ÿØÿà JFIF    ÿÛ „  ( %!1"%)+...383-7(-.+  -%%--------+------------/----------------------------ÿÀ  ¶" ÿÄ     ÿÄ @    !1AQaq‘¡"±ÁÑð2’BRráS‚ñ3b¢CT²Ò #cÿÄ    ÿÄ '   1!AQ2a"‘±#ÿÚ   ? ò(/p‘—–¢·,M|¯G»R£üešT. ôŸEoCFñ‡ 4ÔkåóxR|µÁ¨ÓDà!Ç´µ˜‡p ÍQ‹§!þž^õWsŒy  åÁ§$á«%ºq˜™JyyË0y«^Ϗ -3ÃÏËÈ£Æ\P’ä„s&•‹Üs üô'àWt¹pñCp$bÚF`·7.^)¾!)ÒÙ˜–ÅÏš^h¾ø³·ìe±ŒaeÖ—Í,e=B}Jéߦ$$½—šÙÜCC¯¶è8β–Åkèwx LÉngT±æ¹£Ócœ¿Í/©Éÿ ‰ÚCÒ­mq;Tt¶–}0"zÖPcd1š­¤tˆ„ÐÓâqú[™öUCŠ2޿د­É(¸ßúçšmW,Ò ºf‹Ån™ÄLêÁ8üÁkÁ€L¥ÍuJ1œôrÂSŒÓöt!7EUíïb)AËi¬â-ÙHk8òÁiXYwÅ)O^"ÇØriÛô{»wRUKÙÏÚlÓ¬€‚’שT ] ªb—ÊîKC^×M“xùäñz¬zJ× {4[¹M'IÆeH1LCWÕ]œûº WDæà°OÅ‚¹c²ÞuA–rL`HšpCez‡V’— Ž‚Ë„–ñ­'µR0ÕÖ=À:±G»C\nÆÉ5*¢ †3šhQ4ýÒi$Õ1"Ü]¢p-q3zcQ$ªö¨¥æf›‘»´ÝÚHá„e²JÇ–iÊ:·à¬Øc5Åk»Laª*wi [0Ówk ¦a¦0Õ²ÅÅ‚T¸’³q:Æ<¹ú Ò˜Æ}2VE•Ð€p¡Ô3Úº …h³^LJºçì¥Ánó|˜ÖˆÎˆ+« ¦dø‘Mº–d\ªDðÛ„Ì×LÝ——Ð9Ç|•FèçVm™¨€™3õS–9Äå¢<̉Ìm¢±`·º˜&Z²ž Ë®D«¶»6™‰©­HÈ Àá«h­i³04æ’hxœi3ï¨(ÓL·†‹¶ËpŒ ƒÜÒ? :õdsÀ –3æÓ·Üjâ¬9—]8n¼&]I F£¼…ì–—Œ0v°LǐÅfÛ2TÖ’aµ˜N@ÖBSÏ^à´4-±°b×nÈÈœÆD=KdŒø…ÄÈK,›ÖR§fjü$^ÔÎ!„6^ s:Üun\ôkCÞò÷<—Lúl Í›G¹ÀPá¼Nc¡šÒ…ÙWͳœ±vÊáЄ×9‹P‰cEØ‘™›µŸP<×g1 º©Ø¬wiÁ^l5× I/';Ë+´Z‡ÓÄFÕp[Èð’ HÄ ó 9¬Dl4“é±Ï”V=^Hð;žLädÉa‚°Ë,#/Ž~²BÔÛ QãñQtIeórVB,ÏÂf‹4#Îœc‹É3ZIÖ Œ¢¥·üxa‡Ãçè„jŠ[5 Ä!U?,3žÎ×…ðdÓ÷háŠA‰ìÄ4÷ÃÜZÃE{‰®+W\ZÍE[‰»µk»MÝ­`¢©†˜ÃV‹-f¢¡†¢a«eŠ%«Y¨©q%jâd,Ôq`) ¤¦…šˆ ¦E>0Ùb²t–Ÿ  ÷jsÏ‚Ò’KÈcø(é›;k(’#ôŒQ ™C> õ³M9óºÆµ¤çâ;uÀ)5>RÔ¸fÓ~Ȧ—’-$fe«"FâUˆÊwµPÏu w+"åÉó¨6s™Û9(À¨ù©hE°½†n`m~“@©›p!Vkhµ Á1šbEqqÊ@ºèl›2 –Yã%‘‚hÛ{a¶‡ÅÞM²¬çL34®Çl]®‹ŽØŒm'RÜe35æöˆ­Á­ cP9šeÁköo´L³Ì=p8]”‡B¶,šº|ɏdzXˆØk*ÇÚ{#ñ‰pã(€¶‡9ý'šÜ³½¯kƒ†Â’ëSOƒ•Å®H6+a¢µˆ‹Y¨b˜b+XˆÖ!°u!¢"µˆˆn2ˆ Å0Ä`Å Ô®c(ÓÜGº•Ä»Œ âWî%q.áÐÄ÷î%umÍ£+ÜQ,Vn¦-GphU¸¢X­&,Gt ·K¢ÅÅ·¥RÄÊÉbKn N­R2g$VµÕó Qr#–ÓZUÏð0ÎtÙÀœz ëöo“Îk¯n„T°"SÞ+³/…€½"ižãO%Í%&Δâ‘ËØ´IˆÓ°Ë‰ÞM3.™yçÁzit›`4C`k¢¼á!álÄï sÂ[×!¤l¾æo"ƒIÔ'@ªu)3›ô®“@Z à¾] üœ'‡4¸PÞkÁ-qÄH‰ÓÍBd´ÿ —¹°ÄA&ÊUC„öz‚‚RæŠtf¬>˜ÑidšEçÑL÷áý¡V±h§­c¿¥¨ƒ@g¼…Ýö^ÞËc.ž„æ“I[ ª+·zÐÒÚ,½Ð»¶€C›7jk$๖€Ž¾ÅÙpp¶ÍþéΤ ½ØÎŒq ñpæžÅ¥#Øâ49ÃÂK^MYV“,¶Éz_òæ:…;Õ«¦I3âJ£¤û5$7Èxün\â]Êe¯(Ÿ&Ž‹¶2<6Ćf× æ¢ƱqWı[(ÙÂŽç‚T7¨@ÈÉÍß‚ïÙ"&3TYlGŽ†)†#5ŠA©^T2ÆÁ†)©†©†¤yGXÁ†©"†)©¼ÅV WS†#©]R–r‹q5ÕbâWþBh¯u+ªÅÄ×ü„nÑ^êkªÁj‰jeœWˆÕÕ`µDµ2Ì+Ä µDµµ5Ô{¤Þ0RF’H÷AÛ<ÊÁ§ ƈæ0Ñ£ê4 öÚµ[¬/1²€â<-¬šö²r×0o×w ´xÐÒË„ g01¬„åEM蛇Ã\6µE›‘fÙO k÷CºnÓ1`iîÒ² áÂ!ÑLÄÿ ³¬\õ*:M=Ç»c‹2[‰ØsÕLò\ŒK L^™üÄN\¶#» Ç\……ßïIœÉ$¸ÎñÍ®ÔHÇ Ûí/´>Li”„†g^$ 7NÍÑÑ2M2ªNg=k½Ð}Ÿl6‡ —JWˆ”ÞéT·+µ¦üÂFè¢Vs6ýÆ4»2+2IÝ9ô9®ÇGÙÇ1+Ä8;*Õ§ž½D*îÑWÚçá3Ma¤·ˆ¥t}š²Ü…Q+Æüµ8HíS”üxGéÁˆ¦Ël„éÈ 5 µÄƒ6äÜ(kIš¯S†fÖ&¸®×v|Äyˆ*禌Éù@7-®Ä[]ÎÖ¿ê`º…=:…žJVnݳvðÖKE¼‚ »mà ÷f®:Ë ™–4rð¡4` ܹçž~‹C=œ…¾Ïj|VDtK.ƒ"9 Ï ­–éXá³6WÒïIL-Ї Ç smkb8269/public_html/wa.smk-almanshuriyah.sch.id/vendor/markbaker/complex/classes/src/Functions.php000064400000073501152267532140030243 0ustar00homegetReal() - $invsqrt->getImaginary(), $complex->getImaginary() + $invsqrt->getReal() ); $log = self::ln($adjust); return new Complex( $log->getImaginary(), -1 * $log->getReal() ); } /** * Returns the inverse hyperbolic cosine of a complex number. * * Formula from Wolfram Alpha: * cosh^(-1)z = ln(z + sqrt(z + 1) sqrt(z - 1)). * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The inverse hyperbolic cosine of the complex argument. * @throws Exception If argument isn't a valid real or complex number. */ public static function acosh($complex): Complex { $complex = Complex::validateComplexArgument($complex); if ($complex->isReal() && ($complex->getReal() > 1)) { return new Complex(\acosh($complex->getReal())); } $acosh = self::ln( Operations::add( $complex, Operations::multiply( self::sqrt(Operations::add($complex, 1)), self::sqrt(Operations::subtract($complex, 1)) ) ) ); return $acosh; } /** * Returns the inverse cotangent of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The inverse cotangent of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * @throws \InvalidArgumentException If function would result in a division by zero */ public static function acot($complex): Complex { $complex = Complex::validateComplexArgument($complex); return self::atan(self::inverse($complex)); } /** * Returns