diff --git a/.vscode/settings.json b/.vscode/settings.json index 0ce7a27d..de42f7c3 100644 --- a/.vscode/settings.json +++ b/.vscode/settings.json @@ -16,5 +16,9 @@ "command": "extension.execute", "priority": 4 } - ] -} \ No newline at end of file + ], + "cmake.generator": "MinGW Makefiles", + "files.associations": { + "algebra.h": "c" + } +} diff --git a/CMakeLists.txt b/CMakeLists.txt index e69de29b..22649d80 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -0,0 +1,11 @@ +cmake_minimum_required(VERSION 4.0) + +project (main) + +set (EXECUTABLE_OUTPUT_PATH ${PROJECT_SOURCE_DIR}/bin) + +aux_source_directory (src SRC_LIST) + +include_directories (inc) + +add_executable (main ${SRC_LIST}) \ No newline at end of file diff --git a/README.md b/README.md index 6baf26c2..4599a931 100644 --- a/README.md +++ b/README.md @@ -1,66 +1,50 @@ # algebra -硬件技术团队编程基础作业 -## 课件资料 | Reference -* [课程PPT](https://tannin-1316822731.cos.ap-nanjing.myqcloud.com/2025-04-19-2025%E7%A1%AC%E4%BB%B6%E7%AC%AC%E4%B8%80%E6%AC%A1%E5%86%85%E8%AE%AD.pdf) -* [VSCode的C/C++环境配置教程](https://www.bilibili.com/video/BV1UZ421e7ty/?share_source=copy_web&vd_source=d82c2ec75577b6834f9f580f066180c1) -* [Git使用教程](https://www.bilibili.com/video/BV1og4y1u7XU/?share_source=copy_web&vd_source=d82c2ec75577b6834f9f580f066180c1) -## 预修要求｜Requirements -修读过《C程序设计基础》、《线性代数》以及X·Lab硬件技术团队编程基础课程或其对应的高阶课程。 -## 说明｜Explainations -本题目的难度对于初学者而言相对较高，主要考察了基础的数学能力、通过编程解决问题的能力以及工程管理、CMake、git等综合能力。该作业的最终得分仅作参考，同学们可根据自己的能力来决定实现哪些函数。 -## 题目背景｜Background -《线性代数》作为浙江大学工科多数专业必修的数学基础课程，对于其掌握是至关重要的，后续各大专业的专业课程也都离不开线性代数。然而，在后续的专业课程学习中，我们往往只需要计算一些矩阵的数值解，这个过程如果用手去计算的话是十分痛苦的。秉承着“我都学编程了就不要自己做一些无意义的事情”的原则，我们决定实现一个线性代数计算库，来辅助我们进行运算。 -> 当然，如MATLAB、Python等高级编程语言已经可以做到这类事情，且做得更好，但这并不妨碍我们通过这样一种方式来锻炼自己的C语言编程能力。 -## 题目介绍｜Introduction -本仓库给出了我们在内训中提到的工程模板，同学们要做的任务如下： -1. 自学git，注册GitHub账号，将本仓库在自己的GitHub账户下Fork一份（注意是Fork，禁止直接clone本仓库到本地，否则你将无法完成后续提交），并按照`yourname_hw1`的格式更改仓库名称（在仓库中的Settings处可修改，记得不要用中文，仓库权限为public，如涉及到隐私保护，可设为private，但要将`tanninrachel@yinlin.wiki`这个账户设置为协作者）。 -2. 将你的仓库clone到本地。 -3. 按照内训所讲的工程模板补充所缺的文件夹。 -4. 根据`inc/algebra.h`中的注释和预定义，在`src/algebra.c`中实现对应的函数。 -5. 根据内训所讲，自行编写`CMakeLists.txt`文件，使你的工程能够在本地成功编译运行。 -6. 自学Markdown，修改`README.md`文件，需要包含你的实现思路（大致描述即可）以及本地运行截图。 -7. 将你的修改提交到远程仓库，并将仓库链接提交（提交方式见下文）。 -## 思路参考｜Thinking -见`doc`文件夹。 -## 交互格式｜Format -在本题目中，`main.c`文件已给出，不需要同学们自己实现，也请不要更改这个文件，否则可能出现判题错误。 -### 输入格式 -本题目采用帧判定的思路进行，每一帧的第一行指令代码，`+`、`-`、`*`、`.`、`t`、`d`、`i`、`r`、`j`分别测试`add_matrix`、`sub_matrix`、`mul_matrix`、`scale_matrix`、`transpose_matrix`、`det_matrix`、`inv_matrix`、`rank_matrix`、`trace_matrix`函数，`q`表示退出。 - -接下来的一行输入矩阵 $\mathbf{A}$ 的行数 $m$ 和列数 $n$ ，在接下来的 $m$ 行中输入 $n$ 个双精度浮点数，以空格分开。 -对于二元运算函数的测试，需要再按照上述过程输入矩阵 $\textbf{B}$ 。 - -可能的一次运行输入如下： -``` -+ -2 2 -1.1 1.3 -2.4 3.7 -2 2 -3.1 4.3 -5.1 7.1 -+ -2 2 -1.1 1.2 -2.4 3.5 -2 3 -1 2 2.1 -3 2 3.3 -q -``` -### 输出格式 -在每一帧中，依次根据输入的指令代码运行对应的函数，并给出函数的输出与标准值比对。