Numpy

Numpy
Author

Benedict Thekkel

Import Numpy

!pip list | grep numpy
numpy                         1.23.5
import numpy as np

Creating Numpy Arrays

Python sequences to NumPy Arrays

a1D = np.array([1, 2, 3, 4])

a2D = np.array([[1, 2], [3, 4]])

a3D = np.array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]])

a1D, a2D, a3D
(array([1, 2, 3, 4]),
 array([[1, 2],
        [3, 4]]),
 array([[[1, 2],
         [3, 4]],
 
        [[5, 6],
         [7, 8]]]))
a = np.array([127, 128, 129], dtype=np.int8)
a
array([ 127, -128, -127], dtype=int8)

Intrinsic NumPy array creation functions

np.arange(10)
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
np.arange(2, 10, dtype=float)
array([2., 3., 4., 5., 6., 7., 8., 9.])
np.arange(2, 3, 0.1)
array([2. , 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9])
np.linspace(1., 4., 6)
array([1. , 1.6, 2.2, 2.8, 3.4, 4. ])
np.eye(3)
array([[1., 0., 0.],
       [0., 1., 0.],
       [0., 0., 1.]])
np.eye(3, 5)
array([[1., 0., 0., 0., 0.],
       [0., 1., 0., 0., 0.],
       [0., 0., 1., 0., 0.]])
np.diag([1, 2, 3])
array([[1, 0, 0],
       [0, 2, 0],
       [0, 0, 3]])
np.diag([1, 2, 3], 1)
array([[0, 1, 0, 0],
       [0, 0, 2, 0],
       [0, 0, 0, 3],
       [0, 0, 0, 0]])
np.vander(np.linspace(0, 2, 5), 3)
array([[0.  , 0.  , 1.  ],
       [0.25, 0.5 , 1.  ],
       [1.  , 1.  , 1.  ],
       [2.25, 1.5 , 1.  ],
       [4.  , 2.  , 1.  ]])
np.zeros((2, 3))
array([[0., 0., 0.],
       [0., 0., 0.]])
np.ones((2, 3, 2))
array([[[1., 1.],
        [1., 1.],
        [1., 1.]],

       [[1., 1.],
        [1., 1.],
        [1., 1.]]])
from numpy.random import default_rng
default_rng(42).random((2,3))
array([[0.77395605, 0.43887844, 0.85859792],
       [0.69736803, 0.09417735, 0.97562235]])
np.indices((3,3))
array([[[0, 0, 0],
        [1, 1, 1],
        [2, 2, 2]],

       [[0, 1, 2],
        [0, 1, 2],
        [0, 1, 2]]])

Replicating, joining, or mutating existing arrays

a = np.array([1, 2, 3, 4, 5, 6])

b = a[:2]

b += 1

print('a =', a, '; b =', b)
a = [2 3 3 4 5 6] ; b = [2 3]
a = np.array([1, 2, 3, 4])

b = a[:2].copy()

b += 1

print('a = ', a, 'b = ', b)
a =  [1 2 3 4] b =  [2 3]
A = np.ones((2, 2))

B = np.eye(2, 2)

C = np.zeros((2, 2))

D = np.diag((-3, -4))

np.block([[A, B], [C, D]])
array([[ 1.,  1.,  1.,  0.],
       [ 1.,  1.,  0.,  1.],
       [ 0.,  0., -3.,  0.],
       [ 0.,  0.,  0., -4.]])

Indexing

Basic indexing

x = np.arange(10)
x,x[2]
(array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]), 2)
x[-2]
8
x.shape = (2, 5)  # now x is 2-dimensional

x, x[1, 3]
(array([[0, 1, 2, 3, 4],
        [5, 6, 7, 8, 9]]),
 8)
x[0], x[0][2]
(array([0, 1, 2, 3, 4]), 2)

Slicing and striding

x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

x[1:7:2]
array([1, 3, 5])
x[-2:10]
array([8, 9])
x[-3:3:-1]
array([7, 6, 5, 4])
x[5:]
array([5, 6, 7, 8, 9])
x = np.array([[[1],[2],[3]], [[4],[5],[6]]])

x.shape, x[1:2]
((2, 3, 1),
 array([[[4],
         [5],
         [6]]]))

Dimensional indexing tools

x[..., 0]
array([[1, 2, 3],
       [4, 5, 6]])
x[:, :, 0]
array([[1, 2, 3],
       [4, 5, 6]])
x[:, np.newaxis, :, :].shape
(2, 1, 3, 1)
x[:, None, :, :].shape
(2, 1, 3, 1)
x = np.arange(5)
x
array([0, 1, 2, 3, 4])
x[:, np.newaxis] + x[np.newaxis, :]
array([[0, 1, 2, 3, 4],
       [1, 2, 3, 4, 5],
       [2, 3, 4, 5, 6],
       [3, 4, 5, 6, 7],
       [4, 5, 6, 7, 8]])

Advanced indexing

x = np.arange(10, 1, -1)
x[np.array([3, 3, 1, 8])]
array([7, 7, 9, 2])
x = np.array([[1, 2], [3, 4], [5, 6]])
y = np.arange(35).reshape(5, 7)

y
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, 25, 26, 27],
       [28, 29, 30, 31, 32, 33, 34]])
y[np.array([0, 2, 4]), np.array([0, 1, 2])]
array([ 0, 15, 30])
y[np.array([0, 2, 4]), 1]
array([ 1, 15, 29])
y[np.array([0, 2, 4])]
array([[ 0,  1,  2,  3,  4,  5,  6],
       [14, 15, 16, 17, 18, 19, 20],
       [28, 29, 30, 31, 32, 33, 34]])
x = np.array([[1, 2], [3, 4], [5, 6]])

x[[0, 1, 2], [0, 1, 0]]
array([1, 4, 5])
x = np.array([[ 0,  1,  2],

              [ 3,  4,  5],

              [ 6,  7,  8],

              [ 9, 10, 11]])

rows = np.array([[0, 0],

                 [3, 3]], dtype=np.intp)

columns = np.array([[0, 2],

                    [0, 2]], dtype=np.intp)

x[rows, columns]
array([[ 0,  2],
       [ 9, 11]])
rows = np.array([0, 3], dtype=np.intp)

columns = np.array([0, 2], dtype=np.intp)

rows[:, np.newaxis]
array([[0],
       [3]])
x[rows[:, np.newaxis], columns]
array([[ 0,  2],
       [ 9, 11]])
x[np.ix_(rows, columns)]
array([[ 0,  2],
       [ 9, 11]])
x = np.array([[1., 2.], [np.nan, 3.], [np.nan, np.nan]])

x[~np.isnan(x)]
array([1., 2., 3.])
x = np.array([1., -1., -2., 3])

x[x < 0] += 20

x
array([ 1., 19., 18.,  3.])
x = np.arange(35).reshape(5, 7)

b = x > 20
b
array([[False, False, False, False, False, False, False],
       [False, False, False, False, False, False, False],
       [False, False, False, False, False, False, False],
       [ True,  True,  True,  True,  True,  True,  True],
       [ True,  True,  True,  True,  True,  True,  True]])
b[:, 5]
array([False, False, False,  True,  True])
x[b[:, 5]]
array([[21, 22, 23, 24, 25, 26, 27],
       [28, 29, 30, 31, 32, 33, 34]])
x = np.array([[ 0,  1,  2],

