cvs: pear /Math_Complex Complex.php ComplexOp.php package.xml testcomplex.php
| From: | Jesus M. Castagnetto | Date: | Sun, 24 Nov 2002 07:14:22 +0000 |
| Subject: | cvs: pear /Math_Complex Complex.php ComplexOp.php package.xml testcomplex.php | ||
| Groups: | php.pear.cvs | ||
| Request: | Send a blank email to pear-cvs+get-7556@lists.php.net to get a copy of this message | ||
jmcastagnetto Sun Nov 24 02:14:22 2002 EDT
Added files:
/pear/Math_Complex Complex.php ComplexOp.php package.xml
testcomplex.php
Log:
Initial import, with some added methods for complex operations
Index: pear/Math_Complex/Complex.php +++ pear/Math_Complex/Complex.php <?php // // +----------------------------------------------------------------------+ // | PHP Version 4 | // +----------------------------------------------------------------------+ // | Copyright (c) 1997-2002 The PHP Group | // +----------------------------------------------------------------------+ // | This source file is subject to version 2.0 of the PHP license, | // | that is bundled with this package in the file LICENSE, and is | // | available at through the world-wide-web at | // | http://www.php.net/license/2_02.txt. | // | If you did not receive a copy of the PHP license and are unable to | // | obtain it through the world-wide-web, please send a note to | // | license@php.net so we can mail you a copy immediately. | // +----------------------------------------------------------------------+ // | Authors: Jesus M. Castagnetto <jmcastagnetto@php.net> | // +----------------------------------------------------------------------+ // // $Id: Complex.php,v 1.1 2002/11/24 07:14:22 jmcastagnetto Exp $ // include_once "PEAR.php"; /** * Math_Complex: class to represent an manipulate complex numbers (z = a + b*i) * * Originally this class was part of NumPHP (Numeric PHP package) * * @author Jesus M. Castagnetto <jmcastagnetto@php.net> * @version 0.8 * @access public * @package Math_Complex */ class Math_Complex {/*{{{*/ /** * The real part of the complex number * * @var float * @access private */ var $real; /** * The imaginary part of the complex number * * @var float * @access private */ var $im; /** * Constructor for Math_Complex * * @param float $real Real part of the number * @param float $im Imaginary part of the number * @returns object Math_Complex * @access public */ function Math_Complex($real, $im) {/*{{{*/ $this->real = floatval($real); $this->im = floatval($im); }/*}}}*/ /** * Simple string representation of the number * * @returns string * @access public */ function toString() {/*{{{*/ $r = $this->getReal(); $i = $this->getIm(); $str = $r; $str .= ($i < 0) ? ' - ' : ' + '; $str .= abs($i).'i'; return $str; }/*}}}*/ /** * Returns the square of the magnitude of the number * * @returns float * @access public */ function abs2() {/*{{{*/ return ($this->real*$this->real + $this->im*$this->im); } /*}}}*/ /** * Returns the magnitude (also referred as norm) of the number * * @returns float * @access public */ function abs() {/*{{{*/ return sqrt($this->abs2()); }/*}}}*/ /** * Returns the norm of the number * Alias of Math_Complex::abs() * * @returns float * @access public */ function norm() {/*{{{*/ return $this->abs(); }/*}}}*/ /** * Returns the argument of the complex number * * @returns mixed A float on success, a PEAR_Error otherwise * @access public */ function arg() {/*{{{*/ $arg = atan2($this->im,$this->real); if (M_PI < $arg || $arg < -1*M_PI) { return PEAR::raiseError('Argument has an impossible value'); } else { return $arg; } }/*}}}*/ /** * Returns the angle (argument) associated with the complex number * Alias of Math_Complex::arg() * * @returns mixed A float on success, a PEAR_Error otherwise * @access public */ function angle() {/*{{{*/ return $this->arg(); }/*}}}*/ /** * Returns the real part of the complex number * * @return float * @access pulic */ function getReal() {/*{{{*/ return $this->real; }/*}}}*/ /** * Returns the imaginary part of the complex number * @return float * @access public */ function getIm() {/*{{{*/ return $this->im; }/*}}}*/ } /* end of Math_Complex class *//*}}}*/ ?> Index: pear/Math_Complex/ComplexOp.php +++ pear/Math_Complex/ComplexOp.php <?php // // +----------------------------------------------------------------------+ // | PHP Version 4 | // +----------------------------------------------------------------------+ // | Copyright (c) 1997-2002 The PHP Group | // +----------------------------------------------------------------------+ // | This source file is subject to version 2.0 of the PHP license, | // | that is bundled with this package in the file LICENSE, and is | // | available at through the world-wide-web at | // | http://www.php.net/license/2_02.txt. | // | If you did not receive a copy of the PHP license and are unable to | // | obtain it through the world-wide-web, please send a note to | // | license@php.net so we can mail you a copy immediately. | // +----------------------------------------------------------------------+ // | Authors: Jesus M. Castagnetto <jmcastagnetto@php.net> | // +----------------------------------------------------------------------+ // // $Id: ComplexOp.php,v 1.1 2002/11/24 07:14:22 jmcastagnetto Exp $ // include_once 'PEAR.php'; include_once 'Math/Complex.php'; include_once 'Math/TrigOp.php'; /** * Math_ComplexOp: static class to operate on Math_Complex objects * * Originally this class was part of NumPHP (Numeric PHP package) * * @author Jesus M. Castagnetto <jmcastagnetto@php.net> * @version 0.8 * @access public * @package Math_Complex */ class Math_ComplexOp {/*{{{*/ /** * Checks if a given object is an instance of PEAR::Math_Complex * * @returns boolean * @access public */ function isComplex(&$c1) {/*{{{*/ if (function_exists('is_a')) { return is_a(&$c1, 'math_complex'); } else { return (get_class($c1) == 'math_complex' || is_subclass_of($c1, 'math_complex')); } }/*}}}*/ /** * Converts a polar complex z = r*exp(theta*i) to z = a + b*i * * @param float $r * @param float $theta * @returns object Math_Complex * @access public */ function &createFromPolar ($r, $theta) {/*{{{*/ $r = floatval($r); $theta = floatval($theta); $a = $r * cos($theta); $b = sin($theta); return new Math_Complex ( $a, $b ); }/*}}}*/ // methods below need a valid Math_Complex object as parameter /** * Calculates the complex square root of a complex number * z = sqrt(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &sqrt (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $x = abs($c1->getReal()); $y = abs($c1->getIm()); if ($x == 0.0 && $y == 0) { $r = $i = 0.0; } else { if ($x >= $y) { $t = $y / $x; $w = sqrt($x) * sqrt(0.5 * (1.0 + sqrt(1.0 + $t*$t))); } else { $t = $x / $y; $w = sqrt($y) * sqrt(0.5 * ($t + sqrt(1.0 + $t*$t))); } if ($c1->getReal() >= 0.0) { $r = $w; $i = $c1->getIm() / (2.0 * $w); } else { $i = ($c1->getIm() >= 0) ? $w : -1 * $w; $r = $c1->getIm() / (2.0 * $i); } } return new Math_Complex ($r, $i); }/*}}}*/ /** * Calculates the complex square root of a real number * z = sqrt(realnumber) * * @param float $realnum A float * @returns object Math_Complex * @access public */ function &sqrtReal ($realnum) {/*{{{*/ if ($realnum >= 0) { $r = sqrt($realnum); $i = 0.0; } else { $r = 0.0; $i = sqrt(-1 * $realnum); } return new Math_Complex($r, $i); }/*}}}*/ /** * Calculates the exponential of a complex number * z = exp(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &exp (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $rho = exp($c1->getReal()); $theta = $c1->getIm(); $r = $rho * cos($theta); $i = $rho * sin($theta); return new Math_Complex($r, $i); }/*}}}*/ /** * Calculates the logarithm (base 2) of a complex number * z = log(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &log (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $r = log($c1->abs()); $i = $c1->arg(); return new Math_Complex($r, $i); }/*}}}*/ /** * Calculates the logarithm (base 10) of a complex number * z = log10(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &log10 (&$c1) {/*{{{*/ $log = Math_ComplexOp::log($c1); if (PEAR::isError($log)) return $log; return Math_ComplexOp::multReal ($log, 1/log(10)); }/*}}}*/ /** * Calculates the conjugate of a complex number * z = conj(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &conjugate (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); return new Math_Complex($c1->getReal(), -1 * $c1->getIm()); }/*}}}*/ /** * Calculates the negative of a complex number * z = -c1 * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &negative (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) { return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); } else { return new Math_Complex(-1 * $c1->getReal(), -1 * $c1->getIm()); } }/*}}}*/ /** * Calculates the inverse of a complex number * z = 1/c1 * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &inverse (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $abs = $c1->abs(); if ($abs == 0.0) return PEAR::raiseError('Math_Complex object\'s norm is zero'); $temp = 1.0 / $c1->abs(); $r = $c1->getReal() * $temp * $temp; $i = -1 * $c1->getIm() * $temp * $temp; return new Math_Complex ($r, $i); }/*}}}*/ // Trigonometric methods /** * Calculates the sine of a complex number * z = sin(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &sin (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $a = $c1->getReal(); $b = $c1->getIm(); $r = sin($a)*cosh($b); $i = cos($a)*sinh($b); return new Math_Complex( $r, $i ); }/*}}}*/ /** * Calculates the cosine of a complex number * z = cos(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &cos (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $a = $c1->getReal(); $b = $c1->getIm(); $r = cos($a)*cosh($b); $i = sin($a)*sinh($b); return new Math_Complex( $r, $i ); }/*}}}*/ /** * Calculates the tangent of a complex number * z = tan(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &tan (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $a = $c1->getReal(); $b = $c1->getIm(); $den = 1 + pow(tan($a),2)*pow(tanh($b),2); if ($den == 0.0) return PEAR::raiseError('Division by zero while calculating Math_ComplexOp::tan()'); $r = pow(Math_TrigOp::sech($b),2)*tan($a)/$den; $i = pow(Math_TrigOp::sec($a),2)*tanh($b)/$den; return new Math_Complex( $r, $i ); }/*}}}*/ /** * Calculates the secant of a complex number * z = sec(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &sec (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $z = Math_ComplexOp::cos($c1); return Math_ComplexOP::inverse($z); }/*}}}*/ /** * Calculates the cosecant of a complex number * z = csc(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &csc (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $z = Math_ComplexOp::sin($c1); return Math_ComplexOP::inverse($z); }/*}}}*/ /** * Calculates the cotangent of a complex number * z = cot(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &cot (&$c1) {/*{{{*/ $z = Math_ComplexOp::tan($c1); if (PEAR::isError($z)) { return $z; } else { return Math_ComplexOP::inverse($z); } }/*}}}*/ // Inverse trigonometric methods /** * Calculates the inverse sine of a complex number * z = asin(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &asin (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $t = Math_ComplexOp::mult($c1, $c1); $v = Math_ComplexOp::sub(new Math_Complex(1,0), $t); $t = Math_ComplexOp::sqrt($v); $v = new Math_Complex($t->getReal() - $c1->getIm(), $t->getIm() + $c1->getReal()); $z = Math_ComplexOp::log($v); return new Math_Complex($z->getIm(), -1*$z->getReal()); }/*}}}*/ // alternative method function &asinAlt (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $r = $c1->getReal(); $i = $c1->getIm(); if ($i == 0) { return Math_ComplexOp::asinReal($r); } else { $x = abs($r); $y = abs($i); $r = hypot($x + 1, $y); $s = hypot($x - 1, $y); $a = ($r + $s)/2; $b = $x / $a; $y2 = $y * $y; $ac = 1.5; $bc = 0.6417; // crossover values if ($b <= $bc) { $real = asin($b); } else { if ($x <= 1) { $d = 0.5 * ($a + $x) * ($y2 / ($r + $x + 1) + ($s + (1 - $x))); $real = atan2($x, sqrt($d)); } else { $ax = $a + $x; $d = 0.5 * ($ax / ($r + $x + 1) + $ax / ($s + ($x - 1))); $real = atan2($x, $y * sqrt($d)); } } if ($a <= $ac) { if ($x < 1) { $m = 0.5 * ($y2 / ($r + ($x + 1)) + $y2 / ($s + (1 - $x))); } else { $m = 0.5 * ($y2 / ($r + ($x + 1)) + ($s + ($x - 1))); } $im = log1p($m + sqrt($m * ($a + 1))); } else { $im = log($a + sqrt($a * $a - 1)); } $real = ($r >= 0) ? $real : -1*$real; $im = ($i >= 0) ? $im : -1*$im; return new Math_Complex($real, $im); } }/*}}}*/ /** * Calculates the complex inverse sine of a real number * z = asinReal(r) * * @param float $r * @returns object Math_Complex * @access public */ function &asinReal($r) {/*{{{*/ $r = floatval($r); if (abs($r) <= 1.0) { return new Math_Complex(asin($r), 0.0); } else { if ($r < 0.0) { return new Math_Complex(-1*M_PI_2, acosh($r)); } else { return new Math_Complex(M_PI_2, -1*acosh($r)); } } }/*}}}*/ /** * Calculates the inverse cosine of a complex number * z = acos(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &acos (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $t = Math_ComplexOp::mult($c1, $c1); $v = Math_ComplexOp::sub(new Math_Complex(1,0), $t); $t = Math_ComplexOp::sqrt($v); $v = new Math_Complex($c1->getReal() - $t->getIm(), $c1->getIm() + $t->getReal()); $z = Math_ComplexOp::log($v); return new Math_Complex($z->getIm(), -1*$z->getReal()); }/*}}}*/ /** * Calculates the inverse tangent of a complex number * z = atan(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &atan (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $u = new Math_Complex(-1*$c1->getIm(), $c1->getReal()); $t = new Math_Complex(1,0); $d1 = Math_ComplexOp::sub($t, $u); $d2 = Math_ComplexOp::add($t, $u); $u = Math_ComplexOp::div($d1, $d2); if (PEAR::isError($u)) { return $u; } else { return Math_ComplexOp::multIm(Math_ComplexOp::log($u), 0.5); } }/*}}}*/ /** * Calculates the inverse secant of a complex number * z = asec(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &asec (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $z = Math_ComplexOp::inverse($c1); // get the cosine if (PEAR::isError($z)) { return $z; } else { return Math_ComplexOp::acos($z); } }/*}}}*/ /** * Calculates the inverse cosecant of a complex number * z = acsc(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &acsc (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $z = Math_ComplexOp::inverse($c1); // get the sine if (PEAR::isError($z)) { return $z; } else { return Math_ComplexOp::asin($z); } }/*}}}*/ /** * Calculates the inverse cotangent of a complex number * z = acot(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &acot (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $z = Math_ComplexOp::inverse($c1); // get the tangent if (PEAR::isError($z)) { return $z; } else { return Math_ComplexOp::atan($z); } }/*}}}*/ // TODO Document Hyperbolic methods function &sinh (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) { return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); } $r = $c1->getReal(); $i = $c1->getIm(); return new Math_Complex(sinh($r) * cos($i), cosh($r) * sin($i)); }/*}}}*/ function &cosh (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) { return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); } $r = $c1->getReal(); $i = $c1->getIm(); return new Math_Complex(cosh($r) * cos($i), sinh($r) * sin($i)); }/*}}}*/ function &tanh (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) { return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); } $r = $c1->getReal(); $i = $c1->getIm(); $d = cos($i) * cos($i) + sinh($r) * sinh($r); return new Math_Complex(sinh($r) * cosh($r) / $d, 0.5 * sin(2 * $i) / $d); }/*}}}*/ function &sech (&$c1) {/*{{{*/ $c2 = Math_ComplexOp::cosh($c1); if (PEAR::isError($c2)) { return $c2; } else { return Math_ComplexOp::inverse($c2); } }/*}}}*/ function &csch (&$c1) {/*{{{*/ $c2 = Math_ComplexOp::sinh($c1); if (PEAR::isError($c2)) { return $c2; } else { return Math_ComplexOp::inverse($c2); } }/*}}}*/ function &coth (&$c1) {/*{{{*/ $c2 = Math_ComplexOp::tanh($c1); if (PEAR::isError($c2)) { return $c2; } else { return Math_ComplexOp::inverse($c2); } }/*}}}*/ // TODO Document Inverse hyperbolic function &asinh (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) { return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); } $z = Math_ComplexOp::multIm($c1, 1.0); $z = Math_ComplexOp::asin($z); if (PEAR::isError($z)) { return $z; } else { return Math_ComplexOp::multIm($z, -1.0); } }/*}}}*/ function &acosh (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) { return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); } $z = Math_ComplexOp::acos($c1); if (PEAR::isError($z)) { return $z; } else { return Math_ComplexOp::multIm($z, (($z->getIm() > 0) ? 1.0 : -1.0)); } }/*}}}*/ function &atanh (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) { return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); } }/*}}}*/ // functions below need 2 valid Math_Complex objects as parameters /** * Determines if is c1 == c2 * * @param object Math_Complex $c1 * @param object Math_Complex $c2 * @returns mixed True if $c1 == $c2, False if $c1 != $c2, PEAR_Error object on error * @access public */ function &areEqual (&$c1, &$c2) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1) || !Math_ComplexOp::isComplex($c2)) { return PEAR::raiseError('Both arguments must be PEAR::Math_Complex objects'); } else { $same_class = ( get_class($c1) == get_class($c2) ); $same_real = ( $c1->getReal() == $c2->getReal() ); $same_im = ( $c1->getIm() == $c2->getIm() ); return ( $same_class && $same_real && $same_im ); } }/*}}}*/ /** * Returns the sum of two complex numbers: z = c1 + c2 * * @param object Math_Complex $c1 * @param object Math_Complex $c2 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &add (&$c1, &$c2) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1) || !Math_ComplexOp::isComplex($c2)) { return PEAR::raiseError('Both arguments must be PEAR::Math_Complex objects'); } else { return new Math_Complex( $c1->getReal() + $c2->getReal(), $c1->getIm() + $c2->getIm()); } }/*}}}*/ /** * Returns the difference of two complex numbers: z = c1 - c2 * * @param object Math_Complex $c1 * @param object Math_Complex $c2 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &sub (&$c1, &$c2) {/*{{{*/ $nc2 = Math_ComplexOp::negative($c2); if (PEAR::isError($nc2)) { return $nc2; } else { return Math_ComplexOp::add($c1, $nc2); } }/*}}}*/ /** * Returns the product of two complex numbers: z = c1 * c2 * * @param object Math_Complex $c1 * @param object Math_Complex $c2 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &mult (&$c1, &$c2) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1) || !Math_ComplexOp::isComplex($c2)) { return PEAR::raiseError('Both arguments must be PEAR::Math_Complex objects'); } else { $r = ($c1->getReal() * $c2->getReal()) - ($c1->getIm() * $c2->getIm()); $i = ($c1->getReal() * $c2->getIm()) + ($c2->getReal() * $c1->getIm()); return new Math_Complex( $r, $i ); } }/*}}}*/ /** * Returns the division of two complex numbers: z = c1 * c2 * * @param object Math_Complex $c1 * @param object Math_Complex $c2 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &div (&$c1, &$c2) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1) || !Math_ComplexOp::isComplex($c2)) { return PEAR::raiseError('Both arguments must be PEAR::Math_Complex objects'); } else { $a = $c1->getReal(); $b = $c1->getIm(); $c = $c2->getReal(); $d = $c2->getIm(); $div = $c*$c + $d*$d; if ($div == 0.0) { return PEAR::raiseError('Division by zero in Math_ComplexOp::div()'); } else { $r = ($a*$c + $b*$d)/$div; $i = ($b*$c - $a*$d)/$div; return new Math_Complex( $r, $i ); } } }/*}}}*/ /** * Returns the complex power of two complex numbers: z = c1^c2 * * @param object Math_Complex $c1 * @param object Math_Complex $c2 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &pow (&$c1, &$c2) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1) || !Math_ComplexOp::isComplex($c2)) { return PEAR::raiseError('Both arguments must be PEAR::Math_Complex objects'); } else { $ar = $c1->getReal(); $ai = $c1->getIm(); $br = $c2->getReal(); $bi = $c2->getIm(); if ($ar == 0.0 && $ai == 0.0) { $r = $i = 0.0; } else { $logr = Math_ComplexOp::log($c1); $theta = $c1->arg(); $rho = exp($logr * $br - $bi * $theta); $beta = $theta * $br + $bi * $logr; $r = $rho * cos($beta); $i = $rho * sin($beta); } return new Math_Complex($r, $i); } }/*}}}*/ /** * Returns the logarithm of base c2 of the complex number c1 * * @param object Math_Complex $c1 * @param object Math_Complex $c2 