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atrg.h
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#ifndef ATRG
#define ATRG
#include <vector>
#include <string>
#include <tuple>
#include <chrono>
#include <armadillo>
#include <sptensor.h>
#include <tensor.h>
#include <svd.h>
#include <sys/resource.h>
double get_usage() {
struct rusage usage;
getrusage(RUSAGE_SELF, &usage);
return static_cast<double>(usage.ru_maxrss) / 1e6;
}
namespace ATRG {
enum BlockingMode {
alt_blocking,
t_blocking,
s_blocking
};
template <typename T>
void swap_bonds(ATRG::Tensor<T> &B, ATRG::Tensor<T> &C, ATRG::Tensor<T> &X, ATRG::Tensor<T> &Y, const uint blocking_direction, T &error,
const std::vector<uint> &forward_indices, std::vector<uint> &forward_dimensions_and_alpha, const uint D_truncated, const bool use_redsvd,
arma::Mat<T> &U_B_reference, arma::Mat<T> &U_M_reference,
arma::Mat<T> &U_B, arma::Mat<T> &U_C, arma::Mat<T> &U_M) {
arma::Mat<T> B_flat;
arma::Mat<T> C_flat;
auto not_blocked_indices(forward_indices);
not_blocked_indices.erase(not_blocked_indices.begin() + blocking_direction);
// separate the not blocked indices
B.flatten(not_blocked_indices, {blocking_direction, B.get_order() - 1}, B_flat);
C.flatten(not_blocked_indices, {blocking_direction, C.get_order() - 1}, C_flat);
arma::Col<T> S_B;
error += svd(B_flat, U_B, S_B, use_redsvd, U_B_reference);
uint mu_dimension = U_B.n_cols;
// make a tensor of S*V with indices: x_trunc, alpha, mu
// forward and backward dimensions are the same!
B.reshape({forward_dimensions_and_alpha[blocking_direction], forward_dimensions_and_alpha.back(), mu_dimension});
B_flat = B_flat.t() * U_B;
B.inflate({0, 1}, {2}, B_flat);
B.flatten({0}, {1, 2}, B_flat);
arma::Col<T> S_C;
error += svd(C_flat, U_C, S_C, use_redsvd, U_B);
uint nu_dimension = U_C.n_cols;
// make a tensor of S*V with indices: x_trunc, beta, nu
C.reshape({forward_dimensions_and_alpha[blocking_direction], forward_dimensions_and_alpha.back(), nu_dimension});
C_flat = C_flat.t() * U_C;
C.inflate({0, 1}, {2}, C_flat);
C.flatten({0}, {1, 2}, C_flat);
X.reshape({forward_dimensions_and_alpha.back(), mu_dimension, forward_dimensions_and_alpha.back(), nu_dimension});
// B.t() * C with indices: alpha, mu, beta, nu
B_flat = B_flat.t() * C_flat;
X.inflate({0, 1}, {2, 3}, B_flat);
X.flatten({0, 3}, {2, 1}, B_flat);
arma::Col<T> S;
// B_flat has indices: {alpha, nu} {beta, mu}
error += svd(B_flat, U_M, S, D_truncated, use_redsvd, U_M_reference);
uint truncated_dimension = U_M.n_cols;
C_flat = B_flat.t() * U_M;
B_flat = U_M;
U_B_reference = U_B;
U_M_reference = U_M;
#ifdef DEBUG
std::cout << "U_B:" << std::endl << U_B << std::endl;
std::cout << "U_C:" << std::endl << U_C << std::endl;
std::cout << "U_M:" << std::endl << U_M << std::endl;
#endif
// X has indices: alpha, nu, x_trunc (index from SVD)
X.reshape({forward_dimensions_and_alpha.back(), nu_dimension, truncated_dimension});
X.inflate({0, 1}, {2}, B_flat);
X.flatten({1}, {0, 2}, B_flat);
B_flat = U_C * B_flat;
// new indices: all forward indices, alpha
auto X_dimensions = forward_dimensions_and_alpha;
X_dimensions[blocking_direction] = truncated_dimension;
X.reshape(X_dimensions);
X.inflate(not_blocked_indices, {X.get_order() - 1, blocking_direction}, B_flat);
// Y has indices: beta, mu, x_trunc (index from SVD)
Y.reshape({forward_dimensions_and_alpha.back(), mu_dimension, truncated_dimension});
Y.inflate({0, 1}, {2}, C_flat);
Y.flatten({1}, {0, 2}, C_flat);
C_flat = U_B * C_flat;
// new indices: all backward indices, beta
// -> backward and forward dimensions are the same!
