zhangyiss/gctl_optimization
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

initial upload

Browse Source
This commit is contained in:
张壹 2024-09-10 20:04:47 +08:00
parent 12b778cd3e
commit b4b4275576
40 changed files with 8751 additions and 35 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

37
.gitignore vendored
View File

@ -1,34 +1,3 @@
# ---> C++ .DS_Store
# Prerequisites build/
*.d .vscode/
# Compiled Object files
*.slo
*.lo
*.o
*.obj
# Precompiled Headers
*.gch
*.pch
# Compiled Dynamic libraries
*.so
*.dylib
*.dll
# Fortran module files
*.mod
*.smod
# Compiled Static libraries
*.lai
*.la
*.a
*.lib
# Executables
*.exe
*.out
*.app

28
CMakeLists.txt Normal file
View File

@ -0,0 +1,28 @@
cmake_minimum_required(VERSION 3.15.2)
# 设置项目名称与语言
project(GCTL_OPTIMIZATION VERSION 1.0)
# 添加配置配件编写的函数
include(CMakePackageConfigHelpers)
message(STATUS "Platform: " ${CMAKE_HOST_SYSTEM_NAME})
message(STATUS "Install prefix: " ${CMAKE_INSTALL_PREFIX})
message(STATUS "Processor: " ${CMAKE_HOST_SYSTEM_PROCESSOR})
option(GCTL_OPTIMIZATION_TOML "Use the TOML library" ON)
message(STATUS "[GCTL_OPTIMIZATION] Use the TOML library: " ${GCTL_OPTIMIZATION_TOML})
find_package(GCTL REQUIRED)
include_directories(${GCTL_INC_DIR})
# 加入一个头文件配置，让cmake对源码进行操作
configure_file(
"${PROJECT_SOURCE_DIR}/config.h.in"
"${PROJECT_SOURCE_DIR}/lib/optimization/gctl_optimization_config.h"
)
# 添加库源文件地址
add_subdirectory(lib)
# 去掉注释编译示例
add_subdirectory(example)

25
GCTL_OPTIMIZATIONConfig.cmake.in Normal file
View File

@ -0,0 +1,25 @@
@PACKAGE_INIT@
set(@PROJECT_NAME@_VERSION "@PROJECT_VERSION@")
set_and_check(@PROJECT_NAME@_INSTALL_PREFIX "${PACKAGE_PREFIX_DIR}")
set_and_check(@PROJECT_NAME@_INC_DIR "${PACKAGE_PREFIX_DIR}/include")
set_and_check(@PROJECT_NAME@_INCLUDE_DIR "${PACKAGE_PREFIX_DIR}/include")
set_and_check(@PROJECT_NAME@_LIB_DIR "${PACKAGE_PREFIX_DIR}/lib")
set_and_check(@PROJECT_NAME@_LIBRARY_DIR "${PACKAGE_PREFIX_DIR}/lib")
set(@PROJECT_NAME@_LIB gctl_optimization)
set(@PROJECT_NAME@_LIBRARY gctl_optimization)
set(@PROJECT_NAME@_TOML @GCTL_OPTIMIZATION_TOML@)
message(STATUS "[GCTL_OPTIMIZATION] Use the TOML library: " @GCTL_OPTIMIZATION_TOML@)
if(NOT GCTL_FOUND)
find_package(GCTL REQUIRED)
include_directories(${GCTL_INC_DIR})
endif()
# include target information
include("${CMAKE_CURRENT_LIST_DIR}/@PROJECT_NAME@Targets.cmake")
check_required_components(@PROJECT_NAME@)

17
README.md
View File

@ -1,2 +1,17 @@
# gctl_optimization ## lcg_solver 共轭梯度求解器
### 求解器参数设置
#### 1. 从toml文件读取参数
用户可以从toml文件中读取并设置求解器参数。所有的参数都定义在名为lcg的顶级表格下，可设置的参数及类型如下所示：
```toml
[lcg]
max_iterations=<int>
epsilon=<float>
abs_diff=0|1
restart_epsilon=<float>
step=<float>
sigma=<float>
beta=<float>
maxi_m=<int>
```

1
config.h.in Normal file
View File

@ -0,0 +1 @@
#cmakedefine GCTL_OPTIMIZATION_TOML

20
example/CMakeLists.txt Normal file
View File

@ -0,0 +1,20 @@
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -O3")
set(EXECUTABLE_OUTPUT_PATH ${PROJECT_BINARY_DIR}/bin/examples)
macro(add_example name switch)
if(${switch})
add_executable(${name} ${name}.cpp)
set_target_properties(${name} PROPERTIES CXX_STANDARD 17 CXX_STANDARD_REQUIRED ON)
target_link_libraries(${name} PRIVATE ${GCTL_LIB})
target_link_libraries(${name} PRIVATE gctl_optimization)
endif()
endmacro()
add_example(ex1 ON)
add_example(ex2 ON)
add_example(ex3 ON)
add_example(ex4 ON)
add_example(ex5 ON)
add_example(ex6 ON)
add_example(ex7 ON)
add_example(ex8 ON)

164
example/ex1.cpp Normal file
View File

@ -0,0 +1,164 @@
/********************************************************
* ██████╗ ███████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗███████╗ ██║ ██║
* ██║ ██║╚════██║ ██║ ██║
* ╚██████╔╝███████║ ██║ ███████╗
* ╚═════╝ ╚══════╝ ╚═╝ ╚══════╝
* Generic Scientific Template Library
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* The GSTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License (LGPL) along with
* this program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GSTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GSTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include "../lib/optimization.h"
#define M 1000
#define N 800
double max_diff(const gctl::array<double> &a, const gctl::array<double> &b)
{
double max = -1.0;
for (size_t i = 0; i < a.size(); i++)
{
max = std::max(sqrt((a[i] - b[i])*(a[i] - b[i])), max);
}
return max;
}
class ex1 : public gctl::lcg_solver
{
public:
ex1();
virtual ~ex1();
// 计算共轭梯度的B项
void cal_partb(const gctl::array<double> &x, gctl::array<double> &B);
//定义共轭梯度中Ax的算法
virtual void LCG_Ax(const gctl::array<double> &x, gctl::array<double> &ax);
virtual void LCG_Mx(const gctl::array<double> &x, gctl::array<double> &mx);
private:
gctl::matrix<double> kernel; // 普通二维数组做核矩阵
gctl::array<double> tmp_arr; // 中间结果数组
gctl::array<double> p; // 预优矩阵
};
ex1::ex1()
{
kernel.resize(M, N);
kernel.random(-1.0, 1.0, gctl::RdUniform);
tmp_arr.resize(M);
p.resize(N);
for (size_t i = 0; i < N; i++)
{
p[i] = 1.0;
}
double diag;
for (size_t i = 0; i < N; i++)
{
diag = 0.0;
for (size_t j = 0; j < M; j++)
{
diag += kernel[j][i]*kernel[j][i];
}
p[i] = 1.0/diag;
}
}
ex1::~ex1(){}
void ex1::cal_partb(const gctl::array<double> &x, gctl::array<double> &B)
{
LCG_Ax(x, B);
return;
}
void ex1::LCG_Ax(const gctl::array<double> &x, gctl::array<double> &ax)
{
matvec(tmp_arr, kernel, x);
matvec(ax, kernel, tmp_arr, gctl::Trans);
return;
}
void ex1::LCG_Mx(const gctl::array<double> &x, gctl::array<double> &mx)
{
vecmul(mx, p, x);
return;
}
int main(int argc, char const *argv[])
{
// 生成一组正演解
gctl::array<double> fm(N);
gctl::random(fm, 1.0, 2.0, gctl::RdUniform);
ex1 test;
// 计算共轭梯度B项
gctl::array<double> B(N);
test.cal_partb(fm, B);
// 声明一组解
gctl::array<double> m(N, 0.0);
test.set_lcg_message(gctl::LCG_SOLUTION);
std::ofstream ofile("log.txt");
test.LCG_Minimize(m, B, gctl::LCG_CG, ofile);
ofile << "maximal difference: " << max_diff(fm, m) << std::endl;
m.assign_all(0.0);
test.LCG_Minimize(m, B, gctl::LCG_PCG, ofile);
ofile << "maximal difference: " << max_diff(fm, m) << std::endl;
m.assign_all(0.0);
test.LCG_Minimize(m, B, gctl::LCG_CGS, ofile);
ofile << "maximal difference: " << max_diff(fm, m) << std::endl;
ofile.close();
test.set_lcg_message(gctl::LCG_SOLUTION);
m.assign_all(0.0);
test.LCG_Minimize(m, B, gctl::LCG_BICGSTAB);
std::clog << "maximal difference: " << max_diff(fm, m) << std::endl;
m.assign_all(0.0);
test.LCG_Minimize(m, B, gctl::LCG_BICGSTAB2);
std::clog << "maximal difference: " << max_diff(fm, m) << std::endl;
gctl::array<double> low(N, 1.0);
gctl::array<double> hig(N, 2.0);
m.assign_all(0.0);
test.LCG_MinimizeConstrained(m, B, low, hig, gctl::LCG_PG);
std::clog << "maximal difference: " << max_diff(fm, m) << std::endl;
m.assign_all(0.0);
test.LCG_MinimizeConstrained(m, B, low, hig, gctl::LCG_SPG);
std::clog << "maximal difference: " << max_diff(fm, m) << std::endl;
return 0;
}

175
example/ex2.cpp Normal file
View File

@ -0,0 +1,175 @@
/********************************************************
* ██████╗ ███████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗███████╗ ██║ ██║
* ██║ ██║╚════██║ ██║ ██║
* ╚██████╔╝███████║ ██║ ███████╗
* ╚═════╝ ╚══════╝ ╚═╝ ╚══════╝
* Generic Scientific Template Library
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* The GSTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License (LGPL) along with
* this program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GSTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GSTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include "../lib/optimization.h"
#define M 100
#define N 90
// get random floating points
double random_double(double l, double t)
{
return (t-l)*rand()*1.0/RAND_MAX + l;
}
// get random integral numbers
int random_int(int small, int big)
{
return (rand() % (big - small)) + small;
}
class ex2 : public gctl::lgd_solver
{
protected:
gctl::matrix<double> kernel;
gctl::array<double> obs, tmp;
protected:
double LGD_Evaluate(const gctl::array<double> &x, gctl::array<double> &g);
public:
ex2();
virtual ~ex2(){}
void CalObs(const gctl::array<double> &x);
};
ex2::ex2()
{
kernel.resize(M, N);
tmp.resize(M);
obs.resize(M);
srand(time(0));
// 添加一些大数
int tmp_id, tmp_size;
double tmp_val;
for (int i = 0; i < M; i++)
{
tmp_size = random_int(25, 35);
for (int j = 0; j < tmp_size; j++)
{
tmp_id = random_int(0, N);
tmp_val = random_double(-10, 10);
kernel[i][tmp_id] = tmp_val;
}
}
}
double ex2::LGD_Evaluate(const gctl::array<double> &x, gctl::array<double> &g)
{
for (int i = 0; i < M; i++)
{
tmp[i] = 0.0;
for (int j = 0; j < N; j++)
{
tmp[i] += kernel[i][j] * x[j];
}
tmp[i] -= obs[i];
//tmp[i] /= 1e-1;
}
for (int j = 0; j < N; j++)
{
g[j] = 0.0;
for (int i = 0; i < M; i++)
{
g[j] += kernel[i][j]*tmp[i];
}
g[j] *= 2.0/M;
}
double sum = 0.0;
for (int i = 0; i < M; i++)
{
sum += tmp[i]*tmp[i];
}
return sum/M;
}
void ex2::CalObs(const gctl::array<double> &x)
{
// 计算正演值
for (int i = 0; i < M; i++)
{
obs[i] = 0.0;
for (int j = 0; j < N; j++)
{
obs[i] += kernel[i][j]*x[j];
}
// 添加噪声
obs[i] += random_double(-1e-3, 1e-3);
}
}
int main(int argc, char const *argv[])
{
gctl::array<double> m(N, 0.0), mean_m(N, 0.0), stddev_m(N, 0.0), low(N), hig(N);
// 生成一组正演解 包含一些大值和一些小值
gctl::array<double> fm(N);
int N2 = (int) N/2;
for (int i = 0; i < N2; i++)
{
//fm[i] = random_double(5, 10);
fm[i] = 10.0;
}
for (int i = N2; i < N; i++)
{
//fm[i] = random_double(1, 2);
fm[i] = 1.0;
}
for (int i = 0; i < N2; i++)
{
low[i] = 9.0; // 对解的范围进行约束
hig[i] = 11.0;
}
for (int i = N2; i < N; i++)
{
low[i] = 0.0;
hig[i] = 2.0;
}
ex2 e;
e.CalObs(fm);
gctl::lgd_para my_para = e.default_lgd_para();
my_para.flight_times = 20000;
my_para.batch = 100;
e.set_lgd_para(my_para);
e.LGD_Minimize(m, mean_m, stddev_m, low, hig);
for (int i = 0; i < N; i++)
{
std::cout << fm[i] << " " << m[i] << " " << mean_m[i] << " " << stddev_m[i] << " " << fabs(mean_m[i] - fm[i]) << std::endl;
}
return 0;
}

69
example/ex3.cpp Normal file
View File

@ -0,0 +1,69 @@
#include "../lib/optimization.h"
class TEST_FUNC : public gctl::lbfgs_solver
{
public:
TEST_FUNC();
~TEST_FUNC();
virtual double LBFGS_Evaluate(const gctl::array<double> &x, gctl::array<double> &g);
void Routine();
private:
gctl::array<double> m_x;
};
TEST_FUNC::TEST_FUNC()
{
m_x.resize(3, 0.0);
}
TEST_FUNC::~TEST_FUNC(){}
// test functions
// 3 = 3*x1 + x2 + 2*x3*x3
// 1 = -3*x1 + 5*x2*x2 + 2*x1*x3
// -12 = 25*x1*x2 + 20*x3
double TEST_FUNC::LBFGS_Evaluate(const gctl::array<double> &x, gctl::array<double> &g)
{
double f0,f1,f2,temp;
f0 = 3*x[0] + x[1] + 2*x[2]*x[2] - 3.012; //这里添加一点噪声
f1 = -3*x[0] + 5*x[1]*x[1] + 2*x[0]*x[2] - 1.04252;
f2 = 25*x[0]*x[1] + 20*x[2] + 12.12479;
temp = sqrt(f0*f0+f1*f1+f2*f2);
g[0] = 0.5*(6*f0+2*f1*(2*x[2]-3)+50*f2*x[1])/temp;
g[1] = 0.5*(2*f0+20*f1*x[1]+50*f2*x[0])/temp;
g[2] = 0.5*(8*f0*x[2]+4*f1*x[0]+40*f2)/temp;
return temp;
}
void TEST_FUNC::Routine()
{
gctl::lbfgs_para self_para = default_lbfgs_para();
self_para.m = 10;
self_para.past = 5;
self_para.residual = 1e-10;
//self_para.min_step = 1e-30;
//self_para.max_linesearch = 40;
//self_para.linesearch = gctl::LBFGS_LINESEARCH_BACKTRACKING_WOLFE;
set_lbfgs_para(self_para);
std::ofstream ofile("log.txt");
show_lbfgs_para(ofile);
double fx = LBFGS_Minimize(m_x, ofile);
ofile.close();
m_x.show();
return;
}
int main(int argc, char const *argv[])
{
TEST_FUNC test;
test.Routine();
return 0;
}

91
example/ex4.cpp Normal file
View File

@ -0,0 +1,91 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include "gctl/core.h"
#include "gctl/algorithm.h"
#include "../lib/optimization.h"
#include "iostream"
#include "iomanip"
using std::cout;
using std::endl;
using std::setw;
int main(int argc, char const *argv[])
{
gctl::matrix<double> A(4, 3);
for (int i = 0; i < A.row_size(); i++)
{
for (int j = 0; j < A.col_size(); j++)
{
A[i][j] = 3*(i+1) + j - 2;
}
}
A[3][1] = 1;
cout<<"A(" << A.row_size() << ", " << A.col_size() << ") = " <<endl;
A.show();
gctl::svd svdd;
svdd.decompose(A);
cout<<"U(" << svdd.U.row_size() << ", " << svdd.U.col_size() << ") = " <<endl;
svdd.U.show();
cout<<"S(" << svdd.S.size() << ") = " << endl;
svdd.S.show();
cout<<"V(" << svdd.V.row_size() << ", " << svdd.V.col_size() << ") = " <<endl;
svdd.V.show();
int sig_num = svdd.get_singular_number();
double tmp_d;
gctl::array<double> tmp(sig_num);
cout<<"U^T * S * V(" << A.row_size() << ", " << A.col_size() << ") = " <<endl;
for(int i=0;i<A.row_size();i++)
{
for (int k = 0; k < sig_num; k++)
{
tmp[k] = svdd.U[k][i] * svdd.S[k];
}
for(int j=0;j<A.col_size();j++)
{
tmp_d = 0.0;
for (int k = 0; k < sig_num; k++)
{
tmp_d += tmp[k] * svdd.V[k][j];
}
cout<<setw(12)<<tmp_d<<' ';
}
cout<<endl;
}
cout<<endl;
return 0;
}

78
example/ex5.cpp Normal file
View File

@ -0,0 +1,78 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include "gctl/core.h"
#include "gctl/algorithm.h"
#include "../lib/optimization.h"
int main(int argc, char const *argv[])
{
gctl::matrix<double> A(5, 5);
for (int i = 0; i < 5; i++)
{
for (int j = 0; j < 5; j++)
{
A[i][j] = 3*(i+1) + j - 2;
}
}
// 注意A要满秩
A[1][2] = 3.4;
A[4][1] = 2.1;
A[3][4] = 9.7;
A[2][3] = 2.7;
std::cout<<"A(5, 5) = " <<std::endl;
for(int i=0;i<5;i++){
for(int j=0;j<5;j++){
std::cout<<A[i][j]<<' ';
}
std::cout<<std::endl;
}
std::cout<<std::endl;
gctl::array<double> m(5, 0.5), x(5, 0.0);
gctl::array<double> B(5);
for (int i = 0; i < 5; i++)
{
B[i] = 0.0;
for (int j = 0; j < 5; j++)
{
B[i] += A[i][j] * m[j];
}
}
gctl::lu glu(A);
glu.decompose();
glu.solve(B, x);
for (size_t i = 0; i < 5; i++)
{
std::cout << m[i] << " " << x[i] << std::endl;
}
return 0;
}

90
example/ex6.cpp Normal file
View File

@ -0,0 +1,90 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include "gctl/core.h"
#include "gctl/algorithm.h"
#include "../lib/optimization.h"
// get random floating points
double random_double(double l, double t)
{
return (t-l)*rand()*1.0/RAND_MAX + l;
}
int main(int argc, char const *argv[])
{
srand(time(0));
gctl::matrix<double> A(5, 5);
for (int i = 0; i < 5; i++)
{
for (int j = i; j < 5; j++)
{
if (i == j) A[i][j] = random_double(1.0, 3.0);
else A[i][j] = random_double(0.1, 1.0);
}
}
for (int i = 0; i < 5; i++)
{
for (int j = i; j < 5; j++)
{
A[j][i] = A[i][j];
}
}
std::cout<<"A(5, 5) = " <<std::endl;
for(int i=0;i<5;i++){
for(int j=0;j<5;j++){
std::cout<<A[i][j]<<' ';
}
std::cout<<std::endl;
}
std::cout<<std::endl;
gctl::array<double> m(5, 0.5), x(5, 0.0);
gctl::array<double> B(5);
for (int i = 0; i < 5; i++)
{
B[i] = 0.0;
for (int j = 0; j < 5; j++)
{
B[i] += A[i][j] * m[j];
}
}
gctl::cholesky gck(A);
gck.decompose();
gck.solve(B, x);
for (size_t i = 0; i < 5; i++)
{
std::cout << m[i] << " " << x[i] << std::endl;
}
return 0;
}

