Note

This notebook is already available in your BattMo installation. In Matlab, run

open functionInterfaceExample

Example of the function interface

We load a parameter set

[1]:

jsonstruct = parseBattmoJson('ParameterData/MaterialProperties/LFP/LFP_Xu2015.json');

In this json structure, we have the description of a function for the OCP. In this case, we have a tabulated function

[2]:

disp(jsonstruct.openCircuitPotential)

[2]:

    functionFormat: 'tabulated'
      argumentList: {'stoichiometry'}
             dataX: [29x1 double]
             dataY: [29x1 double]

We use the function setupFunction to parse the input structure

[3]:

[fn, func] = setupFunction(jsonstruct.openCircuitPotential);

The function returns a function handler and a Function object. The function handler can be directly evaluated.

[4]:

disp(func)

[4]:

  TabulatedFunction1D with properties:
                dataX: [29x1 double]
                dataY: [29x1 double]
       functionFormat: 'tabulated'
         argumentList: {'stoichiometry'}
    numberOfArguments: 1

We have access to the tabulated values

[5]:

val = [func.dataX, func.dataY];
disp(val)

[5]:

         0    4.1433
    0.0100    3.9121
    0.0200    3.7272
    0.0300    3.6060
    0.0400    3.5326
    0.0500    3.4898
    0.1000    3.4360
    0.1500    3.4326
    0.2000    3.4323
    0.2500    3.4323
    0.3000    3.4323
    0.3500    3.4323
    0.4000    3.4323
    0.4500    3.4323
    0.5000    3.4323
    0.5500    3.4323
    0.6000    3.4323
    0.6500    3.4323
    0.7000    3.4323
    0.7500    3.4323
    0.8000    3.4322
    0.8500    3.4311
    0.9000    3.4142
    0.9500    3.2515
    0.9600    3.1645
    0.9700    3.0477
    0.9800    2.8999
    0.9900    2.7312
1.0000    2.5895

The function handler can be used directly as any other matlab function. For example, let us plot this function

[6]:

x = linspace(0, 1, 100);
y = fn(x);

figure
plot(x, y);
xlabel('Stoichiometry');
ylabel('Voltage / V');
title('OCP function LFP Xu 2015')

[6]:
figure_0.png

The interface is the same for a function defined with an other format. Let us load a function using a string format

[7]:

jsonstruct = parseBattmoJson('ParameterData/ParameterSets/Chen2020/chen2020_positive_electrode_interface.json');

In this json structure, we have the description of a function for the OCP. In this case, we have a tabulated function

[8]:

disp(jsonstruct.openCircuitPotential)

[8]:

    functionFormat: 'string expression'
      argumentList: {'stoichiometry'}
       expressions: [2x1 struct]

[9]:

disp(jsonstruct.openCircuitPotential.expressions(1))

[9]:

         language: 'matlab'
    variableNames: {'sto'}
          formula: '-0.8090*sto + 4.4875 - 0.0428*tanh(18.5138*(sto - 0.5542)) - 17.7326*tanh(15.7890*(sto - 0.3117)) + 17.5842*tanh(15.9308*(sto - 0.3120))'

We setup the function and obtain a function object of the class FormulaFunction and the function handler.

[10]:

[fn, func] = setupFunction(jsonstruct.openCircuitPotential);
disp(func)

[10]:

  FormulaFunction with properties:
                      formula: '-0.8090*sto + 4.4875 - 0.0428*tanh(18.5138*(sto - 0.5542)) - 17.7326*tanh(15.7890*(sto - 0.3117)) + 17.5842*tanh(15.9308*(sto - 0.3120))'
                variableNames: {'sto'}
                outputVarName: 'y'
    formattedStringExpression: 'sto = varargin{1}; y = -0.8090*sto + 4.4875 - 0.0428*tanh(18.5138*(sto - 0.5542)) - 17.7326*tanh(15.7890*(sto - 0.3117)) + 17.5842*tanh(15.9308*(sto - 0.3120));'
               functionFormat: 'string expression'
                 argumentList: {'stoichiometry'}
            numberOfArguments: 1

We can use the function handler to evaluate the function

[11]:

fn(0.5)

[11]:

ans = 3.9720

Note that the function handler is a short cut for the generic method eval of the parent class Function

[12]:

func.eval(0.5)

[12]:

ans = 3.9720

As previously, we can plot the function

[13]:

x = linspace(0, 1, 100);
y = fn(x);

figure
plot(x, y);
xlabel('Stoichiometry');
ylabel('Voltage / V');
title('OCP function NMC Chen 2020')

[13]:
figure_1.png