上述输入的正确输出如下： -``` -4.20 5.60 -7.50 10.80 -Error: Matrix a and b must have the same rows and cols. -``` -## 评分标准｜Standard -* 成功运行：+25分 -* `add_matrix`、`sub_matrix`、`mul_matrix`、`scale_matrix`、`transpose_matrix`、`trace_matrix`功能正常每个+5分 -* `det_matrix`、`inv_matrix`、`rank_matrix`功能正常共+10分（此处为附加题，有一定难度，可选做） -> 为了保证题目难度，每个函数具体的评分标准不予公布。 -## 提交方式｜Submit -将你的每个函数的测试运行结果以截图的形式放在你仓库的`README.md`文件中（请注意Markdown中图片的引用要包含源文件）。并将你的最终代码仓库链接（在浏览器上的那个，不要带有`.git`的）填写如下问卷发送： - -![](https://tannin-1316822731.cos.ap-nanjing.myqcloud.com/2025-04-19-%E7%AC%AC%E4%B8%80%E6%AC%A1%E5%86%85%E8%AE%AD%E4%BD%9C%E4%B8%9A%E6%8F%90%E4%BA%A4.png) +## 运行截图在文件夹pic中，README中以相对路径形式引用。 +## add_matrix +思路：对应元素相加。 +![](.\pic\add_matrix.png) +## sub_matrix +思路：对应元素相减 +![](.\pic\sub_matrix.png) +## mul_matrix +思路：取a的第i行和b的第j列的元素对应相乘后相加得到目标矩阵第i行第j列的元素。 +![](.\pic\mul_matrix.png) +## scale_matrix +思路：对每个元素数乘即可。 +![](.\pic\scale_matrix.png) +## transpose_matrix +思路：目标矩阵的第i行第j列的元素为原矩阵第j行第i列的元素。 +![](.\pic\transpose_matrix.png) +## det_matrix +思路：按照公式递归即可。 +![](.\pic\det_matrix.png) +## inv_matrix +思路：使用伴随矩阵法，先求行列式的值，再求伴随矩阵。 +![](.\pic\inv_matrix.png) +## rank_matrix +思路：将矩阵化为行（列）最简型矩阵，检查非零行（列）个数即为秩。 +![](.\pic\rank_matrix.png) +## trace_matrix +思路：求主对角线元素之和。 +![](.\pic\trace_matrix.png) + + + + + + + + + + + + + + + + + + + + + diff --git a/bin/main.exe b/bin/main.exe new file mode 100644 index 00000000..0d4012bf Binary files /dev/null and b/bin/main.exe differ diff --git a/build/.cmake/api/v1/reply/cache-v2-481f72de5c1890774a1a.json b/build/.cmake/api/v1/reply/cache-v2-08942ad841ecf0d87646.json similarity index 91% rename from build/.cmake/api/v1/reply/cache-v2-481f72de5c1890774a1a.json rename to build/.cmake/api/v1/reply/cache-v2-08942ad841ecf0d87646.json index 5bafaadb..9a3efe1e 100644 --- a/build/.cmake/api/v1/reply/cache-v2-481f72de5c1890774a1a.json +++ b/build/.cmake/api/v1/reply/cache-v2-08942ad841ecf0d87646.json @@ -15,7 +15,7 @@ } ], 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a/build/CMakeCache.txt b/build/CMakeCache.txt index f7847617..4fb3e2a6 100644 --- a/build/CMakeCache.txt +++ b/build/CMakeCache.txt @@ -1,6 +1,6 @@ # This is the CMakeCache file. -# For build in directory: f:/zzy/code/algebra/build -# It was generated by CMake: C:/ST/STM32CubeCLT_1.15.1/CMake/bin/cmake.exe +# For build in directory: d:/x-lab/cuidongjie_hw1-main/cuidongjie_hw1-main/build +# It was generated by CMake: E:/Cmake/bin/cmake.exe # You can edit this file to change values found and used by cmake. # If you do not want to change any of the values, simply exit the editor. # If you do want to change a value, simply edit, save, and exit the editor. @@ -15,24 +15,27 @@ ######################## //Path to a program. -CMAKE_ADDR2LINE:FILEPATH=C:/Program Files (x86)/Dev-Cpp/MinGW64/bin/addr2line.exe +CMAKE_ADDR2LINE:FILEPATH=E:/gcc/ucrt64/bin/addr2line.exe //Path to a program. -CMAKE_AR:FILEPATH=C:/Program Files (x86)/Dev-Cpp/MinGW64/bin/ar.exe +CMAKE_AR:FILEPATH=E:/gcc/ucrt64/bin/ar.exe //No