the inverse hyperbolic cotangent of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The inverse hyperbolic cotangent of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * @throws \InvalidArgumentException If function would result in a division by zero */ public static function acoth($complex): Complex { $complex = Complex::validateComplexArgument($complex); return self::atanh(self::inverse($complex)); } /** * Returns the inverse cosecant of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The inverse cosecant of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * @throws \InvalidArgumentException If function would result in a division by zero */ public static function acsc($complex): Complex { $complex = Complex::validateComplexArgument($complex); if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) { return new Complex(INF); } return self::asin(self::inverse($complex)); } /** * Returns the inverse hyperbolic cosecant of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The inverse hyperbolic cosecant of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * @throws \InvalidArgumentException If function would result in a division by zero */ public static function acsch($complex): Complex { $complex = Complex::validateComplexArgument($complex); if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) { return new Complex(INF); } return self::asinh(self::inverse($complex)); } /** * Returns the argument of a complex number. * Also known as the theta of the complex number, i.e. the angle in radians * from the real axis to the representation of the number in polar coordinates. * * This function is a synonym for theta() * * @param Complex|mixed $complex Complex number or a numeric value. * @return float The argument (or theta) value of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * * @see theta */ public static function argument($complex): float { return self::theta($complex); } /** * Returns the inverse secant of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The inverse secant of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * @throws \InvalidArgumentException If function would result in a division by zero */ public static function asec($complex): Complex { $complex = Complex::validateComplexArgument($complex); if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) { return new Complex(INF); } return self::acos(self::inverse($complex)); } /** * Returns the inverse hyperbolic secant of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The inverse hyperbolic secant of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * @throws \InvalidArgumentException If function would result in a division by zero */ public static function asech($complex): Complex { $complex = Complex::validateComplexArgument($complex); if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) { return new Complex(INF); } return self::acosh(self::inverse($complex)); } /** * Returns the inverse sine of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The inverse sine of the complex argument. * @throws Exception If argument isn't a valid real or complex number. */ public static function asin($complex): Complex { $complex = Complex::validateComplexArgument($complex); $invsqrt = self::sqrt(Operations::subtract(1, Operations::multiply($complex, $complex))); $adjust = new Complex( $invsqrt->getReal() - $complex->getImaginary(), $invsqrt->getImaginary() + $complex->getReal() ); $log = self::ln($adjust); return new Complex( $log->getImaginary(), -1 * $log->getReal() ); } /** * Returns the inverse hyperbolic sine of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The inverse hyperbolic sine of the complex argument. * @throws Exception If argument isn't a valid real or complex number. */ public static function asinh($complex): Complex { $complex = Complex::validateComplexArgument($complex); if ($complex->isReal() && ($complex->getReal() > 1)) { return new Complex(\asinh($complex->getReal())); } $asinh = clone $complex; $asinh = $asinh->reverse() ->invertReal(); $asinh = self::asin($asinh); return $asinh->reverse() ->invertImaginary(); } /** * Returns the inverse tangent of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The inverse tangent of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * @throws \InvalidArgumentException If function would result in a division by zero */ public static function atan($complex): Complex { $complex = Complex::validateComplexArgument($complex); if ($complex->isReal()) { return new Complex(\atan($complex->getReal())); } $t1Value = new Complex(-1 * $complex->getImaginary(), $complex->getReal()); $uValue = new Complex(1, 0); $d1Value = clone $uValue; $d1Value = Operations::subtract($d1Value, $t1Value); $d2Value = Operations::add($t1Value, $uValue); $uResult = $d1Value->divideBy($d2Value); $uResult = self::ln($uResult); $realMultiplier = -0.5; $imaginaryMultiplier = 0.5; if (abs($uResult->getImaginary()) === M_PI) { // If we have an imaginary value at the max or min (PI or -PI), then we need to ensure // that the primary is assigned for the correct quadrant. $realMultiplier = ( ($uResult->getImaginary() === M_PI && $uResult->getReal() > 0.0) || ($uResult->getImaginary() === -M_PI && $uResult->getReal() < 0.0) ) ? 0.5 : -0.5; } return new Complex( $uResult->getImaginary() * $realMultiplier, $uResult->getReal() * $imaginaryMultiplier, $complex->getSuffix() ); } /** * Returns the inverse hyperbolic tangent of a complex number. * * Formula from Wolfram Alpha: * tanh^(-1)z = 1/2 [ln(1 + z) - ln(1 - z)]. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The inverse hyperbolic tangent of the complex argument. * @throws Exception If argument isn't a valid real or complex number. */ public static function atanh($complex): Complex { $complex = Complex::validateComplexArgument($complex); if ($complex->isReal()) { $real = $complex->getReal(); if ($real >= -1.0 && $real <= 1.0) { return new Complex(\atanh($real)); } else { return new Complex(\atanh(1 / $real), (($real < 0.0) ? M_PI_2 : -1 * M_PI_2)); } } $atanh = Operations::multiply( Operations::subtract( self::ln(Operations::add(1.0, $complex)), self::ln(Operations::subtract(1.0, $complex)) ), 0.5 ); return $atanh; } /** * Returns the complex conjugate of a complex number * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The conjugate of the complex argument. * @throws Exception If argument isn't a valid real or complex number. */ public static function conjugate($complex): Complex { $complex = Complex::validateComplexArgument($complex); return new Complex( $complex->getReal(), -1 * $complex->getImaginary(), $complex->getSuffix() ); } /** * Returns the cosine of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The cosine of the complex argument. * @throws Exception If argument isn't a valid real or complex number. */ public static function cos($complex): Complex { $complex = Complex::validateComplexArgument($complex); if ($complex->isReal()) { return new Complex(\cos($complex->getReal())); } return self::conjugate( new Complex( \cos($complex->getReal()) * \cosh($complex->getImaginary()), \sin($complex->getReal()) * \sinh($complex->getImaginary()), $complex->getSuffix() ) ); } /** * Returns the hyperbolic cosine of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The hyperbolic cosine of the complex argument. * @throws Exception If argument isn't a valid real or complex number. */ public static function cosh($complex): Complex { $complex = Complex::validateComplexArgument($complex); if ($complex->isReal()) { return new Complex(\cosh($complex->getReal())); } return new