/**
* Convert if possible a supplied argument to a rational
*
* @param int|float|string|NumericTypeInterface $value
*
* @return \Chippyash\Math\Matrix\RationalNumber
*
* @throws \Chippyash\Matrix\Exceptions\MatrixException
* @throws \Exception
*/
protected function convertNumberToRational($value)
{
if ($value instanceof NumericTypeInterface) {
return $value->asRational();
}
switch (gettype($value)) {
case 'integer':
return RationalTypeFactory::create($value, 1);
case 'double':
return RationalTypeFactory::fromFloat($value);
case 'string':
try {
return RationalTypeFactory::fromString($value);
} catch (\Exception $e) {
try {
return ComplexTypeFactory::fromString($value)->asRational();
} catch (\Exception $ex) {
throw new MatrixException('The string representation of the number is invalid for a rational');
}
}
case 'NULL':
return RationalTypeFactory::create(0, 1);
case 'boolean':
return RationalTypeFactory::create($value ? 1 : 0, 1);
default:
throw new MatrixException('Rational expects int, float, string, Rational or NumericTypeInterface ');
}
}
public function testComputeReturnsCorrectResult()
{
$testArray = [[1, 2, 3], [3, 2, 1], [2, 1, 3]];
$expectedArray = [[RationalTypeFactory::create(3), RationalTypeFactory::create(4), RationalTypeFactory::create(5)], [RationalTypeFactory::create(5), RationalTypeFactory::create(4), RationalTypeFactory::create(3)], [RationalTypeFactory::create(4), RationalTypeFactory::create(3), RationalTypeFactory::create(5)]];
$object = new RationalMatrix($testArray);
$computation = new \Chippyash\Math\Matrix\Computation\Add\Scalar();
$this->assertEquals($expectedArray, $object->compute($computation, 2)->toArray());
}
/**
* Construct a complete Matrix with all entries set to a complex number
* Takes a source matrix or array (which can be incomplete and converts each
* entry to complex number type, setting a default value if entry does not exist.
*
* If a Matrix is supplied as $source, the data is cloned into the ComplexMatrix
* converting to complex number values, with no further checks, although you
* may get exceptions thrown if conversion is not possible.
*
* If you don't supply a default value, then 0+0i will be used
*
* @param Matrix|array $source Array to initialise the matrix with
* @param ComplexType $normalizeDefault Value to set missing vertices
*
*/
public function __construct($source, ComplexType $normalizeDefault = null)
{
if (is_null($normalizeDefault)) {
$ri = RationalTypeFactory::create(0, 1);
$normalizeDefault = ComplexTypeFactory::create($ri, clone $ri);
}
parent::__construct($source, $normalizeDefault);
}
function createMatrix($size)
{
$c = 0;
$fn = function ($r, $c) use(&$c) {
return RationalTypeFactory::create($c++, 1);
};
$iSize = TypeFactory::createInt($size);
return MatrixFactory::createFromFunction($fn, $iSize, $iSize, new StringType('rational'));
}
/**
* Create a new scalar based on type of original matrix
*
* @param \Chippyash\Math\Matrix\NumericMatrix $originalMatrix
* @param scalar $scalar
* @return Chippyash\Type\Interfaces\NumericTypeInterface
*
*/
protected function createCorrectScalarType(NumericMatrix $originalMatrix, $scalar)
{
if ($scalar instanceof NumericTypeInterface) {
if ($originalMatrix instanceof RationalMatrix) {
return $scalar->asRational();
}
if ($originalMatrix instanceof ComplexMatrix) {
return $scalar->asComplex();
}
return $scalar;
}
if ($originalMatrix instanceof ComplexMatrix) {
if (is_numeric($scalar)) {
return ComplexTypeFactory::create($scalar, 0);
}
if (is_string($scalar)) {
try {
return RationalTypeFactory::create($scalar)->asComplex();
} catch (\Exception $e) {
//do nothing
}
}
if (is_bool($scalar)) {
return ComplexTypeFactory::create($scalar ? 1 : 0, 0);
}
return ComplexTypeFactory::create($scalar);
}
if ($originalMatrix instanceof RationalMatrix) {
if (is_bool($scalar)) {
$scalar = $scalar ? 1 : 0;
}
return RationalTypeFactory::create($scalar);
}
//handling for NumericMatrix
if (is_int($scalar)) {
return TypeFactory::createInt($scalar);
} elseif (is_float($scalar)) {
