Now that we have derived the expression (the Inverse Dot Product) for calculating the magnitude of eye movements, we can begin its implementation. The C++ code for it is pretty simple:

```
int remDetect::evaluate_EOG_REM_Epoch(double *EOG1, double *EOG2, double min_EOG)
{
// Resat accumulator
avg_EOG_IP = 0;
// Optimized algorithm - it is equivalent with += (EOG1 - EOG2)^2 - (EOG1 + EOG2)^2
for (int i = 0; i < m_size_window; i++) {
avg_EOG_IP += -1.0 * EOG1[i] * EOG2[i];
}
// Average
avg_EOG_IP /= m_size_window;
// if the value is within the limit window then return 1, else 0
if (avg_EOG_IP > min_EOG) {
rem_eog_Counter++;
return 1;
} else return 0;
}
```

In the code, you can see that I average (divide by number of EOG data points) the IDP after it has been calculated. This is to make sure that the constant min_EOG does not depend on the length of the signals and hence is portable across different EEG sampling frequencies. This function will return a **1** if it detects enough eye movements (above the min_EOG threshold) and a **0** otherwise.

**There it is. We are done with the Lucid Dream Trigger portion of this project. In the next Project Log, I will give a general overview of how to use the OpenLD Software.**

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