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better documentation of algorithm

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This commit is contained in:
Krishna Vedala
2020-06-21 18:30:31 -04:00
parent 21e93919f3
commit e71ee9ccb0
1 changed files with 14 additions and 6 deletions
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20
numerical_methods/golden_search_extrema.cpp
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@@ -14,12 +14,11 @@
#include <limits>
#define EPSILON 1e-7 ///< solution accuracy limit
#define M_GOLDEN_RATIO \
static_cast<double>(1.618033988749894848204586834) ///< golden ratio value
/**
* @brief Get the minima of a function in the given interval. To get the maxima,
* simply negate the function.
* simply negate the function. The golden ratio used here is:\f[
* k=\frac{3-\sqrt{5}}{2} \approx 0.381966\ldots\f]
*
* @param f function to get minima for
* @param lim_a lower limit of search window
@@ -32,6 +31,9 @@ double get_minima(const std::function<double(double)> &f, double lim_a,
double c, d;
double prev_mean, mean = std::numeric_limits<double>::infinity();
// golden ratio value
const double M_GOLDEN_RATIO = (1.f + std::sqrt(5.f)) / 2.f;
// ensure that lim_a < lim_b
if (lim_a > lim_b) {
std::swap(lim_a, lim_b);
@@ -43,18 +45,24 @@ double get_minima(const std::function<double(double)> &f, double lim_a,
do {
prev_mean = mean;
c = lim_b - (lim_b - lim_a) / M_GOLDEN_RATIO;
d = lim_a + (lim_b - lim_a) / M_GOLDEN_RATIO;
// compute the section ratio width
double ratio = (lim_b - lim_a) / M_GOLDEN_RATIO;
c = lim_b - ratio; // right-side section start
d = lim_a + ratio; // left-side section end
if (f(c) < f(d)) {
// select left section
lim_b = d;
} else {
// selct right section
lim_a = c;
}
mean = (lim_a + lim_b) / 2.f;
iters++;
} while (std::abs(mean - prev_mean) > EPSILON);
// continue till the interval width is greater than sqrt(system epsilon)
} while (std::abs(lim_a - lim_b) > EPSILON);
std::cout << " (iters: " << iters << ") ";
return prev_mean;