              [ 3,  4,  5],

              [ 6,  7,  8],

              [ 9, 10, 11]])

rows = (x.sum(-1) % 2) == 0

rows
array([False,  True, False,  True])
columns = [0, 2]

x[np.ix_(rows, columns)]
array([[ 3,  5],
       [ 9, 11]])
rows = rows.nonzero()[0]

x[rows[:, np.newaxis], columns]
array([[ 3,  5],
       [ 9, 11]])
x = np.arange(30).reshape(2, 3, 5)

x
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],
        [25, 26, 27, 28, 29]]])
b = np.array([[True, True, False], [False, True, True]])

x[b]
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [20, 21, 22, 23, 24],
       [25, 26, 27, 28, 29]])
y = np.arange(35).reshape(5,7)

y[np.array([0, 2, 4]), 1:3]
array([[ 1,  2],
       [15, 16],
       [29, 30]])
y[:, 1:3][np.array([0, 2, 4]), :]
array([[ 1,  2],
       [15, 16],
       [29, 30]])
x = np.array([[ 0,  1,  2],

              [ 3,  4,  5],

              [ 6,  7,  8],

              [ 9, 10, 11]])

x[1:2, 1:3]
array([[4, 5]])
x[1:2, [1, 2]]
array([[4, 5]])
x = np.arange(35).reshape(5, 7)

b = x > 20

b
array([[False, False, False, False, False, False, False],
       [False, False, False, False, False, False, False],
       [False, False, False, False, False, False, False],
       [ True,  True,  True,  True,  True,  True,  True],
       [ True,  True,  True,  True,  True,  True,  True]])
x[b[:, 5], 1:3]
array([[22, 23],
       [29, 30]])

Field Access

x = np.zeros((2, 2), dtype=[('a', np.int32), ('b', np.float64, (3, 3))])
x
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.]])]],
      dtype=[('a', '<i4'), ('b', '<f8', (3, 3))])
x['a'].shape, x['b'].shape
((2, 2), (2, 2, 3, 3))
x['a'].dtype, x['b'].dtype
(dtype('int32'), dtype('float64'))

Assigning values to indexed arrays

x = np.arange(10)

x[2:7] = 1
x[2:7] = np.arange(5)
x[1] = 1.2

x[1]
1
x = np.arange(0, 50, 10)
x
array([ 0, 10, 20, 30, 40])
x[np.array([1, 1, 3, 1])] += 1

x
array([ 0, 11, 20, 31, 40])

Dealing with variable numbers of indices within programs

z = np.arange(81).reshape(3, 3, 3, 3)

indices = (1, 1, 1, 1)

z[indices]
40
indices = (1, 1, 1, slice(0, 2))  # same as [1, 1, 1, 0:2]

z[indices]
array([39, 40])
indices = (1, Ellipsis, 1)  # same as [1, ..., 1]

z[indices]
array([[28, 31, 34],
       [37, 40, 43],
       [46, 49, 52]])
z[[1, 1, 1, 1]]  # produces a large array
array([[[[27, 28, 29],
         [30, 31, 32],
         [33, 34, 35]],

        [[36, 37, 38],
         [39, 40, 41],
         [42, 43, 44]],

        [[45, 46, 47],
         [48, 49, 50],
         [51, 52, 53]]],


       [[[27, 28, 29],
         [30, 31, 32],
         [33, 34, 35]],

        [[36, 37, 38],
         [39, 40, 41],
         [42, 43, 44]],

        [[45, 46, 47],
         [48, 49, 50],
         [51, 52, 53]]],


       [[[27, 28, 29],
         [30, 31, 32],
         [33, 34, 35]],

        [[36, 37, 38],
         [39, 40, 41],
         [42, 43, 44]],

        [[45, 46, 47],
         [48, 49, 50],
         [51, 52, 53]]],


       [[[27, 28, 29],
         [30, 31, 32],
         [33, 34, 35]],

        [[36, 37, 38],
         [39, 40, 41],
         [42, 43, 44]],

        [[45, 46, 47],
         [48, 49, 50],
         [51, 52, 53]]]])
z[(1, 1, 1, 1)]  # returns a single value
40

I/O with Numpy

Splitting the lines into columns

import numpy as np

from io import StringIO
data = u"1, 2, 3\n4, 5, 6"

np.genfromtxt(StringIO(data), delimiter=",")
array([[1., 2., 3.],
       [4., 5., 6.]])
data = u"  1  2  3\n  4  5 67\n890123  4"

np.genfromtxt(StringIO(data), delimiter=3)
array([[  1.,   2.,   3.],
       [  4.,   5.,  67.],
       [890., 123.,   4.]])
data = u"123456789\n   4  7 9\n   4567 9"

np.genfromtxt(StringIO(data), delimiter=(4, 3, 2))
array([[1234.,  567.,   89.],
       [   4.,    7.,    9.],
       [   4.,  567.,    9.]])
data = u"1, abc , 2\n 3, xxx, 4"

# Without autostrip

np.genfromtxt(StringIO(data), delimiter=",", dtype="|U5")
array([['1', ' abc ', ' 2'],
       ['3', ' xxx', ' 4']], dtype='<U5')
np.genfromtxt(StringIO(data), delimiter=",", dtype="|U5", autostrip=True)
array([['1', 'abc', '2'],
       ['3', 'xxx', '4']], dtype='<U5')
data = u"""#

# Skip me !

# Skip me too !

1, 2

3, 4

5, 6 #This is the third line of the data

7, 8

# And here comes the last line

9, 0

"""

np.genfromtxt(StringIO(data), comments="#", delimiter=",")
array([[1., 2.],
       [3., 4.],
       [5., 6.],
       [7., 8.],
       [9., 0.]])