return TypeFactory::createRational($scalar);
} elseif (is_bool($scalar)) {
return TypeFactory::createInt($scalar ? 1 : 0);
} elseif (is_string($scalar)) {
try {
return TypeFactory::createRational($scalar);
} catch (\InvalidArgumentException $e) {
try {
return ComplexTypeFactory::create($scalar);
} catch (\InvalidArgumentException $e) {
//do nothing
}
}
}
throw new ComputationException('Scalar parameter is not a supported type for numeric matrices: ' . getType($scalar));
}
/**
* @dataProvider luData
*
*/
public function testDecomposeReturnsCorrectResult($source, $LUD, $LD, $UD, $pivotVectorD, $permutationMatrixD, $det)
{
$mA = new RationalMatrix($source);
$LU = new RationalMatrix($LUD);
$L = new RationalMatrix($LD);
$U = new RationalMatrix($UD);
$pivotVector = new RationalMatrix($pivotVectorD);
$permutationMatrix = new RationalMatrix($permutationMatrixD);
$decomp = $this->object->decompose($mA);
// var_dump($decomp->Det);return;
$this->assertEquals($LU, $this->object->LU, 'LU matrix incorrect');
$this->assertEquals($L, $this->object->L, 'L matrix incorrect');
$this->assertEquals($U, $this->object->U, 'U matrix incorrect');
$this->assertEquals($pivotVector, $this->object->PivotVector, 'PivotVector matrix incorrect');
$this->assertEquals($permutationMatrix, $this->object->PermutationMatrix, 'Permutation matrix incorrect');
$det = is_null($det) ? null : RTF::create($det);
$this->assertEquals($det, $this->object->Det, 'Determinant incorrect');
}
/**
* Construct a square NumericMatrix whose entries on the diagonal == 1, 1/1 or 1+0i
* All other entries == 0, 0/1 or 0+0i
*
* @param IntType $size Number of required rows and columns
* @param IntType $identityType Type of identity entries: default == IDM_TYPE_INT
*
* @throws \InvalidArgumentException
*/
public function __construct(IntType $size, IntType $identityType = null)
{
if (is_null($identityType)) {
$idt = self::IDM_TYPE_INT;
} else {
$idt = $identityType();
}
if (!in_array($idt, $this->availableTypes)) {
throw new \InvalidArgumentException('Identity type invalid');
}
if ($size() < 1) {
throw new \InvalidArgumentException('size must be >= 1');
}
$f = function ($row, $col) use($idt) {
if ($idt == self::IDM_TYPE_RATIONAL) {
return RationalTypeFactory::create($row == $col ? 1 : 0, 1);
} elseif ($idt == self::IDM_TYPE_COMPLEX) {
return ComplexTypeFactory::create(RationalTypeFactory::create($row == $col ? 1 : 0, 1), RationalTypeFactory::create(0, 1));
} else {
return TypeFactory::createInt($row == $col ? 1 : 0);
}
};
parent::__construct($f, $size, $size);
}
public function testCreateRationalMatrixWithRationalTypeEntriesReturnsRationalMatrix()
{
$data = [[RF::create(1, -3), RF::create(-4, 6), RF::create(12, 3)]];
$this->assertInstanceOf('Chippyash\\Math\\Matrix\\RationalMatrix', MatrixFactory::createRational($data));
}
public function nonComplexNumbers()
{
return [[RationalTypeFactory::create(2, 5)]];
}
/**
* Return the modulus, also known as absolute value or magnitude of this number
* = sqrt(r^2 + i^2);
*
* @return \Chippyash\Type\Number\Rational\GMPRationalType
*/
public function modulus()
{
if ($this->isReal()) {
//sqrt(r^2 + 0^2) = sqrt(r^2) = abs(r)
/** @noinspection PhpUndefinedMethodInspection */
return $this->value['real']->abs();
}
//get r^2 and i^2
$sqrR = array('n' => gmp_pow($this->value['real']->numerator()->gmp(), 2), 'd' => gmp_pow($this->value['real']->denominator()->gmp(), 2));
$sqrI = array('n' => gmp_pow($this->value['imaginary']->numerator()->gmp(), 2), 'd' => gmp_pow($this->value['imaginary']->denominator()->gmp(), 2));
//r^2 + i^2
$den = $this->lcm($sqrR['d'], $sqrI['d']);
$numRaw = gmp_strval(gmp_add(gmp_div_q(gmp_mul($sqrR['n'], $den), $sqrR['d']), gmp_div_q(gmp_mul($sqrI['n'], $den), $sqrI['d'])));
$num = TypeFactory::createInt($numRaw);
//sqrt(num/den) = sqrt(num)/sqrt(den)
//now this a fudge - we ought to be able to get a proper square root using
//factors etc but what we do instead is to do an approximation by converting
//to intermediate rationals using as much precision as we can i.e.
