tensors.h: new header with implementation of 3 and 4 index Euclidean Levi-Civita

Author: kostrzewa

tensors.h

@@ -0,0 +1,95 @@
+/***********************************************************************
+ *
+ * Copyright (C) 2018 Bartosz Kostrzewa 
+ *
+ * This file is part of tmLQCD.
+ *
+ * tmLQCD is free software: you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation, either version 3 of the License, or
+ * (at your option) any later version.
+ * 
+ * tmLQCD is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ * 
+ * You should have received a copy of the GNU General Public License
+ * along with tmLQCD.  If not, see <http://www.gnu.org/licenses/>.
+ *
+ ************************************************************************/
+
+#ifndef TENSORS_H
+#define TENSORS_H
+
+typedef struct epsilon4_t {
+  int N;
+  double eps_val[24];
+  int eps_idx[24][4];
+} epsilon4_t; 
+
+typedef struct epsilon3_t {
+  int N;
+  double eps_val[6];
+  int eps_idx[6][3];
+} epsilon3_t;
+
+static inline epsilon3_t new_epsilon3(void) {
+  epsilon3_t ret;
+
+  ret.N = 6;
+
+  int i = 0;
+  int p = 0;
+  for( int i1 = 1; i1 <= 3; i1++ ){
+    for( int i2 = 1; i2 <= 3; i2++ ){
+      for( int i3 = 1; i3 <= 3; i3++ ){
+        // for eps_123 we have: (1 - 2)(1 - 3)(2 - 3) = -2 
+        //                      -> minus sign
+        p = -(i1 - i2)*(i1 - i3)*(i2 - i3);
+        if( p != 0 ){
+          ret.eps_val[i] = p > 0 ? 1 : -1;
+          ret.eps_idx[i][0] = i1-1;
+          ret.eps_idx[i][1] = i2-1;
+          ret.eps_idx[i][2] = i3-1;
+          i++;
+        }
+      } 
+    }
+  }
+  return(ret);
+}
+
+// note that this is the Euclidean eps_ijkl, for which we have eps_1234 = 1,
+// whereas in Minkowski space we have eps_0123 = -1
+static inline epsilon4_t new_epsilon4(void) {
+  epsilon4_t ret;
+
+  ret.N = 24;
+
+  int i = 0;
+  int p = 0;
+  for( int i1 = 1; i1 <= 4; i1++ ){
+    for( int i2 = 1; i2 <= 4; i2++ ){
+      for( int i3 = 1; i3 <= 4; i3++ ){
+        for( int i4 = 1; i4 <= 4; i4++ ){
+          // for eps_1234 we have: (1 - 2)(1 - 3)(1 - 4)(2 - 3)(2 - 4)(3 - 4) = 12 
+          //                       -> NO minus sign
+          p = (i1 - i2)*(i1 - i3)*(i1 - i4)*(i2 - i3)*(i2 - i4)*(i3 - i4);
+          if( p != 0 ){
+            ret.eps_val[i] = p > 0 ? 1 : -1;
+            ret.eps_idx[i][0] = i1-1;
+            ret.eps_idx[i][1] = i2-1;
+            ret.eps_idx[i][2] = i3-1;
+            ret.eps_idx[i][3] = i4-1;
+            i++;
+          }
+        }
+      } 
+    }
+  }
+  return(ret);
+}
+
+#endif
+