Skipping lines and choosing columns

data = u"\n".join(str(i) for i in range(10))

np.genfromtxt(StringIO(data),)
array([0., 1., 2., 3., 4., 5., 6., 7., 8., 9.])
np.genfromtxt(StringIO(data),
              skip_header=3, skip_footer=5)
array([3., 4.])
data = u"1 2 3\n4 5 6"

np.genfromtxt(StringIO(data), usecols=(0, -1))
array([[1., 3.],
       [4., 6.]])
data = u"1 2 3\n4 5 6"

np.genfromtxt(StringIO(data),
              names="a, b, c", usecols=("a", "c"))
array([(1., 3.), (4., 6.)], dtype=[('a', '<f8'), ('c', '<f8')])
np.genfromtxt(StringIO(data),
              names="a, b, c", usecols=("a, c"))
array([(1., 3.), (4., 6.)], dtype=[('a', '<f8'), ('c', '<f8')])

Choosing the data type

The main way to control how the sequences of strings we have read from the file are converted to other types is to set the dtype argument. Acceptable values for this argument are:

  • a single type, such as dtype=float. The output will be 2D with the given dtype, unless a name has been associated with each column with the use of the names argument (see below). Note that dtype=float is the default for genfromtxt.

  • a sequence of types, such as dtype=(int, float, float).

  • a comma-separated string, such as dtype=“i4,f8,|U3”.

  • a dictionary with two keys ‘names’ and ‘formats’.

  • a sequence of tuples (name, type), such as dtype=[(‘A’, int), (‘B’, float)].

  • an existing numpy.dtype object.

  • the special value None. In that case, the type of the columns will be determined from the data itself (see below).

In all the cases but the first one, the output will be a 1D array with a structured dtype. This dtype has as many fields as items in the sequence. The field names are defined with the names keyword.

When dtype=None, the type of each column is determined iteratively from its data. We start by checking whether a string can be converted to a boolean (that is, if the string matches true or false in lower cases); then whether it can be converted to an integer, then to a float, then to a complex and eventually to a string.

The option dtype=None is provided for convenience. However, it is significantly slower than setting the dtype explicitly.

Setting the names

data = StringIO("1 2 3\n 4 5 6")

a = np.genfromtxt(data, dtype=[(_, int) for _ in "abc"])
a
array([(1, 2, 3), (4, 5, 6)],
      dtype=[('a', '<i8'), ('b', '<i8'), ('c', '<i8')])
a['a']
array([1, 4])
data = StringIO("1 2 3\n 4 5 6")

np.genfromtxt(data, names="A, B, C")
array([(1., 2., 3.), (4., 5., 6.)],
      dtype=[('A', '<f8'), ('B', '<f8'), ('C', '<f8')])
data = StringIO("So it goes\n#a b c\n1 2 3\n 4 5 6")

np.genfromtxt(data, skip_header=1, names=True)
array([(1., 2., 3.), (4., 5., 6.)],
      dtype=[('a', '<f8'), ('b', '<f8'), ('c', '<f8')])
data = StringIO("1 2 3\n 4 5 6")

ndtype=[('a',int), ('b', float), ('c', int)]

names = ["A", "B", "C"]

np.genfromtxt(data, names=names, dtype=ndtype)
array([(1, 2., 3), (4, 5., 6)],
      dtype=[('A', '<i8'), ('B', '<f8'), ('C', '<i8')])
data = StringIO("1 2 3\n 4 5 6")

np.genfromtxt(data, dtype=(int, float, int))
array([(1, 2., 3), (4, 5., 6)],
      dtype=[('f0', '<i8'), ('f1', '<f8'), ('f2', '<i8')])
data = StringIO("1 2 3\n 4 5 6")

np.genfromtxt(data, dtype=(int, float, int), names="a")
array([(1, 2., 3), (4, 5., 6)],
      dtype=[('a', '<i8'), ('f0', '<f8'), ('f1', '<i8')])
data = StringIO("1 2 3\n 4 5 6")

np.genfromtxt(data, dtype=(int, float, int), defaultfmt="var_%02i")
array([(1, 2., 3), (4, 5., 6)],
      dtype=[('var_00', '<i8'), ('var_01', '<f8'), ('var_02', '<i8')])

Tweaking the conversion

convertfunc = lambda x: float(x.strip(b"%"))/100.

data = u"1, 2.3%, 45.\n6, 78.9%, 0"

names = ("i", "p", "n")

# General case .....
np.genfromtxt(StringIO(data), delimiter=",", names=names)
array([(1., nan, 45.), (6., nan,  0.)],
      dtype=[('i', '<f8'), ('p', '<f8'), ('n', '<f8')])
# Converted case ...
np.genfromtxt(StringIO(data), delimiter=",", names=names,
              converters={1: convertfunc})
array([(1., 0.023, 45.), (6., 0.789,  0.)],
      dtype=[('i', '<f8'), ('p', '<f8'), ('n', '<f8')])
# Using a name for the converter ...

np.genfromtxt(StringIO(data), delimiter=",", names=names,
              converters={"p": convertfunc})
array([(1., 0.023, 45.), (6., 0.789,  0.)],
      dtype=[('i', '<f8'), ('p', '<f8'), ('n', '<f8')])
data = u"1, , 3\n 4, 5, 6"

convert = lambda x: float(x.strip() or -999)

np.genfromtxt(StringIO(data), delimiter=",",

              converters={1: convert})
array([[   1., -999.,    3.],
       [   4.,    5.,    6.]])
data = u"N/A, 2, 3\n4, ,???"

kwargs = dict(delimiter=",",

              dtype=int,

              names="a,b,c",

              missing_values={0:"N/A", 'b':" ", 2:"???"},

              filling_values={0:0, 'b':0, 2:-999})

np.genfromtxt(StringIO(data), **kwargs)
array([(0, 2,    3), (4, 0, -999)],
      dtype=[('a', '<i8'), ('b', '<i8'), ('c', '<i8')])

Data types

Array types and conversions between types

Numpy type C type Description
numpy.bool_ bool Boolean (True or False) stored as a byte
numpy.byte signed char Platform-defined
numpy.ubyte unsigned char Platform-defined
numpy.short short Platform-defined
numpy.ushort unsigned short Platform-defined
numpy.intc int Platform-defined
numpy.uintc unsigned int Platform-defined
numpy.int_ long Platform-defined
numpy.uint unsigned long Platform-defined
numpy.longlong long long Platform-defined
numpy.ulonglong unsigned long long Platform-defined
numpy.half / numpy.float16 Half precision float: sign bit, 5 bits exponent, 10 bits mantissa
numpy.single float Platform-defined single precision float: typically sign bit, 8 bits exponent, 23 bits mantissa
numpy.double double Platform-defined double precision float: typically sign bit, 11 bits exponent, 52 bits mantissa.
numpy.longdouble long double Platform-defined extended-precision float
numpy.csingle float complex Complex number, represented by two single-precision floats (real and imaginary components)
numpy.cdouble double complex Complex number, represented by two double-precision floats (real and imaginary components).
numpy.clongdouble long double complex Complex number, represented by two extended-precision floats (real and imaginary components). 
x = np.float32(1.0)

x
1.0
y = np.int_([1,2,4])