Complex( \cosh($complex->getReal()) * \cos($complex->getImaginary()), \sinh($complex->getReal()) * \sin($complex->getImaginary()), $complex->getSuffix() ); } /** * Returns the cotangent of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The cotangent of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * @throws \InvalidArgumentException If function would result in a division by zero */ public static function cot($complex): Complex { $complex = Complex::validateComplexArgument($complex); if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) { return new Complex(INF); } return self::inverse(self::tan($complex)); } /** * Returns the hyperbolic cotangent of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The hyperbolic cotangent of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * @throws \InvalidArgumentException If function would result in a division by zero */ public static function coth($complex): Complex { $complex = Complex::validateComplexArgument($complex); return self::inverse(self::tanh($complex)); } /** * Returns the cosecant of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The cosecant of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * @throws \InvalidArgumentException If function would result in a division by zero */ public static function csc($complex): Complex { $complex = Complex::validateComplexArgument($complex); if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) { return new Complex(INF); } return self::inverse(self::sin($complex)); } /** * Returns the hyperbolic cosecant of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The hyperbolic cosecant of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * @throws \InvalidArgumentException If function would result in a division by zero */ public static function csch($complex): Complex { $complex = Complex::validateComplexArgument($complex); if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) { return new Complex(INF); } return self::inverse(self::sinh($complex)); } /** * Returns the exponential of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The exponential of the complex argument. * @throws Exception If argument isn't a valid real or complex number. */ public static function exp($complex): Complex { $complex = Complex::validateComplexArgument($complex); if (($complex->getReal() == 0.0) && (\abs($complex->getImaginary()) == M_PI)) { return new Complex(-1.0, 0.0); } $rho = \exp($complex->getReal()); return new Complex( $rho * \cos($complex->getImaginary()), $rho * \sin($complex->getImaginary()), $complex->getSuffix() ); } /** * Returns the inverse of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The inverse of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * @throws InvalidArgumentException If function would result in a division by zero */ public static function inverse($complex): Complex { $complex = clone Complex::validateComplexArgument($complex); if ($complex->getReal() == 0.0 && $complex->getImaginary() == 0.0) { throw new InvalidArgumentException('Division by zero'); } return $complex->divideInto(1.0); } /** * Returns the natural logarithm of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The natural logarithm of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * @throws InvalidArgumentException If the real and the imaginary parts are both zero */ public static function ln($complex): Complex { $complex = Complex::validateComplexArgument($complex); if (($complex->getReal() == 0.0) && ($complex->getImaginary() == 0.0)) { throw new InvalidArgumentException(); } return new Complex( \log(self::rho($complex)), self::theta($complex), $complex->getSuffix() ); } /** * Returns the base-2 logarithm of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The base-2 logarithm of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * @throws InvalidArgumentException If the real