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &logBase (&$c1, &$c2) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1) || !Math_ComplexOp::isComplex($c2)) { return PEAR::raiseError('Both arguments must be PEAR::Math_Complex objects'); } else { return Math_ComplexOp::div(Math_ComplexOp::log($c1), Math_ComplexOp::log($c2)); } }/*}}}*/ // these functions need a complex number and a real number /** * Multiplies a complex number by a real number * * z = realnumber * c1 * * @param object Math_Complex $c1 * @param float $real * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &multReal (&$c1, $real) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) { return PEAR::raiseError('First argument is not a PEAR::Math_Complex object'); } if (!is_numeric($real)) { return PEAR::raiseError('Second argument is not valid real number'); } $r = $c1->getReal() * $real; $i = $c1->getIm() * $real; return new Math_Complex($r, $i); }/*}}}*/ /** * Returns the product of a complex number and an imaginary number * x = b + c*i * y = a*i * z = x * y = multIm(x, a); * * @param object Math_Complex $c1 * @param float $im * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &multIm ($c1, $im) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) { return PEAR::raiseError('First arguments must be PEAR::Math_Complex object'); } elseif (!is_numeric($im)) { return PEAR::raiseError("An imaginary coefficient is needed as second parameter"); } else { $r = -1 * $c1->getIm() * $im; $i = $c1->getReal() * $im; return new Math_Complex($r, $i); } }/*}}}*/ /** * Returns the exponentiation of a complex numbers to a real power: z = c1^(real) * * @param object Math_Complex $c1 * @param float $real * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &powReal ($c1, $real) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) { return PEAR::raiseError('First arguments must be PEAR::Math_Complex object'); } elseif (!is_numeric($real)) { return PEAR::raiseError("An real number is needed as second parameter"); } else { $ar = $c1->getReal(); $ai = $c1->getIm(); if ($ar == 0 && $ai == 0) { $r = $i = 0.0; } else { $logr = log($c1->abs()); $theta = $c1->arg(); $rho = exp($logr * $real); $beta = $theta * $real; $r = $rho * cos($beta); $i = $rho * sin($beta); } return new Math_Complex($r, $i); } }/*}}}*/ }/*}}} End of Math_ComplexOp*/ ?> Index: pear/Math_Complex/package.xml +++ pear/Math_Complex/package.xml <?xml version="1.0" encoding="ISO-8859-1"?> <!DOCTYPE package SYSTEM "../package.dtd"> <!-- do not use the "Type" attribute here, that one is only for generated package.xml files --> <package> <name>Math_Complex</name> <summary>Classes that define complex numbers and their operations</summary> <description> Classes that represent and manipulate complex numbers. Contain definitions for basic arithmetic functions, as well as trigonometric, exponential and logarithms of complex numbers. </description> <maintainers> <maintainer> <user>jmcastagnetto</user> <name>Jesus M. Castagnetto</name> <email>jmcastagnetto@php.net</email> <role>lead</role> </maintainer> </maintainers> <release> <license>PHP</license> <version>0.8</version> <date>2002-11-19</date> <notes> Initial release under PEAR. </notes> <state>beta</state> <filelist> <dir name="/" baseinstalldir="Math"> <file role="php">Complex.php</file> <file role="php">ComplexOp.php</file> </dir> </filelist> <deps> <dep type="pkg" rel="ge" version="1.0">Math_TrigOp</dep> </deps> </release> <changelog> <release> </release> </changelog> </package> Index: pear/Math_Complex/testcomplex.php +++ pear/Math_Complex/testcomplex.php <?php /* * To test class.complex.php * numPHP (c) Jesus M. Castagnetto 1999,2000. * $Id: testcomplex.php,v 1.1 2002/11/24 07:14:22 jmcastagnetto Exp $ */ require_once './ComplexOp.php'; $a = new Math_Complex(2.0,-1.0); $b = new Math_Complex(1,-2); $c = new Math_Complex (1.455347, -0.3435607); echo "a: ".$a->toString()."\n"; echo "b: ".$b->toString()."\n"; echo "c: ".$c->toString()."\n"; echo "abs(a): ".$a->abs()." arg(a): ".$a->arg()."\n"; echo "real(a): ".$a->getReal()." imag(a): ".$a->getIm()."\n"; $d = Math_ComplexOp::sqrt($a); echo "sqrt: ".$d->toString()."\n"; $e = Math_ComplexOp::exp($a); echo "exp: ".$e->toString()."\n"; $e = Math_ComplexOp::log($a); echo "log: ".$e->toString()."\n"; $e = Math_ComplexOp::log10($a); echo "log10: ".$e->toString()."\n"; $e = Math_ComplexOp::conjugate($a); echo "conjugate: ".$e->toString()."\n"; $e = Math_ComplexOp::negative($a); echo "negative: ".$e->toString()."\n"; $e = Math_ComplexOp::multReal($a, M_PI); echo "z * real: ".$e->toString()."\n"; if (!Math_ComplexOp::areEqual($a, Math_ComplexOp::negative($a))) {echo "a and neg(a) are different\n";} echo "a is ".$a->toString()."\n"; $t=Math_ComplexOp::negative($a); echo "Neg(a) is ".$t->toString()."\n"; $t=Math_ComplexOp::conjugate($a); echo "Conj(a) is ".$t->toString()."\n"; $t=Math_ComplexOp::sin($a); echo "Sin(a) is ".$t->toString()."\n"; $v = Math_ComplexOp::asin($t); echo "ArcSin(Sin(a)) is ".$v->toString()."\n"; $t=Math_ComplexOp::cos($a); echo "Cos(a) is ".$t->toString()."\n"; $v = Math_ComplexOp::acos($t); echo "ArcCos(Cos(a)) is ".$v->toString()."\n"; $t=Math_ComplexOp::tan($a); echo "Tan(a) is ".$t->toString()."\n"; $v = Math_ComplexOp::atan($t); echo "ArcTan(Tan(a)) is ".$v->toString()."\n"; $foo = new Math_Complex(0.3, 0.5); $sin = Math_ComplexOp::sin($foo); $asin = Math_ComplexOp::asin($sin); $tan = Math_ComplexOp::tan($foo); $atan = Math_ComplexOp::atan($tan); echo "foo is ".$foo->toString()."\n"; echo "sin(foo) is ".$sin->toString()."\n"; echo "asin(sin(foo)) is ".$asin->toString()."\n"; echo "tan(foo) is ".$tan->toString()."\n"; echo "atan(tan(foo)) is ".$atan->toString()."\n"; echo "====\n"; $h = Math_ComplexOp::sinh($foo); echo "sinh(foo) is ".$h->toString()."\n"; $h = Math_ComplexOp::cosh($foo); echo "cosh(foo) is ".$h->toString()."\n"; $h = Math_ComplexOp::tanh($foo); echo "tanh(foo) is ".$h->toString()."\n"; $h = Math_ComplexOp::sech($foo); echo "sech(foo) is ".$h->toString()."\n"; $h = Math_ComplexOp::csch($foo); echo "csch(foo) is ".$h->toString()."\n"; $h = Math_ComplexOp::coth($foo); echo "coth(foo) is ".$h->toString()."\n"; echo "====\n"; $v = Math_ComplexOp::mult($c,$c); echo "test c*c: ".$v->toString()."\n"; $t=Math_ComplexOp::sqrt($a); echo "sqrt(a): ".$t->toString()."\n"; $t=Math_ComplexOp::sqrt($b); $v = Math_ComplexOp::mult($t,$t); echo "sqrt(b): ".$t->toString()."\n"; echo "test sqrt(b)*sqrt(b): ".$v->toString()."\n"; $t=Math_ComplexOp::mult($a,$b); echo "a*b: ".$t->toString()."\n"; $t=Math_ComplexOp::div($a,$b); echo "a/b: ".$t->toString()."\n"; $t=Math_ComplexOp::add($a,$b); echo "a+b: ".$t->toString()."\n"; $t=Math_ComplexOp::sub($a,$b); echo "a-b: ".$t->toString()."\n"; $t=Math_ComplexOp::sub($b,$a); echo "b-a: ".$t->toString()."\n"; $t=Math_ComplexOp::sub($b,Math_ComplexOp::conjugate($a)); echo "b-a': ".$t->toString()."\n"; $v=Math_ComplexOp::conjugate($b); $t=Math_ComplexOp::sub($v,$a); echo "b'-a: ".$t->toString()."\n"; $v=Math_ComplexOp::conjugate($b); $t=Math_ComplexOp::sub($v,Math_ComplexOp::conjugate($a)); echo "b'-a': ".$t->toString()."\n"; ?>
