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dft_tools/triqs/det_manip/det_manip.hpp

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/*******************************************************************************
*
* TRIQS: a Toolbox for Research in Interacting Quantum Systems
*
* Copyright (C) 2011-2013 by M. Ferrero, O. Parcollet
*
* TRIQS is free software: you can redistribute it and/or modify it under the
* terms of the GNU General Public License as published by the Free Software
* Foundation, either version 3 of the License, or (at your option) any later
* version.
*
* TRIQS is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
* FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
* details.
*
* You should have received a copy of the GNU General Public License along with
* TRIQS. If not, see <http://www.gnu.org/licenses/>.
*
******************************************************************************/
#ifndef TRIQS_DETMANIP_H
#define TRIQS_DETMANIP_H
#include <triqs/utility/first_include.hpp>
#include <vector>
#include <iterator>
#include <triqs/arrays.hpp>
#include <triqs/arrays/algorithms.hpp>
#include <triqs/arrays/linalg/det_and_inverse.hpp>
#include <triqs/arrays/blas_lapack/dot.hpp>
#include <triqs/arrays/blas_lapack/ger.hpp>
#include <triqs/arrays/blas_lapack/gemm.hpp>
#include <triqs/arrays/blas_lapack/gemv.hpp>
#include <triqs/utility/function_arg_ret_type.hpp>
namespace triqs { namespace det_manip {
namespace blas = arrays::blas;
/**
* \brief Standard matrix/det manipulations used in several QMC.
*/
template<typename FunctionType>
class det_manip {
private:
typedef utility::function_arg_ret_type<FunctionType> f_tr;
static_assert(f_tr::arity == 2, "det_manip : the function must take two arguments !");
// Do we REALLY need this ?
static_assert(std::is_same< typename f_tr::template decay_arg<0>::type, typename f_tr::template decay_arg<1>::type>::value,
"det_manip : the two arguments must of the function must have the same type");
public:
typedef typename f_tr::template decay_arg<0>::type xy_type;
typedef typename f_tr::result_type value_type;
static_assert( std::is_floating_point<value_type>::value || triqs::is_complex<value_type>::value, "det_manip : the function must return a floating number or a complex number");
typedef arrays::vector<value_type> vector_type;
typedef arrays::matrix<value_type> matrix_type;
typedef arrays::matrix_view<value_type> matrix_view_type;
protected: // the data
typedef std::ptrdiff_t int_type;
typedef arrays::range range;
FunctionType f;
// serialized data. There are all VALUES.
value_type det;
size_t Nmax,N, last_try;
std::vector<size_t> row_num,col_num;
std::vector<xy_type> x_values,y_values;
int sign;
matrix_type mat_inv;
long long n_opts, n_opts_max_before_check;
private:
// ------------ BOOST Serialization ------------
// What about f ? Not serialized at the moment.
friend class boost::serialization::access;
template<class Archive>
void serialize(Archive & ar) {
ar & TRIQS_MAKE_NVP("Nmax",Nmax) & TRIQS_MAKE_NVP("N",N)
& TRIQS_MAKE_NVP("n_opts",n_opts) & TRIQS_MAKE_NVP("n_opts_max_before_check",n_opts_max_before_check)
& TRIQS_MAKE_NVP("det",det) & TRIQS_MAKE_NVP("sign",sign)
& TRIQS_MAKE_NVP("Minv",mat_inv)
& TRIQS_MAKE_NVP("row_num",row_num) & TRIQS_MAKE_NVP("col_num",col_num)
& TRIQS_MAKE_NVP("x_values",x_values) & TRIQS_MAKE_NVP("y_values",y_values);
}
/// Write into HDF5
friend void h5_write (h5::group fg, std::string subgroup_name, det_manip const & g) {
auto gr = fg.create_group(subgroup_name);
h5_write(gr,"N",g.N);
h5_write(gr,"mat_inv",g.mat_inv);
h5_write(gr,"det",g.det);
h5_write(gr,"sign",g.sign);
//h5_write(gr,"row_num",g.row_num);
//h5_write(gr,"col_num",g.col_num);
h5_write(gr,"x_values",g.x_values);
h5_write(gr,"y_values",g.y_values);
h5_write(gr,"n_opts",g.n_opts);
h5_write(gr,"n_opts_max_before_check",g.n_opts_max_before_check);
}
/// Read from HDF5
friend void h5_read (h5::group fg, std::string subgroup_name, det_manip & g){
auto gr = fg.open_group(subgroup_name);
h5_read(gr,"N",g.N);
h5_read(gr,"mat_inv",g.mat_inv);
g.Nmax = first_dim(g.mat_inv); // restore Nmax
g.last_try = 0;
h5_read(gr,"det",g.det);
h5_read(gr,"sign",g.sign);
//h5_read(gr,"row_num",g.row_num);
//h5_read(gr,"col_num",g.col_num);
h5_read(gr,"x_values",g.x_values);
h5_read(gr,"y_values",g.y_values);
h5_read(gr,"n_opts",g.n_opts);
h5_read(gr,"n_opts_max_before_check",g.n_opts_max_before_check);
}
private:
// temporary work data, not saved, serialized, etc....
