The det_manip class

Parameter & construction

The template parameter is the FunctionType, the type of F, which is completely general but has to model the concept

• return_type: type returned by the function
• argument_type: type of the argument of the function (type of x and y).

Public types

name	description
xy_type	?
value_type	?
vector_type	tqa::vector<value_type>
matrix_type	tqa::matrix<value_type>
matrix_view_type	tqa::matrix_view<value_type

Public member functions

return type	member function	description
	det_manip(FunctionType F, size_t init_size)	constructor
	det_manip(FunctionType F, ArgumentContainer1 const &X, ArgumentContainer2 const &Y)	constructor
	det_manip(det_manip const &)	constructor
	det_manip(det_manip &&rhs) noexcept	constructor
det_manip &	operator=(const det_manip &)
det_manip &	operator=(det_manip && rhs) no except	?
void	clear()	put to size 0 (like a vector)
size_t	size() const	current size of the matrix
xy_type const &	get_x(size_t i) const	returns the i-th values of x
xy_type const &	get_y(size_t j) const	returns the j-th values of y
value_type	determinant() const	determinant
value_type	inverse_matrix(size_t i, size_t j) const	?
matrix_view_type	inverse_matrix() const	Returns the inverse matrix. Warning: this is slow, since it create a new copy, and reorder the lines/cols.
matrix_view_type	matrix() const	Rebuild the matrix. Warning: this is slow, since it create a new matrix and re-evaluate the function.
value_type	try_insert(size_t i, size_t j, xy_type const &x, xy_type const &y)	returns determinant ratio corresponding to the insertion of an element x-y on line i, column j without actually doing it. In particular, does not change determinant size.
template<typename Fx, typename Fy> value_type	try_insert_from_function (size_t i, size_t j, Fx fx, Fy fy, value_type const ksi)	?
value_type	try_insert2 (size_t i0, size_t i1, size_t j0, size_t j1, xy_type const &x0, xy_type const &x1, xy_type const &y0, xy_type const &y1)	?
value_type	try_remove (size_t i, size_t j)	?
value_type	try_remove2 (size_t i0, size_t i1, size_t j0, size_t j1)	?
value_type	try_change_col (size_t j, xy_type const &y)	?
value_type	try_change_row (size_t i, xy_type const &x)	?
void	complete_operation()	?
int	roll_matrix (RollDirection roll)	?

Synopsis

• The possible operations on the matrix M are:

Operation	Effect
insert	adding a line and a column
remove	removing a line and a column
insert2	adding 2 lines and 2 columns
remove2	removing 2 lines and 2 columns
change_col	changing one y
change_raw	changing one x

• Each operation OP is called in two steps:

  • value_type try_OP(arguments ...)
    

    Returns the ratio

    \[\frac{det M'}{det M}\]

    where M’ would be the matrix after the operation is completed.

    try_OP does NOT modify the matrix \(M\).

  • void complete_operation()
    

    Complete the last operation OP (the last called try_OP), by updating the list of x and y and the inverse of the matrix to \((M')^{-1}\).

• This structure is designed to write Monte Carlo algorithms:

  • the try part of the move calls some try_OP
  • if and only if the move is accepted, is the complete_operation called.

Under the hood …

• All matrix algebra is made with BLAS calls.
• The storage is done in a compact way: when a column or row is added, no data are shifted, it is added at the end of the matrix. However, the permutation of row and columns are handled by this class so that this is transparent for the user.

Full documentation/manual/triqs

Warning

In construction

Example

#include <triqs/det_manip/det_manip.hpp>

struct fun {

  typedef double result_type;
  typedef double argument_type;

  double operator()(double x, double y) const {
    const double pi   = acos(-1.);
    const double beta = 10.0;
    const double epsi = 0.1;
    double tau        = x - y;
    bool s            = (tau > 0);
    tau               = (s ? tau : beta + tau);
    double r          = epsi + tau / beta * (1 - 2 * epsi);
    return -2 * (pi / beta) / std::sin(pi * r);
  }
};

int main() {

  fun f;
  triqs::det_manip::det_manip<fun> D(f, 100);

  /// insertions of 3 lines and 3 columns
  double x = 2., y = 9., detratio;
  std::cout << D.size() << std::endl;
  detratio = D.try_insert(0, 0, x, y);
  std::cout << D.size() << std::endl;
  D.complete_operation();
  std::cout << D.size() << std::endl;
  detratio = D.try_insert(0, 1, 2., 3.);
  D.complete_operation();
  detratio = D.try_insert(0, 0, 4., 5.);
  D.complete_operation();

  /// removal of a line (the 3rd) and a column (the 2nd)
  detratio = D.try_remove(2, 1);
  D.complete_operation();
}