/** * 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); }