struct work_data_type1 {
xy_type x, y;
vector_type MB,MC, B, C;
value_type ksi;
size_t i,j,ireal,jreal;
void reserve(size_t s) { B.resize(s); C.resize(s); MB.resize(s); MC.resize(s); MB()=0; MC()=0; }
};
struct work_data_type2 {
xy_type x[2], y[2];
matrix_type MB,MC, B, C,ksi;
size_t i[2],j[2],ireal[2],jreal[2];
void reserve(size_t s) { MB.resize(s,2); MC.resize(2,s); B.resize(s,2), C.resize(2,s); ksi.resize(2,2); MB() = 0; MC() = 0; }
value_type det_ksi() const { return ksi(0,0) * ksi(1,1) - ksi(1,0)* ksi(0,1);}
};
work_data_type1 w1;
work_data_type2 w2;
value_type newdet;
int newsign;
private: // for the move constructor, I need to separate the swap since f may not be defaulted constructed
void swap_but_f (det_manip & rhs) noexcept {
using std::swap;
#define SW(a) swap(this->a,rhs.a)
SW(det);SW(Nmax);SW(N); SW(last_try);
SW(row_num); SW(col_num);
SW(x_values); SW(y_values);
SW(sign); SW(mat_inv); SW(n_opts); SW(n_opts_max_before_check);
SW(w1); SW(w2); SW(newdet); SW(newsign);
#undef SW
}
friend void swap(det_manip& lhs, det_manip & rhs) noexcept {
using std::swap;
swap(lhs.f, rhs.f);
lhs.swap_but_f(rhs);
}
public:
/**
* Like for std::vector, reserve memory for a bigger size.
* Preserves only the matrix, not the temporary working vectors/matrices, so do NOT use it
* between a try_XXX and acomplete_operation
*/
void reserve (size_t new_size) {
if (new_size <= Nmax) return;
matrix_type Mcopy(mat_inv);
size_t N0 = Nmax; Nmax = new_size;
mat_inv.resize(Nmax,Nmax); mat_inv(range(0,N0), range(0,N0)) = Mcopy; // keep the content of mat_inv ---> into the lib ?
row_num.reserve(Nmax);col_num.reserve(Nmax); x_values.reserve(Nmax);y_values.reserve(Nmax);
w1.reserve(Nmax); w2.reserve(Nmax);
}
private:
void _construct_common() {
last_try=0; sign =1;
n_opts=0; n_opts_max_before_check = 100;
}
public:
/**
* \brief Constructor.
*
* \param F The function (NB : a copy is made of the F object in this class).
* \param init_size The maximum size of the matrix before a resize (like reserve in std::vector).
* Like std::vector, resize is automatic (by a factor 2) but can yield a performance penalty
* if it happens too often.
*/
det_manip(FunctionType F,size_t init_size):
f(std::move(F)), Nmax(0) , N(0){
reserve(init_size);
mat_inv()=0;
det = 1;
_construct_common();
}
/** \brief Constructor.
*
* \param F The function (NB : a copy is made of the F object in this class).
* \tparam ArgumentContainer
* \param X, Y : container for X,Y.
*/
template<typename ArgumentContainer1, typename ArgumentContainer2>
det_manip(FunctionType F, ArgumentContainer1 const & X, ArgumentContainer2 const & Y) : f(std::move(F)), Nmax(0) {
if (X.size() != Y.size()) TRIQS_RUNTIME_ERROR<< " X.size != Y.size";
_construct_common();
N =X.size();
if (N==0) { det = 1; reserve(30); return;}
if (N>Nmax) reserve(2*N); // put some margin..
std::copy(X.begin(),X.end(), std::back_inserter(x_values));
std::copy(Y.begin(),Y.end(), std::back_inserter(y_values));
mat_inv()=0;
for (size_t i=0; i<N; ++i) {
row_num.push_back(i);col_num.push_back(i);
for (size_t j=0; j<N; ++j)
mat_inv(i,j) = f(x_values[i],y_values[j]);
}
range R(0,N);
det = arrays::determinant(mat_inv(R,R));
mat_inv(R,R) = inverse(mat_inv(R,R));
}
det_manip (det_manip const&) = default;
det_manip (det_manip && rhs) noexcept : f(std::move(rhs.f)) { this->swap_but_f(rhs);} // f need not have a default constructor and we dont swap the temp data...
