/**
* 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 testInvokeProxiesToDerive()
{
$f = $this->object;
$m = new NumericMatrix([]);
$this->assertInstanceOf('Chippyash\\Math\\Matrix\\NumericMatrix', $f($m));
$this->assertEquals([[TypeFactory::createInt(2)]], $f($m)->toArray());
}
/**
* @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);
}
/**
* Convert if possible a supplied argument to a strong numeric type
*
* @param int|float|string|NumericTypeInterface $numerator
* @return Chippyash\Type\Interfaces\NumericTypeInterface
* @throws UndefinedComputationException
*/
protected function convertNumberToNumeric($value)
{
switch (gettype($value)) {
case 'integer':
return TypeFactory::createInt($value);
case 'double':
return TypeFactory::createRational($value);
case 'string':
try {
if (is_numeric($value)) {
$value = floatval($value);
}
return TypeFactory::createRational($value);
} catch (\Exception $e) {
try {
return TypeFactory::createComplex($value);
} catch (\Exception $ex) {
throw new MatrixException("The string representation of the number ('{$value}') is invalid for a complex");
}
}
case 'object':
if ($value instanceof NumericTypeInterface) {
return $value;
} else {
throw new MatrixException('NumberToNumeric expects int, float, string or Rational value');
}
case 'NULL':
return TypeFactory::createInt(0);
case 'boolean':
return TypeFactory::createInt($value ? 1 : 0);
default:
throw new MatrixException('NumberToNumeric expects int, float, string or Rational ');
}
}
public function testInvokeProxiesToCompute()
{
$this->object->expects($this->exactly(2))->method('compute')->will($this->returnValue(new NumericMatrix([[2]])));
$f = $this->object;
$m = new NumericMatrix(array());
$this->assertInstanceOf('Chippyash\\Math\\Matrix\\NumericMatrix', $f($m));
$this->assertEquals([[TypeFactory::createInt(2)]], $f($m)->toArray());
}
public function setUp()
{
RequiredType::getInstance()->set(RequiredType::TYPE_NATIVE);
$this->object = new AsciiNumeric();
$this->rationalOne = TypeFactory::createRational(TypeFactory::createInt(1), TypeFactory::createInt(1));
$this->rationalHalf = TypeFactory::createRational(TypeFactory::createInt(1), TypeFactory::createInt(2));
$this->complexTwo = TypeFactory::createComplex(TypeFactory::createRational(TypeFactory::createInt(2), TypeFactory::createInt(1)), TypeFactory::createRational(TypeFactory::createInt(0), TypeFactory::createInt(1)));
$this->complexThree = TypeFactory::createComplex(TypeFactory::createRational(TypeFactory::createInt(3), TypeFactory::createInt(1)), TypeFactory::createRational(TypeFactory::createInt(-3), TypeFactory::createInt(2)));
}
function createMatrix($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'));
}
private function toStrongType(array $values)
{
$ret = [];
foreach ($values as $r => $row) {
foreach ($row as $c => $item) {
$ret[$r][$c] = TypeFactory::createInt($item);
}
}
return $ret;
}
public function testYouCanPickTheNextLinkInAChain()
{
$chain = new NumericMatrix([[2, 0, 6, 2], [0, 0, 6, 4], [8, 1, 1, 0], [0, 5, 0, 5]]);
$res = [2 => 0, 3 => 0];
for ($x = 0; $x < 100; $x++) {
$test = $this->sut->derive($chain, TypeFactory::createInt(2));
$res[$test() - 1]++;
}
$this->assertEquals(100, array_sum($res));
}
public function testConstructGivesExpectedOutput()
{
$expected = [[TypeFactory::createInt(0), TypeFactory::createInt(-1), TypeFactory::createInt(-2)], [TypeFactory::createInt(1), TypeFactory::createInt(0), TypeFactory::createInt(-1)], [TypeFactory::createInt(2), TypeFactory::createInt(1), TypeFactory::createInt(0)]];
$this->object = new FunctionMatrix($this->function, TypeFactory::createInt(3), TypeFactory::createInt(3));
$this->assertEquals($expected, $this->object->toArray());
$this->assertTrue($this->object->is('Complete'));
$this->assertTrue($this->object->is('Square'));
$this->assertFalse($this->object->is('Empty'));
$this->assertFalse($this->object->is('RowVector'));
$this->assertFalse($this->object->is('ColumnVector'));
}
/**
* 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));
}
/**
* ShiftMatrix constructor.
