scp_iteration

plot_scp_convergence_histories(result: OptimizationResults) -> go.Figure

Plot SCP convergence histories: trust region weight, reduction histories, and acceptance ratio.

Creates three separate plots: 1. Trust region weight (lam_prox) history 2. Actual and predicted reduction histories (overlaid) 3. Acceptance ratio history

Parameters:

Name	Type	Description	Default
result	OptimizationResults	OptimizationResults containing the convergence histories.	required

Returns:

Type	Description
Figure	Plotly figure with three subplots

Example

problem.initialize() result = problem.solve() plot_scp_convergence_histories(result).show()

Source code in openscvx/plotting/scp_iteration.py

def plot_scp_convergence_histories(result: OptimizationResults) -> go.Figure:
    """Plot SCP convergence histories: trust region weight, reduction histories,
    and acceptance ratio.

    Creates three separate plots:
    1. Trust region weight (lam_prox) history
    2. Actual and predicted reduction histories (overlaid)
    3. Acceptance ratio history

    Args:
        result: OptimizationResults containing the convergence histories.

    Returns:
        Plotly figure with three subplots

    Example:
        >>> problem.initialize()
        >>> result = problem.solve()
        >>> plot_scp_convergence_histories(result).show()
    """
    if not isinstance(result, OptimizationResults):
        raise TypeError(f"Expected OptimizationResults, got {type(result)}")

    # Create subplots: 3 rows, 1 column
    fig = make_subplots(
        rows=3,
        cols=1,
        subplot_titles=(
            "Trust Region Weight History",
            "Actual vs Predicted Reduction History",
            "Acceptance Ratio History",
        ),
        vertical_spacing=0.12,
    )

    # Prepare iteration indices (0-indexed for plotting)
    iterations_lam_prox = np.arange(len(result.lam_prox_history))
    iterations_reduction = np.arange(len(result.actual_reduction_history))
    iterations_ratio = np.arange(len(result.acceptance_ratio_history))

    # Plot 1: Trust region weight history (plot max across all variables)
    if len(result.lam_prox_history) > 0:
        lam_prox_max_per_iter = [float(np.max(lp)) for lp in result.lam_prox_history]
        fig.add_trace(
            go.Scatter(
                x=iterations_lam_prox,
                y=lam_prox_max_per_iter,
                mode="lines+markers",
                name="lam_prox",
                line={"color": "cyan", "width": 2},
                marker={"size": 6},
                hovertemplate="Iteration: %{x}<br>lam_prox: %{y:.3g}<extra></extra>",
            ),
            row=1,
            col=1,
        )
    else:
        fig.add_annotation(
            text="No trust region weight history available",
            xref="x1",
            yref="y1",
            x=0.5,
            y=0.5,
            showarrow=False,
            row=1,
            col=1,
        )

    # Plot 2: Actual and predicted reduction histories
    if len(result.actual_reduction_history) > 0 and len(result.pred_reduction_history) > 0:
        # Ensure both histories have the same length
        min_len = min(len(result.actual_reduction_history), len(result.pred_reduction_history))
        actual_reduction = result.actual_reduction_history[:min_len]
        predicted_reduction = result.pred_reduction_history[:min_len]
        iterations_reduction = np.arange(min_len)

        fig.add_trace(
            go.Scatter(
                x=iterations_reduction,
                y=actual_reduction,
                mode="lines+markers",
                name="Actual Reduction",
                line={"color": "green", "width": 2},
                marker={"size": 6},
                hovertemplate="Iteration: %{x}<br>Actual Reduction: %{y:.3g}<extra></extra>",
            ),
            row=2,
            col=1,
        )

        fig.add_trace(
            go.Scatter(
                x=iterations_reduction,
                y=predicted_reduction,
                mode="lines+markers",
                name="Predicted Reduction",
                line={"color": "orange", "width": 2},
                marker={"size": 6},
                hovertemplate="Iteration: %{x}<br>Predicted Reduction: %{y:.3g}<extra></extra>",
            ),
            row=2,
            col=1,
        )
    else:
        fig.add_annotation(
            text="No reduction history available",
            xref="x2",
            yref="y2",
            x=0.5,
            y=0.5,
            showarrow=False,
            row=2,
            col=1,
        )

    # Plot 3: Acceptance ratio history
    if len(result.acceptance_ratio_history) > 0:
        fig.add_trace(
            go.Scatter(
                x=iterations_ratio,
                y=result.acceptance_ratio_history,
                mode="lines+markers",
                name="Acceptance Ratio",
                line={"color": "magenta", "width": 2},
                marker={"size": 6},
                hovertemplate="Iteration: %{x}<br>Acceptance Ratio: %{y:.3g}<extra></extra>",
            ),
            row=3,
            col=1,
        )

