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/* SPDX-License-Identifier: BSD-2-Clause */
/*
* Copyright (C) 2019, Raspberry Pi (Trading) Limited
*
* pwl.cpp - piecewise linear functions
*/
#include <cassert>
#include <stdexcept>
#include "pwl.hpp"
using namespace RPiController;
void Pwl::Read(boost::property_tree::ptree const ¶ms)
{
for (auto it = params.begin(); it != params.end(); it++) {
double x = it->second.get_value<double>();
assert(it == params.begin() || x > points_.back().x);
it++;
double y = it->second.get_value<double>();
points_.push_back(Point(x, y));
}
assert(points_.size() >= 2);
}
void Pwl::Append(double x, double y, const double eps)
{
if (points_.empty() || points_.back().x + eps < x)
points_.push_back(Point(x, y));
}
void Pwl::Prepend(double x, double y, const double eps)
{
if (points_.empty() || points_.front().x - eps > x)
points_.insert(points_.begin(), Point(x, y));
}
Pwl::Interval Pwl::Domain() const
{
return Interval(points_[0].x, points_[points_.size() - 1].x);
}
Pwl::Interval Pwl::Range() const
{
double lo = points_[0].y, hi = lo;
for (auto &p : points_)
lo = std::min(lo, p.y), hi = std::max(hi, p.y);
return Interval(lo, hi);
}
bool Pwl::Empty() const
{
return points_.empty();
}
double Pwl::Eval(double x, int *span_ptr, bool update_span) const
{
int span = findSpan(x, span_ptr && *span_ptr != -1
? *span_ptr
: points_.size() / 2 - 1);
if (span_ptr && update_span)
*span_ptr = span;
return points_[span].y +
(x - points_[span].x) * (points_[span + 1].y - points_[span].y) /
(points_[span + 1].x - points_[span].x);
}
int Pwl::findSpan(double x, int span) const
{
// Pwls are generally small, so linear search may well be faster than
// binary, though could review this if large PWls start turning up.
int last_span = points_.size() - 2;
// some algorithms may call us with span pointing directly at the last
// control point
span = std::max(0, std::min(last_span, span));
while (span < last_span && x >= points_[span + 1].x)
span++;
while (span && x < points_[span].x)
span--;
return span;
}
Pwl::PerpType Pwl::Invert(Point const &xy, Point &perp, int &span,
const double eps) const
{
assert(span >= -1);
bool prev_off_end = false;
for (span = span + 1; span < (int)points_.size() - 1; span++) {
Point span_vec = points_[span + 1] - points_[span];
double t = ((xy - points_[span]) % span_vec) / span_vec.Len2();
if (t < -eps) // off the start of this span
{
if (span == 0) {
perp = points_[span];
return PerpType::Start;
} else if (prev_off_end) {
perp = points_[span];
return PerpType::Vertex;
}
} else if (t > 1 + eps) // off the end of this span
{
if (span == (int)points_.size() - 2) {
perp = points_[span + 1];
return PerpType::End;
}
prev_off_end = true;
} else // a true perpendicular
{
perp = points_[span] + span_vec * t;
return PerpType::Perpendicular;
}
}
return PerpType::None;
}
Pwl Pwl::Inverse(bool *true_inverse, const double eps) const
{
bool appended = false, prepended = false, neither = false;
Pwl inverse;
for (Point const &p : points_) {
if (inverse.Empty())
inverse.Append(p.y, p.x, eps);
else if (std::abs(inverse.points_.back().x - p.y) <= eps ||
std::abs(inverse.points_.front().x - p.y) <= eps)
/* do nothing */;
else if (p.y > inverse.points_.back().x) {
inverse.Append(p.y, p.x, eps);
appended = true;
} else if (p.y < inverse.points_.front().x) {
inverse.Prepend(p.y, p.x, eps);
prepended = true;
} else
neither = true;
}
// This is not a proper inverse if we found ourselves putting points
// onto both ends of the inverse, or if there were points that couldn't
// go on either.
if (true_inverse)
*true_inverse = !(neither || (appended && prepended));
return inverse;
}
Pwl Pwl::Compose(Pwl const &other, const double eps) const
{
double this_x = points_[0].x, this_y = points_[0].y;
int this_span = 0, other_span = other.findSpan(this_y, 0);
Pwl result({ { this_x, other.Eval(this_y, &other_span, false) } });
while (this_span != (int)points_.size() - 1) {
double dx = points_[this_span + 1].x - points_[this_span].x,
dy = points_[this_span + 1].y - points_[this_span].y;
if (abs(dy) > eps &&
other_span + 1 < (int)other.points_.size() &&
points_[this_span + 1].y >=
other.points_[other_span + 1].x + eps) {
// next control point in result will be where this
// function's y reaches the next span in other
this_x = points_[this_span].x +
(other.points_[other_span + 1].x -
points_[this_span].y) * dx / dy;
this_y = other.points_[++other_span].x;
} else if (abs(dy) > eps && other_span > 0 &&
points_[this_span + 1].y <=
other.points_[other_span - 1].x - eps) {
// next control point in result will be where this
// function's y reaches the previous span in other
this_x = points_[this_span].x +
(other.points_[other_span + 1].x -
points_[this_span].y) * dx / dy;
this_y = other.points_[--other_span].x;
} else {
// we stay in the same span in other
this_span++;
this_x = points_[this_span].x,
this_y = points_[this_span].y;
}
result.Append(this_x, other.Eval(this_y, &other_span, false),
eps);
}
return result;
}
void Pwl::Map(std::function<void(double x, double y)> f) const
{
for (auto &pt : points_)
f(pt.x, pt.y);
}
void Pwl::Map2(Pwl const &pwl0, Pwl const &pwl1,
std::function<void(double x, double y0, double y1)> f)
{
int span0 = 0, span1 = 0;
double x = std::min(pwl0.points_[0].x, pwl1.points_[0].x);
f(x, pwl0.Eval(x, &span0, false), pwl1.Eval(x, &span1, false));
while (span0 < (int)pwl0.points_.size() - 1 ||
span1 < (int)pwl1.points_.size() - 1) {
if (span0 == (int)pwl0.points_.size() - 1)
x = pwl1.points_[++span1].x;
else if (span1 == (int)pwl1.points_.size() - 1)
x = pwl0.points_[++span0].x;
else if (pwl0.points_[span0 + 1].x > pwl1.points_[span1 + 1].x)
x = pwl1.points_[++span1].x;
else
x = pwl0.points_[++span0].x;
f(x, pwl0.Eval(x, &span0, false), pwl1.Eval(x, &span1, false));
}
}
Pwl Pwl::Combine(Pwl const &pwl0, Pwl const &pwl1,
std::function<double(double x, double y0, double y1)> f,
const double eps)
{
Pwl result;
Map2(pwl0, pwl1, [&](double x, double y0, double y1) {
result.Append(x, f(x, y0, y1), eps);
});
return result;
}
void Pwl::MatchDomain(Interval const &domain, bool clip, const double eps)
{
int span = 0;
Prepend(domain.start, Eval(clip ? points_[0].x : domain.start, &span),
eps);
span = points_.size() - 2;
Append(domain.end, Eval(clip ? points_.back().x : domain.end, &span),
eps);
}
Pwl &Pwl::operator*=(double d)
{
for (auto &pt : points_)
pt.y *= d;
return *this;
}
void Pwl::Debug(FILE *fp) const
{
fprintf(fp, "Pwl {\n");
for (auto &p : points_)
fprintf(fp, "\t(%g, %g)\n", p.x, p.y);
fprintf(fp, "}\n");
}
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