Y.reshape(X_dimensions);
Y.inflate(not_blocked_indices, {Y.get_order() - 1, blocking_direction}, C_flat);
}
template <typename T>
void swap_bonds(ATRG::Tensor<T> &B, ATRG::Tensor<T> &C, ATRG::Tensor<T> &X, ATRG::Tensor<T> &Y, const uint blocking_direction, T &error,
const std::vector<uint> &forward_indices, std::vector<uint> &forward_dimensions_and_alpha, const uint D_truncated, const bool use_redsvd,
arma::Mat<T> &U_B_reference, arma::Mat<T> &U_M_reference) {
arma::Mat<T> U_B;
arma::Mat<T> U_C;
arma::Mat<T> U_M;
swap_bonds(B, C, X, Y, blocking_direction, error,
forward_indices, forward_dimensions_and_alpha, D_truncated, use_redsvd,
U_B_reference, U_M_reference,
U_B, U_C, U_M);
}
template <typename T>
void swap_impure_bonds(ATRG::Tensor<T> &B, ATRG::Tensor<T> &C, ATRG::Tensor<T> &Y, const uint blocking_direction,
const std::vector<uint> &forward_indices, std::vector<uint> &forward_dimensions_and_alpha,
const arma::Mat<T> &U_B, const arma::Mat<T> &U_C, const arma::Mat<T> &U_M) {
arma::Mat<T> B_flat;
arma::Mat<T> C_flat;
auto not_blocked_indices(forward_indices);
not_blocked_indices.erase(not_blocked_indices.begin() + blocking_direction);
// separate the not blocked indices
B.flatten(not_blocked_indices, {blocking_direction, B.get_order() - 1}, B_flat);
C.flatten(not_blocked_indices, {blocking_direction, C.get_order() - 1}, C_flat);
uint mu_dimension = U_B.n_cols;
uint nu_dimension = U_C.n_cols;
// make a tensor of S*V with indices: x_trunc, alpha, mu
// forward and backward dimensions are the same!
B.reshape({forward_dimensions_and_alpha[blocking_direction], forward_dimensions_and_alpha.back(), mu_dimension});
B_flat = B_flat.t() * U_B;
B.inflate({0, 1}, {2}, B_flat);
B.flatten({0}, {1, 2}, B_flat);
// make a tensor of S*V with indices: x_trunc, beta, nu
C.reshape({forward_dimensions_and_alpha[blocking_direction], forward_dimensions_and_alpha.back(), nu_dimension});
C_flat = C_flat.t() * U_C;
C.inflate({0, 1}, {2}, C_flat);
C.flatten({0}, {1, 2}, C_flat);
Y.reshape({forward_dimensions_and_alpha.back(), mu_dimension, forward_dimensions_and_alpha.back(), nu_dimension});
// B.t() * C with indices: alpha, mu, beta, nu
B_flat = B_flat.t() * C_flat;
Y.inflate({0, 1}, {2, 3}, B_flat);
Y.flatten({0, 3}, {2, 1}, B_flat);
C_flat = B_flat.t() * U_M;
uint truncated_dimension = U_M.n_cols;
// new indices: all forward indices, alpha
auto Y_dimensions = forward_dimensions_and_alpha;
Y_dimensions[blocking_direction] = truncated_dimension;
// Y has indices: beta, mu, x_trunc (index from SVD)
Y.reshape({forward_dimensions_and_alpha.back(), mu_dimension, truncated_dimension});
Y.inflate({0, 1}, {2}, C_flat);
Y.flatten({1}, {0, 2}, C_flat);
C_flat = U_B * C_flat;
// new indices: all backward indices, beta
// -> backward and forward dimensions are the same!
Y.reshape(Y_dimensions);
Y.inflate(not_blocked_indices, {Y.get_order() - 1, blocking_direction}, C_flat);
}
/**
* helper function for squeeze_bonds; computes an isometry from two tensors
*/
template <typename T>
void isometry(ATRG::Tensor<T> &A, ATRG::Tensor<T> &X, arma::Mat<T> &U_P, const uint index, T &error,
const std::vector<uint> &psi_indices, const uint D_truncated, const bool use_redsvd,
arma::Mat<T> &U_P_reference) {
arma::Mat<T> L_mat;
// single out "index" and alpha
A.flatten({index, A.get_order() - 1}, psi_indices, L_mat);
// .t() gives the complex conjugate for complex matrices
L_mat = L_mat * L_mat.t();
// matrix is sorted: "index", alpha, "index", alpha
// we want the tensor to be: "index", "index", alpha, alpha
auto A_dimensions = A.get_dimensions();
ATRG::Tensor<T> L({A_dimensions[index], A_dimensions[index],
A_dimensions.back(), A_dimensions.back()});
L.inflate({0, 2}, {1, 3}, L_mat);
L.flatten({0, 1}, {2, 3}, L_mat);
arma::Mat<T> W_mat;
X.flatten({index, X.get_order() - 1}, psi_indices, W_mat);
W_mat = W_mat * W_mat.t();
// reuse L to save memory
auto X_dimensions = X.get_dimensions();
L.reshape({X_dimensions[index], X_dimensions[index],
X_dimensions.back(), X_dimensions.back()});
L.inflate({0, 2}, {1, 3}, W_mat);
L.flatten({0, 1}, {2, 3}, W_mat);
arma::Mat<T> P = L_mat * W_mat.t();
// reuse L to save memory
L.reshape({A_dimensions[index], A_dimensions[index], X_dimensions[index], X_dimensions[index]});
// order in P: index_A, index_A, index_X, index_X
// reorder to: index_A, index_X, index_A, index_X
L.inflate({0, 2}, {1, 3}, P);
L.flatten({0, 1}, {2, 3}, P);
arma::Col<T> S;
// U should be an isometry
// V.t() * U = 1
// order in U/V: {index_A, index_X}, eta
error += svd(P, U_P, S, D_truncated, use_redsvd, U_P_reference);
U_P_reference = U_P;
}
/**
* helper function for squeeze_bonds; applys the squeezers to A/X, Y/D
*/
template <typename T>
std::vector<uint> squeeze(ATRG::Tensor<T> &A, ATRG::Tensor<T> &X, ATRG::Tensor<T> &G, std::vector<arma::Mat<T>> E_i, const uint blocking_direction,
const std::vector<uint> &forward_indices, const std::vector<uint> &backward_indices, const uint D_truncated) {
arma::Mat<T> A_flat;
arma::Mat<T> X_flat;
A.flatten(forward_indices, {A.get_order() - 1}, A_flat);
X.flatten(forward_indices, {X.get_order() - 1}, X_flat);
// reuse A for the product A * X
A_flat = A_flat * X_flat.t();
// index order will be: x1, y1, z1, ... x2, y2, z2, ...
