From 6be7bceed91069d3aa7db4d268ef0624482e0f90 Mon Sep 17 00:00:00 2001 From: k-yoshimi Date: Mon, 29 Oct 2018 14:55:40 +0900 Subject: [PATCH 01/20] add pade, fft and gf --- CMakeLists.txt | 31 +- {src => c++}/.doxyrc | 0 c++/CMakeLists.txt | 3 + c++/include/Gf.h | 56 + c++/include/SVD_matrix.h | 58 + c++/include/admm_svd.h | 106 + c++/include/common.h | 48 + c++/include/errorcode.h | 23 + c++/include/fft.h | 18 + c++/include/kernel.h | 55 + c++/include/pade.h | 29 + c++/include/set_initial.h | 87 + c++/include/spm_core.h | 89 + c++/include/spm_param.h | 68 + {src => c++/src}/CMakeLists.txt | 8 +- {src => c++/src}/G2spectrum.cpp | 0 c++/src/Gf.cpp | 96 + {src => c++/src}/SVD_matrix.cpp | 0 {src => c++/src}/admm_svd.cpp | 0 {src => c++/src}/common.cpp | 0 c++/src/fft.cpp | 106 + {src => c++/src}/kernel.cpp | 0 c++/src/pade.cpp | 69 + {src => c++/src}/set_initial.cpp | 0 {src => c++/src}/spm_core.cpp | 0 cmake/EnableGtests.cmake | 28 + cmake/FindFFTW.cmake | 294 + 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test/c++/data/standard/Gtau.in create mode 100644 test/c++/data/standard/param.in create mode 100644 test/c++/gtest-all.cc create mode 100644 test/c++/gtest.h create mode 100644 test/c++/gtest_main.cc create mode 100644 test/c++/test_fft.cpp create mode 100644 test/c++/test_pade.cpp create mode 100644 test/python/CMakeLists.txt create mode 100644 test/python/data/CMakeLists.txt create mode 100644 test/python/data/standard/Gtau.in create mode 100644 test/python/data/standard/param.in create mode 100644 test/python/hello.py diff --git a/CMakeLists.txt b/CMakeLists.txt index 40341ea..e1cf201 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -3,7 +3,7 @@ cmake_minimum_required(VERSION 2.8.4 FATAL_ERROR) project(sparse CXX C) # add common modules from ../common/cmake -list(APPEND CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/common/cmake) +list(APPEND CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake) if(NOT CMAKE_BUILD_TYPE) set(CMAKE_BUILD_TYPE "Release" CACHE STRING "Type of build" FORCE) @@ -16,12 +16,12 @@ set(CMAKE_CXX_FLAGS_DEBUG "-std=c++11 -D_DEBUG -g -Wall -Wextra -pedantic -Wcast set(CMAKE_CXX_FLAGS_RELEASE "-std=c++11 -O3") #include directories -include_directories(${CMAKE_SOURCE_DIR}/include ${CMAKE_SOURCE_DIR}/thirdparty/cpplapack/include) +include_directories(${CMAKE_SOURCE_DIR}/thirdparty/cpplapack/include) -find_package(OpenMP) -if(OPENMP_FOUND) - set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${OpenMP_CXX_FLAGS}") -endif(OPENMP_FOUND) +#find_package(OpenMP) +#if(OPENMP_FOUND) +# set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${OpenMP_CXX_FLAGS}") +#endif(OPENMP_FOUND) #Find BLAS find_package(BLAS REQUIRED) @@ -29,6 +29,21 @@ find_package(BLAS REQUIRED) #Find LAPACK find_package(LAPACK REQUIRED) +#Find FFTW3 +find_package(FFTW REQUIRED) +include_directories(${FFTW_INCLUDE_DIRS}) + +# Build and enable tests +# testing setup +# enable_testing() must be called in the top-level CMakeLists.txt before any add_subdirectory() is called. +option(Testing "Enable testing" ON) + +if (Testing) + enable_testing(test) + add_subdirectory(test/c++) + add_subdirectory(test/python) +endif() + #Find SWIG #find_package(SWIG REQUIRED) #include(${SWIG_USE_FILE}) @@ -52,6 +67,4 @@ find_package(LAPACK REQUIRED) # CPPLAPACK #include_directories(${CPPLAPACK_INCLUDE_DIR}) -add_subdirectory(src) - -#add_subdirectory(python) +add_subdirectory(c++) diff --git a/src/.doxyrc b/c++/.doxyrc similarity index 100% rename from src/.doxyrc rename to c++/.doxyrc diff --git a/c++/CMakeLists.txt b/c++/CMakeLists.txt new file mode 100644 index 0000000..4abc3c1 --- /dev/null +++ b/c++/CMakeLists.txt @@ -0,0 +1,3 @@ +#include directories +include_directories(include) +add_subdirectory(src) diff --git a/c++/include/Gf.h b/c++/include/Gf.h new file mode 100644 index 0000000..5a200d1 --- /dev/null +++ b/c++/include/Gf.h @@ -0,0 +1,56 @@ + +#ifndef _GF_H +#define _GF_H + +#include +#include +#include "pade.h" + +class Gf{ +public: + Gf(): flag_pade(false) {}; + + enum statistics{ FERMION, BOSON }; + + // initialize by G(tau). tau=[0:beta), N points (N=2^integer is recommended) + void set_Gtau(const std::vector &G_tau, const statistics stat, const double beta, const double tail=1.); + + // initialize by G(iw_n). n=[0:N/2) + void set_Giw(const std::vector< std::complex > &G_iw, const statistics stat, const double beta, const double tail=1.); + + int get_size() { return N; }; + double get_tail() { return tail; }; + double get_beta() { return beta; }; + statistics get_statistics() { return stat; }; + + // get G(tau) + void get_Gtau(std::vector &G_tau); + + // get G(iw) + void get_Giw(std::vector< std::complex > &G_iw); + + // get G(w). w=[omega_min:omega_max], n-points + // void get_Gomega(std::vector< std::complex > &G_omega, const double omega_min, const double omega_max, const int n); + + // return G(omega) + std::complex Gomega(const double omega); + + // return rho(omega) + double rho(const double omega); + +private: + int N; + double beta; + double tail; + statistics stat; + std::vector gtau; // size N + std::vector< std::complex > giw; // size N/2 + + bool flag_pade; + Pade pade; + + void compute_tau2iw(); // G(tau) --> G(iw) + void compute_iw2tau(); // G(iw) --> G(tau) +}; + +#endif // _GF_H diff --git a/c++/include/SVD_matrix.h b/c++/include/SVD_matrix.h new file mode 100644 index 0000000..90f447a --- /dev/null +++ b/c++/include/SVD_matrix.h @@ -0,0 +1,58 @@ +/* SPM - Sparse Modeling tool */ +/* Copyright (C) 2017 Junya Otsuki, Kazuyoshi Yoshimi, Hiroshi Shinaoka, Masayuki Ohzeki*/ + +/* This program 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. */ + +/* This program 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 this program. If not, see . */ +/* + perform SVD, A = U*S*V^t, and store those matrices + SVs smaller than 'SV_min' are dropped. + All SVs are retained if SV_min=0. +*/ + +#ifndef _SVD_MATRIX_H +#define _SVD_MATRIX_H + +#include +#include "cpplapack.h" + +class SVD_matrix { + friend class admm; + friend class admm_svd; + +public: + SVD_matrix(CPPL::dgematrix A, double SV_min = 0); // copy the matrix A because it is destroyed in SVD + int get_rank(); + + CPPL::dgematrix At(); // A^t + CPPL::dgematrix At_A(); // A^t * A + CPPL::dgematrix At_A_inv(); // (A^t * A)^{-1} + CPPL::dgematrix At_A_inv_At(); // (A^t * A)^{-1} * A^t + void rearrange_col(std::vector &); // rearrange column of A (actaully VT) + void print_basis(std::string _file_U, std::string _file_V, int); + + CPPL::dcovector transform_x2sv(const CPPL::dcovector &); // V^t * x (to original basis) + CPPL::dcovector transform_y2sv(const CPPL::dcovector &); // U^t * y (to original basis) + CPPL::dcovector transform_sv2x(const CPPL::dcovector &); // V * x' (to SV basis) + CPPL::dcovector transform_sv2y(const CPPL::dcovector &); // U * y' (to SV basis) + void OutputSVD(std::string _file_SVD); +private: + CPPL::dcovector S_temp; + CPPL::dgematrix U_temp, VT_temp; + // K <= M,N + CPPL::dgbmatrix S, S_inv; // singular values, K*K diagonal matrix + CPPL::dgematrix U, VT, VT_full; // M*K, K*N + std::string file_SVD; + std::string file_U, file_V; +}; + +#endif diff --git a/c++/include/admm_svd.h b/c++/include/admm_svd.h new file mode 100644 index 0000000..f18ecbd --- /dev/null +++ b/c++/include/admm_svd.h @@ -0,0 +1,106 @@ +/* SPM - Sparse Modeling tool */ +/* Copyright (C) 2017 Junya Otsuki, Kazuyoshi Yoshimi, Hiroshi Shinaoka, Masayuki Ohzeki*/ + +/* This program 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. */ + +/* This program 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 this program. If not, see . */ +/* + compute sparse solution x of the equation y = A.x by solving + min_x { (1/2/lambda) ||y-A.x||_2^2 + ||V^t.x||_1 } + subject to x_i >= 0 & sum_i x_i = 'sum_x' + where V^t is defined by SVD of A: A = U.W.V^t + + x: N-dimensional vector + y: M-dimensional vector + A: (M * N) matrix + B: (K * N) matrix, where K is number of singular values retained +*/ + +#ifndef _ADMM_H +#define _ADMM_H + +#include +#include "cpplapack.h" + +class SVD_matrix; +struct admm_result{ + // w/ sv : results in SV basis + // w/o sv : results in omega-tau basis + std::vector x, xsv, z1, z1sv, z2, z2sv; + std::vector y, ysv, y_recovered_x, y_recovered_z1, ysv_recovered_x, ysv_recovered_z1; +}; +struct admm_info{ + double res1_pri, res1_dual, res2_pri, res2_dual; // residual errors + double mse, mse_full; + double l1_norm, sum_x_calc, negative_weight; + int iter; +}; + +class admm_svd{ +public: + admm_svd(CPPL::dgematrix &A, double SV_min=0); // A + ~admm_svd(); + + // [optional] + void set_sumrule(double sum_x); + void set_nonnegative(bool _flag); + void set_fileout_iter(const std::string filename); // output convergence in a file. unset if filename="" + void set_print_level(int); // 0: none, 1: results, 2: verbose + + // [required] + void set_coef(double lambda, double penalty1=1.0, double penalty2=1.0, bool flag_penalty_auto=false); + void set_y(const std::vector &y); + + // [optional] + void clear_x(); + + // [required] + int solve(double tolerance=1e-6, int max_iter=1000, int min_iter=10); // return 0 if converged, and 1 if not converged + + struct admm_result result; + struct admm_info info; + + double validate(const std::vector &y); // return MSE + +private: + const CPPL::dgematrix A; + SVD_matrix *svd; + + bool flag_nonnegative; + bool flag_sumrule; + double sum_x; + + CPPL::dcovector x, Vx, z1, u1, z2, u2; // 1 for L1 norm, 2 for non-negativity + CPPL::dcovector y, y_sv; + + double regulariz, penalty1, penalty2; + bool flag_penalty_auto; + static const int PENALTY_UPDATE_INTERVAL; + + int print_level; + bool flag_fileout_iter; + std::string file_iter; + + void pre_update(); // This function must be called before calling update_x, and must be recalled when one of values of lambda, penalty1, penalty2 are changed + void update_x(); + + // quantities used in functions update_x and set_y (set in function pre_update) + struct quantities_for_update{ + CPPL::dgbmatrix Y, B; // diagonal matrix + CPPL::dgematrix C; + CPPL::dcovector Yy, w; + CPPL::drovector v_row; + double sum_Vw; + } pre; +}; + +#endif diff --git a/c++/include/common.h b/c++/include/common.h new file mode 100644 index 0000000..146c5c5 --- /dev/null +++ b/c++/include/common.h @@ -0,0 +1,48 @@ +/* SPM - Sparse Modeling tool */ +/* Copyright (C) 2017 Junya Otsuki, Kazuyoshi Yoshimi, Hiroshi Shinaoka, Masayuki Ohzeki*/ + +/* This program 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. */ + +/* This program 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 this program. If not, see . */ +#ifndef _COMMON_H +#define _COMMON_H + +#include +#include "cpplapack.h" + +// converter +CPPL::dcovector vec2cppl_col(const std::vector &); // vector -> CPPL +std::vector cppl2vec(const CPPL::dcovector &); // CPPL -> vector +std::vector cppl2vec(const CPPL::drovector &); // CPPL -> vector + +double norm_l1(const CPPL::dcovector &); // L1 norm +double norm_l2(const CPPL::dcovector &); // L2 norm +double norm_l2_sq(const CPPL::dcovector &); // square of L2 norm +double sum_vector(const CPPL::dcovector &); // sum of vector elements +double innerproduct(const CPPL::dcovector &, const CPPL::dcovector &); //innerproduct + +bool if_negative(const CPPL::dcovector &); // true if at least one component is x_i<0 +bool if_negative(const CPPL::dgematrix &); + +CPPL::dcovector dcovector_all1(int n); // return a covector with elements all being 1 +CPPL::drovector drovector_all1(int n); // return a rovector with elements all being 1 + +CPPL::dcovector positive(const CPPL::dcovector &); // set negative elements at zero +CPPL::dgematrix positive(const CPPL::dgematrix &); + +// return shrinked matrix +CPPL::dgematrix low_rank_matrix(CPPL::dgematrix &mat, int m, int n); + +// return matrix in which the columns are rearranged according to 'index_col' (it can be smaller than the original column-length) +CPPL::dgematrix arrange_matrix_col(const CPPL::dgematrix &mat_full, const std::vector &index_col); + +#endif diff --git a/c++/include/errorcode.h b/c++/include/errorcode.h new file mode 100644 index 0000000..f15f449 --- /dev/null +++ b/c++/include/errorcode.h @@ -0,0 +1,23 @@ +/* SPM - Sparse Modeling tool */ +/* Copyright (C) 2017 Junya Otsuki, Kazuyoshi Yoshimi, Hiroshi Shinaoka, Masayuki Ohzeki*/ + +/* This program 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. */ + +/* This program 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 this program. If not, see . */ +#ifndef _ERRORCODE_H +#define _ERRORCODE_H + +#define ERROR_SUCCESS 0 +#define ERROR_INVALID_SIZE 1 +#define ERROR_INVALID_MATRIX_SIZE 2 + +#endif diff --git a/c++/include/fft.h b/c++/include/fft.h new file mode 100644 index 0000000..3a95a04 --- /dev/null +++ b/c++/include/fft.h @@ -0,0 +1,18 @@ + + +#ifndef _FFT_H +#define _FFT_H + +#include +#include + +void fft_fermion_tau2iw(const std::vector &G_tau, std::vector< std::complex > &G_iw, const double beta, const double tail=1.); + +void fft_fermion_iw2tau(std::vector &G_tau, const std::vector< std::complex > &G_iw, const double beta, const double tail=1.); + + +void fft_boson_tau2iw(const std::vector &G_tau, std::vector< std::complex > &G_iw, const double beta, const double tail=0.); + +void fft_boson_iw2tau(std::vector &G_tau, const std::vector< std::complex > &G_iw, const double beta, const double tail=0.); + +#endif // _FFT_H diff --git a/c++/include/kernel.h b/c++/include/kernel.h new file mode 100644 index 0000000..f168383 --- /dev/null +++ b/c++/include/kernel.h @@ -0,0 +1,55 @@ +/* SPM - Sparse Modeling tool */ +/* Copyright (C) 2017 Junya Otsuki, Kazuyoshi Yoshimi, Hiroshi Shinaoka, Masayuki Ohzeki*/ + +/* This program 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. */ + +/* This program 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 this program. If not, see . */ +/* + perform SVD, A = U*S*V^t, and store those matrices + SVs smaller than 'SV_min' are dropped. + All SVs are retained if SV_min=0. +*/ + +#ifndef _KERNEL_H +#define _KERNEL_H + +#include +#include +#include "cpplapack.h" + +class Kernel{ + +private: + CPPL::dgematrix A; + std::vector omega; + std::vector lambda; + std::vector valid; + static double kernel_f(double beta, double tau, double omega); + static double kernel_b(double beta, double tau, double omega); + +public: + + std::vector mesh_linear(double x_min, double x_max, int N); + std::vector mesh_log(double x_min, double x_max, int N); + + int MakeKernelLinear( + const std::string _StatisticsType, + const double _Beta, + const std::vector &_Tau, + const std::vector &_Omega, + std::vector > &_Aout, + const int _ANrow, const int _ANcolum + ); + +}; + +#endif diff --git a/c++/include/pade.h b/c++/include/pade.h new file mode 100644 index 0000000..09a82cd --- /dev/null +++ b/c++/include/pade.h @@ -0,0 +1,29 @@ +/*! + \file pade_c.h + \brief Declaration of class Pade +*/ + +#include +#include + +//! Analytic continuation by the Pade approximation + +//! HOW TO USE: +//! Pade obj(z, u); || Pade obj; obj.init(z,u); +//! for(w){ +//! g = obj.eval(w); +//! } +class Pade{ +public: + Pade() {}; + Pade(std::vector > &z, std::vector > &u); + //! initialize a rational function u_{pade}(w) using N values of (u_i, z_i) + void init(std::vector > &z, std::vector > &u); + //! evaluate u_{pade}(w) + std::complex eval(std::complex w); +private: + int m_n; // size + //! coefficient set of the approximated function 'u_{pade}(z)' + std::vector > m_a; + std::vector > m_z; +}; diff --git a/c++/include/set_initial.h b/c++/include/set_initial.h new file mode 100644 index 0000000..39cf76a --- /dev/null +++ b/c++/include/set_initial.h @@ -0,0 +1,87 @@ +/* SPM - Sparse Modeling tool */ +/* Copyright (C) 2017 Junya Otsuki, Kazuyoshi Yoshimi, Hiroshi Shinaoka, Masayuki Ohzeki*/ + +/* This program 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. */ + +/* This program 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 this program. If not, see . */ +#ifndef _SET_INITIAL_HEADER +#define _SET_INITIAL_HEADER +#include +#include +#include +#include "spm_param.h" +#include + +class SetInitial { +private: + struct OmegaInfo { + int NW; + double omega_min; + double omega_max; + }; + struct FileInfo { + std::string filein_G; + int col; + int output_interval; + std::string fileout_spec; + int print_level; + FileInfo(){ + print_level=1; + output_interval=1; + } + }; + + struct CalcInfo { + std::string statistics; + double beta; + }; + + int argc; + std::vector vargv; + SPM_Param param; + SPM_Flags flags; + + std::map mapForKeyWordToValue; + std::map mapForKeyWordToRead; + + template + std::string argv_or_defaultvalue(int n, T value); + bool SetDefaultValue(); + void SetInputValue(); + void RegisterMap(std::string _keyword, std::string _value); + void DeleteSpace(std::string &_item){ + size_t c; + while((c = _item.find_first_of(" \"\'")) != std::string::npos){ + _item.erase(c,1); + } + } + + std::string GetValue(std::string _keyword){ + std::transform(_keyword.begin(), _keyword.end(), _keyword.begin(), toupper); + return mapForKeyWordToValue[_keyword]; + } + +public: + SPM_Param GetParam() { return param; } + SPM_Flags GetFlags() { return flags; } + + OmegaInfo omegaInfo; + FileInfo fileInfo; + CalcInfo calcInfo; + bool AddDefaulValueMap(char* _filename); + bool ReadParam(char* _filename); + bool InputFromArgs(int argc, char *argv[]); + void PrintInfo(); +}; + + +#endif diff --git a/c++/include/spm_core.h b/c++/include/spm_core.h new file mode 100644 index 0000000..2096c27 --- /dev/null +++ b/c++/include/spm_core.h @@ -0,0 +1,89 @@ +/* SPM - Sparse Modeling tool */ +/* Copyright (C) 2017 Junya Otsuki, Kazuyoshi Yoshimi, Hiroshi Shinaoka, Masayuki Ohzeki*/ + +/* This program 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. */ + +/* This program 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 this program. If not, see . */ +/* + perform SVD, A = U*S*V^t, and store those matrices + SVs smaller than 'SV_min' are dropped. + All SVs are retained if SV_min=0. +*/ + +#ifndef _SPM_CORE_H +#define _SPM_CORE_H + +#include +#include "cpplapack.h" +#include "errorcode.h" +#include "admm_svd.h" +#include "spm_param.h" + +class SPM_Core { + +private: + CPPL::dgematrix A; + SPM_Param param; + SPM_Flags flags; + std::vector lambda; + std::vector valid; + std::vector omega; + std::vector result; + std::vector info; + + double integrate(std::vector &y, double width); + + int find_kink(std::vector &x, std::vector &y, std::vector &diff, std::vector &log_f); + + void print_results_admm(admm_result &r, std::vector w, double dw, std::string prefix); + +public: + + int SetKernel(std::vector > &_AIn); + + void SetParameters(const SPM_Param &_param){param=_param;} + + void SetFlags (const SPM_Flags &_flags){flags=_flags;} + + int SetParametersSVD(double _SVD_min); + + int SetParametersLambda(int _NLambda, double _lbegin, double _lend); + + int SetParametersAdmm(double _penalty, double _tolerance, int _max_iter); + + int SetFlagValidation(bool _flag_validation); + + void GetLambdaOpt(std::vector &_lambda, int *_opt_l); + + void GetSpectrum(std::vector &_spectrum); + + void GetResults(std::vector &_vmse, std::vector &_vmse_full, std::vector &_vl1_norm, + std::vector &_valid); + + int SolveEquation( + std::string _StatisticsType, + double _Beta, + std::vector > &_AIn, + std::vector &_Gtau, + std::vector &_lambda, + std::vector &_omega); + + int SolveEquationCore( + std::vector > &_AIn, + std::vector &_Gtau, + std::vector &_omega, + std::vector &_lambda, + const double _sum_G + ); +}; + +#endif diff --git a/c++/include/spm_param.h b/c++/include/spm_param.h new file mode 100644 index 0000000..cc54e9d --- /dev/null +++ b/c++/include/spm_param.h @@ -0,0 +1,68 @@ +/* SPM - Sparse Modeling tool */ +/* Copyright (C) 2017 Junya Otsuki, Kazuyoshi Yoshimi, Hiroshi Shinaoka, Masayuki Ohzeki*/ + +/* This program 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. */ + +/* This program 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 this program. If not, see . */ +#ifndef _SPM_PARAM_HEADER +#define _SPM_PARAM_HEADER + +class SPM_Param{ + private: + struct Lambda{ + int Nl; + double lbegin; + double lend; + int lvalid; + double dlambda; + Lambda(){ + Nl=1; + lbegin = 1e-1; + lend = 1e+0; + lvalid=0; + dlambda=-1; + } + }; + + struct Admm{ + double penalty; + double tolerance; + int max_iter; + bool flag_penalty_auto; + Admm(){ + penalty=10.; + tolerance = 1e-6; + max_iter=1000; + flag_penalty_auto=false; + } + }; + + struct SVD{ + double sv_min; + SVD(){ + sv_min=0; + } + }; + + public: + Lambda lambda; + Admm admm; + SVD svd; + +}; + +struct SPM_Flags{ + bool validation; + bool nonnegative; +}; + +#endif diff --git a/src/CMakeLists.txt b/c++/src/CMakeLists.txt similarity index 51% rename from src/CMakeLists.txt rename to c++/src/CMakeLists.txt index 2f9598c..fdf89fe 100644 --- a/src/CMakeLists.txt +++ b/c++/src/CMakeLists.txt @@ -1,7 +1,13 @@ #include directories #include_directories(../include) +# SPM library add_library(spm common.cpp SVD_matrix.cpp admm_svd.cpp spm_core.cpp kernel.cpp set_initial.cpp) + +# GF library +add_library(gf Gf.cpp fft.cpp pade.cpp) +target_link_libraries(gf ${FFTW_LIBRARIES}) + #execable add_executable(SpM.out G2spectrum.cpp ) -target_link_libraries(SpM.out spm ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES}) +target_link_libraries(SpM.out spm gf ${BLAS_LIBRARIES} ${LAPACK_LIBRARIES}) diff --git a/src/G2spectrum.cpp b/c++/src/G2spectrum.cpp similarity index 100% rename from src/G2spectrum.cpp rename to c++/src/G2spectrum.cpp diff --git a/c++/src/Gf.cpp b/c++/src/Gf.cpp new file mode 100644 index 0000000..13ae194 --- /dev/null +++ b/c++/src/Gf.cpp @@ -0,0 +1,96 @@ +#include "Gf.h" +#include "fft.h" +#include + +using namespace std; +const complex IMAG = complex(0, 1.); + +void Gf::set_Gtau(const std::vector &G_tau, const statistics stat, const double beta, const double tail) +{ + if( stat == BOSON ){ + // TODO + cout << "BOSON not yet implemented" << endl; + exit(0); + } + gtau = G_tau; // copy + N = G_tau.size(); + this->stat = stat; + this->beta = beta; + this->tail = tail; + + giw.clear(); + flag_pade = false; +} + +// initialize by G(iw_n). n=[0:N/2) +void Gf::set_Giw(const std::vector< std::complex > &G_iw, const statistics stat, const double beta, const double tail) +{ + if( stat == BOSON ){ + // TODO + cout << "BOSON not yet implemented" << endl; + exit(0); + } + giw = G_iw; // copy + N = G_iw.size()*2; + this->stat = stat; + this->beta = beta; + this->tail = tail; + + gtau.clear(); + flag_pade = false; +} + +void Gf::get_Gtau(std::vector &G_tau) +{ + if( gtau.empty() ) compute_iw2tau(); + G_tau = gtau; // copy +} + +void Gf::get_Giw(std::vector< std::complex > &G_iw) +{ + if( giw.empty() ) compute_tau2iw(); + G_iw = giw; // copy +} + +// void get_Gomega(std::vector< std::complex > &G_omega, const double omega_min, const double omega_max, const int n) +// { +// +// } + +std::complex Gf::Gomega(const double omega) +{ + if( !flag_pade ){ + if( giw.empty() ) compute_tau2iw(); + + vector< complex > matsubara(N); + // TODO: boson + for(int i=0; i +#include +#include +#include + +using namespace std; +const complex IMAG = complex(0, 1.); + +static void fft_tau2iw(const std::vector &g_tau, std::vector< std::complex > &g_iw, const double beta) +{ + int N = g_tau.size(); + + fftw_complex *in, *out; + fftw_plan p; + + in = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * 2*N); + out = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * 2*N); + p = fftw_plan_dft_1d(2*N, in, out, FFTW_BACKWARD, FFTW_ESTIMATE); + + for(int i=0; i(out[n_odd][0], out[n_odd][1]) / double(2*N) * beta; + } + + fftw_destroy_plan(p); + fftw_free(in); + fftw_free(out); +} + +static void fft_iw2tau(std::vector &g_tau, const std::vector< std::complex > &g_iw, const double beta) +{ + int N = g_iw.size()*2; + + fftw_complex *in, *out; + fftw_plan p; + + in = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * 2*N); + out = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * 2*N); + p = fftw_plan_dft_1d(2*N, in, out, FFTW_FORWARD, FFTW_ESTIMATE); + + for(int i=0; i<2*N; i++) in[i][0] = in[i][1] = 0; + + for(int i=0; i &G_tau, std::vector< std::complex > &G_iw, const double beta, const double tail) +{ + double N = G_tau.size(); + G_iw.resize(N/2); + vector G_tau_dif(N); + + for(int i=0; i &G_tau, const std::vector< std::complex > &G_iw, const double beta, const double tail) +{ + double N = G_iw.size()*2; + G_tau.resize(N); + vector< complex > G_iw_dif(N/2); + + for(int i=0; i > &z, vector > &u) +{ + init(z, u); +} + +void Pade::init(vector > &z, vector > &u) +{ + m_n = min(z.size(), u.size()); + m_z = z; // copy + m_a.resize(m_n); + + // g_n(z_i) + vector > *g0 = new vector >(u); // copy + vector > *g1 = new vector >(m_n); + + m_a[0] = u[0]; + for(int n=1; n Pade::eval(complex w) +{ + complex A0 = 0.0, A1 = m_a[0], A2, B0 = 1.0, B1 = 1.0, B2; + + for(int i=1; izN*15>#a#sB)_MfhvXvD0mEc_X6RrHX8HApQQ!