/* FIXME */
double fd_amer_put(double spot, double strike, double r, double d, double vol,
double expiry, int ssteps, int tsteps) {
/* M needs to be even */
int M = ssteps + ssteps % 2;
int N = tsteps;
double ds = 2.0 * spot / M;
double dt = expiry / N;
double vv = vol * vol;
double *prices, *x, res;
gsl_vector *diag, *e, *f, *B;
gsl_vector_view X;
int i, step;
if ((prices = ALLOC((M + 1) * sizeof (double))) == NULL)
return 0.0;
if ((x = ALLOC((M + 1) * sizeof (double))) == NULL) {
FREE(prices);
return 0.0;
}
for (i = 0; i <= M; ++i)
prices[i] = i * ds;
/* tridiagonal systems */
diag = gsl_vector_alloc(M + 1);
gsl_vector_set(diag, 0, 1.0);
for (i = 1; i < M; ++i)
gsl_vector_set(diag, i, 1.0 + dt * (vv * i * i + r));
gsl_vector_set(diag, M, 1.0);
e = gsl_vector_alloc(M);
gsl_vector_set(e, 0, 0.0);
for (i = 1; i < M; ++i)
gsl_vector_set(e, i, 0.5 * i * dt * (-r + d - vv * i));
f = gsl_vector_alloc(M);
for (i = 0; i < M - 1; ++i)
gsl_vector_set(f, i, 0.5 * i * dt * (r - d - vv * i));
gsl_vector_set(f, M - 1, 0.0);
B = gsl_vector_alloc(M + 1);
for (i = 0; i <= M; ++i)
gsl_vector_set(B, i, MAX(0.0, strike - prices[i]));
X = gsl_vector_view_array(x, M + 1);
gsl_linalg_solve_tridiag(diag, e, f, B, &X.vector);
for (step = N - 1; step > 0; --step) {
gsl_vector_memcpy(B, &X.vector);
gsl_linalg_solve_tridiag(diag, e, f, B, &X.vector);
for (i = 1; i < M; ++i)
x[i] = MAX(x[i], strike - prices[i]);
}
res = x[M / 2];
gsl_vector_free(B);
gsl_vector_free(f);
gsl_vector_free(e);
gsl_vector_free(diag);
FREE(x);
FREE(prices);
return res;
}
void GSLRunMyProgram(int N, double *A, double *X, FILE *output){
int i;
gsl_vector * x = gsl_vector_alloc (N);
gsl_vector * e = gsl_vector_alloc (N-1);
gsl_vector * d = gsl_vector_alloc (N);
gsl_vector * f = gsl_vector_alloc (N-1);
gsl_vector * b = gsl_vector_alloc (N);
for (i = 0; i < N; i++)
{
gsl_vector_set (b, i, X[i]);
gsl_vector_set (d, i, A[1 + 3*i]);
}
for(i = 0; i < N-1; i++){
gsl_vector_set (e, i, A[2 + 3*i]);
gsl_vector_set (f, i, A[3*(i+1)]);
}
clock_t startTime = clock();
gsl_linalg_solve_tridiag(d, e, f, b, x);
fprintf(output, "%f\n", 1000*(double)(clock()-startTime)/(double)(CLOCKS_PER_SEC));
// for(i = 0; i < N; i++){
// printf("GSL x%i: %g\n", i, gsl_vector_get(x, i));
// }
gsl_vector_free (x);
gsl_vector_free (e);
gsl_vector_free (d);
gsl_vector_free (f);
gsl_vector_free (b);
return;
}
CAMLprim value ml_gsl_linalg_solve_tridiag(value DIAG, value ABOVE, value BELOW,
value B, value X)
{
_DECLARE_VECTOR5(DIAG, ABOVE, BELOW, B, X);
_CONVERT_VECTOR5(DIAG, ABOVE, BELOW, B, X);
gsl_linalg_solve_tridiag(&v_DIAG, &v_ABOVE, &v_BELOW, &v_B, &v_X);
return Val_unit;
}
/**
* C++ version of gsl_linalg_solve_tridiag().
* @param diag A vector of diagonal elements
* @param abovediag Off-diagonal vector (one element shorte than @c diag)
* @param belowdiag Off-diagonal vector (one element shorte than @c diag)
* @param b A vector
* @param x A vector
* @return Error code on failure
*/
inline int solve_tridiag( vector const& diag, vector const& abovediag, vector const& belowdiag,
vector const& b, vector& x ){
return gsl_linalg_solve_tridiag( diag.get(), abovediag.get(), belowdiag.get(), b.get(), x.get() ); }