C语言矩阵的逆、矩阵乘法、矩阵行列式、矩阵转置

#include "cmatrix.h" /*行列式*/ double hhlx(double** arr, int na) { if (na == 1) { return arr[0][0]; } else { double s = 0; for (int i = 0; i < na; i++) { if (arr[0][i] != 0) { double** arr1; arr1 = (double**)malloc((na - 1) * sizeof(double)); for (int i = 0; i < na - 1; i++) { arr1[i] = (double*)malloc((na - 1) * sizeof(double)); } for (int j = 1; j < na; j++) { for (int k = 0; k < na - 1; k++) { if (k >= i) { arr1[j - 1][k] = arr[j][k + 1]; } else { arr1[j - 1][k] = arr[j][k]; } } } s = s + hhlx(arr1, na - 1) * pow(-1, i) * arr[0][i]; for (int i = 0; i < na - 1; i++) { free(arr1[i]); } free(arr1); } } return s; } } /*逆矩阵*/ double** inv(double** a, int n) { double det = hhlx(a, n); double** as; as = (double**)malloc(n * sizeof(double)); for (int i = 0; i < n; i++) { as[i] = (double*)malloc(n * sizeof(double)); } for (int is = 0; is < n; is++) { for (int js = 0; js < n; js++) { double** ab; ab = (double**)malloc((n - 1) * sizeof(double)); for (int i = 0; i < n - 1; i++) { ab[i] = (double*)malloc((n - 1) * sizeof(double)); } for (int i = 0; i < n - 1; i++) { for (int j = 0; j < n - 1; j++) { if (i >= is) { if (j >= js) ab[i][j] = a[i + 1][j + 1]; else ab[i][j] = a[i + 1][j]; } else { if (j >= js) ab[i][j] = a[i][j + 1]; else ab[i][j] = a[i][j]; } } } as[js][is] = pow(-1, (double)is + (double)js) * hhlx(ab, n - 1); for (int i = 0; i < n - 1; i++) { free(ab[i]); } free(ab); } } double** ai; ai = (double**)malloc(n * sizeof(double)); for (int i = 0; i < n; i++) { ai[i] = (double*)malloc(n * sizeof(double)); } for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { ai[i][j] = as[i][j] / det; } } return ai; } /*矩阵相乘*/ double** AB(double** a, int ma, int na, double** b, int mb, int nb) { if (na != mb) { printf("计算错误！"); return NULL; } else { double** ab; ab = (double**)malloc(ma * sizeof(double)); for (int i = 0; i < ma; i++) { ab[i] = (double*)malloc(nb * sizeof(double)); } for (int i = 0; i < ma; i++) { for (int j = 0; j < nb; j++) { ab[i][j] = 0; for (int k = 0; k < na; k++) { ab[i][j] = ab[i][j] + a[i][k] * b[k][j]; } } } return ab; } } /*矩阵转置*/ double** TA(double** a, int ma, int na) { double** ta; ta = (double**)malloc(na * sizeof(double)); for (int i = 0; i < na; i++) { ta[i] = (double*)malloc(ma * sizeof(double)); } for (int i = 0; i < na; i++) { for (int j = 0; j < ma; j++) { ta[i][j] = a[j][i]; } } return ta; } matrix* Mnew(int m, int n) { matrix* a; a = (matrix*)malloc(sizeof(matrix)); a->A = (double**)malloc(m * sizeof(double)); for (int i = 0; i < m; i++) { a->A[i] = (double*)malloc(n * sizeof(double)); } a->m = m; a->n = n; return a; } void Minit(matrix* a) { a->inv = Minv(a); a->inv->inv = a; a->T = Mtrans(a); a->T->T = a; a->inv->T = Mtrans(a->inv); a->T->inv = a->inv->T; a->inv->T->T = a->inv; a->T->inv->inv = a->T; a->inv->T->inv = a->T; a->T->inv->T = a->inv; a->det = hhlx(a->A, a->m); a->inv->det = 1 / a->det; a->T->det = a->det; a->inv->T->det = a->inv->det; } void Mprintf(matrix* a) { for (int i = 0; i < a->m; i++) { for (int j = 0; j < a->n; j++) { printf("%f ", a->A[i][j]); } printf("\n"); } } matrix* Minv(matrix* a) { matrix* ai; ai = (matrix*)malloc(sizeof(matrix)); ai->A = inv(a->A, a->m); ai->m = a->m; ai->n = a->m; return ai; } matrix* Mmulti(matrix* a, matrix* b) { matrix* ab; ab = (matrix*)malloc(sizeof(matrix)); ab->A = AB(a->A, a->m, a->n, b->A, b->m, b->n); ab->m = a->m; ab->n = b->n; return ab; } matrix* Mtrans(matrix* a) { matrix* at; at = (matrix*)malloc(sizeof(matrix)); at->A = TA(a->A, a->m, a->n); at->m = a->n; at->n = a->m; return at; } matrix* Mplus(matrix* a, matrix* b) { matrix* c; c = (matrix*)malloc(sizeof(matrix)); c->A = (double**)malloc(a->m * sizeof(double)); for (int i = 0; i < a->m; i++) { c->A[i] = (double*)malloc(a->n * sizeof(double)); } c->m = a->m; c->n = a->n; for (int i = 0; i < a->m; i++) { for (int j = 0; j < a->n; j++) { c->A[i][j] = a->A[i][j] + b->A[i][j]; } } return c; } matrix* Mminus(matrix* a, matrix* b) { matrix* c; c = (matrix*)malloc(sizeof(matrix)); c->A = (double**)malloc(a->m * sizeof(double)); for (int i = 0; i < a->m; i++) { c->A[i] = (double*)malloc(a->n * sizeof(double)); } c->m = a->m; c->n = a->n; for (int i = 0; i < a->m; i++) { for (int j = 0; j < a->n; j++) { c->A[i][j] = a->A[i][j] - b->A[i][j]; } } return c; } matrix* Mdotpro(matrix* a, matrix* b) { matrix* c; c = (matrix*)malloc(sizeof(matrix)); c->A = (double**)malloc(a->m * sizeof(double)); for (int i = 0; i < a->m; i++) { c->A[i] = (double*)malloc(a->n * sizeof(double)); } c->m = a->m; c->n = a->n; for (int i = 0; i < a->m; i++) { for (int j = 0; j < a->n; j++) { c->A[i][j] = (a->A[i][j]) * (b->A[i][j]); } } return c; } matrix* Mdiv(matrix* a, matrix* b) { matrix* c; c = (matrix*)malloc(sizeof(matrix)); c->A = (double**)malloc(a->m * sizeof(double)); for (int i = 0; i < a->m; i++) { c->A[i] = (double*)malloc(a->n * sizeof(double)); } c->m = a->m; c->n = a->n; for (int i = 0; i < a->m; i++) { for (int j = 0; j < a->n; j++) { c->A[i][j] = a->A[i][j] / b->A[i][j]; } } return c; } void mfree(matrix* a) { for (int i = 0; i < a->m; i++) { free(a->A[i]); } free(a->A); free(a); } void Mfree(matrix* a) { mfree(a->inv->T); mfree(a->inv); mfree(a->T); mfree(a); }