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vendor/markbaker/complex/classes/src/Complex.php

@@ -0,0 +1,388 @@
+<?php
+
+/**
+ *
+ * Class for the management of Complex numbers
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Complex Number object.
+ *
+ * @package Complex
+ *
+ * @method float abs()
+ * @method Complex acos()
+ * @method Complex acosh()
+ * @method Complex acot()
+ * @method Complex acoth()
+ * @method Complex acsc()
+ * @method Complex acsch()
+ * @method float argument()
+ * @method Complex asec()
+ * @method Complex asech()
+ * @method Complex asin()
+ * @method Complex asinh()
+ * @method Complex atan()
+ * @method Complex atanh()
+ * @method Complex conjugate()
+ * @method Complex cos()
+ * @method Complex cosh()
+ * @method Complex cot()
+ * @method Complex coth()
+ * @method Complex csc()
+ * @method Complex csch()
+ * @method Complex exp()
+ * @method Complex inverse()
+ * @method Complex ln()
+ * @method Complex log2()
+ * @method Complex log10()
+ * @method Complex negative()
+ * @method Complex pow(int|float $power)
+ * @method float rho()
+ * @method Complex sec()
+ * @method Complex sech()
+ * @method Complex sin()
+ * @method Complex sinh()
+ * @method Complex sqrt()
+ * @method Complex tan()
+ * @method Complex tanh()
+ * @method float theta()
+ * @method Complex add(...$complexValues)
+ * @method Complex subtract(...$complexValues)
+ * @method Complex multiply(...$complexValues)
+ * @method Complex divideby(...$complexValues)
+ * @method Complex divideinto(...$complexValues)
+ */
+class Complex
+{
+    /**
+     * @constant    Euler's Number.
+     */
+    const EULER = 2.7182818284590452353602874713526624977572;
+
+    /**
+     * @constant    Regexp to split an input string into real and imaginary components and suffix
+     */
+    const NUMBER_SPLIT_REGEXP =
+        '` ^
+            (                                   # Real part
+                [-+]?(\d+\.?\d*|\d*\.?\d+)          # Real value (integer or float)
+                ([Ee][-+]?[0-2]?\d{1,3})?           # Optional real exponent for scientific format
+            )
+            (                                   # Imaginary part
+                [-+]?(\d+\.?\d*|\d*\.?\d+)          # Imaginary value (integer or float)
+                ([Ee][-+]?[0-2]?\d{1,3})?           # Optional imaginary exponent for scientific format
+            )?
+            (                                   # Imaginary part is optional
+                ([-+]?)                             # Imaginary (implicit 1 or -1) only
+                ([ij]?)                             # Imaginary i or j - depending on whether mathematical or engineering
+            )
+        $`uix';
+
+    /**
+     * @var    float    $realPart    The value of of this complex number on the real plane.
+     */
+    protected $realPart = 0.0;
+
+    /**
+     * @var    float    $imaginaryPart    The value of of this complex number on the imaginary plane.
+     */
+    protected $imaginaryPart = 0.0;
+
+    /**
+     * @var    string    $suffix    The suffix for this complex number (i or j).
+     */
+    protected $suffix;
+
+
+    /**
+     * Validates whether the argument is a valid complex number, converting scalar or array values if possible
+     *
+     * @param     mixed    $complexNumber   The value to parse
+     * @return    array
+     * @throws    Exception    If the argument isn't a Complex number or cannot be converted to one
+     */
+    private static function parseComplex($complexNumber)
+    {
+        // Test for real number, with no imaginary part
+        if (is_numeric($complexNumber)) {
+            return [$complexNumber, 0, null];
+        }
+
+        // Fix silly human errors
+        $complexNumber = str_replace(
+            ['+-', '-+', '++', '--'],
+            ['-', '-', '+', '+'],
+            $complexNumber
+        );
+
+        // Basic validation of string, to parse out real and imaginary parts, and any suffix
+        $validComplex = preg_match(
+            self::NUMBER_SPLIT_REGEXP,
+            $complexNumber,
+            $complexParts
+        );
+
+        if (!$validComplex) {
+            // Neither real nor imaginary part, so test to see if we actually have a suffix
+            $validComplex = preg_match('/^([\-\+]?)([ij])$/ui', $complexNumber, $complexParts);
+            if (!$validComplex) {
+                throw new Exception('Invalid complex number');
+            }
+            // We have a suffix, so set the real to 0, the imaginary to either 1 or -1 (as defined by the sign)
+            $imaginary = 1;
+            if ($complexParts[1] === '-') {
+                $imaginary = 0 - $imaginary;
+            }
+            return [0, $imaginary, $complexParts[2]];
+        }
+
+        // If we don't have an imaginary part, identify whether it should be +1 or -1...
+        if (($complexParts[4] === '') && ($complexParts[9] !== '')) {
+            if ($complexParts[7] !== $complexParts[9]) {
+                $complexParts[4] = 1;
+                if ($complexParts[8] === '-') {
+                    $complexParts[4] = -1;
+                }
+            } else {
+                // ... or if we have only the real and no imaginary part
+                //  (in which case our real should be the imaginary)
+                $complexParts[4] = $complexParts[1];
+                $complexParts[1] = 0;
+            }
+        }
+
+        // Return real and imaginary parts and suffix as an array, and set a default suffix if user input lazily
+        return [
+            $complexParts[1],
+            $complexParts[4],
+            !empty($complexParts[9]) ? $complexParts[9] : 'i'
+        ];
+    }
+
+
+    public function __construct($realPart = 0.0, $imaginaryPart = null, $suffix = 'i')
+    {
+        if ($imaginaryPart === null) {
+            if (is_array($realPart)) {
+                // We have an array of (potentially) real and imaginary parts, and any suffix
+                list ($realPart, $imaginaryPart, $suffix) = array_values($realPart) + [0.0, 0.0, 'i'];
+            } elseif ((is_string($realPart)) || (is_numeric($realPart))) {
+                // We've been given a string to parse to extract the real and imaginary parts, and any suffix
+                list($realPart, $imaginaryPart, $suffix) = self::parseComplex($realPart);
+            }
+        }
+
+        if ($imaginaryPart != 0.0 && empty($suffix)) {
+            $suffix = 'i';
+        } elseif ($imaginaryPart == 0.0 && !empty($suffix)) {
+            $suffix = '';
+        }
+
+        // Set parsed values in our properties
+        $this->realPart = (float) $realPart;
+        $this->imaginaryPart = (float) $imaginaryPart;
+        $this->suffix = strtolower($suffix ?? '');
+    }
+
+    /**
+     * Gets the real part of this complex number
+     *
+     * @return Float
+     */
+    public function getReal(): float
+    {
+        return $this->realPart;
+    }
+
+    /**
+     * Gets the imaginary part of this complex number
+     *
+     * @return Float
+     */
+    public function getImaginary(): float
+    {
+        return $this->imaginaryPart;
+    }
+
+    /**
+     * Gets the suffix of this complex number
+     *
+     * @return String
+     */
+    public function getSuffix(): string
+    {
+        return $this->suffix;
+    }
+
+    /**
+     * Returns true if this is a real value, false if a complex value
+     *
+     * @return Bool
+     */
+    public function isReal(): bool
+    {
+        return $this->imaginaryPart == 0.0;
+    }
+
+    /**
+     * Returns true if this is a complex value, false if a real value
+     *
+     * @return Bool
+     */
+    public function isComplex(): bool
+    {
+        return !$this->isReal();
+    }
+
+    public function format(): string
+    {
+        $str = "";
+        if ($this->imaginaryPart != 0.0) {
+            if (\abs($this->imaginaryPart) != 1.0) {
+                $str .= $this->imaginaryPart . $this->suffix;
+            } else {
+                $str .= (($this->imaginaryPart < 0.0) ? '-' : '') . $this->suffix;
+            }
+        }
+        if ($this->realPart != 0.0) {
+            if (($str) && ($this->imaginaryPart > 0.0)) {
+                $str = "+" . $str;
+            }
+            $str = $this->realPart . $str;
+        }
+        if (!$str) {
+            $str = "0.0";
+        }
+
+        return $str;
+    }
+
+    public function __toString(): string
+    {
+        return $this->format();
+    }
+
+    /**
+     * Validates whether the argument is a valid complex number, converting scalar or array values if possible
+     *
+     * @param     mixed    $complex   The value to validate
+     * @return    Complex
+     * @throws    Exception    If the argument isn't a Complex number or cannot be converted to one
+     */
+    public static function validateComplexArgument($complex): Complex
+    {
+        if (is_scalar($complex) || is_array($complex)) {
+            $complex = new Complex($complex);
+        } elseif (!is_object($complex) || !($complex instanceof Complex)) {
+            throw new Exception('Value is not a valid complex number');
+        }
+
+        return $complex;
+    }
+
+    /**
+     * Returns the reverse of this complex number
+     *
+     * @return    Complex
+     */
+    public function reverse(): Complex
+    {
+        return new Complex(
+            $this->imaginaryPart,
+            $this->realPart,
+            ($this->realPart == 0.0) ? null : $this->suffix
+        );
+    }
+
+    public function invertImaginary(): Complex
+    {
+        return new Complex(
+            $this->realPart,
+            $this->imaginaryPart * -1,
+            ($this->imaginaryPart == 0.0) ? null : $this->suffix
+        );
+    }
+
+    public function invertReal(): Complex
+    {
+        return new Complex(
+            $this->realPart * -1,
+            $this->imaginaryPart,
+            ($this->imaginaryPart == 0.0) ? null : $this->suffix
+        );
+    }
+
+    protected static $functions = [
+        'abs',
+        'acos',
+        'acosh',
+        'acot',
+        'acoth',
+        'acsc',
+        'acsch',
+        'argument',
+        'asec',
+        'asech',
+        'asin',
+        'asinh',
+        'atan',
+        'atanh',
+        'conjugate',
+        'cos',
+        'cosh',
+        'cot',
+        'coth',
+        'csc',
+        'csch',
+        'exp',
+        'inverse',
+        'ln',
+        'log2',
+        'log10',
+        'negative',
+        'pow',
+        'rho',
+        'sec',
+        'sech',
+        'sin',
+        'sinh',
+        'sqrt',
+        'tan',
+        'tanh',
+        'theta',
+    ];
+
+    protected static $operations = [
+        'add',
+        'subtract',
+        'multiply',
+        'divideby',
+        'divideinto',
+    ];
+
+    /**
+     * Returns the result of the function call or operation
+     *
+     * @return    Complex|float
+     * @throws    Exception|\InvalidArgumentException
+     */
+    public function __call($functionName, $arguments)
+    {
+        $functionName = strtolower(str_replace('_', '', $functionName));
+
+        // Test for function calls
+        if (in_array($functionName, self::$functions, true)) {
+            return Functions::$functionName($this, ...$arguments);
+        }
+        // Test for operation calls
+        if (in_array($functionName, self::$operations, true)) {
+            return Operations::$functionName($this, ...$arguments);
+        }
+        throw new Exception('Complex Function or Operation does not exist');
+    }
+}

vendor/markbaker/complex/classes/src/Exception.php

@@ -0,0 +1,13 @@
+<?php
+
+/**
+ * Exception.
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+class Exception extends \Exception
+{
+}

