Math

SquareRoot Block

Calculates the n-th root of the input signal

# SquareRoot Block

Description

The SquareRoot block calculates the n-th root of the input signal. While named SquareRoot for common usage (where n=2), it is a versatile root-calculation block that supports cube roots (n=3) and any other numeric root order.

Mathematical Model

The block implements the following calculation:

y(t) = in(t) ^ (1/n)

Where:

y(t) is the output signal
in(t) is the input signal
n is the root order (default is 2.0)

Handling of Negative Inputs

Calculating the root of a negative number can be problematic for even root orders (e.g., √-1). The block provides several configurable safety modes:

1. Return Zero (Default): Outputs 0.0 when a negative input is encountered. This is the safest option for simulation stability and includes a one-time visual warning. 2. Use Absolute Value: Calculates the root of the absolute value of the input. Useful when the sign of the signal is irrelevant for the root calculation. 3. Return NaN: Returns "Not a Number". Note that this value will propagate through your diagram and may cause other blocks to output NaN.

Parameters

Root Order (n)

The order of the root to calculate.

2.0 for square root (default)
3.0 for cube root
0.5 is equivalent to squaring the signal

Negative Input

Specifies the behavior when the input signal falls below zero.

Return Zero: Stable fallback.
Use Absolute Value: Mathematical alternative.
Return NaN: Scientific standard.

Report Warning

When enabled (true), displays a visual popup warning in the UI the first time a negative input is detected.

Examples

Distance Calculation

Calculate the distance from coordinates (x, y):

Sum (x^2 + y^2) → SquareRoot (n=2) → Distance

Flow Measurement

Calculate fluid flow rate from differential pressure (where flow ∝ √ΔP):

PressureDifference → SquareRoot (n=2) → FlowRate

Remarks

Negative inputs: Even root orders (n = 2, 4, 6) produce NaN for negative inputs; use the "Use Absolute Value" mode or the "Return Zero" safety option
Zero input: Returns 0 for any positive root order
Root order < 1: Equivalent to raising the input to a power > 1 (e.g., n = 0.5 squares the signal)
Performance: Very low computational cost; safe for real-time simulation
Numerical stability: Root of very small positive numbers can produce large outputs; consider clamping near-zero inputs