Evaluating a Minimum of Expression
Use the function mphmin to evaluate the minimum of a given expression over an inner solution list.
To evaluate the minimum of the COMSOL expressions e1,... use the command mphmin:
[d1,...] = mphmin(model,{'e1',...},edim)
where edim is a string to define the element entity dimension: 'volume', 'surface', or 'line'. edim can also be a positive integer (3,  2, or 1 respectively). The output variables d1,... are an NxP array where N is the number of inner solutions and P the number of outer solutions.
The rest of this section has additional information for the function mphmin:
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Specify the Evaluation Data
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Output Format
Specify the Evaluation Data
The function mphmin supports the following properties to set the data of the evaluation to perform:
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dataset, specify the solution dataset to use in the evaluation:
data = mphmin(model,<expr>,edim,'dataset',<dsettag>)
<dsettag> is the tag of a solution dataset. The default value is the current solution dataset of the model.
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selection, specify the domain selection for evaluation:
data = mphmin(model,<expr>,edim,'selection',<seltag>)
where <seltag> is the tag of a selection node to use for the data evaluation. <seltag> can also be a positive integer array that corresponds to the domain index list. The default selection is all domains where the expression is defined. If the evaluation point does not belong to the specified domain selection the output value is NaN.
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solnum, specify the inner solution number for data evaluation. Inner solutions are generated for the following analysis types: time domain, frequency domain, eigenvalue, or stationary with continuation parameters:
data = mphmin(model,<expr>,edim,'solnum',<solnum>)
where <solnum> is an integer array corresponding to the inner solution index. <solnum> can also be a string:'end' or 'all' to evaluate the expression for the last inner solution or all inner solutions, respectively. By default the evaluation is performed on all inner solutions.
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outersolnum, specify the outer solution number for data evaluation. Outer solutions are generated with parametric sweeps:
data = mphmin(model,<expr>,edim,'outersolnum',<outersolnum>)
where <outersolnum> is a positive integer array corresponding to the outer solution index. <outersolnum> can also be a string, 'all' or 'end', to evaluate the expression for all or the last outer solution, respectively. The default setting uses the first outer solution for the data evaluation.
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To evaluate the expression data at a specific time use the property t:
data = mphmin(model,<expr>,edim,'t',<time>)
where <time> is a double array. The default value corresponds to all the stored time steps.
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In case of data series, such as from a parametric or a transient study, an operation can be applied. To perform data series operation use the function mphmin as in the command below:
data = mphmin(model,<expr>,edim,'dataseries',<dataoperation>)
where <dataoperation> can be one of the following value: 'none' (no operation performed), 'average' (to compute average of the selected series), 'integral' (to integrate over series), 'maximum' (to evaluate the maximum over series), 'minimum' (to evaluate the minimum), 'rms' (to compute the root mean square), 'stddev' (to compute the standard deviation), or 'variance' (to compute the variance).
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To get the position of the minimum, you can set the property position to on as in the command below:
data = mphmin(model,<expr>,edim,'position', on)
where data(:,1) contains the minimum value of the expression for each solution step, and data(:,2:Sdim+1) returns the position of the minimum, with Sdim the space dimension number.
Output Format
The function mphmin also supports other output formats.
To extract the unit of the evaluated expression, define an extra output variable:
[data,unit] = mphmin(model,<expr>,edim)
where unit is a 1xN cell array, and N is the number of expressions to evaluate.
By default mphmin returns the results as a squeezed singleton. To get the full singleton set the squeeze property to off:
data = mphmin(model,<expr>,edim,'squeeze','off')
Set the property matrix to off to return the data as a cell array instead of a double array:
data = mphmin(model,<expr>,edim,'matrix','off')