and the imaginary parts are both zero */ public static function log2($complex): Complex { $complex = Complex::validateComplexArgument($complex); if (($complex->getReal() == 0.0) && ($complex->getImaginary() == 0.0)) { throw new InvalidArgumentException(); } elseif (($complex->getReal() > 0.0) && ($complex->getImaginary() == 0.0)) { return new Complex(\log($complex->getReal(), 2), 0.0, $complex->getSuffix()); } return self::ln($complex) ->multiply(\log(Complex::EULER, 2)); } /** * Returns the common logarithm (base 10) of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The common logarithm (base 10) of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * @throws InvalidArgumentException If the real and the imaginary parts are both zero */ public static function log10($complex): Complex { $complex = Complex::validateComplexArgument($complex); if (($complex->getReal() == 0.0) && ($complex->getImaginary() == 0.0)) { throw new InvalidArgumentException(); } elseif (($complex->getReal() > 0.0) && ($complex->getImaginary() == 0.0)) { return new Complex(\log10($complex->getReal()), 0.0, $complex->getSuffix()); } return self::ln($complex) ->multiply(\log10(Complex::EULER)); } /** * Returns the negative of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The negative value of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * * @see rho * */ public static function negative($complex): Complex { $complex = Complex::validateComplexArgument($complex); return new Complex( -1 * $complex->getReal(), -1 * $complex->getImaginary(), $complex->getSuffix() ); } /** * Returns a complex number raised to a power. * * @param Complex|mixed $complex Complex number or a numeric value. * @param float|integer $power The power to raise this value to * @return Complex The complex argument raised to the real power. * @throws Exception If the power argument isn't a valid real */ public static function pow($complex, $power): Complex { $complex = Complex::validateComplexArgument($complex); if (!is_numeric($power)) { throw new Exception('Power argument must be a real number'); } if ($complex->getImaginary() == 0.0 && $complex->getReal() >= 0.0) { return new Complex(\pow($complex->getReal(), $power)); } $rValue = \sqrt(($complex->getReal() * $complex->getReal()) + ($complex->getImaginary() * $complex->getImaginary())); $rPower = \pow($rValue, $power); $theta = $complex->argument() * $power; if ($theta == 0) { return new Complex(1); } return new Complex($rPower * \cos($theta), $rPower * \sin($theta), $complex->getSuffix()); } /** * Returns the rho of a complex number. * This is the distance/radius from the centrepoint to the representation of the number in polar coordinates. * * @param Complex|mixed $complex Complex number or a numeric value. * @return float The rho value of the complex argument. * @throws Exception If argument isn't a valid real or complex number. */ public static function rho($complex): float { $complex = Complex::validateComplexArgument($complex); return \sqrt( ($complex->getReal() * $complex->getReal()) + ($complex->getImaginary() * $complex->getImaginary()) ); } /** * Returns the secant of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The secant of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * @throws \InvalidArgumentException If function would result in a division by zero */ public static function sec($complex): Complex { $complex = Complex::validateComplexArgument($complex); return self::inverse(self::cos($complex)); } /** * Returns the hyperbolic secant of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The hyperbolic secant of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * @throws \InvalidArgumentException If function would result in a division by zero */ public static function sech($complex): Complex { $complex = Complex::validateComplexArgument($complex); return