// rNum = GMPRationaType(sqrt(num))
// rDen = GMPRationalType(sqrt(den))
// mod = rN/1 * 1/rD
$rNum = RationalTypeFactory::fromFloat(sqrt($num()));
$rDen = RationalTypeFactory::fromFloat(sqrt(gmp_strval($den)));
$modN = gmp_mul($rNum->numerator()->gmp(), $rDen->denominator()->gmp());
$modD = gmp_mul($rNum->denominator()->gmp(), $rDen->numerator()->gmp());
return RationalTypeFactory::create((int) gmp_strval($modN), (int) gmp_strval($modD));
}
public function computeMatrices()
{
//set required type as data is generated before tests
RequiredType::getInstance()->set(RequiredType::TYPE_NATIVE);
return [[[[1, 2, 3], [3, 2, 1], [2, 1, 3]], [[TypeFactory::createInt(2), TypeFactory::createInt(4), TypeFactory::createInt(6)], [TypeFactory::createInt(6), TypeFactory::createInt(4), TypeFactory::createInt(2)], [TypeFactory::createInt(4), TypeFactory::createInt(2), TypeFactory::createInt(6)]], 2], [[[1, 2, 3]], [[RationalTypeFactory::create(2.5), RationalTypeFactory::create(5.0), RationalTypeFactory::create(7.5)]], 2.5], [[[1.5, 2.5, 3.5]], [[RationalTypeFactory::create(3.0), RationalTypeFactory::create(5.0), RationalTypeFactory::create(7.0)]], 2], [[[1.12, 2.12, 3.12]], [[RationalTypeFactory::create(1.12), RationalTypeFactory::create(2.12), RationalTypeFactory::create(3.12)]], 1.0], [[[1, 2, 3]], [[TypeFactory::createInt(1), TypeFactory::createInt(2), TypeFactory::createInt(3)]], true], [[[1, 2, 3]], [[TypeFactory::createInt(0), TypeFactory::createInt(0), TypeFactory::createInt(0)]], false], [[[true, false]], [[TypeFactory::createInt(1), TypeFactory::createInt(0)]], true], [[[true, false]], [[TypeFactory::createInt(0), TypeFactory::createInt(0)]], false]];
}
/**
* @expectedException Chippyash\Type\Exceptions\InvalidTypeException
* @expectedExceptionMessage Invalid Type: integer:object for Rational type construction
*/
public function testCreateFromUnsupportedTypeForDenominatorThrowsException()
{
RationalTypeFactory::create(2, new \stdClass());
}
public function correctResults()
{
//set required type as data created before tests are run
RequiredType::getInstance()->set(RequiredType::TYPE_NATIVE);
return [[1, 2, new IntType(3)], [new IntType(1), 2, new IntType(3)], [1, new IntType(2), new IntType(3)], [new IntType(1), new IntType(2), new IntType(3)], [2.0, 3.0, new FloatType(5.0)], [new FloatType(2.0), 3.0, new FloatType(5.0)], [2.0, new FloatType(3.0), new FloatType(5.0)], [new FloatType(2.0), new FloatType(3.0), new FloatType(5.0)], [new IntType(2), 3.0, new FloatType(5.0)], [new WholeIntType(2), 3, new WholeIntType(5)], [2, new WholeIntType(3), new WholeIntType(5)], [new NaturalIntType(2), 3, new NaturalIntType(5)], [2, new NaturalIntType(3), new NaturalIntType(5)], [RationalTypeFactory::create(4), RationalTypeFactory::create(4), RationalTypeFactory::create(8)]];
}
public function mixedMatrices()
{
return [[[[1, 2, 3]], TypeFactory::createInt(6)], [[[1], [2], [3]], TypeFactory::createInt(6)], [[[1, 2, 3], [1, 2, 3]], TypeFactory::createInt(12)], [[[1.1, 2, 3], [1, 2.2, 3]], RationalTypeFactory::fromFloat(12.3)], [[[0.5, 0.5]], RationalTypeFactory::create(1)]];
}
public function testCanComputeRootsUsingPow()
{
$this->assertEquals(3, $this->object->pow(new IntType(27), RationalTypeFactory::create(1, 3))->get());
$this->assertEquals('3/4', (string) $this->object->pow(RationalTypeFactory::create(27, 64), RationalTypeFactory::create(1, 3)));
$this->assertEquals('32479891/17872077+17872077/32479891i', (string) $this->object->pow(ComplexTypeFactory::fromString('3+2i'), RationalTypeFactory::create(1, 2)));
}
/**
* Create and return a rational number matrix
* $data elements are either:
* - a RationalType