std::vector<uint> all_dimensions(A.get_dimensions());
all_dimensions.resize(all_dimensions.size() - 1);
auto X_dimensions = X.get_dimensions();
all_dimensions.insert(all_dimensions.end(), X_dimensions.begin(), X_dimensions.end() - 1);
auto all_indices(forward_indices);
all_indices.insert(all_indices.end(), backward_indices.begin(), backward_indices.end());
G.reshape(all_dimensions);
G.inflate(forward_indices, backward_indices, A_flat);
uint number_backward_indices = forward_indices.size();
for(decltype(E_i.size()) i = 0; i < E_i.size(); ++i) {
uint index = i;
if(index >= blocking_direction) {
++index;
}
auto remaining_indices(all_indices);
remaining_indices.erase(remaining_indices.begin() + index);
// we already remove an index!
remaining_indices.erase(remaining_indices.begin() + index + number_backward_indices - 1);
// single out y1, y2 or z1, z2 etc.
G.flatten(remaining_indices, {index, index + number_backward_indices}, A_flat);
// remaining_indices, y_new -> the order decreases by one
A_flat = A_flat * E_i[i];
// we insert the new index at the position of the forward index
all_dimensions.erase(all_dimensions.begin() + index + number_backward_indices);
all_dimensions[index] = A_flat.n_cols;
// we remove the backward index at forward_index + number_backward_indices -> move all indices above that
all_indices.resize(all_indices.size() - 1);
remaining_indices = all_indices;
remaining_indices.erase(remaining_indices.begin() + index);
--number_backward_indices;
G.reshape(all_dimensions);
G.inflate(remaining_indices, {index}, A_flat);
}
return all_dimensions;
}
template <typename T>
void compute_squeezers(ATRG::Tensor<T> &A, ATRG::Tensor<T> &D, ATRG::Tensor<T> &X, ATRG::Tensor<T> &Y, const uint blocking_direction, T &error,
const std::vector<uint> &forward_indices, const std::vector<uint> &backward_indices, std::vector<uint> &forward_dimensions_and_alpha,
const uint D_truncated, const bool use_redsvd,
std::vector<arma::Mat<T>> &U_P_reference, std::vector<arma::Mat<T>> &U_N_reference,
std::vector<arma::Mat<T>> &E_i, std::vector<arma::Mat<T>> &F_i) {
/*
* indices A: all forward, alpha
* indices D: all backward, beta
* indices X: all forward, alpha
* indices Y: all backward, beta
*/
// make separate squeezers for each not blocked mode
E_i.resize(forward_indices.size() - 1);
F_i.resize(forward_indices.size() - 1);
for(uint index = 0; index < forward_indices.size(); ++index) {
if(index == blocking_direction) {
continue;
}
auto psi_indices(forward_indices);
psi_indices.erase(psi_indices.begin() + index);
// compute an isometry from A and X
arma::Mat<T> U_P;
isometry(A, X, U_P, index, error, psi_indices, D_truncated, use_redsvd, U_P_reference[index]);
// repeat for Y and D
arma::Mat<T> U_Q;
isometry(Y, D, U_Q, index, error, psi_indices, D_truncated, use_redsvd, U_P_reference[index]);
// insert the isometries U/V between A-X and Y-D: U_P_T - U_P = U_Q - U_Q_T
// and remodel U_P = U_Q to get one instead of two bonds
arma::Mat<T> N = U_P.t() * U_Q;
arma::Col<T> S;
arma::Mat<T> U_N;
error += svd(N, U_N, S, use_redsvd, U_N_reference[index]);
// compute the index in E_i, F_i
uint i = index;
if(i > blocking_direction) {
--i;
}
/*
* !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
* ! U_P and U_Q should be complex conjugated !
