Matrix_hub

矩阵运算库--C语言

A lib for Matrix Operations in C language. (矩阵运算库--C语言)

Author: Amoiensis (Xiping.Yu)

Email: [email protected]

Data: 2020.02.12~2023.08.21

更多资料和信息：

https://github.com/Amoiensis/Matrix_hub

[Releases 快速下载]: Matrix_Hub_v1.52.zip

具体应用例子：

Optimization-Algorithm(最优化算法)：https://github.com/Amoiensis/Optimization-Algorithm

具体： Folder_--lib.lib文件_+_.h文件

Folder_--_code_.c文件_+_.h文件

CONTENT

操作-函数

操作	Func Name	Operation (detailed)
生成矩阵	Matrix_gen	Generate a new Matrix.
复制矩阵	Matrix_copy	Copy to a new Matrix.
释放内存	M_free	Free the memory of the Matrix (create).
矩阵显示	M_print	Print, Display.
单位矩阵(生成)	M_I	Generate a identity Matrix (create).
生成(全)零矩阵	M_Zeros	Generation All-Zeros-Matrix (create).
生成(全)一矩阵	M_Ones	Generation All-Ones-Matrix (create).
生成希尔伯特矩阵	Hilbert	Generate Hilbert Matrix (create).
加减法	M_add_sub	Addition/ subtraction (create).
乘法	M_mul	Matrix multiplication (create new one, abbr. create).
矩阵数乘	M_numul	Number Multiplication (create).
矩阵对应元素乘/除 (哈达玛积)	M_pmuldiv	Hadamard Product : Multiply / Divide every element in the two Matrix-s (create).
矩阵对矩阵，对各行进行数乘	M_numul_m	Matrix Number Multiplication (using matrix transfer)
求逆	M_Inverse	Inverse (create).
伪逆	M_pinv	left and right inverses / pseudo-inverse of Matrix. (create).
转置	M_T	Transpose (create).
行列式	M_det	Determinant.
迹	M_tr	Trace.
范数	M_norm	Norm (1/ 2/ p/ INF/ FRO).
矩阵求秩	M_rank	Rank.
矩阵求条件数	M_cond	Conditon Value of the Matrix.
矩阵最大特征值、特征向量	M_eigen_max	The maximum eigenvalue/ eigen-vector of the Matrix (create).
矩阵特征值	M_eigen_val	The eigenvalues of the Matrix (create).
矩阵特征值, 及其对应特征向量(矩阵)	M_eigen	The eigenvalues and eigen-vectors of the Matrix (create).
矩阵绝对值	M_abs	Absolute the value of elements in the Matrix (create).
矩阵行(列)调换	M_Swap	Swap row or cloumn of the Matrix.
矩阵基本变换	M_E_trans	Matrix elementary transformation.
基本变换矩阵	Etrans_2_Matrix	Transforms the elementary transformation into Matrix (create).
基本变换矩阵的逆矩阵	Etrans_4_Inverse	Inverse Matrix of elementary transformations (create).
上三角化	M_Uptri_	Upper-Triangulation transformation on the Matrix (create).
下三角化	M_Lowtri_	Lower-Triangulation transformation on the Matrix (create).
对角化	M_Diatri_	Diagonalization (create).
对角矩阵求逆	M_Dia_Inv	The inverse of the diagonal Matrix (create).
上三角化(求逆用)	M_Uptri_4inv	For inverse, upper-triangulation transformation on the Matrix (create).
下三角化(求逆用)	M_Lowtri_4inv	For inverse , lower-triangulation transformation on the Matrix (create).
向量householder变换, 返回变换矩阵H	householder	Householder transformation for the Vector, return Transformating-Matrix: H (create).
矩阵householder变换	M_householder	Householder transformation for the Matrix, return Transformated-Matrix: H_Mat (create).
矩阵QR分解	M_QR	QR Decomposition (create).
矩阵SVD分解	M_SVD	SVD Decomposition. (create).
切取部分矩阵	M_Cut	Cut out a part-matrix from the Matrix (create).
从矩阵中抽取/采样特定的行/列.	M_Sample	Sample some row/col from Matrix. (create).
填充	M_full	Full the Matrix with data (create).
(使用矩阵)填充矩阵	M_matFull	Full the Matrix with another Matrix.
矩阵按列求和/向量元素和	M_sum	Matrix Column-Summation (create). / Vector element Sum (create) .
寻找矩阵对应值位置(列优先)	M_find	Find all the positions with a certain value in the Matrix (create).
矩阵按列最小行位置 /向量最小元素位置	M_min	Minimum-value position for each row in the Matrix (create) . / Vector minimum element position (create) .
矩阵按列最大行位置 /向量最大元素位置	M_max	Maximum-value position for each row in the Matrix (create)./ Vector Maximum element position (create) .
矩阵各列指定行位置的值	M_minax_val	The value of those given (row) positions for each column in the matrix (create).
矩阵各位置与给定值比较 (返回矩阵,取值0/1)	M_logic_equal	Compare every element /pisition of the Matrix with certain value (create). [ More : Return a new Matrix, whose every value is 0/1. ]
两矩阵对应位置逻辑运算	M_logic	Logical operation of corresponding positions of two matrices
矩阵批量赋值(使用矩阵传递)	M_setval	Setting Values of a Matrix with another Matrix.
(函数: M_rank) 释放初等变换内存空间	Etrans_free	(In Func: M_rank) Free memory for Elementary Transformation.
帮助	help	Help.