        # Add reference lines at typical thresholds (eta_1=1e-6, eta_2=0.9)
        fig.add_hline(
            y=1e-6,
            line_dash="dash",
            line_color="red",
            opacity=0.5,
            annotation_text="η₁ = 1e-6",
            row=3,
            col=1,
        )
        fig.add_hline(
            y=0.9,
            line_dash="dash",
            line_color="yellow",
            opacity=0.5,
            annotation_text="η₂ = 0.9",
            row=3,
            col=1,
        )
    else:
        fig.add_annotation(
            text="No acceptance ratio history available",
            xref="x3",
            yref="y3",
            x=0.5,
            y=0.5,
            showarrow=False,
            row=3,
            col=1,
        )

    # Update layout
    fig.update_layout(
        title_text="SCP Convergence Histories",
        template="plotly_dark",
        showlegend=True,
        height=900,
        legend={
            "yanchor": "top",
            "y": 0.99,
            "xanchor": "left",
            "x": 1.02,
            "bgcolor": "rgba(0, 0, 0, 0.5)",
        },
    )

    # Update axes labels
    fig.update_xaxes(title_text="Iteration", row=1, col=1)
    fig.update_yaxes(title_text="lam_prox", type="log", row=1, col=1)

    fig.update_xaxes(title_text="Iteration", row=2, col=1)
    fig.update_yaxes(title_text="Reduction", row=2, col=1)  # Linear scale

    fig.update_xaxes(title_text="Iteration", row=3, col=1)
    fig.update_yaxes(title_text="Acceptance Ratio (ρ)", row=3, col=1, range=[-0.5, 1.5])

    return fig

plot_scp_iterations(result: OptimizationResults, state_names: list[VarSpec] | None = None, control_names: list[VarSpec] | None = None, cmap_name: str = 'viridis', show_propagation: bool = True, style: PlotStyle = 'dark', pdf_path: str | Path | None = None) -> go.Figure

Plot all SCP iterations overlaid with colormap-based coloring.

Shows the evolution of states and controls across SCP iterations. Early iterations are dark, later iterations are bright (following the colormap). This makes convergence visible at a glance.

Parameters:

Name	Type	Description	Default
result	OptimizationResults	Optimization results containing iteration history	required
state_names	list[VarSpec] | None	Optional list of state names to include. If None, plots all states. For multidimensional states, pass a single component with ("position", 0), "position:0", or "position[0]".	None
control_names	list[VarSpec] | None	Optional list of control names to include. If None, plots all controls. Component selection uses the same syntax as state_names.	None
cmap_name	str	Matplotlib colormap name (default: "viridis")	'viridis'
show_propagation	bool	If True, show multi-shot propagation lines (default: True)	True
style	PlotStyle	"dark" for the default Plotly theme, "publication" for a white theme with Latin Modern fonts, LaTeX labels, and automatic PDF export, or "publication_dark" for the same figure on the dark palette (the exported PDF stays white for print).	'dark'
pdf_path	str | Path | None	Output path for the PDF when style="publication". Defaults to figures/scp_iterations.pdf.	None

Returns:

Type	Description
Figure	Plotly figure, or a :class:~openscvx.plotting.publication.PublicationFigure
Figure	wrapper when style="publication".

Example

results = problem.solve() plot_scp_iterations(results, ["position", "velocity"]).show() plot_scp_iterations(results, ["position:0"], style="publication").show()

Source code in openscvx/plotting/scp_iteration.py

def plot_scp_iterations(
    result: OptimizationResults,
    state_names: list[VarSpec] | None = None,
    control_names: list[VarSpec] | None = None,
    cmap_name: str = "viridis",
    show_propagation: bool = True,
    style: PlotStyle = "dark",
    pdf_path: str | Path | None = None,
) -> go.Figure:
    """Plot all SCP iterations overlaid with colormap-based coloring.

    Shows the evolution of states and controls across SCP iterations. Early
    iterations are dark, later iterations are bright (following the colormap).
    This makes convergence visible at a glance.

    Args:
        result: Optimization results containing iteration history
        state_names: Optional list of state names to include. If None, plots all states.
            For multidimensional states, pass a single component with
            ``("position", 0)``, ``"position:0"``, or ``"position[0]"``.
        control_names: Optional list of control names to include. If None, plots all controls.
            Component selection uses the same syntax as ``state_names``.
        cmap_name: Matplotlib colormap name (default: "viridis")
        show_propagation: If True, show multi-shot propagation lines (default: True)
        style: ``"dark"`` for the default Plotly theme, ``"publication"`` for a
            white theme with Latin Modern fonts, LaTeX labels, and automatic PDF
            export, or ``"publication_dark"`` for the same figure on the dark
            palette (the exported PDF stays white for print).
        pdf_path: Output path for the PDF when ``style="publication"``. Defaults
            to ``figures/scp_iterations.pdf``.

