#include <triqs/det_manip/det_manip_basic.hpp>

Detailed Description

template<typename FunctionType>
class triqs::det_manip::det_manip_basic< FunctionType >

Simple reference implementation of determinant manipulation for CTQMC solvers.

This class manipulates the determinant \( \det(F^{(n)}) \) of a matrix whose elements are given by a callable \( F^{(n)}_{ij} = f(x_i, y_j) \) (see Determinant manipulation for the general setup).

It exposes the same API as triqs::det_manip::det_manip (the same try/complete operations, accessors and HDF5 support), but uses a straightforward implementation: instead of the fast rank-update algorithm, it rebuilds the matrix and recomputes the determinant (and, on demand, the inverse) from scratch on every operation. It does not track row/column permutations or a sign, so the matrix is stored in the user's order, i.e. the internal order equals the user order.

This makes it simpler and easier to verify, but asymptotically slower than triqs::det_manip::det_manip; it is primarily useful as a reference/testing implementation.

Template Parameters

FunctionType Callable object \( f \) that takes two arguments and returns a real or complex value. It determines the elements of the matrix via \( F^{(n)}_{ij} = f(x_i, y_j) \).

Definition at line 65 of file det_manip_basic.hpp.

Public Types
enum	RollDirection
	Direction of the roll_matrix() operation. More...

Public Member Functions
template<typename ArgumentContainer1, typename ArgumentContainer2>
	det_manip_basic (FunctionType F, ArgumentContainer1 const &X, ArgumentContainer2 const &Y)
	Construct a det_manip_basic object with a callable FunctionType and two containers holding the arguments for the matrix builder.
	det_manip_basic (FunctionType F, long init_size)
	Construct a det_manip_basic object with a callable FunctionType and an initial capacity for the data storages.
matrix_type	build_matrix_scratch ()
	Build the matrix \( F^{(n)} \) from scratch from the stored arguments.
value_type	change_col (long j, y_type const &y)
	Change one column.
value_type	change_one_row_and_one_col (long i, long j, x_type const &x, y_type const &y)
	Change one row and one column.
value_type	change_row (long i, x_type const &x)
	Change one row.
void	clear ()
	Clear the data storages and reset the matrix to size zero.
void	complete_operation ()
	Complete the last try-operation.
auto	determinant ()
	Get the determinant of the matrix \( F^{(n)} \).
FunctionType const &	get_function () const
	Get the callable FunctionType object \( f \) used as the matrix builder.
auto	get_x () const
	Get a vector with all matrix builder arguments \( \mathbf{x} \).
x_type const &	get_x (long i) const
	Get the matrix builder argument \( x_i \) that determines the elements of the i^th row.
auto const &	get_x_internal_order () const
	Get the matrix builder arguments \( \mathbf{x} \) in internal storage order.
auto	get_y () const
	Get a vector with all matrix builder arguments \( \mathbf{y} \).
y_type const &	get_y (long j) const
	Get the matrix builder argument \( y_j \) that determines the elements of the j^th column.
auto const &	get_y_internal_order () const
	Get the matrix builder arguments \( \mathbf{y} \) in internal storage order.
value_type	insert (long i, long j, x_type const &x, y_type const &y)
	Insert one row and column.
value_type	insert2 (long i0, long i1, long j0, long j1, x_type const &x0, x_type const &x1, y_type const &y0, y_type const &y1)
	Insert two rows and columns.
value_type	insert2_at_end (x_type const &x0, x_type const &x1, y_type const &y0, y_type const &y1)
	Insert two rows and columns at the end of the matrix.
value_type	insert_at_end (x_type const &x, y_type const &y)
	Insert one row and column at the end of the matrix.
template<nda::Array X, nda::Array Y> requires (nda::get_rank<X> == nda::get_rank<Y>)
auto	insert_ratios (long i, long j, X const &xs, Y const &ys) const -> nda::array< value_type, nda::get_rank< X > >
	Compute independent single-insertion determinant ratios at position \( (i, j) \) for paired elements of xs and ys.
nda::matrix_const_view< value_type >	inverse_matrix () const
	Get the full inverse matrix \( [F^{(n)}]^{-1} \).
value_type	inverse_matrix (int i, int j) const
	Get an element of the inverse matrix \( [F^{(n)}]^{-1} \).
nda::matrix_const_view< value_type >	inverse_matrix_internal_order () const
	Get the full inverse matrix in internal storage order.
value_type	inverse_matrix_internal_order (int i, int j) const
	Get an element of the inverse matrix in internal storage order.
matrix_type	matrix () const
	Get the matrix \( F^{(n)} \).
value_type	matrix (int i, int j) const
	Get an element of the matrix \( F^{(n)} \).
void	reject_last_try ()
	Reject the last try-operation.
value_type	remove (long i, long j)
	Remove one row and column.
value_type	remove2 (long i0, long i1, long j0, long j1)
	Remove two rows and columns.
value_type	remove2_at_end ()
	Remove the last two rows and columns of the matrix.
value_type	remove_at_end ()
	Remove the last row and column of the matrix.
void	reserve (long new_size, long new_k=1)
	Reserve memory to increase the capacity of the data storages.
int	roll_matrix (RollDirection roll)
	Perform a circular shift permutation on the rows or columns of the matrix \( F^{(n)} \).
auto	size () const
	Get the current size of the matrix.
value_type	try_change_col (long j, y_type const &y)
	Try to change one column in the matrix \( F^{(n)} \).
value_type	try_change_col_row (long i, long j, x_type const &x, y_type const &y)
	Try to change one column and one row in the matrix \( F^{(n)} \).
value_type	try_change_row (long i, x_type const &x)
	Try to change one row in the matrix \( F^{(n)} \).
value_type	try_insert (long i, long j, x_type const &x, y_type const &y)
	Try to insert one row and column.
value_type	try_insert2 (long i0, long i1, long j0, long j1, x_type const &x0_, x_type const &x1_, y_type const &y0_, y_type const &y1_)
	Try to insert two rows and columns.
value_type	try_insert_k (std::vector< long > i, std::vector< long > j, std::vector< x_type > x, std::vector< y_type > y)
	Try to insert \( k \) rows and columns.
template<typename ArgumentContainer1, typename ArgumentContainer2>
value_type	try_refill (ArgumentContainer1 const &X, ArgumentContainer2 const &Y)
	Try to fill the matrix \( F^{(n)} \) with new elements.
value_type	try_remove (long i, long j)
	Try to remove one row and column.
value_type	try_remove2 (long i0, long i1, long j0, long j1)
	Try to remove two rows and two columns.
value_type	try_remove_k (std::vector< long > i, std::vector< long > j)
	Try to remove \( k \) rows and columns.

