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Math expressions

All @Record instances (Species, Process, etc.) include assignments property which is set of assignments for different scopes: initial assignment start_, rule assignment ode_ and any number of switcher assignments. The right hand side (RHS) of assignments is string of the specific format MathExpr.

@CSwitcher includes MathExpr inside property trigger.

The trigger property of @DSwitcher and StopSwitcher also include MathExpr but this expression must return boolean result.

MathExpr may include: numbers, identifiers, operators, functions, parentheses.

Numbers

All numbers in "math expression" are double. You can use any form of number: 0.001, 1e-3, 1E-3, 1.0e-3, etc.

The another possible values of double are:

  • Infinity which means infinite value.
  • -Infinity which negative infinite value.
  • NaN which means infinite or negative infinite, i.e. 0/0.

Boolean values

Boolean constants: true, false. It is also possible to use 1 and 0 as a boolean values.

Pre defined constants

There is a set of identifiers which can be used in MathExpr but they are not components of platform.

  • e is the Euler's number, i.e. exp(0).
  • pi is π=3.141592... number.

Identifiers

The identifiers inside expressions should be interpreted as references to the values of Record or Const instances of the same namespace. The math expression p1 .= 1*y implies there is constant or record with the id y.

Operators

There are 5 numeric operators in MathExpr: +, -, *, /, ^.

There are 6 comparison operators in MathExpr: >, >=, <, <=, ==, !=.

There are 4 boolean operators in MathExpr: and, or, xor, not.

Heta support ternary (conditional) operator in format: b1 < b2 ? x : y. Here the first operand b1 < b2 is the boolean expression, then an expression to execute if the condition is true, and finally the expression to execute if the condition is false.

List of functions

Arithmetic functions

id explanation
abs(x) The absolute value of a number.
add(x, y) Add two or more values, x + y.
ceil(x) Round a value towards plus.
cube(x) The cube of a value, x * x * x.
divide(x, y) Divide two values, x / y.
exp(x) The exponent of a value.
floor(x) Round a value towards minus.
ln(x) Natural logarithm of a value
log(x) Natural logarithm of a value
logbase(x, base) The logarithm of a value with base.
log10(x) The 10-base logarithm of a value.
log2(x) The 2-base of a value.
multiply(x, y) Multiply two or more values, x * y.
pow(x, y) The power of x to y, x ^ y.
sign(x) Compute the sign of a value.
sqrt(x) Calculate the square root of a value.
nthRoot(x, n) n-th root of x
square(x) Compute the square of a value, x * x.
subtract(x, y) Subtract two values, x - y.
max(x, y) Maximum from two numbers
max(x, y, z) Maximum from 3 numbers
min(x, y) Minimum from two numbers
min(x, y, z) Minimum from 3 numbers
factorial(n) Factorial of number
ifgt(x, y, z1, z2) Equivalent to : x > y ? z1 : z2
ifge(x, y, z1, z2) Equivalent to : x >= y ? z1 : z2
iflt(x, y, z1, z2) Equivalent to : x < y ? z1 : z2
ifle(x, y, z1, z2) Equivalent to : x <= y ? z1 : z2
ifeq(x, y, z1, z2) Equivalent to : x == y ? z1 : z2

Trigonometric functions

acos(x), acot(x), acsc(x), asec(x), asin(x), atan(x), cos(x), cot(x), csc(x), sec(x), sin(x), tan(x)

piecewise function (experimental)

piecewise is a special function which can be used to switch values based on conditions. It can be applied as an extension of the ternary operator or ifgt-like functions for more than one condition.

The piecewise function can have several arguments with the following meaning.

y1 := piecewise(value1, cond1, value2, cond2, ..., otherwise)

value1 is returned if cond1 is true, value2 is returned if cond2 is true, etc.

If neither conditions is true, than it returns otherwise value. otherwise value can be skipped. In that case the function returns NaN.

Each condition argument must be of boolean type: comparison operator, boolean value, etc.

Example

// 0 -> human, 1 -> monkey, 2 -> rat, default -> mouse
animal @Const = 999;
body_weight @Record .= piecewise(BW_human, animal==0, BW_monkey, animal==1, BW_rat, animal==2, BW_mouse);

// the body_weight value will be equal to BW_mouse