y
array([1, 2, 4])
z = np.arange(3, dtype=np.uint8)

z
array([0, 1, 2], dtype=uint8)
np.array([1, 2, 3], dtype='f')
array([1., 2., 3.], dtype=float32)
z.astype(float)
array([0., 1., 2.])
np.int8(z)
array([0, 1, 2], dtype=int8)
z.dtype
dtype('uint8')
d = np.dtype(int)

d
dtype('int64')
np.issubdtype(d, np.integer)
True
np.issubdtype(d, np.floating)
False
np.power(100, 8, dtype=np.int64)
10000000000000000
np.power(100, 8, dtype=np.int32)
1874919424
np.iinfo(int) # Bounds of the default integer on this system.
iinfo(min=-9223372036854775808, max=9223372036854775807, dtype=int64)
np.iinfo(np.int32) # Bounds of a 32-bit integer
iinfo(min=-2147483648, max=2147483647, dtype=int32)
np.iinfo(np.int64) # Bounds of a 64-bit integer
iinfo(min=-9223372036854775808, max=9223372036854775807, dtype=int64)
np.power(100, 100, dtype=np.int64) # Incorrect even with 64-bit int
0
np.power(100, 100, dtype=np.float64)
1e+200

Broadcastable arrays

a = np.array([1.0, 2.0, 3.0])

b = np.array([2.0, 2.0, 2.0])

a * b
array([2., 4., 6.])
a = np.array([1.0, 2.0, 3.0])

b = 2.0

a * b
array([2., 4., 6.])
a = np.array([[ 0.0,  0.0,  0.0],

              [10.0, 10.0, 10.0],

              [20.0, 20.0, 20.0],

              [30.0, 30.0, 30.0]])

b = np.array([1.0, 2.0, 3.0])

a + b
array([[ 1.,  2.,  3.],
       [11., 12., 13.],
       [21., 22., 23.],
       [31., 32., 33.]])
a = np.array([0.0, 10.0, 20.0, 30.0])

b = np.array([1.0, 2.0, 3.0])

a[:, np.newaxis] + b
array([[ 1.,  2.,  3.],
       [11., 12., 13.],
       [21., 22., 23.],
       [31., 32., 33.]])
from numpy import array, argmin, sqrt, sum
observation = array([111.0, 188.0])

codes = array([[102.0, 203.0],

               [132.0, 193.0],

               [45.0, 155.0],

               [57.0, 173.0]])

diff = codes - observation    # the broadcast happens here

dist = sqrt(sum(diff**2,axis=-1))

argmin(dist)
0

Copies and views

Indexing operations

x = np.arange(10)

x
array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
y = x[1:3]  # creates a view

y
array([1, 2])
x[1:3] = [10, 11]
x
array([ 0, 10, 11,  3,  4,  5,  6,  7,  8,  9])
y
array([10, 11])
x = np.arange(9).reshape(3, 3)
x
array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])
y = x[[1, 2]]
y
array([[3, 4, 5],
       [6, 7, 8]])
y.base is None
True
x[[1, 2]] = [[10, 11, 12], [13, 14, 15]]
x
array([[ 0,  1,  2],
       [10, 11, 12],
       [13, 14, 15]])
y
array([[3, 4, 5],
       [6, 7, 8]])
x = np.ones((2, 3))

y = x.T  # makes the array non-contiguous

y
array([[1., 1.],
       [1., 1.],
       [1., 1.]])

How to tell if the array is a view or a copy

x = np.arange(9)

x
array([0, 1, 2, 3, 4, 5, 6, 7, 8])
y = x.reshape(3, 3)

y
array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])
y.base  # .reshape() creates a view
array([0, 1, 2, 3, 4, 5, 6, 7, 8])
z = y[[2, 1]]
z
array([[6, 7, 8],
       [3, 4, 5]])
z.base is None  # advanced indexing creates a copy
True

Structured arrays

x = np.array([('Rex', 9, 81.0), ('Fido', 3, 27.0)],
             dtype=[('name', 'U10'), ('age', 'i4'), ('weight', 'f4')])
x
array([('Rex', 9, 81.), ('Fido', 3, 27.)],
      dtype=[('name', '<U10'), ('age', '<i4'), ('weight', '<f4')])
x[1]
('Fido', 3, 27.)
x['age']
array([9, 3], dtype=int32)
x['age'] = 5
x
array([('Rex', 5, 81.), ('Fido', 5, 27.)],
      dtype=[('name', '<U10'), ('age', '<i4'), ('weight', '<f4')])
np.dtype([('x', 'f4'), ('y', np.float32), ('z', 'f4', (2, 2))])
dtype([('x', '<f4'), ('y', '<f4'), ('z', '<f4', (2, 2))])
np.dtype([('x', 'f4'), ('', 'i4'), ('z', 'i8')])
dtype([('x', '<f4'), ('f1', '<i4'), ('z', '<i8')])
np.dtype('i8, f4, S3')
dtype([('f0', '<i8'), ('f1', '<f4'), ('f2', 'S3')])
np.dtype('3int8, float32, (2, 3)float64')
dtype([('f0', 'i1', (3,)), ('f1', '<f4'), ('f2', '<f8', (2, 3))])
np.dtype({'names': ['col1', 'col2'], 'formats': ['i4', 'f4']})
dtype([('col1', '<i4'), ('col2', '<f4')])
np.dtype({'names': ['col1', 'col2'],
          'formats': ['i4', 'f4'],
          'offsets': [0, 4],
          'itemsize': 12})
dtype({'names': ['col1', 'col2'], 'formats': ['<i4', '<f4'], 'offsets': [0, 4], 'itemsize': 12})
np.dtype({'col1': ('i1', 0), 'col2': ('f4', 1)})
dtype([('col1', 'i1'), ('col2', '<f4')])

Manipulating and Displaying Structured Datatypes

d = np.dtype([('x', 'i8'), ('y', 'f4')])

d.names
('x', 'y')
d['x']
dtype('int64')
d.fields
mappingproxy({'x': (dtype('int64'), 0), 'y': (dtype('float32'), 8)})
def print_offsets(d):

    print("offsets:", [d.fields[name][1] for name in d.names])

    print("itemsize:", d.itemsize)
print_offsets(np.dtype('u1, u1, i4, u1, i8, u2'))
offsets: [0, 1, 2, 6, 7, 15]
itemsize: 17
print_offsets(np.dtype('u1, u1, i4, u1, i8, u2', align=True))
offsets: [0, 1, 4, 8, 16, 24]
itemsize: 32
np.dtype([(('my title', 'name'), 'f4')])
dtype([(('my title', 'name'), '<f4')])
np.dtype({'name': ('i4', 0, 'my title')})
dtype([(('my title', 'name'), '<i4')])
for name in d.names:
    print(d.fields[name][:2])
(dtype('int64'), 0)
(dtype('float32'), 8)

