pub fn extended_breaks(dmin: f64, dmax: f64, m: usize) -> Vec<f64> {
if !(dmin.is_finite() && dmax.is_finite()) || dmax <= dmin || m < 2 {
return vec![];
}
const Q: [f64; 6] = [1.0, 5.0, 2.0, 2.5, 4.0, 3.0];
const W: [f64; 4] = [0.25, 0.2, 0.5, 0.05];
let m = m as f64;
let simplicity = |qi: usize, j: f64, lmin: f64, lmax: f64, step: f64| {
let eps = 1e-10;
let modulo = lmin.rem_euclid(step);
let v = if (modulo < eps || step - modulo < eps) && lmin <= 0.0 && lmax >= 0.0 {
1.0
} else {
0.0
};
1.0 - qi as f64 / (Q.len() as f64 - 1.0) - j + v
};
let simplicity_max = |qi: usize, j: f64| 1.0 - qi as f64 / (Q.len() as f64 - 1.0) - j + 1.0;
let coverage = |lmin: f64, lmax: f64| {
let r = dmax - dmin;
1.0 - 0.5 * ((dmax - lmax).powi(2) + (dmin - lmin).powi(2)) / (0.1 * r).powi(2)
};
let coverage_max = |span: f64| {
let r = dmax - dmin;
if span > r {
let half = (span - r) / 2.0;
1.0 - 0.5 * (half * half + half * half) / (0.1 * r).powi(2)
} else {
1.0
}
};
let density = |k: f64, lmin: f64, lmax: f64| {
let r = (k - 1.0) / (lmax - lmin);
let rt = (m - 1.0) / (lmax.max(dmax) - lmin.min(dmin));
2.0 - (r / rt).max(rt / r)
};
let density_max = |k: f64| {
if k >= m {
2.0 - (k - 1.0) / (m - 1.0)
} else {
1.0
}
};
let mut best_score = -2.0;
let mut best = (dmin, dmax, (dmax - dmin) / (m - 1.0));
for j_i in 1..=4u32 {
let j = j_i as f64;
for (qi, &q) in Q.iter().enumerate() {
let sm = simplicity_max(qi, j);
if W[0] * sm + W[1] + W[2] + W[3] < best_score {
break;
}
for k_i in 2..=(2.0 * m + 4.0) as usize {
let k = k_i as f64;
let dm = density_max(k);
if W[0] * sm + W[1] + W[2] * dm + W[3] < best_score {
break;
}
let delta = (dmax - dmin) / (k + 1.0) / j / q;
let z0 = delta.log10().ceil() as i32;
for z in z0..(z0 + 6) {
let step = j * q * 10f64.powi(z);
let cm = coverage_max(step * (k - 1.0));
if W[0] * sm + W[1] * cm + W[2] * dm + W[3] < best_score {
break;
}
let min_start = (dmax / step).floor() * j - (k - 1.0) * j;
let max_start = (dmin / step).ceil() * j;
if min_start > max_start {
continue;
}
let mut start = min_start;
while start <= max_start {
let lmin = start * step / j;
let lmax = lmin + step * (k - 1.0);
let s = simplicity(qi, j, lmin, lmax, step);
let c = coverage(lmin, lmax);
let g = density(k, lmin, lmax);
let score = W[0] * s + W[1] * c + W[2] * g + W[3];
if score > best_score {
best_score = score;
best = (lmin, lmax, step);
}
start += 1.0;
}
}
}
}
}
let (lmin, lmax, step) = best;
if step <= 0.0 {
return vec![];
}
let n = ((lmax - lmin) / step).round() as usize;
(0..=n).map(|i| lmin + i as f64 * step).collect()
}
pub fn nice_step(raw: f64) -> f64 {
let magnitude = 10f64.powf(raw.abs().log10().floor());
let fraction = raw / magnitude;
let nice = if fraction <= 1.5 {
1.0
} else if fraction <= 3.5 {
2.0
} else if fraction <= 7.5 {
5.0
} else {
10.0
};
nice * magnitude
}
pub fn format_number(v: f64) -> String {
if v == v.round() && v.abs() < 1e10 {
format!("{}", v as i64)
} else {
let s = format!("{:.2}", v);
s.trim_end_matches('0').trim_end_matches('.').to_string()
}
}