Friends
template<typename LambdaType>
void	foreach (det_manip_basic const &d, LambdaType const &func)
	For-each implementation for triqs::det_manip::det_manip_basic objects.
void	h5_read (h5::group fg, std::string subgroup_name, det_manip_basic &g)
	Read a triqs::det_manip::det_manip_basic object from HDF5.
void	h5_write (h5::group fg, std::string subgroup_name, det_manip_basic const &g)
	Write a triqs::det_manip::det_manip_basic object to HDF5.

Member Enumeration Documentation

◆ RollDirection

template<typename FunctionType>

enum triqs::det_manip::det_manip_basic::RollDirection

Direction of the roll_matrix() operation.

It specifies the direction of the circular shift performed on either the rows or columns of the matrix \( F^{(n)} \). The following directions are supported:

None: No roll operation is performed.
Up: Roll the rows up (move the first row to the last, cyclically).
Down: Roll the rows down (move the last row to the first, cyclically).
Left: Roll the columns to the left (move the first column to the last, cyclically).
Right: Roll the columns to the right (move the last column to the first, cyclically).

Definition at line 1503 of file det_manip_basic.hpp.

Constructor & Destructor Documentation

◆ det_manip_basic() [1/2]

template<typename FunctionType>

triqs::det_manip::det_manip_basic< FunctionType >::det_manip_basic	(	FunctionType	F,
		long	init_size )

inline

Construct a det_manip_basic object with a callable FunctionType and an initial capacity for the data storages.

Like for std::vector, the capacity grows automatically (by a factor of 2) when needed, but this can yield a performance penalty if it happens too often.

Parameters

F	Callable FunctionType object (a copy is stored in the class).
init_size	Initial capacity for the size of the matrix, i.e. the maximum number of rows and columns.

Definition at line 245 of file det_manip_basic.hpp.

◆ det_manip_basic() [2/2]

template<typename FunctionType>

template<typename ArgumentContainer1, typename ArgumentContainer2>

triqs::det_manip::det_manip_basic< FunctionType >::det_manip_basic	(	FunctionType	F,
		ArgumentContainer1 const &	X,
		ArgumentContainer2 const &	Y )

inline

Construct a det_manip_basic object with a callable FunctionType and two containers holding the arguments for the matrix builder.

Template Parameters

ArgumentContainer1	Container type holding the first arguments.
ArgumentContainer2	Container type holding the second arguments.

Parameters

F	Callable FunctionType object (a copy is stored in the class).
X	Container holding the first arguments \( \mathbf{x} \).
Y	Container holding the second arguments \( \mathbf{y} \).

Definition at line 261 of file det_manip_basic.hpp.