* !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
*/
// {index_A, index_X}, new index
E_i[i] = U_P * U_N;
F_i[i] = U_Q * N.t() * U_N;
U_N_reference[index] = U_N[index];
#ifdef DEBUG
std::cout << "U_P:" << std::endl << U_P << std::endl;
std::cout << "U_Q:" << std::endl << U_Q << std::endl;
std::cout << "U_N:" << std::endl << U_N << std::endl;
std::cout << "E_" << i << ":" << std::endl << E_i[i] << std::endl;
std::cout << "F_" << i << ":" << std::endl << F_i[i] << std::endl;
#endif
}
}
template <typename T>
void compute_squeezers(ATRG::Tensor<T> &A, ATRG::Tensor<T> &D, ATRG::Tensor<T> &X, ATRG::Tensor<T> &Y, ATRG::Tensor<T> &G, ATRG::Tensor<T> &H, const uint blocking_direction, T &error,
const std::vector<uint> &forward_indices, const std::vector<uint> &backward_indices, std::vector<uint> &forward_dimensions_and_alpha,
const uint D_truncated, const bool use_redsvd,
std::vector<arma::Mat<T>> &U_P_reference, std::vector<arma::Mat<T>> &U_N_reference) {
std::vector<arma::Mat<T>> E_i;
std::vector<arma::Mat<T>> F_i;
compute_squeezers(A, D, X, Y, blocking_direction, error,
forward_indices, backward_indices, forward_dimensions_and_alpha,
D_truncated, use_redsvd,
U_P_reference, U_N_reference, E_i, F_i);
// squeeze the bonds to make G and H
auto all_dimensions = squeeze(A, X, G, E_i, blocking_direction, forward_indices, backward_indices, D_truncated);
squeeze(Y, D, H, F_i, blocking_direction, forward_indices, backward_indices, D_truncated);
// update the bond size
for(decltype(all_dimensions.size()) i = 0; i < all_dimensions.size(); ++i) {
forward_dimensions_and_alpha[i] = all_dimensions[i];
}
}
template <typename T>
void contract_bond(ATRG::Tensor<T> &G, ATRG::Tensor<T> &H, ATRG::Tensor<T> &A, ATRG::Tensor<T> &B, ATRG::Tensor<T> &C, ATRG::Tensor<T> &D, const uint blocking_direction, T &error,
const std::vector<uint> &forward_indices, std::vector<uint> &forward_dimensions_and_alpha, const bool use_redsvd,
arma::Mat<T> &U_G_reference, arma::Mat<T> &U_K_reference,
arma::Mat<T> &U_G, arma::Mat<T> &U_H, arma::Mat<T> &U_K, arma::Mat<T> &V_K) {
arma::Mat<T> flat_G;
// order in G: all forward indices, contraction direction backward
G.flatten(forward_indices, {G.get_order() - 1}, flat_G);
arma::Col<T> S_G;
error += svd(flat_G, U_G, S_G, use_redsvd, U_G_reference);
arma::Mat<T> flat_H;
// H has the bond to G and the backward index in blocking direction swapped.
auto backward_indices_in_H(forward_indices);
backward_indices_in_H[blocking_direction] = H.get_order() - 1;
H.flatten(backward_indices_in_H, {blocking_direction}, flat_H);
arma::Col<T> S_H;
error += svd(flat_H, U_H, S_H, use_redsvd, U_G);
flat_G = flat_G.t() * U_G;
flat_H = flat_H.t() * U_H;
// reuse flat for K to save memory:
flat_G = flat_G.t() * flat_H;
flat_H.set_size(0);
arma::Col<T> S_K;
error += svd(flat_G, U_K, V_K, S_K, use_redsvd, U_K_reference);
// update the alpha bond
forward_dimensions_and_alpha[forward_dimensions_and_alpha.size() - 1] = S_K.n_elem;
flat_G = U_G * U_K;
A.reshape(forward_dimensions_and_alpha);
A.inflate(forward_indices, {A.get_order() - 1}, flat_G);
arma::Mat<T> SV_K = U_times_S(V_K, S_K);
flat_G = U_H * SV_K;
B.reshape(forward_dimensions_and_alpha);
B.inflate(forward_indices, {B.get_order() - 1}, flat_G);
SV_K = U_times_S(U_K, S_K);
flat_G = U_G * SV_K;
C.reshape(forward_dimensions_and_alpha);
C.inflate(forward_indices, {C.get_order() - 1}, flat_G);
flat_G = U_H * V_K;
D.reshape(forward_dimensions_and_alpha);
D.inflate(forward_indices, {D.get_order() - 1}, flat_G);
U_G_reference = U_G;
U_K_reference = U_K;
#ifdef DEBUG
std::cout << "U_G:" << std::endl << U_G << std::endl;
std::cout << "S_G:" << std::endl << S_G << std::endl;
std::cout << "U_H:" << std::endl << U_H << std::endl;
std::cout << "S_H:" << std::endl << S_H << std::endl;
std::cout << "U_K:" << std::endl << U_K << std::endl;
std::cout << "V_K:" << std::endl << V_K << std::endl;
#endif
}
template <typename T>