help, variable specified on the command line. CMAKE_BUILD_TYPE:STRING=Debug +//Enable/Disable color output during build. +CMAKE_COLOR_MAKEFILE:BOOL=ON + //CXX compiler -CMAKE_CXX_COMPILER:FILEPATH=C:/Program Files (x86)/Dev-Cpp/MinGW64/bin/c++.exe +CMAKE_CXX_COMPILER:STRING=E:/gcc/ucrt64/bin/g++.exe //A wrapper around 'ar' adding the appropriate '--plugin' option // for the GCC compiler -CMAKE_CXX_COMPILER_AR:FILEPATH=C:/Program Files (x86)/Dev-Cpp/MinGW64/bin/gcc-ar.exe +CMAKE_CXX_COMPILER_AR:FILEPATH=E:/gcc/ucrt64/bin/gcc-ar.exe //A wrapper around 'ranlib' adding the appropriate '--plugin' option // for the GCC compiler -CMAKE_CXX_COMPILER_RANLIB:FILEPATH=C:/Program Files (x86)/Dev-Cpp/MinGW64/bin/gcc-ranlib.exe +CMAKE_CXX_COMPILER_RANLIB:FILEPATH=E:/gcc/ucrt64/bin/gcc-ranlib.exe //Flags used by the CXX compiler during all build types. CMAKE_CXX_FLAGS:STRING= @@ -53,15 +56,15 @@ CMAKE_CXX_FLAGS_RELWITHDEBINFO:STRING=-O2 -g -DNDEBUG CMAKE_CXX_STANDARD_LIBRARIES:STRING=-lkernel32 -luser32 -lgdi32 -lwinspool -lshell32 -lole32 -loleaut32 -luuid -lcomdlg32 -ladvapi32 //C compiler -CMAKE_C_COMPILER:FILEPATH=C:/Program Files (x86)/Dev-Cpp/MinGW64/bin/gcc.exe +CMAKE_C_COMPILER:STRING=E:/gcc/ucrt64/bin/gcc.exe //A wrapper around 'ar' adding the appropriate '--plugin' option // for the GCC compiler -CMAKE_C_COMPILER_AR:FILEPATH=C:/Program Files (x86)/Dev-Cpp/MinGW64/bin/gcc-ar.exe +CMAKE_C_COMPILER_AR:FILEPATH=E:/gcc/ucrt64/bin/gcc-ar.exe //A wrapper around 'ranlib' adding the appropriate '--plugin' option // for the GCC compiler -CMAKE_C_COMPILER_RANLIB:FILEPATH=C:/Program Files (x86)/Dev-Cpp/MinGW64/bin/gcc-ranlib.exe +CMAKE_C_COMPILER_RANLIB:FILEPATH=E:/gcc/ucrt64/bin/gcc-ranlib.exe //Flags used by the C compiler during all build types. CMAKE_C_FLAGS:STRING= @@ -82,7 +85,7 @@ CMAKE_C_FLAGS_RELWITHDEBINFO:STRING=-O2 -g -DNDEBUG CMAKE_C_STANDARD_LIBRARIES:STRING=-lkernel32 -luser32 -lgdi32 -lwinspool -lshell32 -lole32 -loleaut32 -luuid -lcomdlg32 -ladvapi32 //Path to a program. -CMAKE_DLLTOOL:FILEPATH=C:/Program Files (x86)/Dev-Cpp/MinGW64/bin/dlltool.exe +CMAKE_DLLTOOL:FILEPATH=E:/gcc/ucrt64/bin/dlltool.exe //Flags used by the linker during all build types. 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DEC(__open_xl_modification__) # define COMPILER_VERSION_TWEAK DEC(__open_xl_ptf_fix_level__) +# define COMPILER_VERSION_INTERNAL_STR __clang_version__ #elif defined(__ibmxl__) && defined(__clang__) @@ -335,6 +336,13 @@ # define COMPILER_VERSION_PATCH DEC(__ARMCOMPILER_VERSION/100 % 100) # define COMPILER_VERSION_INTERNAL DEC(__ARMCOMPILER_VERSION) +#elif defined(__clang__) && defined(__ti__) +# define COMPILER_ID "TIClang" + # define COMPILER_VERSION_MAJOR DEC(__ti_major__) + # define COMPILER_VERSION_MINOR DEC(__ti_minor__) + # define COMPILER_VERSION_PATCH DEC(__ti_patchlevel__) +# define COMPILER_VERSION_INTERNAL DEC(__ti_version__) + #elif defined(__clang__) # define COMPILER_ID "Clang" # if defined(_MSC_VER) @@ -679,6 +687,14 @@ char const *info_cray = "INFO" ":" "compiler_wrapper[CrayPrgEnv]"; # define ARCHITECTURE_ID "" # endif +#elif defined(__clang__) && defined(__ti__) +# if defined(__ARM_ARCH) +# define ARCHITECTURE_ID "ARM" + +# else /* unknown architecture */ +# define ARCHITECTURE_ID "" +# endif + #elif defined(__TI_COMPILER_VERSION__) # if defined(__TI_ARM__) # define ARCHITECTURE_ID "ARM" @@ -710,7 +726,7 @@ char const *info_cray = "INFO" ":" "compiler_wrapper[CrayPrgEnv]"; # elif defined(__CMCS__) # define ARCHITECTURE_ID "MCS" -# elif defined(__CARM__) +# elif defined(__CARM__) || defined(__CPARM__) # define ARCHITECTURE_ID "ARM" # elif defined(__CARC__) @@ -812,19 +828,28 @@ char const* info_arch = "INFO" ":" "arch[" ARCHITECTURE_ID "]"; +#define C_STD_99 199901L +#define C_STD_11 201112L +#define C_STD_17 201710L +#define C_STD_23 202311L + +#ifdef __STDC_VERSION__ +# define C_STD __STDC_VERSION__ +#endif + #if !defined(__STDC__) && !defined(__clang__) # if defined(_MSC_VER) || defined(__ibmxl__) || defined(__IBMC__) # define C_VERSION "90" # else # define C_VERSION # endif -#elif __STDC_VERSION__ > 201710L +#elif C_STD > C_STD_17 # define C_VERSION "23" -#elif __STDC_VERSION__ >= 201710L +#elif C_STD > C_STD_11 # define C_VERSION "17" -#elif 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__clang_version__ #elif defined(__ibmxl__) && defined(__clang__) @@ -329,6 +324,13 @@ # define COMPILER_VERSION_PATCH DEC(__ARMCOMPILER_VERSION/100 % 100) # define COMPILER_VERSION_INTERNAL DEC(__ARMCOMPILER_VERSION) +#elif defined(__clang__) && defined(__ti__) +# define COMPILER_ID "TIClang" + # define COMPILER_VERSION_MAJOR DEC(__ti_major__) + # define COMPILER_VERSION_MINOR DEC(__ti_minor__) + # define COMPILER_VERSION_PATCH DEC(__ti_patchlevel__) +# define COMPILER_VERSION_INTERNAL DEC(__ti_version__) + #elif defined(__clang__) # define COMPILER_ID "Clang" # if defined(_MSC_VER) @@ -664,6 +666,14 @@ char const *info_cray = "INFO" ":" "compiler_wrapper[CrayPrgEnv]"; # define ARCHITECTURE_ID "" # endif +#elif defined(__clang__) && defined(__ti__) +# if defined(__ARM_ARCH) +# define ARCHITECTURE_ID "ARM" + +# else /* unknown architecture */ +# define ARCHITECTURE_ID "" +# endif + #elif defined(__TI_COMPILER_VERSION__) # if defined(__TI_ARM__) # define ARCHITECTURE_ID "ARM" @@ -695,7 +705,7 @@ char const *info_cray = "INFO" ":" "compiler_wrapper[CrayPrgEnv]"; # elif defined(__CMCS__) # define ARCHITECTURE_ID "MCS" -# elif defined(__CARM__) +# elif defined(__CARM__) || defined(__CPARM__) # define ARCHITECTURE_ID "ARM" # elif defined(__CARC__) @@ -797,32 +807,73 @@ char const* info_arch = "INFO" ":" "arch[" ARCHITECTURE_ID "]"; -#if defined(__INTEL_COMPILER) && defined(_MSVC_LANG) && _MSVC_LANG < 201403L -# if defined(__INTEL_CXX11_MODE__) -# if defined(__cpp_aggregate_nsdmi) -# define CXX_STD 201402L -# else -# define CXX_STD 201103L -# endif +#define CXX_STD_98 