Table look-up with respect to time and linear/periodic extrapolation methods (data from matrix/file)

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This information is part of the Modelica Standard Library maintained by the Modelica Association.

This block generates an output signal y[:] by linear interpolation in a table. The time points and function values are stored in a matrix table[i,j], where the first column table[:,1] contains the time points and the other columns contain the data to be interpolated.


Via parameter columns it can be defined which columns of the table are interpolated. If, e.g., columns={2,4}, it is assumed that 2 output signals are present and that the first output is computed by interpolation of column 2 and the second output is computed by interpolation of column 4 of the table matrix. The table interpolation has the following properties:

  • The time points need to be strictly increasing if smoothness is ContinuousDerivative, otherwise monotonically increasing.
  • Discontinuities are allowed, by providing the same time point twice in the table.
  • Values outside of the table range, are computed by extrapolation according to the setting of parameter extrapolation:
      extrapolation = 1: hold the first or last value of the table,
                         if outside of the table scope.
                    = 2: extrapolate by using the derivative at the first/last table
                         points if outside of the table scope.
                         (If smoothness is LinearSegments or ConstantSegments
                         this means to extrapolate linearly through the first/last
                         two table points.).
                    = 3: periodically repeat the table data
                         (periodical function).
                    = 4: no extrapolation, i.e. extrapolation triggers an error
  • Via parameter smoothness it is defined how the data is interpolated:
      smoothness = 1: linear interpolation
                 = 2: Akima interpolation: Smooth interpolation by cubic Hermite
                      splines such that der(y) is continuous, also if extrapolated.
                 = 3: constant segments
                 = 4: Fritsch-Butland interpolation: Smooth interpolation by cubic
                      Hermite splines such that y preserves the monotonicity and
                      der(y) is continuous, also if extrapolated.
                 = 5: Steffen interpolation: Smooth interpolation by cubic Hermite
                      splines such that y preserves the monotonicity and der(y)
                      is continuous, also if extrapolated.
  • If the table has only one row, no interpolation is performed and the table values of this row are just returned.
  • Via parameters startTime and offset the curve defined by the table can be shifted both in time and in the ordinate value. The time instants stored in the table are therefore relative to startTime. If time < startTime, no interpolation is performed and the offset is used as ordinate value for all outputs.
  • The table is implemented in a numerically sound way by generating time events at interval boundaries. An interval boundary is defined by two identical time values following each other. For example
       table = [0, 0;
                1, 0;
                1, 1;
                2, 3;
                3, 5;
                3, 2;
                4, 4;
                5, 5];
    defines three intervalls: 0..1, 1..3, 3..5. Within an interval the defined interpolation method is applied (so the table outputs within an interval are continuous,and if the interpolation method is smooth, also continuously differentiable). No time events are generated within an interval in order that also intervals with many points do not reduce the simulation efficiency (note in package Modelica version 3.2 and earlier, time events had been generated).
    If the table points are largely changing, it is adviseable to force time events by duplicating every time point (especially, if the model in which the table is present allows the variable step integrator to make large integrator steps). For example, if a sawtooth signal is defined with the table, it is more reliable to define the table as:
       table = [0, 0;
                1, 2;
                1, 2;
                2, 0;
                2, 0;
                3, 2;
                3, 2];
    instead of
       table = [0, 0;
                1, 2;
                2, 0;
                3, 2];
    because time events are then generated at every time point.
  • Via parameter timeScale the first column of the table array can be scaled, e.g. if the table array is given in hours (instead of seconds) timeScale shall be set to 3600.
  • For special applications it is sometimes needed to know the minimum and maximum time instant defined in the table as a parameter. For this reason parameters t_min/t_minScaled and t_max/t_maxScaled are provided and can be accessed from the outside of the table object. Whereas t_min and t_max define the scaled abscissa values (using parameter timeScale) in SIunits.Time, t_minScaled and t_maxScaled define the unitless original abscissa values of the table.


   table = [0, 0;
            1, 0;
            1, 1;
            2, 4;
            3, 9;
            4, 16]; extrapolation = 3 (default)
If, e.g., time = 1.0, the output y =  0.0 (before event), 1.0 (after event)
    e.g., time = 1.5, the output y =  2.5,
    e.g., time = 2.0, the output y =  4.0,
    e.g., time = 5.0, the output y = 23.0 (i.e., extrapolation via last 2 points).

