CombiTable1D

Description

Univariate constant, linear or cubic Hermitespline interpolation in one dimension of atable.Via parameter columns it can be defined how many columns of thetable are interpolated. If, e.g., columns={2,4}, it is assumed that 2 inputand 2 output signals are present and that the first output interpolatesthe first input via column 2 and the second output interpolates thesecond 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 theother 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 thesource 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 thefollowing structure ("-----" is not part of the file content):

-----------------------------------------------------#1double tab1(5,2)   # comment line  0   0  1   1  2   4  3   9  4  16double 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 declaredwith type (= "double" or "float"), name and actual dimensions.Finally, in successive rows of the file, the elements of the matrixhave to be given. The elements have to be provided as a sequence ofnumbers in row-wise order (therefore a matrix row can span severallines 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 startwith 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.

MATLAB is a registered trademark of The MathWorks, Inc.