vendor/markbaker/complex/classes/src/Functions.php

@@ -0,0 +1,823 @@
+<?php
+
+namespace Complex;
+
+use InvalidArgumentException;
+
+class Functions
+{
+    /**
+     * Returns the absolute value (modulus) of a complex number.
+     * Also known as the rho of the complex number, i.e. the distance/radius
+     *   from the centrepoint to the representation of the number in polar coordinates.
+     *
+     * This function is a synonym for rho()
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    float            The absolute (or rho) value of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     *
+     * @see    rho
+     *
+     */
+    public static function abs($complex): float
+    {
+        return self::rho($complex);
+    }
+
+    /**
+     * Returns the inverse cosine of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The inverse cosine of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     */
+    public static function acos($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        $invsqrt = self::sqrt(Operations::subtract(1, Operations::multiply($complex, $complex)));
+        $adjust = new Complex(
+            $complex->getReal() - $invsqrt->getImaginary(),
+            $complex->getImaginary() + $invsqrt->getReal()
+        );
+        $log = self::ln($adjust);
+
+        return new Complex(
+            $log->getImaginary(),
+            -1 * $log->getReal()
+        );
+    }
+
+    /**
+     * Returns the inverse hyperbolic cosine of a complex number.
+     *
+     * Formula from Wolfram Alpha:
+     *   cosh^(-1)z = ln(z + sqrt(z + 1) sqrt(z - 1)).
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The inverse hyperbolic cosine of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     */
+    public static function acosh($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($complex->isReal() && ($complex->getReal() > 1)) {
+            return new Complex(\acosh($complex->getReal()));
+        }
+
+        $acosh = self::ln(
+            Operations::add(
+                $complex,
+                Operations::multiply(
+                    self::sqrt(Operations::add($complex, 1)),
+                    self::sqrt(Operations::subtract($complex, 1))
+                )
+            )
+        );
+
+        return $acosh;
+    }
+
+    /**
+     * Returns the inverse cotangent of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The inverse cotangent of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     * @throws    \InvalidArgumentException    If function would result in a division by zero
+     */
+    public static function acot($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        return self::atan(self::inverse($complex));
+    }
+
+    /**
+     * Returns the inverse hyperbolic cotangent of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The inverse hyperbolic cotangent of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     * @throws    \InvalidArgumentException    If function would result in a division by zero
+     */
+    public static function acoth($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        return self::atanh(self::inverse($complex));
+    }
+
+    /**
+     * Returns the inverse cosecant of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The inverse cosecant of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     * @throws    \InvalidArgumentException    If function would result in a division by zero
+     */
+    public static function acsc($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+            return new Complex(INF);
+        }
+
+        return self::asin(self::inverse($complex));
+    }
+
+    /**
+     * Returns the inverse hyperbolic cosecant of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The inverse hyperbolic cosecant of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     * @throws    \InvalidArgumentException    If function would result in a division by zero
+     */
+    public static function acsch($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+            return new Complex(INF);
+        }
+
+        return self::asinh(self::inverse($complex));
+    }
+
+    /**
+     * Returns the argument of a complex number.
+     * Also known as the theta of the complex number, i.e. the angle in radians
+     *   from the real axis to the representation of the number in polar coordinates.
+     *
+     * This function is a synonym for theta()
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    float            The argument (or theta) value of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     *
+     * @see    theta
+     */
+    public static function argument($complex): float
+    {
+        return self::theta($complex);
+    }
+
+    /**
+     * Returns the inverse secant of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The inverse secant of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     * @throws    \InvalidArgumentException    If function would result in a division by zero
+     */
+    public static function asec($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+            return new Complex(INF);
+        }
+
+        return self::acos(self::inverse($complex));
+    }
+
+    /**
+     * Returns the inverse hyperbolic secant of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The inverse hyperbolic secant of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     * @throws    \InvalidArgumentException    If function would result in a division by zero
+     */
+    public static function asech($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+            return new Complex(INF);
+        }
+
+        return self::acosh(self::inverse($complex));
+    }
+
+    /**
+     * Returns the inverse sine of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The inverse sine of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     */
+    public static function asin($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        $invsqrt = self::sqrt(Operations::subtract(1, Operations::multiply($complex, $complex)));
+        $adjust = new Complex(
+            $invsqrt->getReal() - $complex->getImaginary(),
+            $invsqrt->getImaginary() + $complex->getReal()
+        );
+        $log = self::ln($adjust);
+
+        return new Complex(
+            $log->getImaginary(),
+            -1 * $log->getReal()
+        );
+    }
+
+    /**
+     * Returns the inverse hyperbolic sine of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The inverse hyperbolic sine of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     */
+    public static function asinh($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($complex->isReal() && ($complex->getReal() > 1)) {
+            return new Complex(\asinh($complex->getReal()));
+        }
+
+        $asinh = clone $complex;
+        $asinh = $asinh->reverse()
+            ->invertReal();
+        $asinh = self::asin($asinh);
+
+        return $asinh->reverse()
+            ->invertImaginary();
+    }
+
+    /**
+     * Returns the inverse tangent of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The inverse tangent of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     * @throws    \InvalidArgumentException    If function would result in a division by zero
+     */
+    public static function atan($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($complex->isReal()) {
+            return new Complex(\atan($complex->getReal()));
+        }
+
+        $t1Value = new Complex(-1 * $complex->getImaginary(), $complex->getReal());
+        $uValue = new Complex(1, 0);
+
+        $d1Value = clone $uValue;
+        $d1Value = Operations::subtract($d1Value, $t1Value);
+        $d2Value = Operations::add($t1Value, $uValue);
+        $uResult = $d1Value->divideBy($d2Value);
+        $uResult = self::ln($uResult);
+
+        $realMultiplier = -0.5;
+        $imaginaryMultiplier = 0.5;
+
+        if (abs($uResult->getImaginary()) === M_PI) {
+            // If we have an imaginary value at the max or min (PI or -PI), then we need to ensure
+            //    that the primary is assigned for the correct quadrant.
+            $realMultiplier = (
+                ($uResult->getImaginary() === M_PI && $uResult->getReal() > 0.0) ||
+                ($uResult->getImaginary() === -M_PI && $uResult->getReal() < 0.0)
+            ) ? 0.5 : -0.5;
+        }
+
+        return new Complex(
+            $uResult->getImaginary() * $realMultiplier,
+            $uResult->getReal() * $imaginaryMultiplier,
+            $complex->getSuffix()
+        );
+    }
+
+    /**
+     * Returns the inverse hyperbolic tangent of a complex number.
+     *
+     * Formula from Wolfram Alpha:
+     *  tanh^(-1)z = 1/2 [ln(1 + z) - ln(1 - z)].
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The inverse hyperbolic tangent of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     */
+    public static function atanh($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($complex->isReal()) {
+            $real = $complex->getReal();
+            if ($real >= -1.0 && $real <= 1.0) {
+                return new Complex(\atanh($real));
+            } else {
+                return new Complex(\atanh(1 / $real), (($real < 0.0) ? M_PI_2 : -1 * M_PI_2));
+            }
+        }
+
+        $atanh = Operations::multiply(
+            Operations::subtract(
+                self::ln(Operations::add(1.0, $complex)),
+                self::ln(Operations::subtract(1.0, $complex))
+            ),
+            0.5
+        );
+
+        return $atanh;
+    }
+
+    /**
+     * Returns the complex conjugate of a complex number
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The conjugate of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     */
+    public static function conjugate($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        return new Complex(
+            $complex->getReal(),
+            -1 * $complex->getImaginary(),
+            $complex->getSuffix()
+        );
+    }
+
+    /**
+     * Returns the cosine of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The cosine of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     */
+    public static function cos($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($complex->isReal()) {
+            return new Complex(\cos($complex->getReal()));
+        }
+
+        return self::conjugate(
+            new Complex(
+                \cos($complex->getReal()) * \cosh($complex->getImaginary()),
+                \sin($complex->getReal()) * \sinh($complex->getImaginary()),
+                $complex->getSuffix()
+            )
+        );
+    }
+
+    /**
+     * Returns the hyperbolic cosine of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The hyperbolic cosine of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     */
+    public static function cosh($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($complex->isReal()) {
+            return new Complex(\cosh($complex->getReal()));
+        }
+
+        return new Complex(
+            \cosh($complex->getReal()) * \cos($complex->getImaginary()),
+            \sinh($complex->getReal()) * \sin($complex->getImaginary()),
+            $complex->getSuffix()
+        );
+    }
+
+    /**
+     * Returns the cotangent of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The cotangent of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     * @throws    \InvalidArgumentException    If function would result in a division by zero
+     */
+    public static function cot($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+            return new Complex(INF);
+        }
+
+        return self::inverse(self::tan($complex));
+    }
+
+    /**
+     * Returns the hyperbolic cotangent of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The hyperbolic cotangent of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     * @throws    \InvalidArgumentException    If function would result in a division by zero
+     */
+    public static function coth($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        return self::inverse(self::tanh($complex));
+    }
+
+    /**
+     * Returns the cosecant of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The cosecant of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     * @throws    \InvalidArgumentException    If function would result in a division by zero
+     */
+    public static function csc($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+            return new Complex(INF);
+        }
+
+        return self::inverse(self::sin($complex));
+    }
+
+    /**
+     * Returns the hyperbolic cosecant of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The hyperbolic cosecant of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     * @throws    \InvalidArgumentException    If function would result in a division by zero
+     */
+    public static function csch($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+            return new Complex(INF);
+        }
+
+        return self::inverse(self::sinh($complex));
+    }
+
+    /**
+     * Returns the exponential of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The exponential of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     */
+    public static function exp($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if (($complex->getReal() == 0.0) && (\abs($complex->getImaginary()) == M_PI)) {
+            return new Complex(-1.0, 0.0);
+        }
+
+        $rho = \exp($complex->getReal());
+
+        return new Complex(
+            $rho * \cos($complex->getImaginary()),
+            $rho * \sin($complex->getImaginary()),
+            $complex->getSuffix()
+        );
+    }
+
+    /**
+     * Returns the inverse of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The inverse of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     * @throws    InvalidArgumentException    If function would result in a division by zero
+     */
+    public static function inverse($complex): Complex
+    {
+        $complex = clone Complex::validateComplexArgument($complex);
+
+        if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+            throw new InvalidArgumentException('Division by zero');
+        }
+
+        return $complex->divideInto(1.0);
+    }
+
+    /**
+     * Returns the natural logarithm of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The natural logarithm of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     * @throws    InvalidArgumentException  If the real and the imaginary parts are both zero
+     */
+    public static function ln($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if (($complex->getReal() == 0.0) && ($complex->getImaginary() == 0.0)) {
+            throw new InvalidArgumentException();
+        }
+
+        return new Complex(
+            \log(self::rho($complex)),
+            self::theta($complex),
+            $complex->getSuffix()
+        );
+    }
+
+    /**
+     * Returns the base-2 logarithm of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The base-2 logarithm of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     * @throws    InvalidArgumentException  If the real and the imaginary parts are both zero
+     */
+    public static function log2($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if (($complex->getReal() == 0.0) && ($complex->getImaginary() == 0.0)) {
+            throw new InvalidArgumentException();
+        } elseif (($complex->getReal() > 0.0) && ($complex->getImaginary() == 0.0)) {
+            return new Complex(\log($complex->getReal(), 2), 0.0, $complex->getSuffix());
+        }
+
+        return self::ln($complex)
+            ->multiply(\log(Complex::EULER, 2));
+    }
+
+    /**
+     * Returns the common logarithm (base 10) of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The common logarithm (base 10) of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     * @throws    InvalidArgumentException  If the real and the imaginary parts are both zero
+     */
+    public static function log10($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if (($complex->getReal() == 0.0) && ($complex->getImaginary() == 0.0)) {
+            throw new InvalidArgumentException();
+        } elseif (($complex->getReal() > 0.0) && ($complex->getImaginary() == 0.0)) {
+            return new Complex(\log10($complex->getReal()), 0.0, $complex->getSuffix());
+        }
+
+        return self::ln($complex)
+            ->multiply(\log10(Complex::EULER));
+    }
+
+    /**
+     * Returns the negative of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The negative value of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     *
+     * @see    rho
+     *
+     */
+    public static function negative($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        return new Complex(
+            -1 * $complex->getReal(),
+            -1 * $complex->getImaginary(),
+            $complex->getSuffix()
+        );
+    }
+
+    /**
+     * Returns a complex number raised to a power.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @param     float|integer    $power      The power to raise this value to
+     * @return    Complex          The complex argument raised to the real power.
+     * @throws    Exception        If the power argument isn't a valid real
+     */
+    public static function pow($complex, $power): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if (!is_numeric($power)) {
+            throw new Exception('Power argument must be a real number');
+        }
+
+        if ($complex->getImaginary() == 0.0 && $complex->getReal() >= 0.0) {
+            return new Complex(\pow($complex->getReal(), $power));
+        }
+
+        $rValue = \sqrt(($complex->getReal() * $complex->getReal()) + ($complex->getImaginary() * $complex->getImaginary()));
+        $rPower = \pow($rValue, $power);
+        $theta = $complex->argument() * $power;
+        if ($theta == 0) {
+            return new Complex(1);
+        }
+
+        return new Complex($rPower * \cos($theta), $rPower * \sin($theta), $complex->getSuffix());
+    }
+
+    /**
+     * Returns the rho of a complex number.
+     * This is the distance/radius from the centrepoint to the representation of the number in polar coordinates.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    float            The rho value of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     */
+    public static function rho($complex): float
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        return \sqrt(
+            ($complex->getReal() * $complex->getReal()) +
+            ($complex->getImaginary() * $complex->getImaginary())
+        );
+    }
+
+    /**
+     * Returns the secant of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The secant of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     * @throws    \InvalidArgumentException    If function would result in a division by zero
+     */
+    public static function sec($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        return self::inverse(self::cos($complex));
+    }
+
+    /**
+     * Returns the hyperbolic secant of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The hyperbolic secant of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     * @throws    \InvalidArgumentException    If function would result in a division by zero
+     */
+    public static function sech($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        return self::inverse(self::cosh($complex));
+    }
+
+    /**
+     * Returns the sine of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The sine of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     */
+    public static function sin($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($complex->isReal()) {
+            return new Complex(\sin($complex->getReal()));
+        }
+
+        return new Complex(
+            \sin($complex->getReal()) * \cosh($complex->getImaginary()),
+            \cos($complex->getReal()) * \sinh($complex->getImaginary()),
+            $complex->getSuffix()
+        );
+    }
+
+    /**
+     * Returns the hyperbolic sine of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The hyperbolic sine of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     */
+    public static function sinh($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($complex->isReal()) {
+            return new Complex(\sinh($complex->getReal()));
+        }
+
+        return new Complex(
+            \sinh($complex->getReal()) * \cos($complex->getImaginary()),
+            \cosh($complex->getReal()) * \sin($complex->getImaginary()),
+            $complex->getSuffix()
+        );
+    }
+
+    /**
+     * Returns the square root of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The Square root of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     */
+    public static function sqrt($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        $theta = self::theta($complex);
+        $delta1 = \cos($theta / 2);
+        $delta2 = \sin($theta / 2);
+        $rho = \sqrt(self::rho($complex));
+
+        return new Complex($delta1 * $rho, $delta2 * $rho, $complex->getSuffix());
+    }
+
+    /**
+     * Returns the tangent of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The tangent of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     * @throws    InvalidArgumentException    If function would result in a division by zero
+     */
+    public static function tan($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($complex->isReal()) {
+            return new Complex(\tan($complex->getReal()));
+        }
+
+        $real = $complex->getReal();
+        $imaginary = $complex->getImaginary();
+        $divisor = 1 + \pow(\tan($real), 2) * \pow(\tanh($imaginary), 2);
+        if ($divisor == 0.0) {
+            throw new InvalidArgumentException('Division by zero');
+        }
+
+        return new Complex(
+            \pow(self::sech($imaginary)->getReal(), 2) * \tan($real) / $divisor,
+            \pow(self::sec($real)->getReal(), 2) * \tanh($imaginary) / $divisor,
+            $complex->getSuffix()
+        );
+    }
+
+    /**
+     * Returns the hyperbolic tangent of a complex number.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    Complex          The hyperbolic tangent of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     * @throws    \InvalidArgumentException    If function would result in a division by zero
+     */
+    public static function tanh($complex): Complex
+    {
+        $complex = Complex::validateComplexArgument($complex);
+        $real = $complex->getReal();
+        $imaginary = $complex->getImaginary();
+        $divisor = \cos($imaginary) * \cos($imaginary) + \sinh($real) * \sinh($real);
+        if ($divisor == 0.0) {
+            throw new InvalidArgumentException('Division by zero');
+        }
+
+        return new Complex(
+            \sinh($real) * \cosh($real) / $divisor,
+            0.5 * \sin(2 * $imaginary) / $divisor,
+            $complex->getSuffix()
+        );
+    }
+
+    /**
+     * Returns the theta of a complex number.
+     *   This is the angle in radians from the real axis to the representation of the number in polar coordinates.
+     *
+     * @param     Complex|mixed    $complex    Complex number or a numeric value.
+     * @return    float            The theta value of the complex argument.
+     * @throws    Exception        If argument isn't a valid real or complex number.
+     */
+    public static function theta($complex): float
+    {
+        $complex = Complex::validateComplexArgument($complex);
+
+        if ($complex->getReal() == 0.0) {
+            if ($complex->isReal()) {
+                return 0.0;
+            } elseif ($complex->getImaginary() < 0.0) {
+                return M_PI / -2;
+            }
+            return M_PI / 2;
+        } elseif ($complex->getReal() > 0.0) {
+            return \atan($complex->getImaginary() / $complex->getReal());
+        } elseif ($complex->getImaginary() < 0.0) {
+            return -(M_PI - \atan(\abs($complex->getImaginary()) / \abs($complex->getReal())));
+        }
+
+        return M_PI - \atan($complex->getImaginary() / \abs($complex->getReal()));
+    }
+}