199711L +#define CXX_STD_11 201103L +#define CXX_STD_14 201402L +#define CXX_STD_17 201703L +#define CXX_STD_20 202002L +#define CXX_STD_23 202302L + +#if defined(__INTEL_COMPILER) && defined(_MSVC_LANG) +# if _MSVC_LANG > CXX_STD_17 +# define CXX_STD _MSVC_LANG +# elif _MSVC_LANG == CXX_STD_17 && defined(__cpp_aggregate_paren_init) +# define CXX_STD CXX_STD_20 +# elif _MSVC_LANG > CXX_STD_14 && __cplusplus > CXX_STD_17 +# define CXX_STD CXX_STD_20 +# elif _MSVC_LANG > CXX_STD_14 +# define CXX_STD CXX_STD_17 +# elif defined(__INTEL_CXX11_MODE__) && defined(__cpp_aggregate_nsdmi) +# define CXX_STD CXX_STD_14 +# elif defined(__INTEL_CXX11_MODE__) +# define CXX_STD CXX_STD_11 # else -# define CXX_STD 199711L +# define CXX_STD CXX_STD_98 # endif #elif defined(_MSC_VER) && defined(_MSVC_LANG) -# define CXX_STD _MSVC_LANG +# if _MSVC_LANG > __cplusplus +# define CXX_STD _MSVC_LANG +# else +# define CXX_STD __cplusplus +# endif +#elif defined(__NVCOMPILER) +# if __cplusplus == CXX_STD_17 && defined(__cpp_aggregate_paren_init) +# define CXX_STD CXX_STD_20 +# else +# define CXX_STD __cplusplus +# endif +#elif defined(__INTEL_COMPILER) || defined(__PGI) +# if __cplusplus == CXX_STD_11 && defined(__cpp_namespace_attributes) +# define CXX_STD CXX_STD_17 +# elif __cplusplus == CXX_STD_11 && defined(__cpp_aggregate_nsdmi) +# define CXX_STD CXX_STD_14 +# else +# define CXX_STD __cplusplus +# endif +#elif (defined(__IBMCPP__) || defined(__ibmxl__)) && defined(__linux__) +# if __cplusplus == CXX_STD_11 && defined(__cpp_aggregate_nsdmi) +# define CXX_STD CXX_STD_14 +# else +# define CXX_STD __cplusplus +# endif +#elif __cplusplus == 1 && defined(__GXX_EXPERIMENTAL_CXX0X__) +# define CXX_STD CXX_STD_11 #else # define CXX_STD __cplusplus #endif const char* info_language_standard_default = "INFO" ":" "standard_default[" -#if CXX_STD > 202002L +#if CXX_STD > CXX_STD_23 + "26" +#elif CXX_STD > CXX_STD_20 "23" -#elif CXX_STD > 201703L +#elif CXX_STD > CXX_STD_17 "20" -#elif CXX_STD >= 201703L +#elif CXX_STD > CXX_STD_14 "17" -#elif CXX_STD >= 201402L +#elif CXX_STD > CXX_STD_11 "14" -#elif CXX_STD >= 201103L +#elif CXX_STD >= CXX_STD_11 "11" #else "98" @@ -850,7 +901,7 @@ int main(int argc, char* argv[]) #ifdef COMPILER_VERSION_MAJOR require += info_version[argc]; #endif -#ifdef COMPILER_VERSION_INTERNAL +#if defined(COMPILER_VERSION_INTERNAL) || defined(COMPILER_VERSION_INTERNAL_STR) 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-# Set default install directory permissions. +# Set path to fallback-tool for dependency-resolution. if(NOT DEFINED CMAKE_OBJDUMP) - set(CMAKE_OBJDUMP "C:/Program Files (x86)/Dev-Cpp/MinGW64/bin/objdump.exe") + set(CMAKE_OBJDUMP "E:/gcc/ucrt64/bin/objdump.exe") endif() +string(REPLACE ";" "\n" CMAKE_INSTALL_MANIFEST_CONTENT + "${CMAKE_INSTALL_MANIFEST_FILES}") +if(CMAKE_INSTALL_LOCAL_ONLY) + file(WRITE "D:/x-lab/cuidongjie_hw1-main/cuidongjie_hw1-main/build/install_local_manifest.txt" + "${CMAKE_INSTALL_MANIFEST_CONTENT}") +endif() if(CMAKE_INSTALL_COMPONENT) - set(CMAKE_INSTALL_MANIFEST "install_manifest_${CMAKE_INSTALL_COMPONENT}.txt") + if(CMAKE_INSTALL_COMPONENT MATCHES "^[a-zA-Z0-9_.