// log transform:
// - useful when values vary dramatically in magnitude, like brightness of stars
// - edges are not exactly at 10, 100, 1000, because of finite floating point precision
- // - value >= 0 below is mapped to -1
- // - value < 0 below is mapped to `size()`, because the result of std::log is NaN
+ // - values >= 0 but smaller than the starting value of the axis are mapped to -1
+ // - values < 0 are mapped to `size()`, because the result of std::log(value) is NaN
assert(r_log.index(10.1) == 0);
assert(r_log.index(100.1) == 1);
assert(r_log.index(1000.1) == 2);
axis::regular<double, axis::transform::sqrt> r_sqrt{3, 4., 25.};
// sqrt transform:
// - bin widths are more mildly increasing compared to log transform
- // - starting axis at value == 0 is ok, sqrt(0) == 0 unlike log transform
- // - value < 0 is mapped to `size()`, because the result of std::sqrt is NaN
+ // - axis starting at value == 0 is ok, sqrt(0) == 0 unlike log transform
+ // - values < 0 are mapped to `size()`, because the result of std::sqrt(value) is NaN
assert(r_sqrt.index(0) == -1);
assert(r_sqrt.index(4.1) == 0);
assert(r_sqrt.index(9.1) == 1);
using pow_trans = axis::transform::pow;
axis::regular<double, pow_trans> r_pow(pow_trans{1. / 3.}, 3, 1., 64.);
// pow transform:
- // - generalization of the sqrt transform, power index is first argument of ctor
- // - starting the axis at value == 0 is ok, 0^p == 0 for p != 0
- // - value < 0 is mapped to `size()`, because the result of std::pow is NaN
+ // - generalization of the sqrt transform
+ // - starting the axis at value == 0 is ok for power p > 0, 0^p == 0 for p > 0
+ // - values < 0 are mapped to `size()` if power p is not a positive integer
assert(r_pow.index(0) == -1);
assert(r_pow.index(1.1) == 0);
assert(r_pow.index(8.1) == 1);