self::inverse(self::cosh($complex)); } /** * Returns the sine of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The sine of the complex argument. * @throws Exception If argument isn't a valid real or complex number. */ public static function sin($complex): Complex { $complex = Complex::validateComplexArgument($complex); if ($complex->isReal()) { return new Complex(\sin($complex->getReal())); } return new Complex( \sin($complex->getReal()) * \cosh($complex->getImaginary()), \cos($complex->getReal()) * \sinh($complex->getImaginary()), $complex->getSuffix() ); } /** * Returns the hyperbolic sine of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The hyperbolic sine of the complex argument. * @throws Exception If argument isn't a valid real or complex number. */ public static function sinh($complex): Complex { $complex = Complex::validateComplexArgument($complex); if ($complex->isReal()) { return new Complex(\sinh($complex->getReal())); } return new Complex( \sinh($complex->getReal()) * \cos($complex->getImaginary()), \cosh($complex->getReal()) * \sin($complex->getImaginary()), $complex->getSuffix() ); } /** * Returns the square root of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The Square root of the complex argument. * @throws Exception If argument isn't a valid real or complex number. */ public static function sqrt($complex): Complex { $complex = Complex::validateComplexArgument($complex); $theta = self::theta($complex); $delta1 = \cos($theta / 2); $delta2 = \sin($theta / 2); $rho = \sqrt(self::rho($complex)); return new Complex($delta1 * $rho, $delta2 * $rho, $complex->getSuffix()); } /** * Returns the tangent of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The tangent of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * @throws InvalidArgumentException If function would result in a division by zero */ public static function tan($complex): Complex { $complex = Complex::validateComplexArgument($complex); if ($complex->isReal()) { return new Complex(\tan($complex->getReal())); } $real = $complex->getReal(); $imaginary = $complex->getImaginary(); $divisor = 1 + \pow(\tan($real), 2) * \pow(\tanh($imaginary), 2); if ($divisor == 0.0) { throw new InvalidArgumentException('Division by zero'); } return new Complex( \pow(self::sech($imaginary)->getReal(), 2) * \tan($real) / $divisor, \pow(self::sec($real)->getReal(), 2) * \tanh($imaginary) / $divisor, $complex->getSuffix() ); } /** * Returns the hyperbolic tangent of a complex number. * * @param Complex|mixed $complex Complex number or a numeric value. * @return Complex The hyperbolic tangent of the complex argument. * @throws Exception If argument isn't a valid real or complex number. * @throws \InvalidArgumentException If function would result in a division by zero */ public static function tanh($complex): Complex { $complex = Complex::validateComplexArgument($complex); $real = $complex->getReal(); $imaginary = $complex->getImaginary(); $divisor = \cos($imaginary) * \cos($imaginary) + \sinh($real) * \sinh($real); if ($divisor == 0.0) { throw new InvalidArgumentException('Division by zero'); } return new Complex( \sinh($real) * \cosh($real) / $divisor, 0.5 * \sin(2 * $imaginary) / $divisor, $complex->getSuffix() ); } /** * Returns the theta of a complex number. * This is the angle in radians from the real axis to the representation of the number in polar coordinates. * * @param Complex|mixed $complex Complex number or a numeric value. * @return float The theta value of the complex argument. * @throws Exception If argument isn't a valid real or complex number. */ public static function theta($complex): float { $complex = Complex::validateComplexArgument($complex); if ($complex->getReal() == 0.0) { if ($complex->isReal()) { return 0.0; } elseif ($complex->getImaginary() < 