`B;^hBW3-=@$1D&0>nngyQduoH$l2(@q` 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zx*w73eP_Ao+yt(|1}-#TYDXTsrGY6Gt(r8Vvyy>>#eW&X))$={1R~@yiS)iI&!U6b z=)l$=CZat9N#gW_ zqQTAVl}=O59Vky_num$`p~#{+Q7srzzp46=VF-V={z0p?Jxdo5Qci7Z+{MH!<`-EM z3y(MX*i4c13_kOCTrk62a~$kiHDTQbtAg(BR@L>y*`!B0?mcljE6%f9Yd#M(x{tOF zb=Y^H5jC+1_lUb&r<&_%JXine;DjImRA#aW5J?zdzIZ>&&Nl8Rgh;Ip+p#vLp7>j8Rx6rk>&##-}6e3r>agQFAa0y0s$gg&^XqJ;L zn&OcCT+*>b*#CYi{4g5J*2CJ*^h7Lv_D0tQdM@J1CMsXK(IzIWvG6;I=|yWN(GAoX zuhum>F6MwPP;bkD1P9^gU$HAZVcTISxYrcFgYt&~>!e<4W?(T}45|}aZ z5=^yd_FPGz@bhF^`gUSeZoJWaHCdg;$c%m%VL-kNP<=$*FD)0-y4}BfwA6%Hp6+gw z3#FMS7==I0_`bn#SRgnp!gy%fWErP9&YVCa`#sJN1j0B?;lE&&4pJ;2&dA4{j96n26E|Gx7}4*WoM29)ru(=$q`>WrBxpn9MMo57JNF6mz3e->#hKgCWM=z(D)KuBrrowCZUk z7^MgQ0eXUC9(x~EHB{8k{MvOYdKJJWUI|??m1~tD#9smGf{dfa=kD{`_ +results in NaN. +Even if one manages to derive a definite solution, it is quite sensitive to numerical noise and often breaks preconditions that any physical spectra must satisfy. +This becomes particularly problematic when :math:`\bm{G}` is evaluated by quantum Monte Carlo technique. + +``SpM`` provides a **physical** solution which fulfills the equation of concern within a certain accuracy. +The solution satisfies the constraints such as sum rule and nonnegativity. +The engine of ``SpM`` program uses the method of **L1-norm regularization** to separate relevant information in :math:`\bm{G}` from irrelevant one which makes the spectrum unphysical. This process is automatically done without hand-tuning parameters. + +For details, see the original article + + J. Otsuki, M. Ohzeki, H. Shinaoka, K. Yoshimi, + "Sparse modeling approach to analytical continuation of imaginary-time quantum Monte Carlo data" + `Phys. Rev. E 95, 061302(R) (2017). `_ diff --git a/docs/manual/source/_build/html/_sources/docs/function.rst.txt b/docs/manual/source/_build/html/_sources/docs/function.rst.txt new file mode 100644 index 0000000..79a3000 --- /dev/null +++ b/docs/manual/source/_build/html/_sources/docs/function.rst.txt @@ -0,0 +1,82 @@ +.. SpM documentation master file, created by + sphinx-quickstart on Thu Aug 10 10:08:31 2017. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +Calculation flow +=============================== +In this chapter, the calculation flow in SpM is shown. + + +Overview of calculation flow +---------------------------- +The main function for SpM is defined in G2spectrum.cpp +and the calculation is done by following procedures. + +.. blockdiag:: + + blockdiag { + "Set initial condition" -> "Solve equation" -> "Output results"; + group{ + color ="orange" + "Set initial condition" + } + group{ + color ="red" + "Solve equation" + } + group{ + color ="blue" + "Output results" + } + } + +1. Set initial condition + + .. blockdiag:: + + blockdiag { + "Read parameters" -> "Read Gtau" -> "Make a kernel"; + + group{ + color ="orange" + "Read parameters" -> "Read Gtau" -> "Make a kernel"; + } + } + + - Read parameters (ReadParam function in set_initial.cpp). + + - Read Gtau (read_Gtau function in G2spectrum.cpp). + + - Make a kernel (mesh_linear, mesh_log and MakeKernelLinear functions in kernel.cpp). + +2. Solve equation + + + .. blockdiag:: + + blockdiag { + "Set parameters" -> "Solve equation by \n ADMM method" -> "Get results "; + + group{ + color ="red" + "Set parameters" -> "Solve equation by \n ADMM method" -> "Get results "; + } + } + + + + - Set parameters (SetParameters and SetFlags functions in spm_core.cpp). + + - Solve equation by ADMM method (SolveEquation function in spm_core.cpp). + + + - Get results (GetSpectrum and GetResults functions in spm_core.cpp) + +3. Output results + + This procedure is directly implemented in G2spectrum.cpp. + +Sparse modeling procedure +------------------------- +to be updated... diff --git a/docs/manual/source/_build/html/_sources/docs/inputfile.rst.txt b/docs/manual/source/_build/html/_sources/docs/inputfile.rst.txt new file mode 100644 index 0000000..ff56082 --- /dev/null +++ b/docs/manual/source/_build/html/_sources/docs/inputfile.rst.txt @@ -0,0 +1,74 @@ +.. SpM documentation master file, created by + sphinx-quickstart on Thu Aug 10 10:08:31 2017. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +.. _inputfiles: + +Input files +=============================== +1. Parameter file (param.in) + +The variables for which default value is not given are mandatory. + +* INPUT/OUTPUT + + .. csv-table:: + :header-rows: 1 + :widths: 1,1,2,4 + + Name, Type, Default value, Description + statistics, String, ---, Choose "fermion" or "boson". + beta, Double, ---, The inverse temperature + filein_G, String, Gtau.in, The name of an input file for Green's function. + column, Integer, 1, The column number where the values of G(tau) are stored in the filein_G file. + fileout_spec, String, spectrum.out, The name of output file of spectrum. + + + +* OMEGA + + .. csv-table:: + :header-rows: 1 + :widths: 1,1,2,4 + + Name, Type, Default value, Description + NOmega, Integer, 1001, The number of omega to be calculated. + omegamin, Double, -4, The minimum value of omega. + omegamax, Double, 4, The maximum value of omega. + + Note: The i-th omega where i=[0:Nomega) is given by + :math:`\verb|omega|[i]=\verb|omegamin|+(\verb|omegamax|-\verb|omegamin|)/(\verb|NOmega|-1) * i`. + +* SVD + + .. csv-table:: + :header-rows: 1 + :widths: 1,1,2,4 + + Name, Type, Default value, Description + SVmin, Double, 1e-10, Truncation value of singular values. + + +* ADMM + + .. csv-table:: + :header-rows: 1 + :widths: 1,1,2,4 + + Name, Type, Default value, Description + lambdalogmesh, Double, 0.2, The log mesh of lambda. + lambdalogbegin, Double, 0, The log value of maximum lambda. lambda_max is given by :math:`10^{\verb|lambdalogbegin|}`. + lambdalogend, Double, -1, The log value of minimum lambda. lambda_min is given by :math:`10^{\verb|lambdalogend|}` + Nlambda, Integer, ---, The number of lambda to be calculated. + penalty, Double, 10.0, "The value of penalty coefficient. If negative, penalty is optimized during the iteration starting with its absolute value." + tolerance, Double, 1e-6, The criteria of convergence. + maxiteration, Integer,1000, The maximum number of iterations. + printlevel, Integer,2, "0; minimum, 1; moderate, 2; verbose." + +2. Green's function (Gtau.in) + + In SPM, the values of Green's function is only used for calculation, + i.e. tau is automatically determined by the beta and the step. + Please indicate the column number where the values of G(tau) are + stored by "column" in the parameter file. diff --git a/docs/manual/source/_build/html/_sources/docs/install.rst.txt b/docs/manual/source/_build/html/_sources/docs/install.rst.txt new file mode 100644 index 0000000..ff9441a --- /dev/null +++ b/docs/manual/source/_build/html/_sources/docs/install.rst.txt @@ -0,0 +1,75 @@ +.. SpM documentation master file, created by + sphinx-quickstart on Thu Aug 10 10:08:31 2017. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +How to install +=============================== + +Requirement +-------------- +* LAPACK, BLAS +* cpplapack (included in this package) + + +Download +--------- +* **Stable version** + + You can download a stable version of the ``SpM`` program in https://github.com/SpM-lab/SpM/releases. After download the archive, decompress it by + + :: + + $ tar zxvf v1.0.tar.gz + +* **Latest codes** + + You can get the latest codes from `our GitHub repository `_. Execute the following command + + :: + + $ git clone https://github.com/SpM-lab/SpM.git spm.src + + and then the source codes are downloaded in the directory ``spm.src``. + +Build +------ + +1. First, create an empty directory and move into it: + + :: + + $ mkdir spm.build && cd spm.build + + We assume that ``spm.build`` is located on the same level as ``spm.src``. + +2. Call cmake + + :: + + $ cmake ../spm.src + + and all necessary files including ``Makefile`` are created according to your system configuration. [any cmake options?] + +3. Now, you can compile the codes by + + :: + + $ make + + The executable file ``SpM.out`` is created in the ``spm.build/src`` directory. + + +Test +------------------ + +Some sample data are provided for test calculations. +Just enter into ``samples/fermion`` directory and execute it by + +:: + + $ ./run.sh + +You may need to change the parameter ``file_exe="../SpM.out"`` in the script (absolute or relative path to ``SpM.out``) according to your environment. +If succeeded, results including graphs in EPS format are generated in ``output`` directory. +For details of the sample script, see :ref:`tutorials`. diff --git a/docs/manual/source/_build/html/_sources/docs/outputfile.rst.txt b/docs/manual/source/_build/html/_sources/docs/outputfile.rst.txt new file mode 100644 index 0000000..d206824 --- /dev/null +++ b/docs/manual/source/_build/html/_sources/docs/outputfile.rst.txt @@ -0,0 +1,245 @@ +.. SpM documentation master file, created by + sphinx-quickstart on Thu Aug 10 10:08:31 2017. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +.. _outputfiles: + +Output files +=============================== + +After computation is done, numerical results are stored in directory ``output``. + +List of files +------------------ + +:: + + output + ├── spectrum.dat + ├── lambda_dep.dat + ├── find_lambda_opt.dat + ├── SV.dat + ├── lambda_opt + │ ├── iter.dat + │ ├── x_sv.dat + │ ├── x_tw.dat + │ ├── y_sv.dat + │ └── y_tw.dat + ├── lambda + │ ├── lambda_1.00e+00 + │ │ ├── iter.dat + │ │ ├── x_sv.dat + │ │ ├── x_tw.dat + │ │ ├── y_sv.dat + │ │ └── y_tw.dat + │ ├── lambda_1.58e+00 + │ │ ├── ... + │ │ ├── ... + │ (for all values of lambda) + +The four files just below the output directory summarize the results. +More detailed results for a given value lambda are stored in directory ``lambda_*`` +In particular, the directory ``lambda_opt`` is for the optimal values of lambda, and the other directories ending with numbers, e.g. ``lambda_1.00e+00``, contain results for the specific value of lambda. + +Details of each files +--------------------------- +Each files stores list of real numbers separated with a white space. +Some comments may be given at the header of files (lines beginning with '#'). + +* *spectrum.dat* + + Real frequency spectrum :math:`\rho(\omega)` for the optimal value of :math:`\lambda`. This is the final solution. + + * 1st column: :math:`\omega_i` + * 2nd column: :math:`\rho(\omega_i)` + + ex.) calculated results for fermion sample outputted as ``samles/fermion/spectrum.dat``. + + :: + + # lambda=1.585e-02 (l=19) + -4.00000e+00 0.00000e+00 + -3.99200e+00 0.00000e+00 + -3.98400e+00 0.00000e+00 + -3.97600e+00 0.00000e+00 + +* *lambda_dep.dat* + + Several quantities as a function of lambda. + + * 1st column: :math:`\lambda` + * 2nd column: Square error in the SV basis, :math:`\| \bm{y}'-S\bm{x}' \|_2^2` (the first term in :math:`F`) + * 3rd column: Square error computed in the original basis, :math:`\| \bm{y}-K\bm{x} \|_2^2` + * 4th column: L1 norm of :math:`\bm{x}'`, :math:`\| \bm{x}' \|_1` (the second term in :math:`F`) + * 5th column: not used + + ex.) calculated results for fermion sample outputted as ``samles/fermion/lambda_dep.dat``. + + :: + + 1.00000e+02 1.09110e-01 1.13080e-01 4.81361e-02 0.00000e+00 + 6.30957e+01 1.08854e-01 1.12824e-01 4.81376e-02 0.00000e+00 + 3.98107e+01 1.08752e-01 1.12722e-01 4.81386e-02 0.00000e+00 + 2.51189e+01 1.08710e-01 1.12679e-01 4.81394e-02 0.00000e+00 + 1.58489e+01 1.08609e-01 1.12578e-01 4.81459e-02 0.00000e+00 + + +* *find_lambda_opt.dat* + + Auxiliary data that are used to determine the optimal value of lambda. See ref.?? for details. + + * 1st column: :math:`\log_{10}(\lambda)` + * 2nd column: :math:`\log_{10}(f(x)/\chi^2)` + * 3rd column: :math:`\log_{10}(\chi^2)` + * 4th column: :math:`\log_{10}(f(x))` + + ex.) calculated results for fermion sample outputted as ``samles/fermion/find_lambda_opt.dat``. + + :: + + # log(x) diff log(y) log(f(x)) [all in log10 scale] + 2.00000e+00 1.92865e-16 -9.621340e-01 -9.621340e-01 + 1.80000e+00 -8.94525e-02 -9.631547e-01 -1.052607e+00 + 1.60000e+00 -1.79519e-01 -9.635618e-01 -1.143080e+00 + 1.40000e+00 -2.69822e-01 -9.637317e-01 -1.233554e+00 + +* *SV.dat* + + Singular values of the kernel :math:`K(\tau, \omega)`. + + * 1st column: index :math:`l` (starting from 0) + * 2nd column: The singular value :math:`S_l` in descending order + + ex.) calculated results for fermion sample outputted as ``samles/fermion/find_lambda_opt.dat``. + + :: + + 0 1.07898e+02 + 1 9.75830e+01 + 2 6.93652e+01 + 3 5.27590e+01 + 4 3.57046e+01 + + +* *iter.dat* + + Several quantities as a function of the iteration number. + The 2nd--6th quantities should be small. + + * 1st column: iteration (starting from 1) + * 2nd column: :math:`\| \bm{x}'(n) - \bm{x}'(n-1) \|_1` + * 3rd column: primary residual error for the constraint :math:`\bm{z}'=\bm{x}', \| \bm{z}'-\bm{x}' \|_2` + * 4th column: dual residual error for the constraint :math:`\bm{z}'=\bm{x}'`, :math:`|| \bm{z}'(n) - \bm{z}'(n-1) ||_2` + * 5th column: primary residual error for the constraint :math:`\bm{z}=V\bm{x}'`, :math:`\| \bm{z}-V\bm{x}' \|_2` + * 6th column: dual residual error for the constraint :math:`\bm{z}=V\bm{x}'`, :math:`\| \bm{z}(n) - \bm{z}(n-1) \|_2` + * 7th column: Square error in the SV basis (the quantity of 2nd column in lambda_dep.dat) + * 8th column: :math:`\| \bm{x} \|_1'` (the quantity of 4th column in lambda_dep.dat) + * 9th column: sum of spectrum, :math:`\langle V\bm{x}' \rangle` + * 10th column: negative weight in the spectrum :math:`V\bm{x}'` + + ex.) calculated results for fermion sample outputted as ``samles/fermion/lambda_opt/iter.dat``. + + :: + + # iter diff(x,x_old) res1_pri res1_dual res2_pri res2_dual RMSE L1_norm sum(x) negative_weight + 1 3.854841e-03 2.119714e-03 1.369725e-04 5.289078e-04 4.523259e-04 5.618012e-05 9.396320e-02 1.000546e+00 3.481495e-03 + 2 2.399056e-03 1.526513e-03 3.273800e-05 4.131063e-04 6.433491e-04 5.652371e-05 9.203257e-02 1.000546e+00 2.717878e-03 + 3 2.166172e-03 1.024876e-03 1.232067e-05 4.091785e-04 6.751225e-04 5.686296e-05 9.031303e-02 1.000546e+00 3.234967e-03 + 4 1.425573e-03 8.163075e-04 4.198961e-06 3.879910e-04 4.450555e-04 5.711656e-05 8.963409e-02 1.000546e+00 3.396003e-03 + +* *x_sv.dat* + + spectrum in the SV basis (solution of the minimization problem) + + * 1st column: The singular value index :math:`l` + * 2nd column: :math:`x'_l` + * 3rd column: :math:`z'_l` (**must be sparse**) + * 4th column: :math:`V^{\rm t}\bm{z}` + + ex.) calculated results for fermion sample outputted as ``samles/fermion/lambda_opt/x_sv.dat``. + + :: + + 0 -4.61300e-02 -4.61300e-02 -4.61492e-02 + 1 1.14335e-06 0.00000e+00 -5.52982e-06 + 2 -6.65757e-03 -6.65757e-03 -6.69485e-03 + 3 -2.29934e-05 0.00000e+00 -1.16960e-05 + 4 -3.21754e-03 -3.21754e-03 -3.16677e-03 + + +* *x_tw.dat* + + spectrum \rho(\omega) in the real-frequency domain + + * 1st column: :math:`\omega_i` + * 2nd column: :math:`V\bm{x}'` + * 3rd column: :math:`V\bm{z}'` (final result for a given lambda when non-negativity is not imposed) + * 4th column: :math:`\bm{z}` (**final result** for a given lambda when non-negativity is imposed) + + ex.) calculated results for fermion sample outputted as ``samles/fermion/lambda_opt/x_tw.dat``. + + :: + + -4.00000e+00 8.98641e-04 3.95646e-03 0.00000e+00 + -3.99200e+00 8.73662e-04 3.79795e-03 0.00000e+00 + -3.98400e+00 8.41470e-04 3.64070e-03 0.00000e+00 + -3.97600e+00 8.02778e-04 3.48473e-03 0.00000e+00 + -3.96800e+00 7.58271e-04 3.33005e-03 0.00000e+00 + + +* *y_sv.dat* + + input data transformed into the SV basis + + * 1st column: The singular value index :math:`l` + * 2nd column: :math:`y'_l` computed by :math:`U^{\rm t} \bm{y}` + * 3rd column: :math:`S\bm{x}'` + * 4th column: :math:`S\bm{z}'` + + ex.) calculated results for fermion sample outputted as ``samles/fermion/lambda_opt/y_sv.dat``. + + :: + + 0 -4.97866e+00 -4.97734e+00 -4.97734e+00 + 1 1.16952e-04 1.11571e-04 0.00000e+00 + 2 -4.63728e-01 -4.61804e-01 -4.61804e-01 + 3 -1.28769e-03 -1.21311e-03 0.00000e+00 + 4 -1.13754e-01 -1.14881e-01 -1.14881e-01 + +* *y_tw.dat* + + input data :math:`G(\tau)` in the imaginary-time domain + + * 1st column: :math:`\tau_i` + * 2nd column: :math:`y_i=G(\tau_i)` (**input data**) + * 3rd column: :math:`U S \bm{x}'` + * 4th column: :math:`U S \bm{z}'` + + ex.) calculated results for fermion sample outputted as ``samles/fermion/lambda_opt/y_tw.dat``. + + :: + + 0.00000e+00 5.00734e-01 5.00687e-01 5.00294e-01 + 2.49938e-04 4.90130e-01 4.90315e-01 4.89958e-01 + 4.99875e-04 4.81350e-01 4.80277e-01 4.79953e-01 + 7.49813e-04 4.71476e-01 4.70561e-01 4.70268e-01 + 9.99750e-04 4.61762e-01 4.61154e-01 4.60890e-01 + +.. + + How to generate PDF files + ----------------------------- + + Gnuplot script files are given in the sample directory. + In the ``output`` directory, type + + :: + + gnuplot path_to_SpM/samples/plt/* + + and in ``lambda_*`` directory, type + + :: + + gnuplot path_to_SpM/samples/plt/lambda_fix/* diff --git a/docs/manual/source/_build/html/_sources/docs/tutorials.rst.txt b/docs/manual/source/_build/html/_sources/docs/tutorials.rst.txt new file mode 100644 index 0000000..0bcfb13 --- /dev/null +++ b/docs/manual/source/_build/html/_sources/docs/tutorials.rst.txt @@ -0,0 +1,169 @@ +.. SpM documentation master file, created by + sphinx-quickstart on Thu Aug 10 10:08:31 2017. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +.. _tutorials: + +Tutorials +=============================== + +Sample data are provided both for fermionic and bosonic cases: + + - ``samples/fermion`` # a sample for fermionic spectrum (data in the article) + - ``samples/boson`` # a sample for bosonic spectrum + +Here, an explanation is given for the fermionic case. + +Script +---------------------------------- + +User can execute all the steps explained below using a single script file ``run.sh``. +Edit some variables in the top of the script (explained later) and then run the script by + +:: + + $ ./run.sh + +If succeeded, text files containing numerical data and graphs in EPS format are generated in ``output`` directory. +There are some parameters to control the behavior of the script; + +:: + + # ========================= + file_exe="../SpM.out" + dir_plt="../plt" + plot_level=1 # 0: no plot, 1: plot major data, 2: plot all data + eps_or_pdf='eps' # 'eps' or 'pdf' (epstopdf is required) + # ========================= + +The fist one must be modified, at least, before running. + +Make input files +---------------------------------- + +#. Green's function + + Input data for the imaginary time Green's function :math:`G(\tau)` should be provided on a linearly discretized mesh between :math:`\tau=0` and :math:`\beta`. + The file ``Gtau.in`` contains sample data in the following manner + + :: + + #beta=100.000000 + #omega_max=4.000000 + 0.0 -0.500733991018 -0.499999977255 + 0.00025 -0.490129692246 -0.489780138726 + 0.0005 -0.481350067927 -0.47987901351 + 0.00075 -0.471476482364 -0.470285052549 + 0.001 -0.46176235397 -0.460987168435 + ... + 0.999 -0.461487347988 -0.460987168435 + 0.99925 -0.467256984842 -0.470285052549 + 0.9995 -0.479129683576 -0.47987901351 + 0.99975 -0.490428417896 -0.489780138726 + 1.0 -0.499812460744 -0.499999977255 + + Lines beginning with '#' are skipped. + There are 3 columns, which corresponds to :math:`\tau_i/\beta`, :math:`G^{\rm input}(\tau_i)`, and :math:`G^{\rm exact}(\tau_i)`. + ``SpM`` program actually reads only one column, in this case, the second column containing :math:`G^{\rm input}(\tau_i)`. + User is requested to specify with ``column`` parameter which column should be read. + Note that the value of :math:`G(\tau=\beta)` needs to be given in order to evaluate the integral intensity of :math:`\rho(\omega)`. It means that the integrated intensity is not necessarily be equal to 1 (0 for off-diagonal Green's function and some finite value for the self energy). + +#. Parameters + + Parameters are passed to the ``SpM`` program by a text file. + The file ``param.in`` shows a setting used in obtaining the demonstrative results; + + :: + + # INPUT/OUTPUT + statistics="fermion" + beta=100 + filein_G="Gtau.in" + column=1 + fileout_spec="spectrum.dat" + # OMEGA + Nomega=1001 + omegamin=-4 + omegamax=4 + # ADMM + lambdalogbegin=2 + lambdalogend=-6 + tolerance=1e-10 + maxiteration=1000 + + As in Gtau.in, lines beginning with '#' are skipped. + For details of each parameter and further optional parameters, see :ref:`inputfiles` + + +Run SpM +------- + +In the directory ``samples/fermion/``, just type the command + +:: + + $ build_directory/src/SpM.out -i param.in + +Results +------- + +Results are stored as ordinary text format in ``output`` directory. +See :ref:`outputfiles` for details of each file. + + +Plot +------------- + +User can generate graphs either in EPS format or in PDF format using gnuplot. +Move into directory ``output``, and type + +:: + + gnuplot path_to_SpM/samples/plt/* + +to generate EPS files of main results. If you prefer PDF format, put ``flag_pdf=1`` option as + +:: + + gnuplot -e flag_pdf=1 path_to_SpM/samples/plt/* + +Note that it requires ``epstopdf`` program in the PATH. +Next, move into directory ``lambda_opt`` and type + +:: + + gnuplot path_to_SpM/samples/plt/lambda_opt/* + +Detailed results for the optimal value of :math:`\lambda` are then plotted. +Again, the option ``flag_pdf=1`` may be put to obtain PDF files. + +Let us look at some graphs below. + +- *spectrum.eps* + + The final result for the spectrum :math:`\rho(\omega)` is given in the file ``output/spectrum.eps``. + + .. image:: figs/spectrum.jpg + + The red line shows the computed spectrum, and the blue line shows the exact spectrum, which is provided in the file ``Gtau.in.dos`` (not output of the ``SpM`` program). + +- *find_lambda_opt.eps* + + User should check how the regularization parameter :math:`\lambda` is determined and whether the choice is reasonable. + Loot at the file ``output/find_lambda_opt.eps`` + + .. image:: figs/find_lambda_opt.jpg + + The peak position gives the optimal choice :math:`\lambda_{\rm opt}=10^{-1.8}`. + If the peak is not clear, the choice might not be reasonable. In this case, accuracy of the input should be improved. + +- *y_sv-log.eps* + + One can see how much information in the input data is used for constructing the spectrum. + See the file ``output/lambda_opt/y_sv-log.eps`` + + .. image:: figs/y_sv-log.jpg + + The light blue points show the input data :math:`G'_l` transformed into the SVD basis, and red circles are data used in computing :math:`\rho(\omega)` above. + The blue points show, for comparison, the exact :math:`G'_l` without noise, which is provided in the file ``Gtau.in.sv_basis`` (not output of the ``SpM`` program). diff --git a/docs/manual/source/_build/html/_sources/index.rst.txt b/docs/manual/source/_build/html/_sources/index.rst.txt new file mode 100644 index 0000000..590459d --- /dev/null +++ b/docs/manual/source/_build/html/_sources/index.rst.txt @@ -0,0 +1,40 @@ +.. SpM documentation master file, created by + sphinx-quickstart on Thu Aug 10 10:08:31 2017. