Updates to 3rd party libraries

Add Dockerfile and specific docker-php.ini

inc/vendor/markbaker/complex/classes/src/functions/abs.php

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+<?php
+
+/**
+ *
+ * Function code for the complex abs() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * 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    $complex    Complex number or a numeric value.
+ * @return    float            The absolute (or rho) value of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ *
+ * @see    rho
+ *
+ */
+function abs($complex)
+{
+    return rho($complex);
+}

inc/vendor/markbaker/complex/classes/src/functions/acos.php

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+<?php
+
+/**
+ *
+ * Function code for the complex acos() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse cosine of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse cosine of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function acos($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    $square = clone $complex;
+    $square = multiply($square, $complex);
+    $invsqrt = new Complex(1.0);
+    $invsqrt = subtract($invsqrt, $square);
+    $invsqrt = sqrt($invsqrt);
+    $adjust = new Complex(
+        $complex->getReal() - $invsqrt->getImaginary(),
+        $complex->getImaginary() + $invsqrt->getReal()
+    );
+    $log = ln($adjust);
+
+    return new Complex(
+        $log->getImaginary(),
+        -1 * $log->getReal()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/acosh.php

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+<?php
+
+/**
+ *
+ * Function code for the complex acosh() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse hyperbolic cosine of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse hyperbolic cosine of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function acosh($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->isReal() && ($complex->getReal() > 1)) {
+        return new Complex(\acosh($complex->getReal()));
+    }
+
+    $acosh = acos($complex)
+        ->reverse();
+    if ($acosh->getReal() < 0.0) {
+        $acosh = $acosh->invertReal();
+    }
+
+    return $acosh;
+}

inc/vendor/markbaker/complex/classes/src/functions/acot.php

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+<?php
+
+/**
+ *
+ * Function code for the complex acot() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse cotangent of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse cotangent of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function acot($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    return atan(inverse($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/acoth.php

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+<?php
+
+/**
+ *
+ * Function code for the complex acoth() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse hyperbolic cotangent of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse hyperbolic cotangent of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function acoth($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    return atanh(inverse($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/acsc.php

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+<?php
+
+/**
+ *
+ * Function code for the complex acsc() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse cosecant of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse cosecant of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function acsc($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+        return INF;
+    }
+
+    return asin(inverse($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/acsch.php

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+<?php
+
+/**
+ *
+ * Function code for the complex acsch() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse hyperbolic cosecant of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse hyperbolic cosecant of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function acsch($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+        return INF;
+    }
+
+    return asinh(inverse($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/argument.php

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+<?php
+
+/**
+ *
+ * Function code for the complex argument() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace 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    $complex    Complex number or a numeric value.
+ * @return    float            The argument (or theta) value of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ *
+ * @see    theta
+ */
+function argument($complex)
+{
+    return theta($complex);
+}

inc/vendor/markbaker/complex/classes/src/functions/asec.php

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+<?php
+
+/**
+ *
+ * Function code for the complex asec() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse secant of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse secant of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function asec($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+        return INF;
+    }
+
+    return acos(inverse($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/asech.php

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+<?php
+
+/**
+ *
+ * Function code for the complex asech() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse hyperbolic secant of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse hyperbolic secant of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function asech($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+        return INF;
+    }
+
+    return acosh(inverse($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/asin.php

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+<?php
+
+/**
+ *
+ * Function code for the complex asin() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse sine of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse sine of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function asin($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    $square = multiply($complex, $complex);
+    $invsqrt = new Complex(1.0);
+    $invsqrt = subtract($invsqrt, $square);
+    $invsqrt = sqrt($invsqrt);
+    $adjust = new Complex(
+        $invsqrt->getReal() - $complex->getImaginary(),
+        $invsqrt->getImaginary() + $complex->getReal()
+    );
+    $log = ln($adjust);
+
+    return new Complex(
+        $log->getImaginary(),
+        -1 * $log->getReal()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/asinh.php