//det_manip& operator=(const det_manip&) = default;
det_manip& operator=(const det_manip&) = delete;
det_manip& operator=(det_manip&& rhs) noexcept { assert((last_try==0)&&(rhs.last_try==0)); swap(*this,rhs); return *this; }
/// Put to size 0 : like a vector
void clear () {
N = 0; sign = 1;det =1; last_try = 0;
row_num.clear(); col_num.clear(); x_values.clear(); y_values.clear();
}
//----------------------- READ ACCESS TO DATA ----------------------------------
/// Current size of the matrix
size_t size() const { return N; }
/// Returns the i-th values of x
xy_type const & get_x(size_t i) const { return x_values[row_num[i]]; }
/// Returns the vector of x values
std::vector<xy_type> const & get_x_values() const { return x_values; }
/// Returns the j-th values of y
xy_type const & get_y(size_t j) const { return y_values[col_num[j]]; }
/// Returns the vector of y values
std::vector<xy_type> const & get_y_values() const { return y_values; }
/** det M of the current state of the matrix. */
value_type determinant() const {return sign*det;}
/** Returns M^{-1}(i,j) */
value_type inverse_matrix(size_t i,size_t j) const {return mat_inv(col_num[i],row_num[j]);} // warning : need to invert the 2 permutations.
/// Returns the inverse matrix. Warning : this is slow, since it create a new copy, and reorder the lines/cols
matrix_view_type inverse_matrix() const {
matrix_type res(N,N);
for (size_t i=0; i<N;i++)
for (size_t j=0; j<N;j++)
res(i,j) = inverse_matrix(i,j);
return res;
}
/// Rebuild the matrix. Warning : this is slow, since it create a new matrix and re-evaluate the function.
matrix_view_type matrix() const {
matrix_type res(N,N);
for (size_t i=0; i<N;i++)
for (size_t j=0; j<N;j++)
res(i,j) = f(get_x(i), get_y(j));
return res;
}
// Given a lambda f : x,y,M, it calls f(x_i,y_j,M_ji) for all i,j
// Order of iteration is NOT fixed, it is optimised (for memory traversal)
template<typename LambdaType>
friend void foreach(det_manip const & d, LambdaType const & f) {
//for (size_t i=0; i<d.N;i++)
//for (size_t j=0; j<d.N;j++)
// f(d.x_values[i], d.y_values[j], d.mat_inv(j,i));
range R(0,d.N);
foreach(d.mat_inv(R,R), [&f,&d](int i, int j) { return f(d.x_values[i], d.y_values[j], d.mat_inv(j,i));});
}
// ------------------------- OPERATIONS -----------------------------------------------
/**
* Insert operation at colum j0 and row i0.
*
* The operation consists in adding :
*
* * a column f(x_i, y_{j0})
* * and a row f(x_{i0}, x_j)
*
* The new colum/row will be at col j0, row i0.
*
* 0 <= i0,j0 <= N, where N is the current size of the matrix.
* The current column j0 (resp. row i0) will become column j0+1 (resp. row i0+1).
* Inserting at N simply add the new col at the end.
* Returns the ratio of det Minv_new / det Minv.
*
* This routine does NOT make any modification. It has to be completed with complete_operation().
*/
value_type try_insert(size_t i, size_t j, xy_type const & x, xy_type const & y) {
// check input and store it for complete_operation
assert(i<=N); assert(j<=N); assert(i>=0); assert(j>=0);
if (N==Nmax) reserve(2*Nmax);
last_try = 1;
w1.i=i; w1.j=j; w1.x=x; w1.y = y;
// treat empty matrix separately
if (N==0) { newdet = f(x,y); newsign = 1; return newdet; }
// I add the row and col and the end. If the move is rejected,
// no effect since N will not be changed : Minv(i,j) for i,j>=N has no meaning.
for (size_t k= 0; k< N; k++) {
w1.B(k) = f(x_values[k],y);
w1.C(k) = f(x, y_values[k]);
}
range R(0,N);
//w1.MB(R) = mat_inv(R,R) * w1.B(R);// OPTIMIZE BELOW
blas::gemv(1.0, mat_inv(R,R), w1.B(R),0.0,w1.MB(R));
w1.ksi = f(x,y) - arrays::dot( w1.C(R) , w1.MB(R) );
newdet = det*w1.ksi;
newsign = ((i + j)%2==0 ? sign : -sign); // since N-i0 + N-j0 = i0+j0 [2]
return w1.ksi*(newsign*sign); // sign is unity, hence 1/sign == sign
}
//fx gives the new line coefficients, fy gives the new column coefficients and ksi is the last coeff (at the intersection of the line and the column).