Indexing and Assignment to Structured arrays

x = np.array([(1, 2, 3), (4, 5, 6)], dtype='i8, f4, f8')
x
array([(1, 2., 3.), (4, 5., 6.)],
      dtype=[('f0', '<i8'), ('f1', '<f4'), ('f2', '<f8')])
x[1] = (7, 8, 9)
x
array([(1, 2., 3.), (7, 8., 9.)],
      dtype=[('f0', '<i8'), ('f1', '<f4'), ('f2', '<f8')])
x = np.zeros(2, dtype='i8, f4, ?, S1')
x[:] = 3
x
array([(3, 3.,  True, b'3'), (3, 3.,  True, b'3')],
      dtype=[('f0', '<i8'), ('f1', '<f4'), ('f2', '?'), ('f3', 'S1')])
x[:] = np.arange(2)
x
array([(0, 0., False, b'0'), (1, 1.,  True, b'1')],
      dtype=[('f0', '<i8'), ('f1', '<f4'), ('f2', '?'), ('f3', 'S1')])
a = np.zeros(3, dtype=[('a', 'i8'), ('b', 'f4'), ('c', 'S3')])
b = np.ones(3, dtype=[('x', 'f4'), ('y', 'S3'), ('z', 'O')])
b[:] = a
b
array([(0., b'0.0', b''), (0., b'0.0', b''), (0., b'0.0', b'')],
      dtype=[('x', '<f4'), ('y', 'S3'), ('z', 'O')])
x = np.array([(1, 2), (3, 4)], dtype=[('foo', 'i8'), ('bar', 'f4')])

x['foo']
array([1, 3])
x['foo'] = 10

x
array([(10, 2.), (10, 4.)], dtype=[('foo', '<i8'), ('bar', '<f4')])
y = x['bar']

y[:] = 11

x
array([(10, 11.), (10, 11.)], dtype=[('foo', '<i8'), ('bar', '<f4')])
y.dtype, y.shape, y.strides
(dtype('float32'), (2,), (12,))
x = np.zeros((2, 2), dtype=[('a', np.int32), ('b', np.float64, (3, 3))])

x['a'].shape
(2, 2)
x['b'].shape
(2, 2, 3, 3)
a = np.zeros(3, dtype=[('a', 'i4'), ('b', 'i4'), ('c', 'f4')])

a[['a', 'c']]
array([(0, 0.), (0, 0.), (0, 0.)],
      dtype={'names': ['a', 'c'], 'formats': ['<i4', '<f4'], 'offsets': [0, 8], 'itemsize': 12})
from numpy.lib.recfunctions import repack_fields

repack_fields(a[['a', 'c']]).view('i8')  # supported in 1.16
array([0, 0, 0])
b = np.zeros(3, dtype=[('x', 'f4'), ('y', 'f4'), ('z', 'f4')])

b[['x', 'z']].view('f4')
array([0., 0., 0., 0., 0., 0., 0., 0., 0.], dtype=float32)
from numpy.lib.recfunctions import structured_to_unstructured

structured_to_unstructured(b[['x', 'z']])
array([[0., 0.],
       [0., 0.],
       [0., 0.]], dtype=float32)
a[['a', 'c']] = (2, 3)

a
array([(2, 0, 3.), (2, 0, 3.), (2, 0, 3.)],
      dtype=[('a', '<i4'), ('b', '<i4'), ('c', '<f4')])
a[['a', 'c']] = a[['c', 'a']]
x = np.array([(1, 2., 3.)], dtype='i, f, f')

scalar = x[0]

scalar
(1, 2., 3.)
type(scalar)
numpy.void
x = np.array([(1, 2), (3, 4)], dtype=[('foo', 'i8'), ('bar', 'f4')])
s = x[0]
s['bar'] = 100
x
array([(1, 100.), (3,   4.)], dtype=[('foo', '<i8'), ('bar', '<f4')])
scalar = np.array([(1, 2., 3.)], dtype='i, f, f')[0]
scalar[0]
1
scalar[1] = 4
scalar.item(), type(scalar.item())
((1, 4.0, 3.0), tuple)

Structure Comparison and Promotiona

a = np.array([(1, 1), (2, 2)], dtype=[('a', 'i4'), ('b', 'i4')])

b = np.array([(1, 1), (2, 3)], dtype=[('a', 'i4'), ('b', 'i4')])

a == b
array([ True, False])
a = np.array([(1, 1), (2, 2)], dtype=[('a', 'i4'), ('b', 'i4')])

b = np.array([(1, 1), (2, 3)], dtype=[('a', 'i4'), ('b', 'i4')])

a == b
array([ True, False])
b = np.array([(1.0, 1), (2.5, 2)], dtype=[("a", "f4"), ("b", "i4")])

a == b
array([ True, False])
np.result_type(np.dtype("i,>i"))
dtype([('f0', '<i4'), ('f1', '<i4')])
np.result_type(np.dtype("i,>i"), np.dtype("i,i"))
dtype([('f0', '<i4'), ('f1', '<i4')])
dt = np.dtype("i1,V3,i4,V1")[["f0", "f2"]]
dt
dtype({'names': ['f0', 'f2'], 'formats': ['i1', '<i4'], 'offsets': [0, 4], 'itemsize': 9})
np.result_type(dt)
dtype([('f0', 'i1'), ('f2', '<i4')])
dt = np.dtype("i1,V3,i4,V1", align=True)[["f0", "f2"]]

dt
dtype({'names': ['f0', 'f2'], 'formats': ['i1', '<i4'], 'offsets': [0, 4], 'itemsize': 12}, align=True)
np.result_type(dt)
dtype([('f0', 'i1'), ('f2', '<i4')], align=True)
np.result_type(dt).isalignedstruct
True
np.result_type(np.dtype("i,i"), np.dtype("i,i", align=True))
dtype([('f0', '<i4'), ('f1', '<i4')], align=True)

