├── 报告.pdf ├── 空间后方交会.xmind ├── 后方交会 ├── Debug │ ├── Space Resection.exe │ └── Space Resection.pdb ├── Space Resection │ ├── 影像坐标.txt │ ├── Debug │ │ ├── Main.obj │ │ ├── matrix.obj │ │ ├── Space Resection.ilk │ │ ├── Space Resection.tlog │ │ │ ├── CL.read.1.tlog │ │ │ ├── CL.write.1.tlog │ │ │ ├── link.read.1.tlog │ │ │ ├── CL.command.1.tlog │ │ │ ├── link.command.1.tlog │ │ │ ├── link.write.1.tlog │ │ │ └── Space Resection.lastbuildstate │ │ ├── Space Resection.exe.recipe │ │ ├── Space Resection.log │ │ └── Space Resection.Build.CppClean.log │ ├── SpaceResection.h │ ├── SpaceResection.cpp │ ├── 地面坐标.txt │ ├── Space Resection.vcxproj.user │ ├── Main.cpp │ ├── Space Resection.vcxproj.filters │ ├── matrix.h │ ├── Space Resection.vcxproj │ └── matrix.cpp └── Space Resection.sln └── README.md /报告.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Raymond1030/WHURS-Photogrammetry-Space-Resection/HEAD/报告.pdf 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Resection/影像坐标.txt: -------------------------------------------------------------------------------- 1 | x y 2 | -86.15 -68.99 3 | -53.40 82.21 4 | -14.78 -76.63 5 | 10.46 64.43 6 | -------------------------------------------------------------------------------- /后方交会/Space Resection/Debug/Main.obj: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Raymond1030/WHURS-Photogrammetry-Space-Resection/HEAD/后方交会/Space Resection/Debug/Main.obj -------------------------------------------------------------------------------- /后方交会/Space Resection/Debug/matrix.obj: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Raymond1030/WHURS-Photogrammetry-Space-Resection/HEAD/后方交会/Space Resection/Debug/matrix.obj -------------------------------------------------------------------------------- /后方交会/Space Resection/SpaceResection.h: 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-------------------------------------------------------------------------------- 1 | X Y Z 2 | 36589.41 25273.32 2195.17 3 | 37631.08 31324.51 728.69 4 | 39100.71 24934.98 2386.50 5 | 40426.54 30319.81 757.31 -------------------------------------------------------------------------------- /后方交会/Space Resection/Debug/Space Resection.tlog/CL.read.1.tlog: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Raymond1030/WHURS-Photogrammetry-Space-Resection/HEAD/后方交会/Space Resection/Debug/Space Resection.tlog/CL.read.1.tlog -------------------------------------------------------------------------------- /后方交会/Space Resection/Debug/Space Resection.tlog/CL.write.1.tlog: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Raymond1030/WHURS-Photogrammetry-Space-Resection/HEAD/后方交会/Space Resection/Debug/Space Resection.tlog/CL.write.1.tlog 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-------------------------------------------------------------------------------- 1 | PlatformToolSet=v142:VCToolArchitecture=Native32Bit:VCToolsVersion=14.29.30133:TargetPlatformVersion=10.0.19041.0: 2 | Debug|Win32|C:\AImportantFile\AStudy\大三上\摄影测量学\Space Resection\| 3 | -------------------------------------------------------------------------------- /后方交会/Space Resection/Debug/Space Resection.exe.recipe: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | C:\AImportantFile\AStudy\大三上\摄影测量学\Space Resection\Debug\Space Resection.exe 6 | 7 | 8 | 9 | 10 | 11 | -------------------------------------------------------------------------------- /后方交会/Space Resection/Main.cpp: -------------------------------------------------------------------------------- 1 | // Space Resection.cpp : 此文件包含 "main" 函数。