+-]+$") + set(CMAKE_INSTALL_MANIFEST "install_manifest_${CMAKE_INSTALL_COMPONENT}.txt") + else() + string(MD5 CMAKE_INST_COMP_HASH "${CMAKE_INSTALL_COMPONENT}") + set(CMAKE_INSTALL_MANIFEST "install_manifest_${CMAKE_INST_COMP_HASH}.txt") + unset(CMAKE_INST_COMP_HASH) + endif() else() 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create_matrix(int row, int col) Matrix add_matrix(Matrix a, Matrix b) { - // ToDo + if (a.rows != b.rows || a.cols != b.cols) + { + printf("Error: Matrix a and b must have the same rows and cols.\n"); + } + else + { + Matrix sum; + sum.cols = a.cols; + sum.rows = a.rows; + for (int i = 0; i < sum.rows; i++) + { + for (int j = 0; j < sum.cols; j++) + { + sum.data[i][j] = a.data[i][j] + b.data[i][j]; + } + } + return sum; + } return create_matrix(0, 0); } Matrix sub_matrix(Matrix a, Matrix b) { - // ToDo + if (a.rows != b.rows || a.cols != b.cols) + { + printf("Error: Matrix a and b must have the same rows and cols.\n"); + } + else + { + Matrix sub; + sub.cols = a.cols; + sub.rows = a.rows; + for (int i = 0; i < sub.rows; i++) + { + for (int j = 0; j < sub.cols; j++) + { + sub.data[i][j] = a.data[i][j] - b.data[i][j]; + } + } + return sub; + } return create_matrix(0, 0); } Matrix mul_matrix(Matrix a, Matrix b) { - // ToDo + if (a.cols != b.rows) + { + printf("Error: The number of cols of matrix a must be equal to the number of rows of matrix b.\n"); + } + else + { + Matrix res; + res.rows = a.rows; + res.cols = b.cols; + for (int i = 0; i < res.rows; i++) + { + for (int j = 0; j < res.cols; j++) + { + double sum = 0; + for (int k = 0; k < a.cols; k++) + { + sum += a.data[i][k] * b.data[k][j]; + } + res.data[i][j] = sum; + } + } + return res; + } return create_matrix(0, 0); } Matrix scale_matrix(Matrix a, double k) { - // ToDo + Matrix res; + res.rows = a.rows; + res.cols = a.cols; + for (int i = 0; i < res.rows; i++) + { + for (int j = 0; j < res.cols; j++) + { + res.data[i][j] = k * a.data[i][j]; + } + } + return res; return create_matrix(0, 0); } Matrix transpose_matrix(Matrix a) { - // ToDo + Matrix res; + res.rows = a.cols; + res.cols = a.rows; + for (int i = 0; i < res.rows; i++) + { + for (int j = 0; j < res.cols; j++) + { + res.data[i][j] = a.data[j][i]; + } + } + return res; return create_matrix(0, 0); } double det_matrix(Matrix a) { - // ToDo - return 0; + if (a.rows != a.cols) + { + printf("Error: The matrix must be a square matrix.