计算数学
C语言矩阵与向量运算
C语言对矩阵与向量运算比较简洁的方式是动态数组。由于矩阵与向量在数值计算中较为频繁，也可以单独定义为结构体。 以下为C语言实现矩阵与向量相乘范例，分别给出范例。至于矩阵的其他运算可以参考前面的算法。
/*------------------------------------------------------
Created : Song Yezhi 2024-2-8 14:40
include 需包含 stdio.h 与 stdlib.h 因显示问题，使用时注意
--------------------------------------------------------
Email : song.yz@foxmail.com
Copyrigt (C) : Chinese Academy of Sciences
All rights reserved, 2024
-------------------------------------------------------*/
#include
#include
// Function to allocate a matrix
double** matrix(int rows, int cols)
{
double **matrix = (double**) malloc(rows * sizeof(double*));
for (int i = 0; i < rows; i++)
{
matrix[i] = (double*) malloc(cols * sizeof(double));
}
return matrix;
}
double* vector(int cols)
{
double *vec = (double*) malloc(cols * sizeof(double));
return vec;
}
// Function to free a matrix
void freeMatrix(int rows, double **matrix)
{
for (int i = 0; i < rows; i++)
{
free(matrix[i]);
}
free(matrix);
}
// Function to multiply a matrix by a vector
void matmul(int rows, int cols, double **matrix, double *vector, double *result)
{
for (int i = 0; i < rows; i++)
{
result[i] = 0.0;
for (int j = 0; j < cols; j++)
{
result[i] = result[i] + matrix[i][j] * vector[j];
}
}
}
// Function to print a vector
void printVector(int size, double *vector)
{
for (int i = 0; i < size; i++)
{
printf("%.4f\t", vector[i]);
}
printf("\n");
}
void printMatrix(int rows, int cols, double **matrix)
{
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < cols; j++)
{
printf("%.4f\t", matrix[i][j]);
}
printf("\n");
}
}
int main()
{
// Define matrix dimensions
int rows = 8;
int cols = 3;
// Allocate matrix
double **A = matrix(rows, cols);
// Initialize matrix
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < cols; j++)
{
A[i][j] = (i + j) * 1.0;
}
}
double *b = vector(cols);
for (int i = 0; i < cols; i++)
{
b[i] = i * 1.0;
}
double *result = vector(rows);
// Multiply matrix by vector
matmul(rows, cols, A, b, result);
// Print the results
printf("Matrix:\n");
printMatrix(rows, cols, A);
printf("\nVector:\n");
printVector(cols, b);
printf("\nResulting Vector:\n");
printVector(rows, result);
// Free allocated memory
freeMatrix(rows, A);
free(b);
free(result);
return 0;
}
或者定义为结构体形式，这样在矩阵与向量运算时，维数可以包含在结构体的元素中，而不必作为参数输入输出。
#include
#include
// 定义向量结构体
typedef struct
{
int size; // 向量的大小
double *data; // 指向向量数据的指针
} Vector;
// 初始化向量
Vector createVector(int size)
{
Vector vector;
vector.size = size;
vector.data = (double*) malloc(size * sizeof(double));
return vector;
}
// 释放向量内存
void freeVector(Vector *vector)
{
free(vector->data);
vector->data = NULL;
vector->size = 0;
}
// 定义矩阵结构体
typedef struct
{
int rows; // 矩阵的行数
int cols; // 矩阵的列数
double **data; // 指向矩阵数据的二维指针
} Matrix;
// 初始化矩阵
Matrix createMatrix(int rows, int cols)
{
Matrix matrix;
matrix.rows = rows;
matrix.cols = cols;
// 分配指向行指针的内存
matrix.data = (double**) malloc(rows * sizeof(double*));
if (matrix.data == NULL)
{
perror("Error allocating memory for matrix rows");
exit(EXIT_FAILURE);
}
// 分配每行元素的内存
for (int i = 0; i < rows; i++)
{
matrix.data[i] = (double*) malloc(cols * sizeof(double));
if (matrix.data[i] == NULL)
{
perror("Error allocating memory for matrix elements");
// 释放之前已分配的内存
for (int j = 0; j < i; j++)
{
free(matrix.data[j]);
}
free(matrix.data);
exit(EXIT_FAILURE);
}
}
return matrix;
}
// 释放矩阵内存
void freeMatrix(Matrix *matrix)
{
for (int i = 0; i < matrix->rows; i++)
{
free(matrix->data[i]);
}
free(matrix->data);
matrix->data = NULL;
matrix->rows = 0;
matrix->cols = 0;
}
// 矩阵与向量相乘
Vector matmul(Matrix matrix, Vector vector)
{
if (matrix.cols != vector.size)
{
printf("Error: Matrix columns must match vector size.\n");
exit(1);
}
Vector result = createVector(matrix.rows);
for (int i = 0; i < matrix.rows; i++)
{
result.data[i] = 0;
for (int j = 0; j < matrix.cols; j++)
{
result.data[i] += matrix.data[i][j] * vector.data[j];
}
}
return result;
}
int main()
{
// 创建一个3x2的矩阵
Matrix matrix;
matrix = createMatrix(3, 2);
// 初始化矩阵数据
for (int i = 0; i < matrix.rows; i++)
{
for (int j = 0; j < matrix.cols; j++)
{
matrix.data[i][j] = i + j + 1; // 填充矩阵为1, 2, 3, 4, 5, 6
}
}
// 创建一个2维的向量
Vector vector = createVector(2);
// 初始化向量数据
vector.data[0] = 1;
vector.data[1] = 2;
// 执行矩阵乘以向量的操作
Vector result = matmul(matrix, vector);
// 打印结果
for (int i = 0; i < result.size; i++)
{
printf("%f\n", result.data[i]);
}
// 释放内存
freeVector(&vector);
freeMatrix(&matrix);
freeVector(&result);
return 0;
}