// Copyright (c) 2017 Tigera, 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.

// Code copied from https://gist.github.com/ota42y/db4ff0298d9c945cd261, with some modifications.

package leastsquares

type Point struct {
	X float64
	Y float64
}

func LeastSquaresMethod(points []Point) (a float64, b float64) {
	// Calculate a and b such that y = ax + b is the best fit to the given points.
	//
	// http://ja.wikipedia.org/wiki/%E6%9C%80%E5%B0%8F%E4%BA%8C%E4%B9%97%E6%B3%95

	n := float64(len(points))

	sumX := 0.0
	sumY := 0.0
	sumXY := 0.0
	sumXX := 0.0

	for _, p := range points {
		sumX += p.X
		sumY += p.Y
		sumXY += p.X * p.Y
		sumXX += p.X * p.X
	}

	base := (n*sumXX - sumX*sumX)
	a = (n*sumXY - sumX*sumY) / base
	b = (sumXX*sumY - sumXY*sumX) / base

	return a, b
}