vendor/markbaker/complex/classes/src/Operations.php

@@ -0,0 +1,210 @@
+<?php
+
+namespace Complex;
+
+use InvalidArgumentException;
+
+class Operations
+{
+    /**
+     * Adds two or more complex numbers
+     *
+     * @param     array of string|integer|float|Complex    $complexValues   The numbers to add
+     * @return    Complex
+     */
+    public static function add(...$complexValues): Complex
+    {
+        if (count($complexValues) < 2) {
+            throw new \Exception('This function requires at least 2 arguments');
+        }
+
+        $base = array_shift($complexValues);
+        $result = clone Complex::validateComplexArgument($base);
+
+        foreach ($complexValues as $complex) {
+            $complex = Complex::validateComplexArgument($complex);
+
+            if ($result->isComplex() && $complex->isComplex() &&
+                $result->getSuffix() !== $complex->getSuffix()) {
+                throw new Exception('Suffix Mismatch');
+            }
+
+            $real = $result->getReal() + $complex->getReal();
+            $imaginary = $result->getImaginary() + $complex->getImaginary();
+
+            $result = new Complex(
+                $real,
+                $imaginary,
+                ($imaginary == 0.0) ? null : max($result->getSuffix(), $complex->getSuffix())
+            );
+        }
+
+        return $result;
+    }
+
+    /**
+     * Divides two or more complex numbers
+     *
+     * @param     array of string|integer|float|Complex    $complexValues   The numbers to divide
+     * @return    Complex
+     */
+    public static function divideby(...$complexValues): Complex
+    {
+        if (count($complexValues) < 2) {
+            throw new \Exception('This function requires at least 2 arguments');
+        }
+
+        $base = array_shift($complexValues);
+        $result = clone Complex::validateComplexArgument($base);
+
+        foreach ($complexValues as $complex) {
+            $complex = Complex::validateComplexArgument($complex);
+
+            if ($result->isComplex() && $complex->isComplex() &&
+                $result->getSuffix() !== $complex->getSuffix()) {
+                throw new Exception('Suffix Mismatch');
+            }
+            if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+                throw new InvalidArgumentException('Division by zero');
+            }
+
+            $delta1 = ($result->getReal() * $complex->getReal()) +
+                ($result->getImaginary() * $complex->getImaginary());
+            $delta2 = ($result->getImaginary() * $complex->getReal()) -
+                ($result->getReal() * $complex->getImaginary());
+            $delta3 = ($complex->getReal() * $complex->getReal()) +
+                ($complex->getImaginary() * $complex->getImaginary());
+
+            $real = $delta1 / $delta3;
+            $imaginary = $delta2 / $delta3;
+
+            $result = new Complex(
+                $real,
+                $imaginary,
+                ($imaginary == 0.0) ? null : max($result->getSuffix(), $complex->getSuffix())
+            );
+        }
+
+        return $result;
+    }
+
+    /**
+     * Divides two or more complex numbers
+     *
+     * @param     array of string|integer|float|Complex    $complexValues   The numbers to divide
+     * @return    Complex
+     */
+    public static function divideinto(...$complexValues): Complex
+    {
+        if (count($complexValues) < 2) {
+            throw new \Exception('This function requires at least 2 arguments');
+        }
+
+        $base = array_shift($complexValues);
+        $result = clone Complex::validateComplexArgument($base);
+
+        foreach ($complexValues as $complex) {
+            $complex = Complex::validateComplexArgument($complex);
+
+            if ($result->isComplex() && $complex->isComplex() &&
+                $result->getSuffix() !== $complex->getSuffix()) {
+                throw new Exception('Suffix Mismatch');
+            }
+            if ($result->getReal() == 0.0 && $result->getImaginary() == 0.0) {
+                throw new InvalidArgumentException('Division by zero');
+            }
+
+            $delta1 = ($complex->getReal() * $result->getReal()) +
+                ($complex->getImaginary() * $result->getImaginary());
+            $delta2 = ($complex->getImaginary() * $result->getReal()) -
+                ($complex->getReal() * $result->getImaginary());
+            $delta3 = ($result->getReal() * $result->getReal()) +
+                ($result->getImaginary() * $result->getImaginary());
+
+            $real = $delta1 / $delta3;
+            $imaginary = $delta2 / $delta3;
+
+            $result = new Complex(
+                $real,
+                $imaginary,
+                ($imaginary == 0.0) ? null : max($result->getSuffix(), $complex->getSuffix())
+            );
+        }
+
+        return $result;
+    }
+
+    /**
+     * Multiplies two or more complex numbers
+     *
+     * @param     array of string|integer|float|Complex    $complexValues   The numbers to multiply
+     * @return    Complex
+     */
+    public static function multiply(...$complexValues): Complex
+    {
+        if (count($complexValues) < 2) {
+            throw new \Exception('This function requires at least 2 arguments');
+        }
+
+        $base = array_shift($complexValues);
+        $result = clone Complex::validateComplexArgument($base);
+
+        foreach ($complexValues as $complex) {
+            $complex = Complex::validateComplexArgument($complex);
+
+            if ($result->isComplex() && $complex->isComplex() &&
+                $result->getSuffix() !== $complex->getSuffix()) {
+                throw new Exception('Suffix Mismatch');
+            }
+
+            $real = ($result->getReal() * $complex->getReal()) -
+                ($result->getImaginary() * $complex->getImaginary());
+            $imaginary = ($result->getReal() * $complex->getImaginary()) +
+                ($result->getImaginary() * $complex->getReal());
+
+            $result = new Complex(
+                $real,
+                $imaginary,
+                ($imaginary == 0.0) ? null : max($result->getSuffix(), $complex->getSuffix())
+            );
+        }
+
+        return $result;
+    }
+
+    /**
+     * Subtracts two or more complex numbers
+     *
+     * @param     array of string|integer|float|Complex    $complexValues   The numbers to subtract
+     * @return    Complex
+     */
+    public static function subtract(...$complexValues): Complex
+    {
+        if (count($complexValues) < 2) {
+            throw new \Exception('This function requires at least 2 arguments');
+        }
+
+        $base = array_shift($complexValues);
+        $result = clone Complex::validateComplexArgument($base);
+
+        foreach ($complexValues as $complex) {
+            $complex = Complex::validateComplexArgument($complex);
+
+            if ($result->isComplex() && $complex->isComplex() &&
+                $result->getSuffix() !== $complex->getSuffix()) {
+                throw new Exception('Suffix Mismatch');
+            }
+
+            $real = $result->getReal() - $complex->getReal();
+            $imaginary = $result->getImaginary() - $complex->getImaginary();
+
+            $result = new Complex(
+                $real,
+                $imaginary,
+                ($imaginary == 0.0) ? null : max($result->getSuffix(), $complex->getSuffix())
+            );
+        }
+
+        return $result;
+    }
+}