*
* @param IntType $size Number of required rows and columns
* @param StringType $shiftType SM_TYPE_UPPER|SM_TYPE_LOWER
* @param IntType|null $identityType Type of identity entries: default == IdentityType::IDM_TYPE_INT
*
*/
public function __construct(IntType $size, StringType $shiftType, IntType $identityType = null)
{
$mA = (new Identity())->create([$size()]);
$new = TypeFactory::createInt(0);
$fS = new Shift();
if ($shiftType() == self::SM_TYPE_UPPER) {
$mB = $fS($mA, [1, $new]);
}
if ($shiftType() == self::SM_TYPE_LOWER) {
$mB = $fS($mA, [-1, $new]);
}
parent::__construct($mB);
}
/**
* Format the matrix contents for outputting
*
* @param Matrix $mA Matrix to format
* @param array $options Options for formatter
* - attribs => Collection of VertexDescription
* - optional: edgeFunc => function($weight){return $newWeight;}
* - optional: output:string script|object default = script
*
* If output is script, return the graphviz dot file contents
* If output is object then return Fhaculty\Graph\Graph for your own
* processing via Graphp\GraphViz\GraphViz
*
* @return Graph|string
*/
public function format(Matrix $mA, array $options = array())
{
if (!$mA instanceof NumericMatrix) {
throw new \InvalidArgumentException('Matrix is not NumericMatrix');
}
return FFor::create(['mA' => $mA, 'graph' => new Graph(), 'options' => $options])->attribs(function ($options) {
$attribs = array_key_exists('attribs', $options) ? $options['attribs'] : new Collection([], 'string');
if ($attribs instanceof Collection) {
return $attribs;
}
throw new \InvalidArgumentException('options[attribs]');
})->edgeFunc(function ($options) {
$edgeFunc = array_key_exists('edgeFunc', $options) ? $options['edgeFunc'] : function ($w) {
return $w;
};
if ($edgeFunc instanceof \Closure) {
return $edgeFunc;
}
throw new \InvalidArgumentException('pptions[edgeFunc]');
})->output(function ($options) {
return array_key_exists('output', $options) ? $options['output'] : 'script';
})->vertices(function (Collection $attribs, Matrix $mA, Graph $graph) {
$vertices = [];
foreach (range(0, $mA->rows() - 1) as $idx) {
if (array_key_exists($idx, $attribs)) {
$attribute = $attribs[$idx];
$vertices[$idx + 1] = $graph->createVertex($attribute->getName());
foreach ($attribute->getAttributes() as $key => $val) {
$vertices[$idx + 1]->setAttribute($key, $val);
}
} else {
$vertices[$idx + 1] = $graph->createVertex();
}
}
return $vertices;
})->graphViz(function (Graph $graph, Matrix $mA, array $vertices, \Closure $edgeFunc, $output) {
$comp = new Comparator();
$zero = TypeFactory::createInt(0);
$rows = $mA->rows();
for ($row = 1; $row <= $rows; $row++) {
for ($col = 1; $col <= $rows; $col++) {
if ($comp->compare($zero, $mA->get($row, $col)) != 0) {
$vertices[$row]->createEdgeTo($vertices[$col])->setWeight($edgeFunc($mA->get($row, $col)->get()));
}
}
}
return $output == 'script' ? (new GraphViz())->createScript($graph) : $graph;
})->fyield('graphViz');
}
/**
* @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);
}
/**
* @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));
}
/**
* Construct a Matrix with all entries set to IntType(0)
*
* @param NumericTypeInterface $rows Number of required rows
* @param NumericTypeInterface $cols Number of required columns
*
* @throws \InvalidArgumentException
*/
public function __construct(NumericTypeInterface $rows, NumericTypeInterface $cols)
{
$comp = new Comparator();
$one = TypeFactory::createInt(1);
if ($comp->lt($rows, $one)) {
throw new \InvalidArgumentException('$rows must be >= 1');
}
if ($comp->lt($cols, $one)) {
throw new \InvalidArgumentException('$cols must be >= 1');
}
$f = function ($row, $col) {
return TypeFactory::createInt(0);
};
parent::__construct($f, $rows, $cols);
}
/**
* 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');
}
}
/**
* @param RationalType $radius
* @param RationalType $sin
*
* @return array
*
* @throws InvalidTypeException
*/
private static function getImaginaryPartsFromRadiusAndSin(RationalType $radius, RationalType $sin)
{
return array(TypeFactory::create('int', $radius->numerator()->get() * $sin->numerator()->get()), TypeFactory::create('int', $radius->denominator()->get() * $sin->denominator()->get()));