Index: pear/Math_Complex/Complex.php +++ pear/Math_Complex/Complex.php <?php // // +----------------------------------------------------------------------+ // | PHP Version 4 | // +----------------------------------------------------------------------+ // | Copyright (c) 1997-2002 The PHP Group | // +----------------------------------------------------------------------+ // | This source file is subject to version 2.0 of the PHP license, | // | that is bundled with this package in the file LICENSE, and is | // | available at through the world-wide-web at | // | http://www.php.net/license/2_02.txt. | // | If you did not receive a copy of the PHP license and are unable to | // | obtain it through the world-wide-web, please send a note to | // | license@php.net so we can mail you a copy immediately. | // +----------------------------------------------------------------------+ // | Authors: Jesus M. Castagnetto <jmcastagnetto@php.net> | // +----------------------------------------------------------------------+ // // $Id: Complex.php,v 1.1 2002/11/24 07:14:22 jmcastagnetto Exp $ // include_once "PEAR.php"; /** * Math_Complex: class to represent an manipulate complex numbers (z = a + b*i) * * Originally this class was part of NumPHP (Numeric PHP package) * * @author Jesus M. Castagnetto <jmcastagnetto@php.net> * @version 0.8 * @access public * @package Math_Complex */ class Math_Complex {/*{{{*/ /** * The real part of the complex number * * @var float * @access private */ var $real; /** * The imaginary part of the complex number * * @var float * @access private */ var $im; /** * Constructor for Math_Complex * * @param float $real Real part of the number * @param float $im Imaginary part of the number * @returns object Math_Complex * @access public */ function Math_Complex($real, $im) {/*{{{*/ $this->real = floatval($real); $this->im = floatval($im); }/*}}}*/ /** * Simple string representation of the number * * @returns string * @access public */ function toString() {/*{{{*/ $r = $this->getReal(); $i = $this->getIm(); $str = $r; $str .= ($i < 0) ? ' - ' : ' + '; $str .= abs($i).'i'; return $str; }/*}}}*/ /** * Returns the square of the magnitude of the number * * @returns float * @access public */ function abs2() {/*{{{*/ return ($this->real*$this->real + $this->im*$this->im); } /*}}}*/ /** * Returns the magnitude (also referred as norm) of the number * * @returns float * @access public */ function abs() {/*{{{*/ return sqrt($this->abs2()); }/*}}}*/ /** * Returns the norm of the number * Alias of Math_Complex::abs() * * @returns float * @access public */ function norm() {/*{{{*/ return $this->abs(); }/*}}}*/ /** * Returns the argument of the complex number * * @returns mixed A float on success, a PEAR_Error otherwise * @access public */ function arg() {/*{{{*/ $arg = atan2($this->im,$this->real); if (M_PI < $arg || $arg < -1*M_PI) { return PEAR::raiseError('Argument has an impossible value'); } else { return $arg; } }/*}}}*/ /** * Returns the angle (argument) associated with the complex number * Alias of Math_Complex::arg() * * @returns mixed A float on success, a PEAR_Error otherwise * @access public */ function angle() {/*{{{*/ return $this->arg(); }/*}}}*/ /** * Returns the real part of the complex number * * @return float * @access pulic */ function getReal() {/*{{{*/ return $this->real; }/*}}}*/ /** * Returns the imaginary part of the complex number * @return float * @access public */ function getIm() {/*{{{*/ return $this->im; }/*}}}*/ } /* end of Math_Complex class *//*}}}*/ ?> Index: pear/Math_Complex/ComplexOp.php +++ pear/Math_Complex/ComplexOp.php <?php // // +----------------------------------------------------------------------+ // | PHP Version 4 | // +----------------------------------------------------------------------+ // | Copyright (c) 1997-2002 The PHP Group | // +----------------------------------------------------------------------+ // | This source file is subject to version 2.0 of the PHP license, | // | that is bundled with this package in the file LICENSE, and is | // | available at through the world-wide-web at | // | http://www.php.net/license/2_02.txt. | // | If you did not receive a copy of the PHP license and are unable to | // | obtain it through the world-wide-web, please send a note to | // | license@php.net so we can mail you a copy immediately. | // +----------------------------------------------------------------------+ // | Authors: Jesus M. Castagnetto <jmcastagnetto@php.net> | // +----------------------------------------------------------------------+ // // $Id: ComplexOp.php,v 1.1 2002/11/24 07:14:22 jmcastagnetto Exp $ // include_once 'PEAR.php'; include_once 'Math/Complex.php'; include_once 'Math/TrigOp.php'; /** * Math_ComplexOp: static class to operate on Math_Complex objects * * Originally this class was part of NumPHP (Numeric PHP package) * * @author Jesus M. Castagnetto <jmcastagnetto@php.net> * @version 0.8 * @access public * @package Math_Complex */ class Math_ComplexOp {/*{{{*/ /** * Checks if a given object is an instance of PEAR::Math_Complex * * @returns boolean * @access public */ function isComplex(&$c1) {/*{{{*/ if (function_exists('is_a')) { return is_a(&$c1, 'math_complex'); } else { return (get_class($c1) == 'math_complex' || is_subclass_of($c1, 'math_complex')); } }/*}}}*/ /** * Converts a polar complex z = r*exp(theta*i) to z = a + b*i * * @param float $r * @param float $theta * @returns object Math_Complex * @access public */ function &createFromPolar ($r, $theta) {/*{{{*/ $r = floatval($r); $theta = floatval($theta); $a = $r * cos($theta); $b = sin($theta); return new Math_Complex ( $a, $b ); }/*}}}*/ // methods below need a valid Math_Complex object as parameter /** * Calculates the complex square root of a complex number * z = sqrt(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &sqrt (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $x = abs($c1->getReal()); $y = abs($c1->getIm()); if ($x == 0.0 && $y == 0) { $r = $i = 0.0; } else { if ($x >= $y) { $t = $y / $x; $w = sqrt($x) * sqrt(0.5 * (1.0 + sqrt(1.0 + $t*$t))); } else { $t = $x / $y; $w = sqrt($y) * sqrt(0.5 * ($t + sqrt(1.0 + $t*$t))); } if ($c1->getReal() >= 0.0) { $r = $w; $i = $c1->getIm() / (2.0 * $w); } else { $i = ($c1->getIm() >= 0) ? $w : -1 * $w; $r = $c1->getIm() / (2.0 * $i); } } return new Math_Complex ($r, $i); }/*}}}*/ /** * Calculates the complex square root of a real number * z = sqrt(realnumber) * * @param float $realnum A float * @returns object Math_Complex * @access public */ function &sqrtReal ($realnum) {/*{{{*/ if ($realnum >= 0) { $r = sqrt($realnum); $i = 