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) {
// check input and store it for complete_operation
assert(i<=N); assert(j<=N); assert(i>=0); assert(j>=0);
if (N==Nmax) reserve(2*Nmax);
last_try = 1;
w1.i=i; w1.j=j;
// treat empty matrix separately
if (N==0) { newdet = ksi; newsign = 1; return newdet; }
// I add the row and col and the end. If the move is rejected,
// no effect since N will not be changed : Minv(i,j) for i,j>=N has no meaning.
for (size_t k= 0; k< N; k++) {
w1.B(k) = fx(x_values[k]);
w1.C(k) = fy(y_values[k]);
}
range R(0,N);
//w1.MB(R) = mat_inv(R,R) * w1.B(R);// OPTIMIZE BELOW
blas::gemv(1.0, mat_inv(R,R), w1.B(R),0.0,w1.MB(R));
w1.ksi = ksi - arrays::dot( w1.C(R) , w1.MB(R) );
newdet = det*w1.ksi;
newsign = ((i + j)%2==0 ? sign : -sign); // since N-i0 + N-j0 = i0+j0 [2]
return w1.ksi*(newsign*sign); // sign is unity, hence 1/sign == sign
}
//------------------------------------------------------------------------------------------
private :
void complete_insert () {
// store the new value of x,y. They are seen through the same permutations as rows and cols resp.
x_values.push_back(w1.x); y_values.push_back(w1.y);
row_num.push_back(0); col_num.push_back(0);
// special empty case again
if (N==0) { N=1; mat_inv(0,0) = 1/newdet; return; }
range R1(0,N);
//w1.MC(R1) = mat_inv(R1,R1).transpose() * w1.C(R1); //OPTIMIZE BELOW
blas::gemv(1.0, mat_inv(R1,R1).transpose(), w1.C(R1),0.0,w1.MC(R1));
w1.MC(N) = -1;
w1.MB(N) = -1;
N++;
// keep the real position of the row/col
// since we insert a col/row, we have first to push the col at the right
// and then say that col w1.i is stored in N, the last col.
// same for rows
for (int_type i =N-2; i>=int_type(w1.i); i--) row_num[i+1]= row_num[i];
row_num[w1.i] = N-1;
for (int_type i =N-2; i>=int_type(w1.j); i--) col_num[i+1]= col_num[i];
col_num[w1.j] = N-1;
// Minv is ok, we need to complete
w1.ksi = 1/w1.ksi;
// compute the change to the inverse
// M += w1.ksi w1.MB w1.MC with BLAS. first put the 0
range R(0,N);
mat_inv(R,N-1) = 0;
mat_inv(N-1,R) = 0;
//mat_inv(R,R) += w1.ksi* w1.MB(R) * w1.MC(R)// OPTIMIZE BELOW
blas::ger(w1.ksi, w1.MB(R) ,w1.MC(R),mat_inv(R,R));
}
public :
//------------------------------------------------------------------------------------------
/**
* Double Insert operation at colum j0,j1 and row i0,i1.
*
* The operation consists in adding :
* * a column f(x_i, y_{j0})
* * and a row f(x_{i0}, x_j)
* The new colum/row will be at col j0, row i0.
*
* 0 <= i0,i1,j0,j1 <= N+1, where N is the current size of the matrix.
* Returns the ratio of det Minv_new / det Minv.
* This routine does NOT make any modification. It has to be completed with complete_operation().
*/
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) {
// check input and store it for complete_operation
assert(i0!=i1); assert(j0!=j1);assert(i0<=N); assert(j0<=N); assert(i0>=0); assert(j0>=0);
assert(i1<=N+1); assert(j1<=N+1); assert(i1>=0); assert(j1>=0);
if (N >= Nmax) reserve(2*Nmax); // check this resize ... we add 2 lines
last_try = 10;
w2.i[0]=i0;w2.i[1]=i1; w2.j[0]=j0;w2.j[1]=j1;
w2.x[0] = x0;w2.y[0] = y0; w2.x[1] = x1;w2.y[1] = y1;
// w1.ksi = Delta(x_values,y_values) - Cw.MB using BLAS
w2.ksi(0,0) = f(x0,y0);
w2.ksi(0,1) = f(x0,y1);
w2.ksi(1,0) = f(x1,y0);
w2.ksi(1,1) = f(x1,y1);
// treat empty matrix separately
if (N==0) {
newdet = w2.det_ksi();
newsign = 1;
return newdet;
}
// I add the rows and cols and the end. If the move is rejected,
// no effect since N will not be changed : inv_mat(i,j) for i,j>=N has no meaning.
