/**
* @param NumArray $matrix
* @param NumArray $vector
* @return NumArray
*/
protected static function backSubstitution(NumArray $matrix, NumArray $vector)
{
$shape = $matrix->getShape();
$xVector = \NumPHP\Core\NumPHP::zeros($shape[0]);
for ($i = $shape[0] - 1; $i >= 0; $i--) {
$sum = 0;
for ($j = $i + 1; $j < $shape[0]; $j++) {
$sum += $matrix->get($i, $j)->dot($xVector->get($j))->getData();
}
$xVector->set($i, ($vector->get($i)->getData() - $sum) / $matrix->get($i, $i)->getData());
}
return $xVector;
}
/**
* Tests if a NumArray is a square matrix
*
* @param NumArray $numArray given NumArray
*
* @return bool
*
* @since 1.0.0
*/
public static function isSquareMatrix(NumArray $numArray)
{
$shape = $numArray->getShape();
return self::isMatrix($numArray) && $shape[0] === $shape[1];
}
/**
* Searches the pivot index in an array
*
* @param NumArray $numArray given array
* @param int $iIndex index
*
* @return int
*
* @since 1.0.0
*/
protected static function getPivotIndex(NumArray $numArray, $iIndex)
{
$shape = $numArray->getShape();
$mAxis = $shape[0];
$max = abs($numArray->get($iIndex, $iIndex)->getData());
$maxIndex = $iIndex;
for ($j = $iIndex + 1; $j < $mAxis; $j++) {
$abs = abs($numArray->get($j, $iIndex)->getData());
if ($abs > $max) {
$max = $abs;
$maxIndex = $j;
}
}
return $maxIndex;
}
/**
* Multiplies an array, NumArray or numeric value to the existing NumArray
*
* @param mixed $factor an other int, float, array or NumArray
*
* @return $this
*
* @api
* @since 1.0.0
*/
public function dot($factor)
{
if (!$factor instanceof NumArray) {
$factor = new NumArray($factor);
}
$result = Dot::dotArray($this->data, $this->shape, $factor->getData(), $factor->getShape());
$this->data = $result['data'];
$this->shape = $result['shape'];
$this->flushCache();
return $this;
}
/**
* Returns a NumArray with the same size, but filled with random values
*
* @param NumArray $numArray given NumArray
*
* @return NumArray
*
* @api
* @since 1.0.0
*/
public static function randLike(NumArray $numArray)
{
return new NumArray(Generate::generateArray($numArray->getShape()));
}
/**
* Back Substitution solves a linear system with a upper triangular matrix of
* size n*n and a vector of size n or a matrix of size n*m
*
* @param NumArray $uMatrix upper triangular matrix of size n*n
* @param NumArray $numArray vector of size n or matrix of size n*m
*
* @return NumArray
*
* @since 1.0.0
*/
protected static function backSubstitution(NumArray $uMatrix, NumArray $numArray)
{
$shape = $numArray->getShape();
if (Helper::isVector($numArray)) {
$xVector = NumPHP::zerosLike($numArray);
for ($i = $shape[0] - 1; $i >= 0; $i--) {
$slice = sprintf("%d:%d", $i + 1, $shape[0]);
$sum = $uMatrix->get($i, $slice)->dot($xVector->get($slice));
$xVector->set($i, $numArray->get($i)->sub($sum)->div($uMatrix->get($i, $i)));
}
return $xVector;
}
// $numArray is a matrix
$copy = clone $numArray;
for ($i = 0; $i < $shape[1]; $i++) {
$copy->set(':', $i, self::backSubstitution($uMatrix, $copy->get(':', $i)));
}
return $copy;
}
