Difference between revisions of "User:Tohline/Appendix/ComputerAlgorithms/Riemann"

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=Riemann Algorithms=
=Riemann Algorithms=


These are algorithms that I have stored under the directory, …/numRecipes/EllipticalIntegrals/Riemann
These are algorithms that I have stored under the directory, …/numRecipes/EllipticIntegrals/Riemann




Line 10: Line 10:


==Riemann02 (12 June 2020)==
==Riemann02 (12 June 2020)==
Basically the same as "Riemann01," but with the output formatted more clearly.
Basically the same as "Riemann01," but with the output formatted more clearly. The example output file shown immediately below refers to …
<ul>
<li>'''TEST (part 1)''', which is in the context of our [[User:Tohline/ThreeDimensionalConfigurations/RiemannStype#General_Coefficient_Expressions|discussion of ''General Coefficient Expressions'']].</li>
<li>'''TEST (part 2)''', which is in the context of the evaluation of several [[User:Tohline/ThreeDimensionalConfigurations/RiemannStype#Based_on_Virial_Equilibrium|''Virial-Equilibrium-based'' expressions]].</li>
<li>'''Table 2''', which contains [[User:Tohline/ThreeDimensionalConfigurations/RiemannStype#Our_Parameter_Determinations|''Other Parameter Determinations'']].</li>
</ul>


<div align="center">
'''Example Output File'''
</div>
<div style="width: 100%;">
<pre>
Riemann S-type Ellipsoid having: (b/a,c/a) = (9.000000000000D-01,6.410000000000D-01)
*************
TEST (part 1):
Elliptic Integrals of the 1st and 2nd kinds:
          phi(deg)            (rad)          asin(k) (deg)          (rad)                F(phi,k)            E(phi,k)
    5.013357254094D+01  8.749959066267D-01  3.253852919374D+01  5.679044681871D-01  9.090259485521D-01  8.431180475729D-01
            A1                  A2                  A3     
    5.214502732782D-01  5.951310119083D-01  8.834187148135D-01
*************
TEST (part 2):
          a2A12                B12                alpha              beta
    3.877933612108D-01  2.073376506975D-01  2.472452000855D-01  3.797483470425D+00
            f                omega                f_Ad              omega_Ad
    -2.680088866444D-01  1.131374738327D+00 -1.509117086331D+01 -1.507716218767D-01
*************
Table 2:
  Direct (omega,lambda,zeta,f):        1.131374738327      0.150771621841    -0.303218483925    -0.268008886644
  Adjoint (omega,lambda,zeta,f):      -0.150771621877    -1.131374730590      2.275320291519    -15.091170863305
*************
</pre>
</div>


==Riemann01 (21 August 2019)==
==Riemann01 (21 August 2019)==

Latest revision as of 16:32, 13 June 2020


Riemann Algorithms

These are algorithms that I have stored under the directory, …/numRecipes/EllipticIntegrals/Riemann


Whitworth's (1981) Isothermal Free-Energy Surface
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Riemann02 (12 June 2020)

Basically the same as "Riemann01," but with the output formatted more clearly. The example output file shown immediately below refers to …

Example Output File


Riemann S-type Ellipsoid having: (b/a,c/a) = (9.000000000000D-01,6.410000000000D-01)

*************
TEST (part 1):

 Elliptic Integrals of the 1st and 2nd kinds:

          phi(deg)             (rad)           asin(k) (deg)          (rad)                 F(phi,k)            E(phi,k)
     5.013357254094D+01  8.749959066267D-01  3.253852919374D+01  5.679044681871D-01  9.090259485521D-01  8.431180475729D-01

            A1                  A2                  A3      
     5.214502732782D-01  5.951310119083D-01  8.834187148135D-01

*************
TEST (part 2):

           a2A12                B12                alpha               beta 
     3.877933612108D-01  2.073376506975D-01  2.472452000855D-01  3.797483470425D+00

             f                 omega                 f_Ad              omega_Ad
    -2.680088866444D-01  1.131374738327D+00 -1.509117086331D+01 -1.507716218767D-01

*************
Table 2:


  Direct (omega,lambda,zeta,f):        1.131374738327      0.150771621841     -0.303218483925     -0.268008886644

  Adjoint (omega,lambda,zeta,f):      -0.150771621877     -1.131374730590      2.275320291519    -15.091170863305

*************

Riemann01 (21 August 2019)

Evaluate terms associated with construction of various Riemann S-type Ellipsoids, especially for comparison with work by Ou (2006). Enter two axis-ratio values: bovera covera (separated by space).

See Also

Whitworth's (1981) Isothermal Free-Energy Surface

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