DIFF returns the derivative in a location in a two- or more dimensional space

Syntax

1. DIFF(Pno%, Ndim%, "ColLab$_1,.., "ColLab$_Ndim%", Xint_1, ..., Xint_Ndim%-1, [DirivNo%])
2. DIFF(0, Npoints%, x_1, y_1, x_2, y_2,…, x_n, y_n, Xint, [DirivNo%=1]) (only in 2D)
3. DIFF(@ObjFn(..), Ndim%, @ObjColPar_1,.., @ObjColPar_Ndim%, Xint_1, ..., Xint_Ndim%-1, [DirivNo%])
4. DIFF(Telitab$, Ndim%, "ColLab$_1",.., "ColLab$_Ndim%", Xint_1, ..., Xint_Ndim%-1, [DirivNo%])

Arguments

• Pno% is  is the number that refers to the TeLiTab sets in the Data slot. Pno% should be an integer value or a parameter which is assigned an integer value and is the number of the TeLiTab set in the expressions' data slot.
• Npoints% is  is the number of points (x,y) that are given in direct definition.
• @ObjFn() refers  refers to the Object from which data will be used.
• TeLiTab$ TeLiTab$ refers to the string parameter that contains the TeLiTab.
• Ndim% is  is the number of dimensions (or columns in the table...).
• "ColLab$_1" and @ObjColPar_1 refer  refer to the column that will be used as the first parameter in the differentiation.
• "ColLab$_2" and @ObjColPar_2 refer  refer to the column that will be used as the second parameter in the differentiation.
• Xint are  are the coordinates on which to compute the derivative dx/dy.
• DirivNo% is  is an optional argument by which can be indicated for which index of x_i the differential dx_i has to be computed. In y=f(x) DirivNo% should either be one (1) or omitted. If omitted or larger than Ndim%-1, the x_Ndim%-1 is assumed as differential

...

1. See also Telitab access for a generic description on the use of TeLiTab data
2. Similar to other Data analysis functions, the DIFF is a convenient way to evaluate data. Please also look at these functions for syntax examples
3. Please realise the dataset provided to DIFF should be a function. Every x-value should have one y-value. Furthermore, in case of a multi-dimensional dataset you should provide a matrix of coordinates.
4. Extrapolation outside the x-range is performed parabolically.

Examples

Syntax 1: TeLiTab in Dataslot

In this example, the TeLiTab is addressed in the Dataslot. The function y is defined as y = DIFF(1, 2, "XC", "YC", x, 1) With the following Telitab set in the Data slot:

|DIFF1|
0
2
"XC" "YC"
"1" 1 1
"2" 2 4
"3" 3 9
"4" 4 16
"5" 5 25
"6" 6 36
"7" 7 49
"8" 8 64
"9" 9 81
"10" 10 100|

For x = 2.5, the function returns

y=5 NOTE: 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.

...

In direct definition, the points of the curve are stated in the Relation itself. This method can only be used for 2D derivatives, the syntax is: DIFF(Pno%, Ndim%, "ColLab$_1,.., "ColLab$_Ndim%", Xint, [DirivNo%]) If  If Pno%=0 then all x_i and y_i values should be numeric expressions. The minimum number of x,y data points Ndim% in the list is 2 in which case the interpolation (and differentiation) is performed linear. Let the function y be defined as

y = DIFF(0, 4, 1, 1, 2, 4, 3, 9, 4, 16, x, 1) For  For x=2.5, this function returns

y=5

Syntax 3: TeLiTab in string

We have a relation:

DataSet2# DataSet2# = TEXTITEM$(1) 

With in its dataslot:

TEXTITEM1= |0
 3   "X" "Y" "Z"
"1"    1   1   2
"2"    1   4   8
"3"    1   9  18
"4"    1  16  32
"5"    1  25  50
"6"    1  36  72
"7"    1  49  98
"8"    1  64 128
"9"    1  81 162
"10"   1 100 200
"11"    2   1   12
"12"    2   4   18
"13"    2   9  118
"14"    2  16  132
"15"    2  25  150
"16"    2  36  172
"17"    2  49  198
"18"    2  64 1128
"19"    2  81 1162
"20"   2 100 1200
"21"    3   1   22
"22"    3   4   28
"23"    3   9  218
"24"    3  16  232
"25"    3  25  250
"26"    3  36  272
"27"    3  49  298
"28"    3  64 2128
"29"    3  81 2162
"30"   3 100 2200|

And use the following relation to determine the derivative:

Calculated_Value=DIFF(DataSet2#DataSet2#,3,"X","Y","Z", Input_Value_x, Input_Value_y, OptionalDirivNo) 

With  InputWith Input_Value_x = 1,Input Input_Value_y = 2 and OptionalDirivNo OptionalDirivNo = 2 this gives Calculated_Value=2

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