124
example/ex7.cpp Normal file
View File

@ -0,0 +1,124 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include "gctl/core.h"
#include "gctl/algorithm.h"
#include "../lib/optimization.h"
typedef gctl::array<std::complex<double>> cd_array;
#define N 1000
double max_diff(const cd_array &a, const cd_array &b)
{
double max = -1;
std::complex<double> t;
for (size_t i = 0; i < a.size(); i++)
{
t = a[i] - b[i];
max = std::max(std::norm(t), max);
}
return max;
}
class ex7 : public gctl::clcg_solver
{
public:
ex7();
virtual ~ex7();
virtual void CLCG_Ax(const cd_array &x, cd_array &ax, gctl::matrix_layout_e layout, gctl::conjugate_type_e conj);
// 计算共轭梯度的B项
void cal_partb(const cd_array &x, cd_array &B);
private:
gctl::matrix<std::complex<double>> kernel; // 普通二维数组做核矩阵
};
ex7::ex7()
{
gctl::array<double> tmp(round(0.5*(N+1)*N));
gctl::random(tmp, 1.0, 2.0, gctl::RdUniform);
size_t c = 0;
kernel.resize(N, N);
for (int i = 0; i < N; i++)
{
for (int j = i; j < N; j++)
{
kernel[i][j] = tmp[c];
kernel[j][i] = kernel[i][j];
c++;
}
}
}
ex7::~ex7(){}
void ex7::cal_partb(const cd_array &x, cd_array &B)
{
gctl::matvec(B, kernel, x);
return;
}
void ex7::CLCG_Ax(const cd_array &x, cd_array &ax, gctl::matrix_layout_e layout, gctl::conjugate_type_e conj)
{
gctl::matvec(ax, kernel, x, layout, conj);
return;
}
int main(int argc, char const *argv[])
{
// 生成一组正演解
gctl::array<double> tmp(2*N);
gctl::random(tmp, 1.0, 2.0, gctl::RdUniform);
cd_array fm(N);
for (size_t i = 0; i < N; i++)
{
fm[i].real(tmp[2*i]);
fm[i].imag(tmp[2*i + 1]);
}
ex7 test;
// 计算共轭梯度B项
cd_array B(N);
test.cal_partb(fm, B);
// 声明一组解
cd_array m(N, std::complex<double>(0.0, 0.0));
gctl::clcg_para my_para = test.default_clcg_para();
my_para.abs_diff = 1;
test.set_clcg_para(my_para);
test.CLCG_Minimize(m, B, gctl::CLCG_BICG_SYM);
std::clog << "maximal difference: " << max_diff(fm, m) << std::endl;
return 0;
}

233
example/ex8.cpp Normal file
View File

@ -0,0 +1,233 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include "gctl/core.h"
#include "gctl/algorithm.h"
#include "../lib/optimization.h"
#define M 1000
#define N 900
// get random floating points
double random_double(double l, double t)
{
return (t-l)*rand()*1.0/RAND_MAX + l;
}
// get random integral numbers
int random_int(int small, int big)
{
return (rand() % (big - small)) + small;
}
double max_diff(const gctl::_1d_array &a, const gctl::_1d_array &b)
{
double max = -1.0;
for (size_t i = 0; i < a.size(); i++)
{
max = std::max(fabs(a[i] - b[i]), max);
}
return max;
}
class ex8 : public gctl::lbfgs_solver, public gctl::grad_norm
{
public:
ex8();
virtual ~ex8();
virtual double LBFGS_Evaluate(const gctl::_1d_array &x, gctl::_1d_array &g);
virtual int LBFGS_Progress(const gctl::_1d_array &x, const gctl::_1d_array &g, const double fx,
const double converge, const double rate, const gctl::lbfgs_para param, int k, int ls, std::ostream &ss);
void CalTarget(const gctl::_1d_array &x);
private:
gctl::_1d_array obs1, obs2, obs3, tmp, grad;
gctl::_2d_matrix k1, k2, k3;
};
ex8::ex8()
{
srand(time(0));
tmp.resize(M);
grad.resize(N);
k1.resize(M, N);
obs1.resize(M);
// 添加一些大数
int tmp_id, tmp_size;
double tmp_val;
for (int i = 0; i < M; i++)
{
tmp_size = random_int(25, 35);
for (int j = 0; j < tmp_size; j++)
{
tmp_id = random_int(0, N);
tmp_val = random_double(-1.0, 1.0);
k1[i][tmp_id] = tmp_val;
}
}
k2.resize(M, N);
obs2.resize(M);
// 添加一些大数
for (int i = 0; i < M; i++)
{
tmp_size = random_int(25, 35);
for (int j = 0; j < tmp_size; j++)
{
tmp_id = random_int(0, N);
tmp_val = random_double(-200.0, 200.0);
k2[i][tmp_id] = tmp_val;
}
}
k3.resize(M, N);
obs3.resize(M);
// 添加一些大数
for (int i = 0; i < M; i++)
{
tmp_size = random_int(25, 35);
for (int j = 0; j < tmp_size; j++)
{
tmp_id = random_int(0, N);
tmp_val = random_double(-0.01, 0.01);
k3[i][tmp_id] = tmp_val;
}
}
}
ex8::~ex8(){}
double ex8::LBFGS_Evaluate(const gctl::_1d_array &x, gctl::_1d_array &g)
{
gctl::matvec(tmp, k1, x);
tmp -= obs1;
gctl::matvec(grad, k1, tmp, gctl::Trans);
gctl::scale(grad, 2.0/M);
AddSingleLoss(gctl::power2(gctl::module(tmp, gctl::L2))/M, grad);
gctl::matvec(tmp, k2, x);
tmp -= obs2;
gctl::matvec(grad, k2, tmp, gctl::Trans);
gctl::scale(grad, 2.0/M);
AddSingleLoss(gctl::power2(gctl::module(tmp, gctl::L2))/M, grad);
gctl::matvec(tmp, k3, x);
tmp -= obs3;
gctl::matvec(grad, k3, tmp, gctl::Trans);
gctl::scale(grad, 2.0/M);
AddSingleLoss(gctl::power2(gctl::module(tmp, gctl::L2))/M, grad);
return GradNormLoss(g);
}
int ex8::LBFGS_Progress(const gctl::_1d_array &x, const gctl::_1d_array &g, const double fx,
const double converge, const double rate, const gctl::lbfgs_para param, int k, int ls, std::ostream &ss)
{
UpdateWeights();
return gctl::lbfgs_solver::LBFGS_Progress(x, g, fx, converge, rate, param, k, ls, ss);
}
void ex8::CalTarget(const gctl::_1d_array &x)
{
// 计算正演值
gctl::matvec(obs1, k1, x);
for (int i = 0; i < M; i++)
{
// 添加噪声
obs1[i] += random_double(-1e-3, 1e-3);
}
gctl::matvec(obs2, k2, x);
for (int i = 0; i < M; i++)
{
// 添加噪声
obs2[i] += random_double(-1e-3, 1e-3);
}
gctl::matvec(obs3, k3, x);
for (int i = 0; i < M; i++)
{
// 添加噪声
obs3[i] += random_double(-1e-3, 1e-3);
}
return;
}
int main(int argc, char const *argv[])
{
// 生成一组正演解
gctl::_1d_array fm(N);
random(fm, 1.0, 2.0, gctl::RdUniform);
ex8 test;
// 计算拟合目标项
test.CalTarget(fm);
// 声明一组解
gctl::_1d_array m(N, 0.0);
gctl::lbfgs_para self_para = test.default_lbfgs_para();
self_para.linesearch = gctl::LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE;
self_para.epsilon = 1e-6;
test.set_lbfgs_para(self_para);
test.show_lbfgs_para();
test.InitGradNorm(3, N);
test.set_control_weight(1.0);
test.set_weight_step(0.00001);
double fx = test.LBFGS_Minimize(m);
std::clog << "maximal difference: " << max_diff(fm, m) << std::endl;
gctl::_1d_array records;
test.get_records(records);
for (size_t i = 0; i < records.size(); i++)
{
if ((i+1)%3 == 0)
{
std::cout << records[i] << "\n";
}
else std::cout << records[i] << " ";
}
return 0;
}

54
installer Executable file
View File

@ -0,0 +1,54 @@
#!/bin/bash
if [[ $# == 0 || ${1} == "help" ]]; then
echo "Compiles executables/libraries and maintains installed files. Two tools 'Cmake' and 'stow' are empolyed here. For more information, see https://cmake.org and https://www.gnu.org/software/stow/."
echo ""
echo "School of Earth Sciences, Zhejiang University"
echo "Yi Zhang (yizhang-geo@zju.edu.cn)"
echo ""
echo "Usage: ./installer [option] [Cmake options]"
echo ""
echo "Options:"
echo "(1) configure: Configure Cmake project(s). This option could take extra Cmake options as in <option>=<value>."
echo "(2) build: Build executables/libraries."
echo "(3) install: Install executables/libraries to the directory of CMAKE_INSTALL_PREFIX and sym-links them to the target address. This offers a quick and clean remove of the installed files."
echo "(4) clean: Clean build/ folder(s)."
echo "(5) uninstall: Delete the installed files and sym-links."
echo "(6) info: Print out current setups."
echo "(7) help: Show help information."
exit 0
fi
package=gctl_optimization
address=/opt/stow
taress=/usr/local
option="-DCMAKE_BUILD_TYPE=Release -DCMAKE_INSTALL_PREFIX=${address}/${package}"
if [[ $# -gt 1 ]]; then
for opt in "$@"; do
if [[ ${opt} != "configure" ]]; then
option="${option} -D${opt}"
fi
done
fi
if [[ ${1} == "configure" && ! -d "build/" ]]; then
mkdir build && cd build && cmake .. ${option}
elif [[ ${1} == "configure" ]]; then
cd build && rm -rf * && cmake .. ${option}
elif [[ ${1} == "build" ]]; then
cd build && make
elif [[ ${1} == "install" ]]; then
cd build && sudo make install
sudo stow --dir=${address} --target=${taress} -S ${package}
elif [[ ${1} == "clean" ]]; then
rm -rf build/
elif [[ ${1} == "uninstall" ]]; then
sudo stow --dir=${address} --target=${taress} -D ${package}
sudo rm -rf ${address}/${package}
elif [[ ${1} == "info" ]]; then
echo "package name:" ${package}
echo "stow address:" ${address}
echo "target address:" ${taress}
echo "Cmake options:" ${option}
fi

64
lib/CMakeLists.txt Normal file
View File

@ -0,0 +1,64 @@
# 设置编译选项
set(CMAKE_C_FLAGS "${CMAKE_C_FLAGS} -O3")
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -O3")
# 设置库文件的输出地址
set(LIBRARY_OUTPUT_PATH ${PROJECT_BINARY_DIR}/lib)
# 设定库源文件文件夹
aux_source_directory(optimization/ GCTL_OPTIMAL_SRC)
# 以下部分为库的编译
# 注意目标名必须唯一 所以不能直接生成相同名称的动态库与静态库
# 注意此处不必为目标名称添加lib前缀和相应后缀，cmake会自行添加
add_library(gctl_optimization SHARED ${GCTL_OPTIMAL_SRC})
# 首先添加静态库的生成命令
add_library(gctl_optimization_static STATIC ${GCTL_OPTIMAL_SRC})
# 设置静态库的输出名称从而获得与动态库名称相同的静态库
set_target_properties(gctl_optimization_static PROPERTIES OUTPUT_NAME "gctl_optimization")
# 设置输出目标属性以同时输出动态库与静态库
set_target_properties(gctl_optimization PROPERTIES CLEAN_DIRECT_OUTPUT 1)
set_target_properties(gctl_optimization_static PROPERTIES CLEAN_DIRECT_OUTPUT 1)
# 设置动态库的版本号
set_target_properties(gctl_optimization PROPERTIES VERSION ${PROJECT_VERSION} SOVERSION ${PROJECT_VERSION_MAJOR}.${PROJECT_VERSION_MINOR})
# 设置动态库的运行搜索地址
set_target_properties(gctl_optimization PROPERTIES INSTALL_RPATH /usr/local/lib)
set_target_properties(gctl_optimization_static PROPERTIES INSTALL_RPATH /usr/local/lib)
set_target_properties(gctl_optimization PROPERTIES CXX_STANDARD 17 CXX_STANDARD_REQUIRED ON)
set_target_properties(gctl_optimization_static PROPERTIES CXX_STANDARD 17 CXX_STANDARD_REQUIRED ON)
#连接动态库
target_link_libraries(gctl_optimization PUBLIC ${GCTL_LIB})
target_link_libraries(gctl_optimization_static ${GCTL_LIB})
set(CONFIG_FILE_PATH lib/cmake/${PROJECT_NAME})
configure_package_config_file(${PROJECT_SOURCE_DIR}/${PROJECT_NAME}Config.cmake.in
${CMAKE_BINARY_DIR}/${PROJECT_NAME}Config.cmake
INSTALL_DESTINATION ${CONFIG_FILE_PATH})
write_basic_package_version_file(${CMAKE_BINARY_DIR}/${PROJECT_NAME}ConfigVersion.cmake
VERSION ${PROJECT_VERSION}
COMPATIBILITY SameMajorVersion)
# 库的安装命令
if(WIN32)
install(TARGETS gctl_optimization DESTINATION lib)
install(TARGETS gctl_optimization_static DESTINATION lib)
else()
install(TARGETS gctl_optimization gctl_optimization_static
EXPORT ${PROJECT_NAME}Targets
LIBRARY DESTINATION lib
ARCHIVE DESTINATION lib)
install(EXPORT ${PROJECT_NAME}Targets
DESTINATION ${CONFIG_FILE_PATH})
install(FILES
${CMAKE_BINARY_DIR}/${PROJECT_NAME}Config.cmake
${CMAKE_BINARY_DIR}/${PROJECT_NAME}ConfigVersion.cmake
DESTINATION ${CONFIG_FILE_PATH})
endif()
# 头文件安装命令
file(GLOB GCTL_HEAD *.h)
file(GLOB GCTL_OPTIMAL_HEAD optimization/*.h)
install(FILES ${GCTL_HEAD} DESTINATION include/gctl)
install(FILES ${GCTL_OPTIMAL_HEAD} DESTINATION include/gctl/optimization)

43
lib/optimization.h Normal file
View File

@ -0,0 +1,43 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#ifndef _GCTL_OPTIMIZATION_H
#define _GCTL_OPTIMIZATION_H
#include "optimization/loss_func.h"
#include "optimization/lu.h"
#include "optimization/cholesky.h"
#include "optimization/svd.h"
#include "optimization/lcg.h"
#include "optimization/clcg.h"
#include "optimization/lgd.h"
#include "optimization/lbfgs.h"
#include "optimization/sgd.h"
#include "optimization/gradnorm.h"
#include "optimization/dwa.h"
#endif // _GCTL_OPTIMIZATION_H

127
lib/optimization/cholesky.cpp Normal file
View File

@ -0,0 +1,127 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include "cholesky.h"
// Constructor
gctl::cholesky::cholesky(matrix<double> &sourceMatrix) : decomposedMatrix(sourceMatrix)
{
if (sourceMatrix.empty() || sourceMatrix.row_size() != sourceMatrix.col_size())
{
throw domain_error("Invalid input matrix. From cholesky::cholesky(...)");
}
}
// Decomposition into triangular matrices
void gctl::cholesky::decompose()
{
// Enumerate matrix columnwise
for (int j = 0; j < decomposedMatrix.col_size(); j++)
{
for (int i = j; i < decomposedMatrix.row_size(); i++)
{
if (i == j)
{
double sum = 0.0;
for (int k = 0; k < i; k++)
{
sum += std::pow(decomposedMatrix[i][k], 2.0);
}
if (decomposedMatrix[i][j] - sum <= 0.0)
{
// Not positive definite matrix
throw runtime_error("The input matrix is not positively defined. From gctl::cholesky::decompose()");
return;
}
decomposedMatrix[i][j] = std::sqrt(decomposedMatrix[i][j] - sum);
}
else
{
double sum = 0.0;
for (int k = 0; k < j; k++)
{
sum += (decomposedMatrix[i][k] * decomposedMatrix[j][k]);
}
decomposedMatrix[i][j] = (1 / decomposedMatrix[j][j]) * (decomposedMatrix[i][j] - sum);
decomposedMatrix[j][i] = decomposedMatrix[i][j];
}
}
}
return;
}
// Solve for x in form Ax = b. A is the original input matrix.
void gctl::cholesky::solve(const array<double>& b, array<double> &x)
{
if (b.empty())
{
throw domain_error("Invalid target vector. From lu<double>::solve(...)");
}
x.resize(b.size());
// First solve lower triangular * x = b with forward substitution
for (int i = 0; i < b.size(); i++)
{
double sum = 0.0;
for (int j = 0; j < i; j++)
{
sum += (decomposedMatrix[i][j] * x[j]);
}
x[i] = (b[i] - sum) / decomposedMatrix[i][i];
}
// Now solve upper triangular (transpose of lower triangular) * x = x with back substitution.
// Note that x can be solved in place using the existing x vector. No need to allocate
// another vector.
for (int i = static_cast<int>(b.size()) - 1; i >= 0; i--)
{
double sum = 0.0;
for (int j = static_cast<int>(b.size()) - 1; j > i; j--)
{
sum += (decomposedMatrix[i][j] * x[j]);
}
x[i] = (x[i] - sum) / decomposedMatrix[i][i];
}
return;
}

55
lib/optimization/cholesky.h Normal file
View File

@ -0,0 +1,55 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#ifndef _CHOLESKY_H
#define _CHOLESKY_H
#include "gctl/core.h"
namespace gctl
{
/**
* @brief Cholesky matrix decomposition to lower triangular matrix and its conjugate transpose
*
* @note Restricted to positive-definite matrices
*/
class cholesky
{
public:
cholesky(matrix<double> &sourceMatrix); // Matrix is decomposed in-place
virtual ~cholesky(){}
void decompose(); ///< Decomposition into triangular matrices.
void solve(const array<double>& b, array<double> &x); ///< Solve for x in form Ax = b. A is the original input matrix.
protected:
cholesky(const gctl::cholesky&) = delete;
void operator=(const gctl::cholesky&) = delete;
matrix<double> &decomposedMatrix;
};
}
#endif // _CHOLESKY_H

