int
gsl_sf_lambert_Wm1_e(double x, gsl_sf_result * result)
{
if(x > 0.0) {
return gsl_sf_lambert_W0_e(x, result);
}
else if(x == 0.0) {
result->val = 0.0;
result->err = 0.0;
return GSL_SUCCESS;
}
else {
static const unsigned int MAX_ITERS = 32;
const double one_over_E = 1.0/M_E;
const double q = x + one_over_E;
double w;
if (q < 0.0) {
/* As in the W0 branch above, return some reasonable answer anyway. */
result->val = -1.0;
result->err = sqrt(-q);
return GSL_EDOM;
}
if(x < -1.0e-6) {
/* Obtain initial approximation from series about q = 0,
* as long as we're not very close to x = 0.
* Use full series and try to bail out if q is too small,
* since the Halley iteration has bad convergence properties
* in finite arithmetic for q very small, because the
* increment alternates and p is near zero.
*/
const double r = -sqrt(q);
w = series_eval(r);
if(q < 3.0e-3) {
/* this approximation is good enough */
result->val = w;
result->err = 5.0 * GSL_DBL_EPSILON * fabs(w);
return GSL_SUCCESS;
}
}
else {
/* Obtain initial approximation from asymptotic near zero. */
const double L_1 = log(-x);
const double L_2 = log(-L_1);
w = L_1 - L_2 + L_2/L_1;
}
return halley_iteration(x, w, MAX_ITERS, result);
}
}
double gsl_sf_lambert_W0(double x)
{
EVAL_RESULT(gsl_sf_lambert_W0_e(x, &result));
}
double optimizeLambda(unsigned int x, unsigned int y) {
#ifdef NEW_WAY
double A = getComputedExpectation(x, y) * exp(-lambda_(x, y));
double B = 2 * beta2_;
double C = empirical_pair_(x, y) - beta1_;
#else
double A = getComputedExpectation(x, y);
double B = 2 * beta2_;
double C = empirical_pair_(x, y) - beta1_ - 2 * beta2_ * lambda_(x, y);
#endif
// #define DEBUGGING_NOISE
#ifdef DEBUGGING_NOISE
if (empirical_pair_(x, y) > 0 && rand() < RAND_MAX / 1000) {
double overcount_x = lambda_(x,y) * singleton_expectation_[y];
double overcount_y = lambda_(x,y) * singleton_expectation_[x];
double p10 = q_lambda_[x] + kappa_[x] - overcount_x;
double p01 = q_lambda_[y] + kappa_[y] - overcount_y;
double p11 = estimates_(x,y) - overcount_x - overcount_y;
std::cout << getComputedExpectation(x, y) << " "
<< empirical_pair_(x, y) << " "
<< kappa_[x] << " "
<< kappa_[y] << " "
<< lambda_(x,y) << " "
<< x << " " << y << " "
<< q_lambda_[x] << " "
<< q_lambda_[y] << " "
<< estimates_(x,y) << " "
<< overcount_x << " " << overcount_y << " "
<< p10 << " " << p01 << " " << p11 << " "
<< std::endl;
}
#endif
double delta1 = 0;
double delta2 = 0;
if (beta2_ == 0) {
delta1 = log(C / A);
} else {
gsl_sf_result result;
gsl_sf_lambert_W0_e(A / B * exp(C / B), &result);
delta1 = C/B - result.val;
}
C += 2 * beta1_;
if (beta2_ == 0) {
delta2 = log(C / A);
} else {
gsl_sf_result result;
gsl_sf_lambert_W0_e(A / B * exp(C / B), &result);
delta2 = C/B - result.val;
}
double new_lambda = lambda_(x,y);
if (new_lambda + delta1 >= 0) {
new_lambda += delta1;
} else if (new_lambda + delta2 <= 0) {
new_lambda += delta2;
} else {
new_lambda = 0;
}
double delta = fabs(new_lambda - lambda_(x,y));
if (delta - delta != 0) {
delta = 0.0;
}
lambda_(x,y) = new_lambda;
lambda_(y,x) = new_lambda;
return delta;
}
static VALUE Lambert_W0_e(VALUE self, VALUE x) {
int ret;
gsl_sf_result r;
ret = gsl_sf_lambert_W0_e(NUM2DBL(x), &r);
return RESULT(&r);
}