void contract_bond(ATRG::Tensor<T> &G, ATRG::Tensor<T> &H, ATRG::Tensor<T> &A, ATRG::Tensor<T> &B, ATRG::Tensor<T> &C, ATRG::Tensor<T> &D, const uint blocking_direction, T &error,
const std::vector<uint> &forward_indices, std::vector<uint> &forward_dimensions_and_alpha, const bool use_redsvd,
arma::Mat<T> &U_G_reference, arma::Mat<T> &U_K_reference) {
arma::Mat<T> U_G;
arma::Mat<T> U_H;
arma::Mat<T> U_K;
arma::Mat<T> V_K;
contract_bond(G, H, A, B, C, D, blocking_direction, error,
forward_indices, forward_dimensions_and_alpha, use_redsvd, U_G_reference, U_K_reference, U_G, U_H, U_K, V_K);
}
template <typename T>
void contract_impure_bond(ATRG::Tensor<T> &G, ATRG::Tensor<T> &H, ATRG::Tensor<T> &B_t, ATRG::Tensor<T> &C_b, const uint blocking_direction,
const std::vector<uint> &forward_indices, const std::vector<uint> &forward_dimensions_and_alpha,
arma::Mat<T> &U_G, arma::Mat<T> &U_H, arma::Mat<T> &U_K, arma::Mat<T> &V_K) {
arma::Mat<T> flat;
// order in G: all forward indices, contraction direction backward
G.flatten(forward_indices, {G.get_order() - 1}, flat);
arma::Mat<T> SV_G = flat.t() * U_G;
// H has the bond to G and the backward index in blocking direction swapped.
auto backward_indices_in_H(forward_indices);
backward_indices_in_H[blocking_direction] = H.get_order() - 1;
H.flatten(backward_indices_in_H, {blocking_direction}, flat);
arma::Mat<T> SV_H = flat.t() * U_H;
// K = SV_G.t() * SV_H; We want U_K.t() * K to get S_K * V_K.t(),
// but we transpose the operation to make the flattening easier
flat = SV_H.t() * SV_G * U_K;
flat = U_H * flat;
B_t.reshape(forward_dimensions_and_alpha);
B_t.inflate(forward_indices, {B_t.get_order() - 1}, flat);
flat = SV_G.t() * SV_H * V_K;
flat = U_G * flat;
C_b.reshape(forward_dimensions_and_alpha);
C_b.inflate(forward_indices, {C_b.get_order() - 1}, flat);
}
/**
* compute the last trace; G and H have the forward and backward indices first
* and then their common bond index last
*/
template<typename T>
T trace(const ATRG::Tensor<T> &G, const ATRG::Tensor<T> &H) {
T result = 0;
for(decltype(G.get_size()) i = 0; i < G.get_size(); ++i) {
result += G(i) * H(i);
}
return result;
}
/**
* compute the final result including the scalefactors that were removed earlier
*/
template<typename T>
T result_with_scalefactors(const ATRG::Tensor<T> &G, const ATRG::Tensor<T> &H, const long double logScalefactors, const int volume,
T &error, bool print = true) {
auto last_result = trace(G, H);
long double result = (logScalefactors + std::log(last_result)) / volume;
#ifdef DEBUG
std::cout << "logScalefactors: " << logScalefactors / volume << std::endl;
std::cout << "log(last_result): " << std::log(last_result) / volume << std::endl;
#endif
if(std::isnan(result) || std::isinf(result)) {
if(print) {
std::cerr << " the last step went wrong; use only scaling factor..." << std::endl;
error += std::log(std::abs(last_result)) * std::log(std::abs(last_result))
/ (logScalefactors * logScalefactors);
}
result = logScalefactors / volume;
}
return result;
}
/**
* compute the log value of the partition sum for the given tensor and a lattice of given dimensions
* returns log(Z) and an error estimate
*/
template <typename T>
std::tuple<T, T> compute_logZ(ATRG::Tensor<T> &tensor, const std::vector<uint> lattice_dimensions, const uint D_truncated, const bool use_redsvd,
const BlockingMode blocking_mode = alt_blocking) {
std::cout << " computing log(Z):" << std::endl;
auto starttime = std::chrono::high_resolution_clock::now();
auto splittime = starttime;
if(tensor.get_order() != lattice_dimensions.size() * 2) {
std::cerr << " In ATRG::compute_logZ: order of tensor and lattice dimensions don't match!" << std::endl;
throw 0;
}
for(uint i = 0; i < tensor.get_order() / 2; ++i) {
if(tensor.get_dimensions(i) != tensor.get_dimensions(i + tensor.get_order() / 2)) {
std::cerr << " In ATRG::compute_logZ: dimensions of forward and backward mode don't match!" << std::endl;
throw 0;
}
}
auto lattice_sizes(lattice_dimensions);
std::for_each(lattice_sizes.begin(), lattice_sizes.end(), [](auto &element) {element = std::pow(2, element);});
