Diff

Description

The Diff function calculates the difference between each element in a sequence and the element delay positions before it. This allows for quick derivation of trends or changes over a given interval.

Equation:

\[ y[i] = x[i] - x[i - \text{delay}] \]

Parameters:

• delay (int): The number of steps backward to use for the difference calculation. Must be non-negative.

NaN handling: When delay exceeds the available data points at the start of the sequence, the resulting elements are set to NaN.

Usage Example and Plot

import numpy as np
import plotly.graph_objects as go
from plotly.subplots import make_subplots
from screamer import Diff

data = np.cumsum(np.random.normal(size=50) + 0.5)
diff_data = Diff(3)(data)

fig = make_subplots(rows=2, cols=1, shared_xaxes=True, row_heights=[1/2, 1/2], vertical_spacing=0.1)

fig.add_trace(go.Scatter(y=data, mode='lines+markers', name='Original Data'), row=1, col=1)
fig.add_trace(go.Scatter(y=diff_data, mode='lines+markers', name='Diff (3-step)', line=dict(color='green')), row=2, col=1)

fig.update_layout(
    title="Difference Computation (3-step Delay)",
    xaxis_title="Index",
    yaxis_title="Original Data",
    yaxis2_title="Difference",
    margin=dict(l=20, r=20, t=60, b=20),
    legend=dict(orientation="h", yanchor="bottom", y=1.02, xanchor="right", x=1)
)

fig.show()

Implementation Details

Diff uses a simple array subtraction operation with efficient memory handling to produce the difference between elements separated by the delay. For edge cases where data points are not available due to the delay, the function outputs NaN to maintain alignment.