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Diffstat (limited to 'src/determinant.c')
-rw-r--r-- | src/determinant.c | 93 |
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); +} |