for (size_t k= 0; k< N; k++) {
w2.B(k,0) = f(x_values[k],y0);
w2.B(k,1) = f(x_values[k],y1);
w2.C(0,k) = f(x0, y_values[k]);
w2.C(1,k) = f(x1, y_values[k]);
}
range R(0,N), R2(0,2);
//w2.MB(R,R2) = mat_inv(R,R) * w2.B(R,R2); // OPTIMIZE BELOW
blas::gemm(1.0, mat_inv(R,R) , w2.B(R,R2),0.0,w2.MB(R,R2));
//w2.ksi -= w2.C (R2, R) * w2.MB(R, R2); // OPTIMIZE BELOW
blas::gemm(-1.0, w2.C(R2,R), w2.MB(R, R2),1.0,w2.ksi);
newdet = det * w2.det_ksi();
newsign = ((i0 + j0 + i1 + j1)%2==0 ? sign : -sign); // since N-i0 + N-j0 + N + 1 -i1 + N+1 -j1 = i0+j0 [2]
return (newdet/det)*(newsign*sign); // sign is unity, hence 1/sign == sign
}
//------------------------------------------------------------------------------------------
private:
void complete_insert2 () {
// store the new value of x,y. They are seen through the same permutations as rows and cols resp.
for (int k=0; k<2; ++k) {
x_values.push_back(w2.x[k]); y_values.push_back(w2.y[k]);
row_num.push_back(0); col_num.push_back(0);
}
range R2(0,2);
if (N==0) {N=2; mat_inv(R2,R2)=inverse(w2.ksi); row_num[w2.i[1]]=1; col_num[w2.j[1]]=1; return;}
range Ri(0,N);
//w2.MC(R2,Ri) = w2.C(R2,Ri) * mat_inv(Ri,Ri);// OPTIMIZE BELOW
blas::gemm(1.0, w2.C(R2,Ri), mat_inv(Ri,Ri),0.0,w2.MC(R2,Ri));
w2.MC(R2, range(N, N+2) ) = -1; // identity matrix
w2.MB(range(N,N+2), R2 ) = -1; // identity matrix !
// keep the real position of the row/col
// since we insert a col/row, we have first to push the col at the right
// and then say that col w2.i[0] is stored in N, the last col.
// same for rows
for (int k =0; k<2; ++k) {
N++;
for (int_type i =N-2; i>=int_type(w2.i[k]); i--) row_num[i+1]= row_num[i];
row_num[w2.i[k]] = N-1;
for (int_type i =N-2; i>=int_type(w2.j[k]); i--) col_num[i+1]= col_num[i];
col_num[w2.j[k]] = N-1;
}
w2.ksi = inverse (w2.ksi);
range R(0,N);
mat_inv(R,range(N-2,N)) = 0;
mat_inv(range(N-2,N),R) = 0;
//mat_inv(R,R) += w2.MB(R,R2) * (w2.ksi * w2.MC(R2,R)); // OPTIMIZE BELOW
blas::gemm(1.0, w2.MB(R,R2), (w2.ksi * w2.MC(R2,R)),1.0,mat_inv(R,R) );
}
public:
//------------------------------------------------------------------------------------------
/**
* Consider the removal the colj0 and row i0 from the matrix.
*
* Returns the ratio of det Minv_new / det Minv.
* This routine does NOT make any modification. It has to be completed with complete_operation().
*/
value_type try_remove(size_t i, size_t j){
assert(i<N); assert(j<N); assert(i>=0); assert(j>=0);
w1.i=i;w1.j=j;last_try = 2;
w1.jreal = col_num[w1.j];
w1.ireal = row_num[w1.i];
// compute the newdet
// first we resolve the w1.ireal,w1.jreal, with the permutation of the Minv, then we pick up what
// will become the 'corner' coefficient, if the move is accepted, after the exchange of row and col.
w1.ksi = mat_inv(w1.jreal,w1.ireal);
newdet = det*w1.ksi;
newsign = ((i + j)%2==0 ? sign : -sign);
return (newdet/det)*(newsign*sign); // sign is unity, hence 1/sign == sign
}
//------------------------------------------------------------------------------------------
private:
void complete_remove() {
if (N==1) { clear(); return; }
// repack the matrix inv_mat
// swap the rows w1.ireal and N, w1.jreal and N in inv_mat
// Remember that for M row/col is interchanged by inversion, transposition.
