Expressions

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Overview

It is possible to define properties using mathematical expressions. In the GUI, spin boxes or input fields that are bound to properties show a blue icon Bound-expression.svg when activated. Clicking on the icon or typing the equal sign = opens the expression editor for that particular property. If the input field shows a ... button instead of an icon, the expression editor can be opened by right-clicking the property and selecting Expression... from the context menu.

A LabRPS expression is a mathematical expression using the standard mathematical operators, functions and predefined constants as described below. In addition, the expression may reference object properties, and also use conditionals. Numbers in an expression may have an optional unit attached to them.

Numbers may use either a comma , or a decimal point . to separate whole digits from decimals. When the decimal marker is used, it must be followed by at least one digit. Thus, the expressions 1. + 2. and 1, + 2, are invalid, but 1.0 + 2.0 and 1,0 + 2,0 are valid.

Operators and functions are unit-aware, and require valid combinations of units, if supplied. For example, 2mm + 4mm is a valid expression, while 2mm + 4 is not. This also applies to references to object properties that have units, such as Length properties. Thus Pad001.Length + 1 is invalid since it adds a pure number to a property with length units, it requires Pad001.Length + 1mm.

Some unit related errors can seem unintuitive, with expressions either being rejected or producing results that do not match the units of the property being set. Here are some examples:

1/2mm is not interpreted as half a millimeter but as 1/(2mm), resulting in: 0.5 mm^-1.

sqrt(2)mm is not valid because the function call is not a number. This has to be entered as sqrt(2) * 1mm.

Function arguments

Multiple arguments to a function may be separated by either a semicolon ; or a comma followed by a space , . In the latter case, the comma is converted to a semicolon after entry. When a semicolon is used, no trailing space is necessary.

Arguments may include references to cells in a spreadsheet. A cell reference consists of the cell's uppercase row letter followed by its column number, for example A1. A cell may also be referenced by using the cell's alias instead, for example Spreadsheet.NumberOfSample.

Referencing objects

As already shown above, you can reference an object by its DataName. But you can also use its DataLabel. In the case of a DataLabel, it must be enclosed in double << and >> symbols, such as <<Label>>.

You can reference any property of an object. For example, to reference a Cylinder's height, you may use Cylinder.Height or <<Label_of_cylinder>>.Height.

For more information about referencing objects.

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Supported constants

The following constants are supported:

Constant Description
e Euler's number
pi Pi

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Supported operators

The following operators are supported:

Operator Description
+ Addition
- Subtraction
* Multiplication
/ Floating point Division
% Remainder
^ Exponentiation

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Supported functions

General mathematical functions

The following mathematical functions are supported:

Trigonometric functions

Trigonometric functions use degree as their default unit. For radians add rad following the first value in an expression. So e.g. cos(45) is the same as cos(pi rad / 4). Expressions in degrees can use either deg or °, e.g. 360deg - atan2(3; 4) or 360° - atan2(3; 4). If an expression is without units and needs to be converted to degrees or radians for compatibility, multiply by 1deg, 1° or 1rad as appropriate, e.g. (360 - X) * 1deg; (360 - X) * 1°; (0.5 + pi / 2) * 1rad.

Function Description Input range
acos(x) Arc cosine -1 <= x <= 1
asin(x) Arc sine -1 <= x <= 1
atan(x) Arc tangent, return value in the range -90° < value < 90° all
atan2(y; x) Arc tangent of y/x accounting for quadrant, return value in the range -180° < value <= 180° all, the invalid input x = y = 0 returns 0
cos(x) Cosine all
cosh(x) Hyperbolic cosine all
sin(x) Sine all
sinh(x) Hyperbolic sine all
tan(x) Tangent all, except x = n*90 with n = odd integer
tanh(x) Hyperbolic tangent all
hypot(x; y) Pythagorean addition (hypotenuse), e.g. hypot(4; 3) = 5 x and y >= 0
cath(x; y) Given hypotenuse, and one side, returns other side of triangle, e.g. cath(5; 3) = 4 x >= y >= 0

Exponential and logarithmic functions

Function Description Input range
exp(x) Exponential function all
log(x) Natural logarithm x > 0
log10(x) Common logarithm x > 0
pow(x; y) Exponentiation all
sqrt(x) Square root x >= 0

Rounding, truncation and remainder functions

Function Description Input range
abs(x) Absolute value all
ceil(x) Ceiling function, smallest integer value greater than or equal to x all
floor(x) Floor function, largest integer value less than or equal to x all
mod(x; y) Remainder after dividing x by y, sign of result is that of the dividend. all, except y = 0
round(x) Rounding to the nearest integer all
trunc(x) Truncation to the nearest integer in the direction of zero all

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Statistical / aggregate functions

Aggregate functions take one or more arguments.

