https://sourceforge.net/p/freemuse/wiki/complex%2520valued%2520quantities/Recent changes to complex valued quantitiesenSun, 05 Jun 2011 09:36:45 -0000https://sourceforge.net/p/freemuse/wiki/complex%2520valued%2520quantities/<pre>--- v5 +++ v6 @@ -1,64 +1,63 @@ -Complex valued quantities -=== - +#Complex valued quantities# + MUSE can represent complex valued quantities by the real and imaginary part as well as by an argument (angle) and a magnitude (absolut value or modulus). A complex valued quantity can therefore be described by a two dimensional PDF where one marginal distribution defines the real and the other one the imaginary part. If x is a complex valued quantity re(x) defines the PDF of the real part and im(x) the PDF of the imaginary part of x. MUSE provides three ways to define a complex valued quantity. * The distribution complex * The function complex * The function polar It is also possible to [convert](Conversion of Complex valued quantities) between the two different representations. The distribution complex A complex distribution with a Gaussian distributed real- and imaginary part can be defined as a basic model like follows: ~~~~ <model name="Complex" targetid="s"> <model name="Complex" targetid="s"> <influence id="s" name="Complex"> <distribution id="c"> <complex> <realpart> <distribution> <gauss> <mu parameter="#111">1</mu> <sigma parameter="#112">1</sigma> </gauss> </distribution> </realpart> <imaginarypart> <distribution> <gauss> <mu parameter="#113">1</mu> <sigma parameter="#114">1</sigma> </gauss> </distribution> </imaginarypart> </complex> </distribution> </influence> </model> ~~~~ By this definition the real part is Gaussian distributed with a mean value of 0 and a standard deviation of 1. The imaginary part has a mean of 1 with a standard deviation of 1. This distribution can now be used in the same way like other distributions. So we can define a influence in the initialization section by the statement <instance name="s1" model="complex"></instance> and use it with all the given operators in the formula to calculate the uncertainty. Of course it is possible to use each [supported distribution](Distributions) instead of Gaussian distributions in the definition above. -Function complex ---- +###Function complex### + (since version 0.6) A complex valued quantity can be defined using the function complex. This function returns the complex number which corresponds to a specified real and imaginary part in Cartesian form. For example we can take a Gaussian distribution with a mean of 1 and a standard deviation of 0.1 for the real part and the same one for the imaginary. This can be defined by the following simulation file. ~~~~ <simulation> <initialization> <instance name="_real" model="gaussparam"> <parameters> @@ -72,16 +71,15 @@ <parameter id="#2">.1</parameter> </parameters> </instance> </initialization> <calculation dimensions="-1"> <analyse mode="on" histbars="40" datafiles="delete"/> <uncertainty> complex(_real,_imag) </uncertainty> </calculation> </simulation> ~~~~ -Function polar ---- +###Function polar### (since version 0.6) A complex valued quantity can be defined using the function polar. This function returns the complex number which corresponds to a specified modulus and argument part in the polar form. For example we can take a Gaussian distribution with a mean of 1 and a standard deviation of 0.1 for the modulus part and a Gaussian distribution with a mean value of pi/4 and a standard deviation of 0.1 for the argument. This can be defined by the following simulation file. </pre>Martin MuellerSun, 05 Jun 2011 09:36:45 -0000https://sourceforge.net27b477d4898e4be74482cdf6e61775161b267e22https://sourceforge.net/p/freemuse/wiki/complex%2520valued%2520quantities/<pre>--- v4 +++ v5 @@ -9,52 +9,52 @@ * The function complex * The function polar -It is also possible to [convert](Conversion of complex numbers) between the two different representations. - +It is also possible to [convert](Conversion of Complex valued quantities) between the two different representations. + The distribution complex A complex distribution with a Gaussian distributed real- and imaginary part can be defined as a basic model like follows: ~~~~ <model name="Complex" targetid="s"> <model name="Complex" targetid="s"> <influence id="s" name="Complex"> <distribution