<?php
namespace PhpOffice\PhpSpreadsheet\Shared\Trend;
abstract class BestFit
{
/**
* Indicator flag for a calculation error.
*
* @var bool
*/
protected $error = false;
/**
* Algorithm type to use for best-fit.
*
* @var string
*/
protected $bestFitType = 'undetermined';
/**
* Number of entries in the sets of x- and y-value arrays.
*
* @var int
*/
protected $valueCount = 0;
/**
* X-value dataseries of values.
*
* @var float[]
*/
protected $xValues = [];
/**
* Y-value dataseries of values.
*
* @var float[]
*/
protected $yValues = [];
/**
* Flag indicating whether values should be adjusted to Y=0.
*
* @var bool
*/
protected $adjustToZero = false;
/**
* Y-value series of best-fit values.
*
* @var float[]
*/
protected $yBestFitValues = [];
/** @var float */
protected $goodnessOfFit = 1;
/** @var float */
protected $stdevOfResiduals = 0;
/** @var float */
protected $covariance = 0;
/** @var float */
protected $correlation = 0;
/** @var float */
protected $SSRegression = 0;
/** @var float */
protected $SSResiduals = 0;
/** @var float */
protected $DFResiduals = 0;
/** @var float */
protected $f = 0;
/** @var float */
protected $slope = 0;
/** @var float */
protected $slopeSE = 0;
/** @var float */
protected $intersect = 0;
/** @var float */
protected $intersectSE = 0;
/** @var float */
protected $xOffset = 0;
/** @var float */
protected $yOffset = 0;
/** @return bool */
public function getError()
{
return $this->error;
}
/** @return string */
public function getBestFitType()
{
return $this->bestFitType;
}
/**
* Return the Y-Value for a specified value of X.
*
* @param float $xValue X-Value
*
* @return float Y-Value
*/
abstract public function getValueOfYForX($xValue);
/**
* Return the X-Value for a specified value of Y.
*
* @param float $yValue Y-Value
*
* @return float X-Value
*/
abstract public function getValueOfXForY($yValue);
/**
* Return the original set of X-Values.
*
* @return float[] X-Values
*/
public function getXValues()
{
return $this->xValues;
}
/**
* Return the Equation of the best-fit line.
*
* @param int $dp Number of places of decimal precision to display
*
* @return string
*/
abstract public function getEquation($dp = 0);
/**
* Return the Slope of the line.
*
* @param int $dp Number of places of decimal precision to display
*
* @return float
*/
public function getSlope($dp = 0)
{
if ($dp != 0) {
return round($this->slope, $dp);
}
return $this->slope;
}
/**
* Return the standard error of the Slope.
*
* @param int $dp Number of places of decimal precision to display
*
* @return float
*/
public function getSlopeSE($dp = 0)
{
if ($dp != 0) {
return round($this->slopeSE, $dp);
}
return $this->slopeSE;
}
/**
* Return the Value of X where it intersects Y = 0.
*
* @param int $dp Number of places of decimal precision to display
*
* @return float
*/
public function getIntersect($dp = 0)
{
if ($dp != 0) {
return round($this->intersect, $dp);
}
return $this->intersect;
}
/**
* Return the standard error of the Intersect.
*
* @param int $dp Number of places of decimal precision to display
*
* @return float
*/
public function getIntersectSE($dp = 0)
{
if ($dp != 0) {
return round($this->intersectSE, $dp);
}
return $this->intersectSE;
}
/**
* Return the goodness of fit for this regression.
*
* @param int $dp Number of places of decimal precision to return
*
* @return float
*/
public function getGoodnessOfFit($dp = 0)
{
if ($dp != 0) {
return round($this->goodnessOfFit, $dp);
}
return $this->goodnessOfFit;
}
/**
* Return the goodness of fit for this regression.
*
* @param int $dp Number of places of decimal precision to return
*
* @return float
*/
public function getGoodnessOfFitPercent($dp = 0)
{
if ($dp != 0) {
return round($this->goodnessOfFit * 100, $dp);
}
return $this->goodnessOfFit * 100;
}
/**
* Return the standard deviation of the residuals for this regression.
