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/*
Copyright 2018 Google Inc. All Rights Reserved.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS-IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/
#include "base/misc_math.h"
namespace vraudio {
WorldPosition::WorldPosition() { setZero(); }
WorldRotation::WorldRotation() { setIdentity(); }
bool LinearLeastSquareFitting(const std::vector<float>& x_array,
const std::vector<float>& y_array, float* slope,
float* intercept, float* r_squared) {
// The array sizes must agree.
if (x_array.size() != y_array.size()) {
return false;
}
// At least two points are needed to fit a line.
if (x_array.size() < 2) {
return false;
}
float x_sum = 0.0f;
float y_sum = 0.0f;
float x_square_sum = 0.0f;
float xy_sum = 0.0f;
for (size_t i = 0; i < x_array.size(); ++i) {
const float x = x_array[i];
const float y = y_array[i];
x_sum += x;
y_sum += y;
x_square_sum += x * x;
xy_sum += x * y;
}
const float n_inverse = 1.0f / static_cast<float>(x_array.size());
const float x_mean = x_sum * n_inverse;
const float y_mean = y_sum * n_inverse;
const float x_square_mean = x_square_sum * n_inverse;
const float xy_mean = xy_sum * n_inverse;
const float x_mean_square = x_mean * x_mean;
// Prevent division by zero, which means a vertical line and the slope is
// infinite.
if (x_square_mean == x_mean_square) {
return false;
}
*slope = (xy_mean - x_mean * y_mean) / (x_square_mean - x_mean_square);
*intercept = y_mean - *slope * x_mean;
// Compute the coefficient of determination.
float total_sum_of_squares = 0.0f;
float residual_sum_of_squares = 0.0f;
for (size_t i = 0; i < x_array.size(); ++i) {
const float y_i = y_array[i];
total_sum_of_squares += (y_i - y_mean) * (y_i - y_mean);
const float y_fit = *slope * x_array[i] + *intercept;
residual_sum_of_squares += (y_fit - y_i) * (y_fit - y_i);
}
if (total_sum_of_squares == 0.0f) {
if (residual_sum_of_squares == 0.0f) {
// A special case where all y's are equal, where the |r_squared| should
// be 1.0, and the line is a perfectly horizontal line.
*r_squared = 1.0f;
return true;
} else {
// Division by zero.
return false;
}
}
*r_squared = 1.0f - residual_sum_of_squares / total_sum_of_squares;
return true;
}
} // namespace vraudio