auto volume = std::accumulate(lattice_sizes.begin(), lattice_sizes.end(), 1, std::multiplies<T>());
auto remaining_volume = volume;
/*
* we compute this errors with error propagation:
* if we multiply to quantities we compute:
* error^2 = error1^2 + error2^2
* and take the square root over everything in the end
*/
T error = 0;
long double logScalefactors = 0;
uint physical_dimension = tensor.get_order() / 2;
// make lists of indices from 0 to >physical dimension< and from >physical dimension< to tensor order
std::vector<uint> forward_indices(physical_dimension);
std::iota(forward_indices.begin(), forward_indices.end(), 0);
std::vector<uint> backward_indices(physical_dimension);
std::iota(backward_indices.begin(), backward_indices.end(), physical_dimension);
//=============================================================================================
arma::Mat<T> flat;
tensor.flatten(forward_indices, backward_indices, flat);
arma::Mat<T> U;
arma::Mat<T> V;
arma::Col<T> S;
error += svd(flat, U, V, S, D_truncated, use_redsvd);
arma::Mat<T> SVp = ATRG::U_times_S(V, S);
arma::Mat<T> US = ATRG::U_times_S(U, S);
#ifdef DEBUG
std::cout << "U:" << std::endl << U << std::endl;
#endif
auto dimensions = tensor.get_dimensions();
decltype(dimensions) forward_dimensions(dimensions.begin(), dimensions.begin() + physical_dimension);
decltype(dimensions) backward_dimensions(dimensions.begin() + physical_dimension, dimensions.end());
auto forward_dimensions_and_alpha(forward_dimensions);
forward_dimensions_and_alpha.push_back(U.n_cols);
auto backward_dimensions_and_alpha(backward_dimensions);
backward_dimensions_and_alpha.push_back(U.n_cols);
// create A, B, C, D tensors from our SVD results:
ATRG::Tensor<T> A(forward_dimensions_and_alpha);
ATRG::Tensor<T> B(backward_dimensions_and_alpha);
ATRG::Tensor<T> C(forward_dimensions_and_alpha);
ATRG::Tensor<T> D(backward_dimensions_and_alpha);
// the columns only have alpha as an index, meaning the last index of the tensor
// B and D hold the backward modes, so their indices are relabeled
A.inflate(forward_indices, {A.get_order() - 1}, U);
B.inflate(forward_indices, {B.get_order() - 1}, SVp);
C.inflate(forward_indices, {C.get_order() - 1}, US);
D.inflate(forward_indices, {D.get_order() - 1}, V);
tensor.reshape({0});
// intermediate tensors that we will need during the blocking
ATRG::Tensor<T> X;
ATRG::Tensor<T> Y;
ATRG::Tensor<T> G;
ATRG::Tensor<T> H;
std::cout << " decomposed initial tensor... " <<
std::chrono::duration_cast<std::chrono::milliseconds>(
std::chrono::high_resolution_clock::now() - splittime)
.count() / 1e3
<< " seconds" << std::endl;
splittime = std::chrono::high_resolution_clock::now();
std::cout << " memory footprint: " << get_usage() << " GB" << std::endl;
//=============================================================================================
// contract the lattice
uint blocking_direction = physical_dimension - 1;
if(blocking_mode == s_blocking) {
blocking_direction = 0;
}
std::vector<uint> finished_blockings(lattice_dimensions.size(), 0);
bool finished = false;
// reference matrices that save the last U's of every SVD to rotate the next U's
// so that they match the orientation of the reference
arma::Mat<T> U_B_reference = arma::zeros<arma::Mat<T>>(0);
arma::Mat<T> U_M_reference = arma::zeros<arma::Mat<T>>(0);
std::vector<arma::Mat<T>> U_P_reference(lattice_dimensions.size(), arma::zeros<arma::Mat<T>>(0));
std::vector<arma::Mat<T>> U_N_reference(lattice_dimensions.size(), arma::zeros<arma::Mat<T>>(0));
arma::Mat<T> U_G_reference = arma::zeros<arma::Mat<T>>(0);
arma::Mat<T> U_K_reference = arma::zeros<arma::Mat<T>>(0);
while(!finished) {
remaining_volume /= 2;
//=============================================================================================
// swap the bonds, the not blocked modes between B and C and gain the tensors X and Y:
// !!! after this step only forward_dimensions_and_alpha holds the correct bond sizes !!!
