211 lines
8 KiB
Markdown
211 lines
8 KiB
Markdown
# Boolean matricies and logic functions
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{:.no_toc}
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<nav markdown="1" class="toc-class">
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* TOC
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{:toc}
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</nav>
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## The goal
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Questions to [David Rotermund](mailto:davrot@uni-bremen.de)
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## Boolean matrices
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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.
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```python
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import numpy as np
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a = 1.0 / np.arange(0, 6).reshape((2, 3))
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print(a)
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print()
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print(np.isfinite(a))
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```
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Output:
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```python
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[[ inf 1. 0.5 ]
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[0.33333333 0.25 0.2 ]]
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[[False True True]
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[ True True True]]
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<ipython-input-3-7ead4ee291d3>:4: RuntimeWarning: divide by zero encountered in divide
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a = 1.0 / np.arange(0, 6).reshape((2, 3))
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```
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However, there are other ways to produce Boolean matrixes:
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```python
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import numpy as np
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a = np.arange(0, 6).reshape((2, 3))
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print(a)
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print()
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print((a > 1))
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```
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Output:
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```python
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[[0 1 2]
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[3 4 5]]
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[[False False True]
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[ True True True]]
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```
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## Calculating with boolean matrices
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You can treat them a matricies that are filled with 0 (False) and 1 (True):
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```python
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import numpy as np
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a = np.arange(0, 6).reshape((2, 3))
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print(a)
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print()
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print((a > 1) * (a < 4))
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```
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Output:
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```python
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[[0 1 2]
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[3 4 5]]
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[[False False True]
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[ True False False]]
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```
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Or you can use Boolean logical matrix functions:
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```python
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import numpy as np
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a = np.arange(0, 6).reshape((2, 3))
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print(a)
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print()
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print(np.logical_and((a > 1), (a < 4)))
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```
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Output:
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```python
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[[0 1 2]
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[3 4 5]]
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[[False False True]
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[ True False False]]
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```
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## [np.nonzero()](https://numpy.org/doc/stable/reference/generated/numpy.nonzero.html)
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```python
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numpy.nonzero(a)
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```
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> Return the indices of the elements that are non-zero.
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We can use nonzero for extracting the positions where the boolean value is true:
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```python
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import numpy as np
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a = np.arange(0, 6).reshape((2, 3))
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print(a)
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print()
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print(np.nonzero(a > 1))
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```
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Output:
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```python
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[[0 1 2]
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[3 4 5]]
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(array([0, 1, 1, 1]), array([2, 0, 1, 2]))
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```
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For reversing it, you can use this:
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```python
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import numpy as np
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a = np.arange(0, 6).reshape((2, 3))
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a = (a > 1)
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print(a)
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idx = np.nonzero(a)
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print()
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b = np.zeros((2, 3), dtype=bool)
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b[idx] = True
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print(b)
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```
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Output:
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```python
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[[False False True]
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[ True True True]]