0.0) { return M_PI / -2; } return M_PI / 2; } elseif ($complex->getReal() > 0.0) { return \atan($complex->getImaginary() / $complex->getReal()); } elseif ($complex->getImaginary() < 0.0) { return -(M_PI - \atan(\abs($complex->getImaginary()) / \abs($complex->getReal()))); } return M_PI - \atan($complex->getImaginary() / \abs($complex->getReal())); } } smkb8269/public_html/wa.smk-almanshuriyah.sch.id/vendor/markbaker/matrix/classes/src/Functions.php000064400000025222152267533100030072 0ustar00homeisSquare()) { throw new Exception('Adjoint can only be calculated for a square matrix'); } return self::getAdjoint($matrix); } /** * Calculate the cofactors of the matrix * * @param Matrix $matrix The matrix whose cofactors we wish to calculate * @return Matrix * * @throws Exception */ private static function getCofactors(Matrix $matrix) { $cofactors = self::getMinors($matrix); $dimensions = $matrix->rows; $cof = 1; for ($i = 0; $i < $dimensions; ++$i) { $cofs = $cof; for ($j = 0; $j < $dimensions; ++$j) { $cofactors[$i][$j] *= $cofs; $cofs = -$cofs; } $cof = -$cof; } return new Matrix($cofactors); } /** * Return the cofactors of this matrix * * @param Matrix|array $matrix The matrix whose cofactors we wish to calculate * @return Matrix * * @throws Exception */ public static function cofactors($matrix) { $matrix = self::validateMatrix($matrix); if (!$matrix->isSquare()) { throw new Exception('Cofactors can only be calculated for a square matrix'); } return self::getCofactors($matrix); } /** * @param Matrix $matrix * @param int $row * @param int $column * @return float * @throws Exception */ private static function getDeterminantSegment(Matrix $matrix, $row, $column) { $tmpMatrix = $matrix->toArray(); unset($tmpMatrix[$row]); array_walk( $tmpMatrix, function (&$row) use ($column) { unset($row[$column]); } ); return self::getDeterminant(new Matrix($tmpMatrix)); } /** * Calculate the determinant of the matrix * * @param Matrix $matrix The matrix whose determinant we wish to calculate * @return float * * @throws Exception */ private static function getDeterminant(Matrix $matrix) { $dimensions = $matrix->rows; $determinant = 0; switch ($dimensions) { case 1: $determinant = $matrix->getValue(1, 1); break; case 2: $determinant = $matrix->getValue(1, 1) * $matrix->getValue(2, 2) - $matrix->getValue(1, 2) * $matrix->getValue(2, 1); break; default: for ($i = 1; $i <= $dimensions; ++$i) { $det = $matrix->getValue(1, $i) * self::getDeterminantSegment($matrix, 0, $i - 1); if (($i % 2) == 0) { $determinant -= $det; } else { $determinant += $det; } } break; } return $determinant; } /** * Return the determinant of this matrix * * @param Matrix|array $matrix The matrix whose determinant we wish to calculate * @return float * @throws Exception **/ public static function determinant($matrix) { $matrix = self::validateMatrix($matrix); if (!$matrix->isSquare()) { throw new Exception('Determinant can only be calculated for a square matrix'); } return self::getDeterminant($matrix); } /** * Return the diagonal of this matrix * * @param Matrix|array $matrix The matrix whose diagonal we wish to calculate * @return Matrix * @throws Exception **/ public static function diagonal($matrix) { $matrix = self::validateMatrix($matrix); if (!$matrix->isSquare()) { throw new Exception('Diagonal can only be extracted from a square matrix'); } $dimensions = $matrix->rows; $grid = Builder::createFilledMatrix(0, $dimensions, $dimensions) ->toArray(); for ($i = 0; $i < $dimensions; ++$i) { $grid[$i][$i] = $matrix->getValue($i + 1, $i + 1); } return new Matrix($grid); } /** * Return the antidiagonal of this matrix * * @param Matrix|array $matrix The matrix whose antidiagonal we wish to calculate * @return Matrix * @throws Exception **/ public static function antidiagonal($matrix) { $matrix = self::validateMatrix($matrix); if (!