373
lib/optimization/clcg.cpp Normal file
View File

@ -0,0 +1,373 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include "clcg.h"
/**
* Default parameter for conjugate gradient methods
*/
static const gctl::clcg_para clcg_defparam = {0, 1e-8, 0};
int gctl::clcg_solver::CLCG_Progress(const array<std::complex<double> > &m, const double converge, const clcg_para &param, size_t t)
{
if (converge <= param.epsilon)
{
std::clog << GCTL_CLEARLINE << "\rIteration-times: " << t << "\tconvergence: " << converge;
return 0;
}
if (clcg_inter_ > 0 && t%clcg_inter_ == 0)
{
std::clog << GCTL_CLEARLINE << "\rIteration-times: " << t << "\tconvergence: " << converge;
}
return 0;
}
gctl::clcg_solver::clcg_solver()
{
clcg_param_ = clcg_defparam;
clcg_inter_ = 1;
clcg_silent_ = false;
}
gctl::clcg_solver::~clcg_solver(){}
void gctl::clcg_solver::clcg_silent()
{
clcg_silent_ = true;
return;
}
void gctl::clcg_solver::set_clcg_report_interval(size_t inter)
{
clcg_inter_ = inter;
return;
}
void gctl::clcg_solver::set_clcg_para(const clcg_para &in_param)
{
clcg_param_ = in_param;
return;
}
void gctl::clcg_solver::set_clcg_para(const toml::value &toml_data)
{
clcg_param_ = clcg_defparam;
std::string CLCG = "clcg";
if (toml_data.contains(CLCG))
{
if (toml_data.at(CLCG).contains("max_iterations")) clcg_param_.max_iterations = toml::find<int>(toml_data, CLCG, "max_iterations");
if (toml_data.at(CLCG).contains("epsilon")) clcg_param_.epsilon = toml::find<double>(toml_data, CLCG, "epsilon");
if (toml_data.at(CLCG).contains("abs_diff")) clcg_param_.abs_diff = toml::find<int>(toml_data, CLCG, "abs_diff");
}
return;
}
void gctl::clcg_solver::clcg_error_str(clcg_return_code err_code, std::ostream &ss, bool err_throw)
{
#if defined _WINDOWS || __WIN32__
if (!er_throw)
{
if (err_code >= 0)
{
SetConsoleTextAttribute(GetStdHandle(STD_ERROR_HANDLE), FOREGROUND_INTENSITY | FOREGROUND_GREEN);
ss << "Success! ";
}
else
{
SetConsoleTextAttribute(GetStdHandle(STD_ERROR_HANDLE), FOREGROUND_INTENSITY | FOREGROUND_RED);
ss << "Fail! ";
}
}
#else
if (!err_throw)
{
if (err_code >= 0)
ss << "\033[1m\033[32mCLCG Success! ";
else
ss << "\033[1m\033[31mCLCG Fail! ";
}
#endif
std::string err_str;
switch (err_code)
{
case CLCG_SUCCESS:
err_str = "Iteration reached convergence."; break;
case CLCG_STOP:
err_str = "Iteration is stopped by the progress evaluation function."; break;
case CLCG_ALREADY_OPTIMIZIED:
err_str = "The variables are already optimized."; break;
case CLCG_UNKNOWN_ERROR:
err_str = "Unknown error."; break;
case CLCG_INVILAD_VARIABLE_SIZE:
err_str = "The size of the variables is negative."; break;
case CLCG_INVILAD_MAX_ITERATIONS:
err_str = "The maximal iteration times is negative."; break;
case CLCG_INVILAD_EPSILON:
err_str = "The epsilon is not in the range (0, 1)."; break;
case CLCG_REACHED_MAX_ITERATIONS:
err_str = "The maximal iteration has been reached."; break;
case CLCG_NAN_VALUE:
err_str = "The model values are NaN."; break;
case CLCG_INVALID_POINTER:
err_str = "Invalid pointer."; break;
case CLCG_SIZE_NOT_MATCH:
err_str = "The sizes of the solution and target do not match."; break;
case CLCG_UNKNOWN_SOLVER:
err_str = "Unknown solver."; break;
default:
err_str = "Unknown error."; break;
}
if (err_throw && err_code < 0) throw std::runtime_error(err_str.c_str());
else ss << err_str;
#if defined _WINDOWS || __WIN32__
if (!er_throw)
{
if (err_code >= 0)
{
SetConsoleTextAttribute(GetStdHandle(STD_ERROR_HANDLE), 7);
ss << std::endl;
}
else
{
SetConsoleTextAttribute(GetStdHandle(STD_ERROR_HANDLE), 7);
ss << std::endl;
}
}
#else
if (!err_throw)
{
if (err_code >= 0)
ss << "\033[0m" << std::endl;
else
ss << "\033[0m" << std::endl;
}
#endif
return;
}
gctl::clcg_para gctl::clcg_solver::default_clcg_para()
{
clcg_para dp = clcg_defparam;
return dp;
}
void gctl::clcg_solver::CLCG_Minimize(array<std::complex<double> > &m, const array<std::complex<double> > &B,
clcg_solver_type solver_id, std::ostream &ss, bool verbose, bool er_throw)
{
if (clcg_silent_)
{
clcg_return_code ret;
if (solver_id == CLCG_BICG) ret = clbicg(m, B);
else if (solver_id == CLCG_BICG_SYM) ret = clbicg_symmetric(m, B);
else if (solver_id == CLCG_CGS) ret = clcgs(m, B);
else if (solver_id == CLCG_BICGSTAB) ret = clbicgstab(m, B);
else if (solver_id == CLCG_TFQMR) ret = cltfqmr(m, B);
else throw std::invalid_argument("Invalid solver type. gctl::clcg_solver<T>::Minimize(...)");
if (ret < 0) clcg_error_str(ret, ss, true);
return;
}
#ifdef GCTL_OPENMP
double start = omp_get_wtime();
clcg_return_code ret;
if (solver_id == CLCG_BICG) ret = clbicg(m, B);
else if (solver_id == CLCG_BICG_SYM) ret = clbicg_symmetric(m, B);
else if (solver_id == CLCG_CGS) ret = clcgs(m, B);
else if (solver_id == CLCG_BICGSTAB) ret = clbicgstab(m, B);
else if (solver_id == CLCG_TFQMR) ret = cltfqmr(m, B);
else throw std::invalid_argument("Invalid solver type. gctl::clcg_solver<T>::Minimize(...)");
double end = omp_get_wtime();
double costime = 1000*(end-start);
#else
clock_t start = clock();
clcg_return_code ret;
if (solver_id == CLCG_BICG) ret = clbicg(m, B);
else if (solver_id == CLCG_BICG_SYM) ret = clbicg_symmetric(m, B);
else if (solver_id == CLCG_CGS) ret = clcgs(m, B);
else if (solver_id == CLCG_BICGSTAB) ret = clbicgstab(m, B);
else if (solver_id == CLCG_TFQMR) ret = cltfqmr(m, B);
else throw std::invalid_argument("Invalid solver type. gctl::clcg_solver<T>::Minimize(...)");
clock_t end = clock();
double costime = 1000*(end-start)/(double)CLOCKS_PER_SEC;
#endif
if (!er_throw)
{
ss << std::endl;
switch (solver_id)
{
case CLCG_BICG:
std::clog << "Solver: Bi-CG. Times cost: " << costime << " ms" << std::endl;
break;
case CLCG_BICG_SYM:
std::clog << "Solver: Bi-CG (symmetrically accelerated). Times cost: " << costime << " ms" << std::endl;
break;
case CLCG_CGS:
std::clog << "Solver: CGS. Times cost: " << costime << " ms" << std::endl;
break;
case CLCG_BICGSTAB:
std::clog << "Solver: CGS. Times cost: " << costime << " ms" << std::endl;
break;
case CLCG_TFQMR:
std::clog << "Solver: TFQMR. Times cost: " << costime << " ms" << std::endl;
break;
default:
std::clog << "Solver: Unknown. Times cost: " << costime << " ms" << std::endl;
break;
}
}
if (verbose) clcg_error_str(ret, ss, er_throw);
else if (ret < 0) clcg_error_str(ret, ss, er_throw);
return;
}
gctl::clcg_return_code gctl::clcg_solver::clbicg(array<std::complex<double> > &m, const array<std::complex<double> > &B)
{
clcg_return_code ret;
return ret;
}
gctl::clcg_return_code gctl::clcg_solver::clbicg_symmetric(array<std::complex<double> > &m, const array<std::complex<double> > &B)
{
size_t n_size = B.size();
//check parameters
if (n_size <= 0) return CLCG_INVILAD_VARIABLE_SIZE;
if (clcg_param_.max_iterations < 0) return CLCG_INVILAD_MAX_ITERATIONS;
if (clcg_param_.epsilon <= 0.0 || clcg_param_.epsilon >= 1.0) return CLCG_INVILAD_EPSILON;
r1k.resize(n_size);
d1k.resize(n_size);
Ax.resize(n_size);
CLCG_Ax(m, Ax, gctl::NoTrans, gctl::NoConj);
std::complex<double> one_z(1.0, 0.0);
vecdiff(r1k, B, Ax, one_z, one_z);
veccpy(d1k, r1k, one_z);
std::complex<double> rkrk = vecdot(r1k, r1k);
double r0_square, rk_square;
std::complex<double> r0_mod, rk_mod;
rk_mod = vecinner(r1k, r1k);
r0_square = rk_square = std::norm(rk_mod);
if (r0_square < 1.0) r0_square = 1.0;
clcg_return_code ret;
if (clcg_param_.abs_diff && sqrt(rk_square)/n_size <= clcg_param_.epsilon)
{
ret = CLCG_ALREADY_OPTIMIZIED;
CLCG_Progress(m, sqrt(rk_square)/n_size, clcg_param_, 0);
return ret;
}
else if (rk_square/r0_square <= clcg_param_.epsilon)
{
ret = CLCG_ALREADY_OPTIMIZIED;
CLCG_Progress(m, rk_square/r0_square, clcg_param_, 0);
return ret;
}
double residual;
std::complex<double> ak, rkrk2, betak, dkAx;
size_t t = 0;
while(1)
{
if (clcg_param_.abs_diff) residual = sqrt(rk_square)/n_size;
else residual = rk_square/r0_square;
if (CLCG_Progress(m, residual, clcg_param_, t))
{
ret = CLCG_STOP; return ret;
}
if (residual <= clcg_param_.epsilon)
{
ret = CLCG_CONVERGENCE; return ret;
}
if (clcg_param_.max_iterations > 0 && t+1 > clcg_param_.max_iterations)
{
ret = CLCG_REACHED_MAX_ITERATIONS;
break;
}
t++;
CLCG_Ax(d1k, Ax, gctl::NoTrans, gctl::NoConj);
dkAx = vecdot(d1k, Ax);
ak = rkrk/dkAx;
vecapp(m, d1k, ak);
vecsub(r1k, Ax, ak);
rk_mod = vecdot(r1k, r1k);
rk_square = std::norm(rk_mod);
if (!vecvalid(m))
{
ret = CLCG_NAN_VALUE; return ret;
}
rkrk2 = vecdot(r1k, r1k);
betak = rkrk2/rkrk;
rkrk = rkrk2;
vecadd(d1k, d1k, r1k, betak, one_z);
}
return ret;
}
gctl::clcg_return_code gctl::clcg_solver::clcgs(array<std::complex<double> > &m, const array<std::complex<double> > &B)
{
clcg_return_code ret;
return ret;
}
gctl::clcg_return_code gctl::clcg_solver::clbicgstab(array<std::complex<double> > &m, const array<std::complex<double> > &B)
{
clcg_return_code ret;
return ret;
}
gctl::clcg_return_code gctl::clcg_solver::cltfqmr(array<std::complex<double> > &m, const array<std::complex<double> > &B)
{
clcg_return_code ret;
return ret;
}

166
lib/optimization/clcg.h Normal file
View File

@ -0,0 +1,166 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#ifndef _GCTL_CLCG_H
#define _GCTL_CLCG_H
#include "gctl/core.h"
#include "gctl/maths.h"
#include "gctl/algorithm.h"
#include "gctl_optimization_config.h"
#ifdef GCTL_OPTIMIZATION_TOML
#include "toml.hpp"
#endif // GCTL_OPTIMIZATION_TOML
#if defined _WINDOWS || __WIN32__
#include "windows.h"
#endif // _WINDOWS || __WIN32__
namespace gctl
{
/**
* @brief Types of method that could be recognized by the clcg_solver() function.
*/
enum clcg_solver_type
{
/**
* Jacob's Bi-Conjugate Gradient Method
*/
CLCG_BICG,
/**
* Bi-Conjugate Gradient Method accelerated for complex symmetric A
*/
CLCG_BICG_SYM,
/**
* Conjugate Gradient Squared Method with real coefficients.
*/
CLCG_CGS,
/**
* Biconjugate gradient method.
*/
CLCG_BICGSTAB,
/**
* Transpose Free Quasi-Minimal Residual Method
*/
CLCG_TFQMR,
};
/**
* @brief return value of the clcg_solver() function
*/
enum clcg_return_code
{
CLCG_SUCCESS = 0, ///< The solver function terminated successfully.
CLCG_CONVERGENCE = 0, ///< The iteration reached convergence.
CLCG_STOP, ///< The iteration is stopped by the monitoring function.
CLCG_ALREADY_OPTIMIZIED, ///< The initial solution is already optimized.
// A negative number means a error
CLCG_UNKNOWN_ERROR = -1024, ///< Unknown error.
CLCG_INVILAD_VARIABLE_SIZE, ///< The variable size is negative
CLCG_INVILAD_MAX_ITERATIONS, ///< The maximal iteration times is negative.
CLCG_INVILAD_EPSILON, ///< The epsilon is negative.
CLCG_REACHED_MAX_ITERATIONS, ///< Iteration reached maximal limit.
CLCG_NAN_VALUE, ///< Nan value.
CLCG_INVALID_POINTER, ///< Invalid pointer.
CLCG_SIZE_NOT_MATCH, ///< Sizes of m and B do not match
CLCG_UNKNOWN_SOLVER, ///< Unknown solver
};
/**
* @brief Parameters of the conjugate gradient methods.
*/
struct clcg_para
{
/**
* Maximal iteration times. The process will continue till the convergence is met
* if this option is set to zero (default).
*/
int max_iterations;
/**
* Epsilon for convergence test.
* This parameter determines the accuracy with which the solution is to be found.
* A minimization terminates when ||g||/max(||g0||, 1.0) <= epsilon or sqrt(||g||)/N
* <= epsilon for the lcg_solver() function, where ||.|| denotes the Euclidean (L2) norm.
* The default value of epsilon is 1e-8. For box-constrained methods,the convergence test
* is implemented using ||P(m-g) - m|| <= epsilon, in which P is the projector that
* transfers m into the constrained domain.
*/
double epsilon;
/**
* Whether to use absolute mean differences (AMD) between |Ax - B| to evaluate the process.
* The default value is false which means the gradient based evaluating method is used.
* The AMD based method will be used if this variable is set to true. This parameter is only
* applied to the non-constrained methods.
*/
int abs_diff;
};
class clcg_solver
{
private:
clcg_para clcg_param_;
size_t clcg_inter_;
bool clcg_silent_;
array<std::complex<double> > r1k, r2k, d1k, d2k;
array<std::complex<double> > Ax;
public:
clcg_solver();
virtual ~clcg_solver();
virtual void CLCG_Ax(const array<std::complex<double> > &x, array<std::complex<double> > &ax,
matrix_layout_e layout, conjugate_type_e conj) = 0;
virtual int CLCG_Progress(const array<std::complex<double> > &m, const double converge, const clcg_para &param, size_t t);
void clcg_silent();
void set_clcg_report_interval(size_t inter);
void set_clcg_para(const clcg_para &param);
void clcg_error_str(clcg_return_code err_code, std::ostream &ss = std::clog, bool err_throw = false);
clcg_para default_clcg_para();
#ifdef GCTL_OPTIMIZATION_TOML
void set_clcg_para(const toml::value &toml_data);
#endif // GCTL_OPTIMIZATION_TOML
clcg_return_code clbicg(array<std::complex<double> > &m, const array<std::complex<double> > &B);
clcg_return_code clbicg_symmetric(array<std::complex<double> > &m, const array<std::complex<double> > &B);
clcg_return_code clcgs(array<std::complex<double> > &m, const array<std::complex<double> > &B);
clcg_return_code clbicgstab(array<std::complex<double> > &m, const array<std::complex<double> > &B);
clcg_return_code cltfqmr(array<std::complex<double> > &m, const array<std::complex<double> > &B);
void CLCG_Minimize(array<std::complex<double> > &m, const array<std::complex<double> > &B,
clcg_solver_type solver_id = CLCG_CGS, std::ostream &ss = std::clog,
bool verbose = true, bool er_throw = false);
};
}
#endif // _GCTL_CLCG_H

129
lib/optimization/dwa.cpp Normal file
View File

@ -0,0 +1,129 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include "dwa.h"
gctl::dwa::dwa()
{
fx_c_ = 0;
l_ready_ = false;
}
gctl::dwa::~dwa(){}
void gctl::dwa::InitDWA(size_t num, size_t grad_num)
{
fx_n_ = num;
K_ = 1.0*num;
T_ = 1.0;
wgts_.resize(num, 1.0);
L_p1_.resize(num, 1.0);
L_p2_.resize(num, 1.0);
grad_.resize(grad_num, 0.0);
rcd_wgts_.push_back(wgts_);
return;
}
void gctl::dwa::AddSingleLoss(double fx, const array<double> &g)
{
multi_fx_ += wgts_[fx_c_]*fx;
L_p2_[fx_c_] = L_p1_[fx_c_];
L_p1_[fx_c_] = fx;
for (size_t i = 0; i < g.size(); i++)
{
grad_[i] += wgts_[fx_c_]*g[i];
}
fx_c_++;
return;
}
void gctl::dwa::UpdateWeights()
{
double sum = 0.0;
for (size_t i = 0; i < fx_n_; i++)
{
if (l_ready_) wgts_[i] = exp(L_p1_[i]/(L_p2_[i]*T_));
else wgts_[i] = 1.0;
sum += wgts_[i];
}
for (size_t i = 0; i < fx_n_; i++)
{
wgts_[i] *= K_/sum;
}
l_ready_ = true;
rcd_wgts_.push_back(wgts_);
return;
}
double gctl::dwa::DWALoss(array<double> &g)
{
if (fx_c_ != fx_n_)
{
throw std::runtime_error("Not enough loss functions evaluated. From gctl::dwa::UpdateWeights()");
}
double fx = multi_fx_;
g = grad_;
fx_c_ = 0;
multi_fx_ = 0.0;
grad_.assign_all(0.0);
return fx;
}
void gctl::dwa::set_control_temperature(double t)
{
T_ = t;
return;
}
void gctl::dwa::set_normal_sum(double k)
{
K_ = k;
return;
}
void gctl::dwa::get_records(array<double> &logs)
{
logs.resize(fx_n_*rcd_wgts_.size());
for (size_t i = 0; i < rcd_wgts_.size(); i++)
{
for (size_t j = 0; j < fx_n_; j++)
{
logs[i*fx_n_ + j] = rcd_wgts_[i][j];
}
}
return;
}

114
lib/optimization/dwa.h Normal file
View File

@ -0,0 +1,114 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#ifndef _GCTL_DWA_H
#define _GCTL_DWA_H
#include "gctl/core.h"
namespace gctl
{
/**
* @brief Lost balanced multitask evaluation.
*
* @note Reference: 2019. End-to-end multitask learning with attention.
*
*/
class dwa
{
private:
bool l_ready_;
size_t fx_c_, fx_n_;
double K_, T_, multi_fx_;
array<double> wgts_;
array<double> L_p1_, L_p2_;
array<double> grad_;
std::vector<array<double>> rcd_wgts_;
public:
dwa();
virtual ~dwa();
/**
* @brief Initiate the number of loss functions and size of the model gradients.
*
* @note This function must be called at first.
*
* @param num Number of the loss functions
* @param grad_num Size of the model gradients
*/
void InitDWA(size_t num, size_t grad_num);
/**
* @brief Add the value of a single loss function and the current model gradients.
*
* @param fx objective value
* @param g model gradients
*/
void AddSingleLoss(double fx, const array<double> &g);
/**
* @brief Get the merged objective value and the model gradients.
*
* @note All single loss functions must be added before calling this function. The merged objective value and the model gradients will be reset after the calling.
*
* @param g model gradients
*
* @return objective value
*/
double DWALoss(array<double> &g);
/**
* @brief Update weights for single loss functions using the DWA algorithm.
*
*/
void UpdateWeights();
/**
* @brief Set the cooling temperature. The bigger value is, the closer the weights will be to one. The default is 1.0.
*
* @param t Input temperature
*/
void set_control_temperature(double t);
/**
* @brief Set the normal sum of the weights. Ths default equals to function size.
*
* @param k Input sum
*/
void set_normal_sum(double k);
/**
* @brief Get the recorded weights. Size of the log equals the function size times iteration times.
*
* @param logs Output log
*/
void get_records(array<double> &logs);
};
}
#endif // _GCTL_DWA_H