Member Function Documentation

◆ build_matrix_scratch()

template<typename FunctionType>

matrix_type triqs::det_manip::det_manip_basic< FunctionType >::build_matrix_scratch ( )

inline

Build the matrix \( F^{(n)} \) from scratch from the stored arguments.

Evaluates \( f(x_i, y_j) \) for all \( i, j \) and returns a freshly allocated matrix.

Returns: The matrix \( F^{(n)} \).

Definition at line 299 of file det_manip_basic.hpp.

◆ change_col()

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::change_col	(	long	j,
		y_type const &	y )

inline

Change one column.

Wrapper for try_change_col() followed by a complete_operation() call. See try_change_col() for details.

Parameters

j	Position of the column to be changed in the matrix \( F^{(n)} \).
y	Argument to the matrix builder that determines the new elements of the column.

Returns: Determinant ratio \( \det(\widetilde{F}^{(n)}) / \det(F^{(n)}) \).

Definition at line 1456 of file det_manip_basic.hpp.

◆ change_one_row_and_one_col()

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::change_one_row_and_one_col	(	long	i,
		long	j,
		x_type const &	x,
		y_type const &	y )

inline

Change one row and one column.

Wrapper for try_change_col_row() followed by a complete_operation() call. See try_change_col_row() for details.

Parameters

i	Position of the row to be changed in the matrix \( F^{(n)} \).
j	Position of the column to be changed in the matrix \( F^{(n)} \).
x	Argument to the matrix builder that determines the new elements of the row.
y	Argument to the matrix builder that determines the new elements of the column.

Returns: Determinant ratio \( \det(\widetilde{F}^{(n)}) / \det(F^{(n)}) \).

Definition at line 1485 of file det_manip_basic.hpp.

◆ change_row()

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::change_row	(	long	i,
		x_type const &	x )

inline

Change one row.

Wrapper for try_change_row() followed by a complete_operation() call. See try_change_row() for details.

Parameters

i	Position of the row to be changed in the matrix \( F^{(n)} \).
x	Argument to the matrix builder that determines the new elements of the row.

Returns: Determinant ratio \( \det(\widetilde{F}^{(n)}) / \det(F^{(n)}) \).

Definition at line 1469 of file det_manip_basic.hpp.

◆ complete_operation()

template<typename FunctionType>

void triqs::det_manip::det_manip_basic< FunctionType >::complete_operation ( )

inline

Complete the last try-operation.

It completes the last try-operation by applying the candidate matrix and determinant that were prepared by the corresponding try_* call, depending on the tag set in the last try function call.

Definition at line 1327 of file det_manip_basic.hpp.

◆ determinant()

template<typename FunctionType>

auto triqs::det_manip::det_manip_basic< FunctionType >::determinant ( )

inline

Get the determinant of the matrix \( F^{(n)} \).

Returns: Determinant \( \det(F^{(n)}) \).

Definition at line 402 of file det_manip_basic.hpp.

◆ get_function()

template<typename FunctionType>

FunctionType const & triqs::det_manip::det_manip_basic< FunctionType >::get_function ( ) const

inline

Get the callable FunctionType object \( f \) used as the matrix builder.

Returns: Const reference to the stored callable.

Definition at line 396 of file det_manip_basic.hpp.

◆ get_x() [1/2]

template<typename FunctionType>

auto triqs::det_manip::det_manip_basic< FunctionType >::get_x ( ) const

inline

Get a vector with all matrix builder arguments \( \mathbf{x} \).

Returns: std::vector containing the arguments \( x_i \).

Definition at line 354 of file det_manip_basic.hpp.

◆ get_x() [2/2]

template<typename FunctionType>

x_type const & triqs::det_manip::det_manip_basic< FunctionType >::get_x ( long i ) const

inline

Get the matrix builder argument \( x_i \) that determines the elements of the i^th row.

Parameters

i	Argument index.

Returns: Argument value \( x_i \).

Definition at line 367 of file det_manip_basic.hpp.

◆ get_x_internal_order()

template<typename FunctionType>

auto const & triqs::det_manip::det_manip_basic< FunctionType >::get_x_internal_order ( ) const

inline

Get the matrix builder arguments \( \mathbf{x} \) in internal storage order.

For this class the internal order equals the user order (there is no permutation), so this returns the same as get_x().

Returns: std::vector containing the arguments \( x_i \).

Definition at line 382 of file det_manip_basic.hpp.

◆ get_y() [1/2]

template<typename FunctionType>

auto triqs::det_manip::det_manip_basic< FunctionType >::get_y ( ) const

inline

Get a vector with all matrix builder arguments \( \mathbf{y} \).

Returns: std::vector containing the arguments \( y_j \).

Definition at line 360 of file det_manip_basic.hpp.