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+<?php
+
+/**
+ *
+ * Function code for the complex asinh() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse hyperbolic sine of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse hyperbolic sine of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function asinh($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->isReal() && ($complex->getReal() > 1)) {
+        return new Complex(\asinh($complex->getReal()));
+    }
+
+    $asinh = clone $complex;
+    $asinh = $asinh->reverse()
+        ->invertReal();
+    $asinh = asin($asinh);
+    return $asinh->reverse()
+        ->invertImaginary();
+}

inc/vendor/markbaker/complex/classes/src/functions/atan.php

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+<?php
+
+/**
+ *
+ * Function code for the complex atan() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+//include_once 'Math/Complex.php';
+//include_once 'Math/ComplexOp.php';
+
+/**
+ * Returns the inverse tangent of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse tangent of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function atan($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;
+    $d1Value = subtract($d1Value, $t1Value);
+    $d2Value = add($t1Value, $uValue);
+    $uResult = $d1Value->divideBy($d2Value);
+    $uResult = ln($uResult);
+
+    return new Complex(
+        (($uResult->getImaginary() == M_PI) ? -M_PI : $uResult->getImaginary()) * -0.5,
+        $uResult->getReal() * 0.5,
+        $complex->getSuffix()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/atanh.php

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+<?php
+
+/**
+ *
+ * Function code for the complex atanh() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse hyperbolic tangent of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse hyperbolic tangent of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function atanh($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));
+        }
+    }
+
+    $iComplex = clone $complex;
+    $iComplex = $iComplex->invertImaginary()
+        ->reverse();
+    return atan($iComplex)
+        ->invertReal()
+        ->reverse();
+}

inc/vendor/markbaker/complex/classes/src/functions/conjugate.php

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+<?php
+
+/**
+ *
+ * Function code for the complex conjugate() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the complex conjugate of a complex number
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The conjugate of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function conjugate($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    return new Complex(
+        $complex->getReal(),
+        -1 * $complex->getImaginary(),
+        $complex->getSuffix()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/cos.php

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+<?php
+
+/**
+ *
+ * Function code for the complex cos() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the cosine of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The cosine of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function cos($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->isReal()) {
+        return new Complex(\cos($complex->getReal()));
+    }
+
+    return conjugate(
+        new Complex(
+            \cos($complex->getReal()) * \cosh($complex->getImaginary()),
+            \sin($complex->getReal()) * \sinh($complex->getImaginary()),
+            $complex->getSuffix()
+        )
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/cosh.php

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+<?php
+
+/**
+ *
+ * Function code for the complex cosh() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the hyperbolic cosine of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The hyperbolic cosine of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function cosh($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()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/cot.php

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+<?php
+
+/**
+ *
+ * Function code for the complex cot() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the cotangent of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The cotangent of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function cot($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+        return new Complex(INF);
+    }
+
+    return inverse(tan($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/coth.php

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+<?php
+
+/**
+ *
+ * Function code for the complex coth() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the hyperbolic cotangent of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The hyperbolic cotangent of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function coth($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+    return inverse(tanh($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/csc.php

@@ -0,0 +1,29 @@
+<?php
+
+/**
+ *
+ * Function code for the complex csc() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the cosecant of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The cosecant of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function csc($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+        return INF;
+    }
+
+    return inverse(sin($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/csch.php

@@ -0,0 +1,29 @@
+<?php
+
+/**
+ *
+ * Function code for the complex csch() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the hyperbolic cosecant of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The hyperbolic cosecant of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function csch($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) {
+        return INF;
+    }
+
+    return inverse(sinh($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/exp.php

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+<?php
+
+/**
+ *
+ * Function code for the complex exp() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the exponential of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The exponential of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function exp($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()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/inverse.php

@@ -0,0 +1,29 @@
+<?php
+
+/**
+ *
+ * Function code for the complex inverse() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the inverse of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The inverse of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function inverse($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);
+}

inc/vendor/markbaker/complex/classes/src/functions/ln.php

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+<?php
+
+/**
+ *
+ * Function code for the complex ln() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the natural logarithm of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The natural logarithm of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException  If the real and the imaginary parts are both zero
+ */
+function ln($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    if (($complex->getReal() == 0.0) && ($complex->getImaginary() == 0.0)) {
+        throw new \InvalidArgumentException();
+    }
+
+    return new Complex(
+        \log(rho($complex)),
+        theta($complex),
+        $complex->getSuffix()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/log10.php