*
* @param int $dp Number of places of decimal precision to return
*
* @return float
*/
public function getStdevOfResiduals($dp = 0)
{
if ($dp != 0) {
return round($this->stdevOfResiduals, $dp);
}
return $this->stdevOfResiduals;
}
/**
* @param int $dp Number of places of decimal precision to return
*
* @return float
*/
public function getSSRegression($dp = 0)
{
if ($dp != 0) {
return round($this->SSRegression, $dp);
}
return $this->SSRegression;
}
/**
* @param int $dp Number of places of decimal precision to return
*
* @return float
*/
public function getSSResiduals($dp = 0)
{
if ($dp != 0) {
return round($this->SSResiduals, $dp);
}
return $this->SSResiduals;
}
/**
* @param int $dp Number of places of decimal precision to return
*
* @return float
*/
public function getDFResiduals($dp = 0)
{
if ($dp != 0) {
return round($this->DFResiduals, $dp);
}
return $this->DFResiduals;
}
/**
* @param int $dp Number of places of decimal precision to return
*
* @return float
*/
public function getF($dp = 0)
{
if ($dp != 0) {
return round($this->f, $dp);
}
return $this->f;
}
/**
* @param int $dp Number of places of decimal precision to return
*
* @return float
*/
public function getCovariance($dp = 0)
{
if ($dp != 0) {
return round($this->covariance, $dp);
}
return $this->covariance;
}
/**
* @param int $dp Number of places of decimal precision to return
*
* @return float
*/
public function getCorrelation($dp = 0)
{
if ($dp != 0) {
return round($this->correlation, $dp);
}
return $this->correlation;
}
/**
* @return float[]
*/
public function getYBestFitValues()
{
return $this->yBestFitValues;
}
/** @var mixed */
private static $scrutinizerZeroPointZero = 0.0;
/**
* @param mixed $x
* @param mixed $y
*/
private static function scrutinizerLooseCompare($x, $y): bool
{
return $x == $y;
}
/**
* @param float $sumX
* @param float $sumY
* @param float $sumX2
* @param float $sumY2
* @param float $sumXY
* @param float $meanX
* @param float $meanY
* @param bool|int $const
*/
protected function calculateGoodnessOfFit($sumX, $sumY, $sumX2, $sumY2, $sumXY, $meanX, $meanY, $const): void
{
$SSres = $SScov = $SStot = $SSsex = 0.0;
foreach ($this->xValues as $xKey => $xValue) {
$bestFitY = $this->yBestFitValues[$xKey] = $this->getValueOfYForX($xValue);
$SSres += ($this->yValues[$xKey] - $bestFitY) * ($this->yValues[$xKey] - $bestFitY);
if ($const === true) {
$SStot += ($this->yValues[$xKey] - $meanY) * ($this->yValues[$xKey] - $meanY);
} else {
$SStot += $this->yValues[$xKey] * $this->yValues[$xKey];
}
$SScov += ($this->xValues[$xKey] - $meanX) * ($this->yValues[$xKey] - $meanY);
if ($const === true) {
$SSsex += ($this->xValues[$xKey] - $meanX) * ($this->xValues[$xKey] - $meanX);
} else {
$SSsex += $this->xValues[$xKey] * $this->xValues[$xKey];
}
}
$this->SSResiduals = $SSres;
$this->DFResiduals = $this->valueCount - 1 - ($const === true ? 1 : 0);
if ($this->DFResiduals == 0.0) {
$this->stdevOfResiduals = 0.0;
} else {
$this->stdevOfResiduals = sqrt($SSres / $this->DFResiduals);
}
// Scrutinizer thinks $SSres == $SStot is always true. It is wrong.
if ($SStot == self::$scrutinizerZeroPointZero || self::scrutinizerLooseCompare($SSres, $SStot)) {
$this->goodnessOfFit = 1;
} else {
$this->goodnessOfFit = 1 - ($SSres / $SStot);
}
$this->SSRegression = $this->goodnessOfFit * $SStot;
$this->covariance = $SScov / $this->valueCount;
$this->correlation = ($this->valueCount * $sumXY - $sumX * $sumY) / sqrt(($this->valueCount * $sumX2 - $sumX ** 2) * ($this->valueCount * $sumY2 - $sumY ** 2));
$this->slopeSE = $this->stdevOfResiduals / sqrt($SSsex);
$this->intersectSE = $this->stdevOfResiduals * sqrt(1 / ($this->valueCount - ($sumX * $sumX) / $sumX2));
if ($this->SSResiduals != 0.0) {
if ($this->DFResiduals == 0.0) {
$this->f = 0.0;
} else {
$this->f = $this->SSRegression / ($this->SSResiduals / $this->DFResiduals);
}
} else {
if ($this->DFResiduals == 0.0) {
$this->f = 0.0;
} else {
$this->f = $this->SSRegression / $this->DFResiduals;
}
}
}
/** @return float|int */
private function sumSquares(array $values)
{
return array_sum(
array_map(
function ($value) {
return $value ** 2;
},
$values
)
);
}
/**
* @param float[] $yValues
* @param float[] $xValues
*/
protected function leastSquareFit(array $yValues, array $xValues, bool $const): void
{
// calculate sums
$sumValuesX = array_sum($xValues);
$sumValuesY = array_sum($yValues);
$meanValueX = $sumValuesX / $this->valueCount;
$meanValueY = $sumValuesY / $this->valueCount;
$sumSquaresX = $this->sumSquares($xValues);
$sumSquaresY = $this->sumSquares($yValues);
$mBase = $mDivisor = 0.0;
$xy_sum = 0.0;
for ($i = 0; $i < $this->valueCount; ++$i) {
$xy_sum += $xValues[$i] * $yValues[$i];
if ($const === true) {
$mBase += ($xValues[$i] - $meanValueX) * ($yValues[$i] - $meanValueY);
$mDivisor += ($xValues[$i] - $meanValueX) * ($xValues[$i] - $meanValueX);
} else {
$mBase += $xValues[$i] * $yValues[$i];
$mDivisor += $xValues[$i] * $xValues[$i];
}
}
// calculate slope
$this->slope = $mBase / $mDivisor;
// calculate intersect
$this->intersect = ($const === true) ? $meanValueY - ($this->slope * $meanValueX) : 0.0;
$this->calculateGoodnessOfFit($sumValuesX, $sumValuesY, $sumSquaresX, $sumSquaresY, $xy_sum, $meanValueX, $meanValueY, $const);
}
/**
* Define the regression.
*
* @param float[] $yValues The set of Y-values for this regression
* @param float[] $xValues The set of X-values for this regression
*/
public function __construct($yValues, $xValues = [])
{
// Calculate number of points
$yValueCount = count($yValues);
$xValueCount = count($xValues);
// Define X Values if necessary
if ($xValueCount === 0) {
$xValues = range(1, $yValueCount);
} elseif ($yValueCount !== $xValueCount) {
// Ensure both arrays of points are the same size
$this->error = true;
}
$this->valueCount = $yValueCount;
$this->xValues = $xValues;
$this->yValues = $yValues;
}
}