Demo.c (Matrix_hub)

/*
\ \     __  ___     __      _       __ __     __
 \ \   /  |/  /__ _/ /_____(_)_ __ / // /_ __/ /
 / /  / /|_/ / _ `/ __/ __/ /\ \ // _  / // / _ \
/ /  /_/  /_/\_,_/\__/_/ /_//_\_\/_//_/\_,_/_.__/
* [INFORMATION]
    MATRIX_HUB
    AUTHOR: Xiping.Yu
    E-MAIL: [email protected]
    GITHUB: https://github.com/Amoiensis/Matrix_hub
    DATE: 2020.02.12-2023.08.21
    VERSION: 1.5.2
    CASE: Matrix Operation (C)
    DETAILS: The demo-code for Matrix_Hub.
    LICENSE: Apache-2.0
*/

#include <stdio.h>
#include <stdlib.h>
#include "matrix.h"
// # include "./solver_plugin/plugin_LP_Sover.h"


int main(int argc, char *argv[]) {

/* [Setting Matrix]*/
    //	Mat_1
    ...
    [ 具体矩阵赋值，见 demo.c ]

/* [Matrix Operation]*/
// 乘法
    Matrix *mat_3 = M_mul(mat_2, mat_1);
    M_print(mat_3);
    // 加减法
    Matrix *mat_diff = M_add_sub(1, mat_21, 1, mat_21b);
    M_print(mat_diff);
    // 初等变换
    Etrans_struct _Etrans_;
    _Etrans_.minuend_line = 2;
    _Etrans_.subtractor_line = 1;
    _Etrans_.scale = 2;
    _Etrans_.next_E_trans = NULL;
    _Etrans_.forward_E_trans = NULL;
    M_E_trans(mat_2, &_Etrans_, _ROW_);
    M_print(mat_2);
    // 单位矩阵
    M_print(M_I(5));
    // 初等变换to矩阵
    Matrix *mat_4 = Etrans_2_Matrix(&_Etrans_, 5, _ROW_);
    M_print(mat_4);
    // 上三角变换
    Uptri_struct *_Uptri_ = M_Uptri_(mat_21);
    M_print(_Uptri_->trans_matrix);
    M_print(_Uptri_->Uptri_matrix);
    // 下三角变换
    Lowtri_struct *_Lowtri_ = M_Lowtri_(mat_21);
    M_print(_Lowtri_->Lowtri_matrix);
    M_print(_Lowtri_->trans_matrix);
    // 对角化
    Dia_struct *_Dia_ = M_Diatri_(mat_21);
    M_print(_Dia_->trans_leftmatrix);
    M_print(_Dia_->Diatri_matrix);
    M_print(_Dia_->trans_rightmatrix);
    // 矩阵求逆
    Matrix *_mat_inv = M_Inverse(mat_21);
    M_print(_mat_inv);
    // 行列交换
    M_Swap(_mat_inv, 1, 2, _ROW_);
    M_print(_mat_inv);
    // 切割部分
    Matrix *_mat_cut = M_Cut(_mat_inv, _END_, _END_, 2, 3);
    M_print(_mat_cut);
    // 转置
    Matrix *_mat_T = M_T(_mat_inv);
    M_print(_mat_T);
    // 迹
    MATRIX_TYPE _tr_mat = M_tr(_mat_inv);
    printf("Trace(Matrix_%x) = %.4lf\n", _mat_inv, _tr_mat);
    // 行列式
    MATRIX_TYPE _det_mat = M_det(_mat_inv);
    printf("Det(Matrix_%x) = %.4lf\n", mat_21, _det_mat);
    // 填充
    Matrix *mat_full = M_full(mat_2, 1, 1, 1, 1, 0);
    M_print(mat_full);
    M_print(mat_2);
    // 范数
    printf("NORM_L1(mat_%x) = %lf\n",mat_b, M_norm(mat_b, 1));
    printf("NORM_L2(mat_%x) = %lf\n",mat_b, M_norm(mat_b, 2));