1
lib/optimization/gctl_optimization_config.h Normal file
View File

@ -0,0 +1 @@
#define GCTL_OPTIMIZATION_TOML

328
lib/optimization/gradnorm.cpp Normal file
View File

@ -0,0 +1,328 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include "gradnorm.h"
gctl::grad_norm::grad_norm()
{
fx_c_ = 0;
alpha_ = 1.0;
lamda_ = 0.001;
initialized_ = false;
}
gctl::grad_norm::~grad_norm(){}
void gctl::grad_norm::InitGradNorm(size_t num, size_t grad_num)
{
fx_n_ = num;
T_ = 1.0;
resi_T_ = 0.0;
fst_iter_.resize(num, true);
wgts_.resize(num, 1.0/num);
fx0_.resize(num, 0.0);
Gw_.resize(num, 0.0);
Gdw_.resize(num, 0.0);
Lx_.resize(num, 0.0);
grad_.resize(grad_num, 0.0);
rcd_fxs_.resize(num, 0.0);
fixed_wgts_.resize(num, -1.0);
rcd_wgts_.reserve(100000);
for (size_t i = 0; i < fx_n_; i++)
{
rcd_wgts_.push_back(wgts_[i]);
}
initialized_ = true;
return;
}
double gctl::grad_norm::AddSingleLoss(double fx, const array<double> &g)
{
if (fst_iter_[fx_c_])
{
fx0_[fx_c_] = fx;
fst_iter_[fx_c_] = false;
}
Lx_[fx_c_] = fx/fx0_[fx_c_];
double curr_fx = wgts_[fx_c_]*fx;
multi_fx_ += curr_fx;
rcd_fxs_[fx_c_] = fx;
double sum = 0.0;
for (size_t i = 0; i < g.size(); i++)
{
sum += g[i]*g[i];
grad_[i] += wgts_[fx_c_]*g[i];
}
Gw_[fx_c_] = sqrt(wgts_[fx_c_]*wgts_[fx_c_]*sum);
Gdw_[fx_c_] = sqrt(sum); // wgts_[fx_c_]*sum/Gw_[fx_c_]
fx_c_++;
return curr_fx;
}
void gctl::grad_norm::UpdateWeights()
{
double ac = 0;
double avg_Lx = 0.0, avg_Gw = 0.0;
resi_T_ = T_;
for (size_t i = 0; i < fx_n_; i++)
{
if (fixed_wgts_[i] < 0.0)
{
avg_Lx += Lx_[i];
avg_Gw += Gw_[i];
ac += 1.0;
}
else resi_T_ -= fixed_wgts_[i];
}
avg_Lx /= ac;
avg_Gw /= ac;
double r_i, sum = 0.0;
// L1 norm approach
for (size_t i = 0; i < fx_n_; i++)
{
if (fixed_wgts_[i] < 0.0)
{
r_i = Lx_[i]/avg_Lx;
if (Gw_[i] >= avg_Gw*pow(r_i, alpha_))
{
wgts_[i] -= lamda_*Gdw_[i];
}
else wgts_[i] += lamda_*Gdw_[i];
// make sure the weights are positive
wgts_[i] = std::max(wgts_[i], 1e-16);
sum += wgts_[i];
}
}
for (size_t i = 0; i < fx_n_; i++)
{
if (fixed_wgts_[i] < 0.0) wgts_[i] *= resi_T_/sum;
rcd_wgts_.push_back(wgts_[i]);
}
return;
}
void gctl::grad_norm::ShowStatistics(std::ostream &ss, bool one_line)
{
double s, t = 0.0;
if (one_line)
{
ss << "Wgts:";
for (size_t i = 0; i < fx_n_; i++)
{
ss << " " << wgts_[i];
}
ss << ", Loss:";
for (size_t i = 0; i < fx_n_; i++)
{
ss << " " << rcd_fxs_[i];
}
ss << ", WgtLoss:";
for (size_t i = 0; i < fx_n_; i++)
{
s = wgts_[i]*rcd_fxs_[i];
ss << " " << s;
t += s;
}
ss << ", Total: " << t << "\n";
return;
}
ss << "----------------------------\n";
ss << "GradNorm's Progress\n";
ss << "Tasks' weight: ";
for (size_t i = 0; i < fx_n_; i++)
{
ss << wgts_[i] << " | ";
}
ss << "\n";
ss << "Tasks' loss: ";
for (size_t i = 0; i < fx_n_; i++)
{
ss << rcd_fxs_[i] << " | ";
}
ss << "\n";
ss << "Weighted losses: ";
for (size_t i = 0; i < fx_n_; i++)
{
s = wgts_[i]*rcd_fxs_[i];
ss << s << " | ";
t += s;
}
ss << t << " (total) |\n";
ss << "----------------------------\n";
return;
}
double gctl::grad_norm::GradNormLoss(array<double> &g)
{
if (fx_c_ != fx_n_)
{
throw std::runtime_error("Not all loss functions evaluated. From gctl::grad_norm::GradNormLoss()");
}
if (!initialized_)
{
throw std::runtime_error("GradNorm is not initialized. From gctl::grad_norm::GradNormLoss()");
}
double fx = multi_fx_;
g = grad_;
fx_c_ = 0;
multi_fx_ = 0.0;
grad_.assign_all(0.0);
return fx;
}
void gctl::grad_norm::set_control_weight(double a)
{
alpha_ = a;
return;
}
void gctl::grad_norm::set_normal_sum(double t)
{
T_ = t;
return;
}
void gctl::grad_norm::set_weight_step(double l)
{
lamda_ = l;
return;
}
void gctl::grad_norm::set_fixed_weight(int id, double wgt)
{
if (id < 0 || id >= fx_n_)
{
throw std::runtime_error("Invalid loss function's index. From gctl::grad_norm::set_fixed_weight(...)");
}
if (wgt <= 0.0 || wgt >= T_)
{
throw std::runtime_error("Invalid fixed weight value. From gctl::grad_norm::set_fixed_weight(...)");
}
fixed_wgts_[id] = wgt;
wgts_[id] = wgt;
resi_T_ = T_;
double ac = 0.0;
for (size_t i = 0; i < fx_n_; i++)
{
if (fixed_wgts_[i] > 0.0) resi_T_ -= fixed_wgts_[i];
else ac += 1.0;
}
if (resi_T_ <= 0.0)
{
throw std::runtime_error("Invalid tasks' weight detected. From gctl::grad_norm::UpdateWeights()");
}
for (size_t i = 0; i < fx_n_; i++)
{
if (fixed_wgts_[i] < 0.0) wgts_[i] = resi_T_/ac;
}
for (size_t i = 0; i < fx_n_; i++)
{
rcd_wgts_[i] = wgts_[i];
}
return;
}
void gctl::grad_norm::set_initial_weights(const array<double> &w)
{
if (w.size() != fx_n_)
{
throw std::runtime_error("Invalid input array size. From gctl::grad_norm::set_initial_weights(...)");
}
double sum = 0.0;
for (size_t i = 0; i < fx_n_; i++)
{
wgts_[i] = w[i];
sum += wgts_[i];
}
for (size_t i = 0; i < fx_n_; i++)
{
wgts_[i] *= T_/sum;
rcd_wgts_[i] = wgts_[i];
}
return;
}
void gctl::grad_norm::get_records(array<double> &logs)
{
logs.resize(rcd_wgts_.size());
for (size_t i = 0; i < rcd_wgts_.size(); i++)
{
logs[i] = rcd_wgts_[i];
}
return;
}
void gctl::grad_norm::save_records(std::string file)
{
std::ofstream ofile;
open_outfile(ofile, file, ".txt");
ofile << "# 'tw' for 'task weight'\n# ";
for (size_t j = 0; j < fx_n_; j++)
{
ofile << "tw" << std::to_string(j) << " ";
}
ofile << "\n";
for (int i = 0; i < rcd_wgts_.size(); i++)
{
ofile << rcd_wgts_[i] << " ";
if ((i+1)%fx_n_ == 0) ofile << "\n";
}
ofile.close();
}

159
lib/optimization/gradnorm.h Normal file
View File

@ -0,0 +1,159 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#ifndef _GCTL_GRADNORM_H
#define _GCTL_GRADNORM_H
#include "gctl/core.h"
#include "gctl/io.h"
namespace gctl
{
/**
* @brief Gradient normalized (balanced) multitask evaluation.
*
* @note Reference: Zhao Chen et. al., 2018. GradNorm: Gradient normalization
* for adaptive loss balancing in deep multitask networks.
*
*/
class grad_norm
{
private:
bool initialized_;
size_t fx_n_, fx_c_;
double resi_T_, T_;
double lamda_, alpha_, multi_fx_;
array<bool> fst_iter_;
array<double> wgts_;
array<double> fx0_;
array<double> Gw_, Gdw_, Lx_;
array<double> grad_;
array<double> rcd_fxs_;
array<double> fixed_wgts_;
std::vector<double> rcd_wgts_;
public:
grad_norm();
virtual ~grad_norm();
/**
* @brief Initiate the number of loss functions and size of the model gradients.
*
* @note This function must be called at first.
*
* @param num Number of the total loss functions
* @param grad_num Size of the model gradients
*/
void InitGradNorm(size_t num, size_t grad_num);
/**
* @brief Add the value of a single loss function and the current model gradients.
*
* @param fx objective value
* @param g model gradients
*
* @return weighted value of the current loss function
*/
double AddSingleLoss(double fx, const array<double> &g);
/**
* @brief Get the merged objective value and the model gradients.
*
* @note All single loss functions must be added before calling this function. The
* merged objective value and the model gradients will be reset after the calling.
*
* @param g model gradients
*
* @return objective value
*/
double GradNormLoss(array<double> &g);
/**
* @brief Update weights for single loss functions using the GradNorm algorithm.
*
*/
void UpdateWeights();
/**
* @brief Show statistics of the tasks' weight and loss function's value.
*
*/
void ShowStatistics(std::ostream &ss = std::clog, bool one_line = false);
/**
* @brief Set the control factor alpha. The default is 1.0
*
* @param a Input alpha
*/
void set_control_weight(double a);
/**
* @brief Set the normal sum of the weights. Ths default equals to function size.
*
* @param t Input sum
*/
void set_normal_sum(double t);
/**
* @brief Set a learning rate of the weights. The default is 0.001
*
* @param l Input learning rate
*/
void set_weight_step(double l);
/**
* @brief Set the fixed weight.
*
* @param id Index of the loss function
* @param wgt weight of the loss function
*/
void set_fixed_weight(int id, double wgt);
/**
* @brief Set the initial weights
*
* @param w Input weights
*/
void set_initial_weights(const array<double> &w);
/**
* @brief Get the recorded weights. Size of the log equals the function size times iteration times.
*
* @param logs Output log
*/
void get_records(array<double> &logs);
/**
* @brief Save recored weights to file.
*
* @param file File name
*/
void save_records(std::string file);
};
}
#endif // _GCTL_GRADNORM_H

1897
lib/optimization/lbfgs.cpp Normal file
View File

File diff suppressed because it is too large Load Diff

559
lib/optimization/lbfgs.h Normal file
View File

@ -0,0 +1,559 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#ifndef _GCTL_LBFGS_H
#define _GCTL_LBFGS_H
#include "gctl/core.h"
#include "gctl/maths.h"
#include "gctl/algorithm.h"
#include "gctl_optimization_config.h"
#ifdef GCTL_OPTIMIZATION_TOML
#include "toml.hpp"
#endif // GCTL_OPTIMIZATION_TOML
#if defined _WINDOWS || __WIN32__
#include "windows.h"
#endif // _WINDOWS || __WIN32__
namespace gctl
{
/**
* @brief Return value of the lbfgs() function. Roughly speaking, a negative value indicates an error.
*/
enum lbfgs_return_code
{
/** L-BFGS reaches convergence. */
LBFGS_EPS_CONVERGENCE = 0,
LBFGS_DELTA_CONVERGENCE,
LBFGS_RESI_CONVERGENCE,
LBFGS_STOP, //1
/** The initial variables already minimize the objective function. */
LBFGS_ALREADY_MINIMIZED, //2
/** Unknown error. */
LBFGSERR_UNKNOWNERROR = -1024,
/** Logic error. */
LBFGSERR_LOGICERROR, //-1023
/** Insufficient memory. */
LBFGSERR_OUTOFMEMORY, //-1022
/** The minimization process has been canceled. */
LBFGSERR_CANCELED,
/** Invalid number of variables specified. */
LBFGSERR_INVALID_N,
/** Invalid number of variables (for SSE) specified. */
LBFGSERR_INVALID_N_SSE,
/** The array x must be aligned to 16 (for SSE). */
LBFGSERR_INVALID_X_SSE,
/** Invalid parameter lbfgs_para::epsilon specified. */
LBFGSERR_INVALID_EPSILON,
/** Invalid parameter lbfgs_para::past specified. */
LBFGSERR_INVALID_TESTPERIOD,
/** Invalid parameter lbfgs_para::delta specified. */
LBFGSERR_INVALID_DELTA,
/** Invalid parameter lbfgs_para::linesearch specified. */
LBFGSERR_INVALID_LINESEARCH,
/** Invalid parameter lbfgs_para::max_step specified. */
LBFGSERR_INVALID_MINSTEP,
/** Invalid parameter lbfgs_para::max_step specified. */
LBFGSERR_INVALID_MAXSTEP,
/** Invalid parameter lbfgs_para::ftol specified. */
LBFGSERR_INVALID_FTOL,
/** Invalid parameter lbfgs_para::wolfe specified. */
LBFGSERR_INVALID_WOLFE,
/** Invalid parameter lbfgs_para::gtol specified. */
LBFGSERR_INVALID_GTOL,
/** Invalid parameter lbfgs_para::xtol specified. */
LBFGSERR_INVALID_XTOL,
/** Invalid parameter lbfgs_para::max_linesearch specified. */
LBFGSERR_INVALID_MAXLINESEARCH,
/** Invalid parameter lbfgs_para::orthantwise_c specified. */
LBFGSERR_INVALID_ORTHANTWISE,
/** Invalid parameter lbfgs_para::orthantwise_start specified. */
LBFGSERR_INVALID_ORTHANTWISE_START,
/** Invalid parameter lbfgs_para::orthantwise_end specified. */
LBFGSERR_INVALID_ORTHANTWISE_END,
/** The line-search step went out of the interval of uncertainty. */
LBFGSERR_OUTOFINTERVAL,
/** A logic error occurred; alternatively, the interval of uncertainty
became too small. */
LBFGSERR_INCORRECT_TMINMAX,
/** A rounding error occurred; alternatively, no line-search step
satisfies the sufficient decrease and curvature conditions. */
LBFGSERR_ROUNDING_ERROR,
/** The line-search step became smaller than lbfgs_para::min_step. */
LBFGSERR_MINIMUMSTEP,
/** The line-search step became larger than lbfgs_para::max_step. */
LBFGSERR_MAXIMUMSTEP,
/** The line-search routine reaches the maximum number of evaluations. */
LBFGSERR_MAXIMUMLINESEARCH,
/** The algorithm routine reaches the maximum number of iterations. */
LBFGSERR_MAXIMUMITERATION,
/** Relative width of the interval of uncertainty is at most
lbfgs_para::xtol. */
LBFGSERR_WIDTHTOOSMALL,
/** A logic error (negative line-search step) occurred. */
LBFGSERR_INVALIDPARAMETERS,
/** The current search direction increases the objective function value. */
LBFGSERR_INCREASEGRADIENT,
};
// 枚举类型 线性搜索方法
// 0 MoreThuente方法
// 1 Armijo条件方法
// 2 标准Wolfe条件方法
// 3 增强Wolfe条件方法
/**
* @brief Line search algorithms.
*/
enum line_search_type
{
/** The default algorithm (MoreThuente method). */
LBFGS_LINESEARCH_DEFAULT = 0,
/** MoreThuente method proposd by More and Thuente. */
LBFGS_LINESEARCH_MORETHUENTE = 0,
/**
* Backtracking method with the Armijo condition.
* The backtracking method finds the step length such that it satisfies
* the sufficient decrease (Armijo) condition,
* - f(x + a * d) <= f(x) + lbfgs_para::ftol * a * g(x)^T d,
*
* where x is the current point, d is the current search direction, and
* a is the step length.
*/
LBFGS_LINESEARCH_BACKTRACKING_ARMIJO = 1,
/** The backtracking method with the defualt (regular Wolfe) condition. */
LBFGS_LINESEARCH_BACKTRACKING = 2,
/**
* Backtracking method with regular Wolfe condition.
* The backtracking method finds the step length such that it satisfies
* both the Armijo condition (LBFGS_LINESEARCH_BACKTRACKING_ARMIJO)
* and the curvature condition,
* - g(x + a * d)^T d >= lbfgs_para::wolfe * g(x)^T d,
*
* where x is the current point, d is the current search direction, and
* a is the step length.
*/
LBFGS_LINESEARCH_BACKTRACKING_WOLFE = 2,
/**
* Backtracking method with strong Wolfe condition.
* The backtracking method finds the step length such that it satisfies
* both the Armijo condition (LBFGS_LINESEARCH_BACKTRACKING_ARMIJO)
* and the following condition,
* - |g(x + a * d)^T d| <= lbfgs_para::wolfe * |g(x)^T d|,
*
* where x is the current point, d is the current search direction, and
* a is the step length.
*/
LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE = 3,
LBFGS_LINESEARCH_BACKTRACKING_ARMIJO_QUAD = 4,
//LBFGS_LINESEARCH_BACKTRACKING_QUAD = 5,
//LBFGS_LINESEARCH_BACKTRACKING_WOLFE_QUAD = 5,
//LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE_QUAD = 6,
};
// L-BFGS参数类型。参数很多，简要说明如下：
// m L-BFGS算法中储存的前序sk与yk向量个数，这个值控制了算法使用的内存多少，默认值为6（不建议小于3的值），值多大近似精度越高，计算量也越大。
// epsilon 迭代的终止精度，默认值为1e-5
// past 以delta(不同迭代次数的目标函数值)为基础的迭代终止条件数，past代表了以多少迭代次数之前的目标函数值作为delta计算的间隔，默认值为0，
// 即不以delta为迭代终止条件。
// delta (f' - f) / f 不同迭代次数时目标函数之差与当前目标函数值之比，但past不为0时会计算。
// max_iterations 最大迭代次数，为0时表示一直迭代到终止条件被满足或出现其他错误。
// linesearch 线性搜索方式，由此文件前述枚举类型定义。
// max_linesearch 每次迭代中线性搜索的最大次数，默认值为40
// min_step 线性搜索中的最小步长，默认值为1e-20
// max_step 线性搜索中的最大步长，默认值为1e+20
// ftol 线性搜索的精度值，默认值为1e-4，取值范围（0-0.5）。
// wolfe Wolfe线性搜索中的控制参数，默认值为0.9，大于ftol小于1.0
// gtol 线性搜索中的控制参数，默认值为0.9，大于ftol小于1.0
// xtol 浮点数精度，默认值为1e-16
// orthantwise_c 模型参数x的L1模的乘积参数，默认值为0.0，此时算法即为L2模形式，当此参数大于0时，算法即为OWL-QN
// orthantwise_start 开始计算模型参数x的L1模的迭代序号
// orthantwise_end 终止计算模型参数x的L1模的迭代序号
/**
* L-BFGS optimization parameters.
* Call lbfgs_parameter_init() function to initialize parameters to the
* default values.
*/
struct lbfgs_para
{
/**
* The number of corrections to approximate the inverse hessian matrix.
* The L-BFGS routine stores the computation results of previous \ref m
* iterations to approximate the inverse hessian matrix of the current
* iteration. This parameter controls the size of the limited memories
* (corrections). The default value is \c 6. Values less than \c 3 are
* not recommended. Large values will result in excessive computing time.
*/
int m;
/**
* Epsilon for convergence test.
* This parameter determines the accuracy with which the solution is to
* be found. A minimization terminates when
* ||g|| < \ref epsilon * max(1, ||x||),
* where ||.|| denotes the Euclidean (L2) norm. The default value is
* \c 1e-5.
*/
double epsilon;
/**
* Distance for delta-based convergence test.
* This parameter determines the distance, in iterations, to compute
* the rate of decrease of the objective function. If the value of this
* parameter is zero, the library does not perform the delta-based
* convergence test. The default value is \c 0.
*/
int past;
/**
* Delta for convergence test.
* This parameter determines the minimum rate of decrease of the
* objective function. The library stops iterations when the
* following condition is met:
* (f' - f) / f < \ref delta,
* where f' is the objective value of \ref past iterations ago, and f is
* the objective value of the current iteration.
* The default value is \c 1e-5.
*/
double delta;
/**
* Residual for convergence test.
* This parameter determines the accuracy with which the solution is to
* be found. A minimization terminates when
* f(x) <= residual,
* The default value is \c 1e-8.
*
*/
double residual;
/**
* The maximum number of iterations.
* The lbfgs() function terminates an optimization process with
* ::LBFGSERR_MAXIMUMITERATION status code when the iteration count
* exceedes this parameter. Setting this parameter to zero continues an
* optimization process until a convergence or error. The default value
* is \c 0.
*/
int max_iterations;
/**
* The line search algorithm.
* This parameter specifies a line search algorithm to be used by the
* L-BFGS routine.
*/
int linesearch;
/**
* The maximum number of trials for the line search.
* This parameter controls the number of function and gradients evaluations
* per iteration for the line search routine. The default value is \c 40.
*/
int max_linesearch;
/**
* The minimum step of the line search routine.
* The default value is \c 1e-20. This value need not be modified unless
* the exponents are too large for the machine being used, or unless the
* problem is extremely badly scaled (in which case the exponents should
* be increased).
*/
double min_step;
/**
* The maximum step of the line search.
* The default value is \c 1e+20. This value need not be modified unless
* the exponents are too large for the machine being used, or unless the
* problem is extremely badly scaled (in which case the exponents should
* be increased).
*/
double max_step;
/**
* A parameter to control the accuracy of the line search routine.
* The default value is \c 1e-4. This parameter should be greater
* than zero and smaller than \c 0.5.
*/
double ftol;
/**
* A coefficient for the Wolfe condition.
* This parameter is valid only when the backtracking line-search
* algorithm is used with the Wolfe condition,
* ::LBFGS_LINESEARCH_BACKTRACKING_STRONG_WOLFE or
* ::LBFGS_LINESEARCH_BACKTRACKING_WOLFE .
* The default value is \c 0.9. This parameter should be greater
* the \ref ftol parameter and smaller than \c 1.0.
*/
double wolfe;
/**
* A parameter to control the accuracy of the line search routine.
* The default value is \c 0.9. If the function and gradient
* evaluations are inexpensive with respect to the cost of the
* iteration (which is sometimes the case when solving very large
* problems) it may be advantageous to set this parameter to a small
* value. A typical small value is \c 0.1. This parameter shuold be
* greater than the \ref ftol parameter (\c 1e-4) and smaller than
* \c 1.0.
*/
double gtol;
/**
* The machine precision for floating-point values.
* This parameter must be a positive value set by a client program to
* estimate the machine precision. The line search routine will terminate
* with the status code (::LBFGSERR_ROUNDING_ERROR) if the relative width
* of the interval of uncertainty is less than this parameter.
*/
double xtol;
/**
* Coeefficient for the L1 norm of variables.
* This parameter should be set to zero for standard minimization
* problems. Setting this parameter to a positive value activates
* Orthant-Wise Limited-memory Quasi-Newton (OWL-QN) method, which
* minimizes the objective function F(x) combined with the L1 norm |x|
* of the variables, {F(x) + C |x|}. This parameter is the coeefficient
* for the |x|, i.e., C. As the L1 norm |x| is not differentiable at
* zero, the library modifies function and gradient evaluations from
* a client program suitably; a client program thus have only to return
* the function value F(x) and gradients G(x) as usual. The default value
* is zero.
*/
double orthantwise_c;
/**
* Start index for computing L1 norm of the variables.
* This parameter is valid only for OWL-QN method
* (i.e., \ref orthantwise_c != 0). This parameter b (0 <= b < N)
* specifies the index number from which the library computes the
* L1 norm of the variables x,
* |x| := |x_{b}| + |x_{b+1}| + ... + |x_{N}| .
* In other words, variables x_1, ..., x_{b-1} are not used for
* computing the L1 norm. Setting b (0 < b < N), one can protect
* variables, x_1, ..., x_{b-1} (e.g., a bias term of logistic
* regression) from being regularized. The default value is zero.
*/
int orthantwise_start;
/**
* End index for computing L1 norm of the variables.
* This parameter is valid only for OWL-QN method
* (i.e., \ref orthantwise_c != 0). This parameter e (0 < e <= N)
* specifies the index number at which the library stops computing the
* L1 norm of the variables x,
*/
int orthantwise_end;
};
class lbfgs_solver
{
private:
lbfgs_para lbfgs_param_; ///< lbfgs 算法参数
bool lbfgs_silent_; ///< 显示运行信息
// 算法函数是私有的，不能直接使用，通过Minimize函数调用
// 下面是L-BFGS的主函数，各个参数的说明简要翻译如下：
// n 数组的长度，也就是待求的模型参数的数量
// x 模型参数数组的指针，函数通过指针直接操作模型数组，所以不需要返回计算结果。一开始赋给函数的数组即为
// 初始模型，函数结束后即为最优化结果
// ptr_fx 目标函数的值的指针，设计成指针可以方便在函数外部监控迭代过程的收敛情况
// retval 返回值。无错即为0，非0值代表此文件上部枚举类型中的对应错误。此文件下部定义的错误信息显示即利用此返回值与
// 预定义的枚举类型输出相应的错误信息。
/**
* Start a L-BFGS optimization.
*
* @param x The array of variables. A client program can set
* default values for the optimization and receive the
* optimization result through this array. This array
* must be allocated by ::lbfgs_malloc function
* for libLBFGS built with SSE/SSE2 optimization routine
* enabled. The library built without SSE/SSE2
* optimization does not have such a requirement.
* @param ptr_fx The pointer to the variable that receives the final
* value of the objective function for the variables.
* This argument can be set to \c NULL if the final
* value of the objective function is unnecessary.
* @retval The status code. This function returns zero if the
* minimization process terminates without an error. A
* non-zero value indicates an error.
*/
lbfgs_return_code lbfgs(array<double> &x, double &ptr_fx, std::ostream &ss);
lbfgs_return_code lbfgs_preconditioned(array<double> &x, double &ptr_fx, std::ostream &ss);
// 线性搜索方法 内部私有函数 不能直接使用
lbfgs_return_code line_search_backtracking(int n, gctl::array<double> &x, double *f, gctl::array<double> &g, gctl::array<double> &s,
double *stp, const gctl::array<double> &xp, const gctl::array<double> &gp, gctl::array<double> &wp, int &ls);
lbfgs_return_code line_search_backtracking_quad(int n, gctl::array<double> &x, double *f, gctl::array<double> &g, gctl::array<double> &s,
double *stp, const gctl::array<double> &xp, const gctl::array<double> &gp, gctl::array<double> &wp, int &ls);
lbfgs_return_code line_search_backtracking_owlqn(int n, gctl::array<double> &x, double *f, gctl::array<double> &g, gctl::array<double> &s,
double *stp, const gctl::array<double> &xp, const gctl::array<double> &gp, gctl::array<double> &wp, int &ls);
lbfgs_return_code line_search_morethuente(int n, gctl::array<double> &x, double *f, gctl::array<double> &g, gctl::array<double> &s,
double *stp, const gctl::array<double> &xp, const gctl::array<double> &gp, gctl::array<double> &wa, int &ls);
// 显示lbfgs函数返回值信息 主要是错误信息
void lbfgs_error_str(lbfgs_return_code err_code, std::ostream &ss = std::clog, bool err_throw = false);
public:
lbfgs_solver();
virtual ~lbfgs_solver();
/**
* @brief 不显示运行信息，仅抛出运行错误。
*
*/
void lbfgs_silent();
/**
* @brief 设置算法参数。
*
* @param in_param 参数对象
*/
void set_lbfgs_para(const lbfgs_para &in_param);
#ifdef GCTL_OPTIMIZATION_TOML
/**
* @brief 设置算法参数。
*
* @param toml_data toml数据对象
*/
void set_lbfgs_para(const toml::value &toml_data);
#endif // GCTL_OPTIMIZATION_TOML
/**
* @brief 返回一个全为默认值的参数对象。
*
* @return lbfgs_para
*/
lbfgs_para default_lbfgs_para();
/**
* @brief 显示当前运行参数
*
* @param ss 标准输出流
*/
void show_lbfgs_para(std::ostream &ss = std::clog);
// 目标函数与其梯度值计算函数的接口，参数简要说明如下：
// x 当前的模型参数值的指针
// g 当前模型参数值对应的梯度指针
// step 当前线性搜索所使用的步长
// retval 当前模型参数的目标函数值
/**
* Callback interface to provide objective function and gradient evaluations.
*
* The lbfgs() function call this function to obtain the values of objective
* function and its gradients when needed. A client program must implement
* this function to evaluate the values of the objective function and its
* gradients, given current values of variables.
*
* @param x The current values of variables.
* @param g The gradient vector. The callback function must compute
* the gradient values for the current variables.
* @param step The current step of the line search routine.
* @retval double The value of the objective function for the current
* variables.
*/
virtual double LBFGS_Evaluate(const array<double> &x, array<double> &g) = 0;
/**
* Callback interface to implement the preconditioning process.
*
* The lbfgs() function call this function for each iteration. Implementing
* this function, a client program can preform the preconditioning process.
*
* @param x The current values of variables.
* @param g The current gradient values of variables.
* @param d The current values of search directions.
* @param d_pre The values of search directions being preconditioned.
* The callback function must compute these values.
*/
virtual void LBFGS_Precondition(const array<double> &x, const array<double> &g, const array<double> &d, array<double> &d_pre);
// 进程函数的接口，参数简要说明如下：
// x 当前的模型参数值的指针
// g 当前模型参数值对应的梯度指针
// fx 目标函数的值
// xnorm 模型参数数组的L2模长
// gnorm 模型梯度数组的L2模长
// step 当前线性搜索所使用的步长
// k 迭代的次数
// ls 此次迭代所使用的线性搜索次数
// retval 返回0则lbfgs()函数继续，否则终止
/**
* Callback interface to receive the progress of the optimization process.
*
* The lbfgs() function call this function for each iteration. Implementing
* this function, a client program can store or display the current progress
* of the optimization process.
*
* @param x The current values of variables.
* @param g The current gradient values of variables.
* @param fx The current value of the objective function.
* @param converge Current value of the convergence test.
* @param rate Current value of the delta-based convergence test.
* @param param 这是我们添加了一个指针以使用参数类型来监控迭代流程
* @param k The iteration count.
* @param ls The number of evaluations called for this iteration.
* @param ss Output stream object.
* @retval int Zero to continue the optimization process. Returning a
* non-zero value will cancel the optimization process.
*/
virtual int LBFGS_Progress(const array<double> &x, const array<double> &g, const double fx,
const double converge, const double rate, const lbfgs_para param, int k, int ls, std::ostream &ss);
/**
* @brief 调用算法执行最小化流程
*
* @param m 初始模型，最优化结果也保存在此数组内
* @param ss 信息的输出流
* @param err_throw 仅抛出错误
* @return double 最终的目标函数值
*/
double LBFGS_Minimize(array<double> &m, std::ostream &ss = std::clog, bool err_throw = false);
/**
* @brief 调用算法执行最小化流程
*
* @param m 初始模型，最优化结果也保存在此数组内
* @param ss 信息的输出流
* @param verbose 使用输出详细信息
* @param err_throw 仅抛出错误
* @return double 最终的目标函数值
*/
double LBFGS_MinimizePreconditioned(array<double> &m, std::ostream &ss = std::clog, bool err_throw = false);
};
}
#endif // _GCTL_LBFGS_H