id="c"> <complex> <realpart> <distribution> <gauss> <mu parameter="#111">1</mu> <sigma parameter="#112">1</sigma> </gauss> </distribution> </realpart> <imaginarypart> <distribution> <gauss> <mu parameter="#113">1</mu> <sigma parameter="#114">1</sigma> </gauss> </distribution> </imaginarypart> </complex> </distribution> </influence> </model> ~~~~ By this definition the real part is Gaussian distributed with a mean value of 0 and a standard deviation of 1. The imaginary part has a mean of 1 with a standard deviation of 1. This distribution can now be used in the same way like other distributions. So we can define a influence in the initialization section by the statement <instance name="s1" model="complex"></instance> and use it with all the given operators in the formula to calculate the uncertainty. Of course it is possible to use each [supported distribution](Distributions) instead of Gaussian distributions in the definition above. Function complex --- (since version 0.6) A complex valued quantity can be defined using the function complex. This function returns the complex number which corresponds to a specified real and imaginary part in Cartesian form. For example we can take a Gaussian distribution with a mean of 1 and a standard deviation of 0.1 for the real part and the same one for the imaginary. This can be defined by the following simulation file. ~~~~ @@ -75,28 +75,28 @@ </initialization> <calculation dimensions="-1"> <analyse mode="on" histbars="40" datafiles="delete"/> <uncertainty> complex(_real,_imag) </uncertainty> </calculation> </simulation> ~~~~ Function polar --- (since version 0.6) A complex valued quantity can be defined using the function polar. This function returns the complex number which corresponds to a specified modulus and argument part in the polar form. For example we can take a Gaussian distribution with a mean of 1 and a standard deviation of 0.1 for the modulus part and a Gaussian distribution with a mean value of pi/4 and a standard deviation of 0.1 for the argument. This can be defined by the following simulation file. ~~~~ <simulation> <initialization> <instance name="_mod" model="gaussparam"> <parameters> <parameter id="#1">1</parameter> <parameter id="#2">.1</parameter> </parameters> </instance> <instance name="_arg" model="gaussparam"> <parameters> <parameter id="#1">pi/4</parameter> <parameter id="#2">.1</parameter> </parameters> @@ -104,9 +104,9 @@ </initialization> <calculation dimensions="-1"> <analyse mode="on" histbars="40" datafiles="delete"/> <uncertainty> polar(_mod,_arg) </uncertainty> </calculation> </simulation> ~~~~ -Beware that not all operations are defined in polar coordinates! [Here](Convertion of complex numbers) you can see how to convert between the two different representations of complex numbers. +Beware that not all operations are defined in polar coordinates! [Here](Conversion of Complex valued quantities) you can see how to convert between the two different representations of complex numbers. </pre>Martin MuellerSun, 05 Jun 2011 06:57:39 -0000https://sourceforge.net93f87781b3bc756f5a36f9e355c62146de152766https://sourceforge.net/p/freemuse/wiki/complex%2520valued%2520quantities/<pre>--- v3 +++ v4 @@ -9,7 +9,7 @@ * The function complex * The function polar -It is also possible to [convert] between the two different representations. +It is also possible to [convert](Conversion of complex numbers) between the two different representations. The distribution complex </pre>Martin MuellerSun, 05 Jun 2011 06:55:59 -0000https://sourceforge.net558851559fa568b9c23887b85da82d97f1811cb3https://sourceforge.net/p/freemuse/wiki/complex%2520valued%2520quantities/<pre>--- v2 +++ v3 @@ -1,60 +1,62 @@ Complex valued quantities -===== - +=== + MUSE can represent complex valued quantities by the real and imaginary part as well as by an argument (angle) and a magnitude (absolut value or modulus). A complex valued quantity can therefore be described by a two dimensional PDF where one marginal distribution defines the real and the other one the imaginary part. If x is a complex valued quantity re(x) defines the PDF of the real part and im(x) the PDF of the imaginary part of x. MUSE provides three ways to define a complex valued quantity. * The distribution complex * The function complex * The