程序执行将在此处开始并结束。 2 | // 3 | #include"matrix.h" 4 | #include 5 | #include"SpaceResection.h" 6 | #include 7 | using namespace std; 8 | int main() 9 | { 10 | double m = 15000, f = 0.15324;//m=15000 f=153.24mm 11 | double x0 = 0, y0 = 0; 12 | 13 | SpaceResection Rt(m,f,x0,y0); 14 | Rt.ReadCoordinate(); 15 | Rt.GetStart(); 16 | Rt.calculate(); 17 | 18 | } 19 | 20 | // 运行程序: Ctrl + F5 或调试 >“开始执行(不调试)”菜单 21 | // 调试程序: F5 或调试 >“开始调试”菜单 22 | 23 | // 入门使用技巧: 24 | // 1. 使用解决方案资源管理器窗口添加/管理文件 25 | // 2. 使用团队资源管理器窗口连接到源代码管理 26 | // 3. 使用输出窗口查看生成输出和其他消息 27 | // 4. 使用错误列表窗口查看错误 28 | // 5. 转到“项目”>“添加新项”以创建新的代码文件，或转到“项目”>“添加现有项”以将现有代码文件添加到项目 29 | // 6. 将来，若要再次打开此项目，请转到“文件”>“打开”>“项目”并选择 .sln 文件 30 | -------------------------------------------------------------------------------- /后方交会/Space Resection/Debug/Space Resection.log: -------------------------------------------------------------------------------- 1 | SpaceResection.cpp 2 | C:\AImportantFile\AStudy\大三上\摄影测量学\Space Resection\Space Resection\SpaceResection.cpp(105,22): warning C4244: “参数”: 从“double”转换到“int”，可能丢失数据 3 | C:\AImportantFile\AStudy\大三上\摄影测量学\Space Resection\Space Resection\SpaceResection.cpp(138,23): warning C4244: “参数”: 从“double”转换到“int”，可能丢失数据 4 | C:\AImportantFile\AStudy\大三上\摄影测量学\Space Resection\Space Resection\SpaceResection.cpp(180,25): warning C4244: “参数”: 从“double”转换到“const unsigned int”，可能丢失数据 5 | C:\AImportantFile\AStudy\大三上\摄影测量学\Space Resection\Space Resection\SpaceResection.cpp(180,38): warning C4244: “参数”: 从“double”转换到“const unsigned int”，可能丢失数据 6 | C:\AImportantFile\AStudy\大三上\摄影测量学\Space Resection\Space Resection\SpaceResection.cpp(180,51): warning C4244: “参数”: 从“double”转换到“const unsigned int”，可能丢失数据 7 | Space Resection.vcxproj -> C:\AImportantFile\AStudy\大三上\摄影测量学\Space Resection\Debug\Space Resection.exe 8 | -------------------------------------------------------------------------------- /后方交会/Space Resection/Debug/Space Resection.Build.CppClean.log: -------------------------------------------------------------------------------- 1 | c:\aimportantfile\astudy\大三上\摄影测量学\space resection\space resection\debug\vc142.pdb 2 | c:\aimportantfile\astudy\大三上\摄影测量学\space resection\space resection\debug\vc142.idb 3 | c:\aimportantfile\astudy\大三上\摄影测量学\space resection\space resection\debug\spaceresection.obj 4 | c:\aimportantfile\astudy\大三上\摄影测量学\space resection\space resection\debug\main.obj 5 | c:\aimportantfile\astudy\大三上\摄影测量学\space resection\space resection\debug\matrix.obj 6 | c:\aimportantfile\astudy\大三上\摄影测量学\space resection\debug\space resection.exe 7 | c:\aimportantfile\astudy\大三上\摄影测量学\space resection\space resection\debug\space resection.ilk 8 | c:\aimportantfile\astudy\大三上\摄影测量学\space resection\debug\space resection.pdb 9 | c:\aimportantfile\astudy\大三上\摄影测量学\space resection\space resection\debug\space resection.tlog\cl.command.1.tlog 10 | c:\aimportantfile\astudy\大三上\摄影测量学\space resection\space resection\debug\space resection.tlog\cl.read.1.tlog 11 | c:\aimportantfile\astudy\大三上\摄影测量学\space resection\space resection\debug\space resection.tlog\cl.write.1.tlog 12 | c:\aimportantfile\astudy\大三上\摄影测量学\space resection\space resection\debug\space resection.tlog\link.command.1.tlog 13 | c:\aimportantfile\astudy\大三上\摄影测量学\space resection\space resection\debug\space resection.tlog\link.read.1.tlog 14 | c:\aimportantfile\astudy\大三上\摄影测量学\space resection\space resection\debug\space resection.tlog\link.write.1.tlog 15 | -------------------------------------------------------------------------------- /后方交会/Space Resection/Space Resection.vcxproj.filters: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | {4FC737F1-C7A5-4376-A066-2A32D752A2FF} 6 | cpp;c;cc;cxx;c++;cppm;ixx;def;odl;idl;hpj;bat;asm;asmx 7 | 8 | 9 | {93995380-89BD-4b04-88EB-625FBE52EBFB} 10 | h;hh;hpp;hxx;h++;hm;inl;inc;ipp;xsd 11 | 12 | 13 | {67DA6AB6-F800-4c08-8B7A-83BB121AAD01} 14 | rc;ico;cur;bmp;dlg;rc2;rct;bin;rgs;gif;jpg;jpeg;jpe;resx;tiff;tif;png;wav;mfcribbon-ms 15 | 16 | 17 | 18 | 19 | 源文件 20 | 21 | 22 | 源文件 23 | 24 | 25 | 源文件 26 | 27 | 28 | 29 | 30 | 头文件 31 | 32 | 33 | 头文件 34 | 35 | 36 | -------------------------------------------------------------------------------- /后方交会/Space Resection.sln: -------------------------------------------------------------------------------- 1 | 2 | Microsoft Visual Studio Solution File, Format Version 12.00 3 | # Visual Studio Version 16 4 | VisualStudioVersion = 16.0.31613.86 5 | MinimumVisualStudioVersion = 10.0.40219.1 6 | Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "Space Resection", "Space Resection\Space Resection.vcxproj", "{93E59DAC-7F42-4526-BE51-FF6BCD279E01}" 7 | EndProject 8 | Global 9 | GlobalSection(SolutionConfigurationPlatforms) = preSolution 10 | Debug|x64 = Debug|x64 11 | Debug|x86 = Debug|x86 12 | Release|x64 = Release|x64 13 | Release|x86 = Release|x86 14 | EndGlobalSection 15 | GlobalSection(ProjectConfigurationPlatforms) = postSolution 16 | {93E59DAC-7F42-4526-BE51-FF6BCD279E01}.Debug|x64.ActiveCfg = Debug|x64 17 | {93E59DAC-7F42-4526-BE51-FF6BCD279E01}.Debug|x64.Build.0 = Debug|x64 18 | {93E59DAC-7F42-4526-BE51-FF6BCD279E01}.Debug|x86.ActiveCfg = Debug|Win32 19 | {93E59DAC-7F42-4526-BE51-FF6BCD279E01}.Debug|x86.Build.0 = Debug|Win32 20 | {93E59DAC-7F42-4526-BE51-FF6BCD279E01}.Release|x64.ActiveCfg = Release|x64 21 | {93E59DAC-7F42-4526-BE51-FF6BCD279E01}.Release|x64.Build.0 = Release|x64 22 | {93E59DAC-7F42-4526-BE51-FF6BCD279E01}.Release|x86.ActiveCfg = Release|Win32 23 | {93E59DAC-7F42-4526-BE51-FF6BCD279E01}.Release|x86.Build.0 = Release|Win32 24 | EndGlobalSection 25 | GlobalSection(SolutionProperties) = preSolution 26 | HideSolutionNode = FALSE 27 | EndGlobalSection 28 | GlobalSection(ExtensibilityGlobals) = postSolution 29 | SolutionGuid = {EBF55EA7-4FF4-4994-AE02-8509CDE0E9C9} 30 | EndGlobalSection 31 | EndGlobal 32 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # 摄影测量-空间后方交会 2 | 3 | The Program of Space-Resection(Photogrammetry). 4 | 5 | This is a Homework of Course Photogrammetry in Wuhan University. 6 | 7 | 武大遥感院摄影测量学作业-空间后方交会 8 | 9 | `@date：2021.9.17` `@language：C++` 10 | 11 | **原理：** 12 | 13 | **[空间后方交会.xmind](https://github.com/Raymond1030/WHURS-Photogrammetry-Space-Resection/blob/main/%E7%A9%BA%E9%97%B4%E5%90%8E%E6%96%B9%E4%BA%A4%E4%BC%9A.xmind)** 14 | 15 | **[报告.pdf](https://github.com/Raymond1030/WHURS-Photogrammetry-Space-Resection/blob/main/%E6%8A%A5%E5%91%8A.pdf)** 16 | 17 | **数据：** 18 | 19 | [**地面坐标.txt**](https://github.com/Raymond1030/WHURS-Photogrammetry-Space-Resection/blob/main/%E5%90%8E%E6%96%B9%E4%BA%A4%E4%BC%9A/Space%20Resection/%E5%9C%B0%E9%9D%A2%E5%9D%90%E6%A0%87.txt) 20 | 21 | **[影像坐标.txt](https://github.com/Raymond1030/WHURS-Photogrammetry-Space-Resection/blob/main/后方交会/Space%20Resection/影像坐标.txt)** 22 | 23 | ## 项目文件: 24 | 25 | - **[Main.cpp](https://github.com/Raymond1030/WHURS-Photogrammetry-Space-Resection/blob/main/%E5%90%8E%E6%96%B9%E4%BA%A4%E4%BC%9A/Space%20Resection/Main.cpp)** 26 | 27 | > main 28 | > 29 | > main函数 30 | 31 | - **[SpaceResection.cpp](https://github.com/Raymond1030/WHURS-Photogrammetry-Space-Resection/blob/main/%E5%90%8E%E6%96%B9%E4%BA%A4%E4%BC%9A/Space%20Resection/SpaceResection.cpp)** 32 | 33 | > SpaceResection 34 | > 35 | > 前方交会程序] 36 | 37 | - [**matrix.cpp**](https://github.com/Raymond1030/WHURS-Photogrammetry-Space-Resection/blob/main/%E5%90%8E%E6%96%B9%E4%BA%A4%E4%BC%9A/Space%20Resection/matrix.cpp)/**[matrix.h](https://github.com/Raymond1030/WHURS-Photogrammetry-Space-Resection/blob/main/%E5%90%8E%E6%96%B9%E4%BA%A4%E4%BC%9A/Space%20Resection/matrix.h)** 38 | 39 | > Class of Matrix 40 | > 41 | > 别人写的一个矩阵类 42 | 43 | 44 | 45 | -------------------------------------------------------------------------------- /后方交会/Space Resection/matrix.h: -------------------------------------------------------------------------------- 1 | /* 2 | * matrix.h 3 | */ 4 | 5 | #ifndef __MATRIX_H__ 6 | #define __MATRIX_H__ 7 | 8 | #include 9 | 10 | class Matrix { 11 | public: 12 | Matrix(int, int); 13 | Matrix(double**, int, int); 14 | Matrix(); 15 | ~Matrix(); 16 | Matrix(const Matrix&); 17 | Matrix& operator=(const Matrix&); 18 | 19 | inline double& operator()(int x, int y) { return p[x][y]; } 20 | 21 | Matrix& operator+=(const Matrix&); 22 | Matrix& operator-=(const Matrix&); 23 | Matrix& operator*=(const Matrix&); 24 | Matrix& operator*=(double); 25 | Matrix& operator/=(double); 26 | Matrix operator^(int); 27 | 28 | friend std::ostream& operator<<(std::ostream&, const Matrix&); 29 | friend std::istream& operator>>(std::istream&, Matrix&); 30 | 31 | void swapRows(int, int); 32 | Matrix transpose(); 33 | 34 | static Matrix createIdentity(int); 35 | static Matrix solve(Matrix, Matrix); 36 | static Matrix bandSolve(Matrix, Matrix, int); 37 | 38 | // functions on vectors 39 | static double dotProduct(Matrix, Matrix); 40 | 41 | // functions on augmented matrices 42 | static Matrix augment(Matrix, Matrix); 43 | Matrix gaussianEliminate(); 44 | Matrix rowReduceFromGaussian(); 45 | void readSolutionsFromRREF(std::ostream& os); 46 | Matrix inverse(); 47 | 48 | private: 49 | int rows_, cols_; 50 | double **p; 51 | 52 | void allocSpace(); 53 | Matrix expHelper(const Matrix&, int); 54 | }; 55 | 56 | Matrix operator+(const Matrix&, const Matrix&); 57 | Matrix operator-(const Matrix&, const Matrix&); 58 | Matrix operator*(const Matrix&, const Matrix&); 59 | Matrix operator*(const Matrix&, double); 60 | Matrix operator*(double, const Matrix&); 61 | Matrix operator/(const Matrix&, double); 62 | 63 | #endif 64 | -------------------------------------------------------------------------------- /后方交会/Space Resection/Space Resection.vcxproj: -------------------------------------------------------------------------------- 1 | 2 | 3 | 4 | 5 | Debug 6 | Win32 7 | 8 | 9 | Release 10 | Win32 11 | 12 | 13 | Debug 14 | x64 15 | 16 | 17 | Release 18 | x64 19 | 20 | 21 | 22 | 16.0 23 | Win32Proj 24 | {93e59dac-7f42-4526-be51-ff6bcd279e01} 25 | SpaceResection 26 | 10.0 27 | 28 | 29 | 30 | Application 31 | true 32 | v143 33 | Unicode 34 | 35 | 36 | Application 37 | false 38 | v143 39 | true 40 | Unicode 41 | 42 | 43 | Application 44 | true 45 | v143 46 | Unicode 47 | 48 | 49 | Application 50 | false 51 | v143 52 | true 53 | Unicode 54 | 55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 | 71 | 72 | 73 | 74 | true 75 | 76 | 77 | false 78 | 79 | 80 | true 81 | 82 | 83 | false 84 | 85 | 86 | 87 | Level3 88 | true 89 | WIN32;_DEBUG;_CONSOLE;%(PreprocessorDefinitions) 90 | true 91 | 4996 92 | 93 | 94 | Console 95 | true 96 | 97 | 98 | 99 | 100 | Level3 101 | true 102 | true 103 | true 104 | WIN32;NDEBUG;_CONSOLE;%(PreprocessorDefinitions) 105 | true 106 | 107 | 108 | Console 109 | true 110 | true 111 | true 112 | 113 | 114 | 115 | 116 | Level3 117 | true 118 | _DEBUG;_CONSOLE;%(PreprocessorDefinitions) 119 | true 120 | 121 | 122 | Console 123 | true 124 | 125 | 126 | 127 | 128 | Level3 129 | true 130 | true 131 | true 132 | NDEBUG;_CONSOLE;%(PreprocessorDefinitions) 133 | true 134 | 135 | 136 | Console 137 | true 138 | true 139 | true 140 | 141 | 142 | 143 | 144 | 145 | 146 | 147 | 148 | 149 | 150 | 151 | 152 | 153 | 154 | -------------------------------------------------------------------------------- /后方交会/Space Resection/matrix.cpp: -------------------------------------------------------------------------------- 1 | /* 2 | * matrix.cpp 3 | */ 4 | 5 | #include 6 | #include "matrix.h" 7 | 8 | #define EPS 1e-10 9 | 10 | using std::ostream; using std::istream; using std::endl; 11 | using std::domain_error; 12 | 13 | /* PUBLIC MEMBER FUNCTIONS 14 | ********************************/ 15 | 16 | Matrix::Matrix(int rows, int cols) : rows_(rows), cols_(cols) 17 | { 18 | allocSpace(); 19 | for (int i = 0; i < rows_; ++i) { 20 | for (int j = 0; j < cols_; ++j) { 21 | p[i][j] = 0; 22 | } 23 | } 24 | } 25 | 26 | Matrix::Matrix(double** a, int rows, int cols) : rows_(rows), cols_(cols) 27 | { 28 | allocSpace(); 29 | for (int i = 0; i < rows_; ++i) { 30 | for (int j = 0; j < cols_; ++j) { 31 | p[i][j] = a[i][j]; 32 | } 33 | } 34 | } 35 | 36 | Matrix::Matrix() : rows_(1), cols_(1) 37 | { 38 | allocSpace(); 39 | p[0][0] = 0; 40 | } 41 | 42 | Matrix::~Matrix() 43 | { 44 | for (int i = 0; i < rows_; ++i) { 45 | delete[] p[i]; 46 | } 47 | delete[] p; 48 | } 49 | 50 | Matrix::Matrix(const Matrix& m) : rows_(m.rows_), cols_(m.cols_) 51 | { 52 | allocSpace(); 53 | for (int i = 0; i < rows_; ++i) { 54 | for (int j = 0; j < cols_; ++j) { 55 | p[i][j] = m.p[i][j]; 56 | } 57 | } 58 | } 59 | 60 | Matrix& Matrix::operator=(const Matrix& m) 61 | { 62 | if (this == &m) { 63 | return *this; 64 | } 65 | 66 | if (rows_ != m.rows_ || cols_ != m.cols_) { 67 | for (int i = 0; i < rows_; ++i) { 68 | delete[] p[i]; 69 | } 70 | delete[] p; 71 | 72 | rows_ = m.rows_; 73 | cols_ = m.cols_; 74 | allocSpace(); 75 | } 76 | 77 | for (int i = 0; i < rows_; ++i) { 78 | for (int j = 0; j < cols_; ++j) { 79 | p[i][j] = m.p[i][j]; 80 | } 81 | } 82 | return *this; 83 | } 84 | 85 | Matrix& Matrix::operator+=(const Matrix& m) 86 | { 87 | for (int i = 0; i < rows_; ++i) { 88 | for (int j = 0; j < cols_; ++j) { 89 | p[i][j] += m.p[i][j]; 90 | } 91 | } 92 | return *this; 93 | } 94 | 95 | Matrix& Matrix::operator-=(const Matrix& m) 96 | { 97 | for (int i = 0; i < rows_; ++i) { 98 | for (int j = 0; j < cols_; ++j) { 99 | p[i][j] -= m.p[i][j]; 100 | } 101 | } 102 | return *this; 103 | } 104 | 105 | Matrix& Matrix::operator*=(const Matrix& m) 106 | { 107 | Matrix temp(rows_, m.cols_); 108 | for (int i = 0; i < temp.rows_; ++i) { 109 | for (int j = 0; j < temp.cols_; ++j) { 110 | for (int k = 0; k < cols_; ++k) { 111 | temp.p[i][j] += (p[i][k] * m.p[k][j]); 112 | } 113 | } 114 | } 115 | return (*this = temp); 116 | } 117 | 118 | Matrix& Matrix::operator*=(double num) 119 | { 120 | for (int i = 0; i < rows_; ++i) { 121 | for (int j = 0; j < cols_; ++j) { 122 | p[i][j] *= num; 123 | } 124 | } 125 | return *this; 126 | } 127 | 128 | Matrix& Matrix::operator/=(double num) 129 | { 130 | for (int i = 0; i < rows_; ++i) { 131 | for (int j = 0; j < cols_; ++j) { 132 | p[i][j] /= num; 133 | } 134 | } 135 | return *this; 136 | } 137 | 138 | Matrix Matrix::operator^(int num) 139 | { 140 | Matrix temp(*this); 141 | return expHelper(temp, num); 142 | } 143 | 144 | void Matrix::swapRows(int r1, int r2) 145 | { 146 | double *temp = p[r1]; 147 | p[r1] = p[r2]; 148 | p[r2] = temp; 149 | } 150 | 151 | Matrix Matrix::transpose() 152 | { 153 | Matrix ret(cols_, rows_); 154 | for (int i = 0; i < rows_; ++i) { 155 | for (int j = 0; j < cols_; ++j) { 156 | ret.p[j][i] = p[i][j]; 157 | } 158 | } 159 | return ret; 160 | } 161 | 162 | 163 | /* STATIC CLASS FUNCTIONS 164 | ********************************/ 165 | 166 | Matrix Matrix::createIdentity(int size) 167 | { 168 | Matrix temp(size, size); 169 | for (int i = 0; i < temp.rows_; ++i) { 170 | for (int j = 0; j < temp.cols_; ++j) { 171 | if (i == j) { 172 | temp.p[i][j] = 1; 173 | } else { 174 | temp.p[i][j] = 0; 175 | } 176 | } 177 | } 178 | return temp; 179 | } 180 | 181 | Matrix Matrix::solve(Matrix A, Matrix b) 182 | { 183 | // Gaussian elimination 184 | for (int i = 0; i < A.rows_; ++i) { 185 | if (A.p[i][i] == 0) { 186 | // pivot 0 - throw error 187 | throw domain_error("Error: the coefficient matrix has 0 as a pivot. Please fix the input and try again."); 188 | } 189 | for (int j = i + 1; j < A.rows_; ++j) { 190 | for (int k = i + 1; k < A.cols_; ++k) { 191 | A.p[j][k] -= A.p[i][k] * (A.p[j][i] / A.p[i][i]); 192 | if (A.p[j][k] < EPS && A.p[j][k] > -1*EPS) 193 | A.p[j][k] = 0; 194 | } 195 | b.p[j][0] -= b.p[i][0] * (A.p[j][i] / A.p[i][i]); 196 | if (A.p[j][0] < EPS && A.p[j][0] > -1*EPS) 197 | A.p[j][0] = 0; 198 | A.p[j][i] = 0; 199 | } 200 | } 201 | 202 | // Back substitution 203 | Matrix x(b.rows_, 1); 204 | x.p[x.rows_ - 1][0] = b.p[x.rows_ - 1][0] / A.p[x.rows_ - 1][x.rows_ - 1]; 205 | if (x.p[x.rows_ - 1][0] < EPS && x.p[x.rows_ - 1][0] > -1*EPS) 206 | x.p[x.rows_ - 1][0] = 0; 207 | for (int i = x.rows_ - 2; i >= 0; --i) { 208 | int sum = 0; 209 | for (int j = i + 1; j < x.rows_; ++j) { 210 | sum += A.p[i][j] * x.p[j][0]; 211 | } 212 | x.p[i][0] = (b.p[i][0] - sum) / A.p[i][i]; 213 | if (x.p[i][0] < EPS && x.p[i][0] > -1*EPS) 214 | x.p[i][0] = 0; 215 | } 216 | 217 | return x; 218 | } 219 | 220 | Matrix Matrix::bandSolve(Matrix A, Matrix b, int k) 221 | { 222 | // optimized Gaussian elimination 223 | int bandsBelow = (k - 1) / 2; 224 | for (int i = 0; i < A.rows_; ++i) { 225 | if (A.p[i][i] == 0) { 226 | // pivot 0 - throw exception 227 | throw domain_error("Error: the coefficient matrix has 0 as a pivot. Please fix the input and try again."); 228 | } 229 | for (int j = i + 1; j < A.rows_ && j <= i + bandsBelow; ++j) { 230 | int k = i + 1; 231 | while (k < A.cols_ && A.p[j][k]) { 232 | A.p[j][k] -= A.p[i][k] * (A.p[j][i] / A.p[i][i]); 233 | k++; 234 | } 235 | b.p[j][0] -= b.p[i][0] * (A.p[j][i] / A.p[i][i]); 236 | A.p[j][i] = 0; 237 | } 238 | } 239 | 240 | // Back substitution 241 | Matrix x(b.rows_, 1); 242 | x.p[x.rows_ - 1][0] = b.p[x.rows_ - 1][0] / A.p[x.rows_ - 1][x.rows_ - 1]; 243 | for (int i = x.rows_ - 2; i >= 0; --i) { 244 | int sum = 0; 245 | for (int j = i + 1; j < x.rows_; ++j) { 246 | sum += A.p[i][j] * x.p[j][0]; 247 | } 248 | x.p[i][0] = (b.p[i][0] - sum) / A.p[i][i]; 249 | } 250 | 251 | return x; 252 | } 253 | 254 | // functions on VECTORS 255 | double Matrix::dotProduct(Matrix a, Matrix b) 256 | { 257 | double sum = 0; 258 | for (int i = 0; i < a.rows_; ++i) { 259 | sum += (a(i, 0) * b(i, 0)); 260 | } 261 | return sum; 262 | } 263 | 264 | // functions on AUGMENTED matrices 265 | Matrix Matrix::augment(Matrix A, Matrix B) 266 | { 267 | Matrix AB(A.rows_, A.cols_ + B.cols_); 268 | for (int i = 0; i < AB.rows_; ++i) { 269 | for (int j = 0; j < AB.cols_; ++j) { 270 | if (j < A.cols_) 271 | AB(i, j) = A(i, j); 272 | else 273 | AB(i, j) = B(i, j - B.cols_); 274 | } 275 | } 276 | return AB; 277 | } 278 | 279 | Matrix Matrix::gaussianEliminate() 280 | { 281 | Matrix Ab(*this); 282 | int rows = Ab.rows_; 283 | int cols = Ab.cols_; 284 | int Acols = cols - 1; 285 | 286 | int i = 0; // row tracker 287 | int j = 0; // column tracker 288 | 289 | // iterate through the rows 290 | while (i < rows) 291 | { 292 | // find a pivot for the row 293 | bool pivot_found = false; 294 | while (j < Acols && !pivot_found) 295 | { 296 | if (Ab(i, j) != 0) { // pivot not equal to 0 297 | pivot_found = true; 298 | } else { // check for a possible swap 299 | int max_row = i; 300 | double max_val = 0; 301 | for (int k = i + 1; k < rows; ++k) 302 | { 303 | double cur_abs = Ab(k, j) >= 0 ? Ab(k, j) : -1 * Ab(k, j); 304 | if (cur_abs > max_val) 305 | { 306 | max_row = k; 307 | max_val = cur_abs; 308 | } 309 | } 310 | if (max_row != i) { 311 | Ab.swapRows(max_row, i); 312 | pivot_found = true; 313 | } else { 314 | j++; 315 | } 316 | } 317 | } 318 | 319 | // perform elimination as normal if pivot was found 320 | if (pivot_found) 321 | { 322 | for (int t = i + 1; t < rows; ++t) { 323 | for (int s = j + 1; s < cols; ++s) { 324 | Ab(t, s) = Ab(t, s) - Ab(i, s) * (Ab(t, j) / Ab(i, j)); 325 | if (Ab(t, s) < EPS && Ab(t, s) > -1*EPS) 326 | Ab(t, s) = 0; 327 | } 328 | Ab(t, j) = 0; 329 | } 330 | } 331 | 332 | i++; 333 | j++; 334 | } 335 | 336 | return Ab; 337 | } 338 | 339 | Matrix Matrix::rowReduceFromGaussian() 340 | { 341 | Matrix R(*this); 342 | int rows = R.rows_; 343 | int cols = R.cols_; 344 | 345 | int i = rows - 1; // row tracker 346 | int j = cols - 2; // column tracker 347 | 348 | // iterate through every row 349 | while (i >= 0) 350 | { 351 | // find the pivot column 352 | int k = j - 1; 353 | while (k >= 0) { 354 | if (R(i, k) != 0) 355 | j = k; 356 | k--; 357 | } 358 | 359 | // zero out elements above pivots if pivot not 0 360 | if (R(i, j) != 0) { 361 | 362 | for (int t = i - 1; t >= 0; --t) { 363 | for (int s = 0; s < cols; ++s) { 364 | if (s != j) { 365 | R(t, s) = R(t, s) - R(i, s) * (R(t, j) / R(i, j)); 366 | if (R(t, s) < EPS && R(t, s) > -1*EPS) 367 | R(t, s) = 0; 368 | } 369 | } 370 | R(t, j) = 0; 371 | } 372 | 373 | // divide row by pivot 374 | for (int k = j + 1; k < cols; ++k) { 375 | R(i, k) = R(i, k) / R(i, j); 376 | if (R(i, k) < EPS && R(i, k) > -1*EPS) 377 | R(i, k) = 0; 378 | } 379 | R(i, j) = 1; 380 | 381 | } 382 | 383 | i--; 384 | j--; 385 | } 386 | 387 | return R; 388 | } 389 | 390 | void Matrix::readSolutionsFromRREF(ostream& os) 391 | { 392 | Matrix R(*this); 393 | 394 | // print number of solutions 395 | bool hasSolutions = true; 396 | bool doneSearching = false; 397 | int i = 0; 398 | while (!doneSearching && i < rows_) 399 | { 400 | bool allZeros = true; 401 | for (int j = 0; j < cols_ - 1; ++j) { 402 | if (R(i, j) != 0) 403 | allZeros = false; 404 | } 405 | if (allZeros && R(i, cols_ - 1) != 0) { 406 | hasSolutions = false; 407 | os << "NO SOLUTIONS" << endl << endl; 408 | doneSearching = true; 409 | } else if (allZeros && R(i, cols_ - 1) == 0) { 410 | os << "INFINITE SOLUTIONS" << endl << endl; 411 | doneSearching = true; 412 | } else if (rows_ < cols_ - 1) { 413 | os << "INFINITE SOLUTIONS" << endl << endl; 414 | doneSearching = true; 415 | } 416 | i++; 417 | } 418 | if (!doneSearching) 419 | os << "UNIQUE SOLUTION" << endl << endl; 420 | 421 | // get solutions if they exist 422 | if (hasSolutions) 423 | { 424 | Matrix particular(cols_ - 1, 1); 425 | Matrix special(cols_ - 1, 1); 426 | 427 | for (int i = 0; i < rows_; ++i) { 428 | bool pivotFound = false; 429 | bool specialCreated = false; 430 | for (int j = 0; j < cols_ - 1; ++j) { 431 | if (R(i, j) != 0) { 432 | // if pivot variable, add b to particular 433 | if (!pivotFound) { 434 | pivotFound = true; 435 | particular(j, 0) = R(i, cols_ - 1); 436 | } else { // otherwise, add to special solution 437 | if (!specialCreated) { 438 | special = Matrix(cols_ - 1, 1); 439 | specialCreated = true; 440 | } 441 | special(j, 0) = -1 * R(i, j); 442 | } 443 | } 444 | } 445 | os << "Special solution:" << endl << special << endl; 446 | } 447 | os << "Particular solution:" << endl << particular << endl; 448 | } 449 | } 450 | 451 | Matrix Matrix::inverse() 452 | { 453 | Matrix I = Matrix::createIdentity(rows_); 454 | Matrix AI = Matrix::augment(*this, I); 455 | Matrix U = AI.gaussianEliminate(); 456 | Matrix IAInverse = U.rowReduceFromGaussian(); 457 | Matrix AInverse(rows_, cols_); 458 | for (int i = 0; i < AInverse.rows_; ++i) { 459 | for (int j = 0; j < AInverse.cols_; ++j) { 460 | AInverse(i, j) = IAInverse(i, j + cols_); 461 | } 462 | } 463 | return AInverse; 464 | } 465 | 466 | 467 | /* PRIVATE HELPER FUNCTIONS 468 | ********************************/ 469 | 470 | void Matrix::allocSpace() 471 | { 472 | p = new double*[rows_]; 473 | for (int i = 0; i < rows_; ++i) { 474 | p[i] = new double[cols_]; 475 | } 476 | } 477 | 478 | Matrix Matrix::expHelper(const Matrix& m, int num) 479 | { 480 | if (num == 0) { 481 | return createIdentity(m.rows_); 482 | } else if (num == 1) { 483 | return m; 484 | } else if (num % 2 == 0) { // num is even 485 | return expHelper(m * m, num/2); 486 | } else { // num is odd 487 | return m * expHelper(m * m, (num-1)/2); 488 | } 489 | } 490 | 491 | /* NON-MEMBER FUNCTIONS 492 | ********************************/ 493 | 494 | Matrix operator+(const Matrix& m1, const Matrix& m2) 495 | { 496 | Matrix temp(m1); 497 | return (temp += m2); 498 | } 499 | 500 | Matrix operator-(const Matrix& m1, const Matrix& m2) 501 | { 502 | Matrix temp(m1); 503 | return (temp -= m2); 504 | } 505 | 506 | Matrix operator*(const Matrix& m1, const Matrix& m2) 507 | { 508 | Matrix temp(m1); 509 | return (temp *= m2); 510 | } 511 | 512 | Matrix operator*(const Matrix& m, double num) 513 | { 514 | Matrix temp(m); 515 | return (temp *= num); 516 | } 517 | 518 | Matrix operator*(double num, const Matrix& m) 519 | { 520 | return (m * num); 521 | } 522 | 523 | Matrix operator/(const Matrix& m, double num) 524 | { 525 | Matrix temp(m); 526 | return (temp /= num); 527 | } 528 | 529 | ostream& operator<<(ostream& os, const Matrix& m) 530 | { 531 | for (int i = 0; i < m.rows_; ++i) { 532 | os << m.p[i][0]; 533 | for (int j = 1; j < m.cols_; ++j) { 534 | os << " " << m.p[i][j]; 535 | } 536 | os << endl; 537 | } 538 | return os; 539 | } 540 | 541 | istream& operator>>(istream& is, Matrix& m) 542 | { 543 | for (int i = 0; i < m.rows_; ++i) { 544 | for (int j = 0; j < m.cols_; ++j) { 545 | is >> m.p[i][j]; 546 | } 547 | } 548 | return is; 549 | } 550 | --------------------------------------------------------------------------------