/**
* @inheritDoc
*/
protected function doCompute(NumericTypeInterface $a, NumericTypeInterface $b, Calculator $calc)
{
if ($this->getComparator()->compare($b, TypeFactory::createInt(0)) === 0) {
return null;
}
return $calc->div($a, $b);
}
/**
* @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));
}
/**
* @param NumericMatrix $mA
* @param NumericTypeInterface $start
* @param NumericTypeInterface $target
* @param NumericTypeInterface $limit
*
* @return NumericMatrix
*/
protected function walk(NumericMatrix $mA, NumericTypeInterface $start, NumericTypeInterface $target, NumericTypeInterface $limit)
{
$zero = TypeFactory::createInt(0);
$one = TypeFactory::createInt(1);
$calc = new Calculator();
$comp = new Comparator();
$lim = $calc->sub($limit, $one);
$walk = [$start];
while ($comp->neq($start, $target) && $comp->neq($lim, $zero)) {
$start = $mA('MarkovWeightedRandom', $start);
$walk[] = $start;
$lim = $calc->sub($lim, $one);
}
return new NumericMatrix($walk);
}
/**
* 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;
}
/**
* Multiply each member of the matrix by single scalar value and return result
* Boolean values are converted to 0 (false) and 1 (true). Use the logical
* computations if required.
* String values must conform to the requirements of a rational string number
* i.e. '2/3', else an exception will be thrown
*
* @param Matrix $mA First matrix to act on - required
* @param scalar $extra value to add
*
* @return Matrix
*
* @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();
$lx = $mA->columns();
$ly = $mA->rows();
$calc = new Calculator();
for ($row = 0; $row < $ly; $row++) {
for ($col = 0; $col < $lx; $col++) {
$data[$row][$col] = $calc->mul($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;
}
/**
* @param $sum
* @param $rowArray
*
* @return mixed
*
* @throws MathMatrixException
*/
protected function getNextRow($sum, $rowArray)
{
return FFor::create(['sum' => $sum, 'rowArray' => $rowArray])->targetWeight(function ($sum) {
return TypeFactory::createInt(mt_rand(1, $sum()));
})->nextRow(function ($targetWeight, $rowArray) {
foreach ($rowArray as $key => $weight) {
if ($this->comp->lt($weight, $this->zero)) {
throw new MathMatrixException('Negative weights not allowed');
}
$targetWeight = $this->calc->sub($targetWeight, $weight);
if ($this->comp->lte($targetWeight, $this->zero)) {
return TypeFactory::createInt($key + 1);
}
}
})->fyield('nextRow');
}
/**
* 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 $calc->sub($a, $b);
}
/**
* Invert the matrix
*
* $mA must be square and nonsingular.
* An empty $mA returns an empty matrix
* A single entry matrix e.g. [[n]] returns [[1/n]]
* A zero single item matrix e.g. [[0]] throws an exception (Division by zero)
*
* @param Chippyash\Math\Matrix\NumericMatrix $mA First matrix operand - required
* @param mixed $extra ignored
*
* @return Chippyash\Math\Matrix\NumericMatrix
*
* @throws Chippyash\Matrix\Exceptions\ComputationException
* @throws Chippyash\Matrix\Exceptions\UndefinedComputationException
*/
protected function doTransform(Matrix $mA, $extra = null)
{
$this->assertMatrixIsNumeric($mA);
if ($mA->is('empty')) {
return $this->createCorrectMatrixType($mA);
}
if ($mA->is('singleitem')) {
$item = $mA->get(1, 1)->get();
if ($item == 0 || $item == '0+0i') {
throw new ComputationException('Division by zero');
} else {
$calc = new Calculator();
return $this->createCorrectMatrixType($mA, [$calc->reciprocal($mA->get(1, 1))]);
}
}
$this->assertMatrixIsNonSingular($mA, 'Can only perform inversion on non singular matrix');
$I = $this->invert($mA);
return $I;
}
/**
* Set determinant of original matrix if it is square
*/
protected function setDeterminant(NumericMatrix $mA)
{
if (!$mA->is('square')) {
//determinant undefined for non square matrix
$this->set('Det', null);
return;
}
if ($mA->is('empty')) {
$this->set('Det', $this->createCorrectScalarType($mA, 1));
return;
}
$det = $this->createCorrectScalarType($mA, $this->pivsign);
$LU = $this->LU->toArray();
$calc = new Calculator();
$this->set('Det', function () use($det, $LU, $calc) {
$c = count($LU);
for ($j = 0; $j < $c; $j++) {
$det = $calc->mul($det, $LU[$j][$j]);
}
return $det;
});
}