The table matrix can be defined in the following ways:

  1. Explicitly supplied as parameter matrix "table", and the other parameters have the following values:
       tableName is "NoName" or has only blanks,
       fileName  is "NoName" or has only blanks.
  2. Read from a file "fileName" where the matrix is stored as "tableName". Both ASCII and MAT-file format is possible. (The ASCII format is described below). The MAT-file format comes in four different versions: v4, v6, v7 and v7.3. The library supports at least v4, v6 and v7 whereas v7.3 is optional. It is most convenient to generate the MAT-file from FreeMat or MATLAB® by command
       save tables.mat tab1 tab2 tab3
    or Scilab by command
       savematfile tables.mat tab1 tab2 tab3
    when the three tables tab1, tab2, tab3 should be used from the model.
    Note, a fileName can be defined as URI by using the helper function loadResource.
  3. Statically stored in function "usertab" in file "usertab.c". The matrix is identified by "tableName". Parameter fileName = "NoName" or has only blanks. Row-wise storage is always to be preferred as otherwise the table is reallocated and transposed.

When the constant "NO_FILE_SYSTEM" is defined, all file I/O related parts of the source code are removed by the C-preprocessor, such that no access to files takes place.

If tables are read from an ASCII-file, the file needs to have the following structure ("-----" is not part of the file content):

double tab1(6,2)   # comment line
  0   0
  1   0
  1   1
  2   4
  3   9
  4  16
double tab2(6,2)   # another comment line
  0   0
  2   0
  2   2
  4   8
  6  18
  8  32

Note, that the first two characters in the file need to be "#1" (a line comment defining the version number of the file format). Afterwards, the corresponding matrix has to be declared with type (= "double" or "float"), name and actual dimensions. Finally, in successive rows of the file, the elements of the matrix have to be given. The elements have to be provided as a sequence of numbers in row-wise order (therefore a matrix row can span several lines in the file and need not start at the beginning of a line). Numbers have to be given according to C syntax (such as 2.3, -2, +2.e4). Number separators are spaces, tab ( ), comma (,), or semicolon (;). Several matrices may be defined one after another. Line comments start with the hash symbol (#) and can appear everywhere. Other characters, like trailing non comments, are not allowed in the file.

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Connectors (1)


Type: RealOutput[nout]

Description: Connector of Real output signals

Parameters (18)


Value: max([size(columns, 1); size(offset, 1)])

Type: Integer

Description: Number of outputs


Value: false

Type: Boolean

Description: = true, if table is defined on file or in function usertab


Value: fill(0.0, 0, 2)

Type: Real[:,:]

Description: Table matrix (time = first column; e.g., table=[0,2])


Value: "NoName"

Type: String

Description: Table name on file or in function usertab (see docu)


Value: "NoName"

Type: String

Description: File where matrix is stored


Value: true

Type: Boolean

Description: = true, if info message that file is loading is to be printed


Value: 2:size(table, 2)

Type: Integer[:]

Description: Columns of table to be interpolated


Value: Modelica.Blocks.Types.Smoothness.LinearSegments

Type: Smoothness

Description: Smoothness of table interpolation


Value: Modelica.Blocks.Types.Extrapolation.LastTwoPoints

Type: Extrapolation

Description: Extrapolation of data outside the definition range


Value: {0}

Type: Real[:]

Description: Offsets of output signals


Value: 0

Type: Time (s)

Description: Output = offset for time < startTime


Value: 1

Type: Time (s)

Description: Time scale of first table column



Type: Time (s)

Description: Minimum abscissa value defined in table



Type: Time (s)

Description: Maximum abscissa value defined in table



Type: Real

Description: Minimum (scaled) abscissa value defined in table



Type: Real

Description: Maximum (scaled) abscissa value defined in table


Value: if size(offset, 1) == 1 then ones(nout) * offset[1] else offset

Type: Real[nout]

Description: Offsets of output signals



Type: Real

Description: = 1, if table was successfully read from file

Components (1)


Type: ExternalCombiTimeTable

Description: External table object

Used in Examples (4)


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Second order thermal model of a motor