◆ get_y() [2/2]

template<typename FunctionType>

y_type const & triqs::det_manip::det_manip_basic< FunctionType >::get_y ( long j ) const

inline

Get the matrix builder argument \( y_j \) that determines the elements of the j^th column.

Parameters

j	Argument index.

Returns: Argument value \( y_j \).

Definition at line 374 of file det_manip_basic.hpp.

◆ get_y_internal_order()

template<typename FunctionType>

auto const & triqs::det_manip::det_manip_basic< FunctionType >::get_y_internal_order ( ) const

inline

Get the matrix builder arguments \( \mathbf{y} \) in internal storage order.

For this class the internal order equals the user order (there is no permutation), so this returns the same as get_y().

Returns: std::vector containing the arguments \( y_j \).

Definition at line 390 of file det_manip_basic.hpp.

◆ insert()

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::insert	(	long	i,
		long	j,
		x_type const &	x,
		y_type const &	y )

inline

Insert one row and column.

Wrapper for try_insert() followed by a complete_operation() call. See try_insert() for details.

Parameters

i	Position of the row to be inserted in the matrix \( F^{(n)} \).
j	Position of the column to be inserted in the matrix \( F^{(n)} \).
x	Argument to the matrix builder that determines the elements of the new row.
y	Argument to the matrix builder that determines the elements of the new column.

Returns: Determinant ratio \( \det(F^{(n+1)}) / \det(F^{(n)}) \).

Definition at line 1368 of file det_manip_basic.hpp.

◆ insert2()

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::insert2	(	long	i0,
		long	i1,
		long	j0,
		long	j1,
		x_type const &	x0,
		x_type const &	x1,
		y_type const &	y0,
		y_type const &	y1 )

inline

Insert two rows and columns.

Wrapper for try_insert2() followed by a complete_operation() call. See try_insert2() for details.

Parameters

i0,i1	Positions of the rows to be inserted in the matrix \( F^{(n)} \).
j0,j1	Positions of the columns to be inserted in the matrix \( F^{(n)} \).
x0,x1	Arguments to the matrix builder that determine the elements of the new rows.
y0,y1	Arguments to the matrix builder that determine the elements of the new columns.

Returns: Determinant ratio \( \det(F^{(n+2)}) / \det(F^{(n)}) \).

Definition at line 1392 of file det_manip_basic.hpp.

◆ insert2_at_end()

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::insert2_at_end	(	x_type const &	x0,
		x_type const &	x1,
		y_type const &	y0,
		y_type const &	y1 )

inline

Insert two rows and columns at the end of the matrix.

Same as insert2() but with i0 and j0 set to size() and i1 and j1 set to size() + 1.

Parameters

x0,x1	Arguments to the matrix builder that determine the elements of the new rows.
y0,y1	Arguments to the matrix builder that determine the elements of the new columns.

Returns: Determinant ratio \( \det(F^{(n+2)}) / \det(F^{(n)}) \).

Definition at line 1405 of file det_manip_basic.hpp.

◆ insert_at_end()

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::insert_at_end	(	x_type const &	x,
		y_type const &	y )

inline

Insert one row and column at the end of the matrix.

Same as insert() but with i and j set to size().

Parameters

x	Argument to the matrix builder that determines the elements of the new row.
y	Argument to the matrix builder that determines the elements of the new column.

Returns: Determinant ratio \( \det(F^{(n+1)}) / \det(F^{(n)}) \).

Definition at line 1381 of file det_manip_basic.hpp.

◆ insert_ratios()

template<typename FunctionType>

template<nda::Array X, nda::Array Y>
requires (nda::get_rank<X> == nda::get_rank<Y>)

auto triqs::det_manip::det_manip_basic< FunctionType >::insert_ratios	(	long	i,
		long	j,
		X const &	xs,
		Y const &	ys ) const->nda::array< value_type, nda::get_rank< X > >

inline

Compute independent single-insertion determinant ratios at position \( (i, j) \) for paired elements of xs and ys.

For each pair (xs[m], ys[m]) it computes the determinant ratio that a single try_insert() at position \( (i, j) \) would produce, without modifying the internal state. The inputs must be nda::Array objects with the same rank and shape, and the result has the same shape.

Template Parameters

X	nda::Array type of the first arguments.
Y	nda::Array type of the second arguments.

Parameters

i	Position of the row to be inserted in the matrix \( F^{(n)} \).
j	Position of the column to be inserted in the matrix \( F^{(n)} \).
xs	Array of first arguments to the matrix builder.
ys	Array of second arguments to the matrix builder.

Returns: Array of determinant ratios with the same shape as xs and ys.

Definition at line 718 of file det_manip_basic.hpp.

◆ inverse_matrix() [1/2]

template<typename FunctionType>

nda::matrix_const_view< value_type > triqs::det_manip::det_manip_basic< FunctionType >::inverse_matrix ( ) const

inline

Get the full inverse matrix \( [F^{(n)}]^{-1} \).