{
range R(0,N);
if (w1.jreal !=N-1){
arrays::deep_swap( mat_inv(w1.jreal,R), mat_inv(N-1,R));
y_values[w1.jreal] = y_values[N-1];
}
if (w1.ireal !=N-1){
arrays::deep_swap (mat_inv(R,w1.ireal), mat_inv(R,N-1));
x_values[w1.ireal] = x_values[N-1];
}
}
N--;
// M <- a - d^-1 b c with BLAS
w1.ksi = - 1/mat_inv(N,N);
range R(0,N);
//mat_inv(R,R) += w1.ksi, * mat_inv(R,N) * mat_inv(N,R);
blas::ger(w1.ksi,mat_inv(R,N),mat_inv(N,R), mat_inv(R,R));
// modify the permutations
for (size_t k =w1.i; k<N; k++) {row_num[k]= row_num[k+1];}
for (size_t k =w1.j; k<N; k++) {col_num[k]= col_num[k+1];}
for (size_t k =0; k<N; k++)
{
if (col_num[k]==N) col_num[k]=w1.jreal;
if (row_num[k]==N) row_num[k]=w1.ireal;
}
row_num.pop_back(); col_num.pop_back();
x_values.pop_back(); y_values.pop_back();
}
public:
//------------------------------------------------------------------------------------------
/**
* Double Removal operation of cols j0,j1 and rows i0,i1
*
* Returns the ratio of det Minv_new / det Minv.
* This routine does NOT make any modification. It has to be completed with complete_operation().
*/
value_type try_remove2(size_t i0, size_t i1, size_t j0, size_t j1) {
assert(N>=2); assert(i0!=i1); assert(j0!=j1);
assert(i0<N); assert(j0<N); assert(i0>=0); assert(j0>=0);
assert(i1<N+1); assert(j1<N+1);assert(i1>=0); assert(j1>=0);
last_try =11;
w2.i[0]=std::min(i0,i1);
w2.i[1]=std::max(i0,i1);
w2.j[0]=std::min(j0,j1);
w2.j[1]=std::max(j0,j1);
w2.ireal[0] = row_num[w2.i[0]];
w2.ireal[1] = row_num[w2.i[1]];
w2.jreal[0] = col_num[w2.j[0]];
w2.jreal[1] = col_num[w2.j[1]];
// compute the newdet
w2.ksi(0,0) = mat_inv(w2.jreal[0],w2.ireal[0]);
w2.ksi(1,0) = mat_inv(w2.jreal[1],w2.ireal[0]);
w2.ksi(0,1) = mat_inv(w2.jreal[0],w2.ireal[1]);
w2.ksi(1,1) = mat_inv(w2.jreal[1],w2.ireal[1]);
newdet = det * w2.det_ksi();
newsign = ((i0 + j0+ i1 + j1)%2==0 ? sign : -sign);
return (newdet/det)*(newsign*sign); // sign is unity, hence 1/sign == sign
}
//------------------------------------------------------------------------------------------
private:
void complete_remove2() {
if (N==2) { clear(); return;} // put the sign to 1 also .... Change complete_remove...
size_t i_real_max =std::max(w2.ireal[0],w2.ireal[1]);
size_t i_real_min =std::min(w2.ireal[0],w2.ireal[1]);
size_t j_real_max =std::max(w2.jreal[0],w2.jreal[1]);
size_t j_real_min =std::min(w2.jreal[0],w2.jreal[1]);
range R(0,N);
if (j_real_max != N-1) {
arrays::deep_swap( mat_inv(j_real_max,R), mat_inv(N-1,R));
y_values[ j_real_max ] = y_values[N-1];
}
if (j_real_min != N-2) {
arrays::deep_swap( mat_inv(j_real_min,R), mat_inv(N-2,R));
y_values[ j_real_min ] = y_values[N-2];
}
if (i_real_max != N-1) {
arrays::deep_swap (mat_inv(R,i_real_max), mat_inv(R,N-1));
x_values[ i_real_max ] = x_values[N-1];
}
if (i_real_min != N-2) {
arrays::deep_swap (mat_inv(R,i_real_min), mat_inv(R,N-2));
x_values[ i_real_min ] = x_values[N-2];
}
N -= 2;
// M <- a - d^-1 b c with BLAS
range Rn(0,N), Rl(N,N+2);
//w2.ksi = mat_inv(Rl,Rl);
//w2.ksi = inverse( w2.ksi);
w2.ksi = inverse( mat_inv(Rl,Rl));
// write explicitely the second product on ksi for speed ?
