`CumMax`#

Description#

The CumMax function returns the running maximum of all samples seen since the start of the stream (or since the last reset). The output is monotonically non-decreasing while inputs are finite. It is the streaming equivalent of numpy.maximum.accumulate. Memory is O(1) regardless of how many samples have been processed.

This is an expanding (cumulative-from-zero) reduction, not a sliding window. For a fixed-window peak see RollingMax.

Equation:

\[ y[t] = \max_{0 \le i \le t} x[i] \]

Parameters: none.

NaN handling: Once an input is NaN, every subsequent output is NaN. This matches numpy.maximum.accumulate.

NaN handling#

Policy: ignore. A NaN in any input at index t causes the function to skip that step: output at t is NaN and internal state is unchanged. Subsequent finite samples are processed as if step t had not occurred.

Examples#

Usage example#

import numpy as np
import plotly.graph_objects as go
from screamer import CumMax

rng = np.random.default_rng(2)
x = np.cumsum(rng.normal(0.0, 1.0, size=300))
peak = CumMax()(x)

fig = go.Figure()
fig.add_trace(go.Scatter(y=x, mode='lines',
                         name='x[t]', line=dict(color='steelblue')))
fig.add_trace(go.Scatter(y=peak, mode='lines',
                         name='CumMax(x)[t]',
                         line=dict(color='green', dash='dash')))
fig.update_layout(
    title="CumMax: High-Water Mark of a Random Walk",
    xaxis_title="Index",
    yaxis_title="Value",
    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#

CumMax keeps a single double initialised to -infinity. Each input is compared and the larger value retained. There is no warmup. The numpy reference is numpy.maximum.accumulate.

CumMax#