function polar It is also possible to [convert] between the two different representations. The distribution complex -=== A complex distribution with a Gaussian distributed real- and imaginary part can be defined as a basic model like follows: + ~~~~ <model name="Complex" targetid="s"> <model name="Complex" targetid="s"> <influence id="s" name="Complex"> <distribution id="c"> <complex> <realpart> <distribution> <gauss> <mu parameter="#111">1</mu> <sigma parameter="#112">1</sigma> </gauss> </distribution> </realpart> <imaginarypart> <distribution> <gauss> <mu parameter="#113">1</mu> <sigma parameter="#114">1</sigma> </gauss> </distribution> </imaginarypart> </complex> </distribution> </influence> </model> ~~~~ + By this definition the real part is Gaussian distributed with a mean value of 0 and a standard deviation of 1. The imaginary part has a mean of 1 with a standard deviation of 1. This distribution can now be used in the same way like other distributions. So we can define a influence in the initialization section by the statement <instance name="s1" model="complex"></instance> and use it with all the given operators in the formula to calculate the uncertainty. Of course it is possible to use each [supported distribution](Distributions) instead of Gaussian distributions in the definition above. Function complex -=== +--- (since version 0.6) A complex valued quantity can be defined using the function complex. This function returns the complex number which corresponds to a specified real and imaginary part in Cartesian form. For example we can take a Gaussian distribution with a mean of 1 and a standard deviation of 0.1 for the real part and the same one for the imaginary. This can be defined by the following simulation file. + ~~~~ <simulation> <initialization> @@ -73,26 +75,28 @@ </initialization> <calculation dimensions="-1"> <analyse mode="on" histbars="40" datafiles="delete"/> <uncertainty> complex(_real,_imag) </uncertainty> </calculation> </simulation> ~~~~ + Function polar -=== +--- (since version 0.6) A complex valued quantity can be defined using the function polar. This function returns the complex number which corresponds to a specified modulus and argument part in the polar form. For example we can take a Gaussian distribution with a mean of 1 and a standard deviation of 0.1 for the modulus part and a Gaussian distribution with a mean value of pi/4 and a standard deviation of 0.1 for the argument. This can be defined by the following simulation file. + ~~~~ <simulation> <initialization> <instance name="_mod" model="gaussparam"> <parameters> <parameter id="#1">1</parameter> <parameter id="#2">.1</parameter> </parameters> </instance> <instance name="_arg" model="gaussparam"> <parameters> <parameter id="#1">pi/4</parameter> <parameter id="#2">.1</parameter> </parameters> @@ -100,8 +104,9 @@ </initialization> <calculation dimensions="-1"> <analyse mode="on" histbars="40" datafiles="delete"/> <uncertainty> polar(_mod,_arg) </uncertainty> </calculation> </simulation> ~~~~ + Beware that not all operations are defined in polar coordinates! [Here](Convertion of complex numbers) you can see how to convert between the two different representations of complex numbers. </pre>Martin MuellerSun, 05 Jun 2011 06:52:27 -0000https://sourceforge.netd500a43a41b0bd7d9613be5a18e37780d65d6db3https://sourceforge.net/p/freemuse/wiki/complex%2520valued%2520quantities/<pre>--- v1 +++ v2 @@ -1,18 +1,18 @@ Complex valued quantities -=== - +===== + MUSE can represent complex valued quantities by the real and imaginary part as well as by an argument (angle) and a magnitude (absolut value or modulus). A complex valued quantity can therefore be described by a two dimensional PDF where one marginal distribution defines the real and the other one the imaginary part. If x is a complex valued quantity re(x) defines the PDF of the real part and im(x) the PDF of the imaginary part of x. MUSE provides three ways to define a complex valued quantity. * The distribution complex * The function complex * The function polar It is also possible to [convert] between the two different representations. The distribution complex -==== +=== A complex distribution with a Gaussian distributed real- and imaginary part can be defined as a basic model like follows: ~~~~ </pre>Martin MuellerSun, 05 