//mat_inv(Rn,Rn) -= mat_inv(Rn,Rl) * (w2.ksi * mat_inv(Rl,Rn)); // OPTIMIZE BELOW
blas::gemm(-1.0, mat_inv(Rn,Rl), w2.ksi * mat_inv(Rl,Rn),1.0, mat_inv(Rn,Rn) );
// modify the permutations
for (size_t k =w2.i[0]; k<w2.i[1]-1; k++) row_num[k] = row_num[k+1];
for (size_t k =w2.i[1]-1; k<N; k++) row_num[k] = row_num[k+2];
for (size_t k =w2.j[0]; k<w2.j[1]-1; k++) col_num[k] = col_num[k+1];
for (size_t k =w2.j[1]-1; k<N; k++) col_num[k] = col_num[k+2];
for (size_t k =0; k<N; k++) {
if (col_num[k]==N+1) col_num[k]=j_real_max;
if (col_num[k]==N) col_num[k]=j_real_min;
if (row_num[k]==N+1) row_num[k]=i_real_max;
if (row_num[k]==N) row_num[k]=i_real_min;
}
for (int u=0; u<2; ++u) { row_num.pop_back(); col_num.pop_back(); x_values.pop_back(); y_values.pop_back(); }
}
//------------------------------------------------------------------------------------------
public:
/**
* Consider the change the column j and the corresponding y.
*
* Returns the ratio of det Minv_new / det Minv.
* This routine does NOT make any modification. It has to be completed with complete_operation().
*/
value_type try_change_col(size_t j, xy_type const & y) {
assert(j<N); assert(j>=0);
w1.j=j;last_try = 3;
w1.jreal = col_num[j];
w1.y = y;
// Compute the col B.
for (size_t i= 0; i<N;i++) w1.MC(i) = f(x_values[i] , w1.y) - f(x_values[i], y_values[w1.jreal]);
range R(0,N);
//w1.MB(R) = mat_inv(R,R) * w1.MC(R);// OPTIMIZE BELOW
blas::gemv(1.0, mat_inv(R,R), w1.MC(R) ,0.0, w1.MB(R) );
// compute the newdet
w1.ksi = (1+w1.MB(w1.jreal));
newdet = det*w1.ksi;
newsign = sign;
return (newdet/det)*(newsign*sign); // sign is unity, hence 1/sign == sign
}
//------------------------------------------------------------------------------------------
private:
void complete_change_col() {
range R(0,N);
y_values[w1.jreal] = w1.y;
// modifying M : Mij += w1.ksi Bi Mnj
// using Shermann Morrison formula.
// implemented in 2 times : first Bn=0 so that Mnj is not modified ! and then change Mnj
// Cf notes : simply multiply by -w1.ksi
w1.ksi = - 1/(1+ w1.MB(w1.jreal));
w1.MB(w1.jreal) = 0;
//mat_inv(R,R) += w1.ksi * w1.MB(R) * mat_inv(w1.jreal,R)); // OPTIMIZE BELOW
blas::ger(w1.ksi,w1.MB(R), mat_inv(w1.jreal,R), mat_inv(R,R));
mat_inv(w1.jreal,R)*= -w1.ksi;
}
//------------------------------------------------------------------------------------------
public:
/**
* Consider the change the row i and the corresponding x.
*
* Returns the ratio of det Minv_new / det Minv.
* This routine does NOT make any modification. It has to be completed with complete_operation().
*/
value_type try_change_row(size_t i, xy_type const & x) {
assert(i<N); assert(i>=0);
w1.i=i;last_try = 4;
w1.ireal = row_num[i];
w1.x = x;
// Compute the col B.
for (size_t i= 0; i<N;i++) w1.MB(i) = f(w1.x, y_values[i] ) - f(x_values[w1.ireal], y_values[i] );
range R(0,N);
//w1.MC(R) = mat_inv(R,R).transpose() * w1.MB(R); // OPTIMIZE BELOW
blas::gemv(1.0, mat_inv(R,R).transpose(), w1.MB(R),0.0, w1.MC(R));
// compute the newdet
w1.ksi = (1+w1.MC(w1.ireal));
newdet = det*w1.ksi;
newsign = sign;
return (newdet/det)*(newsign*sign); // sign is unity, hence 1/sign == sign
}
//------------------------------------------------------------------------------------------
private:
void complete_change_row() {
range R(0,N);
x_values[w1.ireal] = w1.x;
// modifying M : M ij += w1.ksi Min Cj
// using Shermann Morrison formula.