* - string representations of rational number
* - a PHP float
* - a 2 item array representing numerator & denominator e.g. [2,-4] = '-2/4'
*
* @param array $data
*
* @return \Chippyash\Math\Matrix\RationalMatrix
*
* @throws \Chippyash\Math\Matrix\Exceptions\MathMatrixException
*/
public static function createRational(array $data)
{
foreach ($data as &$row) {
foreach ($row as &$item) {
if (!$item instanceof RationalType) {
if (is_array($item) && count($item) == 2) {
$item = RationalTypeFactory::create($item[0], $item[1]);
} elseif (is_string($item)) {
try {
$item = RationalTypeFactory::fromString($item);
} catch (\InvalidArgumentException $e) {
throw new MathMatrixException('Invalid item type for Rational Matrix');
}
} elseif (is_float($item)) {
$item = RationalTypeFactory::fromFloat($item);
} else {
throw new MathMatrixException('Invalid item type for Rational Matrix');
}
}
}
}
return new RationalMatrix($data);
}
public function testSqrtRationalTypeReturnsRationalType()
{
$res = $this->object->sqrt(RationalTypeFactory::create(7));
$this->assertInstanceOf('\\Chippyash\\Type\\Number\\Rational\\RationalType', $res);
$this->assertEquals('46256493/17483311', (string) $res);
}
/**
* Complex sqrt
*
* @param ComplexType $a operand
*
* @return ComplexType
*/
public function complexSqrt(ComplexType $a)
{
return $this->complexPow($a, RationalTypeFactory::create(1, 2));
}
public function nonComplexNumbers()
{
return [[2], [-2.4], [new FloatType(2)], [new FloatType(2.6)], [RationalTypeFactory::create(1, 5)], [new WholeIntType(3)], [new NaturalIntType(6)]];
}
/**
* Convert to RationalType
*
* @param mixed $original
*
* @return \Chippyash\Type\Number\Rational\RationalType|\Chippyash\Type\Number\Rational\GMPRationalType
*
* @throws InvalidTypeException
*/
protected static function convertType($original)
{
if ($original instanceof AbstractRationalType) {
return RationalTypeFactory::create($original->numerator()->get(), $original->denominator()->get());
}
if (is_numeric($original)) {
if (is_int($original)) {
return RationalTypeFactory::create($original, 1);
}
//default - convert to float
return RationalTypeFactory::fromFloat(floatval($original));
}
if ($original instanceof FloatType) {
return RationalTypeFactory::fromFloat($original());
}
if ($original instanceof IntType) {
return RationalTypeFactory::create($original, 1);
}
if (is_string($original)) {
try {
return RationalTypeFactory::fromString($original);
} catch (\InvalidArgumentException $e) {
throw new InvalidTypeException("{$original} for Complex type construction");
}
}
$type = gettype($original);
throw new InvalidTypeException("{$type} for Complex type construction");
}
/**
* Return the modulus, also known as absolute value or magnitude of this number
* = sqrt(r^2 + i^2);
*
* @return \Chippyash\Type\Number\Rational\RationalType
*/
public function modulus()
{
if ($this->isReal()) {
//sqrt(r^2 + 0^2) = sqrt(r^2) = abs(r)
/** @noinspection PhpUndefinedMethodInspection */
return $this->value['real']->abs();
}
//r^2 & i^2
$sqrR = array('n' => pow($this->value['real']->numerator()->get(), 2), 'd' => pow($this->value['real']->denominator()->get(), 2));
$sqrI = array('n' => pow($this->value['imaginary']->numerator()->get(), 2), 'd' => pow($this->value['imaginary']->denominator()->get(), 2));
//r^2 + i^2
$den = $this->lcm($sqrR['d'], $sqrI['d']);
$num = $sqrR['n'] * $den / $sqrR['d'] + $sqrI['n'] * $den / $sqrI['d'];
//sqrt(num/den) = sqrt(num)/sqrt(den)
//now this a fudge - we ought to be able to get a proper square root using
//factors etc but what we do instead is to do an approximation by converting
//to intermediate rationals i.e.