The inverse is recomputed from scratch on demand and cached until the next operation.

Returns: The inverse matrix \( [F^{(n)}]^{-1} \).

Definition at line 409 of file det_manip_basic.hpp.

◆ inverse_matrix() [2/2]

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::inverse_matrix	(	int	i,
		int	j ) const

inline

Get an element of the inverse matrix \( [F^{(n)}]^{-1} \).

Parameters

i	Row index.
j	Column index.

Returns: The matrix element \( [F^{(n)}]^{-1}_{ij} \).

Definition at line 421 of file det_manip_basic.hpp.

◆ inverse_matrix_internal_order() [1/2]

template<typename FunctionType>

nda::matrix_const_view< value_type > triqs::det_manip::det_manip_basic< FunctionType >::inverse_matrix_internal_order ( ) const

inline

Get the full inverse matrix in internal storage order.

For this class the internal order equals the user order, so this returns the same as inverse_matrix().

Returns: The inverse matrix \( [F^{(n)}]^{-1} \).

Definition at line 432 of file det_manip_basic.hpp.

◆ inverse_matrix_internal_order() [2/2]

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::inverse_matrix_internal_order	(	int	i,
		int	j ) const

inline

Get an element of the inverse matrix in internal storage order.

For this class the internal order equals the user order, so this returns the same as inverse_matrix(int, int).

Parameters

i	Row index.
j	Column index.

Returns: The matrix element \( [F^{(n)}]^{-1}_{ij} \).

Definition at line 442 of file det_manip_basic.hpp.

◆ matrix() [1/2]

template<typename FunctionType>

matrix_type triqs::det_manip::det_manip_basic< FunctionType >::matrix ( ) const

inline

Get the matrix \( F^{(n)} \).

Returns: The matrix \( F^{(n)} \).

Definition at line 448 of file det_manip_basic.hpp.

◆ matrix() [2/2]

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::matrix	(	int	i,
		int	j ) const

inline

Get an element of the matrix \( F^{(n)} \).

Parameters

i	Row index.
j	Column index.

Returns: The matrix element \( F^{(n)}_{ij} \).

Definition at line 459 of file det_manip_basic.hpp.

◆ reject_last_try()

template<typename FunctionType>

void triqs::det_manip::det_manip_basic< FunctionType >::reject_last_try ( )

inline

Reject the last try-operation.

All try_* operations have to be either accepted (via complete_operation()) or rejected.

Definition at line 1354 of file det_manip_basic.hpp.

◆ remove()

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::remove	(	long	i,
		long	j )

inline

Remove one row and column.

Wrapper for try_remove() followed by a complete_operation() call. See try_remove() for details.

Parameters

i	Position of the row to be removed in the matrix \( F^{(n)} \).
j	Position of the column to be removed in the matrix \( F^{(n)} \).

Returns: Determinant ratio \( \det(F^{(n-1)}) / \det(F^{(n)}) \).

Definition at line 1416 of file det_manip_basic.hpp.

◆ remove2()

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::remove2	(	long	i0,
		long	i1,
		long	j0,
		long	j1 )

inline

Remove two rows and columns.

Wrapper for try_remove2() followed by a complete_operation() call. See try_remove2() for details.

Parameters

i0,i1	Positions of the rows to be removed in the matrix \( F^{(n)} \).
j0,j1	Positions of the columns to be removed in the matrix \( F^{(n)} \).

Returns: Determinant ratio \( \det(F^{(n-2)}) / \det(F^{(n)}) \).

Definition at line 1436 of file det_manip_basic.hpp.

◆ remove2_at_end()

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::remove2_at_end ( )

inline

Remove the last two rows and columns of the matrix.

Same as remove2() but with i0 and j0 set to size() - 1 and i1 and j1 set to size() - 2.

Returns: Determinant ratio \( \det(F^{(n-2)}) / \det(F^{(n)}) \).

Definition at line 1447 of file det_manip_basic.hpp.

◆ remove_at_end()

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::remove_at_end ( )

inline

Remove the last row and column of the matrix.

Same as remove() but with i and j set to size() - 1.

Returns: Determinant ratio \( \det(F^{(n-1)}) / \det(F^{(n)}) \).

Definition at line 1427 of file det_manip_basic.hpp.

◆ reserve()

template<typename FunctionType>

void triqs::det_manip::det_manip_basic< FunctionType >::reserve	(	long	new_size,
		long	new_k = 1 )

inline

Reserve memory to increase the capacity of the data storages.

Like for std::vector, this reserves memory for a bigger matrix size. It only reserves/resizes if the requested capacity is larger than the current one. It preserves the matrix but not the temporary working data, so it must NOT be called between a try_* function and the corresponding complete_operation().