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +Welcome to SpM's documentation! +=============================== +This is a documentation of Sparse Modeling (SpM) tool for analytical continuation. + +What is SpM ? +------------- +A sparse-modeling tool for computing the spectral function from the imaginary-time Green function. It removes statistical errors in quantum Monte Carlo data, and performs a stable analytical continuation. The obtained spectral function fulfills the non-negativity and the sum rule. The computation is fast and free from tuning parameters. + +License +-------------- +This package is distributed under GNU General Public License version 3 (GPL v3). + +We kindly ask you to cite the article + + J. Otsuki, M. Ohzeki, H. Shinaoka, K. Yoshimi, + "*Sparse modeling approach to analytical continuation of imaginary-time quantum Monte Carlo data*" + `Phys. Rev. E 95, 061302(R) (2017) `_. + +in publications that includes results obtained using this package. + + +Contents +-------- +.. toctree:: + :maxdepth: 2 + :numbered: + :glob: + + docs/install.rst + docs/tutorials.rst + docs/algorithm.rst + docs/function.rst + docs/inputfile.rst + docs/outputfile.rst + diff --git a/docs/manual/source/_build/html/_static/SpM.png b/docs/manual/source/_build/html/_static/SpM.png new file mode 100644 index 0000000000000000000000000000000000000000..b8b1117f6f99753f437714000f52c79633d717ee GIT binary patch literal 3593 zcmV+k4)*bhP)|Kv>;yx2~m^9!k!B+w)!6|{10410bpaduZN`Mle1SkQQke`)redmuecvo7< zvUzXDle-MTmb_2<{H2>>7@001B)0DzDH@G^LNdn>Bz zR9)Y6?W!wt`c9-h06Ey7vg+D2gvDG1Xrwm32hsvfEn&!LNO^Geqaq$Ncfm1a z%m?8^-VtN|MD-gOJA7ULyL#3wjFVk`hjVr9%~d`7wdH=N>c{lS-!C}C1|9}84uU`V96BkP3sCE#RE_yFL~5o^ z1@hD-mtmu<#;-8p?;gnr#7)R1DYF5PF(pe&W8uz&5|SdO2b+}u7*t?m+7T$@YKxt1 zel8$3it;=SMo5Z2tp+GxB`D^9rGFxzyNDN_!qF0Vw3zuNB;{r10~M|-_~n14e@1Rv z%wr>?W@^sbkDOSNF(0sSfsp-a$QttqE2n&EZV@5hg=E|)y__RmCe*ur;#}8Sc%JCl z^=I%)Y;yVV`&QL=moXG+(BdGq0!rq*$i6pVlGJF{!XYn|(lgu~pJRr+qPOJuDG87~ zS03Ng;+cztpKm{@7Y0~9bd!j=@+2CKc}W6QPrNuGcLFk|7Nj%_Y}VuWq|aLj7pj{o zA!(9rg?}DlX;TKGiRSns6x7T@UQPokjoaKQ1@7OanuJ_g2>mIP;FI=duW}%n*i8^y z9`sIbw!$8;6j1Vv2M4QhszS)bu72?#SrL>bHwPhmt>?VCypww^8<{Cy*Gi`jixoR= z(Uta)=8Jyz8`}000ipvpvVCj`7MkBJEh4W|--Dtpfsz7%uX~xM|8wP>9i^UhBuXVI z4wK*e8d=DHb=P&^KzjmF5Wq+!QA%qaNj~uZh%fl;vKq(PF{jN>8$D6!(rr}P5Vi&> zMc?KxVzP35^Qm$qa}`M-XQyQLZk&8bVzk8JEd~;NxCzoKU7`Av>Dv|zAviTYmqkQK zl_;V`0L4qbSSZ&Q#<*4*#O4rE64JdyB0M*(XJxK@vnNqso5*xq@_9Odg!#!+F8h)w z2M2}kWu~ZYPp&~7iJ!EN#NXlcZs9uNxzsN(!3b&-SZg~CKj%c9vHNJR$PMV6nXb`U z805(k#XYtZ6XAZJX;8ISlqct)4wsPEh#E$51VhsaPw#3WPl@u@okn1#kM@e(d$Ei4 zDaa$KB`y?$Xk0Ruf`#L%JeU6xQdmqJQ}?#55@{u?ZrbQk>KjHdF9Efss)lT)5E9v* z)Q!S>$`bx|!KEN=r@nJ&;%Kf$)8daNaoMr*ZIuP~l!V`kwxj+nh^gU z&{gzUXt8m;&ph#1d?M72ndKO`&7)_w8ZuK}8HNarvF&RuT}|}cqpP9GZSU!${!=}| z`al_Mg_f2yz{3rIEggEsde@MnZxOG!2e2)fT{!Mqv1!+TQ6B$12~x#$&_+!mP5tAN2@gE{^r-T+-A)rrb0t4WS_$QCCU9K%xA(wd3w2)dF)I z*s5dRe!38`MM#ag`;o|#=vvLFLc1+n!FT0d#R7u7qjoCH86c!Pyqtqbn&VTr0&Dfk zO$E=WF;+=+3`hHM=V7g|cURSi1R>q9_L)v0VfhribS<-$qam-#W8DhA^P!f!Yabdy zJ9;H#sr=H$ZmN1OtS2qRy-%uCT9<|j>uWM)gqGQ^7qth5K`-K36%0;#ef`qq-Eg>|r3d}Qw$k{fDILv#oOtjw%@ zsDu=1$v*)cl10wAkD7rvZMVh6WR=+KfRf)Dz@6wlHXyJDnli|h#eK{#xQ&pK)nkt8 zo}l2qn=Ak!eIM(`)smT@&#JG}wo0veowTe@XQ4T=0#AZzj*>})!TOLE=DER!`P{y$ za{Lj}LaomtJbd%z&DH>xi&sL@;=`50A-0_HM#vv68RIe4Ll#Jd``Y?~F>SxoB+yYY z)e)AE6oryTqKrRz8A+@CEMh`lJrh!*!F-$OM@3(CKLo*>C^*&kf_!+vGcd-4*n)H# zL@GTKvh+?!TAgeMkrOdbR6PNV3)g`Wa_?EA`zIt};W+sw+P9&TqY4xf3<6QrC{xt` z8Ud+$H(71A|2#w88vjD%OdUBOBA66&u#V~T z;%igxtl@922HOGvAC5pzIGSljwD2Z7AhcnEn%OrtSBJ(~$rGG$|k%mxi?kh#j;5${_w z^re9%b$*ZoLS*ZFjjO>>MNP7+-_>+5H*7blEp^IGB_dc$hoGr_`isp z+N)|#ChX`73}}q(W7Wnw4+66_#+@Dg60$joL{8&t*5@{AnR~{B-6=nEEE{y2*a)6$ zpNt!v1!ocXnbfSRpqFev&090u%D;nT$muJD^mfz2RW|adSeLiR?EHzy0i^h+I8}!90}G_-glun3{tw zXPypBozwSA4=&9V?#(@b^OX2GPTb7(p{KEPj{rZ6^{`%#2hLt>k2G&v0d_5p>(B3f zB$LVP_?^hpCZW!?sEM;`)ZWekUM5Py z?ezr-&w9vSfRKHX5%3t5pC}1;h!ykbn@|Her=$+|mje(&5K>t~#ze>v4T579G(*6z ziilrh6T%lk8Iq9GSOzpwLHkJqnPm6~=6Gz#LJ~4neyG^V!X1avQp*6(vnC=g0-31n zd*B$teoR*G%|e`}924o!RPOiYft*GgE~y+03IFjB(ycJSqDId|WWDS(5bl;QeNS$a zBn>liP0w01zN=u6ul}x~?bOJUarW-%)nt8FRK@eeUyDdd;dtqJa<3g^ZO*|G@(K;9 z=|hTy*~h*_+JYqc-lJzijyCWiG>;K!mCeI7G$9REn#a&tY(aAECzEPTECg}<5C*oK zHKc72<=}dnGVQrEHKo#`YuC-G83>8ghX?_vPsl8G?`c8zF) zkh1Z?wDr*LWh{i$sANe&NYVHZ-14x9Peww_|3{~SM3yF#ME@rW>bRssbry-=$XmS?$ya@77uk-lCS_n!ZuYo;6muC8CPJ1G3GZ#X6)JfOpRVKDcNc1&R=~0Jv^cp0o#detIBDzi@&% z1ps?LyZZ5w{2Tl-TJgiis(Qz?0)VqGxzvg=XlO`8-2gxd6A%pmKu7=pKu7=>C?P3A z#33cN;Q&AY4QbGo)HH-e!W;ks5pvm~0a4os0HFv;WNS-&nsTx)^fw{u5vTdk#?4Onts% P00000NkvXXu0mjf2s^PA literal 0 HcmV?d00001 diff --git a/docs/manual/source/_build/html/_static/ajax-loader.gif b/docs/manual/source/_build/html/_static/ajax-loader.gif new file mode 100644 index 0000000000000000000000000000000000000000..61faf8cab23993bd3e1560bff0668bd628642330 GIT binary patch literal 673 zcmZ?wbhEHb6krfw_{6~Q|Nno%(3)e{?)x>&1u}A`t?OF7Z|1gRivOgXi&7IyQd1Pl zGfOfQ60;I3a`F>X^fL3(@);C=vM_KlFfb_o=k{|A33hf2a5d61U}gjg=>Rd%XaNQW zW@Cw{|b%Y*pl8F?4B9 zlo4Fz*0kZGJabY|>}Okf0}CCg{u4`zEPY^pV?j2@h+|igy0+Kz6p;@SpM4s6)XEMg z#3Y4GX>Hjlml5ftdH$4x0JGdn8~MX(U~_^d!Hi)=HU{V%g+mi8#UGbE-*ao8f#h+S z2a0-5+vc7MU$e-NhmBjLIC1v|)9+Im8x1yacJ7{^tLX(ZhYi^rpmXm0`@ku9b53aN zEXH@Y3JaztblgpxbJt{AtE1ad1Ca>{v$rwwvK(>{m~Gf_=-Ro7Fk{#;i~+{{>QtvI yb2P8Zac~?~=sRA>$6{!(^3;ZP0TPFR(G_-UDU(8Jl0?(IXu$~#4A!880|o%~Al1tN literal 0 HcmV?d00001 diff --git a/docs/manual/source/_build/html/_static/alabaster.css b/docs/manual/source/_build/html/_static/alabaster.css new file mode 100644 index 0000000..1d1dc4d --- /dev/null +++ b/docs/manual/source/_build/html/_static/alabaster.css @@ -0,0 +1,693 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +@import url("basic.css"); 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+ margin-right: auto; +} + +table.contentstable p.biglink { + line-height: 150%; +} + +a.biglink { + font-size: 1.3em; +} + +span.linkdescr { + font-style: italic; + padding-top: 5px; + font-size: 90%; +} + +/* -- general index --------------------------------------------------------- */ + +table.indextable { + width: 100%; +} + +table.indextable td { + text-align: left; + vertical-align: top; +} + +table.indextable ul { + margin-top: 0; + margin-bottom: 0; + list-style-type: none; +} + +table.indextable > tbody > tr > td > ul { + padding-left: 0em; +} + +table.indextable tr.pcap { + height: 10px; +} + +table.indextable tr.cap { + margin-top: 10px; + background-color: #f2f2f2; +} + +img.toggler { + margin-right: 3px; + margin-top: 3px; + cursor: pointer; +} + +div.modindex-jumpbox { + border-top: 1px solid #ddd; + border-bottom: 1px solid #ddd; + margin: 1em 0 1em 0; + padding: 0.4em; +} + +div.genindex-jumpbox { + border-top: 1px solid #ddd; + border-bottom: 1px solid #ddd; + margin: 1em 0 1em 0; + padding: 0.4em; +} + +/* -- domain module index --------------------------------------------------- */ + +table.modindextable td { + padding: 2px; + border-collapse: collapse; +} + +/* -- general body styles --------------------------------------------------- */ + +div.body { + min-width: 450px; + max-width: 800px; +} + +div.body p, div.body dd, div.body li, div.body blockquote { + -moz-hyphens: auto; + -ms-hyphens: auto; + -webkit-hyphens: auto; + hyphens: auto; +} + +a.headerlink { + visibility: hidden; +} + +h1:hover > a.headerlink, +h2:hover > a.headerlink, +h3:hover > a.headerlink, +h4:hover > a.headerlink, +h5:hover > a.headerlink, +h6:hover > a.headerlink, +dt:hover > a.headerlink, +caption:hover > a.headerlink, +p.caption:hover > a.headerlink, +div.code-block-caption:hover > a.headerlink { + visibility: visible; +} + +div.body p.caption { + text-align: inherit; +} + +div.body td { + text-align: left; +} + +.first { + margin-top: 0 !important; +} + +p.rubric { + margin-top: 30px; + font-weight: bold; +} + +img.align-left, .figure.align-left, object.align-left { + clear: left; + float: left; + margin-right: 1em; +} + +img.align-right, .figure.align-right, object.align-right { + clear: right; + float: right; + margin-left: 1em; +} + +img.align-center, .figure.align-center, object.align-center { + display: block; + margin-left: auto; + margin-right: auto; +} + +.align-left { + text-align: left; +} + +.align-center { + text-align: center; +} + +.align-right { + text-align: right; +} + +/* -- sidebars -------------------------------------------------------------- */ + +div.sidebar { + margin: 0 0 0.5em 1em; + border: 1px solid #ddb; + padding: 7px 7px 0 7px; + background-color: #ffe; + width: 40%; + float: right; +} + +p.sidebar-title { + font-weight: bold; +} + +/* -- topics ---------------------------------------------------------------- */ + +div.topic { + border: 1px solid #ccc; + padding: 7px 7px 0 7px; + margin: 10px 0 10px 0; +} + +p.topic-title { + font-size: 1.1em; + font-weight: bold; + margin-top: 10px; +} + +/* -- admonitions ----------------------------------------------------------- */ + +div.admonition { + margin-top: 10px; + margin-bottom: 10px; + padding: 7px; +} + +div.admonition dt { + font-weight: bold; +} + +div.admonition dl { + margin-bottom: 0; +} + +p.admonition-title { + margin: 0px 10px 5px 0px; + font-weight: bold; +} + +div.body p.centered { + text-align: center; + margin-top: 25px; +} + +/* -- tables ---------------------------------------------------------------- */ + +table.docutils { + border: 0; + border-collapse: collapse; +} + +table.align-center { + margin-left: auto; + margin-right: auto; +} + +table caption span.caption-number { + font-style: italic; +} + +table caption span.caption-text { +} + +table.docutils td, table.docutils th { + padding: 1px 8px 1px 5px; + border-top: 0; + border-left: 0; + border-right: 0; + border-bottom: 1px solid #aaa; +} + +table.footnote td, table.footnote th { + border: 0 !important; +} + +th { + text-align: left; + padding-right: 5px; +} + +table.citation { + border-left: solid 1px gray; + margin-left: 1px; +} + +table.citation td { + border-bottom: none; +} + +/* -- figures --------------------------------------------------------------- */ + +div.figure { + margin: 0.5em; + padding: 0.5em; +} + +div.figure p.caption { + padding: 0.3em; +} + +div.figure p.caption span.caption-number { + font-style: italic; +} + +div.figure p.caption span.caption-text { +} + +/* -- field list styles ----------------------------------------------------- */ + +table.field-list td, table.field-list th { + border: 0 !important; +} + +.field-list ul { + margin: 0; + padding-left: 1em; +} + +.field-list p { + margin: 0; +} + +.field-name { + -moz-hyphens: manual; + -ms-hyphens: manual; + -webkit-hyphens: manual; + hyphens: manual; +} + +/* -- other body styles ----------------------------------------------------- */ + +ol.arabic { + list-style: decimal; +} + +ol.loweralpha { + list-style: lower-alpha; +} + +ol.upperalpha { + list-style: upper-alpha; +} + +ol.lowerroman { + list-style: lower-roman; +} + +ol.upperroman { + list-style: upper-roman; +} + +dl { + margin-bottom: 15px; +} + +dd p { + margin-top: 0px; +} + +dd ul, dd table { + margin-bottom: 10px; +} + +dd { + margin-top: 3px; + margin-bottom: 10px; + margin-left: 30px; +} + +dt:target, span.highlighted { + background-color: #fbe54e; +} + +rect.highlighted { + fill: #fbe54e; +} + +dl.glossary dt { + font-weight: bold; + font-size: 1.1em; +} + +.optional { + font-size: 1.3em; +} + +.sig-paren { + font-size: larger; +} + +.versionmodified { + font-style: italic; +} + +.system-message { + background-color: #fda; + padding: 5px; + border: 3px solid red; +} + +.footnote:target { + background-color: #ffa; +} + +.line-block { + display: block; + margin-top: 1em; + margin-bottom: 1em; +} + +.line-block .line-block { + margin-top: 0; + margin-bottom: 0; + margin-left: 1.5em; +} + +.guilabel, .menuselection { + font-family: sans-serif; +} + +.accelerator { + text-decoration: underline; +} + +.classifier { + font-style: oblique; +} + +abbr, acronym { + border-bottom: dotted 1px; + cursor: help; +} + +/* -- code displays --------------------------------------------------------- */ + +pre { + overflow: auto; + overflow-y: hidden; /* fixes display issues on Chrome browsers */ +} + +span.pre { + -moz-hyphens: none; + -ms-hyphens: none; + -webkit-hyphens: none; + hyphens: none; +} + +td.linenos pre { + padding: 5px 0px; + border: 0; + background-color: transparent; + color: #aaa; +} + +table.highlighttable { + margin-left: 0.5em; +} + +table.highlighttable td { + padding: 0 0.5em 0 0.5em; +} + +div.code-block-caption { + padding: 2px 5px; + font-size: small; +} + +div.code-block-caption code { + background-color: transparent; +} + +div.code-block-caption + div > div.highlight > pre { + margin-top: 0; +} + +div.code-block-caption span.caption-number { + padding: 0.1em 0.3em; + font-style: italic; +} + +div.code-block-caption span.caption-text { +} + +div.literal-block-wrapper { + padding: 1em 1em 0; 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+ +/** + * make the code below compatible with browsers without + * an installed firebug like debugger +if (!window.console || !console.firebug) { + var names = ["log", "debug", "info", "warn", "error", "assert", "dir", + "dirxml", "group", "groupEnd", "time", "timeEnd", "count", "trace", + "profile", "profileEnd"]; + window.console = {}; + for (var i = 0; i < names.length; ++i) + window.console[names[i]] = function() {}; +} + */ + +/** + * small helper function to urldecode strings + */ +jQuery.urldecode = function(x) { + return decodeURIComponent(x).replace(/\+/g, ' '); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && !jQuery(node.parentNode).hasClass(className)) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var bbox = span.getBBox(); + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + var parentOfText = node.parentNode.parentNode; + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} + +/** + * Small JavaScript module for the documentation. + */ +var Documentation = { + + init : function() { + this.fixFirefoxAnchorBug(); + this.highlightSearchWords(); + this.initIndexTable(); + + }, + + /** + * i18n support + */ + TRANSLATIONS : {}, + PLURAL_EXPR : function(n) { return n === 1 ? 0 : 1; }, + LOCALE : 'unknown', + + // gettext and ngettext don't access this so that the functions + // can safely bound to a different name (_ = Documentation.gettext) + gettext : function(string) { + var translated = Documentation.TRANSLATIONS[string]; + if (typeof translated === 'undefined') + return string; + return (typeof translated === 'string') ? translated : translated[0]; + }, + + ngettext : function(singular, plural, n) { + var translated = Documentation.TRANSLATIONS[singular]; + if (typeof translated === 'undefined') + return (n == 1) ? singular : plural; + return translated[Documentation.PLURALEXPR(n)]; + }, + + addTranslations : function(catalog) { + for (var key in catalog.messages) + this.TRANSLATIONS[key] = catalog.messages[key]; + this.PLURAL_EXPR = new Function('n', 'return +(' + catalog.plural_expr + ')'); + this.LOCALE = catalog.locale; + }, + + /** + * add context elements like header anchor links + */ + addContextElements : function() { + $('div[id] > :header:first').each(function() { + $('\u00B6'). + attr('href', '#' + this.id). + attr('title', _('Permalink to this headline')). + appendTo(this); + }); + $('dt[id]').each(function() { + $('\u00B6'). + attr('href', '#' + this.id). + attr('title', _('Permalink to this definition')). + appendTo(this); + }); + }, + + /** + * workaround a firefox stupidity + * see: https://bugzilla.mozilla.org/show_bug.cgi?id=645075 + */ + fixFirefoxAnchorBug : function() { + if (document.location.hash && $.browser.mozilla) + window.setTimeout(function() { + document.location.href += ''; + }, 10); + }, + + /** + * highlight the search words provided in the url in the text + */ + highlightSearchWords : function() { + var params = $.getQueryParameters(); + var terms = (params.highlight) ? params.highlight[0].split(/\s+/) : []; + if (terms.length) { + var body = $('div.body'); + if (!body.length) { + body = $('body'); + } + window.setTimeout(function() { + $.each(terms, function() { + body.highlightText(this.toLowerCase(), 'highlighted'); + }); + }, 10); + $('

' + _('Hide Search Matches') + '

') + .appendTo($('#searchbox')); + } + }, + + /** + * init the domain index toggle buttons + */ + initIndexTable : function() { + var togglers = $('img.toggler').click(function() { + var src = $(this).attr('src'); + var idnum = $(this).attr('id').substr(7); + $('tr.cg-' + idnum).toggle(); + if (src.substr(-9) === 'minus.png') + $(this).attr('src', src.substr(0, src.length-9) + 'plus.png'); + else + $(this).attr('src', src.substr(0, src.length-8) + 'minus.png'); + }).css('display', ''); + if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) { + togglers.click(); + } + }, + + /** + * helper function to hide the search marks again + */ + hideSearchWords : function() { + $('#searchbox .highlight-link').fadeOut(300); + $('span.highlighted').removeClass('highlighted'); + }, + + /** + * make the url absolute + */ + makeURL : function(relativeURL) { + return DOCUMENTATION_OPTIONS.URL_ROOT + '/' + relativeURL; + }, + + /** + * get the current relative url + */ + getCurrentURL : function() { + var path = document.location.pathname; + var parts = path.split(/\//); + $.each(DOCUMENTATION_OPTIONS.URL_ROOT.split(/\//), function() { + if (this === '..') + parts.pop(); + }); + var url = parts.join('/'); + return path.substring(url.lastIndexOf('/') + 1, path.length - 1); + }, + + initOnKeyListeners: function() { + $(document).keyup(function(event) { + var activeElementType = document.activeElement.tagName; + // don't navigate when in search box or textarea + if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT') { + switch (event.keyCode) { + case 37: // left + var prevHref = $('link[rel="prev"]').prop('href'); + if (prevHref) { + window.location.href = prevHref; + return false; + } + case 39: // right + var nextHref = $('link[rel="next"]').prop('href'); + if (nextHref) { + window.location.href = nextHref; + return false; + } + } + } + }); + } +}; + +// quick alias for translations +_ = Documentation.gettext; + +$(document).ready(function() { + Documentation.init(); +}); \ No newline at end of file diff --git a/docs/manual/source/_build/html/_static/documentation_options.js b/docs/manual/source/_build/html/_static/documentation_options.js new file mode 100644 index 0000000..c0335db --- /dev/null +++ b/docs/manual/source/_build/html/_static/documentation_options.js @@ -0,0 +1,9 @@ +var DOCUMENTATION_OPTIONS = { + URL_ROOT: '', + VERSION: '1.0.0', + LANGUAGE: 'None', + COLLAPSE_INDEX: false, + FILE_SUFFIX: '.html', + HAS_SOURCE: true, + SOURCELINK_SUFFIX: '.txt' +}; \ No newline at end of file diff --git a/docs/manual/source/_build/html/_static/down-pressed.png b/docs/manual/source/_build/html/_static/down-pressed.png new file mode 100644 index 0000000000000000000000000000000000000000..5756c8cad8854722893dc70b9eb4bb0400343a39 GIT binary patch literal 222 zcmeAS@N?(olHy`uVBq!ia0vp^0wB!61|;P_|4#%`OFdm2Ln;`PZ^+1>KjR?B@S0W7 z%OS_REiHONoJ6{+Ks@6k3590|7k9F+ddB6!zw3#&!aw#S`x}3V3&=A(a#84O-&F7T z^k3tZB;&iR9siw0|F|E|DAL<8r-F4!1H-;1{e*~yAKZN5f0|Ei6yUmR#Is)EM(Po_ zi`qJR6|P<~+)N+kSDgL7AjdIC_!O7Q?eGb+L+qOjm{~LLinM4NHn7U%HcK%uoMYO5 VJ~8zD2B3o(JYD@<);T3K0RV0%P>BEl literal 0 HcmV?d00001 diff --git a/docs/manual/source/_build/html/_static/down.png b/docs/manual/source/_build/html/_static/down.png new file mode 100644 index 0000000000000000000000000000000000000000..1b3bdad2ceffae91cee61b32f3295f9bbe646e48 GIT binary patch literal 202 zcmeAS@N?(olHy`uVBq!ia0vp^0wB!60wlNoGJgf6CVIL!hEy=F?b*7pIY7kW{q%Rg zx!yQ<9v8bmJwa`TQk7YSw}WVQ()mRdQ;TC;* literal 0 HcmV?d00001 diff --git a/docs/manual/source/_build/html/_static/file.png b/docs/manual/source/_build/html/_static/file.png new file mode 100644 index 0000000000000000000000000000000000000000..a858a410e4faa62ce324d814e4b816fff83a6fb3 GIT binary patch literal 286 zcmV+(0pb3MP)s`hMrGg#P~ix$^RISR_I47Y|r1 z_CyJOe}D1){SET-^Amu_i71Lt6eYfZjRyw@I6OQAIXXHDfiX^GbOlHe=Ae4>0m)d(f|Me07*qoM6N<$f}vM^LjV8( literal 0 HcmV?d00001 diff --git a/docs/manual/source/_build/html/_static/jquery-3.1.0.js b/docs/manual/source/_build/html/_static/jquery-3.1.0.js new file mode 100644 index 0000000..f2fc274 --- /dev/null +++ b/docs/manual/source/_build/html/_static/jquery-3.1.0.js @@ -0,0 +1,10074 @@ +/*eslint-disable no-unused-vars*/ +/*! + * jQuery JavaScript Library v3.1.0 + * https://jquery.com/ + * + * Includes Sizzle.js + * https://sizzlejs.com/ + * + * Copyright jQuery Foundation and other contributors + * Released under the MIT license + * https://jquery.org/license + * + * Date: 2016-07-07T21:44Z + */ +( function( global, factory ) { + + "use strict"; + + if ( typeof module === "object" && typeof module.exports === "object" ) { + + // For CommonJS and CommonJS-like environments where a proper `window` + // is present, execute the factory and get jQuery. + // For environments that do not have a `window` with a `document` + // (such as Node.js), expose a factory as module.exports. + // This accentuates the need for the creation of a real `window`. + // e.g. var jQuery = require("jquery")(window); + // See ticket #14549 for more info. + module.exports = global.document ? + factory( global, true ) : + function( w ) { + if ( !w.document ) { + throw new Error( "jQuery requires a window with a document" ); + } + return factory( w ); + }; + } else { + factory( global ); + } + +// Pass this if window is not defined yet +} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) { + +// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1 +// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode +// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common +// enough that all such attempts are guarded in a try block. +"use strict"; + +var arr = []; + +var document = window.document; + +var getProto = Object.getPrototypeOf; + +var slice = arr.slice; + +var concat = arr.concat; + +var push = arr.push; + +var indexOf = arr.indexOf; + +var class2type = {}; + +var toString = class2type.toString; + +var hasOwn = class2type.hasOwnProperty; + +var fnToString = hasOwn.toString; + +var ObjectFunctionString = fnToString.call( Object ); + +var support = {}; + + + + function DOMEval( code, doc ) { + doc = doc || document; + + var script = doc.createElement( "script" ); + + script.text = code; + doc.head.appendChild( script ).parentNode.removeChild( script ); + } +/* global Symbol */ +// Defining this global in .eslintrc would create a danger of using the global +// unguarded in another place, it seems safer to define global only for this module + + + +var + version = "3.1.0", + + // Define a local copy of jQuery + jQuery = function( selector, context ) { + + // The jQuery object is actually just the init constructor 'enhanced' + // Need init if jQuery is called (just allow error to be thrown if not included) + return new jQuery.fn.init( selector, context ); + }, + + // Support: Android <=4.0 only + // Make sure we trim BOM and NBSP + rtrim = /^[\s\uFEFF\xA0]+|[\s\uFEFF\xA0]+$/g, + + // Matches dashed string for camelizing + rmsPrefix = /^-ms-/, + rdashAlpha = /-([a-z])/g, + + // Used by jQuery.camelCase as callback to replace() + fcamelCase = function( all, letter ) { + return letter.toUpperCase(); + }; + +jQuery.fn = jQuery.prototype = { + + // The current version of jQuery being used + jquery: version, + + constructor: jQuery, + + // The default length of a jQuery object is 0 + length: 0, + + toArray: function() { + return slice.call( this ); + }, + + // Get the Nth element in the matched element set OR + // Get the whole matched element set as a clean array + get: function( num ) { + return num != null ? + + // Return just the one element from the set + ( num < 0 ? this[ num + this.length ] : this[ num ] ) : + + // Return all the elements in a clean array + slice.call( this ); + }, + + // Take an array of elements and push it onto the stack + // (returning the new matched element set) + pushStack: function( elems ) { + + // Build a new jQuery matched element set + var ret = jQuery.merge( this.constructor(), elems ); + + // Add the old object onto the stack (as a reference) + ret.prevObject = this; + + // Return the newly-formed element set + return ret; + }, + + // Execute a callback for every element in the matched set. + each: function( callback ) { + return jQuery.each( this, callback ); + }, + + map: function( callback ) { + return this.pushStack( jQuery.map( this, function( elem, i ) { + return callback.call( elem, i, elem ); + } ) ); + }, + + slice: function() { + return this.pushStack( slice.apply( this, arguments ) ); + }, + + first: function() { + return this.eq( 0 ); + }, + + last: function() { + return this.eq( -1 ); + }, + + eq: function( i ) { + var len = this.length, + j = +i + ( i < 0 ? len : 0 ); + return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] ); + }, + + end: function() { + return this.prevObject || this.constructor(); + }, + + // For internal use only. + // Behaves like an Array's method, not like a jQuery method. + push: push, + sort: arr.sort, + splice: arr.splice +}; + +jQuery.extend = jQuery.fn.extend = function() { + var options, name, src, copy, copyIsArray, clone, + target = arguments[ 0 ] || {}, + i = 1, + length = arguments.length, + deep = false; + + // Handle a deep copy situation + if ( typeof target === "boolean" ) { + deep = target; + + // Skip the boolean and the target + target = arguments[ i ] || {}; + i++; + } + + // Handle case when target is a string or something (possible in deep copy) + if ( typeof target !== "object" && !jQuery.isFunction( target ) ) { + target = {}; + } + + // Extend jQuery itself if only one argument is passed + if ( i === length ) { + target = this; + i--; + } + + for ( ; i < length; i++ ) { + + // Only deal with non-null/undefined values + if ( ( options = arguments[ i ] ) != null ) { + + // Extend the base object + for ( name in options ) { + src = target[ name ]; + copy = options[ name ]; + + // Prevent never-ending loop + if ( target === copy ) { + continue; + } + + // Recurse if we're merging plain objects or arrays + if ( deep && copy && ( jQuery.isPlainObject( copy ) || + ( copyIsArray = jQuery.isArray( copy ) ) ) ) { + + if ( copyIsArray ) { + copyIsArray = false; + clone = src && jQuery.isArray( src ) ? src : []; + + } else { + clone = src && jQuery.isPlainObject( src ) ? src : {}; + } + + // Never move original objects, clone them + target[ name ] = jQuery.extend( deep, clone, copy ); + + // Don't bring in undefined values + } else if ( copy !== undefined ) { + target[ name ] = copy; + } + } + } + } + + // Return the modified object + return target; +}; + +jQuery.extend( { + + // Unique for each copy of jQuery on the page + expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ), + + // Assume jQuery is ready without the ready module + isReady: true, + + error: function( msg ) { + throw new Error( msg ); + }, + + noop: function() {}, + + isFunction: function( obj ) { + return jQuery.type( obj ) === "function"; + }, + + isArray: Array.isArray, + + isWindow: function( obj ) { + return obj != null && obj === obj.window; + }, + + isNumeric: function( obj ) { + + // As of jQuery 3.0, isNumeric is limited to + // strings and numbers (primitives or objects) + // that can be coerced to finite numbers (gh-2662) + var type = jQuery.type( obj ); + return ( type === "number" || type === "string" ) && + + // parseFloat NaNs numeric-cast false positives ("") + // ...but misinterprets leading-number strings, particularly hex literals ("0x...") + // subtraction forces infinities to NaN + !isNaN( obj - parseFloat( obj ) ); + }, + + isPlainObject: function( obj ) { + var proto, Ctor; + + // Detect obvious negatives + // Use toString instead of jQuery.type to catch host objects + if ( !obj || toString.call( obj ) !== "[object Object]" ) { + return false; + } + + proto = getProto( obj ); + + // Objects with no prototype (e.g., `Object.create( null )`) are plain + if ( !proto ) { + return true; + } + + // Objects with prototype are plain iff they were constructed by a global Object function + Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor; + return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString; + }, + + isEmptyObject: function( obj ) { + + /* eslint-disable no-unused-vars */ + // See https://github.com/eslint/eslint/issues/6125 + var name; + + for ( name in obj ) { + return false; + } + return true; + }, + + type: function( obj ) { + if ( obj == null ) { + return obj + ""; + } + + // Support: Android <=2.3 only (functionish RegExp) + return typeof obj === "object" || typeof obj === "function" ? + class2type[ toString.call( obj ) ] || "object" : + typeof obj; + }, + + // Evaluates a script in a global context + globalEval: function( code ) { + DOMEval( code ); + }, + + // Convert dashed to camelCase; used by the css and data modules + // Support: IE <=9 - 11, Edge 12 - 13 + // Microsoft forgot to hump their vendor prefix (#9572) + camelCase: function( string ) { + return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase ); + }, + + nodeName: function( elem, name ) { + return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase(); + }, + + each: function( obj, callback ) { + var length, i = 0; + + if ( isArrayLike( obj ) ) { + length = obj.length; + for ( ; i < length; i++ ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } else { + for ( i in obj ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } + + return obj; + }, + + // Support: Android <=4.0 only + trim: function( text ) { + return text == null ? + "" : + ( text + "" ).replace( rtrim, "" ); + }, + + // results is for internal usage only + makeArray: function( arr, results ) { + var ret = results || []; + + if ( arr != null ) { + if ( isArrayLike( Object( arr ) ) ) { + jQuery.merge( ret, + typeof arr === "string" ? + [ arr ] : arr + ); + } else { + push.call( ret, arr ); + } + } + + return ret; + }, + + inArray: function( elem, arr, i ) { + return arr == null ? -1 : indexOf.call( arr, elem, i ); + }, + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + merge: function( first, second ) { + var len = +second.length, + j = 0, + i = first.length; + + for ( ; j < len; j++ ) { + first[ i++ ] = second[ j ]; + } + + first.length = i; + + return first; + }, + + grep: function( elems, callback, invert ) { + var callbackInverse, + matches = [], + i = 0, + length = elems.length, + callbackExpect = !invert; + + // Go through the array, only saving the items + // that pass the validator function + for ( ; i < length; i++ ) { + callbackInverse = !callback( elems[ i ], i ); + if ( callbackInverse !== callbackExpect ) { + matches.push( elems[ i ] ); + } + } + + return matches; + }, + + // arg is for internal usage only + map: function( elems, callback, arg ) { + var length, value, + i = 0, + ret = []; + + // Go through the array, translating each of the items to their new values + if ( isArrayLike( elems ) ) { + length = elems.length; + for ( ; i < length; i++ ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + + // Go through every key on the object, + } else { + for ( i in elems ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + } + + // Flatten any nested arrays + return concat.apply( [], ret ); + }, + + // A global GUID counter for objects + guid: 1, + + // Bind a function to a context, optionally partially applying any + // arguments. + proxy: function( fn, context ) { + var tmp, args, proxy; + + if ( typeof context === "string" ) { + tmp = fn[ context ]; + context = fn; + fn = tmp; + } + + // Quick check to determine if target is callable, in the spec + // this throws a TypeError, but we will just return undefined. + if ( !jQuery.isFunction( fn ) ) { + return undefined; + } + + // Simulated bind + args = slice.call( arguments, 2 ); + proxy = function() { + return fn.apply( context || this, args.concat( slice.call( arguments ) ) ); + }; + + // Set the guid of unique handler to the same of original handler, so it can be removed + proxy.guid = fn.guid = fn.guid || jQuery.guid++; + + return proxy; + }, + + now: Date.now, + + // jQuery.support is not used in Core but other projects attach their + // properties to it so it needs to exist. + support: support +} ); + +if ( typeof Symbol === "function" ) { + jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ]; +} + +// Populate the class2type map +jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ), +function( i, name ) { + class2type[ "[object " + name + "]" ] = name.toLowerCase(); +} ); + +function isArrayLike( obj ) { + + // Support: real iOS 8.2 only (not reproducible in simulator) + // `in` check used to prevent JIT error (gh-2145) + // hasOwn isn't used here due to false negatives + // regarding Nodelist length in IE + var length = !!obj && "length" in obj && obj.length, + type = jQuery.type( obj ); + + if ( type === "function" || jQuery.isWindow( obj ) ) { + return false; + } + + return type === "array" || length === 0 || + typeof length === "number" && length > 0 && ( length - 1 ) in obj; +} +var Sizzle = +/*! + * Sizzle CSS Selector Engine v2.3.0 + * https://sizzlejs.com/ + * + * Copyright jQuery Foundation and other contributors + * Released under the MIT license + * http://jquery.org/license + * + * Date: 2016-01-04 + */ +(function( window ) { + +var i, + support, + Expr, + getText, + isXML, + tokenize, + compile, + select, + outermostContext, + sortInput, + hasDuplicate, + + // Local document vars + setDocument, + document, + docElem, + documentIsHTML, + rbuggyQSA, + rbuggyMatches, + matches, + contains, + + // Instance-specific data + expando = "sizzle" + 1 * new Date(), + preferredDoc = window.document, + dirruns = 0, + done = 0, + classCache = createCache(), + tokenCache = createCache(), + compilerCache = createCache(), + sortOrder = function( a, b ) { + if ( a === b ) { + hasDuplicate = true; + } + return 0; + }, + + // Instance methods + hasOwn = ({}).hasOwnProperty, + arr = [], + pop = arr.pop, + push_native = arr.push, + push = arr.push, + slice = arr.slice, + // Use a stripped-down indexOf as it's faster than native + // https://jsperf.com/thor-indexof-vs-for/5 + indexOf = function( list, elem ) { + var i = 0, + len = list.length; + for ( ; i < len; i++ ) { + if ( list[i] === elem ) { + return i; + } + } + return -1; + }, + + booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|ismap|loop|multiple|open|readonly|required|scoped", + + // Regular expressions + + // http://www.w3.org/TR/css3-selectors/#whitespace + whitespace = "[\\x20\\t\\r\\n\\f]", + + // http://www.w3.org/TR/CSS21/syndata.html#value-def-identifier + identifier = "(?:\\\\.