Boolean matricies and logic functions

The goal

Boolean matrices

There are different ways to get a Boolean matrix. For example the result of a np.isfinite() (checks if the values in a matrix are infite values) is a Boolean matrix.

import numpy as np

a = 1.0 / np.arange(0, 6).reshape((2, 3))
print(a)
print()
print(np.isfinite(a))

Output:

[[       inf 1.         0.5       ]
 [0.33333333 0.25       0.2       ]]

[[False  True  True]
 [ True  True  True]]
<ipython-input-3-7ead4ee291d3>:4: RuntimeWarning: divide by zero encountered in divide
  a = 1.0 / np.arange(0, 6).reshape((2, 3))

However, there are other ways to produce Boolean matrixes:

import numpy as np

a = np.arange(0, 6).reshape((2, 3))
print(a)
print()
print((a > 1))

Output:

[[0 1 2]
 [3 4 5]]

[[False False  True]
 [ True  True  True]]

Calculating with boolean matrices

You can treat them a matricies that are filled with 0 (False) and 1 (True):

import numpy as np

a = np.arange(0, 6).reshape((2, 3))
print(a)
print()
print((a > 1) * (a < 4))

Output:

[[0 1 2]
 [3 4 5]]

[[False False  True]
 [ True False False]]

Or you can use Boolean logical matrix functions:

import numpy as np

a = np.arange(0, 6).reshape((2, 3))
print(a)
print()
print(np.logical_and((a > 1), (a < 4)))

Output:

[[0 1 2]
 [3 4 5]]

[[False False  True]
 [ True False False]]

np.nonzero()

numpy.nonzero(a)

Return the indices of the elements that are non-zero.

We can use nonzero for extracting the positions where the boolean value is true:

import numpy as np

a = np.arange(0, 6).reshape((2, 3))
print(a)
print()
print(np.nonzero(a > 1))

Output:

[[0 1 2]
 [3 4 5]]

(array([0, 1, 1, 1]), array([2, 0, 1, 2]))

For reversing it, you can use this:

import numpy as np

a = np.arange(0, 6).reshape((2, 3))
a = (a > 1)
print(a)
idx = np.nonzero(a)
print()

b = np.zeros((2, 3), dtype=bool)
b[idx] = True
print(b)

Output:

[[False False  True]
 [ True  True  True]]

[[False False  True]
 [ True  True  True]]

Logic functions

Truth value testing

all(a[, axis, out, keepdims, where)]	Test whether all array elements along a given axis evaluate to True.
any(a[, axis, out, keepdims, where)]	Test whether any array element along a given axis evaluates to True.

Array contents

isfinite(x, /[, out, where, casting, order, …)]	Test element-wise for finiteness (not infinity and not Not a Number).
isinf(x, /[, out, where, casting, order, …)]	Test element-wise for positive or negative infinity.
isnan(x, /[, out, where, casting, order, …)]	Test element-wise for NaN and return result as a boolean array.
isnat(x, /[, out, where, casting, order, …)]	Test element-wise for NaT (not a time) and return result as a boolean array.
isneginf(x[, out)]	Test element-wise for negative infinity, return result as bool array.
isposinf(x[, out)]	Test element-wise for positive infinity, return result as bool array.

Array type testing

iscomplex(x)	Returns a bool array, where True if input element is complex.
iscomplexobj(x)	Check for a complex type or an array of complex numbers.
isfortran(a)	Check if the array is Fortran contiguous but not C contiguous.
isreal(x)	Returns a bool array, where True if input element is real.
isrealobj(x)	Return True if x is a not complex type or an array of complex numbers.
isscalar(element)	Returns True if the type of element is a scalar type.

Logical operations

logical_and(x1, x2, /[, out, where, …)]	Compute the truth value of x1 AND x2 element-wise.
logical_or(x1, x2, /[, out, where, casting, …)]	Compute the truth value of x1 OR x2 element-wise.
logical_not(x, /[, out, where, casting, …)]	Compute the truth value of NOT x element-wise.
logical_xor(x1, x2, /[, out, where, …)]	Compute the truth value of x1 XOR x2, element-wise.

Comparison

allclose(a, b[, rtol, atol, equal_nan)]	Returns True if two arrays are element-wise equal within a tolerance.
isclose(a, b[, rtol, atol, equal_nan)]	Returns a boolean array where two arrays are element-wise equal within a tolerance.
array_equal(a1, a2[, equal_nan)]	True if two arrays have the same shape and elements, False otherwise.
array_equiv(a1, a2)	Returns True if input arrays are shape consistent and all elements equal.
greater(x1, x2, /[, out, where, casting, …)]	Return the truth value of (x1 > x2) element-wise.
greater_equal(x1, x2, /[, out, where, …)]	Return the truth value of (x1 >= x2) element-wise.
less(x1, x2, /[, out, where, casting, …)]	Return the truth value of (x1 < x2) element-wise.
less_equal(x1, x2, /[, out, where, casting, …)]	Return the truth value of (x1 <= x2) element-wise.
equal(x1, x2, /[, out, where, casting, …)]	Return (x1 == x2) element-wise.
not_equal(x1, x2, /[, out, where, casting, …)]	Return (x1 != x2) element-wise.