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环境：
主机:XP
开发环境:mingw
功能:
在C++中实现矩阵运算
说明：
将这篇文章(http://blog.csdn.net/jdh99/article/details/7360091)中在C++下实现的矩阵运算移植到C下,以便在单片机中运算.
源代码:
matrix.h:
#ifndef _MATRIX_H #define _MATRIX_H//头文件 #include <stdio.h> #include <stdlib.h> //矩阵数据结构 //二维矩阵 struct _Matrix { int m; int n; float *arr; }; //矩阵方法//设置m void matrix_set_m(struct _Matrix *m,int mm); //设置n void matrix_set_n(struct _Matrix *m,int nn); //初始化 void matrix_init(struct _Matrix *m); //释放 void matrix_free(struct _Matrix *m); //读取i,j坐标的数据 //失败返回-31415,成功返回值 float matrix_read(struct _Matrix *m,int i,int j); //写入i,j坐标的数据 //失败返回-1,成功返回1 int matrix_write(struct _Matrix *m,int i,int j,float val); //矩阵运算//成功返回1,失败返回-1 int matrix_add(struct _Matrix *A,struct _Matrix *B,struct _Matrix *C); //C = A - B //成功返回1,失败返回-1 int matrix_subtract(struct _Matrix *A,struct _Matrix *B,struct _Matrix *C); //C = A * B //成功返回1,失败返回-1 int matrix_multiply(struct _Matrix *A,struct _Matrix *B,struct _Matrix *C); //行列式的值,只能计算2 * 2,3 * 3 //失败返回-31415,成功返回值 float matrix_det(struct _Matrix *A); //求转置矩阵,B = AT //成功返回1,失败返回-1 int matrix_transpos(struct _Matrix *A,struct _Matrix *B); //求逆矩阵,B = A^(-1) //成功返回1,失败返回-1 int matrix_inverse(struct _Matrix *A,struct _Matrix *B); #endif matrix.c:
#include "matrix.h"//矩阵方法//设置m void matrix_set_m(struct _Matrix *m,int mm){ m->m = mm; }//设置n void matrix_set_n(struct _Matrix *m,int nn){ m->n = nn;}//初始化 void matrix_init(struct _Matrix *m){ m->arr = (float *)malloc(m->m * m->n * sizeof(float));}//释放 void matrix_free(struct _Matrix *m){ free(m->arr);}//读取i,j坐标的数据 //失败返回-31415,成功返回值 float matrix_read(struct _Matrix *m,int i,int j){ if (i >= m->m || j >= m->n) { return -31415; } return *(m->arr + i * m->n + j); }//写入i,j坐标的数据 //失败返回-1,成功返回1 int matrix_write(struct _Matrix *m,int i,int j,float val){ if (i >= m->m || j >= m->n) { return -1; } *(m->arr + i * m->n + j) = val; return 1; }//矩阵运算//成功返回1,失败返回-1 int matrix_add(struct _Matrix *A,struct _Matrix *B,struct _Matrix *C){ int i = 0; int j = 0; //判断是否可以运算 if (A->m != B->m || A->n != B->n || \ A->m != C->m || A->n != C->n) { return -1; } //运算 for (i = 0;i < C->m;i++) { for (j = 0;j < C->n;j++) { matrix_write(C,i,j,matrix_read(A,i,j) + matrix_read(B,i,j)); } } return 1; }//C = A - B //成功返回1,失败返回-1 int matrix_subtract(struct _Matrix *A,struct _Matrix *B,struct _Matrix *C){ int i = 0; int j = 0; //判断是否可以运算 if (A->m != B->m || A->n != B->n || \ A->m != C->m || A->n != C->n) { return -1; } //运算 for (i = 0;i < C->m;i++) { for (j = 0;j < C->n;j++) { matrix_write(C,i,j,matrix_read(A,i,j) - matrix_read(B,i,j)); } } return 1; }//C = A * B //成功返回1,失败返回-1 int matrix_multiply(struct _Matrix *A,struct _Matrix *B,struct _Matrix *C){ int i = 0; int j = 0; int k = 0; float temp = 0; //判断是否可以运算 if (A->m != C->m || B->n != C->n || \ A->n != B->m) { return -1; } //运算 for (i = 0;i < C->m;i++) { for (j = 0;j < C->n;j++) { temp = 0; for (k = 0;k < A->n;k++) { temp += matrix_read(A,i,k) * matrix_read(B,k,j); } matrix_write(C,i,j,temp); } } return 1; }//行列式的值,只能计算2 * 2,3 * 3 //失败返回-31415,成功返回值 float matrix_det(struct _Matrix *A){ float value = 0; //判断是否可以运算 if (A->m != A->n || (A->m != 2 && A->m != 3)) { return -31415; } //运算 if (A->m == 2) { value = matrix_read(A,0,0) * matrix_read(A,1,1) - matrix_read(A,0,1) * matrix_read(A,1,0); } else { value = matrix_read(A,0,0) * matrix_read(A,1,1) * matrix_read(A,2,2) + \ matrix_read(A,0,1) * matrix_read(A,1,2) * matrix_read(A,2,0) + \ matrix_read(A,0,2) * matrix_read(A,1,0) * matrix_read(A,2,1) - \ matrix_read(A,0,0) * matrix_read(A,1,2) * matrix_read(A,2,1) - \ matrix_read(A,0,1) * matrix_read(A,1,0) * matrix_read(A,2,2) - \ matrix_read(A,0,2) * matrix_read(A,1,1) * matrix_read(A,2,0); } return value; }//求转置矩阵,B = AT //成功返回1,失败返回-1 int matrix_transpos(struct _Matrix *A,struct _Matrix *B){ int i = 0; int j = 0; //判断是否可以运算 if (A->m != B->n || A->n != B->m) { return -1; } //运算 for (i = 0;i < B->m;i++) { for (j = 0;j < B->n;j++) { matrix_write(B,i,j,matrix_read(A,j,i)); } } return 1; }//求逆矩阵,B = A^(-1) //成功返回1,失败返回-1 int matrix_inverse(struct _Matrix *A,struct _Matrix *B){ int i = 0; int j = 0; int k = 0; struct _Matrix m; float temp = 0; float b = 0; //判断是否可以运算 if (A->m != A->n || B->m != B->n || A->m != B->m) { return -1; } /* //如果是2维或者3维求行列式判断是否可逆 if (A->m == 2 || A->m == 3) { if (det(A) == 0) { return -1; } } */ //增广矩阵m = A | B初始化 matrix_set_m(&m,A->m); matrix_set_n(&m,2 * A->m); matrix_init(&m); for (i = 0;i < m.m;i++) { for (j = 0;j < m.n;j++) { if (j <= A->n - 1) { matrix_write(&m,i,j,matrix_read(A,i,j)); } else { if (i == j - A->n) { matrix_write(&m,i,j,1); } else { matrix_write(&m,i,j,0); } } } } //高斯消元 //变换下三角 for (k = 0;k < m.m - 1;k++) { //如果坐标为k,k的数为0,则行变换 if (matrix_read(&m,k,k) == 0) { for (i = k + 1;i < m.m;i++) { if (matrix_read(&m,i,k) != 0) { break; } } if (i >= m.m) { return -1; } else { //交换行 for (j = 0;j < m.n;j++) { temp = matrix_read(&m,k,j); matrix_write(&m,k,j,matrix_read(&m,k + 1,j)); matrix_write(&m,k + 1,j,temp); } } } //消元 for (i = k + 1;i < m.m;i++) { //获得倍数 b = matrix_read(&m,i,k) / matrix_read(&m,k,k); //行变换 for (j = 0;j < m.n;j++) { temp = matrix_read(&m,i,j) - b * matrix_read(&m,k,j); matrix_write(&m,i,j,temp); } } } //变换上三角 for (k = m.m - 1;k > 0;k--) { //如果坐标为k,k的数为0,则行变换 if (matrix_read(&m,k,k) == 0) { for (i = k + 1;i < m.m;i++) { if (matrix_read(&m,i,k) != 0) { break; } } if (i >= m.m) { return -1; } else { //交换行 for (j = 0;j < m.n;j++) { temp = matrix_read(&m,k,j); matrix_write(&m,k,j,matrix_read(&m,k + 1,j)); matrix_write(&m,k + 1,j,temp); } } } //消元 for (i = k - 1;i >= 0;i--) { //获得倍数 b = matrix_read(&m,i,k) / matrix_read(&m,k,k); //行变换 for (j = 0;j < m.n;j++) { temp = matrix_read(&m,i,j) - b * matrix_read(&m,k,j); matrix_write(&m,i,j,temp); } } } //将左边方阵化为单位矩阵 for (i = 0;i < m.m;i++) { if (matrix_read(&m,i,i) != 1) { //获得倍数 b = 1 / matrix_read(&m,i,i); //行变换 for (j = 0;j < m.n;j++) { temp = matrix_read(&m,i,j) * b; matrix_write(&m,i,j,temp); } } } //求得逆矩阵 for (i = 0;i < B->m;i++) { for (j = 0;j < B->m;j++) { matrix_write(B,i,j,matrix_read(&m,i,j + m.m)); } } //释放增广矩阵 matrix_free(&m); return 1; }main.c:(测试代码)
#include <stdio.h>#include "matrix.h"//打印2维矩阵void printf_matrix(struct _Matrix *A){ int i = 0; int j = 0; int m = 0; int n = 0; m = A->m; n = A->n; for (i = 0;i < m;i++) { for (j = 0;j < n;j++) { printf("%f\t",matrix_read(A,i,j)); } printf("\n"); }}int main(){ int i = 0; int j = 0; int k = 0; struct _Matrix m1; struct _Matrix m2; struct _Matrix m3; //初始化内存 matrix_set_m(&m1,3); matrix_set_n(&m1,3); matrix_init(&m1); matrix_set_m(&m2,3); matrix_set_n(&m2,3); matrix_init(&m2); matrix_set_m(&m3,3); matrix_set_n(&m3,3); matrix_init(&m3); //初始化数据 k = 1; for (i = 0;i < m1.m;i++) { for (j = 0;j < m1.n;j++) { matrix_write(&m1,i,j,k++); } } for (i = 0;i < m2.m;i++) { for (j = 0;j < m2.n;j++) { matrix_write(&m2,i,j,k++); } } //原数据 printf("A:\n"); printf_matrix(&m1); printf("B:\n"); printf_matrix(&m2); printf("A:行列式的值%f\n",matrix_det(&m1)); //C = A + B if (matrix_add(&m1,&m2,&m3) > 0) { printf("C = A + B:\n"); printf_matrix(&m3); } //C = A - B if (matrix_subtract(&m1,&m2,&m3) > 0) { printf("C = A - B:\n"); printf_matrix(&m3); } //C = A * B if (matrix_multiply(&m1,&m2,&m3) > 0) { printf("C = A * B:\n"); printf_matrix(&m3); } //C = AT if (matrix_transpos(&m1,&m3) > 0) { printf("C = AT:\n"); printf_matrix(&m3); } if (matrix_inverse(&m1,&m3) > 0) { printf("C = A^(-1):\n"); printf_matrix(&m3); } getchar(); return 0;}给我老师的人工智能教程打call！http://blog.csdn.net/jiangjunshow
