A lib for Matrix Operations in C language. (矩阵运算库--C语言)
Author: Amoiensis (Xiping.Yu)
Email: Amoiensis@outlook.com
Data: 2020.02.12~2023.08.21
更多资料和信息:
https://github.com/Amoiensis/Matrix_hub
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
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 | MUptri | Upper-Triangulation transformation on the Matrix (create). |
下三角化 | MLowtri | Lower-Triangulation transformation on the Matrix (create). |
对角化 | MDiatri | 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. |
/*
\ \ __ ___ __ _ __ __ __
\ \ / |/ /__ _/ /_____(_)_ __ / // /_ __/ /
/ / / /|_/ / _ `/ __/ __/ /\ \ // _ / // / _ \
/ / /_/ /_/\_,_/\__/_/ /_//_\_\/_//_/\_,_/_.__/
* [INFORMATION]
MATRIX_HUB
AUTHOR: Xiping.Yu
E-MAIL: Amoiensis@outlook.com
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;
}
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.
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 - MUptri/ MLowtri/ MDiatri ;
2 - M_full/ M_Inverse/ M_eigen_val/ M_rank / MUptri/ MLowtri/ MDiatri/ M_print ;
3 - M_free/ M_mul/ M_full/ M_Inverse/ M_rank/ M_mul / MUptri/ MLowtri/ MDiatri/ 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:https://github.com/Amoiensis/Matrix_hub/issues/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.
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。
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。
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。
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";
Please feel free to contact with me for any questions, thank you!
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