getsensmatrix
Get 3-D sensitivity matrix from SimData
object
Syntax
Description
[
returns the time t
,r
,outputFactors
,inputFactors
] = getsensmatrix(simdata
)t
and sensitivity data r
as well
as all the outputFactors
and inputFactors
(sensitivity outputs and
inputs) from the SimData
object
simdata
.
[
returns the sensitivity data for only the outputs and inputs specified by
t
,r
,outputFactors
,inputFactors
] = getsensmatrix(simdata
,outputFactorNames
,inputFactorNames
)outputFactorNames
and inputFactorNames
,
respectively.
Examples
Calculate Local Sensitivities Using SimFunctionSensitivity
Object
This example shows how to calculate the local sensitivities of some species in the Lotka-Volterra model using the SimFunctionSensitivity
object.
Load the sample project.
sbioloadproject lotka;
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
).
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
simdata
— Simulation data
SimData
object | array of SimData
objects
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.
outputFactorNames
— Names of sensitivity outputs
[]
(default) | character vector | string | string vector | cell array of character vectors
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
.
inputFactorNames
— Names of sensitivity inputs
[]
(default) | character vector | string | string vector | cell array of character vectors
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
t
— Simulation time points
m-by-1 numeric vector | cell array
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.
r
— Sensitivity data
m-by-n-by-p array | cell array
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.
outputFactors
— Names of sensitivity outputs
n-by-1 cell array
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).
inputFactors
— Names of sensitivity inputs
p-by-1 cell array
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
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