matrix: adding permutation determinant

src/lol/math/matrix.h

@@ -611,7 +611,7 @@ vec_t<int, N> p_vector(mat_t<T, N, N> const & m)
  */
 
 template<typename T, int N>
-mat_t<T, N, N> permute(mat_t<T, N, N> const & m, vec_t<int, N> const & permutation)
+mat_t<T, N, N> permute_rows(mat_t<T, N, N> const & m, vec_t<int, N> const & permutation)
 {
     mat_t<T, N, N> result;
 
@@ -626,6 +626,29 @@ mat_t<T, N, N> permute(mat_t<T, N, N> const & m, vec_t<int, N> const & permutati
     return result;
 }
 
+/*
+ * Compute the determinant of a permutation square matrix corresponding to the permutation vector
+ */
+
+template<int N>
+int permutation_det(vec_t<int, N> const & permutation)
+{
+    int result = 1;
+
+    for (int i = 0 ; i < N ; ++i)
+    {
+        int relative_index = permutation[i];
+
+        for (int j = 0 ; j < i ; ++j)
+            if (permutation[j] < permutation[i])
+                --relative_index;
+
+        result *= (relative_index % 2 ? -1 : 1);
+    }
+
+    return result;
+}
+
 /*
  * Compute L matrix inverse
  */

src/t/math/matrix.cpp

@@ -103,7 +103,7 @@ lolunit_declare_fixture(MatrixTest)
                vec4(0,  0,  1,  0));
 
         vec_t<int, 4> perm1 = p_vector(m1);
-        m1 = permute(m1, perm1);
+        m1 = permute_rows(m1, perm1);
 
         for (int i = 0 ; i < 4 ; ++i)
         {
@@ -122,7 +122,7 @@ lolunit_declare_fixture(MatrixTest)
                vec4(1,  0,  0,  0));
 
         vec_t<int, 4> perm2 = p_vector(m2);
-        m2 = permute(m2, perm2);
+        m2 = permute_rows(m2, perm2);
 
         for (int i = 0 ; i < 4 ; ++i)
         {