`CumProd`#

Description#

The CumProd function returns the running product of all samples seen since the start of the stream (or since the last reset). It is the streaming equivalent of numpy.cumprod. Memory is O(1) regardless of how many samples have been processed.

Equation:

\[ y[t] = \prod_{i=0}^{t} x[i] \]

Parameters: none.

NaN handling: NaN propagates by ordinary IEEE-754 multiplication. A single zero input pins the running product to zero from that point onward.

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 plotly.subplots import make_subplots
from screamer import CumProd

rng = np.random.default_rng(7)
returns = rng.normal(0.0005, 0.01, size=200)
wealth = CumProd()(1.0 + returns)

fig = make_subplots(rows=2, cols=1, shared_xaxes=True,
                    row_heights=[0.5, 0.5], vertical_spacing=0.1)
fig.add_trace(go.Scatter(y=returns, mode='lines', name='Period return r[t]'),
              row=1, col=1)
fig.add_trace(go.Scatter(y=wealth, mode='lines',
                         name='Wealth = CumProd(1+r)',
                         line=dict(color='green')), row=2, col=1)
fig.update_layout(
    title="CumProd: Compounded Wealth from Period Returns",
    xaxis_title="Index",
    yaxis_title="r[t]",
    yaxis2_title="Wealth[t]",
    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#

CumProd keeps a single double accumulator initialised to 1.0. Every input multiplies it in-place, and the running product is returned. There is no warmup. The numpy reference is numpy.cumprod.

CumProd#