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more complete cookbook for det_manip
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Laura Messio
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@ -1,7 +1,5 @@
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Basics
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------
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Here, an exemple of creation of a class det_manip, of use of insert and remove.
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Creation of an empty det_manip class
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-------------------------------------
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.. compileblock::
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@ -9,58 +7,204 @@ Here, an exemple of creation of a class det_manip, of use of insert and remove.
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struct fun {
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typedef double result_type;
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typedef double argument_type;
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typedef double result_type;
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typedef double argument_type;
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//gives the coefficients of the matrix (function F of the documentation)
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double operator()(double x, double y) const {
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return(x-y);
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}
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//gives the coefficients of the matrix
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double operator()(double x, double y) const {
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return(x-y);
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}
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};
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int main() {
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//creation of the class det_manip
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fun f;
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int init_size=100;
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triqs::det_manip::det_manip<fun> D(f,init_size);
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int init_size = 100; // maximum size of the matrix before a resize
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//creation of a class det_manip
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triqs::det_manip::det_manip<fun> D(f, init_size);
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//the initial matrix is empty:
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std::cout<<std::endl<<"After construction: D.matrix()="<<D.matrix()<<std::endl<<std::endl;
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std::cout<<std::endl<< "After construction: D.matrix()=" << D.matrix()<<std::endl<<std::endl;
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double detratio;
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//insertion of a line and a column at position (1,1) in the matrix, with x[i]=x, y[j]=y.
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double x=2, y=9;
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int i=0, j=0;
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detratio = D.try_insert(i,j,x,y);
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D.complete_operation();
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std::cout<<"We add a line and a column for i="<<i<<", j="<<j<<", x="<<x<<", y="<<y<<" (f(x,y)="<<f(x,y)<<")."<<std::endl;
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std::cout<<"D.matrix()="<<D.matrix()<<std::endl<<std::endl;
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x=3; y=4; i=0; j=0;
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detratio = D.try_insert(i,j,x,y);
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D.complete_operation();
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std::cout<<"We add a line and a column for i="<<i<<", j="<<j<<", x="<<x<<", y="<<y<<" (f(x,y)="<<f(x,y)<<")."<<std::endl;
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std::cout<<"D.matrix()="<<D.matrix()<<std::endl;
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std::cout<<"The determinant is "<<D.determinant()<<std::endl;
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std::cout<<"The inverse matrix is"<<D.inverse_matrix()<< std::endl<<std::endl;
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x=-7; y=1; i=1; j=2;
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detratio = D.try_insert(i,j,x,y);
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D.complete_operation();
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std::cout<<"We add a line and a column for i="<<i<<", j="<<j<<", x="<<x<<", y="<<y<<" (f(x,y)="<<f(x,y)<<")."<<std::endl;
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std::cout<<"D.matrix()="<<D.matrix()<<std::endl<<std::endl;
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std::cout<<"The size of the matrix is now "<<D.size()<<std::endl;
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std::cout<<"The value of the parameters for coefficient (i,j)=(0,2) is (x,y)=("<<D.get_x(0)<<","<<D.get_y(2)<<") (f("<<D.get_x(0)<<","<<D.get_y(2)<<")="<<f(D.get_x(0),D.get_y(2))<<")."<<std::endl<<std::endl;
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i=0; j=1;
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detratio = D.try_remove(i,j);
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D.complete_operation();
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std::cout<<"We remove a line and a column for i="<<i<<", j="<<j<<"."<<std::endl;
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std::cout<<"D.matrix()="<<D.matrix()<<std::endl;
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std::cout<<"The determinant is "<<D.determinant()<<std::endl;
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std::cout<<"The inverse matrix is"<<D.inverse_matrix()<< std::endl<<std::endl;
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}
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Creation of a non empty det_manip class
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----------------------------------------
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.. compileblock::
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#include <triqs/det_manip/det_manip.hpp>
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struct fun {
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typedef double result_type;
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typedef double argument_type;
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//gives the coefficients of the matrix (function F of the documentation)