vendor/markbaker/complex/examples/complexTest.php

@@ -0,0 +1,154 @@
+<?php
+
+use Complex\Complex as Complex;
+
+include(__DIR__ . '/../vendor/autoload.php');
+
+echo 'Create', PHP_EOL;
+
+$x = new Complex(123);
+echo $x, PHP_EOL;
+
+$x = new Complex(123, 456);
+echo $x, PHP_EOL;
+
+$x = new Complex(array(123,456,'j'));
+echo $x, PHP_EOL;
+
+$x = new Complex('1.23e-4--2.34e-5i');
+echo $x, PHP_EOL;
+
+
+echo PHP_EOL, 'Add', PHP_EOL;
+
+$x = new Complex(123);
+$x->add(456);
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456);
+$x->add(789.012);
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456, 78.90);
+$x->add(new Complex(-987.654, -32.1));
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456, 78.90);
+$x->add(-987.654);
+echo $x, PHP_EOL;
+
+$x = new Complex(-987.654, -32.1);
+$x->add(new Complex(0, 1));
+echo $x, PHP_EOL;
+
+$x = new Complex(-987.654, -32.1);
+$x->add(new Complex(0, -1));
+echo $x, PHP_EOL;
+
+
+echo PHP_EOL, 'Subtract', PHP_EOL;
+
+$x = new Complex(123);
+$x->subtract(456);
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456);
+$x->subtract(789.012);
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456, 78.90);
+$x->subtract(new Complex(-987.654, -32.1));
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456, 78.90);
+$x->subtract(-987.654);
+echo $x, PHP_EOL;
+
+$x = new Complex(-987.654, -32.1);
+$x->subtract(new Complex(0, 1));
+echo $x, PHP_EOL;
+
+$x = new Complex(-987.654, -32.1);
+$x->subtract(new Complex(0, -1));
+echo $x, PHP_EOL;
+
+
+echo PHP_EOL, 'Multiply', PHP_EOL;
+
+$x = new Complex(123);
+$x->multiply(456);
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456);
+$x->multiply(789.012);
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456, 78.90);
+$x->multiply(new Complex(-987.654, -32.1));
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456, 78.90);
+$x->multiply(-987.654);
+echo $x, PHP_EOL;
+
+$x = new Complex(-987.654, -32.1);
+$x->multiply(new Complex(0, 1));
+echo $x, PHP_EOL;
+
+$x = new Complex(-987.654, -32.1);
+$x->multiply(new Complex(0, -1));
+echo $x, PHP_EOL;
+
+
+echo PHP_EOL, 'Divide By', PHP_EOL;
+
+$x = new Complex(123);
+$x->divideBy(456);
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456);
+$x->divideBy(789.012);
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456, 78.90);
+$x->divideBy(new Complex(-987.654, -32.1));
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456, 78.90);
+$x->divideBy(-987.654);
+echo $x, PHP_EOL;
+
+$x = new Complex(-987.654, -32.1);
+$x->divideBy(new Complex(0, 1));
+echo $x, PHP_EOL;
+
+$x = new Complex(-987.654, -32.1);
+$x->divideBy(new Complex(0, -1));
+echo $x, PHP_EOL;
+
+
+echo PHP_EOL, 'Divide Into', PHP_EOL;
+
+$x = new Complex(123);
+$x->divideInto(456);
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456);
+$x->divideInto(789.012);
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456, 78.90);
+$x->divideInto(new Complex(-987.654, -32.1));
+echo $x, PHP_EOL;
+
+$x = new Complex(123.456, 78.90);
+$x->divideInto(-987.654);
+echo $x, PHP_EOL;
+
+$x = new Complex(-987.654, -32.1);
+$x->divideInto(new Complex(0, 1));
+echo $x, PHP_EOL;
+
+$x = new Complex(-987.654, -32.1);
+$x->divideInto(new Complex(0, -1));
+echo $x, PHP_EOL;

vendor/markbaker/complex/examples/testFunctions.php

@@ -0,0 +1,52 @@
+<?php
+
+namespace Complex;
+
+include(__DIR__ . '/../vendor/autoload.php');
+
+echo 'Function Examples', PHP_EOL;
+
+$functions = array(
+    'abs',
+    'acos',
+    'acosh',
+    'acsc',
+    'acsch',
+    'argument',
+    'asec',
+    'asech',
+    'asin',
+    'asinh',
+    'conjugate',
+    'cos',
+    'cosh',
+    'csc',
+    'csch',
+    'exp',
+    'inverse',
+    'ln',
+    'log2',
+    'log10',
+    'rho',
+    'sec',
+    'sech',
+    'sin',
+    'sinh',
+    'sqrt',
+    'theta'
+);
+
+for ($real = -3.5; $real <= 3.5; $real += 0.5) {
+    for ($imaginary = -3.5; $imaginary <= 3.5; $imaginary += 0.5) {
+        foreach ($functions as $function) {
+            $complexFunction = __NAMESPACE__ . '\\Functions::' . $function;
+            $complex = new Complex($real, $imaginary);
+            try {
+                echo $function, '(', $complex, ') = ', $complexFunction($complex), PHP_EOL;
+            } catch (\Exception $e) {
+                echo $function, '(', $complex, ') ERROR: ', $e->getMessage(), PHP_EOL;
+            }
+        }
+        echo PHP_EOL;
+    }
+}

vendor/markbaker/complex/examples/testOperations.php

@@ -0,0 +1,35 @@
+<?php
+
+use Complex\Complex as Complex;
+use Complex\Operations;
+
+include(__DIR__ . '/../vendor/autoload.php');
+
+$values = [
+    new Complex(123),
+    new Complex(456, 123),
+    new Complex(0.0, 456),
+];
+
+foreach ($values as $value) {
+    echo $value, PHP_EOL;
+}
+
+echo 'Addition', PHP_EOL;
+
+$result = Operations::add(...$values);
+echo '=> ', $result, PHP_EOL;
+
+echo PHP_EOL;
+
+echo 'Subtraction', PHP_EOL;
+
+$result = Operations::subtract(...$values);
+echo '=> ', $result, PHP_EOL;
+
+echo PHP_EOL;
+
+echo 'Multiplication', PHP_EOL;
+
+$result = Operations::multiply(...$values);
+echo '=> ', $result, PHP_EOL;

vendor/markbaker/matrix/buildPhar.php

@@ -0,0 +1,62 @@
+<?php
+
+# required: PHP 5.3+ and zlib extension
+
+// ini option check
+if (ini_get('phar.readonly')) {
+    echo "php.ini: set the 'phar.readonly' option to 0 to enable phar creation\n";
+    exit(1);
+}
+
+// output name
+$pharName = 'Matrix.phar';
+
+// target folder
+$sourceDir = __DIR__ . DIRECTORY_SEPARATOR . 'classes' . DIRECTORY_SEPARATOR . 'src' . DIRECTORY_SEPARATOR;
+
+// default meta information
+$metaData = array(
+    'Author'      => 'Mark Baker <mark@lange.demon.co.uk>',
+    'Description' => 'PHP Class for working with Matrix numbers',
+    'Copyright'   => 'Mark Baker (c) 2013-' . date('Y'),
+    'Timestamp'   => time(),
+    'Version'     => '0.1.0',
+    'Date'        => date('Y-m-d')
+);
+
+// cleanup
+if (file_exists($pharName)) {
+    echo "Removed: {$pharName}\n";
+    unlink($pharName);
+}
+
+echo "Building phar file...\n";
+
+// the phar object
+$phar = new Phar($pharName, null, 'Matrix');
+$phar->buildFromDirectory($sourceDir);
+$phar->setStub(
+<<<'EOT'
+<?php
+    spl_autoload_register(function ($className) {
+        include 'phar://' . $className . '.php';
+    });
+
+    try {
+        Phar::mapPhar();
+    } catch (PharException $e) {
+        error_log($e->getMessage());
+        exit(1);
+    }
+
+    include 'phar://functions/sqrt.php';
+
+    __HALT_COMPILER();
+EOT
+);
+$phar->setMetadata($metaData);
+$phar->compressFiles(Phar::GZ);
+
+echo "Complete.\n";
+
+exit();

vendor/markbaker/matrix/classes/src/Builder.php

@@ -0,0 +1,70 @@
+<?php
+
+/**
+ *
+ * Class for the creating "special" Matrices
+ *
+ * @copyright  Copyright (c) 2018 Mark Baker (https://github.com/MarkBaker/PHPMatrix)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+
+namespace Matrix;
+
+/**
+ * Matrix Builder class.
+ *
+ * @package Matrix
+ */
+class Builder
+{
+    /**
+     * Create a new matrix of specified dimensions, and filled with a specified value
+     * If the column argument isn't provided, then a square matrix will be created
+     *
+     * @param mixed $fillValue
+     * @param int $rows
+     * @param int|null $columns
+     * @return Matrix
+     * @throws Exception
+     */
+    public static function createFilledMatrix($fillValue, $rows, $columns = null)
+    {
+        if ($columns === null) {
+            $columns = $rows;
+        }
+
+        $rows = Matrix::validateRow($rows);
+        $columns = Matrix::validateColumn($columns);
+
+        return new Matrix(
+            array_fill(
+                0,
+                $rows,
+                array_fill(
+                    0,
+                    $columns,
+                    $fillValue
+                )
+            )
+        );
+    }
+
+    /**
+     * Create a new identity matrix of specified dimensions
+     * This will always be a square matrix, with the number of rows and columns matching the provided dimension
+     *
+     * @param int $dimensions
+     * @return Matrix
+     * @throws Exception
+     */
+    public static function createIdentityMatrix($dimensions, $fillValue = null)
+    {
+        $grid = static::createFilledMatrix($fillValue, $dimensions)->toArray();
+
+        for ($x = 0; $x < $dimensions; ++$x) {
+            $grid[$x][$x] = 1;
+        }
+
+        return new Matrix($grid);
+    }
+}

vendor/markbaker/matrix/classes/src/Decomposition/Decomposition.php

@@ -0,0 +1,27 @@
+<?php
+
+namespace Matrix\Decomposition;
+
+use Matrix\Exception;
+use Matrix\Matrix;
+
+class Decomposition
+{
+    const LU = 'LU';
+    const QR = 'QR';
+
+    /**
+     * @throws Exception
+     */
+    public static function decomposition($type, Matrix $matrix)
+    {
+        switch (strtoupper($type)) {
+            case self::LU:
+                return new LU($matrix);
+            case self::QR:
+                return new QR($matrix);
+            default:
+                throw new Exception('Invalid Decomposition');
+        }
+    }
+}

