使用mpi多线程从文件中读取矩阵并行矩阵求逆并且输出逆矩阵

这是一个比较复杂的问题，需要一定的MPI编程和线性代数知识。以下是一个简单的示例代码，帮助您理解如何使用MPI多线程从文件中读取矩阵、并行矩阵求逆并输出逆矩阵。

#include <stdio.h>
#include <stdlib.h>
#include <mpi.h>
#include <math.h>
#include <stdbool.h>
#include <string.h>
#include <time.h>

#define TAG 0
#define ROOT 0
#define MAX_FILENAME_SIZE 256

int rank, size;
MPI_Status status;

void read_matrix(double *matrix, int n, char *filename) {
    FILE *fp;
    fp = fopen(filename, "r");
    if (fp == NULL) {
        printf("File open error\n");
        return;
    }
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            fscanf(fp, "%lf", &matrix[i * n + j]);
        }
    }
    fclose(fp);
}

void print_matrix(double *matrix, int n) {
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            printf("%.2lf ", matrix[i * n + j]);
        }
        printf("\n");
    }
}

void identity_matrix(double *matrix, int n) {
    memset(matrix, 0, sizeof(double) * n * n);
    for (int i = 0; i < n; i++) {
        matrix[i * n + i] = 1.0;
    }
}

void matrix_multiplication(double *matrix1, double *matrix2, double *result, int n) {
    double *temp = (double*)malloc(sizeof(double) * n * n);
    memset(temp, 0, sizeof(double) * n * n);
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            for (int k = 0; k < n; k++) {
                temp[i * n + j] += matrix1[i * n + k] * matrix2[k * n + j];
            }
        }
    }
    memcpy(result, temp, sizeof(double) * n * n);
    free(temp);
}

void swap(double *a, double *b) {
    double temp = *a;
    *a = *b;
    *b = temp;
}

bool is_zero(double val) {
    return fabs(val) < 1e-8;
}

bool gauss_elimination(double *matrix, double *inverse, int n) {
    int *pivot = (int*)malloc(sizeof(int) * n);
    for (int i = 0; i < n; i++) {
        pivot[i] = i;
    }
    for (int k = 0; k < n; k++) {
        int max_index = k;
        double max_value = fabs(matrix[pivot[k] * n + k]);
        for (int i = k+1; i < n; i++) {
            if (fabs(matrix[pivot[i] * n + k]) > max_value) {
                max_index = i;
                max_value = fabs(matrix[pivot[i] * n + k]);
            }
        }
        if (is_zero(max_value)) {
            printf("Matrix is not invertible!\n");
            return false;
        }
        if (max_index != k) {
            swap(&pivot[k], &pivot[max_index]);
        }
        double pivot_value = matrix[pivot[k] * n + k];
        for (int j = k; j < n; j++) {
            matrix[pivot[k] * n + j] /= pivot_value;
            inverse[pivot[k] * n + j] /= pivot_value;
        }
        for (int i = k+1; i < n; i++) {
            double factor = matrix[pivot[i] * n + k];
            for (int j = k; j < n; j++) {
                matrix[pivot[i] * n + j] -= factor * matrix[pivot[k] * n + j];
                inverse[pivot[i] * n + j] -= factor * inverse[pivot[k] * n + j];
            }
        }
    }
    for (int k = n-1; k >= 0; k--) {
        for (int i = k-1; i >= 0; i--) {
            double factor = matrix[pivot[i] * n + k];
            for (int j = k; j < n; j++) {
                matrix[pivot[i] * n + j] -= factor * matrix[pivot[k] * n + j];
                inverse[pivot[i] * n + j] -= factor * inverse[pivot[k] * n + j];
            }
        }
    }
    free(pivot);
    return true;
}

int main(int argc, char **argv) {
    if (argc < 2) {
        printf("Usage: ./matrix_inverse <filename>\n");
        return -1;
    }
    char filename[MAX_FILENAME_SIZE];
    strcpy(filename, argv[1]);

    MPI_Init(&argc, &argv);
    MPI_Comm_rank(MPI_COMM_WORLD, &rank);
    MPI_Comm_size(MPI_COMM_WORLD, &size);

    double *matrix, *inverse;
    int n;
    double start_time, end_time;

    if (rank == ROOT) {
        // Read matrix from file
        FILE *fp = fopen(filename, "r");
        if (fp == NULL) {
            printf("File open error\n");
            return -1;
        }
        fscanf(fp, "%d", &n);
        fclose(fp);

        matrix = (double*)malloc(sizeof(double) * n * n);
        inverse = (double*)malloc(sizeof(double) * n * n);
        read_matrix(matrix, n, filename);
        identity_matrix(inverse, n);

        start_time = MPI_Wtime();
    }

    MPI_Bcast(&n, 1, MPI_INT, ROOT, MPI_COMM_WORLD);
    int rows_per_process = n / size;
    double *submatrix = (double*)malloc(sizeof(double) * rows_per_process * n);
    double *subinverse = (double*)malloc(sizeof(double) * rows_per_process * n);
    MPI_Scatter(matrix, rows_per_process * n, MPI_DOUBLE, submatrix, rows_per_process * n, MPI_DOUBLE, ROOT, MPI_COMM_WORLD);
    MPI_Scatter(inverse, rows_per_process * n, MPI_DOUBLE, subinverse, rows_per_process * n, MPI_DOUBLE, ROOT, MPI_COMM_WORLD);

    gauss_elimination(submatrix, subinverse, rows_per_process);

    MPI_Gather(subinverse, rows_per_process * n, MPI_DOUBLE, inverse, rows_per_process * n, MPI_DOUBLE, ROOT, MPI_COMM_WORLD);

    if (rank == ROOT) {
        end_time = MPI_Wtime();
        printf("Inverse matrix:\n");
        print_matrix(inverse, n);
        printf("Elapsed time: %lf seconds\n", end_time - start_time);
        free(matrix);
        free(inverse);
    }

    free(submatrix);
    free(subinverse);
    MPI_Finalize();
    return 0;
}

在这个代码中，我们使用MPI的Scatter和Gather函数来将矩阵分发给多个进程，并将结果收集到主进程中。在主进程中，我们使用MPI_Wtime来计算整个算法的运行时间。在每个进程中，我们使用高斯消元法来求解子矩阵的逆矩阵。最后，我们将所有子矩阵的逆矩阵合并成最终的逆矩阵。

需要注意的是，这个代码仅仅是一个简单的示例，实际上还有很多地方可以优化，比如使用更高效的高斯-约旦消元法、使用更好的矩阵乘法算法等都可以进一步提高运行效率。