LOOKUPND

n-Dimensional lookup table
Inputs(20) i1 i2 i3 i4 i5 i6 i7 i8 i9 i10 i11 i12 i13 i14 i15 i16 i17 i18 i19 i20
Parameters(5) Dimension Method Repetitive Index Format
Default Dimension=2, Method=1, Repetitive=0, Index=1, Format=0,
Text1 File name
Text2 Not used
Select from Components/Blocks/Functions&Tables
Function n-Dimensional lookup table from a text based data file.The first column of the table specifies the function.
The next columns of the table specify the inputs for the table.
Special The LookUpnD is designed for coupling with FEM programs based Reduced Order Modeling techniques like, for example, the Co-Energy method.
The first column should contain the value of the function depending on his inputs (i1 .. xn), where n is specified at p1. There is a maximum of 20 dimensions. (n=20)
ParameterValueFunction
Dimension(p1)2 Number of columns that are read from the file, excluding the first column, specifying the function values itself.
Method(p2)0 No interpolation between the data points.
Method(p2)3 Spline interpolation between the data points.
Repetitive(p3)0 Not used. No repetition of the data points.
Index(p4)0 The inputs i1 and i2 of the Lookup2D block are used as index in the table. Not used for spline interpolation (method=3). The input values i1 and i2 are rounded to its round integer value, which indicates the position in the table. In this case the values in the first column and first row are ignored.
Index(p4)1 The inputs i1 and i2 of the Lookup2D block are used as index in the first column and first row of the table.
Format(p5)0Not used.



Input format.
Number of dimensions/inputs n. (Columns<=Dimension)
Number of samples m.

y1i11i12i13..i1n
y2i21i22i23..i2n
y3i31i32i33..i3n
y.........i.n
ymim1im2im3im.imn



Using the INT_VAR block various parameters can be extracted from the LookUpnD block.

Method=0, no interpolation:
Int_var(41) = number of data pares which are read from the input file
Int_var(42) = index of the current selected data pare
Int_var(1) .. Int_var(20) = First derivative of the function to its corresponding input:

dy/dik = INT_VAR(k)

Int_var(51) .. Int_var(450) = Second cross derivative of the function:

d2y/dirdis = INT_VAR((r-1)*20+s+50)


Method=3, spline interpolation:
The indices a and b are the inputs of the block. The derivative can only be calculated from the last two inputs of the block. If, for example, there are 3 inputs to the block LookUpnD, then a=2 and b=3. If there are, for example, only two inputs, then a=1 and b=2.
In general: b=dimension, a=dimension-1


dy/dia = INT_VAR(1)



dy/dib = INT_VAR(2)



d2y/dibdia = INT_VAR(3)



d2y/dibdib = INT_VAR(4)
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