vendor/markbaker/matrix/classes/src/Decomposition/LU.php

@@ -0,0 +1,260 @@
+<?php
+
+namespace Matrix\Decomposition;
+
+use Matrix\Exception;
+use Matrix\Matrix;
+
+class LU
+{
+    private $luMatrix;
+    private $rows;
+    private $columns;
+
+    private $pivot = [];
+
+    public function __construct(Matrix $matrix)
+    {
+        $this->luMatrix = $matrix->toArray();
+        $this->rows = $matrix->rows;
+        $this->columns = $matrix->columns;
+
+        $this->buildPivot();
+    }
+
+    /**
+     * Get lower triangular factor.
+     *
+     * @return Matrix Lower triangular factor
+     */
+    public function getL(): Matrix
+    {
+        $lower = [];
+
+        $columns = min($this->rows, $this->columns);
+        for ($row = 0; $row < $this->rows; ++$row) {
+            for ($column = 0; $column < $columns; ++$column) {
+                if ($row > $column) {
+                    $lower[$row][$column] = $this->luMatrix[$row][$column];
+                } elseif ($row === $column) {
+                    $lower[$row][$column] = 1.0;
+                } else {
+                    $lower[$row][$column] = 0.0;
+                }
+            }
+        }
+
+        return new Matrix($lower);
+    }
+
+    /**
+     * Get upper triangular factor.
+     *
+     * @return Matrix Upper triangular factor
+     */
+    public function getU(): Matrix
+    {
+        $upper = [];
+
+        $rows = min($this->rows, $this->columns);
+        for ($row = 0; $row < $rows; ++$row) {
+            for ($column = 0; $column < $this->columns; ++$column) {
+                if ($row <= $column) {
+                    $upper[$row][$column] = $this->luMatrix[$row][$column];
+                } else {
+                    $upper[$row][$column] = 0.0;
+                }
+            }
+        }
+
+        return new Matrix($upper);
+    }
+
+    /**
+     * Return pivot permutation vector.
+     *
+     * @return Matrix Pivot matrix
+     */
+    public function getP(): Matrix
+    {
+        $pMatrix = [];
+
+        $pivots = $this->pivot;
+        $pivotCount = count($pivots);
+        foreach ($pivots as $row => $pivot) {
+            $pMatrix[$row] = array_fill(0, $pivotCount, 0);
+            $pMatrix[$row][$pivot] = 1;
+        }
+
+        return new Matrix($pMatrix);
+    }
+
+    /**
+     * Return pivot permutation vector.
+     *
+     * @return array Pivot vector
+     */
+    public function getPivot(): array
+    {
+        return $this->pivot;
+    }
+
+    /**
+     *    Is the matrix nonsingular?
+     *
+     * @return bool true if U, and hence A, is nonsingular
+     */
+    public function isNonsingular(): bool
+    {
+        for ($diagonal = 0; $diagonal < $this->columns; ++$diagonal) {
+            if ($this->luMatrix[$diagonal][$diagonal] === 0.0) {
+                return false;
+            }
+        }
+
+        return true;
+    }
+
+    private function buildPivot(): void
+    {
+        for ($row = 0; $row < $this->rows; ++$row) {
+            $this->pivot[$row] = $row;
+        }
+
+        for ($column = 0; $column < $this->columns; ++$column) {
+            $luColumn = $this->localisedReferenceColumn($column);
+
+            $this->applyTransformations($column, $luColumn);
+
+            $pivot = $this->findPivot($column, $luColumn);
+            if ($pivot !== $column) {
+                $this->pivotExchange($pivot, $column);
+            }
+
+            $this->computeMultipliers($column);
+
+            unset($luColumn);
+        }
+    }
+
+    private function localisedReferenceColumn($column): array
+    {
+        $luColumn = [];
+
+        for ($row = 0; $row < $this->rows; ++$row) {
+            $luColumn[$row] = &$this->luMatrix[$row][$column];
+        }
+
+        return $luColumn;
+    }
+
+    private function applyTransformations($column, array $luColumn): void
+    {
+        for ($row = 0; $row < $this->rows; ++$row) {
+            $luRow = $this->luMatrix[$row];
+            // Most of the time is spent in the following dot product.
+            $kmax = min($row, $column);
+            $sValue = 0.0;
+            for ($kValue = 0; $kValue < $kmax; ++$kValue) {
+                $sValue += $luRow[$kValue] * $luColumn[$kValue];
+            }
+            $luRow[$column] = $luColumn[$row] -= $sValue;
+        }
+    }
+
+    private function findPivot($column, array $luColumn): int
+    {
+        $pivot = $column;
+        for ($row = $column + 1; $row < $this->rows; ++$row) {
+            if (abs($luColumn[$row]) > abs($luColumn[$pivot])) {
+                $pivot = $row;
+            }
+        }
+
+        return $pivot;
+    }
+
+    private function pivotExchange($pivot, $column): void
+    {
+        for ($kValue = 0; $kValue < $this->columns; ++$kValue) {
+            $tValue = $this->luMatrix[$pivot][$kValue];
+            $this->luMatrix[$pivot][$kValue] = $this->luMatrix[$column][$kValue];
+            $this->luMatrix[$column][$kValue] = $tValue;
+        }
+
+        $lValue = $this->pivot[$pivot];
+        $this->pivot[$pivot] = $this->pivot[$column];
+        $this->pivot[$column] = $lValue;
+    }
+
+    private function computeMultipliers($diagonal): void
+    {
+        if (($diagonal < $this->rows) && ($this->luMatrix[$diagonal][$diagonal] != 0.0)) {
+            for ($row = $diagonal + 1; $row < $this->rows; ++$row) {
+                $this->luMatrix[$row][$diagonal] /= $this->luMatrix[$diagonal][$diagonal];
+            }
+        }
+    }
+
+    private function pivotB(Matrix $B): array
+    {
+        $X = [];
+        foreach ($this->pivot as $rowId) {
+            $row = $B->getRows($rowId + 1)->toArray();
+            $X[] = array_pop($row);
+        }
+
+        return $X;
+    }
+
+    /**
+     * Solve A*X = B.
+     *
+     * @param Matrix $B a Matrix with as many rows as A and any number of columns
+     *
+     * @throws Exception
+     *
+     * @return Matrix X so that L*U*X = B(piv,:)
+     */
+    public function solve(Matrix $B): Matrix
+    {
+        if ($B->rows !== $this->rows) {
+            throw new Exception('Matrix row dimensions are not equal');
+        }
+
+        if ($this->rows !== $this->columns) {
+            throw new Exception('LU solve() only works on square matrices');
+        }
+
+        if (!$this->isNonsingular()) {
+            throw new Exception('Can only perform operation on singular matrix');
+        }
+
+        // Copy right hand side with pivoting
+        $nx = $B->columns;
+        $X = $this->pivotB($B);
+
+        // Solve L*Y = B(piv,:)
+        for ($k = 0; $k < $this->columns; ++$k) {
+            for ($i = $k + 1; $i < $this->columns; ++$i) {
+                for ($j = 0; $j < $nx; ++$j) {
+                    $X[$i][$j] -= $X[$k][$j] * $this->luMatrix[$i][$k];
+                }
+            }
+        }
+
+        // Solve U*X = Y;
+        for ($k = $this->columns - 1; $k >= 0; --$k) {
+            for ($j = 0; $j < $nx; ++$j) {
+                $X[$k][$j] /= $this->luMatrix[$k][$k];
+            }
+            for ($i = 0; $i < $k; ++$i) {
+                for ($j = 0; $j < $nx; ++$j) {
+                    $X[$i][$j] -= $X[$k][$j] * $this->luMatrix[$i][$k];
+                }
+            }
+        }
+
+        return new Matrix($X);
+    }
+}

vendor/markbaker/matrix/classes/src/Decomposition/QR.php

@@ -0,0 +1,191 @@
+<?php
+
+namespace Matrix\Decomposition;
+
+use Matrix\Exception;
+use Matrix\Matrix;
+
+class QR
+{
+    private $qrMatrix;
+    private $rows;
+    private $columns;
+
+    private $rDiagonal = [];
+
+    public function __construct(Matrix $matrix)
+    {
+        $this->qrMatrix = $matrix->toArray();
+        $this->rows = $matrix->rows;
+        $this->columns = $matrix->columns;
+
+        $this->decompose();
+    }
+
+    public function getHouseholdVectors(): Matrix
+    {
+        $householdVectors = [];
+        for ($row = 0; $row < $this->rows; ++$row) {
+            for ($column = 0; $column < $this->columns; ++$column) {
+                if ($row >= $column) {
+                    $householdVectors[$row][$column] = $this->qrMatrix[$row][$column];
+                } else {
+                    $householdVectors[$row][$column] = 0.0;
+                }
+            }
+        }
+
+        return new Matrix($householdVectors);
+    }
+
+    public function getQ(): Matrix
+    {
+        $qGrid = [];
+
+        $rowCount = $this->rows;
+        for ($k = $this->columns - 1; $k >= 0; --$k) {
+            for ($i = 0; $i < $this->rows; ++$i) {
+                $qGrid[$i][$k] = 0.0;
+            }
+            $qGrid[$k][$k] = 1.0;
+            if ($this->columns > $this->rows) {
+                $qGrid = array_slice($qGrid, 0, $this->rows);
+            }
+
+            for ($j = $k; $j < $this->columns; ++$j) {
+                if (isset($this->qrMatrix[$k], $this->qrMatrix[$k][$k]) && $this->qrMatrix[$k][$k] != 0.0) {
+                    $s = 0.0;
+                    for ($i = $k; $i < $this->rows; ++$i) {
+                        $s += $this->qrMatrix[$i][$k] * $qGrid[$i][$j];
+                    }
+                    $s = -$s / $this->qrMatrix[$k][$k];
+                    for ($i = $k; $i < $this->rows; ++$i) {
+                        $qGrid[$i][$j] += $s * $this->qrMatrix[$i][$k];
+                    }
+                }
+            }
+        }
+
+        array_walk(
+            $qGrid,
+            function (&$row) use ($rowCount) {
+                $row = array_reverse($row);
+                $row = array_slice($row, 0, $rowCount);
+            }
+        );
+
+        return new Matrix($qGrid);
+    }
+
+    public function getR(): Matrix
+    {
+        $rGrid = [];
+
+        for ($row = 0; $row < $this->columns; ++$row) {
+            for ($column = 0; $column < $this->columns; ++$column) {
+                if ($row < $column) {
+                    $rGrid[$row][$column] = $this->qrMatrix[$row][$column] ?? 0.0;
+                } elseif ($row === $column) {
+                    $rGrid[$row][$column] = $this->rDiagonal[$row] ?? 0.0;
+                } else {
+                    $rGrid[$row][$column] = 0.0;
+                }
+            }
+        }
+
+        if ($this->columns > $this->rows) {
+            $rGrid = array_slice($rGrid, 0, $this->rows);
+        }
+
+        return new Matrix($rGrid);
+    }
+
+    private function hypo($a, $b): float
+    {
+        if (abs($a) > abs($b)) {
+            $r = $b / $a;
+            $r = abs($a) * sqrt(1 + $r * $r);
+        } elseif ($b != 0.0) {
+            $r = $a / $b;
+            $r = abs($b) * sqrt(1 + $r * $r);
+        } else {
+            $r = 0.0;
+        }
+
+        return $r;
+    }
+
+    /**
+     * QR Decomposition computed by Householder reflections.
+     */
+    private function decompose(): void
+    {
+        for ($k = 0; $k < $this->columns; ++$k) {
+            // Compute 2-norm of k-th column without under/overflow.
+            $norm = 0.0;
+            for ($i = $k; $i < $this->rows; ++$i) {
+                $norm = $this->hypo($norm, $this->qrMatrix[$i][$k]);
+            }
+            if ($norm != 0.0) {
+                // Form k-th Householder vector.
+                if ($this->qrMatrix[$k][$k] < 0.0) {
+                    $norm = -$norm;
+                }
+                for ($i = $k; $i < $this->rows; ++$i) {
+                    $this->qrMatrix[$i][$k] /= $norm;
+                }
+                $this->qrMatrix[$k][$k] += 1.0;
+                // Apply transformation to remaining columns.
+                for ($j = $k + 1; $j < $this->columns; ++$j) {
+                    $s = 0.0;
+                    for ($i = $k; $i < $this->rows; ++$i) {
+                        $s += $this->qrMatrix[$i][$k] * $this->qrMatrix[$i][$j];
+                    }
+                    $s = -$s / $this->qrMatrix[$k][$k];
+                    for ($i = $k; $i < $this->rows; ++$i) {
+                        $this->qrMatrix[$i][$j] += $s * $this->qrMatrix[$i][$k];
+                    }
+                }
+            }
+            $this->rDiagonal[$k] = -$norm;
+        }
+    }
+
+    public function isFullRank(): bool
+    {
+        for ($j = 0; $j < $this->columns; ++$j) {
+            if ($this->rDiagonal[$j] == 0.0) {
+                return false;
+            }
+        }
+
+        return true;
+    }
+
+    /**
+     * Least squares solution of A*X = B.
+     *
+     * @param Matrix $B a Matrix with as many rows as A and any number of columns
+     *
+     * @throws Exception
+     *
+     * @return Matrix matrix that minimizes the two norm of Q*R*X-B
+     */
+    public function solve(Matrix $B): Matrix
+    {
+        if ($B->rows !== $this->rows) {
+            throw new Exception('Matrix row dimensions are not equal');
+        }
+
+        if (!$this->isFullRank()) {
+            throw new Exception('Can only perform this operation on a full-rank matrix');
+        }
+
+        // Compute Y = transpose(Q)*B
+        $Y = $this->getQ()->transpose()
+            ->multiply($B);
+        // Solve R*X = Y;
+        return $this->getR()->inverse()
+            ->multiply($Y);
+    }
+}

vendor/markbaker/matrix/classes/src/Div0Exception.php

@@ -0,0 +1,13 @@
+<?php
+
+/**
+ * Exception.
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPMatrix)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Matrix;
+
+class Div0Exception extends Exception
+{
+}

vendor/markbaker/matrix/classes/src/Exception.php

@@ -0,0 +1,13 @@
+<?php
+
+/**
+ * Exception.
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPMatrix)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Matrix;
+
+class Exception extends \Exception
+{
+}

