
higher dimensional tensors, it amounts to first flattening the array,
and then iterating over it. Note, however, that the flat iterator does
not consume RAM beyond what is required for holding the position of the
iterator itself, while flattening produces a new copy.
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3, 4], dtype=np.int8)
for _a in a:
print(_a)
a = np.array([[1, 2, 3, 4], [5, 6, 7, 8]], dtype=np.int8)
print('a:\n', a)
for _a in a:
print(_a)
for _a in a.flat:
print(_a)
1
2
3
4
a:
array([[1, 2, 3, 4],
[5, 6, 7, 8]], dtype=int8)
array([1, 2, 3, 4], dtype=int8)
array([5, 6, 7, 8], dtype=int8)
1
2
3
4
5
6
7
8
.flatten¶
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)
.imag¶
numpy
:
https://numpy.org/doc/stable/reference/generated/numpy.ndarray.imag.html
The .imag
property is defined only, if the firmware was compiled
with complex support, and returns a copy with the imaginary part of an
array. If the array is real, then the output is straight zeros with the
dtype
of the input. If the input is complex, the output dtype
is
always float
, irrespective of the values.
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3], dtype=np.uint16)
print("a:\t", a)
print("a.imag:\t", a.imag)
b = np.array([1, 2+1j, 31j], dtype=np.complex)
print("\nb:\t", b)
print("b.imag:\t", b.imag)
a: array([1, 2, 3], dtype=uint16)
a.imag: array([0, 0, 0], dtype=uint16)
b: array([1.0+0.0j, 2.0+1.0j, 3.01.0j], dtype=complex)
b.imag: array([0.0, 1.0, 1.0], dtype=float64)
.itemsize¶
numpy
:
https://numpy.org/doc/stable/reference/generated/numpy.ndarray.itemsize.html
The .itemsize
property is an integer with the size of elements in
the array.
# 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
.real¶
numpy: https://numpy.org/doc/stable/reference/generated/numpy.ndarray.real.html
The .real
property is defined only, if the firmware was compiled
with complex support, and returns a copy with the real part of an array.
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3], dtype=np.uint16)
print("a:\t", a)
print("a.real:\t", a.real)
b = np.array([1, 2+1j, 31j], dtype=np.complex)
print("\nb:\t", b)
print("b.real:\t", b.real)
a: array([1, 2, 3], dtype=uint16)
a.real: array([1, 2, 3], dtype=uint16)
b: array([1.0+0.0j, 2.0+1.0j, 3.01.0j], dtype=complex)
b.real: array([1.0, 2.0, 3.0], dtype=float64)
.reshape¶
numpy
:
https://docs.scipy.org/doc/numpy/reference/generated/numpy.reshape.html
reshape
rewrites the shape properties of an ndarray
, but the
array will not be modified in any other way. The function takes a single
2tuple with two integers as its argument. The 2tuple 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)
# code to be run in CPython
Note that `ndarray.reshape()` can also be called by assigning to `ndarray.shape`.
.shape¶
numpy
:
https://numpy.org/doc/stable/reference/generated/numpy.ndarray.shape.html
The .shape
property is a tuple whose elements are the length of the
array along each axis.
# 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)
By assigning a tuple to the .shape
property, the array can be
reshape
d:
# code to be run in micropython
from ulab import numpy as np
a = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])
print('a:\n', a)
a.shape = (3, 3)
print('\na:\n', a)
a:
array([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0], dtype=float64)
a:
array([[1.0, 2.0, 3.0],
[4.0, 5.0, 6.0],
[7.0, 8.0, 9.0]], dtype=float64)
.size¶
numpy
:
https://numpy.org/doc/stable/reference/generated/numpy.ndarray.size.html
The .size
property is an integer specifying the number of elements
in the array.
# 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
.T
The .T
property of the ndarray
is equivalent to
.transpose.
.tobytes¶
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)
.tolist¶
numpy
:
https://numpy.org/doc/stable/reference/generated/numpy.ndarray.tolist.html
The .tolist
method can be used for converting the numerical array
into a (nested) python
lists.
# code to be run in micropython
from ulab import numpy as np
a = np.array(range(4), dtype=np.uint8)
print('a: ', a)
b = a.tolist()
print('b: ', b)
c = a.reshape((2, 2))
print('='*20)
print('c: ', c)
d = c.tolist()
print('d: ', d)
a: array([0, 1, 2, 3], dtype=uint8)
b: [0, 1, 2, 3]
====================
c: array([[0, 1],
[2, 3]], dtype=uint8)
d: [[0, 1], [2, 3]]
.transpose¶
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)
The transpose of the array can also be gotten through the T
property:
# 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)
print('\ntranspose of a:\n', a.T)
a:
array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]], dtype=uint8)
transpose of a:
array([[1, 4, 7],
[2, 5, 8],
[3, 6, 9]], dtype=uint8)
.sort¶
numpy
:
https://docs.scipy.org/doc/numpy/reference/generated/numpy.sort.html
Inplace 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)
Unary operators¶
With the exception of len
, which returns a single number, all unary
operators manipulate the underlying data elementwise.
len¶
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).
invert¶
The function is defined for integer data types (uint8
, int8
,
uint16
, and int16
) only, takes a single argument, and returns
the elementbyelement, bitwise 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)
abs¶
This function takes a single argument, and returns the
elementbyelement 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)
neg¶
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)
pos¶
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)
Binary operators¶
ulab
implements the +
, 
, *
, /
, **
, <
,
>
, <=
, >=
, ==
, !=
, +=
, =
, *=
, /=
,
**=
binary operators that work elementwise. 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 elementwise 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.
Upcasting¶
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 singleelement
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 

























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)
Benchmarks¶
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.
Comparison operators¶
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'
Iterating over arrays¶
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
onedimensional, the iterator returns scalars, otherwise a new
reduceddimensional 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)
Slicing and indexing¶
Views vs. copies¶
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
nonnegative) 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/understandingslicenotation.
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.
Indexing¶
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 higherdimensional 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 onedimensional. 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)
Slicing and assigning to slices¶
You can also generate subarrays 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 reset 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 subsets 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.