Individual arguments to aggregate functions may consist of ranges of cells. A range of cells is expressed as two cell references separated by a colon :, for example average(B1:B8) or sum(A1:A4; B1:B4). The cell references may also use cell aliases, for example average(StartTemp:EndTemp).

The following aggregate functions are supported:

Function Description Input range
average(a; b; c; ...) Average value of the arguments, same as sum(a; b; c; ...) / count(a; b; c; ...) all
count(a; b; c; ...) Count of the arguments, typically used for cell ranges all
max(a; b; c; ...) Maximum value of the arguments all
min(a; b; c; ...) Minimum value of the arguments all
stddev(a; b; c; ...) Standard deviation of the values of the arguments all
sum(a; b; c; ...) Sum of the values of the arguments, typically used for cell ranges all

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String manipulation

String identification

Strings are identified in expressions by surrounding them with opening/closing double chevrons (as are labels).

In following example, "TEXT" is recognized as a string : <<TEXT>>

String concatenation

Strings can be concatenated using the '+' sign.

Following example <<MY>> + <<TEXT>> will be concatenated to "MYTEXT".

String conversion

Numerical values can be converted to strings with the str function:


str(SimulationPoint.Z.Value)


String formatting

String formatting is supported using the (old) %-style Python way.

All %-specifiers as defined in Python documentation.

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Conditional expressions

Conditional expressions are of the form condition ? resultTrue : resultFalse. The condition is defined as an expression that evaluates to either 0 (false) or non-zero (true).

Note that to use a boolean property as the condition this syntax must be used: VarSet.MyBool == 1 ? 10 mm : 15 mm.

The following relational operators are defined:

Unit Description
== equal to
!= not equal to
> greater than
< less than
>= greater than or equal to
<= less than or equal to

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Units

Units can be used directly in expressions. The parser connects them to the previous value. So 2mm or 2 mm is valid while mm is invalid because there is no preceding value.

All values must have a unit. Therefore you must in general use a unit for values in spreadsheets.
In some cases it works even without a unit, for example if you have e.g. in spreadsheet cell B1 just the number 1.5 and refer to it for a pad height. This only works because the pad height predefines the unit mm that is used if no unit is given. It will nevertheless fail if you use for the pad height e.g. Sketch1.Constraints.Width - Spreadsheet.B1 because Sketch1.Constraints.Width has a unit and Spreadsheet.B1 has not.

Units with exponents can directly be entered. So e.g. mm^3 will be recognized as mm³ and m^3 will be recognized as m³.

If you have a variable whose name is that of a unit you must put the variable between << >> to prevent it from being recognized as a unit. For example if you have the dimension Sketch.Constraints.A it would be recognized as the unit ampere. Therefore you must write it in the expression as Sketch.Constraints.<<A>>.

The following units are recognized by the expression parser:

Amount of substance

Unit Description
mmol Millimole
mol Mole

Angle

Unit Description
° Degree; alternative to the unit deg
deg Degree; alternative to the unit °
rad Radian
gon Gradian
S Second of arc; alternative to the unit ″
″ Second of arc; alternative to the unit S
M Minute of arc; alternative to the unit ′
′ Minute of arc; alternative to the unit M

Current

Unit Description
mA Milliampere
A Ampere
kA Kiloampere
MA Megaampere

Electric capacitance

Unit Description
pF Picofarad
nF Nanofarad
uF Microfarad; alternative to the unit µF
µF Microfarad; alternative to the unit uF
mF Millifarad
F Farad; 1 F = 1 s^4·A^2/m^2/kg