0.0; } else { $r = 0.0; $i = sqrt(-1 * $realnum); } return new Math_Complex($r, $i); }/*}}}*/ /** * Calculates the exponential of a complex number * z = exp(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &exp (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $rho = exp($c1->getReal()); $theta = $c1->getIm(); $r = $rho * cos($theta); $i = $rho * sin($theta); return new Math_Complex($r, $i); }/*}}}*/ /** * Calculates the logarithm (base 2) of a complex number * z = log(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &log (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $r = log($c1->abs()); $i = $c1->arg(); return new Math_Complex($r, $i); }/*}}}*/ /** * Calculates the logarithm (base 10) of a complex number * z = log10(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &log10 (&$c1) {/*{{{*/ $log = Math_ComplexOp::log($c1); if (PEAR::isError($log)) return $log; return Math_ComplexOp::multReal ($log, 1/log(10)); }/*}}}*/ /** * Calculates the conjugate of a complex number * z = conj(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &conjugate (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); return new Math_Complex($c1->getReal(), -1 * $c1->getIm()); }/*}}}*/ /** * Calculates the negative of a complex number * z = -c1 * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &negative (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) { return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); } else { return new Math_Complex(-1 * $c1->getReal(), -1 * $c1->getIm()); } }/*}}}*/ /** * Calculates the inverse of a complex number * z = 1/c1 * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &inverse (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $abs = $c1->abs(); if ($abs == 0.0) return PEAR::raiseError('Math_Complex object\'s norm is zero'); $temp = 1.0 / $c1->abs(); $r = $c1->getReal() * $temp * $temp; $i = -1 * $c1->getIm() * $temp * $temp; return new Math_Complex ($r, $i); }/*}}}*/ // Trigonometric methods /** * Calculates the sine of a complex number * z = sin(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &sin (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $a = $c1->getReal(); $b = $c1->getIm(); $r = sin($a)*cosh($b); $i = cos($a)*sinh($b); return new Math_Complex( $r, $i ); }/*}}}*/ /** * Calculates the cosine of a complex number * z = cos(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &cos (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $a = $c1->getReal(); $b = $c1->getIm(); $r = cos($a)*cosh($b); $i = sin($a)*sinh($b); return new Math_Complex( $r, $i ); }/*}}}*/ /** * Calculates the tangent of a complex number * z = tan(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &tan (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $a = $c1->getReal(); $b = $c1->getIm(); $den = 1 + pow(tan($a),2)*pow(tanh($b),2); if ($den == 0.0) return PEAR::raiseError('Division by zero while calculating Math_ComplexOp::tan()'); $r = pow(Math_TrigOp::sech($b),2)*tan($a)/$den; $i = pow(Math_TrigOp::sec($a),2)*tanh($b)/$den; return new Math_Complex( $r, $i ); }/*}}}*/ /** * Calculates the secant of a complex number * z = sec(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &sec (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $z = Math_ComplexOp::cos($c1); return Math_ComplexOP::inverse($z); }/*}}}*/ /** * Calculates the cosecant of a complex number * z = csc(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &csc (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $z = Math_ComplexOp::sin($c1); return Math_ComplexOP::inverse($z); }/*}}}*/ /** * Calculates the cotangent of a complex number * z = cot(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &cot (&$c1) {/*{{{*/ $z = Math_ComplexOp::tan($c1); if (PEAR::isError($z)) { return $z; } else { return Math_ComplexOP::inverse($z); } }/*}}}*/ // Inverse trigonometric methods /** * Calculates the inverse sine of a complex number * z = asin(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &asin (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $t = Math_ComplexOp::mult($c1, $c1); $v = Math_ComplexOp::sub(new Math_Complex(1,0), $t); $t = Math_ComplexOp::sqrt($v); $v = new Math_Complex($t->getReal() - $c1->getIm(), $t->getIm() + $c1->getReal()); $z = Math_ComplexOp::log($v); return new Math_Complex($z->getIm(), -1*$z->getReal()); }/*}}}*/ // alternative method function &asinAlt (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $r = $c1->getReal(); $i = $c1->getIm(); if ($i == 0) { return Math_ComplexOp::asinReal($r); } else { $x = abs($r); $y = abs($i); $r = hypot($x + 1, $y); $s = hypot($x - 1, $y); $a = ($r + $s)/2; $b = $x / $a; $y2 = $y * $y; $ac = 1.5; $bc = 0.6417; // crossover values if ($b <= $bc) { $real = asin($b); } else { if ($x <= 1) { $d = 0.5 * ($a + $x) * ($y2 / ($r + $x + 1) + ($s + (1 - $x))); $real = atan2($x, sqrt($d)); } else { $ax = $a + $x; $d = 0.5 * ($ax / ($r + $x + 1) + $ax / ($s + ($x - 1))); $real = atan2($x, $y * sqrt($d)); } } if ($a <= $ac) { if ($x < 1) { $m = 0.5 * ($y2 / ($r + ($x + 1)) + $y2 / ($s + (1 - $x))); } else { $m = 0.5 * ($y2 / ($r + ($x + 1)) + ($s + ($x - 1))); } $im = log1p($m + sqrt($m * ($a + 1))); } else { $im = log($a + sqrt($a * $a - 1)); } $real = ($r >= 0) ? $real : -1*$real; $im = ($i >= 0) ? $im : -1*$im; return new Math_Complex($real, $im); } }/*}}}*/ /** * Calculates the complex inverse sine of a real number * z = asinReal(r) * * @param float $r * @returns object Math_Complex * @access public */ function &asinReal($r) {/*{{{*/ $r = floatval($r); if (abs($r) <= 1.0) { return new Math_Complex(asin($r), 0.0); } else { if ($r < 0.0) { return new Math_Complex(-1*M_PI_2, acosh($r)); } else { return new Math_Complex(M_PI_2, -1*acosh($r)); } } }/*}}}*/ /** * Calculates the inverse cosine of a complex number * z = acos(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &acos (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $t = Math_ComplexOp::mult($c1, $c1); $v = Math_ComplexOp::sub(new Math_Complex(1,0), $t); $t = Math_ComplexOp::sqrt($v); $v = new Math_Complex($c1->getReal() - $t->getIm(), $c1->getIm() + $t->getReal()); $z = Math_ComplexOp::log($v); return new Math_Complex($z->getIm(), -1*$z->getReal()); }/*}}}*/ /** * Calculates the inverse tangent of a complex number * z = atan(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &atan (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $u = new Math_Complex(-1*$c1->getIm(), $c1->getReal()); $t = new Math_Complex(1,0); $d1 = Math_ComplexOp::sub($t, $u); $d2 = Math_ComplexOp::add($t, $u); $u = Math_ComplexOp::div($d1, $d2); if (PEAR::isError($u)) { return $u; } else { return Math_ComplexOp::multIm(Math_ComplexOp::log($u), 0.5); } }/*}}}*/ /** * Calculates the inverse secant of a complex number * z = asec(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &asec (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $z = Math_ComplexOp::inverse($c1); // get the cosine if (PEAR::isError($z)) { return $z; } else { return Math_ComplexOp::acos($z); } }/*}}}*/ /** * Calculates the inverse cosecant of a complex number * z = acsc(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &acsc (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $z = Math_ComplexOp::inverse($c1); // get the sine if (PEAR::isError($z)) { return $z; } else { return Math_ComplexOp::asin($z); } }/*}}}*/ /** * Calculates the inverse cotangent of a complex number * z = acot(c1) * * @param object Math_Complex $c1 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &acot (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); $z = Math_ComplexOp::inverse($c1); // get the tangent if (PEAR::isError($z)) { return $z; } else { return Math_ComplexOp::atan($z); } }/*}}}*/ // TODO Document Hyperbolic methods function &sinh (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) { return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); } $r = $c1->getReal(); $i = $c1->getIm(); return new Math_Complex(sinh($r) * cos($i), cosh($r) * sin($i)); }/*}}}*/ function &cosh (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) { return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); } $r = $c1->getReal(); $i = $c1->getIm(); return new Math_Complex(cosh($r) * cos($i), sinh($r) * sin($i)); }/*}}}*/ function &tanh (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) { return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); } $r = $c1->getReal(); $i = $c1->getIm(); $d = cos($i) * cos($i) + sinh($r) * sinh($r); return new Math_Complex(sinh($r) * cosh($r) / $d, 0.5 * sin(2 * $i) / $d); }/*}}}*/ function &sech (&$c1) {/*{{{*/ $c2 = Math_ComplexOp::cosh($c1); if (PEAR::isError($c2)) { return $c2; } else { return Math_ComplexOp::inverse($c2); } }/*}}}*/ function &csch (&$c1) {/*{{{*/ $c2 = Math_ComplexOp::sinh($c1); if (PEAR::isError($c2)) { return $c2; } else { return Math_ComplexOp::inverse($c2); } }/*}}}*/ function &coth (&$c1) {/*{{{*/ $c2 = Math_ComplexOp::tanh($c1); if (PEAR::isError($c2)) { return $c2; } else { return Math_ComplexOp::inverse($c2); } }/*}}}*/ // TODO Document Inverse hyperbolic function &asinh (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) { return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); } $z = Math_ComplexOp::multIm($c1, 1.0); $z = Math_ComplexOp::asin($z); if (PEAR::isError($z)) { return $z; } else { return Math_ComplexOp::multIm($z, -1.0); } }/*}}}*/ function &acosh (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) { return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); } $z = Math_ComplexOp::acos($c1); if (PEAR::isError($z)) { return $z; } else { return Math_ComplexOp::multIm($z, (($z->getIm() > 0) ? 1.0 : -1.0)); } }/*}}}*/ function &atanh (&$c1) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) { return PEAR::raiseError('argument is not a PEAR::Math_Complex object'); } }/*}}}*/ // functions below need 2 valid Math_Complex objects as parameters /** * Determines if is c1 == c2 * * @param object Math_Complex $c1 * @param object Math_Complex $c2 * @returns mixed True if $c1 == $c2, False if $c1 != $c2, PEAR_Error object on error * @access public */ function &areEqual (&$c1, &$c2) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1) || !Math_ComplexOp::isComplex($c2)) { return PEAR::raiseError('Both arguments must be PEAR::Math_Complex objects'); } else { $same_class = ( get_class($c1) == get_class($c2) ); $same_real = ( $c1->getReal() == $c2->getReal() ); $same_im = ( $c1->getIm() == $c2->getIm() ); return ( $same_class && $same_real && $same_im ); } }/*}}}*/ /** * Returns the sum of two complex numbers: z = c1 + c2 * * @param object Math_Complex $c1 * @param object Math_Complex $c2 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &add (&$c1, &$c2) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1) || !Math_ComplexOp::isComplex($c2)) { return PEAR::raiseError('Both arguments must be PEAR::Math_Complex objects'); } else { return new Math_Complex( $c1->getReal() + $c2->getReal(), $c1->getIm() + $c2->getIm()); } }/*}}}*/ /** * Returns the difference of two complex numbers: z = c1 - c2 * * @param object Math_Complex $c1 * @param object Math_Complex $c2 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &sub (&$c1, &$c2) {/*{{{*/ $nc2 = Math_ComplexOp::negative($c2); if (PEAR::isError($nc2)) { return $nc2; } else { return Math_ComplexOp::add($c1, $nc2); } }/*}}}*/ /** * Returns the product of two complex numbers: z = c1 * c2 * * @param object Math_Complex $c1 * @param object Math_Complex $c2 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &mult (&$c1, &$c2) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1) || !Math_ComplexOp::isComplex($c2)) { return PEAR::raiseError('Both arguments must be PEAR::Math_Complex objects'); } else { $r = ($c1->getReal() * $c2->getReal()) - ($c1->getIm() * $c2->getIm()); $i = ($c1->getReal() * $c2->getIm()) + ($c2->getReal() * $c1->getIm()); return new Math_Complex( $r, $i ); } }/*}}}*/ /** * Returns the division of two complex numbers: z = c1 * c2 * * @param object Math_Complex $c1 * @param object Math_Complex $c2 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &div (&$c1, &$c2) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1) || !Math_ComplexOp::isComplex($c2)) { return PEAR::raiseError('Both arguments must be PEAR::Math_Complex objects'); } else { $a = $c1->getReal(); $b = $c1->getIm(); $c = $c2->getReal(); $d = $c2->getIm(); $div = $c*$c + $d*$d; if ($div == 0.0) { return PEAR::raiseError('Division by zero in Math_ComplexOp::div()'); } else { $r = ($a*$c + $b*$d)/$div; $i = ($b*$c - $a*$d)/$div; return new Math_Complex( $r, $i ); } } }/*}}}*/ /** * Returns the complex power of two complex numbers: z = c1^c2 * * @param object Math_Complex $c1 * @param object Math_Complex $c2 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &pow (&$c1, &$c2) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1) || !Math_ComplexOp::isComplex($c2)) { return PEAR::raiseError('Both arguments must be PEAR::Math_Complex objects'); } else { $ar = $c1->getReal(); $ai = $c1->getIm(); $br = $c2->getReal(); $bi = $c2->getIm(); if ($ar == 0.0 && $ai == 0.0) { $r = $i = 0.0; } else { $logr = Math_ComplexOp::log($c1); $theta = $c1->arg(); $rho = exp($logr * $br - $bi * $theta); $beta = $theta * $br + $bi * $logr; $r = $rho * cos($beta); $i = $rho * sin($beta); } return new Math_Complex($r, $i); } }/*}}}*/ /** * Returns the logarithm of base c2 of the complex number c1 * * @param object Math_Complex $c1 * @param object Math_Complex $c2 * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &logBase (&$c1, &$c2) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1) || !Math_ComplexOp::isComplex($c2)) { return PEAR::raiseError('Both arguments must be PEAR::Math_Complex objects'); } else { return