Ian Jauslin
3f0510629e
The update to version 1.5 is rather substantial, and introduces some minor
backward-incompatibilities:
* The header "#!symbols" has been replaced by "#!virtual_fields"
* Multiplying polynomials using the '*' symbol is no longer supported (or,
rather, the symbolic capabilities of meankondo were enhanced, and the
syntax has been changed).
* 'meantools exp' has been removed (its functionality is now handled by
other means)
* 'meantoolds derive' has been replaced by 'meantools differentiate'
* The symbolic capabilities were enhanced: polynomials can now be
multiplied, added, exponentiated, and their logarithms can be taken
directly in the configuration file.
* The flow equation can now be processed after being computed using the
various "#!postprocess_*" entries.
* Deprecated kondo_preprocess.
* Compute the mean using an LU decomposition if possible.
* More detailed checks for syntax errors in configuration file.
* Check that different '#!group' entries are indeed uncorrelated.
* New flags in meankondo: '-p' and '-A'.
* New tool: meantools expand.
* Improve conversion to LaTeX using meantools-convert
* Assign terms randomly to different threads.
* Created vim files to implement syntax highlighting for configuration
files.
* Multiple bug fixes
94 lines
2.2 KiB
C
94 lines
2.2 KiB
C
#include "determinant.h"
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#include "number.h"
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#include "rational.h"
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#include "definitions.cpp"
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// determinant of a matrix
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// replaces the matrix by its LU decomposition
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int determinant_inplace(Number_Matrix M, Number* out){
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int i;
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int sign_correction;
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LU_dcmp_inplace(M, &sign_correction);
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if(sign_correction==0){
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*out=number_zero();
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return(0);
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}
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*out=number_one();
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if(sign_correction==-1){
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number_Qprod_chain(quot(-1,1), out);
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}
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for(i=0;i<M.length;i++){
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number_prod_chain(M.matrix[i][i], out);
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}
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return(0);
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}
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// LU decomposition
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// uses pivoting to avoid dividing by 0
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// the sign_correction should be multiplied to the determinant to obtain the right value
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// if dividing by 0 is unavoidable, then the determinant is 0, and sign_correction is set to 0
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int LU_dcmp_inplace(Number_Matrix M, int* sign_correction){
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int i,j,k,pivot;
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Number tmp;
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*sign_correction=1;
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for(j=0;j<M.length;j++){
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for(i=0;i<=j;i++){
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for(k=0;k<i;k++){
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// -M[i][k]*M[k][j]
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number_prod(M.matrix[i][k], M.matrix[k][j], &tmp);
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number_Qprod_chain(quot(-1,1), &tmp);
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number_add_chain(tmp, M.matrix[i]+j);
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free_Number(tmp);
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}
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}
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for(i=j+1;i<M.length;i++){
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for(k=0;k<j;k++){
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// -M[i][k]*M[k][j]
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number_prod(M.matrix[i][k], M.matrix[k][j], &tmp);
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number_Qprod_chain(quot(-1,1), &tmp);
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number_add_chain(tmp, M.matrix[i]+j);
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free_Number(tmp);
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}
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}
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// pivot if M[j][j]==0
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// find first M[j][j] that is not 0
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for(pivot=j;pivot<M.length && number_is_zero(M.matrix[pivot][j])==1;pivot++){}
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// no non-zero M[j][j] left: return
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if(pivot>=M.length){
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*sign_correction=0;
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return(0);
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}
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// pivot if needed
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if(pivot!=j){
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for(k=0;k<M.length;k++){
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tmp=M.matrix[j][k];
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M.matrix[j][k]=M.matrix[pivot][k];
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M.matrix[pivot][k]=tmp;
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}
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*sign_correction*=-1;
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}
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for(i=j+1;i<M.length;i++){
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// do not use the inplace algorithm if M[j][j] has more than one terms, since it would be modified by the inplace function
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if(M.matrix[j][j].length<=1){
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number_quot_inplace(M.matrix[i]+j, M.matrix[j]+j);
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}
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else{
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number_quot_chain(M.matrix[i]+j, M.matrix[j][j]);
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}
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}
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}
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return(0);
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}
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