Record Arrays

recordarr = np.rec.array([(1, 2., 'Hello'), (2, 3., "World")],

                   dtype=[('foo', 'i4'),('bar', 'f4'), ('baz', 'S10')])
recordarr.bar
array([2., 3.], dtype=float32)
recordarr[1:2]
rec.array([(2, 3., b'World')],
          dtype=[('foo', '<i4'), ('bar', '<f4'), ('baz', 'S10')])
recordarr[1:2].foo
array([2], dtype=int32)
recordarr.foo[1:2]
array([2], dtype=int32)
recordarr[1].baz
b'World'
arr = np.array([(1, 2., 'Hello'), (2, 3., "World")],

            dtype=[('foo', 'i4'), ('bar', 'f4'), ('baz', 'S10')])
recordarr = np.rec.array(arr)
arr = np.array([(1, 2., 'Hello'), (2, 3., "World")],

               dtype=[('foo', 'i4'),('bar', 'f4'), ('baz', 'a10')])
recordarr = arr.view(dtype=np.dtype((np.record, arr.dtype)),

                     type=np.recarray)
recordarr = arr.view(np.recarray)

recordarr.dtype
dtype((numpy.record, [('foo', '<i4'), ('bar', '<f4'), ('baz', 'S10')]))
arr2 = recordarr.view(recordarr.dtype.fields or recordarr.dtype, np.ndarray)
recordarr = np.rec.array([('Hello', (1, 2)), ("World", (3, 4))],

                dtype=[('foo', 'S6'),('bar', [('A', int), ('B', int)])])
type(recordarr.foo)
numpy.ndarray
type(recordarr.bar)
numpy.recarray
from numpy.lib import recfunctions as rfn

b = np.array([(1, 2, 5), (4, 5, 7), (7, 8 ,11), (10, 11, 12)],

             dtype=[('x', 'i4'), ('y', 'f4'), ('z', 'f8')])
rfn.apply_along_fields(np.mean, b)
array([ 2.66666667,  5.33333333,  8.66666667, 11.        ])
rfn.apply_along_fields(np.mean, b[['x', 'z']])
array([ 3. ,  5.5,  9. , 11. ])
from numpy.lib import recfunctions as rfn

a = np.array([(1, (2, 3.0)), (4, (5, 6.0))],

  dtype=[('a', np.int64), ('b', [('ba', np.double), ('bb', np.int64)])])
rfn.drop_fields(a, 'a')
array([((2., 3),), ((5., 6),)],
      dtype=[('b', [('ba', '<f8'), ('bb', '<i8')])])
rfn.drop_fields(a, 'ba')
array([(1, (3,)), (4, (6,))], dtype=[('a', '<i8'), ('b', [('bb', '<i8')])])
rfn.drop_fields(a, ['ba', 'bb'])
array([(1,), (4,)], dtype=[('a', '<i8')])
from numpy.lib import recfunctions as rfn

ndtype = [('a', int)]

a = np.ma.array([1, 1, 1, 2, 2, 3, 3],

        mask=[0, 0, 1, 0, 0, 0, 1]).view(ndtype)
rfn.find_duplicates(a, ignoremask=True, return_index=True)
(masked_array(data=[(1,), (1,), (2,), (2,)],
              mask=[(False,), (False,), (False,), (False,)],
        fill_value=(999999,),
             dtype=[('a', '<i8')]),
 array([0, 1, 3, 4]))
from numpy.lib import recfunctions as rfn

ndtype = np.dtype([('a', '<i4'), ('b', [('ba', '<f8'), ('bb', '<i4')])])

rfn.flatten_descr(ndtype)
(('a', dtype('int32')), ('ba', dtype('float64')), ('bb', dtype('int32')))
from numpy.lib import recfunctions as rfn

ndtype =  np.dtype([('A', int),

                    ('B', [('BA', int),

                           ('BB', [('BBA', int), ('BBB', int)])])])

rfn.get_fieldstructure(ndtype)
{'A': [],
 'B': [],
 'BA': ['B'],
 'BB': ['B'],
 'BBA': ['B', 'BB'],
 'BBB': ['B', 'BB']}
from numpy.lib import recfunctions as rfn

rfn.get_names(np.empty((1,), dtype=[('A', int)]).dtype)
('A',)
rfn.get_names(np.empty((1,), dtype=[('A',int), ('B', float)]).dtype)
('A', 'B')
adtype = np.dtype([('a', int), ('b', [('ba', int), ('bb', int)])])

rfn.get_names(adtype)
('a', ('b', ('ba', 'bb')))
from numpy.lib import recfunctions as rfn

rfn.get_names_flat(np.empty((1,), dtype=[('A', int)]).dtype) is None
False
rfn.get_names_flat(np.empty((1,), dtype=[('A',int), ('B', str)]).dtype)
('A', 'B')
adtype = np.dtype([('a', int), ('b', [('ba', int), ('bb', int)])])

rfn.get_names_flat(adtype)
('a', 'b', 'ba', 'bb')
from numpy.lib import recfunctions as rfn

rfn.merge_arrays((np.array([1, 2]), np.array([10., 20., 30.])))
array([( 1, 10.), ( 2, 20.), (-1, 30.)],
      dtype=[('f0', '<i8'), ('f1', '<f8')])
rfn.merge_arrays((np.array([1, 2], dtype=np.int64),

        np.array([10., 20., 30.])), usemask=False)
array([( 1, 10.), ( 2, 20.), (-1, 30.)],
      dtype=[('f0', '<i8'), ('f1', '<f8')])
rfn.merge_arrays((np.array([1, 2]).view([('a', np.int64)]),

              np.array([10., 20., 30.])),

             usemask=False, asrecarray=True)
rec.array([( 1, 10.), ( 2, 20.), (-1, 30.)],
          dtype=[('a', '<i8'), ('f1', '<f8')])
from numpy.lib import recfunctions as rfn

a = np.array([(1, 10.), (2, 20.)], dtype=[('A', np.int64), ('B', np.float64)])

b = np.zeros((3,), dtype=a.dtype)

rfn.recursive_fill_fields(a, b)
array([(1, 10.), (2, 20.), (0,  0.)], dtype=[('A', '<i8'), ('B', '<f8')])
from numpy.lib import recfunctions as rfn

a = np.array([(1, (2, [3.0, 30.])), (4, (5, [6.0, 60.]))],

  dtype=[('a', int),('b', [('ba', float), ('bb', (float, 2))])])
rfn.rename_fields(a, {'a':'A', 'bb':'BB'})
array([(1, (2., [ 3., 30.])), (4, (5., [ 6., 60.]))],
      dtype=[('A', '<i8'), ('b', [('ba', '<f8'), ('BB', '<f8', (2,))])])
from numpy.lib import recfunctions as rfn

def print_offsets(d):

    print("offsets:", [d.fields[name][1] for name in d.names])

    print("itemsize:", d.itemsize)
dt = np.dtype('u1, <i8, <f8', align=True)

dt
dtype([('f0', 'u1'), ('f1', '<i8'), ('f2', '<f8')], align=True)
print_offsets(dt)
offsets: [0, 8, 16]
itemsize: 24
packed_dt = rfn.repack_fields(dt)

packed_dt
dtype([('f0', 'u1'), ('f1', '<i8'), ('f2', '<f8')])
print_offsets(packed_dt)
offsets: [0, 1, 9]
itemsize: 17
from numpy.lib import recfunctions as rfn

a = np.ones(4, dtype=[('a', 'i4'), ('b', 'f8'), ('c', 'u1')])