Electric charge

Unit Description
C Coulomb; 1 C = 1 A*s

Electric conductivity

Unit Description
uS Microsiemens; alternative to the unit µS
µS Microsiemens; alternative to the unit uS
mS Millisiemens
S Siemens; 1 S = 1 s^3·A^2/kg/m^2
kS KiloSiemens
MS MegaSiemens

Electric inductance

Unit Description
nH Nanohenry
uH Microhenry; alternative to the unit µH
µH Microhenry; alternative to the unit uH
mH Millihenry
H Henry; 1 H = 1 kg·m^2/s^2/A^2

Electric potential

Unit Description
mV Millivolt
V Volt
kV Kilovolt

Electric resistance

Unit Description
Ohm Ohm; 1 Ohm = 1 kg·m^2/s^3/A^2
kOhm Kiloohm
MOhm Megaohm

Energy/work

Unit Description
mJ Millijoule
J Joule
kJ Kilojoule
eV Electronvolt; 1 eV = 1.602176634e-19 J
keV Kiloelectronvolt
MeV Megaelectronvolt
kWh Kilowatt hour; 1 kWh = 3.6e6 J
Ws Watt second; alternative to the unit Joule
VAs Volt-ampere-second; alternative to the unit Joule
CV Coulomb-volt; alternative to the unit Joule
cal Calorie; 1 cal = 4.184 J
kcal Kilocalorie

Force

Unit Description
mN Millinewton
N Newton
kN Kilonewton
MN Meganewton
lbf Pound of force

Length

Unit Description
nm Nanometer
um Micrometer; alternative to the unit µm
µm Micrometer; alternative to the unit um
mm Millimeter
cm Centimeter
dm Decimeter
m Meter
km Kilometer
mil Thousandth of an inch; alternative to the unit thou
thou Thousandth of an inch; alternative to the unit mil
in Inch; alternative to the unit "
" Inch; alternative to the unit in
ft Foot; alternative to the unit '
' Foot; alternative to the unit ft
yd Yard
mi Mile

Luminous intensity

Unit Description
cd Candela

Magnetic flux

Unit Description
Wb Weber; 1 Wb = 1 kg*m^2/s^2/A

Magnetic flux density

Unit Description
G Gauss; 1 G = 1 e-4 T
T Tesla; 1 T = 1 kg/s^2/A

Mass

Unit Description
ug Microgram; alternative to the unit µg
µg Microgram; alternative to the unit ug
mg Milligram
g Gram
kg Kilogram
t Tonne
oz Ounce
lb Pound; alternative to the unit lbm
lbm Pound; alternative to the unit lb
st Stone
cwt Hundredweight

Power

Unit Description
W Watt
kW Kilowatt

Pressure

Unit Description
Pa Pascal
kPa Kilopascal
MPa Megapascal
GPa Gigapascal
uTorr Microtorr; alternative to the unit µTorr
µTorr Microtorr; alternative to the unit uTorr
mTorr Millitorr
Torr Torr; 1 Torr = 133.32 Pa
psi Pound-force per square inch; 1 psi = 6.895 kPa
ksi Kilopound-force per square inch

Temperature

Unit Description
uK Microkelvin; alternative to the unit µK
µK Microkelvin; alternative to the unit uK
mK Millikelvin
K Kelvin

Time

Unit Description
s Second
min Minute
h Hour
Hz (1/s) Hertz
kHz Kilohertz,
MHz Megahertz
GHz Gigahertz
THz Terahertz

Volume

Unit Description
ml Milliliter
l Liter
cft Cubicfoot

Special imperial units

Unit Description
mph Miles per hour
sqft Square foot

Unsupported units

The following commonly used units are not yet supported, for some an alternative is provided:

Unit Description Alternative
°C Celsius [°C] + 273.15 K
°F Fahrenheit; ([°F] + 459.67) × ​5/9
u Atomic mass unit; alternative to the unit Da 1.66053906660e-27 kg
Da Dalton; alternative to the unit u 1.66053906660e-27 kg
sr Steradian not directly
lm Lumen not directly
lx Lux not directly
px Pixel not directly

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Invalid characters and names

The expression feature is very powerful but to achieve this power it has some limitations concerning some characters. To overcome this, LabRPS offers to use labels and reference them instead of the object names. In labels you can use almost all special characters.

