/**
* Calculate the regression parameters by least squares on linearized data
* x / y = x / V + K / V
*/
public function calculate()
{
// Linearize the relationship by dividing x by y
$y’ = Multi::divide($this->xs, $this->ys);
// Perform Least Squares Fit
$linear_parameters = $this->leastSquares($y’, $this->xs)->getColumn(0);
$V = 1 / $linear_parameters[1];
$K = $linear_parameters[0] * $V;
$this->parameters = [$V, $K];
}
/**
* Get the regression residuals
* eᵢ = yᵢ - ŷᵢ
* or in matrix form
* e = (I - H)y
*
* @return array
*/
public function residuals() : array
{
return Multi::subtract($this->reg_ys, $this->reg_Yhat);
}
/**
* Weighted n-point moving average (WMA)
*
* Similar to simple n-point moving average,
* however, each n-point has a weight associated with it,
* and instead of dividing by n, we divide by the sum of the weights.
*
* Each weighted average = ∑(weighted values) / ∑(weights)
*
* @param array $numbers
* @param int $n n-point moving average
* @param array $weights Weights for each n points
*
* @return array of averages
*
* @throws BadDataException if number of weights is not equal to number of n-points
*/
public static function weightedMovingAverage(array $numbers, int $n, array $weights) : array
{
if (count($weights) !== $n) {
throw new Exception\BadDataException('Number of weights must equal number of n-points');
}
$m = count($numbers);
$∑w = array_sum($weights);
$WMA = [];
for ($i = 0; $i <= $m - $n; $i++) {
$∑wp = array_sum(Map\Multi::multiply(array_slice($numbers, $i, $n), $weights));
$WMA[] = $∑wp / $∑w;
}
return $WMA;
}
/**
* Subtract (A - B)
*
* A = [a₁, a₂, a₃]
* B = [b₁, b₂, b₃]
* A - B = [a₁ - b₁, a₂ - b₂, a₃ - b₃]
*
* @param Vector $B
*
* @return Vector
*/
public function subtract(Vector $B) : Vector
{
if ($B->getN() !== $this->n) {
throw new Exception\VectorException('Vectors must be the same length for subtraction');
}
$R = Map\Multi::subtract($this->A, $B->getVector());
return new Vector($R);
}