rfn.require_fields(a, [('b', 'f4'), ('c', 'u1')])
array([(1., 1), (1., 1), (1., 1), (1., 1)],
      dtype=[('b', '<f4'), ('c', 'u1')])
rfn.require_fields(a, [('b', 'f4'), ('newf', 'u1')])
array([(1., 0), (1., 0), (1., 0), (1., 0)],
      dtype=[('b', '<f4'), ('newf', 'u1')])
from numpy.lib import recfunctions as rfn

x = np.array([1, 2,])

rfn.stack_arrays(x) is x
True
z = np.array([('A', 1), ('B', 2)], dtype=[('A', '|S3'), ('B', float)])

zz = np.array([('a', 10., 100.), ('b', 20., 200.), ('c', 30., 300.)],

  dtype=[('A', '|S3'), ('B', np.double), ('C', np.double)])

test = rfn.stack_arrays((z,zz))

test
masked_array(data=[(b'A', 1.0, --), (b'B', 2.0, --), (b'a', 10.0, 100.0),
                   (b'b', 20.0, 200.0), (b'c', 30.0, 300.0)],
             mask=[(False, False,  True), (False, False,  True),
                   (False, False, False), (False, False, False),
                   (False, False, False)],
       fill_value=(b'N/A', 1.e+20, 1.e+20),
            dtype=[('A', 'S3'), ('B', '<f8'), ('C', '<f8')])
from numpy.lib import recfunctions as rfn

a = np.zeros(4, dtype=[('a', 'i4'), ('b', 'f4,u2'), ('c', 'f4', 2)])

a
array([(0, (0., 0), [0., 0.]), (0, (0., 0), [0., 0.]),
       (0, (0., 0), [0., 0.]), (0, (0., 0), [0., 0.])],
      dtype=[('a', '<i4'), ('b', [('f0', '<f4'), ('f1', '<u2')]), ('c', '<f4', (2,))])
rfn.structured_to_unstructured(a)
array([[0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0.],
       [0., 0., 0., 0., 0.]])
b = np.array([(1, 2, 5), (4, 5, 7), (7, 8 ,11), (10, 11, 12)],

             dtype=[('x', 'i4'), ('y', 'f4'), ('z', 'f8')])
np.mean(rfn.structured_to_unstructured(b[['x', 'z']]), axis=-1)
array([ 3. ,  5.5,  9. , 11. ])
from numpy.lib import recfunctions as rfn

dt = np.dtype([('a', 'i4'), ('b', 'f4,u2'), ('c', 'f4', 2)])

a = np.arange(20).reshape((4,5))

a
array([[ 0,  1,  2,  3,  4],
       [ 5,  6,  7,  8,  9],
       [10, 11, 12, 13, 14],
       [15, 16, 17, 18, 19]])
rfn.unstructured_to_structured(a, dt)
array([( 0, ( 1.,  2), [ 3.,  4.]), ( 5, ( 6.,  7), [ 8.,  9.]),
       (10, (11., 12), [13., 14.]), (15, (16., 17), [18., 19.])],
      dtype=[('a', '<i4'), ('b', [('f0', '<f4'), ('f1', '<u2')]), ('c', '<f4', (2,))])

Universal functions

np.array([0,2,3,4]) + np.array([1,1,-1,2])
array([1, 3, 2, 6])
x = np.arange(9).reshape(3,3)

x
array([[0, 1, 2],
       [3, 4, 5],
       [6, 7, 8]])
np.add.reduce(x, 1)
array([ 3, 12, 21])
np.add.reduce(x, (0, 1))
36
x.dtype
dtype('int64')
np.multiply.reduce(x, dtype=float)
array([ 0., 28., 80.])
y = np.zeros(3, dtype=int)

y
array([0, 0, 0])
np.multiply.reduce(x, dtype=float, out=y)
array([ 0, 28, 80])
mark = {False: ' -', True: ' Y'}

def print_table(ntypes):

    print('X ' + ' '.join(ntypes))

    for row in ntypes:

        print(row, end='')

        for col in ntypes:

            print(mark[np.can_cast(row, col)], end='')

        print()


print_table(np.typecodes['All'])
X ? b h i l q p B H I L Q P e f d g F D G S U V O M m
? Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y - Y
b - Y Y Y Y Y Y - - - - - - Y Y Y Y Y Y Y Y Y Y Y - Y
h - - Y Y Y Y Y - - - - - - - Y Y Y Y Y Y Y Y Y Y - Y
i - - - Y Y Y Y - - - - - - - - Y Y - Y Y Y Y Y Y - Y
l - - - - Y Y Y - - - - - - - - Y Y - Y Y Y Y Y Y - Y
q - - - - Y Y Y - - - - - - - - Y Y - Y Y Y Y Y Y - Y
p - - - - Y Y Y - - - - - - - - Y Y - Y Y Y Y Y Y - Y
B - - Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y Y - Y
H - - - Y Y Y Y - Y Y Y Y Y - Y Y Y Y Y Y Y Y Y Y - Y
I - - - - Y Y Y - - Y Y Y Y - - Y Y - Y Y Y Y Y Y - Y
L - - - - - - - - - - Y Y Y - - Y Y - Y Y Y Y Y Y - -
Q - - - - - - - - - - Y Y Y - - Y Y - Y Y Y Y Y Y - -
P - - - - - - - - - - Y Y Y - - Y Y - Y Y Y Y Y Y - -
e - - - - - - - - - - - - - Y Y Y Y Y Y Y Y Y Y Y - -
f - - - - - - - - - - - - - - Y Y Y Y Y Y Y Y Y Y - -
d - - - - - - - - - - - - - - - Y Y - Y Y Y Y Y Y - -
g - - - - - - - - - - - - - - - - Y - - Y Y Y Y Y - -
F - - - - - - - - - - - - - - - - - Y Y Y Y Y Y Y - -
D - - - - - - - - - - - - - - - - - - Y Y Y Y Y Y - -
G - - - - - - - - - - - - - - - - - - - Y Y Y Y Y - -
S - - - - - - - - - - - - - - - - - - - - Y Y Y Y - -
U - - - - - - - - - - - - - - - - - - - - - Y Y Y - -
V - - - - - - - - - - - - - - - - - - - - - - Y Y - -
O - - - - - - - - - - - - - - - - - - - - - - - Y - -
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m - - - - - - - - - - - - - - - - - - - - - - Y Y - Y

np.fft

import matplotlib.pyplot as plt

t = np.arange(256)

sp = np.fft.fft(np.sin(t))

freq = np.fft.fftfreq(t.shape[-1])

plt.plot(freq, sp.real, freq, sp.imag)

plt.show()
import matplotlib.pyplot as plt

t = np.arange(400)

n = np.zeros((400,), dtype=complex)

