User Expressions

In Topological Tree Analyszer user-defined expressions are used to calculate the actual data (e.g., distances between trees) from basic topological values. A set of functions is available to formulate such expressions and to access the basic values. An unlimited number of user expressions can be defined and will be written to a results table at the end of an analysis. It is also possible to reference results from one user expression from another one and reuse the result there.

Operators

The following list contains all valid operators. Each operator binds as strong or more than all operators listed below. The right columns indicate which types the operands need to have.

Name:	Operator:	Numeric:	Textual:	Boolean:	Example:
Power	^				10^-2 (= 0.02)
Unary plus	+				+4
Unary minus	-				-4
Modulo	%				10 % 4 (= 2)
Division	/				treeUserValue("someValue") / 2
Multiplication	*				treeUserValue("someValue") * 100
Addition	+				treeUserValue("someValue") + 10 "Two " + "words"
Less or equal	<=				if(treeUserValue("someValue") <= 100, treeUserValue("someValue"), 100)
Greater or equal	>=				if(treeUserValue("someValue") <= 100, "A", "B")
Less then	<				if(treeUserValue("someValue") < 100, treeUserValue("someValue"), 100)
Greater then	>				if(treeUserValue("someValue") < 100, "A", "B")
Equal	=				if(treeUserValue("value1") = 100, treeUserValue("value2"), treeUserValue("value3"))
Not equal	!=				if(treeUserValue("value1") != "empty", treeUserValue("value2"), 0)
And	&&				if(treeUserValue("value1") < 100 && treeUserValue("value1") > 50, treeUserValue("value2"), "")
Or	||				if(treeUserValue("value1") < 100 || treeUserValue("value2") < 100, treeUserValue("value3"), "undefined")

Text functions

The functions described here can be used to manipulate or characterize textual values. They are especially useful to calculating target column IDs.

Note that none of these functions were available before version 0.2.0.

Name:	Definition:	Description:
To upper case	toUpperCase(Textual text)	Returns a text in upper case letters. Example: toUpperCase(treeUserValue("someValue")) would convert all textual values of a column to upper case.
To lower case	toUpperCase(Textual text)	Returns a text in upper case letters.
Subsequence	subsequence(Textual text, Numeric startIndex)	Returns a suffix of a textual value starting at the specified position (inclusive). The index of the first character is 0. Example: subsequence("ABC", 1) would return "BC".
	subsequence(Textual text, Numeric startIndex, Numeric endIndex)	Returns a part of a textual value ranging from startIndex (inclusive) to endIndex (exclusive). The index of the first character is 0. Example: subsequence("ABCDEF", 1, 3) would return "BC".
Contains text	contains(Textual text, Textual part)	Returns a Boolean value indicating whether part is contained in text.
Starts with	startsWith(Textual text, Textual prefix)	Returns a Boolean value indicating whether text starts with prefix. (Both values may also be identical.)
Ends with	endsWith(Textual text, Textual suffix)	Returns a Boolean value indicating whether text starts with suffix. (Both values may also be identical.)
First position of a text	firstIndexOf(Textual text, Textual part)	Returns the index of the first occurrence of part in text or -1 of it is not contained at all. The index of the first character is 0. Example: firstIndexOf("ABC DBE DB", "BE") would return 5.
	firstIndexOf(Textual text, Textual part, Numeric startIndex)	Returns the index of the first occurrence of part in text at or after startIndex or -1 of it is not contained at all. Example: firstIndexOf("ABC DBE DB", "B", 4) would return 5.
Last position of a text	lastIndexOf(Textual text, Textual part)	Returns the index of the last occurrence of part in text or -1 of it is not contained at all. The index of the first character is 0. Example: lastIndexOf("ABC DBE DB", "D") would return 8.
	lastIndexOf(Textual text, Textual part, Numeric startIndex)	Returns the index of the last occurrence of part in text at or before startIndex or -1 of it is not contained at all. Example: firstIndexOf("ABC DBE DB", "D", 6) would return 4.

General mathematical functions

Name:	Definition:	Description:
Sine	sin(Numeric x)	Calculates the sine of the passed numeric value.
Cosine	cos(Numeric x)	Calculates the cosine of the passed numeric value.
Tangent	tan(Numeric x)	Calculates the tangent of the passed numeric value.
Inverse sine	asin(Numeric x)	Calculates the inverse sine of the passed numeric value.
Inverse cosine	acos(Numeric x)	Calculates the inverse cosine of the passed numeric value.
Inverse tangent	atan(Numeric x)	Calculates the inverse tangent of the passed numeric value.
Inverse tangent	atan2(Numeric x, Numeric y)	Calculates the inverse tangent (or arcus tangent) of y / x given adjacent and x. The result is between -π and π
Hyperbolic sine	sinh(Numeric x)	Calculates the hyperbolic sine of the given angle.
Hyperbolic cosine	cosh(Numeric x)	Calculates the hyperbolic cosine of the given angle.
Hyperbolic tangent	tanh(Numeric x)	Calculates the hyperbolic tangent of the given angle.
Inverse hyperbolic sine	asinh(Numeric x)	Calculates the inverse hyperbolic sine of the given angle.
Inverse hyperbolic cosine	acosh(Numeric x)	Calculates the inverse hyperbolic cosine of the given angle.
Inverse hyperbolic tangent	atanh(Numeric x)	Calculates the inverse hyperbolic tangent of the given angle.
Natural logarithm	ln(Numeric x)	Calculates the natural logarithm of the passed numeric value.
Logarithm to the base 10	log(Numeric x)	Calculates the logarithm to the base 10 of the passed numeric value.
Exponential function	exp(Numeric x)	Calculates the exponential function to the base e. It is the inverse function of the natural logarithm (ln).
Magnitude	abs(Numeric x)	Returns the absolute value of the passed numeric parameter.
Random number	rand(Numeric x)	Returns a random number between 0 and 1.
Square Root	sqrt(Numeric x)	Calculates the square root of the passed numeric parameter.
Alternative	if(Boolean condition, Numeric or textual trueValue, Numeric or textual falseValue)	Returns the second parameter if the condition is true or the third if not.
Number to text	str(Numeric or textual x)	Returns a textual representation of the passed parameter.

General constants

• Euler's number: e
• π: pi