In cases where you cannot use a label, such as the name of a sketch's constraints, you must be aware what characters are not allowed.

Labels

For labels there are no invalid characters, however some characters need to be escaped:

Characters Description
', \, " Need to be escaped by adding \ in front of them.

For example, the label Sketch\002 must be referenced as <<Sketch\\002>>.

Names

Names of objects like dimensions, sketches, etc. may not have the characters or character sequences listed below, otherwise the name is invalid:

Characters / Character sequences Description
+, -, *, /, ^, _, <, >, (, ), {, }, [, ], ., ,, = Characters that are math operators or part of mathematical constructs
A, kA, mA, MA, J, K, ' , ft , °, and many more! Characters and character sequences that are units (see the Units paragraph)
#, !, ?, §, $, %, &, :, ;, \, |, ~, ∆, ¿, and many more! Characters used as placeholder or to trigger special operations
pi, e Mathematical constants
´, `, ' , " Characters used for accents
space A space defines the end of a name and can therefore not be used

For example, the following name is valid: <<Sketch>>.Constraints.T2üßµ@. While these are invalid names: <<Sketch>>.Constraints.test\result_2 (\r means "carriage return") or <<Sketch>>.Constraints.mol (mol is a unit).

Since shorter names (especially if they have only one or two characters) can easily result in invalid names, consider using longer names and/or establishing a suitable naming convention.

Cell aliases

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Cyclic dependencies

LabRPS checks dependencies based on the relationship between document objects, not properties. This means that you cannot provide data to an object and query that same object for results. For example, even though there are no cyclic dependencies when the properties themselves are considered, you may not have an object which gets its dimensions from a spreadsheet and then display the volume of that object in the same spreadsheet. You have to use two spreadsheets, one to drive your model and the other for reporting.

As a workaround it is possible to display a cell range from the second spreadsheet in the first (or vice versa) by creating a cell binding with the Hide dependency of binding option.

Another way to workaround cyclic dependencies is to hide the reference by using the href or hiddenref function for individual expressions, for example: href(Sim.ModulationFunction).

Please note that both mentioned workarounds should be used with caution, and that they do not work if the properties that are reported depend on dimensions that are driven from the same spreadsheet.

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Document-wide global variables

There is no concept of global variables in LabRPS at the moment. Instead, arbitrary variables can be defined as cells in a spreadsheet using the Spreadsheet workbench, and then be given a name using the alias property for the cell (right-click on cell). Then they can be accessed from any expression just as any other object property.

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Cross-document linking

It is possible (with limitations) to define a Property of an object in your current document (".RPSstd" file) by using an Expression to reference a Property of an object contained in a different document (".RPSstd" file). For example, a cell in a spreadsheet etc. in one document can be defined by an Expression that references the X Placement value or another Property of an object contained in a different document.

A document's name is used to reference it from other documents. When saving a document the first time, you choose a file name; this is usually different from the initial default "Unnamed1" (or its translated equivalent). To prevent links being lost when the master document is renamed upon saving, it is recommended that you first create the master document, create a spreadsheet inside it, and save it. Subsequently, you can still make changes to the file and its spreadsheet but you should not rename it.

Once the master document with the spreadsheet is created and saved (named), it is safe to create dependent documents. For example, assuming you name the master document master, the spreadsheet modelConstants, and give a cell an alias-name Length, you can then access the value as:


master#modelConstants.Length


Note that the master document must be loaded for the values in the master to be available to the dependent document.

Of course, it's up to you to load the corresponding documents later when you want to change anything.

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Scripting

import LabRPS as App

doc = App.ActiveDocument
point1 = doc.addObject("WindLabAPI::WindLabFeatureSimulationLocation", "Point1")
point2 = doc.addObject("WindLabAPI::WindLabFeatureSimulationLocation", "Point2")

point1.setExpression("Height", f"{point2}.Z / 2")

doc.recompute()

# Expressions are stored in the ExpressionEngine property:
for prop, exp in point1.ExpressionEngine:
    val = getattr(point1, prop)
    print(f"Property: '{prop}' -- Expression: '{exp}' -- Current value: {val}")

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