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TODO |
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\ No newline at end of file |
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# Introduction
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Within W-SLDA Toolkit we provide a script for generating custom SLDA functional: `extensions/sldae/sldae-dev-tool.c`
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Within the script user can provide its own formulas for:
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```c
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double ground_state_energy (int dn, double _x, int id []);
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double chemical_potential (int dn, double _x, int id []);
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double inverse_effective_mass (int dn, double _x, int id []);
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double pairing_gap (int dn, double _x, int id []);
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```
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In return, the script generates a source file readable by W-SLDA Engine. Once the functional is created, it becomes available for all code within the toolkit.
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# Example: SLDAE with the effective mass equal 1
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The function for the computation of the effective mass has been modified to:
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```c
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double
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inverse_effective_mass (int dn, double _x, int id [])
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{
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int ip0 [1] = {0}; double x0 = xm (dn, _x, ip0);
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// ...
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return x0;
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}
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```
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Next, the code is compiled and executed:
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```bash
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[gabrielw@dell sldae]$ gcc sldae-dev-tool.c -lm -lgsl -lgslcblas -o sldae-dev-tool
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[gabrielw@dell sldae]$ ./sldae-dev-tool
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SLDAE DEV TOOLS
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[padé[4/4] interpolation of sldae parameters p = {beta, gamma, B, C}]
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p a1 x + a2 x^2 + a3 x^3 + c x^4
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----- = ----------------------------------
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p_ufg 1 + b1 x + b2 x^2 + b3 x^3 + c x^4
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beta interpolation (beta_ufg = -0.481506)
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iter = 46 f(x) = 1.110e-16
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a1 = +0.797400;
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a2 = +0.943961;
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a3 = +1.037043;
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b1 = +1.227062;
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b2 = +2.126210;
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b3 = +1.734795;
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c = +0.523445;
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b_functional interpolation (b_functional_ufg = -0.481506)
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iter = 13 f(x) = 8.882e-16
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a1 = +0.698112;
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a2 = +0.034678;
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a3 = +0.455138;
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b1 = +0.353905;
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b2 = +0.806444;
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b3 = +0.403679;
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c = -0.031327;
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inverse_gamma interpolation (inverse_gamma_ufg = -0.094945)
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iter = 14 f(x) = 1.821e-14
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a1 = +2.713374;
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a2 = +1.441196;
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a3 = +3.700251;
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b1 = +0.634303;
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b2 = +3.522427;
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b3 = +3.701347;
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c = +1.877961;
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c_functional interpolation (c_functional_ufg = -10.532397)
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iter = 19 f(x) = 3.664e-15
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a1 = +0.370145;
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a2 = +1.041299;
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a3 = +1.737347;
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b1 = +2.458364;
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b2 = +5.604947;
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b3 = +3.828124;
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c = +1.085400;
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Parameters written to: sldae_parameters.h
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Creating file: sldae_parameters.txt
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```
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Once the functional is generated user should inspect content of file `sldae_parameters.txt`. It contains following columns:
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``` bash
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# 1: lambda=a*k_F
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# 2: ground_state_energy
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# 3: inverse_effective_mass
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# 4: chemical_potential
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# 5: pairing_gap
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# 6: beta_parameter
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# 7: beta_parameter - PADE
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# 8: b_functional
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# 9: b_functional - PADE
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#10: inverse_gamma_parameter
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#11: inverse_gamma_parameter - PADE
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#12: c_functional
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#13: c_functional - PADE
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```
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In particular, it is important to confirm that PADE approximants correctly reproduce functions generated by analytical formulas. Note that W-SLDA Engine uses Pade approximants to deliver the highest performance.
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```bash
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[gabrielw@dell sldae]$ gnuplot
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gnuplot> plot "sldae_parameters.txt" u 1:6 w l, "" u 1:7 w l
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# and similar for other functions
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```
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Finally, file `sldae_parameters.h` should be moved to folder `hpc-engine`. From now new SLDAE functional will be used when `FUNCTIONAL=SLDAE` is selected in predefines.
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# Collection of own SLDAE-like functionals
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The information about PADE approximants for functional coefficients loded to the engine through the file `hpc-engine\sldae_functional.h`, precisely:
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```c
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// Select coefficients
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#ifdef SLDAE_FORCE_A1
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#include "sldae_parameters_A1.h"
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#else
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// default one
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#include "sldae_parameters.h"
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#endif
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```
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User can modify this section to form that uploads a correct file with the desired set of coefficients.
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