// solve a symmetric, positive definite system
static void solve_spd(long double *x, long double *A, long double *b, int n)
{
// factor the matrix A = L * L'
long double L[n*n];
cholesky(L, A, n);
// solve the two triangular systems L * L' * x = b
long double t[n];
solve_lower(t, L, b, n);
solve_upper(x, L, t, n);
}
int main()
{
double **A1 = (double **) malloc(3 * sizeof(double *));
int i,j;
for(i=0; i<3; i++) {
A1[i] = (double *) malloc(3 * sizeof(double));
}
A1[0][0] = 1; A1[0][1] = 0; A1[0][2] = 0;
A1[1][0] = 0; A1[1][1] = 2; A1[1][2] = 0;
A1[2][0] = 0; A1[2][1] = 0; A1[2][2] = 3;
double **A2 = (double **) malloc(3 * sizeof(double *));
for(i=0; i<3; i++) {
A2[i] = (double *) malloc(3 * sizeof(double));
}
A2[0][0] = 1; A2[0][1] = 2; A2[0][2] = 3;
A2[1][0] = 0; A2[1][1] = 4; A2[1][2] = 5;
A2[2][0] = 0; A2[2][1] = 0; A2[2][2] = 6;
double **A3 = (double **) malloc(3 * sizeof(double *));
for(i=0; i<3; i++) {
A3[i] = (double *) malloc(3 * sizeof(double));
}
A3[0][0] = 1; A3[0][1] = 0; A3[0][2] = 0;
A3[1][0] = 2; A3[1][1] = 3; A3[1][2] = 0;
A3[2][0] = 4; A3[2][1] = 5; A3[2][2] = 6;
double b1[3] = {1, 4, 9};
double b2[3] = {6, 9, 6};
double b3[3] = {3, 12, 28};
double x1[3], x2[3], x3[3];
solve_upper(A1, b1, x1, 3);
printf("solve_upper A1:\n");
for(i=0; i<3; i++) {
printf("%f ", x1[i]);
}
printf("\n");
solve_upper(A2, b2, x2, 3);
printf("solve_upper A2:\n");
for(i=0; i<3; i++) {
printf("%f ", x2[i]);
}
printf("\n");
solve_lower(A3, b3, x3, 3);
printf("solve_lower A3:\n");
for(i=0; i<3; i++) {
printf("%f ", x3[i]);
}
printf("\n");
for(i=0; i<3; i++) {
free(A1[i]);
free(A2[i]);
free(A3[i]);
}
free(A1); free(A2); free(A3);
//Aufgabe 2
double **B1 = (double **) malloc(3 * sizeof(double *));
for(i=0; i<3; i++) {
B1[i] = (double *) malloc(3 * sizeof(double));
}
B1[0][0] = 4; B1[0][1] = 2; B1[0][2] = 3;
B1[1][0] = 2; B1[1][1] = 4; B1[1][2] = 2;
B1[2][0] = 3; B1[2][1] = 2; B1[2][2] = 4;
cholesky(B1, 3);
printf("cholesky B1:\n");
for(i=0; i<3; i++) {
for(j=0; j<3; j++) {
printf("%f ", B1[i][j]);
}
printf("\n");
}
printf("\n");
double b4[3] = {1, 1, 1};
double x4[3], x5[3];
solve_lower(B1, b4, x4, 3);
solve_upper(transpose(B1, 3), x4, x5, 3);
printf("solve_B1 mit Cholesky:\n");
for(i=0; i<3; i++) {
printf("%f ", x5[i]);
}
printf("\n");
for(i=0; i<3; i++) {
free(B1[i]);
}
free(B1);
int k;
for(k = 3; k <= 80; k = k * 2)
{
double **B2 = (double **) malloc(k * sizeof(double *));
for(i = 0; i < k; i++) {
B2[i] = (double *) malloc(k * sizeof(double));
for(j = 0; j < k; j++) {
B2[i][j] = 0;
}
}
for(i = 0; i < k; i++) {
if(i - 1 > 0) {
B2[i][i - 1] = -1;
}
B2[i][i] = 2;
if(i + 1 < k) {
B2[i][i + 1] = -1;
}
}
double b[k];
for(i = 0; i < k; i++) {
b[i] = 1;
}
double x[k], y[k];
cholesky(B2, k);
solve_lower(B2, b, x, k);
solve_upper(transpose(B2, k), x, y, k);
printf("solve_B%d mit Cholesky:\n", k);
for(i = 0; i < k; i++) {
printf("%f ", x[i]);
}
printf("\n");
for(i = 0; i < k; i++) {
printf("%f ", y[i]);
}
printf("\n");
for(i = 0; i < k; i++) {
free(B2[i]);
}
free(B2); free(x); free(y); free(b);
}
return 0;
}