vendor/markbaker/matrix/classes/src/Functions.php

@@ -0,0 +1,376 @@
+<?php
+
+namespace Matrix;
+
+class Functions
+{
+    /**
+     * Validates an array of matrix, converting an array to a matrix if required.
+     *
+     * @param Matrix|array $matrix Matrix or an array to treat as a matrix.
+     * @return Matrix The new matrix
+     * @throws Exception If argument isn't a valid matrix or array.
+     */
+    private static function validateMatrix($matrix)
+    {
+        if (is_array($matrix)) {
+            $matrix = new Matrix($matrix);
+        }
+        if (!$matrix instanceof Matrix) {
+            throw new Exception('Must be Matrix or array');
+        }
+
+        return $matrix;
+    }
+
+    /**
+     * Calculate the adjoint of the matrix
+     *
+     * @param Matrix $matrix The matrix whose adjoint we wish to calculate
+     * @return Matrix
+     *
+     * @throws Exception
+     */
+    private static function getAdjoint(Matrix $matrix)
+    {
+        return self::transpose(
+            self::getCofactors($matrix)
+        );
+    }
+
+    /**
+     * Return the adjoint of this matrix
+     * The adjugate, classical adjoint, or adjunct of a square matrix is the transpose of its cofactor matrix.
+     * The adjugate has sometimes been called the "adjoint", but today the "adjoint" of a matrix normally refers
+     *     to its corresponding adjoint operator, which is its conjugate transpose.
+     *
+     * @param Matrix|array $matrix The matrix whose adjoint we wish to calculate
+     * @return Matrix
+     * @throws Exception
+     **/
+    public static function adjoint($matrix)
+    {
+        $matrix = self::validateMatrix($matrix);
+
+        if (!$matrix->isSquare()) {
+            throw new Exception('Adjoint can only be calculated for a square matrix');
+        }
+
+        return self::getAdjoint($matrix);
+    }
+
+    /**
+     * Calculate the cofactors of the matrix
+     *
+     * @param Matrix $matrix The matrix whose cofactors we wish to calculate
+     * @return Matrix
+     *
+     * @throws Exception
+     */
+    private static function getCofactors(Matrix $matrix)
+    {
+        $cofactors = self::getMinors($matrix);
+        $dimensions = $matrix->rows;
+
+        $cof = 1;
+        for ($i = 0; $i < $dimensions; ++$i) {
+            $cofs = $cof;
+            for ($j = 0; $j < $dimensions; ++$j) {
+                $cofactors[$i][$j] *= $cofs;
+                $cofs = -$cofs;
+            }
+            $cof = -$cof;
+        }
+
+        return new Matrix($cofactors);
+    }
+
+    /**
+     * Return the cofactors of this matrix
+     *
+     * @param Matrix|array $matrix The matrix whose cofactors we wish to calculate
+     * @return Matrix
+     *
+     * @throws Exception
+     */
+    public static function cofactors($matrix)
+    {
+        $matrix = self::validateMatrix($matrix);
+
+        if (!$matrix->isSquare()) {
+            throw new Exception('Cofactors can only be calculated for a square matrix');
+        }
+
+        return self::getCofactors($matrix);
+    }
+
+    /**
+     * @param Matrix $matrix
+     * @param int $row
+     * @param int $column
+     * @return float
+     * @throws Exception
+     */
+    private static function getDeterminantSegment(Matrix $matrix, $row, $column)
+    {
+        $tmpMatrix = $matrix->toArray();
+        unset($tmpMatrix[$row]);
+        array_walk(
+            $tmpMatrix,
+            function (&$row) use ($column) {
+                unset($row[$column]);
+            }
+        );
+
+        return self::getDeterminant(new Matrix($tmpMatrix));
+    }
+
+    /**
+     * Calculate the determinant of the matrix
+     *
+     * @param Matrix $matrix The matrix whose determinant we wish to calculate
+     * @return float
+     *
+     * @throws Exception
+     */
+    private static function getDeterminant(Matrix $matrix)
+    {
+        $dimensions = $matrix->rows;
+        $determinant = 0;
+
+        switch ($dimensions) {
+            case 1:
+                $determinant = $matrix->getValue(1, 1);
+                break;
+            case 2:
+                $determinant = $matrix->getValue(1, 1) * $matrix->getValue(2, 2) -
+                    $matrix->getValue(1, 2) * $matrix->getValue(2, 1);
+                break;
+            default:
+                for ($i = 1; $i <= $dimensions; ++$i) {
+                    $det = $matrix->getValue(1, $i) * self::getDeterminantSegment($matrix, 0, $i - 1);
+                    if (($i % 2) == 0) {
+                        $determinant -= $det;
+                    } else {
+                        $determinant += $det;
+                    }
+                }
+                break;
+        }
+
+        return $determinant;
+    }
+
+    /**
+     * Return the determinant of this matrix
+     *
+     * @param Matrix|array $matrix The matrix whose determinant we wish to calculate
+     * @return float
+     * @throws Exception
+     **/
+    public static function determinant($matrix)
+    {
+        $matrix = self::validateMatrix($matrix);
+
+        if (!$matrix->isSquare()) {
+            throw new Exception('Determinant can only be calculated for a square matrix');
+        }
+
+        return self::getDeterminant($matrix);
+    }
+
+    /**
+     * Return the diagonal of this matrix
+     *
+     * @param Matrix|array $matrix The matrix whose diagonal we wish to calculate
+     * @return Matrix
+     * @throws Exception
+     **/
+    public static function diagonal($matrix)
+    {
+        $matrix = self::validateMatrix($matrix);
+
+        if (!$matrix->isSquare()) {
+            throw new Exception('Diagonal can only be extracted from a square matrix');
+        }
+
+        $dimensions = $matrix->rows;
+        $grid = Builder::createFilledMatrix(0, $dimensions, $dimensions)
+            ->toArray();
+
+        for ($i = 0; $i < $dimensions; ++$i) {
+            $grid[$i][$i] = $matrix->getValue($i + 1, $i + 1);
+        }
+
+        return new Matrix($grid);
+    }
+
+    /**
+     * Return the antidiagonal of this matrix
+     *
+     * @param Matrix|array $matrix The matrix whose antidiagonal we wish to calculate
+     * @return Matrix
+     * @throws Exception
+     **/
+    public static function antidiagonal($matrix)
+    {
+        $matrix = self::validateMatrix($matrix);
+
+        if (!$matrix->isSquare()) {
+            throw new Exception('Anti-Diagonal can only be extracted from a square matrix');
+        }
+
+        $dimensions = $matrix->rows;
+        $grid = Builder::createFilledMatrix(0, $dimensions, $dimensions)
+            ->toArray();
+
+        for ($i = 0; $i < $dimensions; ++$i) {
+            $grid[$i][$dimensions - $i - 1] = $matrix->getValue($i + 1, $dimensions - $i);
+        }
+
+        return new Matrix($grid);
+    }
+
+    /**
+     * Return the identity matrix
+     * The identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix
+     *   with ones on the main diagonal and zeros elsewhere
+     *
+     * @param Matrix|array $matrix The matrix whose identity we wish to calculate
+     * @return Matrix
+     * @throws Exception
+     **/
+    public static function identity($matrix)
+    {
+        $matrix = self::validateMatrix($matrix);
+
+        if (!$matrix->isSquare()) {
+            throw new Exception('Identity can only be created for a square matrix');
+        }
+
+        $dimensions = $matrix->rows;
+
+        return Builder::createIdentityMatrix($dimensions);
+    }
+
+    /**
+     * Return the inverse of this matrix
+     *
+     * @param Matrix|array $matrix The matrix whose inverse we wish to calculate
+     * @return Matrix
+     * @throws Exception
+     **/
+    public static function inverse($matrix, string $type = 'inverse')
+    {
+        $matrix = self::validateMatrix($matrix);
+
+        if (!$matrix->isSquare()) {
+            throw new Exception(ucfirst($type) . ' can only be calculated for a square matrix');
+        }
+
+        $determinant = self::getDeterminant($matrix);
+        if ($determinant == 0.0) {
+            throw new Div0Exception(ucfirst($type) . ' can only be calculated for a matrix with a non-zero determinant');
+        }
+
+        if ($matrix->rows == 1) {
+            return new Matrix([[1 / $matrix->getValue(1, 1)]]);
+        }
+
+        return self::getAdjoint($matrix)
+            ->multiply(1 / $determinant);
+    }
+
+    /**
+     * Calculate the minors of the matrix
+     *
+     * @param Matrix $matrix The matrix whose minors we wish to calculate
+     * @return array[]
+     *
+     * @throws Exception
+     */
+    protected static function getMinors(Matrix $matrix)
+    {
+        $minors = $matrix->toArray();
+        $dimensions = $matrix->rows;
+        if ($dimensions == 1) {
+            return $minors;
+        }
+
+        for ($i = 0; $i < $dimensions; ++$i) {
+            for ($j = 0; $j < $dimensions; ++$j) {
+                $minors[$i][$j] = self::getDeterminantSegment($matrix, $i, $j);
+            }
+        }
+
+        return $minors;
+    }
+
+    /**
+     * Return the minors of the matrix
+     * The minor of a matrix A is the determinant of some smaller square matrix, cut down from A by removing one or
+     *     more of its rows or columns.
+     * Minors obtained by removing just one row and one column from square matrices (first minors) are required for
+     *     calculating matrix cofactors, which in turn are useful for computing both the determinant and inverse of
+     *     square matrices.
+     *
+     * @param Matrix|array $matrix The matrix whose minors we wish to calculate
+     * @return Matrix
+     * @throws Exception
+     **/
+    public static function minors($matrix)
+    {
+        $matrix = self::validateMatrix($matrix);
+
+        if (!$matrix->isSquare()) {
+            throw new Exception('Minors can only be calculated for a square matrix');
+        }
+
+        return new Matrix(self::getMinors($matrix));
+    }
+
+    /**
+     * Return the trace of this matrix
+     * The trace is defined as the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right)
+     *     of the matrix
+     *
+     * @param Matrix|array $matrix The matrix whose trace we wish to calculate
+     * @return float
+     * @throws Exception
+     **/
+    public static function trace($matrix)
+    {
+        $matrix = self::validateMatrix($matrix);
+
+        if (!$matrix->isSquare()) {
+            throw new Exception('Trace can only be extracted from a square matrix');
+        }
+
+        $dimensions = $matrix->rows;
+        $result = 0;
+        for ($i = 1; $i <= $dimensions; ++$i) {
+            $result += $matrix->getValue($i, $i);
+        }
+
+        return $result;
+    }
+
+    /**
+     * Return the transpose of this matrix
+     *
+     * @param Matrix|\a $matrix The matrix whose transpose we wish to calculate
+     * @return Matrix
+     **/
+    public static function transpose($matrix)
+    {
+        $matrix = self::validateMatrix($matrix);
+
+        $array = array_values(array_merge([null], $matrix->toArray()));
+        $grid = call_user_func_array(
+            'array_map',
+            $array
+        );
+
+        return new Matrix($grid);
+    }
+}

