- Author:
- David Nickerson <nickerso@users.sourceforge.net>
- Date:
- 2017-08-31 11:16:51+12:00
- Desc:
- adding initial set of test models used in libcellml
- Permanent Source URI:
- https://models.cellml.org/workspace/4b1/rawfile/a984419d72b5dc4ef514f02defb70308fa57b09c/sine_approximations.xml
<?xml version="1.0" encoding="UTF-8"?><model xmlns="http://www.cellml.org/cellml/1.2#" xmlns:cellml="http://www.cellml.org/cellml/1.2#" xmlns:xlink="http://www.w3.org/1999/xlink" name="sin_approximations_import" id="sin_approximations_import">
<component name="main" id="main">
<variable id="x" initial_value="0" name="x" interface="public_and_private"/>
<variable id="sin" name="sin1" interface="public_and_private"/>
<variable id="deriv_approx" name="sin2" interface="public_and_private"/>
<variable id="deriv_approx_initial_value" initial_value="0" name="deriv_approx_initial_value" interface="public_and_private"/>
<variable id="parabolic_approx" name="sin3" interface="public_and_private"/>
</component>
<component name="actual_sin" id="sin">
<variable name="x" interface="public_and_private"/>
<variable id="sin" name="sin" interface="public_and_private"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="actual_sin">
<eq/>
<ci>sin</ci>
<apply>
<sin/>
<ci>x</ci>
</apply>
</apply>
</math>
</component>
<component name="deriv_approx_sin" id="sin">
<variable id="x" name="x" interface="public_and_private"/>
<variable id="sin" initial_value="0" name="sin" interface="public_and_private"/>
<variable name="sin_initial_value" interface="public_and_private"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>x</ci>
</bvar>
<ci>sin</ci>
</apply>
<apply>
<cos/>
<ci>x</ci>
</apply>
</apply>
</math>
</component>
<component name="parabolic_approx_sin" id="sin">
<variable id="x" name="x" interface="public_and_private"/>
<variable id="sin" name="sin" interface="public_and_private"/>
<variable name="k2_oPi" interface="public_and_private"/>
<variable name="k2Pi" interface="public_and_private"/>
<variable name="kPi_2" interface="public_and_private"/>
<variable name="kPi" interface="public_and_private"/>
<variable name="kPi_32" interface="public_and_private"/>
<variable name="z" interface="public_and_private"/>
<variable initial_value="0.75" name="C" interface="public_and_private"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="k2_oPi">
<eq/>
<ci>k2_oPi</ci>
<apply>
<divide/>
<cn cellml:units="dimensionless">2.0</cn>
<pi/>
</apply>
</apply>
<apply id="k2Pi">
<eq/>
<ci>k2Pi</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">2.0</cn>
<pi/>
</apply>
</apply>
<apply id="kPi_2">
<eq/>
<ci>kPi_2</ci>
<apply>
<divide/>
<pi/>
<cn cellml:units="dimensionless">2.0</cn>
</apply>
</apply>
<apply id="kPi">
<eq/>
<ci>kPi</ci>
<pi/>
</apply>
<apply id="kPi_32">
<eq/>
<ci>kPi_32</ci>
<apply>
<divide/>
<apply>
<times/>
<cn cellml:units="dimensionless">3.0</cn>
<pi/>
</apply>
<cn cellml:units="dimensionless">2.0</cn>
</apply>
</apply>
<apply id="z">
<eq/>
<ci>z</ci>
<piecewise>
<piece>
<apply>
<minus/>
<apply>
<times/>
<ci>x</ci>
<ci>k2_oPi</ci>
</apply>
<cn cellml:units="dimensionless">0.5</cn>
</apply>
<apply>
<lt/>
<ci>x</ci>
<ci>kPi_2</ci>
</apply>
</piece>
<piece>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<pi/>
<ci>x</ci>
</apply>
<ci>k2_oPi</ci>
</apply>
<cn cellml:units="dimensionless">0.5</cn>
</apply>
<apply>
<lt/>
<ci>x</ci>
<ci>kPi</ci>
</apply>
</piece>
<piece>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<ci>x</ci>
<pi/>
</apply>
<ci>k2_oPi</ci>
</apply>
<cn cellml:units="dimensionless">0.5</cn>
</apply>
<apply>
<lt/>
<ci>x</ci>
<ci>kPi_32</ci>
</apply>
</piece>
<otherwise>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<ci>k2Pi</ci>
<ci>x</ci>
</apply>
<ci>k2_oPi</ci>
</apply>
<cn cellml:units="dimensionless">0.5</cn>
</apply>
</otherwise>
</piecewise>
</apply>
<apply id="sin">
<eq/>
<ci>sin</ci>
<piecewise>
<piece>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci>z</ci>
<ci>z</ci>
</apply>
</apply>
<ci>C</ci>
<ci>z</ci>
</apply>
<apply>
<lt/>
<ci>x</ci>
<ci>kPi_2</ci>
</apply>
</piece>
<piece>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<times/>
<ci>z</ci>
<ci>z</ci>
</apply>
</apply>
<ci>C</ci>
<ci>z</ci>
</apply>
<apply>
<lt/>
<ci>x</ci>
<ci>kPi</ci>
</apply>
</piece>
<piece>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>z</ci>
<ci>z</ci>
</apply>
<ci>C</ci>
</apply>
<ci>z</ci>
</apply>
<apply>
<lt/>
<ci>x</ci>
<ci>kPi_32</ci>
</apply>
</piece>
<otherwise>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>z</ci>
<ci>z</ci>
</apply>
<ci>C</ci>
</apply>
<ci>z</ci>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<connection component_1="actual_sin" component_2="main">
<map_variables variable_1="sin" variable_2="sin1"/>
<map_variables variable_1="x" variable_2="x"/>
</connection>
<connection component_1="deriv_approx_sin" component_2="main">
<map_variables variable_1="sin" variable_2="sin2"/>
<map_variables variable_1="x" variable_2="x"/>
<map_variables variable_1="sin_initial_value" variable_2="deriv_approx_initial_value"/>
</connection>
<connection component_1="parabolic_approx_sin" component_2="main">
<map_variables variable_1="sin" variable_2="sin3"/>
<map_variables variable_1="x" variable_2="x"/>
</connection>
<encapsulation>
<component_ref component="main">
<component_ref component="actual_sin"/>
<component_ref component="deriv_approx_sin"/>
<component_ref component="parabolic_approx_sin"/>
</component_ref>
</encapsulation>
</model>
