View source for Boolean matricies and logic functions

Questions to [mailto:davrot@uni-bremen.de David Rotermund]

== 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.<syntaxhighlight lang="python">import numpy as np

a = 1.0 / np.arange(0, 6).reshape((2, 3))
print(a)
print()
print(np.isfinite(a))</syntaxhighlight>Output:<syntaxhighlight lang="python">[[       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))</syntaxhighlight>However, there are other ways to produce Boolean matrixes:<syntaxhighlight lang="python">import numpy as np

a = np.arange(0, 6).reshape((2, 3))
print(a)
print()
print((a > 1))</syntaxhighlight>Output:<syntaxhighlight lang="python">[[0 1 2]
 [3 4 5]]

[[False False  True]
 [ True  True  True]]</syntaxhighlight>

== Calculating with boolean matrices ==
You can treat them as a matrix that are filled with 0 (False) and 1 (True):<syntaxhighlight lang="python">import numpy as np

a = np.arange(0, 6).reshape((2, 3))
print(a)
print()
print((a > 1) * (a < 4))</syntaxhighlight>Output:<syntaxhighlight lang="python">[[0 1 2]
 [3 4 5]]

[[False False  True]
 [ True False False]]</syntaxhighlight>Or you can use Boolean logical matrix functions:<syntaxhighlight lang="python">import numpy as np

a = np.arange(0, 6).reshape((2, 3))
print(a)
print()
print(np.logical_and((a > 1), (a < 4)))</syntaxhighlight>Output:<syntaxhighlight lang="python">[[0 1 2]
 [3 4 5]]

[[False False  True]
 [ True False False]]</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/generated/numpy.nonzero.html np.nonzero()] ==
<syntaxhighlight lang="python">numpy.nonzero(a)</syntaxhighlight><blockquote>Return the indices of the elements that are non-zero.</blockquote>We can use nonzero for extracting the positions where the boolean value is true:<syntaxhighlight lang="python">import numpy as np

a = np.arange(0, 6).reshape((2, 3))
print(a)
print()
print(np.nonzero(a > 1))</syntaxhighlight>Output:<syntaxhighlight lang="python">[[0 1 2]
 [3 4 5]]

(array([0, 1, 1, 1]), array([2, 0, 1, 2]))</syntaxhighlight>For reversing it, you can use this:<syntaxhighlight lang="python">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)</syntaxhighlight>Output:<syntaxhighlight lang="python">[[False False  True]
 [ True  True  True]]

[[False False  True]
 [ True  True  True]]</syntaxhighlight>

== [https://numpy.org/doc/stable/reference/routines.logic.html Logic functions] ==

=== [https://numpy.org/doc/stable/reference/routines.logic.html#truth-value-testing Truth value testing] ===
{| class="wikitable"
|[https://numpy.org/doc/stable/reference/generated/numpy.all.html#numpy.all all(a[, axis, out, keepdims, where])]
|Test whether all array elements along a given axis evaluate to True.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.any.html#numpy.any any(a[, axis, out, keepdims, where])]
|Test whether any array element along a given axis evaluates to True.
|}

=== [https://numpy.org/doc/stable/reference/routines.logic.html#array-contents Array contents] ===
{| class="wikitable"
|[https://numpy.org/doc/stable/reference/generated/numpy.isfinite.html#numpy.isfinite isfinite(x, /[, out, where, casting, order, …])]
|Test element-wise for finiteness (not infinity and not Not a Number).
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.isinf.html#numpy.isinf isinf(x, /[, out, where, casting, order, …])]
|Test element-wise for positive or negative infinity.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.isnan.html#numpy.isnan isnan(x, /[, out, where, casting, order, …])]
|Test element-wise for NaN and return result as a boolean array.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.isnat.html#numpy.isnat isnat(x, /[, out, where, casting, order, …])]
|Test element-wise for NaT (not a time) and return result as a boolean array.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.isneginf.html#numpy.isneginf isneginf(x[, out])]
|Test element-wise for negative infinity, return result as bool array.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.isposinf.html#numpy.isposinf isposinf(x[, out])]
|Test element-wise for positive infinity, return result as bool array.
|}

=== [https://numpy.org/doc/stable/reference/routines.logic.html#array-type-testing Array type testing] ===
{| class="wikitable"
|[https://numpy.org/doc/stable/reference/generated/numpy.iscomplex.html#numpy.iscomplex iscomplex(x)]
|Returns a bool array, where True if input element is complex.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.iscomplexobj.html#numpy.iscomplexobj iscomplexobj(x)]
|Check for a complex type or an array of complex numbers.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.isfortran.html#numpy.isfortran isfortran(a)]
|Check if the array is Fortran contiguous but not C contiguous.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.isreal.html#numpy.isreal isreal(x)]
|Returns a bool array, where True if input element is real.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.isrealobj.html#numpy.isrealobj isrealobj(x)]
|Return True if x is a not complex type or an array of complex numbers.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.isscalar.html#numpy.isscalar isscalar(element)]
|Returns True if the type of element is a scalar type.
|}

=== [https://numpy.org/doc/stable/reference/routines.logic.html#logical-operations Logical operations] ===
{| class="wikitable"
|[https://numpy.org/doc/stable/reference/generated/numpy.logical_and.html#numpy.logical_and logical_and(x1, x2, /[, out, where, …])]
|Compute the truth value of x1 AND x2 element-wise.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.logical_or.html#numpy.logical_or logical_or(x1, x2, /[, out, where, casting, …])]
|Compute the truth value of x1 OR x2 element-wise.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.logical_not.html#numpy.logical_not logical_not(x, /[, out, where, casting, …])]
|Compute the truth value of NOT x element-wise.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.logical_xor.html#numpy.logical_xor logical_xor(x1, x2, /[, out, where, …])]
|Compute the truth value of x1 XOR x2, element-wise.
|}

=== [https://numpy.org/doc/stable/reference/routines.logic.html#comparison Comparison] ===
{| class="wikitable"
|[https://numpy.org/doc/stable/reference/generated/numpy.allclose.html#numpy.allclose allclose(a, b[, rtol, atol, equal_nan])]
|Returns True if two arrays are element-wise equal within a tolerance.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.isclose.html#numpy.isclose isclose(a, b[, rtol, atol, equal_nan])]
|Returns a boolean array where two arrays are element-wise equal within a tolerance.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.array_equal.html#numpy.array_equal array_equal(a1, a2[, equal_nan])]
|True if two arrays have the same shape and elements, False otherwise.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.array_equiv.html#numpy.array_equiv array_equiv(a1, a2)]
|Returns True if input arrays are shape consistent and all elements equal.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.greater.html#numpy.greater greater(x1, x2, /[, out, where, casting, …])]
|Return the truth value of (x1 &#x3E; x2) element-wise.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.greater_equal.html#numpy.greater_equal greater_equal(x1, x2, /[, out, where, …])]
|Return the truth value of (x1 &#x3E;= x2) element-wise.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.less.html#numpy.less less(x1, x2, /[, out, where, casting, …])]
|Return the truth value of (x1 &#x3C; x2) element-wise.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.less_equal.html#numpy.less_equal less_equal(x1, x2, /[, out, where, casting, …])]
|Return the truth value of (x1 &#x3C;= x2) element-wise.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.equal.html#numpy.equal equal(x1, x2, /[, out, where, casting, …])]
|Return (x1 == x2) element-wise.
|-
|[https://numpy.org/doc/stable/reference/generated/numpy.not_equal.html#numpy.not_equal not_equal(x1, x2, /[, out, where, casting, …])]
|Return (x1 != x2) element-wise.
|}