vendor/markbaker/matrix/classes/src/Matrix.php

@@ -0,0 +1,423 @@
+<?php
+
+/**
+ *
+ * Class for the management of Matrices
+ *
+ * @copyright  Copyright (c) 2018 Mark Baker (https://github.com/MarkBaker/PHPMatrix)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+
+namespace Matrix;
+
+use Generator;
+use Matrix\Decomposition\LU;
+use Matrix\Decomposition\QR;
+
+/**
+ * Matrix object.
+ *
+ * @package Matrix
+ *
+ * @property-read int $rows The number of rows in the matrix
+ * @property-read int $columns The number of columns in the matrix
+ * @method Matrix antidiagonal()
+ * @method Matrix adjoint()
+ * @method Matrix cofactors()
+ * @method float determinant()
+ * @method Matrix diagonal()
+ * @method Matrix identity()
+ * @method Matrix inverse()
+ * @method Matrix minors()
+ * @method float trace()
+ * @method Matrix transpose()
+ * @method Matrix add(...$matrices)
+ * @method Matrix subtract(...$matrices)
+ * @method Matrix multiply(...$matrices)
+ * @method Matrix divideby(...$matrices)
+ * @method Matrix divideinto(...$matrices)
+ * @method Matrix directsum(...$matrices)
+ */
+class Matrix
+{
+    protected $rows;
+    protected $columns;
+    protected $grid = [];
+
+    /*
+     * Create a new Matrix object from an array of values
+     *
+     * @param array $grid
+     */
+    final public function __construct(array $grid)
+    {
+        $this->buildFromArray(array_values($grid));
+    }
+
+    /*
+     * Create a new Matrix object from an array of values
+     *
+     * @param array $grid
+     */
+    protected function buildFromArray(array $grid): void
+    {
+        $this->rows = count($grid);
+        $columns = array_reduce(
+            $grid,
+            function ($carry, $value) {
+                return max($carry, is_array($value) ? count($value) : 1);
+            }
+        );
+        $this->columns = $columns;
+
+        array_walk(
+            $grid,
+            function (&$value) use ($columns) {
+                if (!is_array($value)) {
+                    $value = [$value];
+                }
+                $value = array_pad(array_values($value), $columns, null);
+            }
+        );
+
+        $this->grid = $grid;
+    }
+
+    /**
+     * Validate that a row number is a positive integer
+     *
+     * @param int $row
+     * @return int
+     * @throws Exception
+     */
+    public static function validateRow(int $row): int
+    {
+        if ((!is_numeric($row)) || (intval($row) < 1)) {
+            throw new Exception('Invalid Row');
+        }
+
+        return (int)$row;
+    }
+
+    /**
+     * Validate that a column number is a positive integer
+     *
+     * @param int $column
+     * @return int
+     * @throws Exception
+     */
+    public static function validateColumn(int $column): int
+    {
+        if ((!is_numeric($column)) || (intval($column) < 1)) {
+            throw new Exception('Invalid Column');
+        }
+
+        return (int)$column;
+    }
+
+    /**
+     * Validate that a row number falls within the set of rows for this matrix
+     *
+     * @param int $row
+     * @return int
+     * @throws Exception
+     */
+    protected function validateRowInRange(int $row): int
+    {
+        $row = static::validateRow($row);
+        if ($row > $this->rows) {
+            throw new Exception('Requested Row exceeds matrix size');
+        }
+
+        return $row;
+    }
+
+    /**
+     * Validate that a column number falls within the set of columns for this matrix
+     *
+     * @param int $column
+     * @return int
+     * @throws Exception
+     */
+    protected function validateColumnInRange(int $column): int
+    {
+        $column = static::validateColumn($column);
+        if ($column > $this->columns) {
+            throw new Exception('Requested Column exceeds matrix size');
+        }
+
+        return $column;
+    }
+
+    /**
+     * Return a new matrix as a subset of rows from this matrix, starting at row number $row, and $rowCount rows
+     * A $rowCount value of 0 will return all rows of the matrix from $row
+     * A negative $rowCount value will return rows until that many rows from the end of the matrix
+     *
+     * Note that row numbers start from 1, not from 0
+     *
+     * @param int $row
+     * @param int $rowCount
+     * @return static
+     * @throws Exception
+     */
+    public function getRows(int $row, int $rowCount = 1): Matrix
+    {
+        $row = $this->validateRowInRange($row);
+        if ($rowCount === 0) {
+            $rowCount = $this->rows - $row + 1;
+        }
+
+        return new static(array_slice($this->grid, $row - 1, (int)$rowCount));
+    }
+
+    /**
+     * Return a new matrix as a subset of columns from this matrix, starting at column number $column, and $columnCount columns
+     * A $columnCount value of 0 will return all columns of the matrix from $column
+     * A negative $columnCount value will return columns until that many columns from the end of the matrix
+     *
+     * Note that column numbers start from 1, not from 0
+     *
+     * @param int $column
+     * @param int $columnCount
+     * @return Matrix
+     * @throws Exception
+     */
+    public function getColumns(int $column, int $columnCount = 1): Matrix
+    {
+        $column = $this->validateColumnInRange($column);
+        if ($columnCount < 1) {
+            $columnCount = $this->columns + $columnCount - $column + 1;
+        }
+
+        $grid = [];
+        for ($i = $column - 1; $i < $column + $columnCount - 1; ++$i) {
+            $grid[] = array_column($this->grid, $i);
+        }
+
+        return (new static($grid))->transpose();
+    }
+
+    /**
+     * Return a new matrix as a subset of rows from this matrix, dropping rows starting at row number $row,
+     *     and $rowCount rows
+     * A negative $rowCount value will drop rows until that many rows from the end of the matrix
+     * A $rowCount value of 0 will remove all rows of the matrix from $row
+     *
+     * Note that row numbers start from 1, not from 0
+     *
+     * @param int $row
+     * @param int $rowCount
+     * @return static
+     * @throws Exception
+     */
+    public function dropRows(int $row, int $rowCount = 1): Matrix
+    {
+        $this->validateRowInRange($row);
+        if ($rowCount === 0) {
+            $rowCount = $this->rows - $row + 1;
+        }
+
+        $grid = $this->grid;
+        array_splice($grid, $row - 1, (int)$rowCount);
+
+        return new static($grid);
+    }
+
+    /**
+     * Return a new matrix as a subset of columns from this matrix, dropping columns starting at column number $column,
+     *     and $columnCount columns
+     * A negative $columnCount value will drop columns until that many columns from the end of the matrix
+     * A $columnCount value of 0 will remove all columns of the matrix from $column
+     *
+     * Note that column numbers start from 1, not from 0
+     *
+     * @param int $column
+     * @param int $columnCount
+     * @return static
+     * @throws Exception
+     */
+    public function dropColumns(int $column, int $columnCount = 1): Matrix
+    {
+        $this->validateColumnInRange($column);
+        if ($columnCount < 1) {
+            $columnCount = $this->columns + $columnCount - $column + 1;
+        }
+
+        $grid = $this->grid;
+        array_walk(
+            $grid,
+            function (&$row) use ($column, $columnCount) {
+                array_splice($row, $column - 1, (int)$columnCount);
+            }
+        );
+
+        return new static($grid);
+    }
+
+    /**
+     * Return a value from this matrix, from the "cell" identified by the row and column numbers
+     * Note that row and column numbers start from 1, not from 0
+     *
+     * @param int $row
+     * @param int $column
+     * @return mixed
+     * @throws Exception
+     */
+    public function getValue(int $row, int $column)
+    {
+        $row = $this->validateRowInRange($row);
+        $column = $this->validateColumnInRange($column);
+
+        return $this->grid[$row - 1][$column - 1];
+    }
+
+    /**
+     * Returns a Generator that will yield each row of the matrix in turn as a vector matrix
+     *     or the value of each cell if the matrix is a column vector
+     *
+     * @return Generator|Matrix[]|mixed[]
+     */
+    public function rows(): Generator
+    {
+        foreach ($this->grid as $i => $row) {
+            yield $i + 1 => ($this->columns == 1)
+                ? $row[0]
+                : new static([$row]);
+        }
+    }
+
+    /**
+     * Returns a Generator that will yield each column of the matrix in turn as a vector matrix
+     *     or the value of each cell if the matrix is a row vector
+     *
+     * @return Generator|Matrix[]|mixed[]
+     */
+    public function columns(): Generator
+    {
+        for ($i = 0; $i < $this->columns; ++$i) {
+            yield $i + 1 => ($this->rows == 1)
+                ? $this->grid[0][$i]
+                : new static(array_column($this->grid, $i));
+        }
+    }
+
+    /**
+     * Identify if the row and column dimensions of this matrix are equal,
+     *     i.e. if it is a "square" matrix
+     *
+     * @return bool
+     */
+    public function isSquare(): bool
+    {
+        return $this->rows === $this->columns;
+    }
+
+    /**
+     * Identify if this matrix is a vector
+     *     i.e. if it comprises only a single row or a single column
+     *
+     * @return bool
+     */
+    public function isVector(): bool
+    {
+        return $this->rows === 1 || $this->columns === 1;
+    }
+
+    /**
+     * Return the matrix as a 2-dimensional array
+     *
+     * @return array
+     */
+    public function toArray(): array
+    {
+        return $this->grid;
+    }
+
+    /**
+     * Solve A*X = B.
+     *
+     * @param Matrix $B Right hand side
+     *
+     * @throws Exception
+     *
+     * @return Matrix ... Solution if A is square, least squares solution otherwise
+     */
+    public function solve(Matrix $B): Matrix
+    {
+        if ($this->columns === $this->rows) {
+            return (new LU($this))->solve($B);
+        }
+
+        return (new QR($this))->solve($B);
+    }
+
+    protected static $getters = [
+        'rows',
+        'columns',
+    ];
+
+    /**
+     * Access specific properties as read-only (no setters)
+     *
+     * @param string $propertyName
+     * @return mixed
+     * @throws Exception
+     */
+    public function __get(string $propertyName)
+    {
+        $propertyName = strtolower($propertyName);
+
+        // Test for function calls
+        if (in_array($propertyName, self::$getters)) {
+            return $this->$propertyName;
+        }
+
+        throw new Exception('Property does not exist');
+    }
+
+    protected static $functions = [
+        'adjoint',
+        'antidiagonal',
+        'cofactors',
+        'determinant',
+        'diagonal',
+        'identity',
+        'inverse',
+        'minors',
+        'trace',
+        'transpose',
+    ];
+
+    protected static $operations = [
+        'add',
+        'subtract',
+        'multiply',
+        'divideby',
+        'divideinto',
+        'directsum',
+    ];
+
+    /**
+     * Returns the result of the function call or operation
+     *
+     * @param string $functionName
+     * @param mixed[] $arguments
+     * @return Matrix|float
+     * @throws Exception
+     */
+    public function __call(string $functionName, $arguments)
+    {
+        $functionName = strtolower(str_replace('_', '', $functionName));
+
+        // Test for function calls
+        if (in_array($functionName, self::$functions, true)) {
+            return Functions::$functionName($this, ...$arguments);
+        }
+        // Test for operation calls
+        if (in_array($functionName, self::$operations, true)) {
+            return Operations::$functionName($this, ...$arguments);
+        }
+        throw new Exception('Function or Operation does not exist');
+    }
+}

vendor/markbaker/matrix/classes/src/Operations.php

@@ -0,0 +1,157 @@
+<?php
+
+namespace Matrix;
+
+use Matrix\Operators\Addition;
+use Matrix\Operators\DirectSum;
+use Matrix\Operators\Division;
+use Matrix\Operators\Multiplication;
+use Matrix\Operators\Subtraction;
+
+class Operations
+{
+    public static function add(...$matrixValues): Matrix
+    {
+        if (count($matrixValues) < 2) {
+            throw new Exception('Addition operation requires at least 2 arguments');
+        }
+
+        $matrix = array_shift($matrixValues);
+
+        if (is_array($matrix)) {
+            $matrix = new Matrix($matrix);
+        }
+        if (!$matrix instanceof Matrix) {
+            throw new Exception('Addition arguments must be Matrix or array');
+        }
+
+        $result = new Addition($matrix);
+
+        foreach ($matrixValues as $matrix) {
+            $result->execute($matrix);
+        }
+
+        return $result->result();
+    }
+
+    public static function directsum(...$matrixValues): Matrix
+    {
+        if (count($matrixValues) < 2) {
+            throw new Exception('DirectSum operation requires at least 2 arguments');
+        }
+
+        $matrix = array_shift($matrixValues);
+
+        if (is_array($matrix)) {
+            $matrix = new Matrix($matrix);
+        }
+        if (!$matrix instanceof Matrix) {
+            throw new Exception('DirectSum arguments must be Matrix or array');
+        }
+
+        $result = new DirectSum($matrix);
+
+        foreach ($matrixValues as $matrix) {
+            $result->execute($matrix);
+        }
+
+        return $result->result();
+    }
+
+    public static function divideby(...$matrixValues): Matrix
+    {
+        if (count($matrixValues) < 2) {
+            throw new Exception('Division operation requires at least 2 arguments');
+        }
+
+        $matrix = array_shift($matrixValues);
+
+        if (is_array($matrix)) {
+            $matrix = new Matrix($matrix);
+        }
+        if (!$matrix instanceof Matrix) {
+            throw new Exception('Division arguments must be Matrix or array');
+        }
+
+        $result = new Division($matrix);
+
+        foreach ($matrixValues as $matrix) {
+            $result->execute($matrix);
+        }
+
+        return $result->result();
+    }
+
+    public static function divideinto(...$matrixValues): Matrix
+    {
+        if (count($matrixValues) < 2) {
+            throw new Exception('Division operation requires at least 2 arguments');
+        }
+
+        $matrix = array_pop($matrixValues);
+        $matrixValues = array_reverse($matrixValues);
+
+        if (is_array($matrix)) {
+            $matrix = new Matrix($matrix);
+        }
+        if (!$matrix instanceof Matrix) {
+            throw new Exception('Division arguments must be Matrix or array');
+        }
+
+        $result = new Division($matrix);
+
+        foreach ($matrixValues as $matrix) {
+            $result->execute($matrix);
+        }
+
+        return $result->result();
+    }
+
+    public static function multiply(...$matrixValues): Matrix
+    {
+        if (count($matrixValues) < 2) {
+            throw new Exception('Multiplication operation requires at least 2 arguments');
+        }
+
+        $matrix = array_shift($matrixValues);
+
+        if (is_array($matrix)) {
+            $matrix = new Matrix($matrix);
+        }
+        if (!$matrix instanceof Matrix) {
+            throw new Exception('Multiplication arguments must be Matrix or array');
+        }
+
+        $result = new Multiplication($matrix);
+
+        foreach ($matrixValues as $matrix) {
+            $result->execute($matrix);
+        }
+
+        return $result->result();
+    }
+
+    public static function subtract(...$matrixValues): Matrix
+    {
+        if (count($matrixValues) < 2) {
+            throw new Exception('Subtraction operation requires at least 2 arguments');
+        }
+
+        $matrix = array_shift($matrixValues);
+
+        if (is_array($matrix)) {
+            $matrix = new Matrix($matrix);
+        }
+        if (!$matrix instanceof Matrix) {
+            throw new Exception('Subtraction arguments must be Matrix or array');
+        }
+
+        $result = new Subtraction($matrix);
+
+        foreach ($matrixValues as $matrix) {
+            $result->execute($matrix);
+        }
+
+        return $result->result();
+    }
+}

