/**
* 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 testIntPowReturnsRationalOrIntOrComplexTypes()
{
$base = new IntType(5);
$exp = new IntType(3);
$this->assertInstanceOf('\\Chippyash\\Type\\Number\\IntType', $this->object->intPow($base, $exp));
$this->assertEquals(125, $this->object->intPow($base, $exp)->get());
$exp2 = new FloatType(3.5);
$this->assertInstanceOf('\\Chippyash\\Type\\Number\\Rational\\RationalType', $this->object->intPow($base, $exp2));
$this->assertEquals('332922571/1191100', (string) $this->object->intPow($base, $exp2));
$exp3 = RationalTypeFactory::fromFloat(3.5);
$this->assertInstanceOf('\\Chippyash\\Type\\Number\\Rational\\RationalType', $this->object->intPow($base, $exp3));
$this->assertEquals('332922571/1191100', (string) $this->object->intPow($base, $exp3));
$base2 = new IntType(4);
$exp4 = ComplexTypeFactory::fromString('5+3i');
$pow = $this->object->intPow($base2, $exp4);
$this->assertInstanceOf('\\Chippyash\\Type\\Number\\Complex\\ComplexType', $pow);
$this->assertEquals('-778299179/1445876', (string) $pow->r());
$this->assertEquals('-861158767/988584', (string) $pow->i());
$exp5 = ComplexTypeFactory::fromString('0+3i');
$pow = $this->object->intPow($base2, $exp5);
$this->assertInstanceOf('\\Chippyash\\Type\\Number\\Complex\\ComplexType', $pow);
$this->assertEquals('-1722722/3277175', (string) $pow->r());
$this->assertEquals('-20905959/24575389', (string) $pow->i());
$exp6 = ComplexTypeFactory::fromString('5+0i');
$pow = $this->object->intPow($base2, $exp6);
$this->assertInstanceOf('\\Chippyash\\Type\\Number\\Rational\\RationalType', $pow);
$this->assertEquals(1024, $pow->get());
}
public function testPowWithRationalBaseReturnsRationalType()
{
$r = RationalTypeFactory::fromFloat(2.5);
$p = $this->object->pow($r, new IntType(3));
$this->assertInstanceOf('Chippyash\\Type\\Number\\Rational\\RationalType', $p);
$this->assertEquals('125/8', (string) $p);
$p1 = $this->object->pow($r, new FloatType(3.2));
$this->assertInstanceOf('Chippyash\\Type\\Number\\Rational\\RationalType', $p1);
$this->assertEquals('9893770810229553/527173799766761', (string) $p1);
}
private function toStrongType(array $values, $expectedType)
{
$ns = '\\Chippyash\\Type\\Number\\';
$class = $ns . $expectedType;
$ret = [];
foreach ($values as $r => $row) {
foreach ($row as $c => $item) {
if ($expectedType == 'Rational\\RationalType') {
$ret[$r][$c] = RationalTypeFactory::fromFloat($item);
} else {
$ret[$r][$c] = new $class($item);
}
}
}
return $ret;
}
/**
* Construct a complete Matrix with all entries set to Chippyash/Type
* Takes a source matrix or array (which can be incomplete and converts each
* entry to Chippyash/Type), setting a default value if entry does not exist.
*
* If a NumericMatrix is supplied as $source, the data is cloned into the Matrix
* with no further checks.
*
* @param NumericMatrix|array $source Array to initialise the matrix with
* @param mixed $normalizeDefault Value to set missing vertices
* @throws \Chippyash\Math\Matrix\Exceptions\MathMatrixException
*/
public function __construct($source, $normalizeDefault = 0)
{
if ($source instanceof self) {
$this->store($source->toArray());
return;
}
if (is_array($source)) {
if (is_int($normalizeDefault)) {
$default = TypeFactory::createInt($normalizeDefault);
} elseif (is_float($normalizeDefault)) {
$default = RationalTypeFactory::fromFloat($normalizeDefault);
} elseif (!$normalizeDefault instanceof NumericTypeInterface) {
throw new MathMatrixException('NumericMatrix expects numeric default value');
} else {
$default = $normalizeDefault;
}
parent::__construct($source, false, true, $default);
} else {
throw new MathMatrixException('NumericMatrix expects NumericMatrix or array as source data');
}
}
/**
* 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);
}
/**
* 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");
}
/**
* @runInSeparateProcess
*/
public function testSetDefaultFromFloatToleranceIsStatic()
{
RationalTypeFactory::setDefaultFromFloatTolerance(1.0E-5);
$this->assertEquals('113/355', (string) RationalTypeFactory::fromFloat(M_1_PI));
RationalTypeFactory::setDefaultFromFloatTolerance(1.0E-15);
$this->assertEquals('25510582/80143857', (string) RationalTypeFactory::fromFloat(M_1_PI));
}
/**
* Return the angle (sometimes known as the argument) of the number
* when expressed in polar notation
*
* The return value is a rational expressing theta as radians
*
* @return \Chippyash\Type\Number\Rational\RationalType
*/
public function theta()
{
return RationalTypeFactory::fromFloat(atan2($this->value['imaginary']->asFloatType()->get(), $this->value['real']->asFloatType()->get()));
}
/**
* Create complex power from natural base and complex exponent
*
* @param int|float $base base
* @param ComplexType $exp exponent
*
* @return NI|ComplexType
*/
private function complexExponent($base, ComplexType $exp)
{
if ($exp->isReal()) {
return $this->rationalPow(RationalTypeFactory::fromFloat($base), $exp->r());
}
//do the imaginary part
//n^bi = cos(b.lg(n)) + i.sin(b.lg(n))
$b = $exp->i()->get();
$n = log($base);
$r = cos($b * $n);
$i = sin($b * $n);
//no real part
if ($exp->r()->get() == 0) {
return new ComplexType(RationalTypeFactory::fromFloat($r), RationalTypeFactory::fromFloat($i));
}
//real and imaginary part
//n^a+bi = n^a(cos(b.lg(n)) + i.sin(b.lg(n)))
$na = pow($base, $exp->r()->get());
$rr = $na * $r;
$ii = $na * $i;
return new ComplexType(RationalTypeFactory::fromFloat($rr), RationalTypeFactory::fromFloat($ii));
}
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 testMagicInvokeReturnsFloatForRealFloatComplexNumber()
{
$c = new ComplexType(RationalTypeFactory::fromFloat(2.5), $this->createRationalType(0));
$this->assertInternalType('float', $c());
$this->assertEquals(2.5, $c());
}
protected function toRational(array $dA)
{
foreach ($dA as &$row) {
foreach ($row as &$entry) {
if ($entry instanceof NumericTypeInterface) {
$entry = $entry->asRational();
} elseif (is_numeric($entry)) {
$entry = RationalTypeFactory::fromFloat(floatval($entry));
} else {
$entry = $entry;
}
}
}
return new Matrix($dA);
}
/**
* Return number as Rational number.
* NB, numerator and denominator will be caste as IntTypes
*
* @return \Chippyash\Type\Number\Rational\RationalType
*/
public function asRational()
{
return RationalTypeFactory::fromFloat($this->value);
}
/**
* Compare int and float types
*
* @param NI $a
* @param NI $b
* @return int
*/
protected function intFloatCompare(NI $a, NI $b)
{
return $this->rationalCompare(RationalTypeFactory::fromFloat($a->asFloatType()), RationalTypeFactory::fromFloat($b->asFloatType()));
}