Math_ComplexOp::div(Math_ComplexOp::log($c1), Math_ComplexOp::log($c2)); } }/*}}}*/ // these functions need a complex number and a real number /** * Multiplies a complex number by a real number * * z = realnumber * c1 * * @param object Math_Complex $c1 * @param float $real * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &multReal (&$c1, $real) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) { return PEAR::raiseError('First argument is not a PEAR::Math_Complex object'); } if (!is_numeric($real)) { return PEAR::raiseError('Second argument is not valid real number'); } $r = $c1->getReal() * $real; $i = $c1->getIm() * $real; return new Math_Complex($r, $i); }/*}}}*/ /** * Returns the product of a complex number and an imaginary number * x = b + c*i * y = a*i * z = x * y = multIm(x, a); * * @param object Math_Complex $c1 * @param float $im * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &multIm ($c1, $im) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) { return PEAR::raiseError('First arguments must be PEAR::Math_Complex object'); } elseif (!is_numeric($im)) { return PEAR::raiseError("An imaginary coefficient is needed as second parameter"); } else { $r = -1 * $c1->getIm() * $im; $i = $c1->getReal() * $im; return new Math_Complex($r, $i); } }/*}}}*/ /** * Returns the exponentiation of a complex numbers to a real power: z = c1^(real) * * @param object Math_Complex $c1 * @param float $real * @returns object Math_Complex on success, PEAR_Error otherwise * @access public */ function &powReal ($c1, $real) {/*{{{*/ if (!Math_ComplexOp::isComplex($c1)) { return PEAR::raiseError('First arguments must be PEAR::Math_Complex object'); } elseif (!is_numeric($real)) { return PEAR::raiseError("An real number is needed as second parameter"); } else { $ar = $c1->getReal(); $ai = $c1->getIm(); if ($ar == 0 && $ai == 0) { $r = $i = 0.0; } else { $logr = log($c1->abs()); $theta = $c1->arg(); $rho = exp($logr * $real); $beta = $theta * $real; $r = $rho * cos($beta); $i = $rho * sin($beta); } return new Math_Complex($r, $i); } }/*}}}*/ }/*}}} End of Math_ComplexOp*/ ?> Index: pear/Math_Complex/package.xml +++ pear/Math_Complex/package.xml <?xml version="1.0" encoding="ISO-8859-1"?> <!DOCTYPE package SYSTEM "../package.dtd"> <!-- do not use the "Type" attribute here, that one is only for generated package.xml files --> <package> <name>Math_Complex</name> <summary>Classes that define complex numbers and their operations</summary> <description> Classes that represent and manipulate complex numbers. Contain definitions for basic arithmetic functions, as well as trigonometric, exponential and logarithms of complex numbers. </description> <maintainers> <maintainer> <user>jmcastagnetto</user> <name>Jesus M. Castagnetto</name> <email>jmcastagnetto@php.net</email> <role>lead</role> </maintainer> </maintainers> <release> <license>PHP</license> <version>0.8</version> <date>2002-11-19</date> <notes> Initial release under PEAR. </notes> <state>beta</state> <filelist> <dir name="/" baseinstalldir="Math"> <file role="php">Complex.php</file> <file role="php">ComplexOp.php</file> </dir> </filelist> <deps> <dep type="pkg" rel="ge" version="1.0">Math_TrigOp</dep> </deps> </release> <changelog> <release> </release> </changelog> </package> Index: pear/Math_Complex/testcomplex.php +++ pear/Math_Complex/testcomplex.php <?php /* * To test class.complex.php * numPHP (c) Jesus M. Castagnetto 1999,2000. * $Id: testcomplex.php,v 1.1 2002/11/24 07:14:22 jmcastagnetto Exp $ */ require_once './ComplexOp.php'; $a = new Math_Complex(2.0,-1.0); $b = new Math_Complex(1,-2); $c = new Math_Complex (1.455347, -0.3435607); echo "a: ".$a->toString()."\n"; echo "b: ".$b->toString()."\n"; echo "c: ".$c->toString()."\n"; echo "abs(a): ".$a->abs()." arg(a): ".$a->arg()."\n"; echo "real(a): ".$a->getReal()." imag(a): ".$a->getIm()."\n"; $d = Math_ComplexOp::sqrt($a); echo "sqrt: ".$d->toString()."\n"; $e = Math_ComplexOp::exp($a); echo "exp: ".$e->toString()."\n"; $e = Math_ComplexOp::log($a); echo "log: ".$e->toString()."\n"; $e = Math_ComplexOp::log10($a); echo "log10: ".$e->toString()."\n"; $e = Math_ComplexOp::conjugate($a); echo "conjugate: ".$e->toString()."\n"; $e = Math_ComplexOp::negative($a); echo "negative: ".$e->toString()."\n"; $e = Math_ComplexOp::multReal($a, M_PI); echo "z * real: ".$e->toString()."\n"; if (!Math_ComplexOp::areEqual($a, Math_ComplexOp::negative($a))) {echo "a and neg(a) are different\n";} echo "a is ".$a->toString()."\n"; $t=Math_ComplexOp::negative($a); echo "Neg(a) is ".$t->toString()."\n"; $t=Math_ComplexOp::conjugate($a); echo "Conj(a) is ".$t->toString()."\n"; $t=Math_ComplexOp::sin($a); echo "Sin(a) is ".$t->toString()."\n"; $v = Math_ComplexOp::asin($t); echo "ArcSin(Sin(a)) is ".$v->toString()."\n"; $t=Math_ComplexOp::cos($a); echo "Cos(a) is ".$t->toString()."\n"; $v = Math_ComplexOp::acos($t); echo "ArcCos(Cos(a)) is ".$v->toString()."\n"; $t=Math_ComplexOp::tan($a); echo "Tan(a) is ".$t->toString()."\n"; $v = Math_ComplexOp::atan($t); echo "ArcTan(Tan(a)) is ".$v->toString()."\n"; $foo = new Math_Complex(0.3, 0.5); $sin = Math_ComplexOp::sin($foo); $asin = Math_ComplexOp::asin($sin); $tan = Math_ComplexOp::tan($foo); $atan = Math_ComplexOp::atan($tan); echo "foo is ".$foo->toString()."\n"; echo "sin(foo) is ".$sin->toString()."\n"; echo "asin(sin(foo)) is ".$asin->toString()."\n"; echo "tan(foo) is ".$tan->toString()."\n"; echo "atan(tan(foo)) is ".$atan->toString()."\n"; echo "====\n"; $h = Math_ComplexOp::sinh($foo); echo "sinh(foo) is ".$h->toString()."\n"; $h = Math_ComplexOp::cosh($foo); echo "cosh(foo) is ".$h->toString()."\n"; $h = Math_ComplexOp::tanh($foo); echo "tanh(foo) is ".$h->toString()."\n"; $h = Math_ComplexOp::sech($foo); echo "sech(foo) is ".$h->toString()."\n"; $h = Math_ComplexOp::csch($foo); echo "csch(foo) is ".$h->toString()."\n"; $h = Math_ComplexOp::coth($foo); echo "coth(foo) is ".$h->toString()."\n"; echo "====\n"; $v = Math_ComplexOp::mult($c,$c); echo "test c*c: ".$v->toString()."\n"; $t=Math_ComplexOp::sqrt($a); echo "sqrt(a): ".$t->toString()."\n"; $t=Math_ComplexOp::sqrt($b); $v = Math_ComplexOp::mult($t,$t); echo "sqrt(b): ".$t->toString()."\n"; echo "test sqrt(b)*sqrt(b): ".$v->toString()."\n"; $t=Math_ComplexOp::mult($a,$b); echo "a*b: ".$t->toString()."\n"; $t=Math_ComplexOp::div($a,$b); echo "a/b: ".$t->toString()."\n"; $t=Math_ComplexOp::add($a,$b); echo "a+b: ".$t->toString()."\n"; $t=Math_ComplexOp::sub($a,$b); echo "a-b: ".$t->toString()."\n"; $t=Math_ComplexOp::sub($b,$a); echo "b-a: ".$t->toString()."\n"; $t=Math_ComplexOp::sub($b,Math_ComplexOp::conjugate($a)); echo "b-a': ".$t->toString()."\n"; $v=Math_ComplexOp::conjugate($b); $t=Math_ComplexOp::sub($v,$a); echo "b'-a: ".$t->toString()."\n"; $v=Math_ComplexOp::conjugate($b); $t=Math_ComplexOp::sub($v,Math_ComplexOp::conjugate($a)); echo "b'-a': ".$t->toString()."\n"; ?>