// impl. Cf case 3
w1.ksi = - 1/(1+ w1.MC(w1.ireal));
w1.MC(w1.ireal) = 0;
//mat_inv(R,R) += w1.ksi * mat_inv(R,w1.ireal) * w1.MC(R);
blas::ger(w1.ksi,mat_inv(R,w1.ireal),w1.MC(R), mat_inv(R,R));
mat_inv(R,w1.ireal) *= -w1.ksi;
}
//------------------------------------------------------------------------------------------
private:
void check_mat_inv (double precision_warning=1.e-8, double precision_error=1.e-5) {
if (N==0) return;
const bool relative = true;
matrix_type res(N,N);
for (size_t i=0; i<N;i++)
for (size_t j=0; j<N;j++)
res(i,j) = f(x_values[i], y_values[j]);
res = inverse(res);
double r = max_element (abs(res - mat_inv(range(0,N),range(0,N))));
double r2= max_element (abs(res + mat_inv(range(0,N),range(0,N))));
//value_type r = max_element (abs(res - mat_inv(range(0,N),range(0,N))));
//value_type r2= max_element (abs(res + mat_inv(range(0,N),range(0,N))));
//#define TRIQS_DET_MANIP_VERBOSE_CHECK
#ifdef TRIQS_DET_MANIP_VERBOSE_CHECK
std::cout << "----------------"<<std::endl
<< "check " << "N = "<< N <<" " <<"r,r2 = "<< r << " "<< r2 << " "<< std::endl;
#endif
bool err = !( r < (relative ? precision_error * r2 : precision_error));
bool war = !( r < (relative ? precision_warning * r2 : precision_warning));
if (err || war) {
std::cerr << "matrix = " <<matrix() <<std::endl;
std::cerr << "inverse_matrix = "<< inverse_matrix()<< std::endl;
}
if (war) std::cerr << "Warning : det_manip deviation above warning threshold "
<< "check " << "N = "<< N <<" " <<"\n max(abs(M^-1 - M^-1_true)) = "<< r
<< "\n precision*max(abs(M^-1 + M^-1_true)) = "<< (relative ? precision_warning * r2 : precision_warning)<< " "<< std::endl;
if (err) TRIQS_RUNTIME_ERROR << "Error : det_manip deviation above critical threshold !! " ;
// since we have the proper inverse, replace the matrix
mat_inv(range(0,N),range(0,N)) = res;
}
//------------------------------------------------------------------------------------------
public:
/**
* Finish the move of the last try_xxx called.
* Throws if no try_xxx has been done or if the last operation was complete_operation.
*/
void complete_operation() {
switch(last_try){
case(1):
complete_insert();
break;
case(2):
complete_remove();
break;
case(3):
complete_change_col();
break;
case(4):
complete_change_row();
break;
case(10):
complete_insert2();
break;
case(11):
complete_remove2();
break;
case(0):
last_try=0; return;
break; // double call of complete_operation...
default:
TRIQS_RUNTIME_ERROR<< "Misuing det_manip";
}
det = newdet;
sign = newsign;
last_try =0;
++n_opts;
if (n_opts > n_opts_max_before_check) { check_mat_inv(); n_opts=0;}
}
///
enum RollDirection {None,Up,Down,Left,Right};
/**
* "Cyclic Rolling" of the determinant.
*
* Right : Move the Nth col to the first col cyclically.
* Left : Move the first col to the Nth, cyclically.
* Up : Move the first row to the Nth, cyclically.
* Down : Move the Nth row to the first row cyclically.
*
* Returns -1 is the roll changes the sign of the det, 1 otherwise
* NB : this routine is not a try_xxx : it DOES make the modification and does not need to be completed...
* WHY is it like this ???? : try_roll : return det +1/-1.
*/
int roll_matrix(RollDirection roll) {
size_t tmp;
const int_type NN=N;
switch (roll) {
case(None) :
return 1;
case(Down) :
tmp = row_num[N-1];
for (int_type i =NN-2; i>=0; i--) row_num[i+1]= row_num[i];
row_num[0] = tmp;
break;
case(Up) :
tmp = row_num[0];
for (int_type i =0; i<N-1; i++) row_num[i]= row_num[i+1];
row_num[N-1] = tmp;
break;
case(Right) :
tmp = col_num[N-1];
for (int_type i =NN-2; i>=0; i--) col_num[i+1]= col_num[i];
col_num[0] = tmp;
break;
case(Left):
tmp = col_num[0];
for (int_type i =0; i<N-1; i++) col_num[i]= col_num[i+1];
col_num[N-1] = tmp;
break;
default:
assert(0);
}
// signature of the cycle of order N : (-1)^(N-1)
if ((N-1)%2==1) { sign *=-1; return -1;}
return 1;
}
};
}}
#endif
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