@@ -0,0 +1,32 @@
+<?php
+
+/**
+ *
+ * Function code for the complex log10() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the common logarithm (base 10) of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The common logarithm (base 10) of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException  If the real and the imaginary parts are both zero
+ */
+function log10($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, $complex->getSuffix());
+    }
+
+    return ln($complex)
+        ->multiply(\log10(Complex::EULER));
+}

inc/vendor/markbaker/complex/classes/src/functions/log2.php

@@ -0,0 +1,32 @@
+<?php
+
+/**
+ *
+ * Function code for the complex log2() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the base-2 logarithm of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The base-2 logarithm of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException  If the real and the imaginary parts are both zero
+ */
+function log2($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, $complex->getSuffix());
+    }
+
+    return ln($complex)
+        ->multiply(\log(Complex::EULER, 2));
+}

inc/vendor/markbaker/complex/classes/src/functions/negative.php

@@ -0,0 +1,31 @@
+<?php
+
+/**
+ *
+ * Function code for the complex negative() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the negative of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    float            The negative value of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ *
+ * @see    rho
+ *
+ */
+function negative($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    return new Complex(
+        -1 * $complex->getReal(),
+        -1 * $complex->getImaginary(),
+        $complex->getSuffix()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/pow.php

@@ -0,0 +1,40 @@
+<?php
+
+/**
+ *
+ * Function code for the complex pow() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns a complex number raised to a power.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @param     float|integer    $power      The power to raise this value to
+ * @return    Complex          The complex argument raised to the real power.
+ * @throws    Exception        If the power argument isn't a valid real
+ */
+function pow($complex, $power)
+{
+    $complex = Complex::validateComplexArgument($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());
+}

inc/vendor/markbaker/complex/classes/src/functions/rho.php

@@ -0,0 +1,28 @@
+<?php
+
+/**
+ *
+ * Function code for the complex rho() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * 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    $complex    Complex number or a numeric value.
+ * @return    float            The rho value of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function rho($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    return \sqrt(
+        ($complex->getReal() * $complex->getReal()) +
+        ($complex->getImaginary() * $complex->getImaginary())
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/sec.php

@@ -0,0 +1,25 @@
+<?php
+
+/**
+ *
+ * Function code for the complex sec() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the secant of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The secant of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function sec($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    return inverse(cos($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/sech.php

@@ -0,0 +1,25 @@
+<?php
+
+/**
+ *
+ * Function code for the complex sech() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the hyperbolic secant of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The hyperbolic secant of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function sech($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    return inverse(cosh($complex));
+}

inc/vendor/markbaker/complex/classes/src/functions/sin.php

@@ -0,0 +1,32 @@
+<?php
+
+/**
+ *
+ * Function code for the complex sin() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the sine of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The sine of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function sin($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()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/sinh.php

@@ -0,0 +1,32 @@
+<?php
+
+/**
+ *
+ * Function code for the complex sinh() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the hyperbolic sine of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The hyperbolic sine of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function sinh($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()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/sqrt.php

@@ -0,0 +1,29 @@
+<?php
+
+/**
+ *
+ * Function code for the complex sqrt() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the square root of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The Square root of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function sqrt($complex)
+{
+    $complex = Complex::validateComplexArgument($complex);
+
+    $theta = theta($complex);
+    $delta1 = \cos($theta / 2);
+    $delta2 = \sin($theta / 2);
+    $rho = \sqrt(rho($complex));
+
+    return new Complex($delta1 * $rho, $delta2 * $rho, $complex->getSuffix());
+}

inc/vendor/markbaker/complex/classes/src/functions/tan.php

@@ -0,0 +1,40 @@
+<?php
+
+/**
+ *
+ * Function code for the complex tan() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the tangent of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The tangent of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function tan($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(sech($imaginary)->getReal(), 2) * \tan($real) / $divisor,
+        \pow(sec($real)->getReal(), 2) * \tanh($imaginary) / $divisor,
+        $complex->getSuffix()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/tanh.php

@@ -0,0 +1,35 @@
+<?php
+
+/**
+ *
+ * Function code for the complex tanh() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * Returns the hyperbolic tangent of a complex number.
+ *
+ * @param     Complex|mixed    $complex    Complex number or a numeric value.
+ * @return    Complex          The hyperbolic tangent of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ * @throws    \InvalidArgumentException    If function would result in a division by zero
+ */
+function tanh($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()
+    );
+}

inc/vendor/markbaker/complex/classes/src/functions/theta.php

@@ -0,0 +1,38 @@
+<?php
+
+/**
+ *
+ * Function code for the complex theta() function
+ *
+ * @copyright  Copyright (c) 2013-2018 Mark Baker (https://github.com/MarkBaker/PHPComplex)
+ * @license    https://opensource.org/licenses/MIT    MIT
+ */
+namespace Complex;
+
+/**
+ * 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    $complex    Complex number or a numeric value.
+ * @return    float            The theta value of the complex argument.
+ * @throws    Exception        If argument isn't a valid real or complex number.
+ */
+function theta($complex)
+{
+    $complex = Complex::validateComplexArgument($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()));
+}