Functions

Your own functions

A line with an argument list defines a function:

f(x, y): sqrt(x^2 + y^2)
g(t): 2 * t
r: f(3, 4) + g(1)

f(x; y) = √(x² + y²)
g(t) = 2·t
r = f(3; 4) + g(1) = 7

Calls take commas in a sheet; the compiler writes the engine’s ;. Calcpad’s own ; works too, in a definition and in a call (f(x; y): x + y, max(3; 7)): inside brackets it means the same as a comma. Functions can use any quantity defined above them, and may be used in plots (plot g(t) for t in 0..5).

Keeping functions for reuse

A function defined in a sheet belongs to that sheet. To use it in other sheets, put its definition in a .cpd file and add the file to the library (File > Library > Add files to the library, or drop it on the page). Any sheet then pulls it in with an include line:

>> #include beam_functions.cpd

The file holds Calcpad text, so its arguments are separated by ;:

delta(w; L; E; I) = 5*w*L^4/(384*E*I)

Two things to watch in definitions that integrate over time or space:

The limits of $Area, $Sum and the other numerical commands must have the same unit. $Area{F(t) @ t = 0ms : 2s} is fine; a bare 0 against 2s is an error.
An angular frequency is a number per second. Write 20 / 1 s, not 20 rad/s.

Copying the definition lines into each sheet also works, and keeps the sheet self-contained when you send it to someone who does not have your library.

Built-in functions

The engine has more than 200 functions: trigonometric, hyperbolic, logarithmic, rounding, statistical, interpolation, complex numbers, and a large set for vectors and matrices. The function reference lists them all, with the argument forms, and the Insert tab in the sidebar finds them as you type.

A few that are used constantly:

a: sqrt(2)
b: round(3.14159)
c: max(3, 7, 5)
d: sum([1, 2, 3])
e: interp(2.5, [1, 2, 3], [10, 20, 30])

There is no hypot in a sheet. For the hypotenuse, or the resultant of any number of components, use srss (square root of the sum of squares), which keeps the unit:

a: 3 m
b: 4 m
c: srss(a, b)

The result is 5 m, and srss(3 m, 4 m, 12 m) is 13 m. (In a Python block math.hypot exists.)

A function whose name is also a variable name needs the Calcpad spelling (a name like gamma or beta used as a variable only keeps working if you write it the Calcpad way). Function calls are not renamed unless the sheet defines the function.

Solving, integrating and slopes

Three numerical operations have a sheet form of their own, written like a plot line:

f(x): x^2
x0: solve f(x) = 2 for x in 0..2 | the positive root
A: integral of f(x) for x in 0..3
k: slope of f(x) at x = 3

solve f(x) = c for x in a..b finds the x between a and b where both sides are equal (Calcpad’s $Root{f(x) = c @ x = a : b}). Without = c it solves f(x) = 0. Both sides may use the variable (solve f(x) = g(x) for x in 0..5 finds where two curves cross). The difference of the sides must change sign once across the range.
integral of f(x) for x in a..b is the numerical integral ($Integral).
slope of f(x) at x = a is the derivative at a point ($Slope).

root(27, 3) is something else: the cube root of 27. The bounds may carry units, and a bare 0 takes the unit of the other bound, so solve x^2 = 4 m^2 for x in 0..5 m -> mm gives 2000 mm. A line that starts like one of these but is malformed (for 2 in 0..5, two = signs) is an error on its line.

Numerical commands

The $Root, $Area, $Sum, $Find and similar commands are Calcpad commands. Apart from the three above, in a sheet they go through >>:

>> f(x) = x^2 - 2
>> x_0 = $Root{f(x) @ x = 0 : 2}
>> I = $Area{x^2 @ x = 0 : 3}

The result of the first is 1.41, of the second 9. See The Calcpad language.