/**
* @inheritDoc
*/
public function derive(NumericMatrix $mA, $extra = null)
{
if ($mA->is('empty')) {
return TypeFactory::createInt(0);
}
if ($mA->is('singleitem')) {
return $mA->get(1, 1);
}
$calc = new Calculator();
return array_reduce($mA->toArray(), function ($c1, $row) use($calc) {
return array_reduce($row, function ($carry, $item) use($calc) {
return $calc->add($item, $carry);
}, $c1);
}, TypeFactory::createInt(0));
}
/**
* Find tr(M)
*
* @param NumericMatrix $mA
* @param mixed $extra
* @return numeric
*
* @throws Chippyash/Math/Matrix/Exceptions/UndefinedComputationException
*/
public function derive(NumericMatrix $mA, $extra = null)
{
if ($mA->is('singleitem')) {
return $mA->get(1, 1);
}
$this->assertMatrixIsNotEmpty($mA, 'No trace for empty matrix')->assertMatrixIsSquare($mA, 'No trace for non-square matrix');
$tr = new FloatType(0);
$size = $mA->rows();
$data = $mA->toArray();
$calc = new Calculator();
for ($x = 0; $x < $size; $x++) {
$tr = $calc->add($tr, $data[$x][$x]);
}
return $tr;
}
/**
* Add single scalar value to each member of the matrix and return result
*
* @param NumericMatrix $mA First matrix to act on - required
* @param scalar $extra value to add
*
* @return NumericMatrix|RationalMatrix|ComplexMatrix
*
* @throws Chippyash/Matrix/Exceptions/ComputationException
*/
public function compute(NumericMatrix $mA, $extra = null)
{
if ($mA->is('empty')) {
return $this->createCorrectMatrixType($mA);
}
$scalar = $this->createCorrectScalarType($mA, $extra);
$data = $mA->toArray();
$m = $mA->rows();
$n = $mA->columns();
$calc = new Calculator();
for ($row = 0; $row < $m; $row++) {
for ($col = 0; $col < $n; $col++) {
$data[$row][$col] = $calc->add($data[$row][$col], $scalar);
}
}
return $this->createCorrectMatrixType($mA, $data);
}
/**
* Carry out the actual multiplication using standard matrix multiplication
* method.
*
* @param \Chippyash\Math\Matrix\NumericMatrix $mA
* @param \Chippyash\Math\Matrix\NumericMatrix $mB
* @return array
* @throws ComputationException
*/
protected function doComputation(NumericMatrix $mA, NumericMatrix $mB)
{
$size = max([$mA->columns(), $mA->rows(), $mB->columns(), $mB->rows()]);
$product = (new ZMatrix())->create([$size, $size])->toArray();
$dA = $mA->toArray();
$dB = $mB->toArray();
$zero = $this->createCorrectScalarType($mA, 0);
$calc = new Calculator();
for ($i = 0; $i < $size; $i++) {
for ($k = 0; $k < $size; $k++) {
for ($j = 0; $j < $size; $j++) {
$a = isset($dA[$i][$k]) ? $dA[$i][$k] : $zero;
$b = isset($dB[$k][$j]) ? $dB[$k][$j] : $zero;
$product[$i][$j] = $calc->add($product[$i][$j], $calc->mul($a, $b));
}
}
}
return $product;
}
/**
* Inter row multiplication
*
* @param array $a
* @param NumericTypeInterface $multiple
* @param int $rowToMultiplyWith
* @param int $rowToAddTo
* @param \Chippyash\Math\Type\Calculator $calc
*/
protected function addMultipleOfOtherRowToRow(array &$a, $multiple, $rowToMultiplyWith, $rowToAddTo, Calculator $calc)
{
$numberOfColumns = count($a[0]);
for ($l = 0; $l < $numberOfColumns; $l++) {
$a[$rowToAddTo][$l] = $calc->add($a[$rowToAddTo][$l], $calc->mul($a[$rowToMultiplyWith][$l], $multiple));
}
}
/**
* @inheritDoc
*/
protected function doCompute(NumericTypeInterface $a, NumericTypeInterface $b, Calculator $calc)
{
return $calc->add($a, $b);
}
/**
* LU Decomposition constructor.
*
* @param \Chippyash\Math\Matrix\NumericMatrix $mA
*/
protected function LUDecomposition(NumericMatrix $mA)
{
// Use a "left-looking", dot-product, Crout/Doolittle algorithm.
$LU = $mA->toArray();
$m = $this->rows = $mA->rows();
$n = $this->cols = $mA->columns();
for ($i = 0; $i < $m; $i++) {
$this->piv[$i] = $i;
}
$this->pivsign = 1;
$LUrowi = [];
$LUcolj = [];
$calc = new Calculator();
$comp = new Comparator();
$zeroInt = $this->createCorrectScalarType($mA, 0);
// Outer loop.
for ($j = 0; $j < $n; $j++) {
// Make a copy of the j-th column to localize references.
for ($i = 0; $i < $m; $i++) {
$LUcolj[$i] =& $LU[$i][$j];
}
// Apply previous transformations.
for ($i = 0; $i < $m; $i++) {
$LUrowi = $LU[$i];
// Most of the time is spent in the following dot product.
$kmax = min($i, $j);
$s = clone $zeroInt;
for ($k = 0; $k < $kmax; $k++) {
$s = $calc->add($s, $calc->mul($LUrowi[$k], $LUcolj[$k]));
}
$LUcolj[$i] = $calc->sub($LUcolj[$i], $s);
$LUrowi[$j] = $LUcolj[$i];
}
// Find pivot and exchange if necessary.
$p = $j;
for ($i = $j + 1; $i < $m; $i++) {
if ($comp->gt($LUcolj[$i]->abs(), $LUcolj[$p]->abs())) {
$p = $i;
}
}
if ($p != $j) {
for ($k = 0; $k < $n; $k++) {
//swap
$t = $LU[$p][$k];
$LU[$p][$k] = $LU[$j][$k];
$LU[$j][$k] = $t;
}
$k = $this->piv[$p];
$this->piv[$p] = $this->piv[$j];
$this->piv[$j] = $k;
$this->pivsign = $this->pivsign * -1;
}
// Compute multipliers.
if ($j < $m && $comp->neq($LU[$j][$j], $zeroInt)) {
for ($i = $j + 1; $i < $m; $i++) {
$LU[$i][$j] = $calc->div($LU[$i][$j], $LU[$j][$j]);
}
}
}
$this->set('LU', $this->createCorrectMatrixType($mA, $LU));
}