    // 秩
    printf("Rank(mat_%x) = %d\n", mat_A10, M_rank(mat_A10));
    printf("Rank(mat_%x) = %d\n", mat_full, M_rank(mat_full));
    // Hilbert 希尔伯特矩阵
    M_print(Hilbert(5));
    // 条件数计算
    printf("->> Condition_Value = %lf\n", M_cond(Hilbert(5),1));
    // 矩阵householder变换
    Matrix * M_H = M_householder(Hilbert(5));
    M_print(M_H);
    // 矩阵特征值 + 特征向量
    Matrix *target = mat_eigen_test;
    M_print(target);
    Matrix ** M_eigen_val_vec = M_eigen(target);
    enum{val=0, vec=1};
    M_print(M_eigen_val_vec[val]);
    M_print(M_eigen_val_vec[vec]);
    //  矩阵QR分解
    Matrix ** M_Q_R = M_QR(Hilbert(5));
    enum{q=0, r=1};
    M_print(M_Q_R[q]);
    M_print(M_Q_R[r]);
    // 矩阵 SVD 分解.
    Matrix ** mat_list_SVD = M_SVD(mat_1);
    enum{U=0, Dia=1, V=2};
    M_print(mat_list_SVD[U]);
    M_print(mat_list_SVD[Dia]);
    M_print(mat_list_SVD[V]);
    // 矩阵求伪逆
    Matrix * mat_pinv = M_pinv(mat_1, _SVD_);
    M_print(mat_pinv);

/* [Application]*/
    /* [CASE 1: LP]
    |    min CX
    |s.t. AX=b,X>=0
    LP: linear programming, 求解线性规划.
    [Note.] 需要在main文件引入 "plugin_LP_Sover.h"
    # include "./solver_plugin/plugin_LP_Sover.h"
    */
    M_LP_struct* LP_result = NULL;
    // [LP-Case 1]
    enum LP_method{_Simplex=1,};
    printf("*** LP-SOLVER START ***\n");
    LP_result = LP_Solver(mat_A_lp, mat_B_lp,mat_C_lp, _Simplex); // 使用单纯形法解线性规划.
    printf("*** LP-SOLVER END ***\n");
    if (LP_result != NULL){
        printf("[COST]\n"); // mat_C_lp, C矩阵, 成本矩阵.
        M_print(LP_result->_matrix_c);
        printf("[BASE]\n"); // 最优解的基构成
        M_print(LP_result->_matrix_base);
        printf("[VALUES]\n"); // 最优值
        M_print(M_T(LP_result->_matrix_b));
        printf("[MAT_A]\n"); // 最后的变换系数矩阵.
        M_print(LP_result->_matrix_A);
        printf("[DELTA]\n"); // 各基的delta.
        M_print(LP_result->_matrix_delta);
        printf(">> OPT-VALUES: %lf\n", LP_result->values_opt); // 求解状态.
        printf(">> iter-num: %d\n", LP_result->iter_num);
        printf(">> [Note.] Please Check is Feasible or Not.\n"); // 求解迭代次数.
        LP_free(LP_result);
    }else{
        system("pause");
        printf("[NO FEASIBLE.] SEARCH ALL BRANCHES.\n");
    }

    // [ CASE 2: linear equations solver]linear equations,
    // 解线性方程. e.g. mat_A*x = mat_b
    printf("# Solver:mat_A*x = mat_b\n");
    Matrix *_mat_result = M_mul(M_Inverse(mat_A10), mat_b10);
    M_print(_mat_result);(M_Inverse(mat_A10), mat_b10);
    M_print(_mat_result);

