Page History

...

1. In case you apply the symbolic addressing of the columns for the description of the point on the curve or surface to compute the differential for, e.g. "Par_x" and "Par_y", please make sure that your Telitab set contains these names. If not, an error message is generated and the calculation is stopped.
2. If you use |1| as data header instead of |LEASQ1| it means that any special function in that expression referring to a data set Pno%=1 can access that data set.
3. In addition to traditional two-dimensional interpolation it is also possible to perform matrix (n-dimensional) interpolation. In that case, a special Telitab set definition format can be applied, clarified by the following database which is an example of an interpolation in a matrix of power and propeller rotation rate on the basis of ship speed and propeller pitch setting (for the sake of compactness, the data set size was reduced): 

| 0
4 "VS" "PDRA" "N" "PS"
17.0 1.0 157.5 2300
18.0 1.0 170.0 2970
19.0 1.0 184.5 3940
20.0 1.0 199.0 5140
17.0 1.1 147.0 2255
18.0 1.1 159.0 2930
19.0 1.1 173.0 3900
20.0 1.1 187.5 5110
17.0 1.2 138.5 2245
18.0 1.2 150.3 2925
19.0 1.2 163.5 3915
20.0 1.2 177.5 5150
17.0 1.3 131.5 2250
18.0 1.3 142.5 2940
19.0 1.3 155.5 3950
20.0 1.3 169.0 5200
17.0 1.4 125.5 2270
18.0 1.4 136.5 2980
19.0 1.4 148.5 3990
20.0 1.4 161.0 5260|

The interpolation of shaft power "PS" is in a sense performed in the 'inward out' direction:
first PS(and idem NS) on PDRA and then PS(and idem NS) for fixed PDRA on VS.
The expressions are the following:

PShaft = LEASQ LEASQ(1, 3, "VS", "PDRA", "PS", VShip, Pitch, 3, 2, 1)
NShaft = LEASQ(1, 3, "VS", "PDRA", "N" ,VShip, Pitch, 3, 2, 1)

in which 1 is the Telitab set number, 3 is the number of address identifiers (Ndim%), the values for "Vs" and "PDRA" are given as interpolation input and "PS"/"N" (third address identifier) are the output values of the example functions. The selected order of the approximating curve in "VS" direction is 3 and in "PDRA" direction 2 is selected. '1' is added as value for Xtrap%, so no warning is issued in the event of extrapolation. The matrix interpolation can be applied in all except Method 2, obviously since only x,y data points are provided in that case.

...

Syntax 2: direct definition

The syntax is

LEASQ(0, Npoints%, x_1, y_1, x_2, y_2,…, x_n, y_n, xint, Order%, [Xtrap%=0,1])

If Pno%=0 (the first parameter in the expression), then all x_i and y_i values should be numeric expressions. The minimum number of x,y data points in the list Npoints%, being of X,Y points of the curve, is 2. Interpolation (and extrapolation) is performed according to the curve form selected in Order%.

...