n[40:60] = np.exp(1j*np.random.uniform(0, 2*np.pi, (20,)))

s = np.fft.ifft(n)

plt.plot(t, s.real, label='real')

plt.plot(t, s.imag, '--', label='imaginary')
plt.legend()

plt.show()

a = np.mgrid[:5, :5][0]

np.fft.fft2(a)
array([[ 50.  +0.j        ,   0.  +0.j        ,   0.  +0.j        ,
          0.  +0.j        ,   0.  +0.j        ],
       [-12.5+17.20477401j,   0.  +0.j        ,   0.  +0.j        ,
          0.  +0.j        ,   0.  +0.j        ],
       [-12.5 +4.0614962j ,   0.  +0.j        ,   0.  +0.j        ,
          0.  +0.j        ,   0.  +0.j        ],
       [-12.5 -4.0614962j ,   0.  +0.j        ,   0.  +0.j        ,
          0.  +0.j        ,   0.  +0.j        ],
       [-12.5-17.20477401j,   0.  +0.j        ,   0.  +0.j        ,
          0.  +0.j        ,   0.  +0.j        ]])
a = 4 * np.eye(4)

np.fft.ifft2(a)
array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],
       [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],
       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]])
import matplotlib.pyplot as plt

[X, Y] = np.meshgrid(2 * np.pi * np.arange(200) / 12,

                     2 * np.pi * np.arange(200) / 34)

S = np.sin(X) + np.cos(Y) + np.random.uniform(0, 1, X.shape)

FS = np.fft.fftn(S)

plt.imshow(np.log(np.abs(np.fft.fftshift(FS))**2))

plt.show()

import matplotlib.pyplot as plt

n = np.zeros((200,200), dtype=complex)

n[60:80, 20:40] = np.exp(1j*np.random.uniform(0, 2*np.pi, (20, 20)))

im = np.fft.ifftn(n).real

plt.imshow(im)

plt.show()

np.fft.fft([0, 1, 0, 0])

np.fft.rfft([0, 1, 0, 0])
array([ 1.+0.j,  0.-1.j, -1.+0.j])
np.fft.ifft([1, -1j, -1, 1j])

np.fft.irfft([1, -1j, -1])
array([0., 1., 0., 0.])
a = np.mgrid[:5, :5][0]

np.fft.rfft2(a)
array([[ 50.  +0.j        ,   0.  +0.j        ,   0.  +0.j        ],
       [-12.5+17.20477401j,   0.  +0.j        ,   0.  +0.j        ],
       [-12.5 +4.0614962j ,   0.  +0.j        ,   0.  +0.j        ],
       [-12.5 -4.0614962j ,   0.  +0.j        ,   0.  +0.j        ],
       [-12.5-17.20477401j,   0.  +0.j        ,   0.  +0.j        ]])
a = np.mgrid[:5, :5][0]

A = np.fft.rfft2(a)

np.fft.irfft2(A, s=a.shape)
array([[0., 0., 0., 0., 0.],
       [1., 1., 1., 1., 1.],
       [2., 2., 2., 2., 2.],
       [3., 3., 3., 3., 3.],
       [4., 4., 4., 4., 4.]])
a = np.ones((2, 2, 2))

np.fft.rfftn(a)
array([[[8.+0.j, 0.+0.j],
        [0.+0.j, 0.+0.j]],

       [[0.+0.j, 0.+0.j],
        [0.+0.j, 0.+0.j]]])
np.fft.rfftn(a, axes=(2, 0))
array([[[4.+0.j, 0.+0.j],
        [4.+0.j, 0.+0.j]],

       [[0.+0.j, 0.+0.j],
        [0.+0.j, 0.+0.j]]])
a = np.zeros((3, 2, 2))

a[0, 0, 0] = 3 * 2 * 2

np.fft.irfftn(a)
array([[[1., 1.],
        [1., 1.]],

       [[1., 1.],
        [1., 1.]],

       [[1., 1.],
        [1., 1.]]])
signal = np.array([1, 2, 3, 4, 3, 2])

np.fft.fft(signal)
array([15.+0.j, -4.+0.j,  0.+0.j, -1.+0.j,  0.+0.j, -4.+0.j])
np.fft.hfft(signal[:4]) # Input first half of signal
array([15., -4.,  0., -1.,  0., -4.])
np.fft.hfft(signal, 6)  # Input entire signal and truncate
array([15., -4.,  0., -1.,  0., -4.])
signal = np.array([[1, 1.j], [-1.j, 2]])

np.conj(signal.T) - signal   # check Hermitian symmetry
array([[ 0.-0.j, -0.+0.j],
       [ 0.+0.j,  0.-0.j]])
freq_spectrum = np.fft.hfft(signal)

freq_spectrum
array([[ 1.,  1.],
       [ 2., -2.]])
spectrum = np.array([ 15, -4, 0, -1, 0, -4])

np.fft.ifft(spectrum)
array([1.+0.j, 2.+0.j, 3.+0.j, 4.+0.j, 3.+0.j, 2.+0.j])
np.fft.ihfft(spectrum)
array([1.-0.00000000e+00j, 2.-3.70074342e-17j, 3.-3.70074342e-17j,
       4.-0.00000000e+00j])
signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)

fourier = np.fft.fft(signal)

n = signal.size

timestep = 0.1

freq = np.fft.fftfreq(n, d=timestep)

freq
array([ 0.  ,  1.25,  2.5 ,  3.75, -5.  , -3.75, -2.5 , -1.25])
signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)

fourier = np.fft.rfft(signal)

n = signal.size

sample_rate = 100

freq = np.fft.fftfreq(n, d=1./sample_rate)

freq
array([  0.,  10.,  20.,  30.,  40., -50., -40., -30., -20., -10.])
freq = np.fft.rfftfreq(n, d=1./sample_rate)

freq
array([ 0., 10., 20., 30., 40., 50.])
freqs = np.fft.fftfreq(10, 0.1)

freqs
array([ 0.,  1.,  2.,  3.,  4., -5., -4., -3., -2., -1.])
np.fft.fftshift(freqs)
array([-5., -4., -3., -2., -1.,  0.,  1.,  2.,  3.,  4.])
freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)

freqs
array([[ 0.,  1.,  2.],
       [ 3.,  4., -4.],
       [-3., -2., -1.]])
np.fft.fftshift(freqs, axes=(1,))
array([[ 2.,  0.,  1.],
       [-4.,  3.,  4.],
       [-1., -3., -2.]])
freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)

freqs
array([[ 0.,  1.,  2.],
       [ 3.,  4., -4.],
       [-3., -2., -1.]])
np.fft.ifftshift(np.fft.fftshift(freqs))
array([[ 0.,  1.,  2.],
       [ 3.,  4., -4.],
       [-3., -2., -1.]])
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