tomsolver

中文 English

Simplest, Well-tested, Non-linear equations solver library by C++14.

origin: https://github.com/tomwillow/tomsolver

Make C++ solve nonlinear equations as easy as Matlab fsolve

Contributors:

• Tom Willow (https://github.com/tomwillow)
• lizho (https://github.com/lizho)

Features

• Simple! Simple! If you know how to use fsolve, you will use this!
• Single header file, just include it!

Functions

• Solving nonlinear equations (Newton-Raphson method, LM method)
• Solving linear equations (Gaussian-column pivot iteration method, inverse matrix)
• Matrix and vector operations (matrix inversion, vector cross multiplication, etc.)
• "Pseudo" symbolic operations (derivatives of expressions, Jacobian matrices of symbolic matrices)

Supported Platforms

Tested at:

• Linux: ubuntu 22.04 x86_64 gcc 11.3.0
• Windows: windows10 x64 Visual Studio 2019

Tested at Github Actions:

• Linux-latest gcc Debug&Release
• Linux-latest clang Debug&Release
• Windows-latest msvc Debug&Release

Example

#include <tomsolver/tomsolver.h>

using namespace tomsolver;

int main() {
    /*
    Translate from Matlab code:

    root2d.m:
        function F = root2d(x)
            F(1) = exp(-exp(-(x(1)+x(2)))) - x(2)*(1+x(1)^2);
            F(2) = x(1)*cos(x(2)) + x(2)*sin(x(1)) - 0.5;
        end

    root2d_solve.m:
        format long
        fun = @root2d;
        x0 = [0,0];
        x = fsolve(fun,x0)

    result:
        x =

            0.353246561920553   0.606082026502285
     */
    try {
        // create equations from string
        SymVec f = {
            "exp(-exp(-(x1 + x2))) - x2 * (1 + x1 ^ 2)"_f,
            "x1 * cos(x2) + x2 * sin(x1) - 0.5"_f,
        };

        // solve it!
        VarsTable ans = Solve(f);

        // print the solution
        std::cout << ans << std::endl;

        // get the values of solution
        std::cout << "x1 = " << ans["x1"] << std::endl;
        std::cout << "x2 = " << ans["x2"] << std::endl;
    } catch (const std::runtime_error &err) {
        // if any error occurs, exception will be thrown
        std::cerr << err.what() << std::endl;
        return -1;
    }

    return 0;
}

Usage

1. Header-Only usage

Just include a single header file: single/include/tomsolver/tomsolver.h

2. VCPKG

You could use vcpkg for unified package usage.

• Manifest mode(recommended) Create a vcpkg.json file:

  {
    "dependencies": [
      "tomsolver"
    ]
  }
  

  Then run the following command in the same directory: $ vcpkg install Tutorial: https://learn.microsoft.com/en-us/vcpkg/get_started/get-started?pivots=shell-bash

• Classic mode $ vcpkg install tomsolver

2. Binary Library + Header Files usage

$ git clone https://github.com/tomwillow/tomsolver
$ mkdir build
$ cd build
$ cmake ../tomsolver
$ cmake --build . --target INSTALL

Then add the include directory and link to the library file.

Directory Structure

• src: source files
• tests: unit tests
• single/include: the folder where the header-only tomsolver.h is located
• single/test: All unit tests are integrated into one .cpp file to test whether tomsolver.h is correct.
• scripts: used to generate single-file header files and single-file tests under single

examples

• examples/solve: Example of solving nonlinear equations, demonstrating basic usage and how to set a unified initial value
• examples/set_initial_value: Example of solving nonlinear equations, demostrating how to set every variable's initial value
• examples/solve2: Example of solving nonlinear equations, demonstrating how to switch solution methods and replace known quantities in the equation
• examples/diff_machine: Derivator, input a line of expression and output the derivation result of this expression

Development Plan

• add doxygen comments + tutorial document (CN+EN)
• add benchmark tests
• add an option to use Eigen library as matrix library
• aim at Matlab fsolve, add more solving methods of nonlinear equations
• add an optional Config parameter in Solve() function (similar to Matlab fsolve's option)
• add support for binary/multivariate functions, such as pow(x, y)
• the current Simplify function is still very simple, modify Simplify to be better
• add LaTeX format formula output

Thanks

https://github.com/taehwan642

WeChat group

If you have any questions, want to communicate, want to participate in development, or want to contact the authors, you are welcome to add the WeChat tomwillow.

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