CVXPY Signal Decompositions#

Signal Decompositions Module for CVXPY

This module contains standardized signal decomposition models for use in the SDT algorithms using CVXPY and the MOSEK solver. The defined signal decompositions are:

  1. _cvx_l2_l1d1_l2d2p365: Separating a piecewise constant component from a smooth and seasonal component, with Gaussian noise - l2: Gaussian noise, sum-of-squares small or l2-norm squared - l1d1: Piecewise constant heuristic, l1-norm of first-order differences - l2d2p365: Small second-order differences (smooth) and 365-periodic

  2. _cvx_tl1_l2d2p365: Similar to (2), estimating a smooth, seasonal component with an asymmetric Laplacian noise model, fitting a local quantile instead of a local average - tl1: ‘Tilted l1-norm,’ also known as quantile cost function - l2d2p365: Small second-order differences (smooth) and 365-periodic

  3. _cvx_l1_l1d1_l2d2p365: Like (1) but with an asymmetric residual cost instead of Gaussian residuals - l1: l1-norm - l1d1: Piecewise constant heuristic, l1-norm of first-order differences - l2d2p365: Small second-order differences (smooth) and 365-periodic

  4. _cvx_l2_l1d2_constrained: - l2: Gaussian noise, sum-of-squares small or l2-norm squared - l1d2: Piecewise linear heuristic - Constrained to have first value at 0 and last value at 1

solardatatools._cvx_signal_decompositions._cvx_l1_pwc_smoothper_trend(signal, use_ixs=None, w2=20.0, w3=1, w4=10.0, solver='CLARABEL', verbose=False, return_all=False)#

Used in solardatatools/algorithms/capacity_change.py

We solve a convex signal decomposition problem, making use of the l1-sparsity heuristic for estimating a piecewise constant component. We use a single pass of iterative reweighting on this term to “polish” the sparse solution (see: https://web.stanford.edu/~boyd/papers/rwl1.html).

Parameters:

  • signal – A 1d numpy array (must support boolean indexing) containing the signal of interest

  • use_ixs – List of booleans indicating indices to use in signal. None is default (uses the entire signal).

  • w2 – Weight on the piecewise constant component

  • w3 – Weight on the smooth, periodic component

  • w4 – Weight on the slope of the trend term (discourages large trends)

  • solver – Solver to use for the decomposition. Standard cvxpy solvers are supported

  • verbose – Sets verbosity

Returns:

A tuple with three 1d numpy arrays containing the three non-noise signal component estimates

solardatatools._cvx_signal_decompositions._cvx_l2_l1d1_l2d2p365(signal, use_ixs=None, w0=10, w1=50, w2=100000.0, yearly_periodic=False, return_all=False, solver='MOSEK', transition_locs=None, verbose=False)#

Used in: solardatatools/algorithms/time_shifts.py

This performs total variation filtering with the addition of a seasonal baseline fit. This introduces a new signal to the model that is smooth and periodic on a yearly time frame. This does a better job of describing real, multi-year solar PV power data sets, and therefore does an improved job of estimating the discretely changing signal.

Parameters:

  • signal (array_like) – A 1d numpy array (must support boolean indexing) containing the signal of interest.

  • w0 (float) – Weight on the residual component.

  • w1 (float) – The regularization parameter to control the total variation in the final output signal.

  • w2 (float) – The regularization parameter to control the smoothness of the seasonal signal.

  • yearly_periodic (bool, optional) – Adds periodicity constraint to signal decomposition.

  • return_all (bool, optional) – Returns all components and the objective value. Used for tests.

  • solver (str, optional) – Solver to use for the decomposition.

  • transition_locs (list of int, optional) – List of indices where transitions are located.

  • verbose (bool, optional) – Sets verbosity.

Returns:

A tuple with two 1d numpy arrays containing the two signal component estimates.

Return type:

tuple of array_like

solardatatools._cvx_signal_decompositions._cvx_l2_l1d2_constrained(signal, w1=10.0, return_all=False, solver='MOSEK', verbose=False)#

Used in solardatatools/algorithms/clipping.py

This is a convex problem and the default solver across SDT is OSQP.

Parameters:

  • signal – A 1d numpy array (must support boolean indexing) containing the signal of interest

  • w0 – Weight on the residual component

  • w1 – The regularization parameter on l1d2 component

  • return_all – Returns all components and the objective value. Used for tests.

  • solver – Solver to use for the decomposition

  • verbose – Sets verbosity

Returns:

A tuple with returning the signal, the l1d2 component estimate, and the weight

solardatatools._cvx_signal_decompositions._cvx_tl1_l2d2p365(signal, use_ixs=None, tau=0.75, w0=1, w1=500, yearly_periodic=True, return_all=False, solver='MOSEK', verbose=False)#
Used in:

solardatatools/algorithms/sunrise_sunset_estimation.py solardatatools/clear_day_detection.py solardatatools/data_quality.py solardatatools/sunrise_sunset.py

Parameters:

  • signal – A 1d numpy array (must support boolean indexing) containing the signal of interest

  • use_ixs – List of booleans indicating indices to use in signal. None is default (uses the entire signal).

  • tau – Quantile regression parameter,between zero and one, and it sets the approximate quantile of the residual distribution that the model is fit to See: https://colab.research.google.com/github/cvxgrp/cvx_short_course/blob/master/applications/quantile_regression.ipynb

  • w0 – Weight on the residual component

  • w1 – The regularization parameter to control the smoothness of the seasonal signal

  • yearly_periodic – Adds periodicity constraint to signal decomposition

  • return_all – Returns all components and the objective value. Used for tests.

  • solver – Solver to use for the decomposition

  • verbose – Sets verbosity

Returns:

A tuple with three 1d numpy arrays containing the three signal component estimates

solardatatools._cvx_signal_decompositions.make_l1_pwc_smoothper_trend_problem(metric, w2, w3, w4, tv_weights=None)#