1 files changed, 93 insertions, 0 deletions
diff --git a/src/determinant.c b/src/determinant.c
new file mode 100644
index 0000000..906c75f
--- /dev/null
+++ b/src/determinant.c
@@ -0,0 +1,93 @@
+#include "determinant.h"
+
+#include "number.h"
+#include "rational.h"
+#include "definitions.cpp"
+
+// determinant of a matrix
+// replaces the matrix by its LU decomposition
+int determinant_inplace(Number_Matrix M, Number* out){
+  int i;
+  int sign_correction;
+
+  LU_dcmp_inplace(M, &sign_correction);
+
+  if(sign_correction==0){
+    *out=number_zero();
+    return(0);
+  }
+
+  *out=number_one();
+  if(sign_correction==-1){
+    number_Qprod_chain(quot(-1,1), out);
+  }
+
+  for(i=0;i<M.length;i++){
+    number_prod_chain(M.matrix[i][i], out);
+  }
+
+  return(0);
+}
+
+// LU decomposition
+// uses pivoting to avoid dividing by 0
+// the sign_correction should be multiplied to the determinant to obtain the right value
+// if dividing by 0 is unavoidable, then the determinant is 0, and sign_correction is set to 0
+int LU_dcmp_inplace(Number_Matrix M, int* sign_correction){
+  int i,j,k,pivot;
+  Number tmp;
+
+  *sign_correction=1;
+
+  for(j=0;j<M.length;j++){
+    for(i=0;i<=j;i++){
+      for(k=0;k<i;k++){
+	// -M[i][k]*M[k][j]
+	number_prod(M.matrix[i][k], M.matrix[k][j], &tmp);
+	number_Qprod_chain(quot(-1,1), &tmp);
+	number_add_chain(tmp, M.matrix[i]+j);
+	free_Number(tmp);
+      }
+    }
+    for(i=j+1;i<M.length;i++){
+      for(k=0;k<j;k++){
+	// -M[i][k]*M[k][j]
+	number_prod(M.matrix[i][k], M.matrix[k][j], &tmp);
+	number_Qprod_chain(quot(-1,1), &tmp);
+	number_add_chain(tmp, M.matrix[i]+j);
+	free_Number(tmp);
+      }
+    }
+
+    // pivot if M[j][j]==0
+    // find first M[j][j] that is not 0
+    for(pivot=j;pivot<M.length && number_is_zero(M.matrix[pivot][j])==1;pivot++){}
+
+    // no non-zero M[j][j] left: return
+    if(pivot>=M.length){
+      *sign_correction=0;
+      return(0);
+    }
+    // pivot if needed
+    if(pivot!=j){
+      for(k=0;k<M.length;k++){
+	tmp=M.matrix[j][k];
+	M.matrix[j][k]=M.matrix[pivot][k];
+	M.matrix[pivot][k]=tmp;
+      }
+      *sign_correction*=-1;
+
+    }
+
+    for(i=j+1;i<M.length;i++){
+      // do not use the inplace algorithm if M[j][j] has more than one terms, since it would be modified by the inplace function
+      if(M.matrix[j][j].length<=1){
+	number_quot_inplace(M.matrix[i]+j, M.matrix[j]+j);
+      }
+      else{
+	number_quot_chain(M.matrix[i]+j, M.matrix[j][j]);
+      }
+    }
+  }
+  return(0);
+}