1002
lib/optimization/lcg.cpp Normal file
View File

File diff suppressed because it is too large Load Diff

387
lib/optimization/lcg.h Normal file
View File

@ -0,0 +1,387 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#ifndef _GCTL_LCG_H
#define _GCTL_LCG_H
#include "gctl/core.h"
#include "gctl/maths.h"
#include "gctl/algorithm.h"
#include "gctl_optimization_config.h"
#ifdef GCTL_OPTIMIZATION_TOML
#include "toml.hpp"
#endif // GCTL_OPTIMIZATION_TOML
#if defined _WINDOWS || __WIN32__
#include "windows.h"
#endif // _WINDOWS || __WIN32__
namespace gctl
{
/**
* @brief Types of method that could be recognized by the lcg_solver() function.
*/
enum lcg_solver_type
{
/**
* Conjugate gradient method.
*/
LCG_CG,
/**
* Preconditioned conjugate gradient method.
*/
LCG_PCG,
/**
* Conjugate gradient squared method.
*/
LCG_CGS,
/**
* Biconjugate gradient method.
*/
LCG_BICGSTAB,
/**
* Biconjugate gradient method with restart.
*/
LCG_BICGSTAB2,
/**
* Conjugate gradient method with projected gradient for inequality constraints.
* This algorithm comes without non-monotonic linear search for the step length.
*/
LCG_PG,
/**
* Conjugate gradient method with spectral projected gradient for inequality constraints.
* This algorithm comes with non-monotonic linear search for the step length.
*/
LCG_SPG,
};
/**
* @brief return value of the lcg_solver() function
*/
enum lcg_return_code
{
LCG_SUCCESS = 0, ///< The solver function terminated successfully.
LCG_CONVERGENCE = 0, ///< The iteration reached convergence.
LCG_STOP, ///< The iteration is stopped by the monitoring function.
LCG_ALREADY_OPTIMIZIED, ///< The initial solution is already optimized.
// A negative number means a error
LCG_UNKNOWN_ERROR = -1024, ///< Unknown error.
LCG_INVILAD_VARIABLE_SIZE, ///< The variable size is negative
LCG_INVILAD_MAX_ITERATIONS, ///< The maximal iteration times is negative.
LCG_INVILAD_EPSILON, ///< The epsilon is negative.
LCG_INVILAD_RESTART_EPSILON, ///< The restart epsilon is negative.
LCG_REACHED_MAX_ITERATIONS, ///< Iteration reached maximal limit.
LCG_NULL_PRECONDITION_MATRIX, ///< Null precondition matrix.
LCG_NAN_VALUE, ///< Nan value.
LCG_INVALID_POINTER, ///< Invalid pointer.
LCG_INVALID_LAMBDA, ///< Invalid range for lambda.
LCG_INVALID_SIGMA, ///< Invalid range for sigma.
LCG_INVALID_BETA, ///< Invalid range for beta.
LCG_INVALID_MAXIM, ///< Invalid range for maxi_m.
LCG_SIZE_NOT_MATCH, ///< Sizes of m and B do not match
};
/**
* @brief Message type of the LCG algorithms.
*
*/
enum lcg_message_type
{
LCG_THROW, ///< throw error only
LCG_ERROR, ///< display error only
LCG_SOLUTION, ///< display info for evry solution
LCG_ITERATION, ///< display info for every iteration
};
/**
* @brief Parameters of the conjugate gradient methods.
*/
struct lcg_para
{
/**
* Maximal iteration times. The process will continue till the convergence is met
* if this option is set to zero (default).
*/
int max_iterations;
/**
* Epsilon for convergence test.
* This parameter determines the accuracy with which the solution is to be
* found. A minimization terminates when ||g||/max(||g0||, 1.0) <= epsilon or
* sqrt(||g||)/N <= epsilon for the lcg_solver() function, where ||.|| denotes
* the Euclidean (L2) norm. The default value of epsilon is 1e-8.
*/
double epsilon;
/**
* Whether to use absolute mean differences (AMD) between |Ax - B| to evaluate the process.
* The default value is false which means the gradient based evaluating method is used.
* The AMD based method will be used if this variable is set to true. This parameter is only
* applied to the non-constrained methods.
*/
int abs_diff;
/**
* Restart epsilon for the LCG_BICGSTAB2 algorithm. The default value is 1e-6
*/
double restart_epsilon;
/**
* Initial step length for the project gradient method. The default is 1.0
*/
double step;
/**
* multiplier for updating solutions with the spectral projected gradient method. The range of
* this variable is (0, 1). The default is given as 0.95
*/
double sigma;
/**
* descending ratio for conducting the non-monotonic linear search. The range of
* this variable is (0, 1). The default is given as 0.9
*/
double beta;
/**
* The maximal record times of the objective values for the SPG method. The method use the
* objective values from the most recent maxi_m times to preform the non-monotonic linear search.
* The default value is 10.
*/
int maxi_m;
};
/**
* @brief This abstract class implements conjugate gradient algorithms for solving
* a linear system like Ax = B where A is a N*N matrix. As the actual variable
* we need is the product of 'Ax', the kernel matrix 'A' is not declared within
* the class definition. Instead, a pure virtual function is declared as the
* callback interface for calculating the product of 'Ax' as 'void LCG_Ax(const
* array<double> &x, array<double> &ax)'. A virtual function "int LCG_Progress(const
* array<double> &m, const double converge, const lcg_para &param, size_t t,
* std::ostream &ss)" could be reloaded for customed convergence tests.
*/
class lcg_solver
{
private:
lcg_para lcg_param_;
size_t lcg_inter_;
lcg_message_type lcg_msg_;
// make them class variables are more suitable for repetitively usages
array<double> zk, gk, dk, Adk;
array<double> rk, r0_T, pk, vk;
array<double> Apx, uk, qk, qk_m, wk;
array<double> m_new, gk_new;
array<double> sk, yk;
/**
* @brief Display info of a given return code. This is a private function
* and can only be called by other class functions.
*
* @param err_code Input retrun code
* @param ss Output stream of runtime info.
*/
void lcg_error_str(lcg_return_code err_code, std::ostream &ss);
public:
lcg_solver(); ///< default constructor
virtual ~lcg_solver(); ///< default de-constructor
/**
* @brief Callback interface for calculating the product of 'A' multipled by an arbitrary vector 'x'.
*
* @param x Multipler
* @param ax Product of Ax
*/
virtual void LCG_Ax(const array<double> &x, array<double> &ax) = 0;
/**
* @brief Callback interface for calculating the product of 'M' multipled by an arbitrary vector 'x'.
* In which 'M' is the inverse of the pre-conditioning matrix. This function must be reloaded for the
* LCG_PCG algorithm.
*
* @param x Multipler
* @param mx Product of Ax
*/
virtual void LCG_Mx(const array<double> &x, array<double> &mx);
/**
* @brief Utility function for monitoring the solving process.
*
* @param m Current solution
* @param converge Current convergence
* @param param Employed parameters
* @param t Current iterative times
* @param ss Output stream of runtime info.
* @return Quit the solver if returned a non-zero value.
*/
virtual int LCG_Progress(const array<double> &m, const double converge, const lcg_para &param, size_t t, std::ostream &ss);
/**
* @brief Set the lcg message object
*
* @param msg Input message type.
*/
void set_lcg_message(lcg_message_type msg);
/**
* @brief Set the lcg report intervals
*
* @param inter Input reprot intervals.
*/
void set_lcg_report_interval(size_t inter);
/**
* @brief Set the lcg para object
*
* @param param Input lcg parameters.
*/
void set_lcg_para(const lcg_para &param);
/**
* @brief Return a lcg_para object with default values
*
* @return lcg_para
*/
lcg_para default_lcg_para();
#ifdef GCTL_OPTIMIZATION_TOML
/**
* @brief Set parameters of the conjugate gradient algorithms using a toml file.
* All parameter options must be listed under a top-level table 'lcg'. Available options
* under the 'lcg' table are as declared in the lcg_para structure.
*
* @param toml_data Input toml data
*/
void set_lcg_para(std::string filename);
/**
* @brief Set parameters of the conjugate gradient algorithms using a toml::value object.
* All parameter options must be listed under a top-level table 'lcg'. Available options
* under the 'lcg' table are as declared in the lcg_para structure.
*
* @param toml_data Input toml data
*/
void set_lcg_para(const toml::value &toml_data);
#endif // GCTL_OPTIMIZATION_TOML
/**
* @brief The allback interface for all CG algorithms. Set message type to LCG_THROW to suppresses all info outputs.
*
* @param m Initial/Input solution.
* @param B Right hand term of the system system.
* @param solver_id Selected solver type.
* @param ss Output stream of runtime info.
*/
void LCG_Minimize(array<double> &m, const array<double> &b, lcg_solver_type solver_id = LCG_CG, std::ostream &ss = std::clog);
/**
* @brief The allback interface for all CG algorithms. Set message type to LCG_THROW to suppresses all info outputs.
*
* @param m Initial/Input solution.
* @param B Right hand term of the system system.
* @param solver_id Selected solver type.
* @param low Lower bound of acceptable solutions.
* @param hig Higher bound of acceptable solutions.
* @param ss Output stream of runtime info.
*/
void LCG_MinimizeConstrained(array<double> &m, const array<double> &b, const array<double> &low, const array<double> &hig, lcg_solver_type solver_id = LCG_PG, std::ostream &ss = std::clog);
/**
* @brief The standalone callback interface for the CG algorithm. Set message type to LCG_THROW to suppresses all info outputs.
*
* @param m Initial/Input solution.
* @param B Right hand term of the system system.
* @param ss Output stream of runtime info.
*/
void lcg(array<double> &m, const array<double> &B, std::ostream &ss = std::clog);
/**
* @brief The standalone callback interface for the PCG algorithm. Set message type to LCG_THROW to suppresses all info outputs.
*
* @param m Initial/Input solution.
* @param B Right hand term of the system system.
* @param ss Output stream of runtime info.
*/
void lpcg(array<double> &m, const array<double> &B, std::ostream &ss = std::clog);
/**
* @brief The standalone callback interface for the CGS algorithm. Set message type to LCG_THROW to suppresses all info outputs.
*
* @param m Initial/Input solution.
* @param B Right hand term of the system system.
* @param ss Output stream of runtime info.
*/
void lcgs(array<double> &m, const array<double> &B, std::ostream &ss = std::clog);
/**
* @brief The standalone callback interface for the BICGSTAB algorithm. Set message type to LCG_THROW to suppresses all info outputs.
*
* @param m Initial/Input solution.
* @param B Right hand term of the system system.
* @param ss Output stream of runtime info.
*/
void lbicgstab(array<double> &m, const array<double> &B, std::ostream &ss = std::clog);
/**
* @brief The standalone callback interface for the BICGSTAB2 algorithm. Set message type to LCG_THROW to suppresses all info outputs.
*
* @param m Initial/Input solution.
* @param B Right hand term of the system system.
* @param ss Output stream of runtime info.
*/
void lbicgstab2(array<double> &m, const array<double> &B, std::ostream &ss = std::clog);
/**
* @brief The standalone callback interface for the PG algorithm. Set message type to LCG_THROW to suppresses all info outputs.
*
* @param m Initial/Input solution.
* @param B Right hand term of the system system.
* @param low Lower bound of acceptable solutions.
* @param hig Higher bound of acceptable solutions.
* @param ss Output stream of runtime info.
*/
void lpg(array<double> &m, const array<double> &B, const array<double> &low, const array<double> &hig, std::ostream &ss = std::clog);
/**
* @brief The standalone callback interface for the SPG algorithm. Set message type to LCG_THROW to suppresses all info outputs.
*
* @param m Initial/Input solution.
* @param B Right hand term of the system system.
* @param low Lower bound of acceptable solutions.
* @param hig Higher bound of acceptable solutions.
* @param ss Output stream of runtime info.
*/
void lspg(array<double> &m, const array<double> &B, const array<double> &low, const array<double> &hig, std::ostream &ss = std::clog);
};
}
#endif // _GCTL_LCG_H