// rNum = RationaType(sqrt(num))
// rDen = RationalType(sqrt(den))
// mod = rN/1 * 1/rD
$rNum = RationalTypeFactory::fromFloat(sqrt($num));
$rDen = RationalTypeFactory::fromFloat(sqrt($den));
$modN = $rNum->numerator()->get() * $rDen->denominator()->get();
$modD = $rNum->denominator()->get() * $rDen->numerator()->get();
return RationalTypeFactory::create($modN, $modD);
}
public function testReciprocalOfRationalTypeReturnsRationalType()
{
$this->assertInstanceOf('Chippyash\\Type\\Number\\Rational\\RationalType', $this->object->reciprocal(RationalTypeFactory::create(2, 1)));
}
/**
* Perform Guass Jordan Elimination on the two supplied matrices
*
* @param NumericMatrix $mA First matrix to act on - required
* @param NumericMatrix $extra Second matrix to act upon - required
*
* @return \Chippyash\Math\Matrix\DecompositionAbstractDecomposition Fluent Interface
*
* @throws \Chippyash\Math\Matrix\Exceptions\SingularMatrixException
*/
public function decompose(NumericMatrix $mA, $extra = null)
{
$this->assertParameterIsMatrix($extra, 'Parameter extra is not a matrix')->assertMatrixIsNumeric($extra, 'Parameter extra is not a numeric matrix')->assertMatrixIsSquare($mA, 'Parameter mA is not a square matrix')->assertMatrixRowsAreEqual($mA, $extra, 'mA->rows != extra->rows');
$rows = $mA->rows();
$dA = $mA->toArray();
$dB = $extra->toArray();
$zero = function () {
return RationalTypeFactory::create(0, 1);
};
$one = function () {
return RationalTypeFactory::create(1, 1);
};
$calc = new Calculator();
$comp = new Comparator();
$ipiv = array_fill(0, $rows, $zero());
$indxr = array_fill(0, $rows, 0);
$indxc = array_fill(0, $rows, 0);
// find the pivot element by searching the entire matrix for its largest value, but excluding columns already reduced.
$irow = $icol = 0;
for ($i = 0; $i < $rows; $i++) {
$big = $zero();
for ($j = 0; $j < $rows; $j++) {
if ($comp->neq($ipiv[$j], $one())) {
for ($k = 0; $k < $rows; $k++) {
if ($comp->eq($ipiv[$k], $zero())) {
$absVal = $dA[$j][$k]->abs();
if ($comp->gt($absVal, $big)) {
unset($big);
$big = clone $absVal;
$irow = $j;
$icol = $k;
}
} elseif ($comp->gt($ipiv[$k], $one())) {
throw new SingularMatrixException('GaussJordanElimination');
}
}
}
}
//Now interchange row to move the pivot element to a diagonal
$ipiv[$icol] = $calc->add($ipiv[$icol], $one());
if ($irow != $icol) {
$this->swapRows($dA, $irow, $icol);
$this->swapRows($dB, $irow, $icol);
}
// Remember permutations to later
$indxr[$i] = $irow;
$indxc[$i] = $icol;
if ($comp->eq($dA[$icol][$icol], $zero())) {
throw new SingularMatrixException('GaussJordanElimination');
}
// Now divide the found row to make the pivot element 1
// To maintain arithmetic integrity we use the reciprocal to multiply by
$pivinv = $calc->reciprocal($dA[$icol][$icol]);
$this->multRow($dA, $icol, $pivinv, $calc);
$this->multRow($dB, $icol, $pivinv, $calc);
// And reduce all other rows but the pivoted row with the value of the pivot row
for ($ll = 0; $ll < $rows; $ll++) {
if ($ll != $icol) {
$multiplier = clone $dA[$ll][$icol];
$multiplier->negate();
$this->addMultipleOfOtherRowToRow($dA, $multiplier, $icol, $ll, $calc);
$this->addMultipleOfOtherRowToRow($dB, $multiplier, $icol, $ll, $calc);
}
}
}
$this->set('left', $this->createCorrectMatrixType($mA, $dA));
$this->set('right', $this->createCorrectMatrixType($extra, $dB));
return clone $this;
}
/**
* Create a Rational number
* @see RationalTypeFactory::create
*
* @param int|string|float $numerator
* @param int $denominator
*
* @return \Chippyash\Type\Number\Rational\RationalType
*/
public static function createRational($numerator, $denominator = 1)
{
return RationalTypeFactory::create($numerator, $denominator);
}
