Table look-up in one dimension (matrix/file) with n inputs and n outputs

Wolfram Language



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

Univariate constant, linear or cubic Hermite spline interpolation in one dimension of a table. Via parameter columns it can be defined how many columns of the table are interpolated. If, e.g., columns={2,4}, it is assumed that 2 input and 2 output signals are present and that the first output interpolates the first input via column 2 and the second output interpolates the second input via column 4 of the table matrix.

The grid points and function values are stored in a matrix "table[i,j]", where the first column "table[:,1]" contains the grid points and the other columns contain the data to be interpolated. Example:

   table = [0,  0;
            1,  1;
            2,  4;
            4, 16]
   If, e.g., the input u = 1.0, the output y =  1.0,
       e.g., the input u = 1.5, the output y =  2.5,
       e.g., the input u = 2.0, the output y =  4.0,
       e.g., the input u =-1.0, the output y = -1.0 (i.e., extrapolation).
  • The interpolation interval is found by a binary search where the interval used in the last call is used as start interval.
  • 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.
  • 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
  • If the table has only one row, the table value is returned, independent of the value of the input signal.
  • The grid values (first column) have to be strictly increasing.

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 text and MATLAB MAT-file format is possible. (The text 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. See the Tables package documentation for more details.

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 a text file, the file needs to have the following structure ("-----" is not part of the file content):

double tab1(5,2)   # comment line
  0   0
  1   1
  2   4
  3   9
  4  16
double tab2(5,2)   # another comment line
  0   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 (\t), comma (,), or semicolon (;). Several matrices may be defined one after another. Line comments start with the hash symbol (#) and can appear everywhere. Text files should either be ASCII or UTF-8 encoded, where UTF-8 encoded strings are only allowed in line comments and an optional UTF-8 BOM at the start of the text file is ignored. Other characters, like trailing non comments, are not allowed in the file.

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Parameters (12)


Value: size(columns, 1)

Type: Integer

Description: Number of inputs (= 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 (grid = first column; e.g., table=[0, 0; 1, 1; 2, 4])


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: false

Type: Boolean

Description: = true, if warning messages are to be printed if table input is outside the definition range


Value: Internal.getTable1DAbscissaUmin(tableID)

Type: Real

Description: Minimum abscissa value defined in table


Value: Internal.getTable1DAbscissaUmax(tableID)

Type: Real

Description: Maximum abscissa value defined in table

Connectors (2)


Type: RealInput[n]

Description: Connector of Real input signals


Type: RealOutput[n]

Description: Connector of Real output signals

Components (1)


Type: ExternalCombiTable1D

Description: External table object

Used in Components (1)



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