505
lib/optimization/lgd.cpp Normal file
View File

@ -0,0 +1,505 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include "lgd.h"
/**
* Default parameter for the Lévy-Gradient Descent (L-GD) method.
*/
static const gctl::lgd_para lgd_defparam = {1000, 0, 1e-5, 1.0, 1.5, 0.01, 1e-8, -1.0};
gctl::lgd_solver::lgd_solver()
{
lgd_param_ = lgd_defparam;
lgd_inter_ = 1; lgd_ques_num_ = 0; lgd_trace_times_ = 0;
lgd_silent_ = lgd_has_range_ = lgd_has_alpha_ = lgd_save_trace_ = false;
}
gctl::lgd_solver::~lgd_solver(){}
int gctl::lgd_solver::LGD_Progress(const int curr_t, const double curr_fx, const double mean_fx, const double best_fx, const lgd_para &param)
{
if (lgd_silent_) return 0;
if (param.epsilon > 0.0 && mean_fx <= param.epsilon)
{
std::clog << GCTL_CLEARLINE << "\rF(x) = " << curr_fx << ", Mean F(x) = " << mean_fx << ", Best F(x) = " << best_fx << ", Times = " << curr_t;
return 0;
}
if (lgd_inter_ > 0 && curr_t%lgd_inter_ == 0)
{
std::clog << GCTL_CLEARLINE << "\rF(x) = " << curr_fx << ", Mean F(x) = " << mean_fx << ", Best F(x) = " << best_fx << ", Times = " << curr_t;
}
return 0;
}
void gctl::lgd_solver::lgd_silent()
{
lgd_silent_ = true;
return;
}
void gctl::lgd_solver::set_lgd_report_interval(int inter)
{
lgd_inter_ = inter;
return;
}
void gctl::lgd_solver::set_lgd_para(const lgd_para &in_param)
{
lgd_param_ = in_param;
return;
}
#ifdef GCTL_OPTIMIZATION_TOML
void gctl::lgd_solver::set_lgd_para(std::string filename)
{
toml::value toml_data;
toml_data = toml::parse(filename);
set_lgd_para(toml_data);
return;
}
void gctl::lgd_solver::set_lgd_para(const toml::value &toml_data)
{
lgd_param_ = lgd_defparam;
std::string LGD = "lgd";
if (toml_data.contains(LGD))
{
if (toml_data.at(LGD).contains("flight_times")) lgd_param_.flight_times = toml::find<int>(toml_data, LGD, "flight_times");
if (toml_data.at(LGD).contains("batch")) lgd_param_.batch = toml::find<int>(toml_data, LGD, "batch");
if (toml_data.at(LGD).contains("epsilon")) lgd_param_.epsilon = toml::find<double>(toml_data, LGD, "epsilon");
if (toml_data.at(LGD).contains("stddev_v")) lgd_param_.stddev_v = toml::find<double>(toml_data, LGD, "stddev_v");
if (toml_data.at(LGD).contains("beta")) lgd_param_.beta = toml::find<double>(toml_data, LGD, "beta");
if (toml_data.at(LGD).contains("alpha")) lgd_param_.alpha = toml::find<double>(toml_data, LGD, "alpha");
if (toml_data.at(LGD).contains("sigma")) lgd_param_.sigma = toml::find<double>(toml_data, LGD, "sigma");
if (toml_data.at(LGD).contains("lambda")) lgd_param_.lambda = toml::find<double>(toml_data, LGD, "lambda");
}
return;
}
#endif // GCTL_OPTIMIZATION_TOML
void gctl::lgd_solver::set_lgd_record_trace()
{
lgd_save_trace_ = true;
return;
}
void gctl::lgd_solver::show_solver()
{
std::clog << "Solver's Setup Panel\n";
std::clog << "-----------------------------\n";
std::clog << "Solver: LGD\n";
std::clog << "Flights = " << lgd_param_.flight_times << ", Batch = " << lgd_param_.batch << ", Epsilon = " << lgd_param_.epsilon << ", Lambda = " << lgd_param_.lambda << "\n";
std::clog << "STD(v) = " << lgd_param_.stddev_v << ", Beta = " << lgd_param_.beta << ", Alpha = " << lgd_param_.alpha << ", Sigma = " << lgd_param_.sigma << "\n";
std::clog << "=============================\n";
return;
}
void gctl::lgd_solver::save_lgd_trace(std::string trace_file)
{
if (lgd_trace_times_ == 0)
{
GCTL_ShowWhatError("[gctl::lgd_solver] No trace is recorded.", GCTL_WARNING_ERROR, 0, 0, 0);
return;
}
std::ofstream ofile;
open_outfile(ofile, trace_file, ".txt");
int m_size = lgd_trace_.size()/lgd_trace_times_;
ofile << "# L-GD flight traces.\n";
ofile << "# Each row represents an accepted solution.\n";
ofile << "# Model size: " << m_size << "\n";
ofile << "# Accepted solutions: " << lgd_trace_times_ << "\n";
for (size_t i = 0; i < lgd_trace_times_; i++)
{
for (size_t j = 0; j < m_size; j++)
{
ofile << lgd_trace_[i*m_size+j] << " ";
}
ofile << "\n";
}
ofile.close();
return;
}
void gctl::lgd_solver::lgd_error_str(lgd_return_code err_code, std::ostream &ss, bool err_throw)
{
#if defined _WINDOWS || __WIN32__
if (!err_throw)
{
if (err_code >= 0)
{
SetConsoleTextAttribute(GetStdHandle(STD_ERROR_HANDLE), FOREGROUND_INTENSITY | FOREGROUND_GREEN);
ss << "Success! ";
}
else
{
SetConsoleTextAttribute(GetStdHandle(STD_ERROR_HANDLE), FOREGROUND_INTENSITY | FOREGROUND_RED);
ss << "Fail! ";
}
}
#else
if (!err_throw)
{
if (err_code >= 0)
ss << "\033[1m\033[32mLGD Success! ";
else
ss << "\033[1m\033[31mLGD Fail! ";
}
#endif
std::string err_str;
switch (err_code)
{
case LGD_CONVERGENCE:
err_str = "The iteration has reached convergence."; break;
case LGD_STOP:
err_str = "The iteration is stopped by the progress monitoring function."; break;
case LGD_REACHED_MAX_ITERATIONS:
err_str = "The maximal flight times has been reached."; break;
case LGD_INVALID_SOLUTION_SIZE:
err_str = "Invalid solution size."; break;
case LGD_INVALID_MAX_ITERATIONS:
err_str = "Invalid flight times."; break;
case LGD_INVALID_EPSILON:
err_str = "Invalid epsilon value."; break;
case LGD_INVALID_STDV:
err_str = "Invalid STD value for generating the levy distribution."; break;
case LGD_INVALID_BETA:
err_str = "Invalid beta value."; break;
case LGD_INVALID_ALPHA:
err_str = "Invalid alpha value."; break;
case LGD_INVALID_SIGMA:
err_str = "Invalid sigma value."; break;
case LGD_NAN_VALUE:
err_str = "NaN values found."; break;
default:
err_str = "Unknown error."; break;
}
if (err_throw && err_code < 0) throw err_str;
else ss << err_str;
#if defined _WINDOWS || __WIN32__
if (!err_throw)
{
if (err_code >= 0)
{
SetConsoleTextAttribute(GetStdHandle(STD_ERROR_HANDLE), 7);
ss << std::endl;
}
else
{
SetConsoleTextAttribute(GetStdHandle(STD_ERROR_HANDLE), 7);
ss << std::endl;
}
}
#else
if (!err_throw)
{
if (err_code >= 0)
ss << "\033[0m" << std::endl;
else
ss << "\033[0m" << std::endl;
}
#endif
return;
}
gctl::lgd_para gctl::lgd_solver::default_lgd_para()
{
lgd_para dp = lgd_defparam;
return dp;
}
void gctl::lgd_solver::LGD_Minimize(array<double> &best_m, array<double> &mean_m, array<double> &std_m,
std::ostream &ss, bool verbose, bool err_throw)
{
if (lgd_silent_)
{
lgd_return_code ret = lgd(best_m, mean_m, std_m);
if (ret < 0) lgd_error_str(ret, ss, true);
return;
}
// 使用lcg求解 注意当我们使用函数指针来调用求解函数时默认参数不可以省略
#ifdef GCTL_OPENMP
double start = omp_get_wtime();
lgd_return_code ret = lgd(best_m, mean_m, std_m);
double end = omp_get_wtime();
double costime = 1000*(end-start);
#else
clock_t start = clock();
lgd_return_code ret = lgd(best_m, mean_m, std_m);
clock_t end = clock();
double costime = 1000*(end-start)/(double)CLOCKS_PER_SEC;
#endif
if (!err_throw) std::clog << std::endl << "Solver: LGD. Time cost: " << costime << " ms" << std::endl;
if (verbose) lgd_error_str(ret, ss, err_throw);
else if (ret < 0) lgd_error_str(ret, ss, err_throw);
return;
}
void gctl::lgd_solver::LGD_Minimize(array<double> &best_m, array<double> &mean_m, array<double> &std_m,
const array<double> &alphas, std::ostream &ss, bool verbose, bool err_throw)
{
lgd_ques_num_ = best_m.size();
if (lgd_ques_num_ != alphas.size())
{
throw std::runtime_error("[gctl::lgd_solver] arraies' size do not match.");
}
lgd_alpha_.resize(lgd_ques_num_);
for (int i = 0; i < lgd_ques_num_; i++)
{
if (alphas[i] <= 0.0)
{
throw std::runtime_error("[gctl::lgd_solver] Invalid scaling value.");
}
lgd_alpha_[i] = alphas[i];
}
lgd_has_alpha_ = true;
LGD_Minimize(best_m, mean_m, std_m, ss, verbose, err_throw);
return;
}
void gctl::lgd_solver::LGD_Minimize(array<double> &best_m, array<double> &mean_m, array<double> &std_m,
const array<double> &lows, const array<double> &higs, std::ostream &ss, bool verbose, bool err_throw)
{
lgd_ques_num_ = best_m.size();
if (lgd_ques_num_ != lows.size() || lgd_ques_num_ != higs.size())
{
throw std::runtime_error("[gctl::lgd_solver] arraies' size do not match.");
}
lgd_low_.resize(lgd_ques_num_);
lgd_hig_.resize(lgd_ques_num_);
for (int i = 0; i < lgd_ques_num_; i++)
{
if (lows[i] >= higs[i])
{
throw std::runtime_error("[gctl::lgd_solver] Invalid bound value.");
}
lgd_low_[i] = lows[i];
lgd_hig_[i] = higs[i];
}
lgd_has_range_ = true;
LGD_Minimize(best_m, mean_m, std_m, ss, verbose, err_throw);
return;
}
void gctl::lgd_solver::LGD_Minimize(array<double> &best_m, array<double> &mean_m, array<double> &std_m,
double low, double hig, std::ostream &ss, bool verbose, bool err_throw)
{
if (low >= hig)
{
throw std::runtime_error("[gctl::lgd_solver] Invalid bound value.");
}
lgd_ques_num_ = best_m.size();
lgd_low_.resize(lgd_ques_num_, low);
lgd_hig_.resize(lgd_ques_num_, hig);
lgd_has_range_ = true;
LGD_Minimize(best_m, mean_m, std_m, ss, verbose, err_throw);
return;
}
gctl::lgd_return_code gctl::lgd_solver::lgd(array<double> &best_m, array<double> &mean_m, array<double> &std_m)
{
lgd_ques_num_ = best_m.size();
// check parameters
if (lgd_ques_num_ <= 0) return LGD_INVALID_SOLUTION_SIZE;
if (lgd_param_.flight_times <= 0) return LGD_INVALID_MAX_ITERATIONS;
if (lgd_param_.epsilon <= 0) return LGD_INVALID_EPSILON;
if (lgd_param_.stddev_v <= 0) return LGD_INVALID_STDV;
if (lgd_param_.beta <= 1.0 || lgd_param_.beta >= 2.0) return LGD_INVALID_BETA;
if (lgd_param_.alpha <= 0) return LGD_INVALID_ALPHA;
if (lgd_param_.sigma <= 0) return LGD_INVALID_SIGMA;
// initiate solutions
mean_m.resize(lgd_ques_num_, 0.0); std_m.resize(lgd_ques_num_, 0.0);
double gamma1 = tgamma(lgd_param_.beta + 1.0);
double gamma2 = tgamma(0.5*(lgd_param_.beta + 1.0));
double stddev_u = pow((gamma1*sin(0.5*GCTL_Pi*lgd_param_.beta)) / (gamma2*lgd_param_.beta*pow(2, 0.5*(lgd_param_.beta-1.0))), 1.0/lgd_param_.beta);
unsigned seed = std::chrono::system_clock::now().time_since_epoch().count();
std::default_random_engine generator(seed);
std::normal_distribution<double> dist_u(0, stddev_u);
std::normal_distribution<double> dist_v(0, lgd_param_.stddev_v);
std::uniform_real_distribution<double> dist_s(1.0, 2.0);
array<double> g, g_mem, g_orth, new_mean, b_m, alphas;
g.resize(lgd_ques_num_); g_mem.resize(2*lgd_ques_num_); g_orth.resize(2*lgd_ques_num_);
new_mean.resize(lgd_ques_num_); b_m.resize(lgd_ques_num_); alphas.resize(lgd_ques_num_);
// 初始化参数变化范围为lgd_param_.alpha
vecset(alphas, lgd_param_.alpha);
if (lgd_has_range_)
{
vecdiff(alphas, lgd_hig_, lgd_low_);
vecscale(alphas, lgd_param_.alpha);
}
if (lgd_has_alpha_)
{
veccpy(alphas, lgd_alpha_, lgd_param_.alpha);
}
double fx_best, fx_tmp, direct_mod, levy_length;
double fx_mean = NAN;
// 开始飞行
int rcd_times = 0;
lgd_trace_times_ = 0;
for (int ft = 0; ft <= lgd_param_.flight_times; ft++)
{
// 计算尝试解
fx_tmp = LGD_Evaluate(best_m, g);
if (ft == 0 || fx_tmp < fx_best)
{
fx_best = fx_tmp;
veccpy(b_m, best_m);
}
// 记录飞行轨迹
if (lgd_param_.lambda <= 0.0 || (lgd_param_.lambda > 0.0 && fx_tmp <= lgd_param_.lambda))
{
for (int i = 0; i < lgd_ques_num_; i++)
{
std_m[i] = dynamic_stddev(std_m[i], rcd_times, mean_m[i], best_m[i], new_mean[i]);
mean_m[i] = new_mean[i];
}
rcd_times++;
if (lgd_save_trace_)
{
lgd_trace_.append_array(best_m);
lgd_trace_times_++;
}
}
if (LGD_Progress(ft, fx_tmp, fx_mean, fx_best, lgd_param_))
{
// 将迭代结果返还给m
veccpy(best_m, b_m);
return LGD_STOP;
}
if (lgd_param_.batch > 0 && (rcd_times+1)%lgd_param_.batch == 0)
{
fx_mean = LGD_Evaluate(mean_m, g);
if (fx_mean < lgd_param_.epsilon)
{
LGD_Progress(ft, fx_tmp, fx_mean, fx_best, lgd_param_);
// 将迭代结果返还给m
veccpy(best_m, b_m);
return LGD_CONVERGENCE;
}
}
// 驻点检测
direct_mod = sqrt(vecdot(g, g));
if (direct_mod < lgd_param_.sigma)
{
if (ft == 0) // 初次飞行时无记录
{
do // 如果梯度消失 则采用一个随机方向
{
for (int i = 0; i < lgd_ques_num_; i++)
{
g[i] = dist_s(generator);
}
direct_mod = sqrt(vecdot(g, g));
}
while (direct_mod < lgd_param_.sigma);
}
else // 如果梯度消失 则朝着上一次迭代方向的正交方向走一步
{
for (int i = 0; i < lgd_ques_num_; i++)
{
g_mem[i+lgd_ques_num_] = dist_s(generator);
}
schmidt_orthogonal(g_mem, g_orth, 2);
for (int i = 0; i < lgd_ques_num_; i++)
{
g[i] = g_orth[i+lgd_ques_num_];
}
direct_mod = 1.0; // 此时的模量为单位模量
}
}
// 莱维飞行的步长 注意原公式中无最外层绝对值符号
// 这是我们需要步长的绝对值 因此取绝对值
levy_length = fabs(dist_u(generator)/pow(fabs(dist_v(generator)), 1.0/lgd_param_.beta));
for (int i = 0; i < lgd_ques_num_; i++)
{
best_m[i] -= levy_length*alphas[i]*g[i]/direct_mod;
}
if (!vecvalid(best_m))
{
return LGD_NAN_VALUE;
}
// 记录梯度方向
for (int i = 0; i < lgd_ques_num_; i++)
{
g_mem[i] = g[i];
}
// 这里可以添加取值范围的约束
if (lgd_has_range_)
{
vecbtm(best_m, lgd_low_);
vectop(best_m, lgd_hig_);
}
}
// 将迭代结果返还给m
veccpy(best_m, b_m);
return LGD_REACHED_MAX_ITERATIONS;
}

212
lib/optimization/lgd.h Normal file
View File

@ -0,0 +1,212 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#ifndef _GCTL_LGD_H
#define _GCTL_LGD_H
#include "gctl/core.h"
#include "gctl/io.h"
#include "gctl/maths.h"
#include "gctl/algorithm.h"
#include "gctl_optimization_config.h"
#ifdef GCTL_OPTIMIZATION_TOML
#include "toml.hpp"
#endif // GCTL_OPTIMIZATION_TOML
#if defined _WINDOWS || __WIN32__
#include "windows.h"
#endif // _WINDOWS || __WIN32__
#ifdef GSTL_OPENMP
#include "omp.h"
#endif // GSTL_OPENMP
namespace gctl
{
/**
* @brief return value of the lgd_solver class.
*/
enum lgd_return_code
{
LGD_CONVERGENCE = 1, ///< The iteration reached convergence.
LGD_STOP, ///< The iteration stopped by the progress monitoring function.
LGD_REACHED_MAX_ITERATIONS, ///< Iteration reached max limit.
LGD_INVALID_SOLUTION_SIZE = -1024, ///< Invalid solution size.
LGD_INVALID_MAX_ITERATIONS, ///< The maximal iteration times is negative.
LGD_INVALID_EPSILON, ///< The epsilon is negative.
LGD_INVALID_STDV,
LGD_INVALID_BETA, ///< Invalid value for beta.
LGD_INVALID_ALPHA,
LGD_INVALID_SIGMA,
LGD_NAN_VALUE, ///< Nan value.
};
/**
* @brief Parameters of the L-GD method.
*/
struct lgd_para
{
/**
* Maximal times of the lévy flight. The iteration process will stop till the maximal
* flight times is reached unless the mean convergence test is set and satisfied. To
* active the test, set the 'batch' parameter which is shown as below. The default value
* is 1000.
*/
int flight_times;
/**
* Batch size for the mean convergence test. This parameter determines the batch size,
* in recorded solutions, to compute the value of the objective function. Note that
* only qualified solutions will be recorded for analyzing if the 'lambda' parameter is
* set. The library does not perform the mean convergence test if the value of this
* parameter is zero. The default is 0.
*/
int batch;
/**
* Epsilon for the mean convergence test. This parameter determines the accuracy
* with which the mean solution is to be found. The default is 1e-5.
*/
double epsilon;
/**
* Standard deviation of v that is used to calculate the distance of each
* lévy flight in length = stddev_u/|stddev_v|^{1/beta}. This parameter is
* typically given as 1.0.
*/
double stddev_v;
/**
* Scale parameter for calculating stddev_u and the flying length. Must be at
* (1.0, 2.0). The default value is 1.5. The bigger beta is the smaller of the
* range of flying length gets.
*/
double beta;
/**
* Scale parameter multiplied by the flying length. The default value is 0.01.
* The parameter should be set according to the expected convergence speed. Normally,
* The bigger alpha is, the faster the L-GD convergences. However, the L-GD may
* miss the optimized solutions if alpha was too big.
*/
double alpha;
/**
* Sigma for the stagnation point test. The algorithm will take one search
* orthogonal with the last iteration if the module of the gradients is smaller
* than sigma. This mechanism helps the algorithm escaping from stagnation
* points such as local minimal or saddle points.The default is 1e-8.
*/
double sigma;
/**
* Threshold for recording the search paths. If the value is bigger then zero, then
* only values of the objective function that are smaller to equal to the threshold be
* used for statistic analyzing. Otherwise, all records will be used. The recorded paths
* could be save to file using the save_lgd_trace(string) function if set_lgd_record_trace()
* is set. The default is -1.0.
*/
double lambda;
};
class lgd_solver
{
public:
lgd_solver(); ///< Default constructor.
virtual ~lgd_solver(); ///< Default de-constructor.
/**
* @brief Interface for the evaluation of the objective function. Concrete
* contents of this function is determined according to the optimizing problem.
*
* @param x Inputs of the current solution.
* @param g Outputs of the model gradient calculated using the input solution.
* @return Current objective value.
*/
virtual double LGD_Evaluate(const array<double> &x, array<double> &g) = 0;
/**
* @brief Default monitoring function of the optimizing process.
*
* @param best_fx Objective value of the best solution.
* @param curr_fx Objective value of the current solution.
* @param mean_fx Objective value of the mean solution.
* @param param L-GD's parameters used for the optimzing process.
* @param curr_t Current flight times.
* @return The optimizing process will be stopped if a non-zero value is returned.
*/
virtual int LGD_Progress(const int curr_t, const double curr_fx, const double mean_fx,
const double best_fx, const lgd_para &param);
void lgd_silent();
void set_lgd_report_interval(int inter);
void show_solver();
void set_lgd_record_trace(); ///< Turn on the recording of fight traces.
// Save fight traces to file. Not that only qualified solutions will be
// saved if the recording threshold is set.
void save_lgd_trace(std::string trace_file);
lgd_para default_lgd_para();
void set_lgd_para(const lgd_para &param);
#ifdef GCTL_OPTIMIZATION_TOML
void set_lgd_para(std::string filename);
void set_lgd_para(const toml::value &toml_data);
#endif // GCTL_OPTIMIZATION_TOML
void LGD_Minimize(array<double> &best_m, array<double> &mean_m, array<double> &std_m,
std::ostream &ss = std::clog, bool verbose = true, bool err_throw = false);
void LGD_Minimize(array<double> &best_m, array<double> &mean_m, array<double> &std_m,
const array<double> &alphas, std::ostream &ss = std::clog,
bool verbose = true, bool err_throw = false);
void LGD_Minimize(array<double> &best_m, array<double> &mean_m, array<double> &std_m,
const array<double> &lows, const array<double> &higs, std::ostream &ss = std::clog,
bool verbose = true, bool err_throw = false);
void LGD_Minimize(array<double> &best_m, array<double> &mean_m, array<double> &std_m,
double low, double hig, std::ostream &ss = std::clog, bool verbose = true,
bool err_throw = false);
private:
void lgd_error_str(lgd_return_code err_code, std::ostream &ss = std::clog, bool err_throw = false);
lgd_return_code lgd(array<double> &best_m, array<double> &mean_m, array<double> &std_m);
private:
lgd_para lgd_param_;
int lgd_inter_, lgd_ques_num_, lgd_trace_times_;
bool lgd_silent_, lgd_has_range_, lgd_has_alpha_, lgd_save_trace_;
array<double> lgd_low_, lgd_hig_, lgd_alpha_, lgd_trace_;
};
}
#endif // _GCTL_LGD_H

