Wedgie: Difference between revisions

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 == Conversion ==
 === Mapping matrix to wedgie ===
-The wedgie may be found from the mapping by taking the {{w|determinant}}s of the mapping's column slices that correspond to all the combinations of formal primes.
+The wedgie may be found from the mapping by taking the {{w|determinant}}s of the mapping's column slices that correspond to all the combinations of formal primes. Below is a minimalistic [https://www.python.org/ Python] script that finds the wedgie from a mapping matrix, using [https://scipy.org/ SciPy].
-Below is a [https://www.python.org/ Python] script that finds the wedgie from a mapping matrix, using [https://scipy.org/ Scipy].
 <syntaxhighlight lang="python">
@@ Line 84: / Line 82: @@
 from scipy import linalg
-def wedgie (breeds):
+def breeds2wedgie (breeds):
+    """Takes a mapping, returns the corresponding wedgie. """
      r, d = breeds.shape # rank and dimensionality
      combinations = itertools.combinations (range (d), r)
@@ Line 103: / Line 103: @@
 === Wedgie to mapping matrix ===
-{{Todo|inline=1| expand }}
+Converting, or ''decomposing'', a wedgie to a mapping matrix is much more complicated. [[Gene Ward Smith]]'s provided an algorithm, explained in [[Dave Keenan & Douglas Blumeyer's guide to EA for RTT #Gene's algorithm]], and implemented in Python by [[Flora Canou]] as part of the [https://github.com/FloraCanou/temperament_evaluator Temperament Evaluator] since v1.21.0. Below is an adaptation. It requires [https://numpy.org/ NumPy] and [https://www.sympy.org/en/index.html SymPy].
+<syntaxhighlight lang="python">
+import itertools, math
+import numpy as np
+from sympy.matrices import Matrix, normalforms
+def wedgie2breeds (wedgie):
+    """
+    Takes a wedgie, returns the corresponding mapping if decomposable,
+    or None otherwise. Gene Ward Smith's algorithm.
+    """
+    def inversion_count (a):
+        """
+        Returns the number of inversions in an array,
+        which equals the number of swaps required to sort it.
+        https://stackoverflow.com/a/20990301
+        """
+        length = len (a)
+        count = 0
+        for i in range (length - 1):
+            for j in range (i + 1, length):
+                if a[i] > a[j]:
+                    count += 1
+        return count
+    def hnf (a):
+        """Normalizes a matrix row-style to the Hermite normal form. """
+        return np.flip (np.array (
+            normalforms.hermite_normal_form (Matrix (np.flip (a).T)).T, dtype = int))
+    # check contorsion
+    if np.gcd.reduce (wedgie.flat) != 1:
+        return None
+    # find the rank r and dimensionality d
+    r = wedgie.ndim
+    length = len (wedgie.flat)
+    for d in itertools.count (start = r):
+        length_current = math.comb (d, r)
+        if length_current == length:
+            break
+        elif length_current > length:
+            raise ValueError ("invalid length for the rank. ")
+    # gene's b and c, converted to tuples
+    # so that they will reset themselves on the beginning of each loop
+    combinations = tuple (itertools.combinations (range (d), r))
+    subcombinations = tuple (itertools.combinations (range (d), r - 1))
+    # main algorithm
+    breeds = np.zeros ((len (subcombinations), d), dtype = int)
+    for i, si in enumerate (subcombinations):
+        for j in range (d):
+            if j in si:
+                continue
+            appended_index = (*si, j)
+            sign = 1 if inversion_count (appended_index) % 2 == 0 else -1
+            k = combinations.index (tuple (sorted (appended_index)))
+            breeds[i][j] = sign*wedgie.flat[k]
+    breeds = hnf (breeds)
+    return breeds if breeds.shape == (r, d) else None
+</syntaxhighlight>
 == Derivation from edo joins ==