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double operator()(double x, double y) const {
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return(x-y);
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}
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};
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int main() {
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fun f;
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std::vector<double> initial_x{1,2}, initial_y{3,4};
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//creation of a class det_manip with a 2 by 2 matrix
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triqs::det_manip::det_manip<fun> D(f, initial_x, initial_y);
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//the initial matrix:
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std::cout<<std::endl<< "After construction: D.matrix()=" << D.matrix()<<std::endl<<std::endl;
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}
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Get informations about a det_manip class
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-----------------------------------------
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.. compileblock::
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#include <triqs/det_manip/det_manip.hpp>
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struct fun {
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typedef double result_type;
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typedef double argument_type;
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double operator()(double x, double y) const { return(x-y); }
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};
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int main() {
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fun f;
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int i=0, j=1;
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std::vector<double> initial_x{1,2}, initial_y{3,4};
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triqs::det_manip::det_manip<fun> D(f, initial_x, initial_y);
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std::cout<<std::endl<<"D.matrix()=" << D.matrix() <<std::endl<<std::endl;
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std::cout<<"The size of the matrix is "<< D.size() <<std::endl<<std::endl;
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std::cout<<"The determinant is "<< D.determinant() <<std::endl<<std::endl;
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std::cout<<"The inverse matrix is"<< D.inverse_matrix() << std::endl<<std::endl;
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std::cout<<"The value of the parameters for coefficient (i,j)=("<<i<<","<<j<<") is (x,y)=("
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<<D.get_x(i)<<","<<D.get_y(j)<<")"<<std::endl<<std::endl;
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}
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Add a line and a column
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-------------------------
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.. compileblock::
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#include <triqs/det_manip/det_manip.hpp>
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struct fun {
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typedef double result_type;
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typedef double argument_type;
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double operator()(double x, double y) const { return(exp(x)-y*y); }
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};
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int main() {
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triqs::det_manip::det_manip<fun> D(fun(), std::vector<double>{1,2,2.5}, std::vector<double>{3,4,9});
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std::cout<<std::endl<<"After construction, D.matrix()="<<D.matrix()<<std::endl<<std::endl;
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double x0 = 2.1, y0 = 7;
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int i = 2, j = 0; // number of the added line and column
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std::cout<<"We want to add a line and a column for i="<<i<<", j="<<j
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<<", x="<<x0<<", y="<<y0<<" (f(x,y)="<<f(x0,y0)<<")."<<std::endl;
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// (try of) insertion of a line and a column at position (3,1) in the matrix
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// with x[i]=x0, y[j]=y0.
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double detratio = D.try_insert(i, j, x0, y0); // the ratio between new and old determinants
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// while the operation is not complete, the matrix stays unchanged
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std::cout<<"After try_insert, D.matrix()="<<D.matrix()<<std::endl;
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// here we validate the insertion: the (inverse) matrix and determinant are updated
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D.complete_operation();
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std::cout<<"After complete_operation, D.matrix()="<<D.matrix()<<std::endl<<std::endl;
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}
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Remove a line and a column
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---------------------------
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.. compileblock::
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#include <triqs/det_manip/det_manip.hpp>
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struct fun {
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typedef double result_type;
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typedef double argument_type;
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double operator()(double x, double y) const { return(exp(x)-y*y); }
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};
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int main() {
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triqs::det_manip::det_manip<fun> D(fun(), std::vector<double>{1,2,2.5}, std::vector<double>{3,4,9});
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std::cout<<std::endl<<"After construction, D.matrix()="<<D.matrix()<<std::endl<<std::endl;
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int i = 1, j = 0; // number of the removed line and column
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std::cout<<"We want to remove a line and a column for i="<<i<<", j="<<j<<"."<<std::endl;
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// (try of) removal of a line and a column at position (1,0) in the matrix.