vendor/markbaker/matrix/classes/src/Operators/Addition.php

@@ -0,0 +1,68 @@
+<?php
+
+namespace Matrix\Operators;
+
+use Matrix\Matrix;
+use Matrix\Exception;
+
+class Addition extends Operator
+{
+    /**
+     * Execute the addition
+     *
+     * @param mixed $value The matrix or numeric value to add to the current base value
+     * @throws Exception If the provided argument is not appropriate for the operation
+     * @return $this The operation object, allowing multiple additions to be chained
+     **/
+    public function execute($value): Operator
+    {
+        if (is_array($value)) {
+            $value = new Matrix($value);
+        }
+
+        if (is_object($value) && ($value instanceof Matrix)) {
+            return $this->addMatrix($value);
+        } elseif (is_numeric($value)) {
+            return $this->addScalar($value);
+        }
+
+        throw new Exception('Invalid argument for addition');
+    }
+
+    /**
+     * Execute the addition for a scalar
+     *
+     * @param mixed $value The numeric value to add to the current base value
+     * @return $this The operation object, allowing multiple additions to be chained
+     **/
+    protected function addScalar($value): Operator
+    {
+        for ($row = 0; $row < $this->rows; ++$row) {
+            for ($column = 0; $column < $this->columns; ++$column) {
+                $this->matrix[$row][$column] += $value;
+            }
+        }
+
+        return $this;
+    }
+
+    /**
+     * Execute the addition for a matrix
+     *
+     * @param Matrix $value The numeric value to add to the current base value
+     * @return $this The operation object, allowing multiple additions to be chained
+     * @throws Exception If the provided argument is not appropriate for the operation
+     **/
+    protected function addMatrix(Matrix $value): Operator
+    {
+        $this->validateMatchingDimensions($value);
+
+        for ($row = 0; $row < $this->rows; ++$row) {
+            for ($column = 0; $column < $this->columns; ++$column) {
+                $this->matrix[$row][$column] += $value->getValue($row + 1, $column + 1);
+            }
+        }
+
+        return $this;
+    }
+}

vendor/markbaker/matrix/classes/src/Operators/DirectSum.php

@@ -0,0 +1,64 @@
+<?php
+
+namespace Matrix\Operators;
+
+use Matrix\Matrix;
+use Matrix\Exception;
+
+class DirectSum extends Operator
+{
+    /**
+     * Execute the addition
+     *
+     * @param mixed $value The matrix or numeric value to add to the current base value
+     * @return $this The operation object, allowing multiple additions to be chained
+     * @throws Exception If the provided argument is not appropriate for the operation
+     */
+    public function execute($value): Operator
+    {
+        if (is_array($value)) {
+            $value = new Matrix($value);
+        }
+
+        if ($value instanceof Matrix) {
+            return $this->directSumMatrix($value);
+        }
+
+        throw new Exception('Invalid argument for addition');
+    }
+
+    /**
+     * Execute the direct sum for a matrix
+     *
+     * @param Matrix $value The numeric value to concatenate/direct sum with the current base value
+     * @return $this The operation object, allowing multiple additions to be chained
+     **/
+    private function directSumMatrix($value): Operator
+    {
+        $originalColumnCount = count($this->matrix[0]);
+        $originalRowCount = count($this->matrix);
+        $valColumnCount = $value->columns;
+        $valRowCount = $value->rows;
+        $value = $value->toArray();
+
+        for ($row = 0; $row < $this->rows; ++$row) {
+            $this->matrix[$row] = array_merge($this->matrix[$row], array_fill(0, $valColumnCount, 0));
+        }
+
+        $this->matrix = array_merge(
+            $this->matrix,
+            array_fill(0, $valRowCount, array_fill(0, $originalColumnCount, 0))
+        );
+
+        for ($row = $originalRowCount; $row < $originalRowCount + $valRowCount; ++$row) {
+            array_splice(
+                $this->matrix[$row],
+                $originalColumnCount,
+                $valColumnCount,
+                $value[$row - $originalRowCount]
+            );
+        }
+
+        return $this;
+    }
+}

vendor/markbaker/matrix/classes/src/Operators/Division.php

@@ -0,0 +1,35 @@
+<?php
+
+namespace Matrix\Operators;
+
+use Matrix\Div0Exception;
+use Matrix\Exception;
+use \Matrix\Matrix;
+use \Matrix\Functions;
+
+class Division extends Multiplication
+{
+    /**
+     * Execute the division
+     *
+     * @param mixed $value The matrix or numeric value to divide the current base value by
+     * @throws Exception If the provided argument is not appropriate for the operation
+     * @return $this The operation object, allowing multiple divisions to be chained
+     **/
+    public function execute($value, string $type = 'division'): Operator
+    {
+        if (is_array($value)) {
+            $value = new Matrix($value);
+        }
+
+        if (is_object($value) && ($value instanceof Matrix)) {
+            $value = Functions::inverse($value, $type);
+
+            return $this->multiplyMatrix($value, $type);
+        } elseif (is_numeric($value)) {
+            return $this->multiplyScalar(1 / $value, $type);
+        }
+
+        throw new Exception('Invalid argument for division');
+    }
+}

vendor/markbaker/matrix/classes/src/Operators/Multiplication.php

@@ -0,0 +1,86 @@
+<?php
+
+namespace Matrix\Operators;
+
+use Matrix\Matrix;
+use \Matrix\Builder;
+use Matrix\Exception;
+use Throwable;
+
+class Multiplication extends Operator
+{
+    /**
+     * Execute the multiplication
+     *
+     * @param mixed $value The matrix or numeric value to multiply the current base value by
+     * @throws Exception If the provided argument is not appropriate for the operation
+     * @return $this The operation object, allowing multiple multiplications to be chained
+     **/
+    public function execute($value, string $type = 'multiplication'): Operator
+    {
+        if (is_array($value)) {
+            $value = new Matrix($value);
+        }
+
+        if (is_object($value) && ($value instanceof Matrix)) {
+            return $this->multiplyMatrix($value, $type);
+        } elseif (is_numeric($value)) {
+            return $this->multiplyScalar($value, $type);
+        }
+
+        throw new Exception("Invalid argument for $type");
+    }
+
+    /**
+     * Execute the multiplication for a scalar
+     *
+     * @param mixed $value The numeric value to multiply with the current base value
+     * @return $this The operation object, allowing multiple mutiplications to be chained
+     **/
+    protected function multiplyScalar($value, string $type = 'multiplication'): Operator
+    {
+        try {
+            for ($row = 0; $row < $this->rows; ++$row) {
+                for ($column = 0; $column < $this->columns; ++$column) {
+                    $this->matrix[$row][$column] *= $value;
+                }
+            }
+        } catch (Throwable $e) {
+            throw new Exception("Invalid argument for $type");
+        }
+
+        return $this;
+    }
+
+    /**
+     * Execute the multiplication for a matrix
+     *
+     * @param Matrix $value The numeric value to multiply with the current base value
+     * @return $this The operation object, allowing multiple mutiplications to be chained
+     * @throws Exception If the provided argument is not appropriate for the operation
+     **/
+    protected function multiplyMatrix(Matrix $value, string $type = 'multiplication'): Operator
+    {
+        $this->validateReflectingDimensions($value);
+
+        $newRows = $this->rows;
+        $newColumns = $value->columns;
+        $matrix = Builder::createFilledMatrix(0, $newRows, $newColumns)
+            ->toArray();
+        try {
+            for ($row = 0; $row < $newRows; ++$row) {
+                for ($column = 0; $column < $newColumns; ++$column) {
+                    $columnData = $value->getColumns($column + 1)->toArray();
+                    foreach ($this->matrix[$row] as $key => $valueData) {
+                        $matrix[$row][$column] += $valueData * $columnData[$key][0];
+                    }
+                }
+            }
+        } catch (Throwable $e) {
+            throw new Exception("Invalid argument for $type");
+        }
+        $this->matrix = $matrix;
+
+        return $this;
+    }
+}

vendor/markbaker/matrix/classes/src/Operators/Operator.php

@@ -0,0 +1,78 @@
+<?php
+
+namespace Matrix\Operators;
+
+use Matrix\Matrix;
+use Matrix\Exception;
+
+abstract class Operator
+{
+    /**
+     * Stored internally as a 2-dimension array of values
+     *
+     * @property mixed[][] $matrix
+     **/
+    protected $matrix;
+
+    /**
+     * Number of rows in the matrix
+     *
+     * @property integer $rows
+     **/
+    protected $rows;
+
+    /**
+     * Number of columns in the matrix
+     *
+     * @property integer $columns
+     **/
+    protected $columns;
+
+    /**
+     * Create an new handler object for the operation
+     *
+     * @param Matrix $matrix The base Matrix object on which the operation will be performed
+     */
+    public function __construct(Matrix $matrix)
+    {
+        $this->rows = $matrix->rows;
+        $this->columns = $matrix->columns;
+        $this->matrix = $matrix->toArray();
+    }
+
+    /**
+     * Compare the dimensions of the matrices being operated on to see if they are valid for addition/subtraction
+     *
+     * @param Matrix $matrix The second Matrix object on which the operation will be performed
+     * @throws Exception
+     */
+    protected function validateMatchingDimensions(Matrix $matrix): void
+    {
+        if (($this->rows != $matrix->rows) || ($this->columns != $matrix->columns)) {
+            throw new Exception('Matrices have mismatched dimensions');
+        }
+    }
+
+    /**
+     * Compare the dimensions of the matrices being operated on to see if they are valid for multiplication/division
+     *
+     * @param Matrix $matrix The second Matrix object on which the operation will be performed
+     * @throws Exception
+     */
+    protected function validateReflectingDimensions(Matrix $matrix): void
+    {
+        if ($this->columns != $matrix->rows) {
+            throw new Exception('Matrices have mismatched dimensions');
+        }
+    }
+
+    /**
+     * Return the result of the operation
+     *
+     * @return Matrix
+     */
+    public function result(): Matrix
+    {
+        return new Matrix($this->matrix);
+    }
+}

vendor/markbaker/matrix/classes/src/Operators/Subtraction.php

@@ -0,0 +1,68 @@
+<?php
+
+namespace Matrix\Operators;
+
+use Matrix\Matrix;
+use Matrix\Exception;
+
+class Subtraction extends Operator
+{
+    /**
+     * Execute the subtraction
+     *
+     * @param mixed $value The matrix or numeric value to subtract from the current base value
+     * @throws Exception If the provided argument is not appropriate for the operation
+     * @return $this The operation object, allowing multiple subtractions to be chained
+     **/
+    public function execute($value): Operator
+    {
+        if (is_array($value)) {
+            $value = new Matrix($value);
+        }
+
+        if (is_object($value) && ($value instanceof Matrix)) {
+            return $this->subtractMatrix($value);
+        } elseif (is_numeric($value)) {
+            return $this->subtractScalar($value);
+        }
+
+        throw new Exception('Invalid argument for subtraction');
+    }
+
+    /**
+     * Execute the subtraction for a scalar
+     *
+     * @param mixed $value The numeric value to subtracted from the current base value
+     * @return $this The operation object, allowing multiple additions to be chained
+     **/
+    protected function subtractScalar($value): Operator
+    {
+        for ($row = 0; $row < $this->rows; ++$row) {
+            for ($column = 0; $column < $this->columns; ++$column) {
+                $this->matrix[$row][$column] -= $value;
+            }
+        }
+
+        return $this;
+    }
+
+    /**
+     * Execute the subtraction for a matrix
+     *
+     * @param Matrix $value The numeric value to subtract from the current base value
+     * @return $this The operation object, allowing multiple subtractions to be chained
+     * @throws Exception If the provided argument is not appropriate for the operation
+     **/
+    protected function subtractMatrix(Matrix $value): Operator
+    {
+        $this->validateMatchingDimensions($value);
+
+        for ($row = 0; $row < $this->rows; ++$row) {
+            for ($column = 0; $column < $this->columns; ++$column) {
+                $this->matrix[$row][$column] -= $value->getValue($row + 1, $column + 1);
+            }
+        }
+
+        return $this;
+    }
+}

vendor/markbaker/matrix/examples/test.php

@@ -0,0 +1,33 @@
+<?php
+
+use Matrix\Matrix;
+use Matrix\Decomposition\QR;
+
+include __DIR__ . '/../vendor/autoload.php';
+
+$grid = [
+    [0, 1],
+    [-1, 0],
+];
+
+$targetGrid = [
+    [-1],
+    [2],
+];
+
+$matrix = new Matrix($grid);
+$target = new Matrix($targetGrid);
+
+$decomposition = new QR($matrix);
+
+$X = $decomposition->solve($target);
+
+echo 'X', PHP_EOL;
+var_export($X->toArray());
+echo PHP_EOL;
+
+$resolve = $matrix->multiply($X);
+
+echo 'Resolve', PHP_EOL;
+var_export($resolve->toArray());
+echo PHP_EOL;

vendor/markbaker/matrix/infection.json.dist

@@ -0,0 +1,17 @@
+{
+    "timeout": 1,
+    "source": {
+        "directories": [
+            "classes\/src"
+        ]
+    },
+    "logs": {
+        "text": "build/infection/text.log",
+        "summary": "build/infection/summary.log",
+        "debug": "build/infection/debug.log",
+        "perMutator": "build/infection/perMutator.md"
+    },
+    "mutators": {
+        "@default": true
+    }
+}