}
public function testYouCanPlaceALimitOnTheWalk()
{
$chain = new NumericMatrix($this->chainData());
$res = $this->sut->transform($chain, array('start' => TypeFactory::createInt(4), 'target' => TypeFactory::createInt(2), 'limit' => TypeFactory::createInt(2)));
$this->assertEquals(2, $res->columns());
$this->assertEquals(1, $res->rows());
}
/**
* @expectedException InvalidArgumentException
* @expectedExceptionMessage $cols must be >= 1
*/
public function testConstructingWithColsLessThanOneThrowsException()
{
$zero = TypeFactory::createInt(0);
$one = TypeFactory::createInt(1);
new ZeroMatrix($one, $zero);
}
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]];
}
public function testSetNumberTypeToDefaultWillSetGmpIfAvailable()
{
RequiredType::getInstance()->set(RequiredType::TYPE_DEFAULT);
$this->assertInstanceOf('Chippyash\\Type\\Number\\Rational\\GMPRationalType', TypeFactory::create('rational', 2));
}
/**
* Create and return a Numeric Identity Matrix with IntType entries
*
* @param \Chippyash\Type\Number\IntType $size
* @return \Chippyash\Math\Matrix\NumericMatrix
*/
public static function numericIdentity(IntType $size)
{
return new self($size, TypeFactory::createInt(self::IDM_TYPE_INT));
}
/**
* @requires extension gmp
* @runInSeparateProcess
*/
public function testCreatingFloatsViaTypeFactoryUnderGmpWillReturnGMPRationalType()
{
RequiredType::getInstance()->set(RequiredType::TYPE_GMP);
$this->assertInstanceOf('Chippyash\\Type\\Number\\Rational\\GMPRationalType', TypeFactory::create('float', 2 / 3));
}
/**
* Return number as a FloatType number.
*
* @return \Chippyash\Type\Number\FloatType
* @throws NotRealComplexException
*/
public function asFloatType()
{
if ($this->isReal()) {
return TypeFactory::create('float', $this->value['real']->get());
} else {
throw new NotRealComplexException();
}
}
public function validNumerics()
{
return [[2], [2.5], ['12.45'], ['2/5'], [true], [false], ['2+3i'], [TypeFactory::createComplex(2)], [TypeFactory::createInt(2)], [TypeFactory::createFloat(2)], [TypeFactory::createRational(2)], [null]];
}
} else {
echo "{$op}({$tA}({$p1})) = {$tR}({$res})" . PHP_EOL;
}
} catch (InvalidTypeException $e) {
$msg = $e->getMessage();
echo "{$tA}({$p1}) {$op} {$tB}({$p2}) is invalid: {$msg}" . PHP_EOL;
}
}
$iphp = 19;
$fphp = 13.27;
$i = F::create('int', 6);
$w = F::create('whole', 21);
$n = F::create('natural', 13);
$f = F::create('float', 2.26);
$r = F::Create('rational', '2/3');
$c = F::create('complex', '2+6i');
$items = [$iphp, $i, $w, $n, $fphp, $f, $r, $c];
echo "Library supported arithmetic operations and return types\n";
echo "Non complex numbers\n";
echo "Addition\n\n";
foreach ($items as $a) {
foreach ($items as $b) {
display('add', $a, $b);
}
}
echo "\nSubtraction\n\n";
foreach ($items as $a) {
foreach ($items as $b) {
display('sub', $a, $b);
}
}
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)]];
}
* we get into an overflow situation.
*
* Setting tolerance to a lower number, say 1e-6, will compute faster but at the
* expense of accuracy
*/
RationalTypeFactory::setDefaultFromFloatTolerance(1.0E-15);
/**
* Set the required number type. System will automatically use GMP if
* it is available. You can force it to use native PHP thus:
*/
RequiredType::getInstance()->set(RequiredType::TYPE_NATIVE);
//now create 10000 numbers for the test
//try playing with this figure to see the results
$numbers = [];
for ($x = 1; $x < 10001; $x++) {
$numbers[$x] = TypeFactory::create('int', $x);
}
//create primes
$primes = [];
$start = microtime(true);
foreach ($numbers as $key => $number) {
$primes[$key] = $number->primeFactors();
}
$end = microtime(true);
$time = $end - $start;
echo "{$time} secs.\n";
echo "And the results were:\n";
foreach ($primes as $key => $res) {
$p = array_keys($res);
$e = array_values($res);
$factors = "{$key}=>";
/**
* Exception to non commutative rule
*/
public function testMultiplicationByAnIdentityMatrixIsCommmutative()
{
$mA = $this->square;
$mB = new IdentityMatrix(TypeFactory::createInt($mA->rows()));
$this->assertEquals($this->object->compute($mA, $mB), $this->object->compute($mB, $mA));
}