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[[False False True]
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[ True True True]]
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```
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## [Logic functions](https://numpy.org/doc/stable/reference/routines.logic.html)
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### [Truth value testing](https://numpy.org/doc/stable/reference/routines.logic.html#truth-value-testing)
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|[all(a[, axis, out, keepdims, where])](https://numpy.org/doc/stable/reference/generated/numpy.all.html#numpy.all)|Test whether all array elements along a given axis evaluate to True.|
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|[any(a[, axis, out, keepdims, where])](https://numpy.org/doc/stable/reference/generated/numpy.any.html#numpy.any)|Test whether any array element along a given axis evaluates to True.|
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### [Array contents](https://numpy.org/doc/stable/reference/routines.logic.html#array-contents)
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|[isfinite(x, /[, out, where, casting, order, ...])](https://numpy.org/doc/stable/reference/generated/numpy.isfinite.html#numpy.isfinite)|Test element-wise for finiteness (not infinity and not Not a Number).|
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|[isinf(x, /[, out, where, casting, order, ...])](https://numpy.org/doc/stable/reference/generated/numpy.isinf.html#numpy.isinf)|Test element-wise for positive or negative infinity.|
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|[isnan(x, /[, out, where, casting, order, ...])](https://numpy.org/doc/stable/reference/generated/numpy.isnan.html#numpy.isnan)|Test element-wise for NaN and return result as a boolean array.|
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|[isnat(x, /[, out, where, casting, order, ...])](https://numpy.org/doc/stable/reference/generated/numpy.isnat.html#numpy.isnat)|Test element-wise for NaT (not a time) and return result as a boolean array.|
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|[isneginf(x[, out])](https://numpy.org/doc/stable/reference/generated/numpy.isneginf.html#numpy.isneginf)|Test element-wise for negative infinity, return result as bool array.|
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|[isposinf(x[, out])](https://numpy.org/doc/stable/reference/generated/numpy.isposinf.html#numpy.isposinf)|Test element-wise for positive infinity, return result as bool array.|
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### [Array type testing](https://numpy.org/doc/stable/reference/routines.logic.html#array-type-testing)
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|[iscomplex(x)](https://numpy.org/doc/stable/reference/generated/numpy.iscomplex.html#numpy.iscomplex)|Returns a bool array, where True if input element is complex.|
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|[iscomplexobj(x)](https://numpy.org/doc/stable/reference/generated/numpy.iscomplexobj.html#numpy.iscomplexobj)|Check for a complex type or an array of complex numbers.|
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|[isfortran(a)](https://numpy.org/doc/stable/reference/generated/numpy.isfortran.html#numpy.isfortran)|Check if the array is Fortran contiguous but not C contiguous.|
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|[isreal(x)](https://numpy.org/doc/stable/reference/generated/numpy.isreal.html#numpy.isreal)|Returns a bool array, where True if input element is real.|
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|[isrealobj(x)](https://numpy.org/doc/stable/reference/generated/numpy.isrealobj.html#numpy.isrealobj)|Return True if x is a not complex type or an array of complex numbers.|
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|[isscalar(element)](https://numpy.org/doc/stable/reference/generated/numpy.isscalar.html#numpy.isscalar)|Returns True if the type of element is a scalar type.|
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### [Logical operations](https://numpy.org/doc/stable/reference/routines.logic.html#logical-operations)
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|[logical_and(x1, x2, /[, out, where, ...])](https://numpy.org/doc/stable/reference/generated/numpy.logical_and.html#numpy.logical_and)|Compute the truth value of x1 AND x2 element-wise.|
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|[logical_or(x1, x2, /[, out, where, casting, ...])](https://numpy.org/doc/stable/reference/generated/numpy.logical_or.html#numpy.logical_or)|Compute the truth value of x1 OR x2 element-wise.|
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|[logical_not(x, /[, out, where, casting, ...])](https://numpy.org/doc/stable/reference/generated/numpy.logical_not.html#numpy.logical_not)|Compute the truth value of NOT x element-wise.|
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|[logical_xor(x1, x2, /[, out, where, ...])](https://numpy.org/doc/stable/reference/generated/numpy.logical_xor.html#numpy.logical_xor)|Compute the truth value of x1 XOR x2, element-wise.|
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### [Comparison](https://numpy.org/doc/stable/reference/routines.logic.html#comparison)
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|[allclose(a, b[, rtol, atol, equal_nan])](https://numpy.org/doc/stable/reference/generated/numpy.allclose.html#numpy.allclose)|Returns True if two arrays are element-wise equal within a tolerance.|
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|[isclose(a, b[, rtol, atol, equal_nan])](https://numpy.org/doc/stable/reference/generated/numpy.isclose.html#numpy.isclose)|Returns a boolean array where two arrays are element-wise equal within a tolerance.|
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|[array_equal(a1, a2[, equal_nan])](https://numpy.org/doc/stable/reference/generated/numpy.array_equal.html#numpy.array_equal)|True if two arrays have the same shape and elements, False otherwise.|
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|[array_equiv(a1, a2)](https://numpy.org/doc/stable/reference/generated/numpy.array_equiv.html#numpy.array_equiv)|Returns True if input arrays are shape consistent and all elements equal.|
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|[greater(x1, x2, /[, out, where, casting, ...])](https://numpy.org/doc/stable/reference/generated/numpy.greater.html#numpy.greater)|Return the truth value of (x1 > x2) element-wise.|
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|[greater_equal(x1, x2, /[, out, where, ...])](https://numpy.org/doc/stable/reference/generated/numpy.greater_equal.html#numpy.greater_equal)|Return the truth value of (x1 >= x2) element-wise.|
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|[less(x1, x2, /[, out, where, casting, ...])](https://numpy.org/doc/stable/reference/generated/numpy.less.html#numpy.less)|Return the truth value of (x1 < x2) element-wise.|
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|[less_equal(x1, x2, /[, out, where, casting, ...])](https://numpy.org/doc/stable/reference/generated/numpy.less_equal.html#numpy.less_equal)|Return the truth value of (x1 <= x2) element-wise.|
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|[equal(x1, x2, /[, out, where, casting, ...])](https://numpy.org/doc/stable/reference/generated/numpy.equal.html#numpy.equal)|Return (x1 == x2) element-wise.|
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|[not_equal(x1, x2, /[, out, where, casting, ...])](https://numpy.org/doc/stable/reference/generated/numpy.not_equal.html#numpy.not_equal)|Return (x1 != x2) element-wise.|
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