# getsensmatrix

Get 3-D sensitivity matrix from SimData object

## Description

example

[t,r,outputFactors,inputFactors] = getsensmatrix(simdata) returns the time t and sensitivity data r as well as all the outputFactors and inputFactors (sensitivity outputs and inputs) from the SimData object simdata.

example

[t,r,outputFactors,inputFactors] = getsensmatrix(simdata,outputFactorNames,inputFactorNames) returns the sensitivity data for only the outputs and inputs specified by outputFactorNames and inputFactorNames, respectively.

## Examples

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This example shows how to calculate the local sensitivities of some species in the Lotka-Volterra model using the SimFunctionSensitivity object.

Define the input parameters.

params = {'Reaction1.c1', 'Reaction2.c2'};

Define the observed species, which are the outputs of simulation.

observables  = {'y1', 'y2'};

Create a SimFunctionSensitivity object. Set the sensitivity output factors to all species (y1 and y2) specified in the observables argument and input factors to those in the params argument (c1 and c2) by setting the name-value pair argument to 'all'.

f = createSimFunction(m1,params,observables,[],'SensitivityOutputs','all','SensitivityInputs','all','SensitivityNormalization','Full')
f =
SimFunction

Parameters:

Name          Value        Type
________________    _____    _____________

{'Reaction1.c1'}      10     {'parameter'}
{'Reaction2.c2'}    0.01     {'parameter'}

Observables:

Name        Type
______    ___________

{'y1'}    {'species'}
{'y2'}    {'species'}

Dosed: None

Sensitivity Input Factors:

Name              Type
________________    _____________

{'Reaction1.c1'}    {'parameter'}
{'Reaction2.c2'}    {'parameter'}

Sensitivity Output Factors:

Name        Type
______    ___________

{'y1'}    {'species'}
{'y2'}    {'species'}

Sensitivity Normalization:

Full

Calculate sensitivities by executing the object with c1 and c2 set to 10 and 0.1, respectively. Set the output times from 1 to 10. t contains time points, y contains simulation data, and sensMatrix is the sensitivity matrix containing sensitivities of y1 and y2 with respect to c1 and c2.

[t,y,sensMatrix] = f([10,0.1],[],[],1:10);

Retrieve the sensitivity information at time point 5.

temp = sensMatrix{:};
sensMatrix2 = temp(t{:}==5,:,:);
sensMatrix2 = squeeze(sensMatrix2)
sensMatrix2 = 2×2

37.6987   -6.8447
-40.2791    5.8225

The rows of sensMatrix2 represent the output factors (y1 and y2). The columns represent the input factors (c1 and c2).

$sensMatrix2=\left[\begin{array}{cc}\begin{array}{c}\frac{\partial y1}{\partial c1}\\ \\ \frac{\partial y2}{\partial c1}\end{array}& \begin{array}{c}\frac{\partial y1}{\partial c2}\\ \\ \frac{\partial y2}{\partial c2}\end{array}\end{array}\right]$

Set the stop time to 15, without specifying the output times. In this case, the output times are the solver time points by default.

sd = f([10,0.1],15);

Retrieve the calculated sensitivities from the SimData object sd.

[t,y,outputs,inputs] = getsensmatrix(sd);

Plot the sensitivities of species y1 and y2 with respect to c1.

figure;
plot(t,y(:,:,1));
legend(outputs);
title('Sensitivities of species y1 and y2 with respect to parameter c1');
xlabel('Time');
ylabel('Sensitivity');

Plot the sensitivities of species y1 and y2 with respect to c2.

figure;
plot(t,y(:,:,2));
legend(outputs);
title('Sensitivities of species y1 and y2 with respect to parameter c2');
xlabel('Time');
ylabel('Sensitivity');

Alternatively, you can use sbioplot.

sbioplot(sd);

You can also plot the sensitivity matrix using the time integral for the calculated sensitivities of y1 and y2. The plot indicates y1 and y2 are more sensitive to c1 than c2.

[~, in, out] = size(y);
result = zeros(in, out);
for i = 1:in
for j = 1:out
result(i,j) = trapz(t(:),abs(y(:,i,j)));
end
end
figure;
hbar = bar(result);
haxes = hbar(1).Parent;
haxes.XTick = 1:length(outputs);
haxes.XTickLabel = outputs;
legend(inputs,'Location','NorthEastOutside');
ylabel('Sensitivity');

## Input Arguments

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Simulation data, specified as a SimData object or array of SimData objects. If simdata is an array of objects, the outputs are cell arrays in which each cell contains data for the corresponding object in the SimData array.

Names of sensitivity outputs, specified as an empty array [], character vector, string, string vector, or cell array of character vectors.

By default, the function uses an empty array [] to return sensitivity data for all output factors in simdata.

Names of sensitivity inputs, specified as an empty array [], character vector, string, string vector, or cell array of character vectors.

By default, the function uses an empty array [] to return sensitivity data on all input factors in simdata.

## Output Arguments

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Simulation time points for the sensitivity data, returned as an m-by-1 numeric vector or cell array. m is the number of time points.

Sensitivity data, returned as an m-by-n-by-p array or cell array. m is the number of time points, n is the number of sensitivity outputs, and p is the number of sensitivity inputs.

The outputFactors output argument labels the second dimension of r and inputFactors labels the third dimension of r. For example, r(:,i,j) is the time course for the sensitivity of the state outputFactors{i} to the input inputFactor{j}.

The function returns only the sensitivity data already in the SimData object. It does not calculate the sensitivities. For details on setting up and performing a sensitivity calculation, see Local Sensitivity Analysis (LSA). During setup, you can also specify how to normalize the sensitivity data.

Names of sensitivity outputs, returned as an n-by-1 cell array. n is the number of sensitivity outputs.

The output factors are the states for which you calculated the sensitivities. In other words, the sensitivity outputs are the numerators. For more information, see Local Sensitivity Analysis (LSA).

Names of sensitivity inputs, returned as an p-by-1 cell array. p is the number of input factors.

The input factors are the states with respect to which you calculated the sensitivities. In other words, the sensivity inputs are the denominators as explained in Local Sensitivity Analysis (LSA).

## Version History

Introduced in R2008b