`RollingPoly1`

Description

The RollingPoly1 class fits a straight line (first-degree polynomial) through data within a specified moving window. It returns either the endpoint of this line or the slope, depending on the derivative_order argument. This approach, also known as a causal Savitzky-Golay filter, provides a way to smooth data or obtain the rate of change across each window. With derivative_order=0, the function returns the y-value at the end of the fitted line, which smooths the data over the window. When derivative_order=1, it outputs the slope, capturing the rate of change within each window.

Parameters:

window_size: Specifies the size of the rolling window.
derivative_order:
- 0: The y-value at the endpoint of the fitted quadratic curve, offering a smooth continuation of the data.
- 1: The slope, representing the rate of change.
start_policy: Defines how the function handles the initial phase when fewer than window_size data points are available. This parameter accepts one of the following three values:
- "strict": Returns NaN for all calculations until window_size elements have been processed.
- "expanding": Adapts the computation by dynamically reducing the window size to include all available data, starting from a single point and growing until window_size is reached.
- "zero": Simulates a full initial window of zeros, effectively pre-filling the data stream with window_size zeros before processing the actual input.

Usage Example and Plot

import numpy as np
import plotly.graph_objects as go
from plotly.subplots import make_subplots
from screamer import RollingPoly1

# Generate example data
data = np.cumsum(np.random.normal(size=300))

# Create subplots with specified row heights and shared x-axis
fig = make_subplots(
    rows=2, cols=1,
    shared_xaxes=True,
    row_heights=[2/3, 1/3],
    vertical_spacing=0.1
)

# RollingPoly1 for endpoint (derivative_order=0)
endpoint_data = RollingPoly1(window_size=30, derivative_order=0)(data)

# RollingPoly1 for slope (derivative_order=1)
slope_data = RollingPoly1(window_size=30, derivative_order=1)(data)

# Add traces for input data and results with different derivative orders
fig.add_trace(go.Scatter(y=data, mode='lines', name='Input Data'), row=1, col=1)
fig.add_trace(go.Scatter(y=endpoint_data, mode='lines', name='Rolling Endpoint (Order 0)', line=dict(color='red')), row=1, col=1)
fig.add_trace(go.Scatter(y=slope_data, mode='lines', name='Rolling Slope (Order 1)', line=dict(color='green')), row=2, col=1)

# Update layout with titles and axis labels
fig.update_layout(
    title="RollingPoly1 with Window Size 30",
    xaxis2_title="Index",
    yaxis=dict(title="Input Data"),
    yaxis2=dict(title="RollingPoly1 Output"),
    margin=dict(l=20, r=20, t=80, b=20),
    legend=dict(orientation="h", yanchor="bottom", y=1.02, xanchor="right", x=1)
)

fig.show()

Implementation Details

Algorithm

RollingPoly1 uses a cyclic buffers to implement an online variant of least-squares regression to fit a straight line through data in the specified window. Depending on derivative_order, it either outputs the endpoint of this line (0th derivative, for smoothing) or the slope (1st derivative, for change rate). This is efficient and suitable for streaming data applications where real-time smoothing or trend analysis is required.

Complexity

Time Complexity: O(1) per element.
Space Complexity: O(window_size), since only elements within the current window are stored.

Performance

RollingPoly1 is hundreds times faster than Pandas rolling apply, and the speed is constant, indepenent of the windows size.

RollingPoly1