Parameters

new_size	New capacity for the size of the matrix, i.e. the maximum number of rows and columns.
new_k	Unused, kept for API compatibility with triqs::det_manip::det_manip.

Definition at line 220 of file det_manip_basic.hpp.

◆ roll_matrix()

template<typename FunctionType>

int triqs::det_manip::det_manip_basic< FunctionType >::roll_matrix ( RollDirection roll )

inline

Perform a circular shift permutation on the rows or columns of the matrix \( F^{(n)} \).

See RollDirection for the supported directions. This routine is not a try_* operation: it does make the modification (it rebuilds the matrix and updates the determinant directly) and does not need to be completed.

A circular shift permutation of a finite set is equivalent to \( N \) transpositions, where \( N \) is the size of the set. The sign of the permutation is therefore given by \( (-1)^{N-1} \).

Parameters

roll	Direction of the roll operation.

Returns: -1 if the roll changes the sign of the determinant, 1 otherwise.

Definition at line 1518 of file det_manip_basic.hpp.

◆ size()

template<typename FunctionType>

auto triqs::det_manip::det_manip_basic< FunctionType >::size ( ) const

inline

Get the current size of the matrix.

Returns: Number of rows/columns of the matrix.

Definition at line 348 of file det_manip_basic.hpp.

◆ try_change_col()

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::try_change_col	(	long	j,
		y_type const &	y )

inline

Try to change one column in the matrix \( F^{(n)} \).

The column at position \( j \) is replaced; its new elements are determined by the given matrix builder argument \( y \). It builds the candidate matrix and recomputes its determinant from scratch.

Warning: This routine does not make any modification. It has to be completed with complete_operation().

Parameters

j	Position of the column to be changed in the matrix \( F^{(n)} \).
y	Argument to the matrix builder that determines the new elements of the column.

Returns: Determinant ratio \( \det(\widetilde{F}^{(n)}) / \det(F^{(n)}) \).

Definition at line 1140 of file det_manip_basic.hpp.

◆ try_change_col_row()

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::try_change_col_row	(	long	i,
		long	j,
		x_type const &	x,
		y_type const &	y )

inline

Try to change one column and one row in the matrix \( F^{(n)} \).

The row at position \( i \) and the column at position \( j \) are replaced; their new elements are determined by the given matrix builder arguments \( x \) and \( y \). It builds the candidate matrix and recomputes its determinant from scratch.

Warning: This routine does not make any modification. It has to be completed with complete_operation().

Parameters

i	Position of the row to be changed in the matrix \( F^{(n)} \).
j	Position of the column to be changed in the matrix \( F^{(n)} \).
x	Argument to the matrix builder that determines the new elements of the row.
y	Argument to the matrix builder that determines the new elements of the column.

Returns: Determinant ratio \( \det(\widetilde{F}^{(n)}) / \det(F^{(n)}) \).

Definition at line 1220 of file det_manip_basic.hpp.

◆ try_change_row()

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::try_change_row	(	long	i,
		x_type const &	x )

inline

Try to change one row in the matrix \( F^{(n)} \).

The row at position \( i \) is replaced; its new elements are determined by the given matrix builder argument \( x \). It builds the candidate matrix and recomputes its determinant from scratch.

Warning: This routine does not make any modification. It has to be completed with complete_operation().

Parameters

i	Position of the row to be changed in the matrix \( F^{(n)} \).
x	Argument to the matrix builder that determines the new elements of the row.

Returns: Determinant ratio \( \det(\widetilde{F}^{(n)}) / \det(F^{(n)}) \).

Definition at line 1179 of file det_manip_basic.hpp.

◆ try_insert()

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::try_insert	(	long	i,
		long	j,
		x_type const &	x,
		y_type const &	y )

inline

Try to insert one row and column.

The row is inserted at position \( i \) and the column at position \( j \) in the matrix \( F^{(n)} \), with elements determined by the given matrix builder arguments \( x \) and \( y \). The current column \( j \) (resp. row \( i \)) becomes column \( j + 1 \) (resp. row \( i + 1 \)); inserting at \( n \) simply appends at the end ( \( 0 \leq i, j \leq n \)).

It builds the candidate matrix and recomputes its determinant from scratch.

Warning: This routine does not make any modification. It has to be completed with complete_operation().

Parameters

i	Position of the row to be inserted in the matrix \( F^{(n)} \).
j	Position of the column to be inserted in the matrix \( F^{(n)} \).
x	Argument to the matrix builder that determines the elements of the new row.
y	Argument to the matrix builder that determines the elements of the new column.

Returns: Determinant ratio \( \det(F^{(n+1)}) / \det(F^{(n)}) \).

Definition at line 497 of file det_manip_basic.hpp.

