/**
* @param Matrix $source
* @throws MatrixException
*/
private function decompose(Matrix $source)
{
$decompositionLiteral = $source->toArray();
if (!$source->isSquare()) {
throw new MatrixException('Operation can only be called on square matrix: ' . print_r($decompositionLiteral, true));
}
$size = $source->getRowCount();
for ($k = 0; $k < $size; $k++) {
for ($i = $k + 1; $i < $size; $i++) {
$decompositionLiteral[$i][$k] = $decompositionLiteral[$i][$k] / $decompositionLiteral[$k][$k];
}
for ($i = $k + 1; $i < $size; $i++) {
for ($j = $k + 1; $j < $size; $j++) {
$decompositionLiteral[$i][$j] = $decompositionLiteral[$i][$j] - $decompositionLiteral[$i][$k] * $decompositionLiteral[$k][$j];
}
}
}
$this->decomposition = new Matrix($decompositionLiteral);
}
/**
* @param Matrix $source
* @throws MatrixException
*/
private function decompose(Matrix $source)
{
$sourceLiteral = $source->toArray();
$decompositionLiteral = $sourceLiteral;
if (!$source->isSquare()) {
throw new MatrixException('Operation can only be called on square matrix: ' . print_r($decompositionLiteral, true));
}
$size = $source->getRowCount();
$this->permutation = range(0, $size - 1);
for ($k = 0; $k < $size; $k++) {
$p = 0.0;
$kPrime = $k;
for ($i = $k; $i < $size; $i++) {
$absolute = abs($decompositionLiteral[$i][$k]);
if ($absolute > $p) {
$p = $absolute;
$kPrime = $i;
}
}
if ($p === 0.0) {
throw new MatrixException('Cannot take the LUP decomposition of a singular matrix: ' . print_r($sourceLiteral, true));
}
if ($k !== $kPrime) {
list($this->permutation[$k], $this->permutation[$kPrime]) = [$this->permutation[$kPrime], $this->permutation[$k]];
$this->parity++;
}
for ($i = 0; $i < $size; $i++) {
list($decompositionLiteral[$k][$i], $decompositionLiteral[$kPrime][$i]) = [$decompositionLiteral[$kPrime][$i], $decompositionLiteral[$k][$i]];
}
for ($i = $k + 1; $i < $size; $i++) {
$decompositionLiteral[$i][$k] = $decompositionLiteral[$i][$k] / $decompositionLiteral[$k][$k];
for ($j = $k + 1; $j < $size; $j++) {
$decompositionLiteral[$i][$j] = $decompositionLiteral[$i][$j] - $decompositionLiteral[$i][$k] * $decompositionLiteral[$k][$j];
}
}
}
$this->decomposition = new Matrix($decompositionLiteral);
}
/**
* @param self $source
* @return self
*/
private function recursiveSolveInverse(self $source) : self
{
$size = $source->getRowCount();
if ($size === 1) {
return new static([[1 / $source->get(0, 0)]]);
}
$half = (int) ($size / 2);
// Partition source matrix.
$B = $source->sliceRows(0, $half)->sliceColumns(0, $half);
$CT = $source->sliceRows(0, $half)->sliceColumns($half);
$D = $source->sliceRows($half)->sliceColumns($half);
$C = $source->sliceRows($half)->sliceColumns(0, $half);
// Handle intermediate calculations.
$Binv = $this->recursiveSolveInverse($B);
$W = $C->multiplyMatrix($Binv);
$WT = $W->transpose();
$X = $W->multiplyMatrix($CT);
$S = $D->subtractMatrix($X);
$Sinv = $this->recursiveSolveInverse($S);
$V = $Sinv;
$Y = $Sinv->multiplyMatrix($W);
$YT = $Y->transpose();
$T = $YT->multiplyScalar(-1);
$U = $Y->multiplyScalar(-1);
$Z = $WT->multiplyMatrix($Y);
$R = $Binv->addMatrix($Z);
// Stitch together intermediate results into the final result
return $R->concatenateRight($T)->concatenateBottom($U->concatenateRight($V));
}
/**
* @param Observations $observations
* @return array
* @throws InvalidArgumentException
*/
public function regress(Observations $observations) : array
{
$design = new Matrix($observations->getFeatures());
$observed = (new Matrix([$observations->getOutcomes()]))->transpose();
if ($design->getRowCount() < $design->getColumnCount()) {
throw new InvalidArgumentException('Not enough observations to perform regression. You need to have more observations than explanatory variables.');
}
$designTranspose = $design->transpose();
$prediction = $designTranspose->multiplyMatrix($design)->inverse()->multiplyMatrix($designTranspose->multiplyMatrix($observed));
return $prediction->transpose()->toArray()[0];
}