100
lib/optimization/loss_func.cpp Normal file
View File

@ -0,0 +1,100 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2023 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include "loss_func.h"
gctl::loss_func::loss_func()
{
uncer_type_ = 0;
}
gctl::loss_func::loss_func(const array<double> &tar, norm_type_e n_type)
{
uncer_type_ = 0;
init(tar, n_type);
}
gctl::loss_func::~loss_func(){}
void gctl::loss_func::init(const array<double> &tar, norm_type_e n_type)
{
tar_num_ = tar.size();
tars_ = tar;
norm_type_ = n_type;
return;
}
void gctl::loss_func::set_uncertainty(double uncer)
{
uncer_type_ = 1;
uncer_ = uncer;
return;
}
void gctl::loss_func::set_uncertainty(const array<double> &uncer)
{
uncer_type_ = 2;
uncers_ = uncer;
return;
}
double gctl::loss_func::get_loss()
{
double l = loss_;
loss_ = 0.0;
return l;
}
double gctl::loss_func::evaluate(double inp, int id)
{
double val = (inp - tars_[id]);
if (uncer_type_ == 1) val /= uncer_;
else if (uncer_type_ == 2) val /= uncers_[id];
if (norm_type_ == L1) val = fabs(val);
if (norm_type_ == L2) val = val*val;
loss_ += val;
return val/tar_num_;
}
double gctl::loss_func::gradient(double inp, int id)
{
double c;
if (uncer_type_ == 1) c = uncer_;
else if (uncer_type_ == 2) c = uncers_[id];
double val = (inp - tars_[id]);
if (norm_type_ == L1 && val >= 0) val = 1.0;
if (norm_type_ == L1 && val < 0) val = -1.0;
if (norm_type_ == L2) val = 2.0*val;
if (norm_type_ == L1 && uncer_type_ != 0) val /= c;
else if (norm_type_ == L2 && uncer_type_ != 0) val /= (c*c);
return val/tar_num_;
}

61
lib/optimization/loss_func.h Normal file
View File

@ -0,0 +1,61 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2023 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#ifndef _GCTL_LOSS_FUNC_H
#define _GCTL_LOSS_FUNC_H
// library's head files
#include "gctl/core.h"
namespace gctl
{
class loss_func
{
public:
loss_func();
loss_func(const array<double> &tar, norm_type_e n_type);
virtual ~loss_func();
void init(const array<double> &tar, norm_type_e n_type);
void set_uncertainty(double uncer);
void set_uncertainty(const array<double> &uncer);
double get_loss();
double evaluate(double inp, int id);
double gradient(double inp, int id);
private:
//unsigned int counter_;
unsigned int tar_num_;
int uncer_type_;
double uncer_, loss_;
norm_type_e norm_type_;
array<double> tars_;
array<double> uncers_;
};
}
#endif // _GCTL_LOSS_FUNC_H

152
lib/optimization/lu.cpp Normal file
View File

@ -0,0 +1,152 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include "lu.h"
gctl::lu::lu(matrix<double> &sourceMatrix) : decomposedMatrix(sourceMatrix)
{
if (sourceMatrix.empty() || sourceMatrix.row_size() != sourceMatrix.col_size())
{
throw domain_error("Invalid input matrix. From lu::lu(...)");
}
}
// Decomposition into triangular matrices
void gctl::lu::decompose()
{
// Initialize the permutation vector
int n = decomposedMatrix.row_size();
rowPermutation.resize(n);
for (int i = 0; i < n; i++)
{
rowPermutation[i] = i;
}
// LU factorization
double tmp, det = 1.0;
for (int p = 1; p <= n - 1; p++)
{
// Find pivot element.
for (int i = p + 1; i <= n; i++)
{
if (std::fabs(decomposedMatrix[rowPermutation[i - 1]][p - 1]) > std::fabs(decomposedMatrix[rowPermutation[p - 1]][p - 1]))
{
// Switch the index for the p-1 pivot row if necessary.
tmp = rowPermutation[p - 1]; rowPermutation[p - 1] = rowPermutation[i - 1]; rowPermutation[i - 1] = tmp;
det = -det;
}
}
if (decomposedMatrix[rowPermutation[p - 1]][p - 1] == 0.0)
{
// The matrix is singular, at least to precision of algorithm
throw runtime_error("The input matrix is singular. From gctl::lu::decompose()");
return;
}
// Multiply the diagonal elements.
det = det * decomposedMatrix[rowPermutation[p - 1]][p - 1];
// Form multiplier.
for (int i = p + 1; i <= n; i++)
{
decomposedMatrix[rowPermutation[i - 1]][p - 1] /= decomposedMatrix[rowPermutation[p - 1]][p - 1];
// Eliminate [p-1].
for (int j = p + 1; j <= n; j++)
{
decomposedMatrix[rowPermutation[i - 1]][j - 1] -= decomposedMatrix[rowPermutation[i - 1]][p - 1] * decomposedMatrix[rowPermutation[p - 1]][j - 1];
}
}
}
det = det * decomposedMatrix[rowPermutation[n - 1]][n - 1];
if (det == 0.0)
{
throw runtime_error("Determinant of the input matrix is zero. From gctl::lu::decompose()");
}
return;
}
// solve for x in form Ax = b. A is the original input matrix.
// Note: b is modified in-place for row permutations
void gctl::lu::solve(const array<double>& b, array<double> &x)
{
// Our decomposed matrix is comprised of both the lower and upper diagonal matrices.
// The rows of this matrix have been permutated during the decomposition process. The
// rowPermutation indicates the proper row order.
// The lower diagonal matrix only include elements below the diagonal with diagonal
// elements set to 1.
// The upper diagonal matrix is fully specified.
// First solve Ly = Pb for x using forward substitution. P is a permutated identity matrix.
if (b.empty())
{
throw domain_error("Invalid target vector. From gctl::lu::solve(...)");
}
x.resize(b.size());
for (int i = 0; i < x.size(); i++)
{
int currentRow = rowPermutation[i];
double sum = 0.0;
for (int j = 0; j < i; j++)
{
sum += (decomposedMatrix[currentRow][j] * x[j]);
}
x[i] = (b[currentRow] - sum);
}
// Now solve Uy = x for y using back substitution. Note that
// y can be solved in place using the existing y vector. No need
// to allocate another vector.
for (int i = b.size()-1; i >= 0; i--)
{
int currentRow = rowPermutation[i];
double sum = 0.0;
for (int j = b.size()-1; j > i; j--)
{
sum += (decomposedMatrix[currentRow][j] * x[j]);
}
x[i] = (x[i] - sum) / decomposedMatrix[currentRow][i];
}
return;
}

56
lib/optimization/lu.h Normal file
View File

@ -0,0 +1,56 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#ifndef _GCTL_LU_H
#define _GCTL_LU_H
#include "gctl/core.h"
namespace gctl
{
/**
* @brief Lower/upper decomposition of matrix into a lower triangular matrix and a upper triangular matrix.
*
* @tparam T template type
*/
class lu
{
public:
lu(matrix<double> &sourceMatrix); // Matrix is decomposed in-place
virtual ~lu(){}
void decompose(); ///< Decomposition into triangular matrices. Return false if failed
void solve(const array<double>& b, array<double> &x); ///< solve for x in form Ax = b. A is the original input matrix.
protected:
lu(const lu&) = delete;
void operator=(const lu&) = delete;
matrix<double> &decomposedMatrix; // Output matrix after decomposition
array<int> rowPermutation; // Permutation of rows during pivoting
};
}
#endif // _GCTL_LU_H

634
lib/optimization/sgd.cpp Normal file
View File

@ -0,0 +1,634 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include "sgd.h"
/**
* Default parameter for the SGD methods.
*/
static const gctl::sgd_para sgd_defparam = {0, 1e-6, 0.01, 0.01, 0.9, 0.999, 1e-8};
gctl::sgd_solver::sgd_solver()
{
sgd_param_ = sgd_defparam;
sgd_inter_ = 1;
sgd_silent_ = false;
solver_name_ = "Undefined";
}
gctl::sgd_solver::~sgd_solver(){}
int gctl::sgd_solver::SGD_Progress(double fx, const array<double> &x, const sgd_para &param, const int k)
{
if (sgd_silent_) return 0;
if (param.epsilon > 0.0 && fx <= param.epsilon)
{
std::clog << GCTL_CLEARLINE << "\rF(x) = " << fx << ", Train-Times = " << k;
return 0;
}
if (sgd_inter_ > 0 && k%sgd_inter_ == 0)
{
std::clog << GCTL_CLEARLINE << "\rF(x) = " << fx << ", Train-Times = " << k;
}
return 0;
}
void gctl::sgd_solver::sgd_silent()
{
sgd_silent_ = true;
return;
}
void gctl::sgd_solver::set_sgd_report_interval(int inter)
{
sgd_inter_ = inter;
return;
}
void gctl::sgd_solver::set_sgd_para(const sgd_para &in_param)
{
sgd_param_ = in_param;
return;
}
void gctl::sgd_solver::set_sgd_para(const toml::value &toml_data)
{
sgd_param_ = sgd_defparam;
std::string SGD = "sgd";
if (toml_data.contains(SGD))
{
if (toml_data.at(SGD).contains("iteration")) sgd_param_.iteration = toml::find<int>(toml_data, SGD, "iteration");
if (toml_data.at(SGD).contains("epsilon")) sgd_param_.epsilon = toml::find<double>(toml_data, SGD, "epsilon");
if (toml_data.at(SGD).contains("mu")) sgd_param_.mu = toml::find<double>(toml_data, SGD, "mu");
if (toml_data.at(SGD).contains("alpha")) sgd_param_.alpha = toml::find<double>(toml_data, SGD, "alpha");
if (toml_data.at(SGD).contains("beta_1")) sgd_param_.beta_1 = toml::find<double>(toml_data, SGD, "beta_1");
if (toml_data.at(SGD).contains("beta_2")) sgd_param_.beta_2 = toml::find<double>(toml_data, SGD, "beta_2");
if (toml_data.at(SGD).contains("sigma")) sgd_param_.sigma = toml::find<double>(toml_data, SGD, "sigma");
}
return;
}
void gctl::sgd_solver::show_solver()
{
std::clog << "Solver's Setup Panel\n";
std::clog << "-----------------------------\n";
std::clog << "Solver: " << solver_name_ << "\n";
std::clog << "Iteration = " << sgd_param_.iteration << ", Epsilon = " << sgd_param_.epsilon << ", Mu = " << sgd_param_.mu << "\n";
std::clog << "Alpha = " << sgd_param_.alpha << ", Beta1 = " << sgd_param_.beta_1 << ", Beta2 = " << sgd_param_.beta_2 << ", Sigma = " << sgd_param_.sigma << "\n";
std::clog << "=============================\n";
return;
}
void gctl::sgd_solver::sgd_error_str(sgd_return_code err_code, std::ostream &ss, bool err_throw)
{
#if defined _WINDOWS || __WIN32__
if (!err_throw)
{
if (err_code >= 0)
{
SetConsoleTextAttribute(GetStdHandle(STD_ERROR_HANDLE), FOREGROUND_INTENSITY | FOREGROUND_GREEN);
ss << "Success! ";
}
else
{
SetConsoleTextAttribute(GetStdHandle(STD_ERROR_HANDLE), FOREGROUND_INTENSITY | FOREGROUND_RED);
ss << "Fail! ";
}
}
#else
if (!err_throw)
{
if (err_code >= 0)
ss << "\033[1m\033[32mSGD Success! ";
else
ss << "\033[1m\033[31mSGD Fail! ";
}
#endif
std::string err_str;
switch (err_code)
{
case SGD_SUCCESS:
err_str = "Success."; break;
case SGD_CONVERGENCE:
err_str = "The iteration reached convergence."; break;
case SGD_STOP:
err_str = "The iteration stopped by the progress evaluation function."; break;
case SGD_UNKNOWN_ERROR:
err_str = "Unknown error."; break;
case SGD_INVALID_VARIABLE_SIZE:
err_str = "Invalid array size."; break;
case SGD_REACHED_MAX_ITERATIONS:
err_str = "The maximal iteration is reached."; break;
case SGD_INVALID_EPSILON:
err_str = "Invalid value for epsilon."; break;
case SGD_INVALID_BETA:
err_str = "Invalid value for beta."; break;
case SGD_INVALID_MU:
err_str = "Invalid value for mu."; break;
case SGD_INVALID_ALPHA:
err_str = "Invalid value for alpha."; break;
case SGD_INVALID_SIGMA:
err_str = "Invalid value for sigma."; break;
case SGD_NAN_VALUE:
err_str = "NaN values found."; break;
default:
err_str = "Unknown error."; break;
}
if (err_throw && err_code < 0) throw err_str;
else ss << err_str;
#if defined _WINDOWS || __WIN32__
if (!err_throw)
{
if (err_code >= 0)
{
SetConsoleTextAttribute(GetStdHandle(STD_ERROR_HANDLE), 7);
ss << std::endl;
}
else
{
SetConsoleTextAttribute(GetStdHandle(STD_ERROR_HANDLE), 7);
ss << std::endl;
}
}
#else
if (!err_throw)
{
if (err_code >= 0)
ss << "\033[0m" << std::endl;
else
ss << "\033[0m" << std::endl;
}
#endif
return;
}
gctl::sgd_para gctl::sgd_solver::default_sgd_para()
{
sgd_para dp = sgd_defparam;
return dp;
}
void gctl::sgd_solver::SGD_Minimize(array<double> &m, sgd_solver_type solver_id, std::ostream &ss, bool verbose, bool err_throw)
{
if (sgd_silent_)
{
sgd_return_code ret;
if (solver_id == MOMENTUM) {solver_name_ = "MOMENTUM"; ret = momentum(m);}
else if (solver_id == NAG) {solver_name_ = "NAG"; ret = nag(m);}
else if (solver_id == ADAGRAD) {solver_name_ = "ADAGRAD"; ret = adagrad(m);}
else if (solver_id == RMSPROP) {solver_name_ = "RMSPROP"; ret = rmsprop(m);}
else if (solver_id == ADAM) {solver_name_ = "ADAM"; ret = adam(m);}
else if (solver_id == NADAM) {solver_name_ = "NADAM"; ret = nadam(m);}
else if (solver_id == ADAMAX) {solver_name_ = "ADAMAX"; ret = adamax(m);}
else if (solver_id == ADABELIEF) {solver_name_ = "ADABELIEF"; ret = adabelief(m);}
else throw std::invalid_argument("Invalid solver type. gstl::sgd_solver::SGD_Minimize(...)");
if (ret < 0) sgd_error_str(ret, ss, true);
return;
}
// 使用lcg求解 注意当我们使用函数指针来调用求解函数时默认参数不可以省略
#ifdef GCTL_OPENMP
double start = omp_get_wtime();
sgd_return_code ret;
if (solver_id == MOMENTUM) {solver_name_ = "MOMENTUM"; ret = momentum(m);}
else if (solver_id == NAG) {solver_name_ = "NAG"; ret = nag(m);}
else if (solver_id == ADAGRAD) {solver_name_ = "ADAGRAD"; ret = adagrad(m);}
else if (solver_id == RMSPROP) {solver_name_ = "RMSPROP"; ret = rmsprop(m);}
else if (solver_id == ADAM) {solver_name_ = "ADAM"; ret = adam(m);}
else if (solver_id == NADAM) {solver_name_ = "NADAM"; ret = nadam(m);}
else if (solver_id == ADAMAX) {solver_name_ = "ADAMAX"; ret = adamax(m);}
else if (solver_id == ADABELIEF) {solver_name_ = "ADABELIEF"; ret = adabelief(m);}
else throw std::invalid_argument("Invalid solver type. gstl::sgd_solver::SGD_Minimize(...)");
double end = omp_get_wtime();
double costime = 1000*(end-start);
#else
clock_t start = clock();
sgd_return_code ret;
if (solver_id == MOMENTUM) {solver_name_ = "MOMENTUM"; ret = momentum(m);}
else if (solver_id == NAG) {solver_name_ = "NAG"; ret = nag(m);}
else if (solver_id == ADAGRAD) {solver_name_ = "ADAGRAD"; ret = adagrad(m);}
else if (solver_id == RMSPROP) {solver_name_ = "RMSPROP"; ret = rmsprop(m);}
else if (solver_id == ADAM) {solver_name_ = "ADAM"; ret = adam(m);}
else if (solver_id == NADAM) {solver_name_ = "NADAM"; ret = nadam(m);}
else if (solver_id == ADAMAX) {solver_name_ = "ADAMAX"; ret = adamax(m);}
else if (solver_id == ADABELIEF) {solver_name_ = "ADABELIEF"; ret = adabelief(m);}
else throw std::invalid_argument("Invalid solver type. gstl::sgd_solver::SGD_Minimize(...)");
clock_t end = clock();
double costime = 1000*(end-start)/(double)CLOCKS_PER_SEC;
#endif
if (!err_throw)
{
std::clog << std::endl;
switch (solver_id)
{
case MOMENTUM:
std::clog << "Solver: MOMENTUM. Time cost: " << costime << " ms" << std::endl;
break;
case NAG:
std::clog << "Solver: NAG. Time cost: " << costime << " ms" << std::endl;
break;
case ADAGRAD:
std::clog << "Solver: ADAGRAD. Time cost: " << costime << " ms" << std::endl;
break;
case RMSPROP:
std::clog << "Solver: RMSPROP. Time cost: " << costime << " ms" << std::endl;
break;
case ADAM:
std::clog << "Solver: ADAM. Time cost: " << costime << " ms" << std::endl;
break;
case NADAM:
std::clog << "Solver: NADAM. Time cost: " << costime << " ms" << std::endl;
break;
case ADAMAX:
std::clog << "Solver: ADAMAX. Time cost: " << costime << " ms" << std::endl;
break;
case ADABELIEF:
std::clog << "Solver: ADABELIEF. Time cost: " << costime << " ms" << std::endl;
break;
default:
std::clog << "Solver: Unknown. Time cost: " << costime << " ms" << std::endl;
break;
}
}
if (verbose) sgd_error_str(ret, ss, err_throw);
else if (ret < 0) sgd_error_str(ret, ss, err_throw);
return;
}
gctl::sgd_return_code gctl::sgd_solver::momentum(array<double> &m)
{
int n_size = m.size();
//check parameters
if (n_size <= 0) return SGD_INVALID_VARIABLE_SIZE;
if (sgd_param_.epsilon < 0) return SGD_INVALID_EPSILON;
if (sgd_param_.mu < 0 || sgd_param_.mu >= 1.0) return SGD_INVALID_MU;
array<double> mk(n_size, 0.0);
array<double> g(n_size);
int t = 0;
double fx;
while (1)
{
fx = SGD_Evaluate(m, g);
if (SGD_Progress(fx, m, sgd_param_, t)) return SGD_STOP;
if (fx < sgd_param_.epsilon) return SGD_CONVERGENCE;
for (int i = 0; i < n_size; i++)
{
mk[i] = sgd_param_.mu*mk[i] + g[i];
m[i] = m[i] - sgd_param_.alpha * mk[i];
if (m[i] != m[i]) return SGD_NAN_VALUE;
}
t++;
if (sgd_param_.iteration > 0 && t >= sgd_param_.iteration) break;
}
return SGD_REACHED_MAX_ITERATIONS;
}
gctl::sgd_return_code gctl::sgd_solver::nag(array<double> &m)
{
int n_size = m.size();
//check parameters
if (n_size <= 0) return SGD_INVALID_VARIABLE_SIZE;
if (sgd_param_.epsilon < 0) return SGD_INVALID_EPSILON;
if (sgd_param_.mu < 0 || sgd_param_.mu >= 1.0) return SGD_INVALID_MU;
array<double> mk(n_size, 0.0);
array<double> xk(n_size);
array<double> g (n_size);
int t = 0;
double fx;
while (1)
{
for (int i = 0; i < n_size; i++)
{
xk[i] = m[i] - sgd_param_.mu*sgd_param_.alpha*mk[i];
}
fx = SGD_Evaluate(xk, g);
if (SGD_Progress(fx, m, sgd_param_, t)) return SGD_STOP;
if (fx < sgd_param_.epsilon) return SGD_CONVERGENCE;
for (int i = 0; i < n_size; i++)
{
mk[i] = sgd_param_.mu*mk[i] + g[i];
m[i] = m[i] - sgd_param_.alpha * mk[i];
if (m[i] != m[i]) return SGD_NAN_VALUE;
}
t++;
if (sgd_param_.iteration > 0 && t >= sgd_param_.iteration) break;
}
return SGD_REACHED_MAX_ITERATIONS;
}
gctl::sgd_return_code gctl::sgd_solver::adagrad(array<double> &m)
{
int n_size = m.size();
//check parameters
if (n_size <= 0) return SGD_INVALID_VARIABLE_SIZE;
if (sgd_param_.epsilon < 0.0) return SGD_INVALID_EPSILON;
if (sgd_param_.sigma < 0.0) return SGD_INVALID_SIGMA;
array<double> mk(n_size, 0.0);
array<double> g (n_size);
int t = 0;
double fx;
while (1)
{
fx = SGD_Evaluate(m, g);
if (SGD_Progress(fx, m, sgd_param_, t)) return SGD_STOP;
if (fx < sgd_param_.epsilon) return SGD_CONVERGENCE;
for (int i = 0; i < n_size; i++)
{
mk[i] = mk[i] + g[i]*g[i];
m[i] = m[i] - sgd_param_.alpha * g[i]/(sqrt(mk[i]) + sgd_param_.sigma);
if (m[i] != m[i]) return SGD_NAN_VALUE;
}
t++;
if (sgd_param_.iteration > 0 && t >= sgd_param_.iteration) break;
}
return SGD_REACHED_MAX_ITERATIONS;
}
gctl::sgd_return_code gctl::sgd_solver::rmsprop(array<double> &m)
{
int n_size = m.size();
//check parameters
if (n_size <= 0) return SGD_INVALID_VARIABLE_SIZE;
if (sgd_param_.epsilon < 0.0) return SGD_INVALID_EPSILON;
if (sgd_param_.sigma < 0.0) return SGD_INVALID_SIGMA;
array<double> vk(n_size, 0.0);
array<double> g (n_size);
int t = 0;
double fx;
while (1)
{
fx = SGD_Evaluate(m, g);
if (SGD_Progress(fx, m, sgd_param_, t)) return SGD_STOP;
if (fx < sgd_param_.epsilon) return SGD_CONVERGENCE;
for (int i = 0; i < n_size; i++)
{
vk[i] = sgd_param_.beta_2 * vk[i] + (1.0 - sgd_param_.beta_2)*g[i]*g[i];
m[i] = m[i] - sgd_param_.alpha * g[i]/(sqrt(vk[i]) + sgd_param_.sigma);
if (m[i] != m[i]) return SGD_NAN_VALUE;
}
t++;
if (sgd_param_.iteration > 0 && t >= sgd_param_.iteration) break;
}
return SGD_REACHED_MAX_ITERATIONS;
}
gctl::sgd_return_code gctl::sgd_solver::adam(array<double> &m)
{
int n_size = m.size();
//check parameters
if (n_size <= 0) return SGD_INVALID_VARIABLE_SIZE;
if (sgd_param_.epsilon < 0) return SGD_INVALID_EPSILON;
if (sgd_param_.alpha < 0) return SGD_INVALID_ALPHA;
if (sgd_param_.beta_1 < 0.0 || sgd_param_.beta_1 >= 1.0) return SGD_INVALID_BETA;
if (sgd_param_.beta_2 < 0.0 || sgd_param_.beta_2 >= 1.0) return SGD_INVALID_BETA;
if (sgd_param_.sigma < 0.0) return SGD_INVALID_SIGMA;
array<double> mk(n_size, 0.0);
array<double> vk(n_size, 0.0);
array<double> g (n_size);
double beta_1t = 1.0, beta_2t = 1.0;
double alpha_k;
int t = 0;
double fx;
while (1)
{
fx = SGD_Evaluate(m, g);
if (SGD_Progress(fx, m, sgd_param_, t)) return SGD_STOP;
if (fx < sgd_param_.epsilon) return SGD_CONVERGENCE;
beta_1t *= sgd_param_.beta_1;
beta_2t *= sgd_param_.beta_2;
alpha_k = sgd_param_.alpha * sqrt(1.0 - beta_2t)/(1.0 - beta_1t);
int i;
#pragma omp parallel for private (i) schedule(guided)
for (i = 0; i < n_size; i++)
{
mk[i] = sgd_param_.beta_1*mk[i] + (1.0 - sgd_param_.beta_1)*g[i];
vk[i] = sgd_param_.beta_2*vk[i] + (1.0 - sgd_param_.beta_2)*g[i]*g[i];
m[i] = m[i] - alpha_k * mk[i]/(sqrt(vk[i]) + sgd_param_.sigma);
//if (m[i] != m[i]) return SGD_NAN_VALUE;
}
t++;
if (sgd_param_.iteration > 0 && t >= sgd_param_.iteration) break;
}
return SGD_REACHED_MAX_ITERATIONS;
}
gctl::sgd_return_code gctl::sgd_solver::nadam(array<double> &m)
{
int n_size = m.size();
//check parameters
if (n_size <= 0) return SGD_INVALID_VARIABLE_SIZE;
if (sgd_param_.epsilon < 0) return SGD_INVALID_EPSILON;
if (sgd_param_.alpha < 0) return SGD_INVALID_ALPHA;
if (sgd_param_.beta_1 < 0.0 || sgd_param_.beta_1 >= 1.0) return SGD_INVALID_BETA;
if (sgd_param_.beta_2 < 0.0 || sgd_param_.beta_2 >= 1.0) return SGD_INVALID_BETA;
if (sgd_param_.sigma < 0.0) return SGD_INVALID_SIGMA;
array<double> mk(n_size, 0.0);
array<double> mk_hat(n_size);
array<double> nk(n_size, 0.0);
array<double> nk_hat(n_size);
array<double> g (n_size);
array<double> g_hat(n_size);
double beta_1t = 1.0, beta_1t1 = sgd_param_.beta_1, beta_2t = 1.0;
int t = 0;
double fx;
while (1)
{
fx = SGD_Evaluate(m, g);
if (SGD_Progress(fx, m, sgd_param_, t)) return SGD_STOP;
if (fx < sgd_param_.epsilon) return SGD_CONVERGENCE;
beta_1t *= sgd_param_.beta_1;
beta_1t1 *= sgd_param_.beta_1;
beta_2t *= sgd_param_.beta_2;
for (int i = 0; i < n_size; i++)
{
g_hat[i] = g[i]/(1.0 - beta_1t);
mk[i] = sgd_param_.beta_1*mk[i] + (1.0 - sgd_param_.beta_1)*g[i];
nk[i] = sgd_param_.beta_2*nk[i] + (1.0 - sgd_param_.beta_2)*g[i]*g[i];
mk_hat[i] = mk[i]/(1.0 - beta_1t1);
nk_hat[i] = nk[i]/(1.0 - beta_2t);
m[i] = m[i] - sgd_param_.alpha * ((1.0 - beta_1t)*g_hat[i]
+ beta_1t1*mk_hat[i])/(sqrt(nk_hat[i]) + sgd_param_.sigma);
if (m[i] != m[i]) return SGD_NAN_VALUE;
}
t++;
if (sgd_param_.iteration > 0 && t >= sgd_param_.iteration) break;
}
return SGD_REACHED_MAX_ITERATIONS;
}
gctl::sgd_return_code gctl::sgd_solver::adamax(array<double> &m)
{
int n_size = m.size();
//check parameters
if (n_size <= 0) return SGD_INVALID_VARIABLE_SIZE;
if (sgd_param_.epsilon < 0) return SGD_INVALID_EPSILON;
if (sgd_param_.alpha < 0) return SGD_INVALID_ALPHA;
if (sgd_param_.beta_1 < 0.0 || sgd_param_.beta_1 >= 1.0) return SGD_INVALID_BETA;
if (sgd_param_.beta_2 < 0.0 || sgd_param_.beta_2 >= 1.0) return SGD_INVALID_BETA;
if (sgd_param_.sigma < 0.0) return SGD_INVALID_SIGMA;
array<double> mk(n_size, 0.0);
array<double> vk(n_size, 0.0);
array<double> g (n_size);
double beta_1t = 1.0;
int t = 0;
double fx;
while (1)
{
fx = SGD_Evaluate(m, g);
if (SGD_Progress(fx, m, sgd_param_, t)) return SGD_STOP;
if (fx < sgd_param_.epsilon) return SGD_CONVERGENCE;
beta_1t *= sgd_param_.beta_1;
for (int i = 0; i < n_size; i++)
{
mk[i] = sgd_param_.beta_1*mk[i] + (1.0 - sgd_param_.beta_1)*g[i];
vk[i] = std::max(sgd_param_.beta_2*vk[i], std::fabs(g[i]));
m[i] = m[i] - sgd_param_.alpha * mk[i]/((1.0 - beta_1t)*vk[i]);
if (m[i] != m[i]) return SGD_NAN_VALUE;
}
t++;
if (sgd_param_.iteration > 0 && t >= sgd_param_.iteration) break;
}
return SGD_REACHED_MAX_ITERATIONS;
}
gctl::sgd_return_code gctl::sgd_solver::adabelief(array<double> &m)
{
int n_size = m.size();
//check parameters
if (n_size <= 0) return SGD_INVALID_VARIABLE_SIZE;
if (sgd_param_.epsilon < 0) return SGD_INVALID_EPSILON;
if (sgd_param_.alpha < 0) return SGD_INVALID_ALPHA;
if (sgd_param_.beta_1 < 0.0 || sgd_param_.beta_1 >= 1.0) return SGD_INVALID_BETA;
if (sgd_param_.beta_2 < 0.0 || sgd_param_.beta_2 >= 1.0) return SGD_INVALID_BETA;
if (sgd_param_.sigma < 0.0) return SGD_INVALID_SIGMA;
array<double> mk(n_size, 0.0);
array<double> vk(n_size, 0.0);
array<double> g (n_size);
double beta_1t = 1.0, beta_2t = 1.0;
double alpha_k;
int t = 0;
double fx;
while (1)
{
fx = SGD_Evaluate(m, g);
if (SGD_Progress(fx, m, sgd_param_, t)) return SGD_STOP;
if (fx < sgd_param_.epsilon) return SGD_CONVERGENCE;
beta_1t *= sgd_param_.beta_1;
beta_2t *= sgd_param_.beta_2;
alpha_k = sgd_param_.alpha * sqrt(1.0 - beta_2t)/(1.0 - beta_1t);
for (int i = 0; i < n_size; i++)
{
mk[i] = sgd_param_.beta_1*mk[i] + (1.0 - sgd_param_.beta_1)*g[i];
vk[i] = sgd_param_.beta_2*vk[i] + (1.0 - sgd_param_.beta_2)*(g[i] - mk[i])*(g[i] - mk[i]);
m[i] = m[i] - alpha_k * mk[i]/(sqrt(vk[i]) + sgd_param_.sigma);
if (m[i] != m[i]) return SGD_NAN_VALUE;
}
t++;
if (sgd_param_.iteration > 0 && t >= sgd_param_.iteration) break;
}
return SGD_REACHED_MAX_ITERATIONS;
}