◆ try_insert2()

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::try_insert2	(	long	i0,
		long	i1,
		long	j0,
		long	j1,
		x_type const &	x0_,
		x_type const &	x1_,
		y_type const &	y0_,
		y_type const &	y1_ )

inline

Try to insert two rows and columns.

The rows are inserted at positions \( i_0 \) and \( i_1 \) and the columns at positions \( j_0 \) and \( j_1 \) in the matrix \( F^{(n)} \), with elements determined by the given matrix builder arguments \( x_0, x_1, y_0, y_1 \) ( \( 0 \leq i_0,i_1,j_0,j_1 \leq n+1 \)).

It builds the candidate matrix and recomputes its determinant from scratch.

Warning: This routine does not make any modification. It has to be completed with complete_operation().

Parameters

i0	Position of the first row to be inserted in the matrix \( F^{(n)} \).
i1	Position of the second row to be inserted in the matrix \( F^{(n)} \).
j0	Position of the first column to be inserted in the matrix \( F^{(n)} \).
j1	Position of the second column to be inserted in the matrix \( F^{(n)} \).
x0_	Argument to the matrix builder that determines the elements of the first new row.
x1_	Argument to the matrix builder that determines the elements of the second new row.
y0_	Argument to the matrix builder that determines the elements of the first new column.
y1_	Argument to the matrix builder that determines the elements of the second new column.

Returns: Determinant ratio \( \det(F^{(n+2)}) / \det(F^{(n)}) \).

Definition at line 574 of file det_manip_basic.hpp.

◆ try_insert_k()

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::try_insert_k	(	std::vector< long >	i,
		std::vector< long >	j,
		std::vector< x_type >	x,
		std::vector< y_type >	y )

inline

Try to insert \( k \) rows and columns.

The new rows and columns are inserted at the positions given by the tuples \( \mathbf{i} \) and \( \mathbf{j} \), with elements determined by the matrix builder arguments \( \mathbf{x} \) and \( \mathbf{y} \) (each position \( i_l, j_l \) valid up to \( n + l \)).

It builds the candidate matrix and recomputes its determinant from scratch.

Warning: This routine does not make any modification. It has to be completed with complete_operation().

Parameters

i	Positions of the rows to be inserted in the matrix \( F^{(n)} \).
j	Positions of the columns to be inserted in the matrix \( F^{(n)} \).
x	Arguments to the matrix builder that determine the elements of the new rows.
y	Arguments to the matrix builder that determine the elements of the new columns.

Returns: Determinant ratio \( \det(F^{(n+k)}) / \det(F^{(n)}) \).

Definition at line 763 of file det_manip_basic.hpp.

◆ try_refill()

template<typename FunctionType>

template<typename ArgumentContainer1, typename ArgumentContainer2>

value_type triqs::det_manip::det_manip_basic< FunctionType >::try_refill	(	ArgumentContainer1 const &	X,
		ArgumentContainer2 const &	Y )

inline

Try to fill the matrix \( F^{(n)} \) with new elements.

Builds a completely new matrix \( \widetilde{F}^{(\widetilde{n})} \) from the given matrix builder arguments \( \mathbf{x} \) and \( \mathbf{y} \) (with \( \widetilde{F}_{ij} = f(x_i, y_j) \)) and recomputes its determinant from scratch.

Warning: This routine does not make any modification. It has to be completed with complete_operation().

Template Parameters

ArgumentContainer1	Container type holding the first arguments.
ArgumentContainer2	Container type holding the second arguments.

Parameters

X	Container holding the first matrix builder arguments.
Y	Container holding the second matrix builder arguments.

Returns: Determinant ratio \( \det(\widetilde{F}^{(\widetilde{n})}) / \det(F^{(n)}) \).

Definition at line 1274 of file det_manip_basic.hpp.

◆ try_remove()

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::try_remove	(	long	i,
		long	j )

inline

Try to remove one row and column.

The row at position \( i \) and the column at position \( j \) are removed from the matrix \( F^{(n)} \). It builds the candidate matrix and recomputes its determinant from scratch.

Warning: This routine does not make any modification. It has to be completed with complete_operation().

Parameters

i	Position of the row to be removed in the matrix \( F^{(n)} \).
j	Position of the column to be removed in the matrix \( F^{(n)} \).

Returns: Determinant ratio \( \det(F^{(n-1)}) / \det(F^{(n)}) \).

Definition at line 885 of file det_manip_basic.hpp.

◆ try_remove2()

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::try_remove2	(	long	i0,
		long	i1,
		long	j0,
		long	j1 )

inline

Try to remove two rows and two columns.

The rows at positions \( i_0, i_1 \) and the columns at positions \( j_0, j_1 \) are removed from the matrix \( F^{(n)} \). It builds the candidate matrix and recomputes its determinant from scratch.