swap_bonds(B, C, X, Y, blocking_direction, error,
forward_indices, forward_dimensions_and_alpha, D_truncated, use_redsvd,
U_B_reference, U_M_reference);
#ifdef DEBUG
std::cout << "X:" << std::endl << X << std::endl;
std::cout << "Y:" << std::endl << Y << std::endl;
#endif
auto Y_scale = std::max(std::abs(Y.max()), std::abs(Y.min()));
Y.rescale(1.0 / Y_scale);
logScalefactors += remaining_volume * std::log(Y_scale);
#ifdef DEBUG
std::cout << "Y_scale: " << Y_scale << std::endl;
#endif
// contract the double bonds of A, X in forward and B, D in backward direction
compute_squeezers(A, D, X, Y, G, H, blocking_direction, error,
forward_indices, backward_indices, forward_dimensions_and_alpha, D_truncated, use_redsvd,
U_P_reference, U_N_reference);
#ifdef DEBUG
std::cout << "G:" << std::endl << G << std::endl;
std::cout << "H:" << std::endl << H << std::endl;
#endif
// rescale G and H
auto G_scale = std::max(std::abs(G.max()), std::abs(G.min()));
G.rescale(1.0 / G_scale);
auto H_scale = std::max(std::abs(H.max()), std::abs(H.min()));
H.rescale(1.0 / H_scale);
logScalefactors += remaining_volume * (std::log(G_scale) + std::log(H_scale));
#ifdef DEBUG
std::cout << "G_scale: " << G_scale << std::endl;
std::cout << "H_scale: " << H_scale << std::endl;
#endif
//=============================================================================================
++finished_blockings[blocking_direction];
auto old_blocking_direction = blocking_direction;
// decide the next truncation direction:
switch(blocking_mode) {
case s_blocking:
if(finished_blockings[blocking_direction] >= lattice_dimensions[blocking_direction]) {
if(blocking_direction == physical_dimension - 1) {
std::cout << " finished s-blocking..." << std::endl;
finished = true;
continue;
} else {
std::cout << " s-blocked direction " << blocking_direction << "... " <<
std::chrono::duration_cast<std::chrono::milliseconds>(
std::chrono::high_resolution_clock::now() - splittime)
.count() / 1e3
<< " seconds" << std::endl;
splittime = std::chrono::high_resolution_clock::now();
// block the next direction
++blocking_direction;
std::cout << " memory footprint: " << get_usage() << " GB" << std::endl;
}
}
break;
case t_blocking:
if(finished_blockings[blocking_direction] >= lattice_dimensions[blocking_direction]) {
if(blocking_direction == 0) {
std::cout << " finished t-blocking..." << std::endl;
finished = true;
continue;
} else {
std::cout << " t-blocked direction " << blocking_direction << "... " <<
std::chrono::duration_cast<std::chrono::milliseconds>(
std::chrono::high_resolution_clock::now() - splittime)
.count() / 1e3
<< " seconds" << std::endl;
splittime = std::chrono::high_resolution_clock::now();
// block the next direction
--blocking_direction;
std::cout << " memory footprint: " << get_usage() << " GB" << std::endl;
}
}
break;
default:
// alt-blocking:
bool all_blocked = true;
for(decltype(finished_blockings.size()) i = 0; i < finished_blockings.size(); ++i) {
if(finished_blockings[i] < lattice_dimensions[i]) {
all_blocked = false;
break;
}
}
if(all_blocked) {
std::cout << " finished alt-blocking..." << std::endl;
finished = true;
continue;
}
std::cout << " alt-blocked direction " << blocking_direction << "... " <<
std::chrono::duration_cast<std::chrono::milliseconds>(
std::chrono::high_resolution_clock::now() - splittime)
.count() / 1e3
<< " seconds" << std::endl;
splittime = std::chrono::high_resolution_clock::now();
// block the next direction
do {
if(blocking_direction == 0) {
blocking_direction = physical_dimension - 1;
} else {
--blocking_direction;
}
} while(finished_blockings[blocking_direction] >= lattice_dimensions[blocking_direction]);
std::cout << " memory footprint: " << get_usage() << " GB" << std::endl;
}
std::cout << " estimated result: " << logScalefactors / volume << std::endl;
// make new A, B, C, D from G and H
contract_bond(G, H, A, B, C, D, old_blocking_direction, error,
forward_indices, forward_dimensions_and_alpha, use_redsvd,
U_G_reference, U_K_reference);
}
std::cout << " memory footprint: " << get_usage() << " GB" << std::endl;
auto logZ = result_with_scalefactors(G, H, logScalefactors, volume, error);
std::cout << std::endl << "\033[1;33m Runtime:\033[0m " <<
std::chrono::duration_cast<std::chrono::milliseconds>(
std::chrono::high_resolution_clock::now() - starttime)
.count() / 1e3
<< " seconds" << std::endl;
return {logZ, std::sqrt(error)};
}
/**
* compute the log value of the partition sum for the given tensor, impurity pair and a lattice of given dimensions
