/**
* @dataProvider polars
*/
public function testCreateFromPolarReturnsComplexType($r, $t)
{
$radius = RationalTypeFactory::fromString($r);
$theta = RationalTypeFactory::fromString($t);
$p = ComplexTypeFactory::fromPolar($radius, $theta);
$this->assertInstanceOf(self::CTYPE_NAME, $p);
}
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());
}
/**
* 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 ');
}
}
/**
* 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);
}
public function testCreateComplexIdentityReturnsComplexMatrix()
{
$cA = IdentityMatrix::complexIdentity(TypeFactory::createInt(2));
$this->assertInstanceOf('Chippyash\\Math\\Matrix\\ComplexMatrix', $cA);
$one = ComplexTypeFactory::create(1, 0);
$zero = ComplexTypeFactory::create(0, 0);
$this->assertEquals([[$one, $zero], [$zero, $one]], $cA->toArray());
}
/**
* 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));
}
/**
* Create and return a complex number matrix
* $data elements are either:
* - a ComplexType
* - string representations of complex number
* - a 2 item array representing r & i e.g. [2,-4] = '2-4i'
*
* @param array $data
*
* @return \Chippyash\Math\Matrix\ComplexMatrix
*
* @throws \Chippyash\Math\Matrix\Exceptions\MathMatrixException
*/
public static function createComplex(array $data)
{
foreach ($data as &$row) {
foreach ($row as &$item) {
if (!$item instanceof ComplexType) {
if (is_array($item) && count($item) == 2) {
$item = ComplexTypeFactory::create($item[0], $item[1]);
} elseif (is_string($item)) {
try {
$item = ComplexTypeFactory::fromString($item);
} catch (\InvalidArgumentException $e) {
throw new MathMatrixException('Invalid item type for Complex Matrix');
}
} else {
throw new MathMatrixException('Invalid item type for Complex Matrix');
}
}
}
}
return new ComplexMatrix($data);
}
/**
* 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);
}
/**
* @dataProvider nonComplexNumbers
* @param numeric $nonComplex
*/
public function testAddNonComplexNumbersWithComplexNumberThrowsException($nonComplex)
{
$this->assertInstanceOf('Chippyash\\Type\\Number\\Complex\\ComplexType', $this->object->add($nonComplex, ComplexTypeFactory::create(1, 5)));
}
/**
* Complex number reciprocal: 1/a+bi
*
* @param ComplexType $a operand
*
* @return ComplexType
*
* @throws \BadMethodCallException
*/
public function complexReciprocal(ComplexType $a)
{
if ($a->isZero()) {
throw new \BadMethodCallException('Cannot compute reciprocal of zero complex number');
}
//div = ar^2 + ai^2
$div = $this->rationalAdd($this->rationalMul($a->r(), $a->r()), $this->rationalMul($a->i(), $a->i()));
$r = $this->rationalDiv($a->r(), $div);
$i = $this->rationalDiv($a->i(), $div);
return ComplexTypeFactory::create($r, $i);
}
public function testSingleMatrixReturnsValueOfItsSingleEntry()
{
$this->assertEquals(2, $this->object->determinant(new NumericMatrix([2]))->get());
$this->assertEquals('2/5', (string) $this->object->determinant(new RationalMatrix([RationalTypeFactory::fromString('2/5')])));
$this->assertEquals('1+3i', $this->object->determinant(new ComplexMatrix([ComplexTypeFactory::fromString('1+3i')]))->get());
}
public function testCreationWillUseGmpAutomaticallyIfItExists()
{
RequiredType::getInstance()->set(RequiredType::TYPE_DEFAULT);
$c = ComplexTypeFactory::create('2+3i');
$this->assertInstanceOf(self::CTYPE_NAME, $c);
}
public function testYouCanGetTheSignOfAComplexNumber()
{
$c1 = ComplexTypeFactory::create(1, 1);
//unreal positive
$c2 = ComplexTypeFactory::create(-1, -3);
//unreal negative
$c3 = ComplexTypeFactory::create(1, 0);
//real positive
$c4 = ComplexTypeFactory::create(-1, 0);
//real negative
$c5 = ComplexTypeFactory::create(0, 0);
//zero
$this->assertEquals(1, $c1->sign());
$this->assertEquals(1, $c2->sign());
//unreal complex use modulus for sign - therefore always positive
$this->assertEquals(1, $c3->sign());
$this->assertEquals(-1, $c4->sign());
$this->assertEquals(0, $c5->sign());
}
protected function toComplex(array $dA)
{
foreach ($dA as &$row) {
foreach ($row as &$entry) {
if ($entry instanceof NumericTypeInterface) {
$entry = $entry->asComplex();
} elseif (is_numeric($entry)) {
$entry = ComplexTypeFactory::create($entry);
} else {
$entry = $entry;
}
}
}
return new Matrix($dA);
}
public function testCreateFromComplexReturnsRationalMatrix()
{
$c = CF::fromString('2+4i');
$mA = MatrixFactory::createFromComplex($c);
$test = MatrixFactory::createRational([['2/1', '-4/1'], ['4/1', '2/1']]);
$this->assertEquals($test, $mA);
}
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)));
}
/**
* @expectedException BadMethodCallException
* @expectedExceptionMessage Cannot divide complex number by zero complex number
*/
public function testDivComplexByZeroComplexThrowsException()
{
$this->object->div(ComplexTypeFactory::create(1, 5), ComplexTypeFactory::create(0, 0));
}
public function testSqrtComplexTypeReturnsComplexType()
{
$res = $this->object->sqrt(ComplexTypeFactory::fromString('3+2i'));
$this->assertInstanceOf('\\Chippyash\\Type\\Number\\Complex\\ComplexType', $res);
$this->assertEquals('32479891/17872077+17872077/32479891i', (string) $res);
}
/**
* @expectedException BadMethodCallException
* @expectedExceptionMessage Cannot compute reciprocal of zero complex number
*/
public function testReciprocalOfZeroComplexThrowsException()
{
$this->object->reciprocal(ComplexTypeFactory::create(0, 0));
}
/**
* Create a Complex number
* If imaginary part is null, a complex equivalent real number is created r+0i
*
* @param int|float|string|NumericTypeInterface $realPart
* @param int|float|string|NumericTypeInterface|null $imaginaryPart
*
* @return \Chippyash\Type\Number\Complex\ComplexType
*/
public static function createComplex($realPart, $imaginaryPart = null)
{
return ComplexTypeFactory::create($realPart, $imaginaryPart);
}
