void eqnsys<nr_type_t>::solve (void) {
#if DEBUG && 0
time_t t = time (NULL);
#endif
switch (algo) {
case ALGO_INVERSE:
solve_inverse ();
break;
case ALGO_GAUSS:
solve_gauss ();
break;
case ALGO_GAUSS_JORDAN:
solve_gauss_jordan ();
break;
case ALGO_LU_DECOMPOSITION_CROUT:
solve_lu_crout ();
break;
case ALGO_LU_DECOMPOSITION_DOOLITTLE:
solve_lu_doolittle ();
break;
case ALGO_LU_FACTORIZATION_CROUT:
factorize_lu_crout ();
break;
case ALGO_LU_FACTORIZATION_DOOLITTLE:
factorize_lu_doolittle ();
break;
case ALGO_LU_SUBSTITUTION_CROUT:
substitute_lu_crout ();
break;
case ALGO_LU_SUBSTITUTION_DOOLITTLE:
substitute_lu_doolittle ();
break;
case ALGO_JACOBI: case ALGO_GAUSS_SEIDEL:
solve_iterative ();
break;
case ALGO_SOR:
solve_sor ();
break;
case ALGO_QR_DECOMPOSITION:
solve_qr ();
break;
case ALGO_QR_DECOMPOSITION_LS:
solve_qr_ls ();
break;
case ALGO_SV_DECOMPOSITION:
solve_svd ();
break;
case ALGO_QR_DECOMPOSITION_2:
solve_qrh ();
break;
}
#if DEBUG && 0
logprint (LOG_STATUS, "NOTIFY: %dx%d eqnsys solved in %ld seconds\n",
A->getRows (), A->getCols (), time (NULL) - t);
#endif
}
int main(int argc, char *argv[])
{
int n;
double length;
pstruct model; /* primary model data structure */
int solver;
/* Parse command-line */
if(argc < 3)
{
printf("\nUsage: laplacian [num_pts] [length] [gauss/cg]\n\n");
printf("\"num_pts\" is the desired number of mesh points \n");
printf("\"length\" is the physical length-scale dimension in one direction\n");
printf("\"gauss/cg\" is which method is used: \n");
printf(" 0 --> Gauss-Seidel \n");
printf(" 1 --> Conjugate Gradient. \n\n");
exit(1);
}
else if(argc == 3)
{
n = atoi(argv[1]);
length = (double) atof(argv[2]);
solver = 0; // default to gauss
}
else
{
n = atoi(argv[1]);
length = (double) atof(argv[2]);
solver = atoi(argv[3]);
if(solver > 1 || solver < 0)
{
printf("solver only accepts 0,1 for input");
exit(1);
}
}
/* Problem Initialization */
problem_initialize (n,length,&model);
assemble_matrix (central_2nd_order,&model);
//assemble_matrix (central_4th_order,&model);
init_masa (&model);
apply_bcs (&model);
print_matrix(&model);
/* Solve */
if(solver == 1)
{
solve_cg (&model);
}
else
{
solve_gauss(&model);
}
/* Compute Error */
printf("\n** Error Analysis\n");
printf(" --> npts = %i\n",model.npts);
printf(" --> h = %12.5e\n",model.h);
printf(" --> l2 error = %12.5e\n",compute_l2_error(&model));
return 0;
}
void a1(void)
{
int N = 3,
M = 1;
data *dat = (data*) malloc(N*sizeof(data));
dat[0] = (data) { .val = 299793.0, .delta = 2.0 };
dat[1] = (data) { .val = 299792.0, .delta = 4.5 };
dat[2] = (data) { .val = 299782.0, .delta = 25.0 };
double avg = average_value(N, dat),
sig_i = sigma_square_intern(N, dat),
sig_e = sigma_square_extern(M, N, dat);
printf("c_avg = %f\n", avg);
printf("sigma_i = %f\n", sqrt(sig_i));
printf("sigma_e = %f\n", sqrt(sig_e));
}
void a2(void)
{
int N;
measurement *m = read_measurements("dat/a2.txt", &N);
double a, b, sig_a, sig_b, chi;
printf("\nLinear regression I = b*U:\n");
linear_regression(N, m, NULL, &b, NULL, &sig_b);
chi = chi_square_(N, m, 0, b);
printf("b = %f +/- %f, chi = %f\n", b, sqrt(sig_b)/2, sqrt(chi));
printf("\nLinear regression I = a + b*U:\n");
linear_regression(N, m, &a, &b, &sig_a, &sig_b);
chi = chi_square_(N, m, a, b);
printf("a = %f +/- %f, b = %f +/- %f, chi = %f\n", a, sqrt(sig_a)/2, b, sqrt(sig_b)/2, sqrt(chi));
}
void a3(void)
{
// order of polynoms + 1
int N[5] = {3, 5, 9, 13, 17};
// output function (%i = current N)
char *output_p_gp = "results/a3/poly-%i.gp",
*output_p_txt = "results/a3/poly-%i.txt",
*output_l_dat = "results/a3/legendre-%i.dat",
*output_l_txt = "results/a3/legendre-%i.txt";
// read data
matrix dat = read_data("dat/a3.txt");
int i;
for (i = 0; i < sizeof(N)/sizeof(int); i++)
{
//
// use polynoms
//
matrix F = init_F(dat, N[i], &polynom);
vector b = init_b(dat, N[i], &polynom);
// solve system of linear equations
vector x = solve_gauss(F,b);
char fp[100];
// parameter output
snprintf(fp, sizeof(fp), output_p_txt, N[i]-1);
printf("Opening file %s...\n", fp);
FILE *file = fopen(fp, "w+");
vector_fprint(file, x);
fclose(file);
// gnuplot output
snprintf(fp, sizeof(fp), output_p_gp, N[i]-1);
printf("Opening file %s...\n", fp);
file = fopen(fp, "w+");
fprintf(file, "plot ");
int k;
for (k = 0; k < x.N; k++)
{
fprintf(file, "%e * x**%i", VectorGET(x,k), k);
if (k < x.N-1)
fprintf(file, " + ");
}
fprintf(file, "\n");
fclose(file);
//
// Use legendre polynoms
//
F = init_F(dat, N[i], &legendre_polynom);
b = init_b(dat, N[i], &legendre_polynom);
// solve system of linear equations
x = solve_gauss(F,b);
// parameter output
snprintf(fp, sizeof(fp), output_l_txt, N[i]-1);
printf("Opening file %s...\n", fp);
file = fopen(fp, "w+");
vector_fprint(file, x);
// "plot" data for legendre polynoms
snprintf(fp, sizeof(fp), output_l_dat, N[i]-1);
printf("Opening file %s...\n", fp);
file = fopen(fp, "w+");
double r = -1.0,
dr = 0.01;
while (r <= 1.0)
{
double sum = 0;
for (k = 0; k < x.N; k++)
{
sum += VectorGET(x,k) * legendre_polynom(k,r);
}
fprintf(file, "%f %e\n", r, sum);
r += dr;
}
fclose(file);
file = NULL;
}
}
int main()
{
//a1();
//a2();
a3();
return 0;
}