\n"); + return 0; + } + if (a.rows == 1) + { + return a.data[0][0]; + } + else if (a.rows == 2) + { + double res; + res = a.data[0][0] * a.data[1][1] - a.data[0][1] * a.data[1][0]; + return res; + } + else + { + double res = 0; + for (int j = 0; j < a.cols; j++) + { + Matrix temp; + temp.rows = a.rows - 1; + temp.cols = a.cols - 1; + int m = 0, n = 0; + for (int p = 0; p < a.rows - 1; p++) + { + for (int q = 0; q < a.cols; q++) + { + if (q == j) + continue; + temp.data[m][n] = a.data[p][q]; + n++; + if (n == temp.cols) + { + n = 0; + m++; + } + } + } + res = res + a.data[a.rows - 1][j] * det_matrix(temp) * pow(-1, a.rows + j + 1); + } + return res; + } } Matrix inv_matrix(Matrix a) { - // ToDo + if (a.cols != a.rows) + { + printf("Error: The matrix must be a square matrix.\n"); + } + else if (det_matrix(a) == 0) + { + printf("The matrix is singular.\n"); + } + else + { + double det = det_matrix(a); + Matrix adj; + adj.rows = a.rows; + adj.cols = a.cols; + for (int i = 0; i < adj.rows; i++) + { + for (int j = 0; j < adj.cols; j++) + { + Matrix temp; + temp.rows = a.rows - 1; + temp.cols = a.cols - 1; + int m = 0, n = 0; + for (int p = 0; p < a.rows; p++) + { + if (p == j) + continue; + for (int q = 0; q < a.cols; q++) + { + if (q == i) + continue; + temp.data[m][n] = a.data[p][q]; + n++; + if (n == temp.cols) + { + n = 0; + m++; + } + } + } + adj.data[i][j] = pow(-1, i + j) * det_matrix(temp); + } + } + return scale_matrix(adj, (1.0 / det)); + } return create_matrix(0, 0); } int rank_matrix(Matrix a) { - // ToDo - return 0; + int i = 0, j = 0; + for (j = 0; j < a.cols;) + { + if (a.data[i][j] == 0) + { + int m; + for (m = i + 1; m < a.rows; m++) + { + if (a.data[m][j] != 0) + break; + } + if (m == a.rows) + j++; + else + { + for (int n = 0; n < a.cols; n++) + { + int temp = a.data[m][n]; + a.data[m][n] = a.data[i][n]; + a.data[i][n] = temp; + } + int x, y; + double n; + n = 1 / a.data[i][j]; + for (y = 0; y < a.cols; y++) + { + a.data[i][y] = n * a.data[i][y]; + } + for (x = 0; x < i; x++) + { + n = -a.data[x][j] / a.data[i][j]; + for (y = 0; y < a.cols; y++) + { + a.data[x][y] = a.data[x][y] + n * a.data[i][y]; + } + } + for (x = i + 1; x < a.rows; x++) + { + n = -a.data[x][j] / a.data[i][j]; + for (y = 0; y < a.cols; y++) + { + a.data[x][y] = a.data[x][y] + n * a.data[i][y]; + } + } + i++; + j++; + } + } + else + { + int x, y; + double n; + n = 1 / a.data[i][j]; + for (y = 0; y < a.cols; y++) + { + a.data[i][y] = n * a.data[i][y]; + } + for (x = 0; x < i; x++) + { + n = -a.data[x][j] / a.data[i][j]; + for (y = 0; y < a.cols; y++) + { + a.data[x][y] = a.data[x][y] + n * a.data[i][y]; + } + } + for (x = i + 1; x < a.rows; x++) + { + n = -a.data[x][j] / a.data[i][j]; + for (y = 0; y < a.cols; y++) + { + a.data[x][y] = a.data[x][y] + n * a.data[i][y]; + } + } + i++; + j++; + } + } + for (i = 0; i < a.rows; i++) + { + for (j = 0; j < a.cols; j++) + { + if (a.data[i][j] != 0) + break; + } + if (j == a.cols) + break; + } + return i; } double trace_matrix(Matrix a) { - // ToDo + if (a.rows != a.cols) + { + printf("Error: The matrix must be a square matrix.\n"); + } + else + { + double sum = 0; + for (int i = 0; i < a.rows; i++) + { + sum += a.data[i][i]; + } + return sum; + } return 0; }