Ian Jauslin
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Diffstat (limited to 'src/determinant.c')
-rw-r--r--src/determinant.c93
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);
+}