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double detratio = D.try_remove(i, j); // the ratio between new and old determinants
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// while the operation is not complete, the matrix stays unchanged
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std::cout<<"After try_remove, D.matrix()="<<D.matrix()<<std::endl;
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// here we validate the removal: the (inverse) matrix and determinant are updated
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D.complete_operation();
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std::cout<<"After complete_operation, D.matrix()="<<D.matrix()<<std::endl<<std::endl;
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}
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Add two lines and two columns
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------------------------------
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.. compileblock::
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#include <triqs/det_manip/det_manip.hpp>
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struct fun {
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typedef double result_type;
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typedef double argument_type;
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double operator()(double x, double y) const { return(exp(x)-y*y); }
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};
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int main() {
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triqs::det_manip::det_manip<fun> D(fun(), std::vector<double>{1,2,2.5}, std::vector<double>{3,4,9});
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std::cout<<std::endl<<"After construction, D.matrix()="<<D.matrix()<<std::endl<<std::endl;
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double x0 = 2.1, y0 = 7, x1 = 3.5, y1 = 5;
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int i0 = 2, i1 = 1, j0 = 0, j1 = 3; // number of the added lines and columns
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std::cout<<"We want to add a line and a column for i0="<<i0<<", j0="<<j0<<", i1="<<i1<<", j1="<<j1
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<<", x0="<<x0<<", y0="<<y0<<", x1="<<x1<<", y1="<<y1<<")."<<std::endl;
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// (try of) insertion of 2 lines and 2 columns in the matrix
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double detratio = D.try_insert2 (i0, i1, j0, j1, x0, x1, y0, y1); // the ratio between new and old determinants
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// while the operation is not complete, the matrix stays unchanged
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std::cout<<"After try_insert2, D.matrix()="<<D.matrix()<<std::endl;
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// here we validate the insertion: the (inverse) matrix and determinant are updated
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D.complete_operation();
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std::cout<<"After complete_operation, D.matrix()="<<D.matrix()<<std::endl<<std::endl;
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}
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Remove two lines and two columns
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--------------------------------
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.. compileblock::
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#include <triqs/det_manip/det_manip.hpp>
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struct fun {
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typedef double result_type;
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typedef double argument_type;
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double operator()(double x, double y) const { return(exp(x)-y*y); }
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};
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int main() {
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triqs::det_manip::det_manip<fun> D(fun(), std::vector<double>{1,2,2.5}, std::vector<double>{3,4,9});
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std::cout<<std::endl<<"After construction, D.matrix()="<<D.matrix()<<std::endl<<std::endl;
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int i0 = 2, i1 = 1, j0 = 0, j1 = 1; // number of the removed lines and columns
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std::cout<<"We want to remove 2 lines and 2 columns for i0="
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<<i0<<", j0="<<j0<<", i1="<<i1<<", j1="<<j1<<"."<<std::endl;
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// (try of) removal of a line and a column at position (1,0) in the matrix.
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double detratio = D.try_remove2(i0, i1, j0, j1); // the ratio between new and old determinants
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// while the operation is not complete, the matrix stays unchanged
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std::cout<<"After try_remove2, D.matrix()="<<D.matrix()<<std::endl;
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// here we validate the removal: the (inverse) matrix and determinant are updated
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D.complete_operation();
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std::cout<<"After complete_operation, D.matrix()="<<D.matrix()<<std::endl<<std::endl;
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}
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Learn more in the full reference, see :ref:`det_manip`
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@ -79,9 +79,11 @@ Doxygen documentation
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The :doxy:`full C++ documentation<triqs::det_manip::det_manip>` is available here.
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Example
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-------------
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---------
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.. code-block:: c
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.. compileblock::
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#include <triqs/det_manip/det_manip.hpp>
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struct fun {
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@ -89,7 +91,7 @@ Example
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typedef double argument_type;
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double operator()(double x, double y) const {
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const double pi = acos(-1);
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const double pi = acos(-1.);
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const double beta = 10.0;
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const double epsi = 0.1;
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double tau = x-y;
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@ -103,14 +105,18 @@ Example
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int main() {
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fun f;
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triqs::det_manip::det_manip<fun> D;
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triqs::det_manip::det_manip<fun> D(f,100);
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/// ....
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double x=2, y=9, detratio;
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detratio = D.try_insert(1,3, x,y);
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/// insertions of 3 lines and 3 columns
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double x=2., y=9., detratio;
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detratio = D.try_insert(0, 0, x, y );
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D.complete_operation();
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detratio = D.try_insert(0, 1, 2., 3.);
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D.complete_operation();
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detratio = D.try_insert(0, 0, 4., 5.);
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D.complete_operation();
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///...
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/// removal of a line (the 3rd) and a column (the 2nd)
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detratio = D.try_remove(2,1);
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D.complete_operation();
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}
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