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#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);
}
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