From 905fb69d33261ffdbe05cac3f1924919ed33221f Mon Sep 17 00:00:00 2001
From: Eirik Keilegavlen <Eirik.Keilegavlen@uib.no>
Date: Mon, 9 Jan 2017 11:31:48 +0100
Subject: [PATCH] Generator for multinary numbers of given base and length.

Also unit tests.
---
 permutations.py            | 46 ++++++++++++++++++++++++++++++++++++++
 tests/test_permutations.py | 46 ++++++++++++++++++++++++++++++++++++++
 2 files changed, 92 insertions(+)
 create mode 100644 permutations.py
 create mode 100644 tests/test_permutations.py

diff --git a/permutations.py b/permutations.py
new file mode 100644
index 0000000000..48aec5b164
--- /dev/null
+++ b/permutations.py
@@ -0,0 +1,46 @@
+
+def multinary_permutations(base, length):
+    """
+    Define a generator over all numbers of a certain length for a number system
+    with a specified base.
+
+    For details on the decomposition into an arbitrary base see
+        http://math.stackexchange.com/questions/111150/changing-a-number-between-arbitrary-bases
+
+    Note that the generator will loop over base**length combinations.
+
+    Examples:
+
+        Construct the numbers [00] to [11] in binary numbers
+        >>> multinary_permutations(2, 2)
+        [array([ 0.,  0.]), array([ 1.,  0.]), array([ 0.,  1.]), array([ 1.,  1.])]
+
+        Construct the numbers from 0 to 99 (permuted) in the decimal number
+        system.
+        >>> it = multinary_permutation(10, 2)
+
+    Parameters:
+        base (int): Base of the number system
+        length (int): Number of digits in the numbers
+
+    Yields:
+        array, size length: Array describing the next number combination.
+
+    """
+
+    # There are in total base ** length numbers to be covered, these need to be
+    # rewritten into the base number system
+    for iter1 in range(base **  length):
+
+        # Array to store the multi-d index of the current index
+        bit_val = [0] * length
+        # Number to be decomposed
+        v = iter1
+
+        # Loop over all digits, find the expression of v in that system
+        for iter2 in range(length):
+            bit_val[iter2] = v % base
+            v = v // base
+        # Yield the next value
+        yield bit_val
+
diff --git a/tests/test_permutations.py b/tests/test_permutations.py
new file mode 100644
index 0000000000..67359d5f46
--- /dev/null
+++ b/tests/test_permutations.py
@@ -0,0 +1,46 @@
+import unittest
+import numpy as np
+
+from utils import permutations
+
+class TestPermutations(unittest.TestCase):
+
+    def compare_lists(self, base, length, lst):
+    # Compare a pre-defined list with the result of multinary_permutations
+    # Define a generator, and check that all values produced are contained within lst
+    # Also count the number of iterations
+        iter_cnt = 0
+        for a in permutations.multinary_permutations(base, length):
+            found = False
+            for b in lst:
+                if np.array_equal(np.array(a), np.array(b)):
+                    found = True
+                    break
+            assert found
+            iter_cnt += 1
+        assert iter_cnt == len(lst)
+
+
+    def test_length_2(self):
+        # Explicitly construct a 2D array of all combination of base 3
+        base = 3
+        length = 2
+        lst = []
+        for i in range(base):
+            for j in range(base):
+                lst.append([i, j])
+        self.compare_lists(base, length, lst)
+
+    def test_base_4(self):
+        # Check with a manually constructed list of length 3
+        base = 4
+        length = 3
+        lst = []
+        for i in range(base):
+            for j in range(base):
+                for k in range(base):
+                    lst.append([i, j, k])
+        self.compare_lists(base, length, lst)
+
+    if __name__ == '__main__':
+        unittest.main()