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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
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+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