/* [Others]*/
    // Free Memory of Matrix, 释放矩阵内存.
    M_free(_mat_T);

/* [Help]*/
    help("help");
    help("M_rank");
    help("Update");
    help("MatrixHub");

    system("pause");
    return 0;
}

[更新说明]

[Matrix Hub v1.52] 2023.08.21

新增函数, 详情见下表 M_SVD: SVD分解/ M_pinv:矩阵伪逆/ M_Sample:矩阵采样 ;

操作	Func Name	Operation (detailed)
矩阵SVD分解	M_SVD	SVD Decomposition. (create).
伪逆	M_pinv	left and right inverses / pseudo-inverse of Matrix. (create).
从矩阵中抽取/采样特定的行/列.	M_Sample	Sample some row/col from Matrix. (create).

[Note.] 目前 M_pinv , 支持左/右逆直接计算、SVD分解计算伪逆;

新增 Matrix_Hub 插件部分 “solver_plugin”.

i. 已添加 LP (线性规划) 求解器, 基于 Simplex-Method (单纯形法), 后续将考虑添加简易MIP 和部分其他优化算法.

ii. 欢迎关注和使用本项目的同学, 分享和贡献在您使用场景中的插件功能.

iii. 其他一些具体优化的应用可以查看 Github/Amoiensis: Optimization-Algorithm.

iv. [Note.] 矩阵的基础功能和插件部分是解耦的, 如果在您的项目中不需要使用插件部分, 不引入插件部分即可.
非常感谢 645770225同学, wtyhainan同学对于特征值计算/householder变换, 相关函数的BUG提出和修改建议.

已经在版本 Matrix_Hub_v1.52 中得到修正, 具体问题请查看 [ISSUE-8]/ [ISSUE-9]/ [ISSUE-10]/ [ISSUE-11].
在版本 Matrix_Hub_v1.52 中, 考虑部分嵌入式设备的需要, 使用 memcpy/memset 实现赋值操作较多的函数, 替换原先逐个赋值的操作.

值得注意的是:

i. 在一定情况下, 编译器会对逐一赋值进行优化;

ii. 因为矩阵是行优先结构存储在内存中, 对于特定场景, 该修改不一定能效改善性能;

iii. 如果有需求也可以将 "memcpy/memset" 修改回"逐个赋值", 该部分作为注释已在源码中, 您可以在 "matrix.h" 中修改即可.

[Matrix Hub v1.51] 2022.05.28

新增函数, 详情见下表 M_eigen_max/ householder/ M_householder/ M_QR/ M_eigen_val;

操作	Func Name	Operation (detailed)
矩阵最大特征值、特征向量	M_eigen_max	The maximum eigenvalue/ eigen-vector of the Matrix (create).
向量householder变换, 返回变换矩阵H	householder	Householder transformation for the Vector, return Transformating-Matrix: H (create).
矩阵householder变换	M_householder	Householder transformation for the Matrix, return Transformated-Matrix: H_Mat (create).
矩阵QR分解	M_QR	QR Decomposition (create).
矩阵特征值	M_eigen_val	The eigenvalues of the Matrix (create).
矩阵特征值, 及其对应特征向量(矩阵)	M_eigen	The eigenvalues and eigen-vectors of the Matrix (create).

新增运算过程的"显示详细等级"(The Level of Details of Output).

位置: DETAILED (state.h)

档位: 0/1/2/3 四等级: 0->3 逐渐详细 ( 默认设置为 2级)

level - 显示详情的函数

0 - M_print （除设定的输出外，不额外显示其他计算细节信息）

1 - M_Uptri_/ M_Lowtri_/ M_Diatri_ ;

2 - M_full/ M_Inverse/ M_eigen_val/ M_rank / M_Uptri_/ M_Lowtri_/ M_Diatri_/ M_print ;

3 - M_free/ M_mul/ M_full/ M_Inverse/ M_rank/ M_mul / M_Uptri_/ M_Lowtri_/ M_Diatri_/ M_print ;
解决求逆运算中存在的问题(感谢@1u2e): 结构体释放问题、一维矩阵求逆; 详见：#4
本版本已完成内存测试，目前测试后暂无内存泄漏问题；
更新"README", 参考"功能表"中 OPERATION 列, 如返回值为新开辟空间则标记有 "create", 用于提供内存管理的参考, 具体请参考对应 OPERATION 说明 help("README").
自Matrix_Hub v1.51 起, 可以使用 help("MatrixHub") 查看当前版本号.