$matrix->isSquare()) { throw new Exception('Anti-Diagonal can only be extracted from a square matrix'); } $dimensions = $matrix->rows; $grid = Builder::createFilledMatrix(0, $dimensions, $dimensions) ->toArray(); for ($i = 0; $i < $dimensions; ++$i) { $grid[$i][$dimensions - $i - 1] = $matrix->getValue($i + 1, $dimensions - $i); } return new Matrix($grid); } /** * Return the identity matrix * The identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix * with ones on the main diagonal and zeros elsewhere * * @param Matrix|array $matrix The matrix whose identity we wish to calculate * @return Matrix * @throws Exception **/ public static function identity($matrix) { $matrix = self::validateMatrix($matrix); if (!$matrix->isSquare()) { throw new Exception('Identity can only be created for a square matrix'); } $dimensions = $matrix->rows; return Builder::createIdentityMatrix($dimensions); } /** * Return the inverse of this matrix * * @param Matrix|array $matrix The matrix whose inverse we wish to calculate * @return Matrix * @throws Exception **/ public static function inverse($matrix, string $type = 'inverse') { $matrix = self::validateMatrix($matrix); if (!$matrix->isSquare()) { throw new Exception(ucfirst($type) . ' can only be calculated for a square matrix'); } $determinant = self::getDeterminant($matrix); if ($determinant == 0.0) { throw new Div0Exception(ucfirst($type) . ' can only be calculated for a matrix with a non-zero determinant'); } if ($matrix->rows == 1) { return new Matrix([[1 / $matrix->getValue(1, 1)]]); } return self::getAdjoint($matrix) ->multiply(1 / $determinant); } /** * Calculate the minors of the matrix * * @param Matrix $matrix The matrix whose minors we wish to calculate * @return array[] * * @throws Exception */ protected static function getMinors(Matrix $matrix) { $minors = $matrix->toArray(); $dimensions = $matrix->rows; if ($dimensions == 1) { return $minors; } for ($i = 0; $i < $dimensions; ++$i) { for ($j = 0; $j < $dimensions; ++$j) { $minors[$i][$j] = self::getDeterminantSegment($matrix, $i, $j); } } return $minors; } /** * Return the minors of the matrix * The minor of a matrix A is the determinant of some smaller square matrix, cut down from A by removing one or * more of its rows or columns. * Minors obtained by removing just one row and one column from square matrices (first minors) are required for * calculating matrix cofactors, which in turn are useful for computing both the determinant and inverse of * square matrices. * * @param Matrix|array $matrix The matrix whose minors we wish to calculate * @return Matrix * @throws Exception **/ public static function minors($matrix) { $matrix = self::validateMatrix($matrix); if (!$matrix->isSquare()) { throw new Exception('Minors can only be calculated for a square matrix'); } return new Matrix(self::getMinors($matrix)); } /** * Return the trace of this matrix * The trace is defined as the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) * of the matrix * * @param Matrix|array $matrix The matrix whose trace we wish to calculate * @return float * @throws Exception **/ public static function trace($matrix) { $matrix = self::validateMatrix($matrix); if (!$matrix->isSquare()) { throw new Exception('Trace can only be extracted from a square matrix'); } $dimensions = $matrix->rows; $result = 0; for ($i = 1; $i <= $dimensions; ++$i) { $result += $matrix->getValue($i, $i); } return $result; } /** * Return the transpose of this matrix * * @param Matrix|\a $matrix The matrix whose transpose we wish to calculate * @return Matrix **/ public static function transpose($matrix) { $matrix = self::validateMatrix($matrix); $array = array_values(array_merge([null], $matrix->toArray())); $grid = call_user_func_array( 'array_map', $array ); return new Matrix($grid); } }