Warning: This routine does not make any modification. It has to be completed with complete_operation().

Parameters

i0	Position of the first row to be removed in the matrix \( F^{(n)} \).
i1	Position of the second row to be removed in the matrix \( F^{(n)} \).
j0	Position of the first column to be removed in the matrix \( F^{(n)} \).
j1	Position of the second column to be removed in the matrix \( F^{(n)} \).

Returns: Determinant ratio \( \det(F^{(n-2)}) / \det(F^{(n)}) \).

Definition at line 946 of file det_manip_basic.hpp.

◆ try_remove_k()

template<typename FunctionType>

value_type triqs::det_manip::det_manip_basic< FunctionType >::try_remove_k	(	std::vector< long >	i,
		std::vector< long >	j )

inline

Try to remove \( k \) rows and columns.

The rows and columns at the positions given by the tuples \( \mathbf{i} \) and \( \mathbf{j} \) are removed from the matrix \( F^{(n)} \). It builds the candidate matrix and recomputes its determinant from scratch.

Warning: This routine does not make any modification. It has to be completed with complete_operation().

Parameters

i	Positions of the rows to be removed in the matrix \( F^{(n)} \).
j	Positions of the columns to be removed in the matrix \( F^{(n)} \).

Returns: Determinant ratio \( \det(F^{(n-k)}) / \det(F^{(n)}) \).

Definition at line 1038 of file det_manip_basic.hpp.

◆ foreach

template<typename FunctionType>

template<typename LambdaType>

void foreach	(	det_manip_basic< FunctionType > const &	d,
		LambdaType const &	func )

friend

For-each implementation for triqs::det_manip::det_manip_basic objects.

It loops over all elements of the inverse matrix and calls the given callable object for each element together with the corresponding arguments \( x_i \) and \( y_j \). The order of iteration is not fixed; it is optimised for memory traversal.

Template Parameters

LambdaType Callable type.

Parameters

d	triqs::det_manip::det_manip_basic object.
func	Callable object that takes three arguments: \( x_i \), \( y_j \), and \( [F^{(n)}]^{-1}_{ji} \).

Definition at line 472 of file det_manip_basic.hpp.

◆ h5_read

template<typename FunctionType>

void h5_read	(	h5::group	fg,
		std::string	subgroup_name,
		det_manip_basic< FunctionType > &	g )

friend

Read a triqs::det_manip::det_manip_basic object from HDF5.

Parameters

fg	h5::group containing the subgroup to be read from.
subgroup_name	Name of the subgroup.
g	Manipulator object to be read into.

Definition at line 197 of file det_manip_basic.hpp.

◆ h5_write

template<typename FunctionType>

void h5_write	(	h5::group	fg,
		std::string	subgroup_name,
		det_manip_basic< FunctionType > const &	g )

friend

Write a triqs::det_manip::det_manip_basic object to HDF5.

Parameters

fg	h5::group containing the subgroup to be written to.
subgroup_name	Name of the subgroup.
g	Manipulator object to be written.

Definition at line 180 of file det_manip_basic.hpp.

The documentation for this class was generated from the following file:

triqs/det_manip/det_manip_basic.hpp

Detailed Description

Public Types

Public Member Functions

Friends

Member Enumeration Documentation

◆ RollDirection

Constructor & Destructor Documentation

◆ det_manip_basic() [1/2]

◆ det_manip_basic() [2/2]

Member Function Documentation

◆ build_matrix_scratch()

◆ change_col()

◆ change_one_row_and_one_col()

◆ change_row()

◆ complete_operation()

◆ determinant()

◆ get_function()

◆ get_x() [1/2]

◆ get_x() [2/2]

◆ get_x_internal_order()

◆ get_y() [1/2]

◆ get_y() [2/2]

◆ get_y_internal_order()

◆ insert()

◆ insert2()

◆ insert2_at_end()

◆ insert_at_end()

◆ insert_ratios()

◆ inverse_matrix() [1/2]

◆ inverse_matrix() [2/2]

◆ inverse_matrix_internal_order() [1/2]

◆ inverse_matrix_internal_order() [2/2]

◆ matrix() [1/2]

◆ matrix() [2/2]

◆ reject_last_try()

◆ remove()

◆ remove2()

◆ remove2_at_end()

◆ remove_at_end()

◆ reserve()

◆ roll_matrix()

◆ size()

◆ try_change_col()

◆ try_change_col_row()

◆ try_change_row()

◆ try_insert()

◆ try_insert2()

◆ try_insert_k()

◆ try_refill()

◆ try_remove()

◆ try_remove2()

◆ try_remove_k()

Friends And Related Symbol Documentation

◆ foreach

◆ h5_read

◆ h5_write