kawin.FreeEnergyHessian

kawin.hessian(chemical_potentials, composition_set)

Returns the hessian of the objective function for a single phase 
 
Parameters 
---------- 
chemical_potentials : 1-D ndarray 
composition_set : pycalphad.core.composition_set.CompositionSet 
 
Returns 
------- 
Matrix of floats for each second derivative 
Derivatives along each axis will be in order of: 
    site fractions, phase amount, lagrangian multipliers, chemical potential

kawin.totalddx(chemical_potentials, composition_set, refElement)

Total derivative of site fractions, phase amount, lagrangian multipliers  
and chemical potential with respect to system composition 
d/dx = partial d/dxA - partial d/dxR where R is reference 
 
Parameters 
---------- 
chemical_potentials : 1-D ndarray 
composition_set : pycalphad.core.composition_set.CompositionSet 
refElement : str 
    Reference element 
 
Returns 
------- 
Array of floats for each derivative 
Derivatives will be in order of: 
    site fractions, phase amount, lagrangian multipliers, chemical potential

kawin.partialddx(chemical_potentials, composition_set)

Partial derivative of site fractions, phase amount, lagrangian multipliers  
and chemical potential with respect to system composition 
 
Parameters 
---------- 
chemical_potentials : 1-D ndarray 
composition_set : pycalphad.core.composition_set.CompositionSet 
 
Returns 
------- 
Array of floats for each derivative 
Derivatives will be in order of: 
    site fractions, phase amount, lagrangian multipliers, chemical potential

kawin.dMudX(chemical_potentials, composition_set, refElement)

Total derivative of chemical potential with respect to system composition 
dmuA/dxB = (partial dmuA/dxB - partial dmuA/dxR) - (partial dmuR/dxB - partial dmuR/dxR)  
where R is reference 
 
This more or less represents the curvature of the free energy surface with reference element R 
 
Parameters 
---------- 
chemical_potentials : 1-D ndarray 
composition_set : pycalphad.core.composition_set.CompositionSet 
refElement : str 
    Reference element 
 
Returns 
------- 
Array of floats for each derivative, (n-1 x n-1) matrix 
Derivatives will be in alphabetical order of elements

kawin.partialdMudX(chemical_potentials, composition_set)

Partial derivative of chemical potential with respect to system composition 
 
Parameters 
---------- 
composition_set : pycalphad.core.composition_set.CompositionSet 
 
Returns 
------- 
Array of floats for each derivative, (n x n) matrix 
Derivatives will be in alphabetical order of elements
← kawin.ElasticFactors
kawin.GrainBoundaries →