Jun 2011 06:41:48 -0000https://sourceforge.net6d1143c27284303b33fe55e3a1e15ead90f349c2https://sourceforge.net/p/freemuse/wiki/complex%2520valued%2520quantities/Complex valued quantities === MUSE can represent complex valued quantities by the real and imaginary part as well as by an argument (angle) and a magnitude (absolut value or modulus). A complex valued quantity can therefore be described by a two dimensional PDF where one marginal distribution defines the real and the other one the imaginary part. If x is a complex valued quantity re(x) defines the PDF of the real part and im(x) the PDF of the imaginary part of x. MUSE provides three ways to define a complex valued quantity. * The distribution complex * The function complex * The function polar It is also possible to [convert] between the two different representations. The distribution complex ==== A complex distribution with a Gaussian distributed real- and imaginary part can be defined as a basic model like follows: ~~~~ <model name="Complex" targetid="s"> <model name="Complex" targetid="s"> <influence id="s" name="Complex"> <distribution id="c"> <complex> <realpart> <distribution> <gauss> <mu parameter="#111">1</mu> <sigma parameter="#112">1</sigma> </gauss> </distribution> </realpart> <imaginarypart> <distribution> <gauss> <mu parameter="#113">1</mu> <sigma parameter="#114">1</sigma> </gauss> </distribution> </imaginarypart> </complex> </distribution> </influence> </model> ~~~~ By this definition the real part is Gaussian distributed with a mean value of 0 and a standard deviation of 1. The imaginary part has a mean of 1 with a standard deviation of 1. This distribution can now be used in the same way like other distributions. So we can define a influence in the initialization section by the statement <instance name="s1" model="complex"></instance> and use it with all the given operators in the formula to calculate the uncertainty. Of course it is possible to use each [supported distribution](Distributions) instead of Gaussian distributions in the definition above. Function complex === (since version 0.6) A complex valued quantity can be defined using the function complex. This function returns the complex number which corresponds to a specified real and imaginary part in Cartesian form. For example we can take a Gaussian distribution with a mean of 1 and a standard deviation of 0.1 for the real part and the same one for the imaginary. This can be defined by the following simulation file. ~~~~ <simulation> <initialization> <instance name="_real" model="gaussparam"> <parameters> <parameter id="#1">1</parameter> <parameter id="#2">.1</parameter> </parameters> </instance> <instance name="_real" model="gaussparam"> <parameters> <parameter id="#1">1</parameter> <parameter id="#2">.1</parameter> </parameters> </instance> </initialization> <calculation dimensions="-1"> <analyse mode="on" histbars="40" datafiles="delete"/> <uncertainty> complex(_real,_imag) </uncertainty> </calculation> </simulation> ~~~~ Function polar === (since version 0.6) A complex valued quantity can be defined using the function polar. This function returns the complex number which corresponds to a specified modulus and argument part in the polar form. For example we can take a Gaussian distribution with a mean of 1 and a standard deviation of 0.1 for the modulus part and a Gaussian distribution with a mean value of pi/4 and a standard deviation of 0.1 for the argument. This can be defined by the following simulation file. ~~~~ <simulation> <initialization> <instance name="_mod" model="gaussparam"> <parameters> <parameter id="#1">1</parameter> <parameter id="#2">.1</parameter> </parameters> </instance> <instance name="_arg" model="gaussparam"> <parameters> <parameter id="#1">pi/4</parameter> <parameter id="#2">.1</parameter> </parameters> </instance> </initialization> <calculation dimensions="-1"> <analyse mode="on" histbars="40" datafiles="delete"/> <uncertainty> polar(_mod,_arg) </uncertainty> </calculation> </simulation> ~~~~ Beware that not all operations are defined in polar coordinates! [Here](Convertion of complex numbers) you can see how to convert between the two different representations of complex numbers. Martin MuellerSun, 05 Jun 2011 06:39:29 -0000https://sourceforge.netacae446bc8e990b86e8d257cf7e51d7daaba05ba