[Matrix Hub v1.50] 2022.04.29

新增函数, 矩阵求条件数 M_cond (matrix.h);
进一步克服 v1.44 内存问题, 完善内存管理, 可使用 help("Memory_Manager") 查看;

注意：本次更新内存管理大幅改善，已修复v1.4x内存问题。

[Matrix Hub v1.44] 2022.04.28

新增函数矩阵求秩: M_rank (matrix.h);
新增函数 Etrans_free, 实现 M_rank 初等变换内存释放; 详见 help("Etrans_free"), (matrix.h)
新增希尔伯特矩阵(病态矩阵)生成: Hilbert (matrix.h);
新增矩阵不可逆报错, Error: M_Dia_Inv_023: "@ERROR: Matrix is not invertible!" (state.h);
已修复 v1.43 计算不稳定问题;

注意：本次更新内存和计算速度都得到提高，已修复v1.43稳定性问题。

[Matrix Hub v1.43] 2021.10.26

更新矩阵求逆算法，所有基于求逆的运算速度提升，更新"M_Inverse"函数；
修复初等变换的内存问题，程序运行内存占用减少；
删除“Etrans_2_Inverse”函数；新增“Etrans_4_Inverse”函数，用于加速矩阵求逆；
更新“M_Uptri_4inv”、“M_Lowtri_4inv”用于加速矩阵求逆；

~~注意：推荐目前请使用 [Matrix Hub v1.42]v1.42版本，本次更新内存和计算速度都得到提高，但是存在一些稳定性问题，正在修复。~~

[Matrix Hub v1.42] 2021.08.06

新增求解矩阵最大特征值函数:M_eigen_max()，可使用help("M_eigen_max")查看具体使用；
新增矩阵取绝对值函数 M_abs()，可使用help("M_abs")查看具体使用；
完善向量和矩阵的各种范数运算M_norm()：新增1范数(1)、2范数(2)、无穷范数(INF)、F范数（FRO）等方法，修正了矩阵二范数计算错误的问题,可使用help("M_norm")查看具体使用；

[Matrix Hub v1.4] 2021.02.02

新增 help() 函数，可以输入各函数名称，查看具体使用方法；如，help("help")、help("Matrix_gen")、help("README")、help("Update")，等;
新增函数“M_numul_m ()”，用于矩阵数乘，矩阵对于矩阵进行操作，各行对应数乘；
将原 M_matFull() 函数中，最左侧，和最上侧，row_up和column_left取值从“0”设置为“1（HEAD）”;
修正原代码中"Matirx"的误写，修正为"Matrix";

ATTENTION

Please feel free to contact with me for any questions, thank you!

Don't spread the files without permission!

所有文件仅仅供学习交流！

Name		Name	Last commit message	Last commit date
Latest commit History 62 Commits
code_src		code_src
dll/Matrix_Hub_v1.42		dll/Matrix_Hub_v1.42
docs		docs
lib/Matrix_Hub_v1.0		lib/Matrix_Hub_v1.0
version		version
.DS_Store		.DS_Store
LICENSE		LICENSE
README.md		README.md

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Matrix_hub

矩阵运算库--C语言

CONTENT

操作-函数

Demo.c (Matrix_hub)

[更新说明]

[Matrix Hub v1.52] 2023.08.21

[Matrix Hub v1.51] 2022.05.28

[Matrix Hub v1.50] 2022.04.29

[Matrix Hub v1.44] 2022.04.28

[Matrix Hub v1.43] 2021.10.26

[Matrix Hub v1.42] 2021.08.06

[Matrix Hub v1.4] 2021.02.02

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Matrix_hub

矩阵运算库--C语言

CONTENT

操作-函数

Demo.c (Matrix_hub)

[更新说明]

[Matrix Hub v1.52] 2023.08.21

[Matrix Hub v1.51] 2022.05.28

[Matrix Hub v1.50] 2022.04.29

[Matrix Hub v1.44] 2022.04.28

[Matrix Hub v1.43] 2021.10.26

[Matrix Hub v1.42] 2021.08.06

[Matrix Hub v1.4] 2021.02.02

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