201
lib/optimization/sgd.h Normal file
View File

@ -0,0 +1,201 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#ifndef _GCTL_SGD_H
#define _GCTL_SGD_H
#include "gctl/core.h"
#include "gctl/algorithm.h"
#include "gctl_optimization_config.h"
#ifdef GCTL_OPTIMIZATION_TOML
#include "toml.hpp"
#endif // GCTL_OPTIMIZATION_TOML
#if defined _WINDOWS || __WIN32__
#include "windows.h"
#endif // _WINDOWS || __WIN32__
#ifdef GSTL_OPENMP
#include "omp.h"
#endif // GSTL_OPENMP
namespace gctl
{
/**
* @brief Types of method that could be recognized by the sgd_solver() function.
*/
enum sgd_solver_type
{
/**
* Classic momentum.
*/
MOMENTUM,
/**
* Nesterov’s accelerated gradient (NAG)
*/
NAG,
/**
* AdaGrad method.
*/
ADAGRAD,
/**
* RMSProp method.
*/
RMSPROP,
/**
* Adam method.
*/
ADAM,
/**
* Nadam method.
*/
NADAM,
/**
* AdaMax method.
*/
ADAMAX,
/**
* AdaBelief method.
*/
ADABELIEF,
};
/**
* @brief return value of the sgd_solver() function.
*/
enum sgd_return_code
{
SGD_SUCCESS = 0, ///< The optimization terminated successfully.
SGD_CONVERGENCE = 1, ///< The optimization reached convergence.
SGD_STOP, ///< The process stopped by the monitoring function.
SGD_UNKNOWN_ERROR = -1024, ///< Unknown error.
SGD_INVALID_VARIABLE_SIZE, ///< The variable size is negative
SGD_INVALID_EPSILON, ///< The epsilon is negative.
SGD_REACHED_MAX_ITERATIONS, ///< Iteration reached max limit.
SGD_INVALID_MU, ///< Invalid value for mu.
SGD_INVALID_ALPHA, ///< Invalid value for alpha.
SGD_INVALID_BETA, ///< Invalid value for beta.
SGD_INVALID_SIGMA, ///< Invalid value for sigma.
SGD_NAN_VALUE, ///< Nan value.
};
/**
* @brief Parameters of the SGD methods.
*/
struct sgd_para
{
/**
* Maximal iteration times. The iteration won't stop unless the convergence
* is reached if this parameter is equal to or smaller than zero. The default
* is 0.
*/
int iteration;
/**
* Epsilon for convergence test. This parameter determines the accuracy
* with which the solution is to be found. Must be bigger than zero and
* the default is 1e-6.
*/
double epsilon;
/**
* Damping rate of the classic momentum method and the NAG method, which
* is typically given between 0 and 1. The default is 0.01.
*/
double mu;
/**
* Step size of the iteration. The default value is 0.01 for Adam and AdaMax.
*/
double alpha;
/**
* Exponential decay rates for the first order moment estimates. The range of this
* parameter is [0, 1) and the default value is 0.9.
*/
double beta_1;
/**
* Exponential decay rates for the second order moment estimates. The range of this
* parameter is [0, 1) and the default value is 0.999.
*/
double beta_2;
/**
* A small positive number validates the algorithm. The default value is 1e-8.
*/
double sigma;
};
class sgd_solver
{
private:
sgd_para sgd_param_;
int sgd_inter_;
bool sgd_silent_;
std::string solver_name_;
public:
sgd_solver();
virtual ~sgd_solver();
virtual double SGD_Evaluate(const array<double> &x, array<double> &g) = 0;
virtual int SGD_Progress(double fx, const array<double> &x, const sgd_para &param, const int k);
void sgd_silent();
void set_sgd_report_interval(int inter);
void set_sgd_para(const sgd_para &param);
void show_solver();
void sgd_error_str(sgd_return_code err_code, std::ostream &ss = std::clog, bool err_throw = false);
sgd_para default_sgd_para();
#ifdef GCTL_OPTIMIZATION_TOML
void set_sgd_para(const toml::value &toml_data);
#endif // GCTL_OPTIMIZATION_TOML
sgd_return_code momentum(array<double> &m);
sgd_return_code nag(array<double> &m);
sgd_return_code adagrad(array<double> &m);
sgd_return_code rmsprop(array<double> &m);
sgd_return_code adam(array<double> &m);
sgd_return_code nadam(array<double> &m);
sgd_return_code adamax(array<double> &m);
sgd_return_code adabelief(array<double> &m);
void SGD_Minimize(array<double> &m, sgd_solver_type solver_id = ADAM, std::ostream &ss = std::clog, bool verbose = true, bool err_throw = false);
};
}
#endif // _GCTL_SGD_H

184
lib/optimization/svd.cpp Normal file
View File

@ -0,0 +1,184 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#include "svd.h"
gctl::svd::svd()
{
reset();
}
gctl::svd::svd(const matrix<double> &src_mat) : svd()
{
decompose(src_mat);
}
void gctl::svd::reset()
{
maxi_iteration = 1000;
K = 0;
epsilon = 1e-8;
U.clear();
V.clear();
S.clear();
return;
}
void gctl::svd::set_singular_number(int k)
{
if (k <= 0)
{
throw invalid_argument("Invalid singular number. From gctl::svd::set_singular_number(...)");
}
K = k;
return;
}
void gctl::svd::set_iteration(int t)
{
if (t <= 0)
{
throw invalid_argument("Invalid singular number. From gctl::svd::set_iteration(...)");
}
maxi_iteration = t;
return;
}
void gctl::svd::set_epsilon(double e)
{
if (e <= 0)
{
throw invalid_argument("Invalid singular number. From gctl::svd::set_epsilon(...)");
}
epsilon = e;
return;
}
void gctl::svd::decompose(const matrix<double> &src_mat)
{
int M = src_mat.row_size();
int N = src_mat.col_size();
if (K == 0) K = N;
S.resize(K, 0.0);
U.resize(K, M, 0.0);
V.resize(K, N, 0.0);
srand(time(0));
array<double> left_vector(M), next_left_vector(M);
array<double> right_vector(N), next_right_vector(N);
array<double> U_tmp(M), V_tmp(N);
double diff, r, d;
for(int col=0;col<K;col++)
{
diff = 1;
r = -1;
while(1)
{
for(int i=0;i<M;i++)
left_vector[i]= (double) rand() / RAND_MAX;
if(normalize(left_vector, epsilon) > epsilon)
break;
}
for(int iter=0; diff >= epsilon && iter < maxi_iteration; iter++)
{
next_left_vector.assign_all(0.0);
next_right_vector.assign_all(0.0);
for(int i=0;i<M;i++)
for(int j=0;j<N;j++)
next_right_vector[j]+=left_vector[i]*src_mat[i][j];
r=normalize(next_right_vector, epsilon);
if(r<epsilon) break;
for(int i=0;i<col;i++)
{
for (int j = 0; j < N; j++)
{
V_tmp[j] = V[i][j];
}
orth(V_tmp, next_right_vector);
}
normalize(next_right_vector, epsilon);
for(int i=0;i<M;i++)
for(int j=0;j<N;j++)
next_left_vector[i]+=next_right_vector[j]*src_mat[i][j];
r=normalize(next_left_vector, epsilon);
if(r<epsilon) break;
for(int i=0;i<col;i++)
{
for (int j = 0; j < M; j++)
{
U_tmp[j] = U[i][j];
}
orth(U_tmp, next_left_vector);
}
normalize(next_left_vector, epsilon);
diff=0;
for(int i=0;i<M;i++)
{
d=next_left_vector[i]-left_vector[i];
diff+=d*d;
}
for (int i = 0; i < M; i++)
{
left_vector[i] = next_left_vector[i];
}
for (int i = 0; i < N; i++)
{
right_vector[i] = next_right_vector[i];
}
}
if(r>=epsilon)
{
S[col]=r;
for (int i = 0; i < M; i++)
{
U[col][i] = left_vector[i];
}
for (int i = 0; i < N; i++)
{
V[col][i] = right_vector[i];
}
}
else break;
}
return;
}

71
lib/optimization/svd.h Normal file
View File

@ -0,0 +1,71 @@
/********************************************************
* ██████╗ ██████╗████████╗██╗
* ██╔════╝ ██╔════╝╚══██╔══╝██║
* ██║ ███╗██║ ██║ ██║
* ██║ ██║██║ ██║ ██║
* ╚██████╔╝╚██████╗ ██║ ███████╗
* ╚═════╝ ╚═════╝ ╚═╝ ╚══════╝
* Geophysical Computational Tools & Library (GCTL)
*
* Copyright (c) 2022 Yi Zhang (yizhang-geo@zju.edu.cn)
*
* GCTL is distributed under a dual licensing scheme. You can redistribute
* it and/or modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation, either version 2
* of the License, or (at your option) any later version. You should have
* received a copy of the GNU Lesser General Public License along with this
* program. If not, see <http://www.gnu.org/licenses/>.
*
* If the terms and conditions of the LGPL v.2. would prevent you from using
* the GCTL, please consider the option to obtain a commercial license for a
* fee. These licenses are offered by the GCTL's original author. As a rule,
* licenses are provided "as-is", unlimited in time for a one time fee. Please
* send corresponding requests to: yizhang-geo@zju.edu.cn. Please do not forget
* to include some description of your company and the realm of its activities.
* Also add information on how to contact you by electronic and paper mail.
******************************************************/
#ifndef _GCTL_SVD_H
#define _GCTL_SVD_H
#include "gctl/core.h"
#include "gctl/algorithm.h"
namespace gctl
{
/**
* @brief SVD奇异值分解
*
* A = U^T \cdot S \cdot V
* A 大小为M*N输入的二维数组
* K 待计算的奇异值与奇异向量的数量
* U 分解后的U矩阵，大小为K*M
* S 分解后的对角S矩阵，以向量的形式表示，即前k个特征值，大小1*K
* V 分解后的V矩阵，大小为K*N
*
*/
class svd
{
public:
matrix<double> U, V;
array<double> S;
svd();
svd(const matrix<double> &src_mat);
virtual ~svd(){}
void reset();
void set_singular_number(int k);
void set_iteration(int t);
void set_epsilon(double e);
int get_singular_number(){return K;}
void decompose(const matrix<double> &src_mat);
protected:
int maxi_iteration, K;
double epsilon;
};
}
#endif // _GCTL_SVD_H