Late April homework
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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int rowcmp(float *row0, float *row1, int n)
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{
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for (int i = 0; i < n; ++i) {
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if (row0[i])
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return 0;
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if (row1[i])
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return 1;
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}
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return 0;
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}
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/* Upper-triangularise matrix mat of size mxn */
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void ut(float *mat, int m, int n)
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{
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long i, j, k;
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float *current, *other, *tmp = malloc(n * sizeof(float));
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for (i = 0; i + 1 < m; ++i) {
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current = mat + i * n;
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for (j = i + 1; j < m; ++j) {
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other = mat + j * n;
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if (rowcmp(current, other, n)) {
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memcpy(tmp, current, n);
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memcpy(current, other, n);
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memcpy(other, tmp, n);
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}
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}
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for (j = i + 1; j < m; ++j) {
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for (k = 0; k < n && !mat[i*n + k]; ++k);
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if (k == n)
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break;
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float c = mat[j*n + k] / mat[i*n + k];
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mat[j*n + k] = 0.0; /* floating point imprecision */
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while (++k < n)
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mat[j*n + k] -= c * mat[i*n + k];
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}
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}
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free(tmp);
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}
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float *transpose(float *mat, int m, int n)
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{
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float *result = malloc(m * n * sizeof(float));
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for (long i = 0; i < m; ++i)
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for (long j = 0; j < n; ++j)
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result[j*m + i] = mat[i*n + j];
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return result;
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}
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void printmatf(char *format, float *mat, int m, int n)
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{
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for (long i = 0; i < m; ++i) {
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for (long j = 0; j < n; ++j)
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printf(format, mat[i*n + j]);
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putchar(10);
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}
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}
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int main()
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{
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int n;
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puts("Please input the size of the square matrix:");
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fputs("n = ", stdout);
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scanf("%d", &n);
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long i, j, k, len = n * n * sizeof(float);
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float sum = 0.0, *a = malloc(len);
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puts("Now please input the matrix:");
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for (i = 0; i < n * n; ++i) {
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scanf("%f", a + i);
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sum += a[i];
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}
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printf("The sum of all the matrix elements: %.2f\n", sum);
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float *b = transpose(a, n, n);
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puts("The transpose of the matrix:");
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printmatf("%8.3f", b, n, n);
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free(a);
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b = realloc(b, len * 2);
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for (i = 0; i < n; ++i)
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for (j = 0; j < n; ++j)
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b[n*n + i*n + j] = i == j;
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a = transpose(b, n * 2, n);
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ut(a, n, n * 2);
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free(b);
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float det = 1.0;
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for (i = 0; i < n; ++i)
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det *= a[i*n*2 + i];
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printf("The determinant of the matrix: %.2f\n", det);
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if (!det) {
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puts("The given matrix is not invertible.");
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free(a);
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return 0;
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}
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for (i = n - 1; i >= 0; --i) {
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float d = a[i*n*2 + i];
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for (j = n; j < n * 2; ++j)
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a[i*n*2 + j] /= d;
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for (k = i - 1; k >= 0; --k) {
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float c = a[k*n*2 + i];
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for (j = n; j < n * 2; ++j)
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a[k*n*2 + j] -= a[i*n*2 + j] * c;
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}
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}
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b = transpose(a, n, n * 2);
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a = transpose(b + n * n, n, n);
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puts("The inverse of the matrix:");
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printmatf("%8.3f", a, n, n);
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free(a);
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free(b);
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return 0;
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}
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