* returns log(Z_impure) and an error estimate
*/
template <typename T>
std::tuple<T, T, T> compute_single_impurity(ATRG::Tensor<T> &tensor, ATRG::Tensor<T> &impurity,
const std::vector<uint> lattice_dimensions, const uint D_truncated, const bool use_redsvd,
const BlockingMode blocking_mode = alt_blocking) {
std::cout << " computing log(Z) with one impurity:" << std::endl;
auto starttime = std::chrono::high_resolution_clock::now();
auto splittime = starttime;
if(tensor.get_order() != lattice_dimensions.size() * 2
|| impurity.get_order() != lattice_dimensions.size() * 2) {
std::cerr << " In ATRG::compute_single_impurity: order of tensor and lattice dimensions don't match!" << std::endl;
throw 0;
}
for(uint i = 0; i < tensor.get_order() / 2; ++i) {
if(tensor.get_dimensions(i) != tensor.get_dimensions(i + tensor.get_order() / 2)
|| impurity.get_dimensions(i) != impurity.get_dimensions(i + impurity.get_order() / 2)) {
std::cerr << " In ATRG::compute_single_impurity: dimensions of forward and backward mode don't match!" << std::endl;
throw 0;
}
}
auto lattice_sizes(lattice_dimensions);
std::for_each(lattice_sizes.begin(), lattice_sizes.end(), [](auto &element) {element = std::pow(2, element);});
auto volume = std::accumulate(lattice_sizes.begin(), lattice_sizes.end(), 1, std::multiplies<T>());
auto remaining_volume = volume;
/*
* we compute this errors with error propagation:
* if we multiply to quantities we compute:
* error^2 = error1^2 + error2^2
* and take the square root over everything in the end
*/
T error = 0;
long double Scalefactors = 1;
long double last_result = 0;
long double logScalefactors = 0;
uint physical_dimension = tensor.get_order() / 2;
// make lists of indices from 0 to >physical dimension< and from >physical dimension< to tensor order
std::vector<uint> forward_indices(physical_dimension);
std::iota(forward_indices.begin(), forward_indices.end(), 0);
std::vector<uint> backward_indices(physical_dimension);
std::iota(backward_indices.begin(), backward_indices.end(), physical_dimension);
//=============================================================================================
arma::Mat<T> flat;
tensor.flatten(forward_indices, backward_indices, flat);
arma::Mat<T> U;
arma::Mat<T> V;
arma::Col<T> S;
error += svd(flat, U, V, S, D_truncated, use_redsvd);
arma::Mat<T> SVp = ATRG::U_times_S(V, S);
arma::Mat<T> US = ATRG::U_times_S(U, S);
arma::Mat<T> flat_impure;
impurity.flatten(forward_indices, backward_indices, flat_impure);
arma::Mat<T> SVp_impure = flat_impure.t() * U;
arma::Mat<T> US_impure = flat_impure * V;
auto dimensions = tensor.get_dimensions();
decltype(dimensions) forward_dimensions(dimensions.begin(), dimensions.begin() + physical_dimension);
decltype(dimensions) backward_dimensions(dimensions.begin() + physical_dimension, dimensions.end());
auto forward_dimensions_and_alpha(forward_dimensions);
forward_dimensions_and_alpha.push_back(U.n_cols);
auto backward_dimensions_and_alpha(backward_dimensions);
backward_dimensions_and_alpha.push_back(U.n_cols);
// create A, B, C, D tensors from our SVD results:
ATRG::Tensor<T> A(forward_dimensions_and_alpha);
ATRG::Tensor<T> B(backward_dimensions_and_alpha);
ATRG::Tensor<T> C(forward_dimensions_and_alpha);
ATRG::Tensor<T> D(backward_dimensions_and_alpha);
// the columns only have alpha as an index, meaning the last index of the tensor
// B and D hold the backward modes, so their indices are relabeled
A.inflate(forward_indices, {A.get_order() - 1}, U);
B.inflate(forward_indices, {B.get_order() - 1}, SVp);
C.inflate(forward_indices, {C.get_order() - 1}, US);
D.inflate(forward_indices, {D.get_order() - 1}, V);
// symmetrize Impurity -> compute contraction with impurity on top and impurity bottom and average
// use the same U for the impure tensor
ATRG::Tensor<T> B_impure_t(backward_dimensions_and_alpha);
ATRG::Tensor<T> C_impure_b(forward_dimensions_and_alpha);
// impure tensor top
B_impure_t.inflate(forward_indices, {B_impure_t.get_order() - 1}, SVp_impure);
// impure tensor bottom
C_impure_b.inflate(forward_indices, {C_impure_b.get_order() - 1}, US_impure);
tensor.reshape({0});
impurity.reshape({0});
// intermediate tensors that we will need during the blocking
ATRG::Tensor<T> X;
ATRG::Tensor<T> Y;
ATRG::Tensor<T> G;
ATRG::Tensor<T> H;
ATRG::Tensor<T> Y_impure_t;
ATRG::Tensor<T> H_impure_t;
ATRG::Tensor<T> Y_impure_b;
ATRG::Tensor<T> H_impure_b;
std::cout << " decomposed initial tensor... " <<
std::chrono::duration_cast<std::chrono::milliseconds>(