|[\\w-]|[^\0-\\xa0])+", + + // Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors + attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace + + // Operator (capture 2) + "*([*^$|!~]?=)" + whitespace + + // "Attribute values must be CSS identifiers [capture 5] or strings [capture 3 or capture 4]" + "*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + whitespace + + "*\\]", + + pseudos = ":(" + identifier + ")(?:\\((" + + // To reduce the number of selectors needing tokenize in the preFilter, prefer arguments: + // 1. quoted (capture 3; capture 4 or capture 5) + "('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" + + // 2. simple (capture 6) + "((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" + + // 3. anything else (capture 2) + ".*" + + ")\\)|)", + + // Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter + rwhitespace = new RegExp( whitespace + "+", "g" ), + rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + whitespace + "+$", "g" ), + + rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ), + rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + "*" ), + + rattributeQuotes = new RegExp( "=" + whitespace + "*([^\\]'\"]*?)" + whitespace + "*\\]", "g" ), + + rpseudo = new RegExp( pseudos ), + ridentifier = new RegExp( "^" + identifier + "$" ), + + matchExpr = { + "ID": new RegExp( "^#(" + identifier + ")" ), + "CLASS": new RegExp( "^\\.(" + identifier + ")" ), + "TAG": new RegExp( "^(" + identifier + "|[*])" ), + "ATTR": new RegExp( "^" + attributes ), + "PSEUDO": new RegExp( "^" + pseudos ), + "CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + whitespace + + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + whitespace + + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ), + "bool": new RegExp( "^(?:" + booleans + ")$", "i" ), + // For use in libraries implementing .is() + // We use this for POS matching in `select` + "needsContext": new RegExp( "^" + whitespace + "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + + whitespace + "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" ) + }, + + rinputs = /^(?:input|select|textarea|button)$/i, + rheader = /^h\d$/i, + + rnative = /^[^{]+\{\s*\[native \w/, + + // Easily-parseable/retrievable ID or TAG or CLASS selectors + rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/, + + rsibling = /[+~]/, + + // CSS escapes + // http://www.w3.org/TR/CSS21/syndata.html#escaped-characters + runescape = new RegExp( "\\\\([\\da-f]{1,6}" + whitespace + "?|(" + whitespace + ")|.)", "ig" ), + funescape = function( _, escaped, escapedWhitespace ) { + var high = "0x" + escaped - 0x10000; + // NaN means non-codepoint + // Support: Firefox<24 + // Workaround erroneous numeric interpretation of +"0x" + return high !== high || escapedWhitespace ? + escaped : + high < 0 ? + // BMP codepoint + String.fromCharCode( high + 0x10000 ) : + // Supplemental Plane codepoint (surrogate pair) + String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 ); + }, + + // CSS string/identifier serialization + // https://drafts.csswg.org/cssom/#common-serializing-idioms + rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\x80-\uFFFF\w-]/g, + fcssescape = function( ch, asCodePoint ) { + if ( asCodePoint ) { + + // U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER + if ( ch === "\0" ) { + return "\uFFFD"; + } + + // Control characters and (dependent upon position) numbers get escaped as code points + return ch.slice( 0, -1 ) + "\\" + ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " "; + } + + // Other potentially-special ASCII characters get backslash-escaped + return "\\" + ch; + }, + + // Used for iframes + // See setDocument() + // Removing the function wrapper causes a "Permission Denied" + // error in IE + unloadHandler = function() { + setDocument(); + }, + + disabledAncestor = addCombinator( + function( elem ) { + return elem.disabled === true; + }, + { dir: "parentNode", next: "legend" } + ); + +// Optimize for push.apply( _, NodeList ) +try { + push.apply( + (arr = slice.call( preferredDoc.childNodes )), + preferredDoc.childNodes + ); + // Support: Android<4.0 + // Detect silently failing push.apply + arr[ preferredDoc.childNodes.length ].nodeType; +} catch ( e ) { + push = { apply: arr.length ? + + // Leverage slice if possible + function( target, els ) { + push_native.apply( target, slice.call(els) ); + } : + + // Support: IE<9 + // Otherwise append directly + function( target, els ) { + var j = target.length, + i = 0; + // Can't trust NodeList.length + while ( (target[j++] = els[i++]) ) {} + target.length = j - 1; + } + }; +} + +function Sizzle( selector, context, results, seed ) { + var m, i, elem, nid, match, groups, newSelector, + newContext = context && context.ownerDocument, + + // nodeType defaults to 9, since context defaults to document + nodeType = context ? context.nodeType : 9; + + results = results || []; + + // Return early from calls with invalid selector or context + if ( typeof selector !== "string" || !selector || + nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) { + + return results; + } + + // Try to shortcut find operations (as opposed to filters) in HTML documents + if ( !seed ) { + + if ( ( context ? context.ownerDocument || context : preferredDoc ) !== document ) { + setDocument( context ); + } + context = context || document; + + if ( documentIsHTML ) { + + // If the selector is sufficiently simple, try using a "get*By*" DOM method + // (excepting DocumentFragment context, where the methods don't exist) + if ( nodeType !== 11 && (match = rquickExpr.exec( selector )) ) { + + // ID selector + if ( (m = match[1]) ) { + + // Document context + if ( nodeType === 9 ) { + if ( (elem = context.getElementById( m )) ) { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( elem.id === m ) { + results.push( elem ); + return results; + } + } else { + return results; + } + + // Element context + } else { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( newContext && (elem = newContext.getElementById( m )) && + contains( context, elem ) && + elem.id === m ) { + + results.push( elem ); + return results; + } + } + + // Type selector + } else if ( match[2] ) { + push.apply( results, context.getElementsByTagName( selector ) ); + return results; + + // Class selector + } else if ( (m = match[3]) && support.getElementsByClassName && + context.getElementsByClassName ) { + + push.apply( results, context.getElementsByClassName( m ) ); + return results; + } + } + + // Take advantage of querySelectorAll + if ( support.qsa && + !compilerCache[ selector + " " ] && + (!rbuggyQSA || !rbuggyQSA.test( selector )) ) { + + if ( nodeType !== 1 ) { + newContext = context; + newSelector = selector; + + // qSA looks outside Element context, which is not what we want + // Thanks to Andrew Dupont for this workaround technique + // Support: IE <=8 + // Exclude object elements + } else if ( context.nodeName.toLowerCase() !== "object" ) { + + // Capture the context ID, setting it first if necessary + if ( (nid = context.getAttribute( "id" )) ) { + nid = nid.replace( rcssescape, fcssescape ); + } else { + context.setAttribute( "id", (nid = expando) ); + } + + // Prefix every selector in the list + groups = tokenize( selector ); + i = groups.length; + while ( i-- ) { + groups[i] = "#" + nid + " " + toSelector( groups[i] ); + } + newSelector = groups.join( "," ); + + // Expand context for sibling selectors + newContext = rsibling.test( selector ) && testContext( context.parentNode ) || + context; + } + + if ( newSelector ) { + try { + push.apply( results, + newContext.querySelectorAll( newSelector ) + ); + return results; + } catch ( qsaError ) { + } finally { + if ( nid === expando ) { + context.removeAttribute( "id" ); + } + } + } + } + } + } + + // All others + return select( selector.replace( rtrim, "$1" ), context, results, seed ); +} + +/** + * Create key-value caches of limited size + * @returns {function(string, object)} Returns the Object data after storing it on itself with + * property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength) + * deleting the oldest entry + */ +function createCache() { + var keys = []; + + function cache( key, value ) { + // Use (key + " ") to avoid collision with native prototype properties (see Issue #157) + if ( keys.push( key + " " ) > Expr.cacheLength ) { + // Only keep the most recent entries + delete cache[ keys.shift() ]; + } + return (cache[ key + " " ] = value); + } + return cache; +} + +/** + * Mark a function for special use by Sizzle + * @param {Function} fn The function to mark + */ +function markFunction( fn ) { + fn[ expando ] = true; + return fn; +} + +/** + * Support testing using an element + * @param {Function} fn Passed the created element and returns a boolean result + */ +function assert( fn ) { + var el = document.createElement("fieldset"); + + try { + return !!fn( el ); + } catch (e) { + return false; + } finally { + // Remove from its parent by default + if ( el.parentNode ) { + el.parentNode.removeChild( el ); + } + // release memory in IE + el = null; + } +} + +/** + * Adds the same handler for all of the specified attrs + * @param {String} attrs Pipe-separated list of attributes + * @param {Function} handler The method that will be applied + */ +function addHandle( attrs, handler ) { + var arr = attrs.split("|"), + i = arr.length; + + while ( i-- ) { + Expr.attrHandle[ arr[i] ] = handler; + } +} + +/** + * Checks document order of two siblings + * @param {Element} a + * @param {Element} b + * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b + */ +function siblingCheck( a, b ) { + var cur = b && a, + diff = cur && a.nodeType === 1 && b.nodeType === 1 && + a.sourceIndex - b.sourceIndex; + + // Use IE sourceIndex if available on both nodes + if ( diff ) { + return diff; + } + + // Check if b follows a + if ( cur ) { + while ( (cur = cur.nextSibling) ) { + if ( cur === b ) { + return -1; + } + } + } + + return a ? 1 : -1; +} + +/** + * Returns a function to use in pseudos for input types + * @param {String} type + */ +function createInputPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for buttons + * @param {String} type + */ +function createButtonPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return (name === "input" || name === "button") && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for :enabled/:disabled + * @param {Boolean} disabled true for :disabled; false for :enabled + */ +function createDisabledPseudo( disabled ) { + // Known :disabled false positives: + // IE: *[disabled]:not(button, input, select, textarea, optgroup, option, menuitem, fieldset) + // not IE: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable + return function( elem ) { + + // Check form elements and option elements for explicit disabling + return "label" in elem && elem.disabled === disabled || + "form" in elem && elem.disabled === disabled || + + // Check non-disabled form elements for fieldset[disabled] ancestors + "form" in elem && elem.disabled === false && ( + // Support: IE6-11+ + // Ancestry is covered for us + elem.isDisabled === disabled || + + // Otherwise, assume any non-