/**
* transpose
*
* Tranpose matrix
* @return Matrix Transposed matrix
*/
public function transpose()
{
$R = new Matrix($this->n, $this->m);
for ($i = 0; $i < $this->m; ++$i) {
for ($j = 0; $j < $this->n; ++$j) {
$R->set($j, $i, $this->matrix[$i][$j]);
}
}
return $R;
}
/**
* Least squares solution of A*X = B
*
* @param Matrix $B A Matrix with as many rows as A and any number of columns.
* @throws MatrixException
* @return Matrix Matrix that minimizes the two norm of Q*R*X-B.
*/
public function solve($B)
{
if ($B->getRowDimension() == $this->m) {
if ($this->isFullRank()) {
// Copy right hand side
$nx = $B->getColumnDimension();
$X = $B->getArray();
// Compute Y = transpose(Q)*B
for ($k = 0; $k < $this->n; ++$k) {
for ($j = 0; $j < $nx; ++$j) {
$s = 0.0;
for ($i = $k; $i < $this->m; ++$i) {
$s += $this->QR[$i][$k] * $X[$i][$j];
}
$s = -$s / $this->QR[$k][$k];
for ($i = $k; $i < $this->m; ++$i) {
$X[$i][$j] += $s * $this->QR[$i][$k];
}
}
}
// Solve R*X = Y;
for ($k = $this->n - 1; $k >= 0; --$k) {
for ($j = 0; $j < $nx; ++$j) {
$X[$k][$j] /= $this->rD[$k];
}
for ($i = 0; $i < $k; ++$i) {
for ($j = 0; $j < $nx; ++$j) {
$X[$i][$j] -= $X[$k][$j] * $this->QR[$i][$k];
}
}
}
$X = new Matrix($X);
return $X->getMatrix(0, $this->n - 1, 0, $nx);
} else {
throw new MatrixException(5);
}
} else {
throw new MatrixException(3);
}
}