    Returns:
        Plotly figure, or a :class:`~openscvx.plotting.publication.PublicationFigure`
        wrapper when ``style="publication"``.

    Example:
        >>> results = problem.solve()
        >>> plot_scp_iterations(results, ["position", "velocity"]).show()
        >>> plot_scp_iterations(results, ["position:0"], style="publication").show()
    """
    import matplotlib.pyplot as plt

    if not result.X:
        raise ValueError("No iteration history available in result.X")

    # Derive dimensions from result data
    n_x = result.X[0].shape[1]
    n_u = result.U[0].shape[1]

    # Find time slice by looking for "time" state
    time_slice = None
    for state in result._states:
        if state.name.lower() == "time":
            time_slice = state._slice
            break

    # Extract multi-shot propagation trajectories
    V_history = result.discretization_history if result.discretization_history else []
    X_prop_history = []
    if V_history and show_propagation:
        from openscvx.algorithms.history import unpack_multishot_V

        for V in V_history:
            n_segments = V.shape[0] // (n_x + n_x * n_x + 2 * n_x * n_u)
            placeholder_t = np.linspace(0.0, 1.0, n_segments + 1)
            prop = unpack_multishot_V(V, n_x=n_x, n_u=n_u, t_nodes=placeholder_t, states=())
            segs = prop.segments()
            X_prop_history.append(np.stack(segs, axis=1))

    n_iterations = len(result.X)
    if X_prop_history:
        n_iterations = min(n_iterations, len(X_prop_history))

    # Filter states and controls (exclude ctcs_aug and time)
    all_states = [
        s for s in result._states if "ctcs_aug" not in s.name.lower() and s.name.lower() != "time"
    ]
    all_controls = list(result._controls) if result._controls else []

    plot_states = state_names is not None or control_names is None
    plot_controls = control_names is not None or state_names is None
    if state_names is not None and control_names is None:
        plot_controls = False
    if control_names is not None and state_names is None:
        plot_states = False

    expanded_states: list[dict] = []
    expanded_controls: list[dict] = []

    if plot_states:
        state_specs = state_names if state_names is not None else None
        if state_specs is not None:
            available = {s.name for s in all_states}
            for spec in state_specs:
                name, _ = parse_var_spec(spec)
                if name not in available:
                    raise ValueError(
                        f"No states matched filter {state_names}. Available: {sorted(available)}"
                    )
        expanded_states = _expand_scp_variables(result, state_specs, all_states)

    if plot_controls:
        control_specs = control_names if control_names is not None else None
        if control_specs is not None:
            available = {c.name for c in all_controls}
            for spec in control_specs:
                name, _ = parse_var_spec(spec)
                if name not in available:
                    raise ValueError(
                        f"No controls matched filter {control_names}. "
                        f"Available: {sorted(available)}"
                    )
        expanded_controls = _expand_scp_variables(result, control_specs, all_controls)

    if not expanded_states and not expanded_controls:
        raise ValueError("No states or controls to plot")

    publication = style in ("publication", "publication_dark")

    # Grid layout
    n_states = len(expanded_states)
    n_controls = len(expanded_controls)
    n_state_cols = min(7, n_states) if n_states > 0 else 1
    n_control_cols = min(3, n_controls) if n_controls > 0 else 1
    n_state_rows = (n_states + n_state_cols - 1) // n_state_cols if n_states > 0 else 0
    n_control_rows = (n_controls + n_control_cols - 1) // n_control_cols if n_controls > 0 else 0
    total_rows = n_state_rows + n_control_rows
    max_cols = max(n_state_cols, n_control_cols)

    if publication:
        subplot_titles = [""] * (len(expanded_states) + len(expanded_controls))
    else:
        subplot_titles = [s["name"] for s in expanded_states] + [
            c["name"] for c in expanded_controls
        ]

    fig = make_subplots(
        rows=total_rows,
        cols=max_cols,
        subplot_titles=subplot_titles,
        vertical_spacing=0.08,
        horizontal_spacing=0.05,
    )

    # Get colormap
    cmap = plt.get_cmap(cmap_name)

    def iter_color(iter_idx):
        rgba = cmap(iter_idx / max(n_iterations - 1, 1))
        return f"rgb({int(rgba[0] * 255)},{int(rgba[1] * 255)},{int(rgba[2] * 255)})"

    # Plot all iterations
    for iter_idx in range(n_iterations):
        X_nodes = result.X[iter_idx]
        U_iter = result.U[iter_idx]
        color = iter_color(iter_idx)
        legend_group = f"iter_{iter_idx}"
        show_legend_for_iter = True  # Show legend for first trace of this iteration

        t_nodes = (
            X_nodes[:, time_slice].flatten()
            if time_slice is not None
            else np.linspace(0, result.t_final, X_nodes.shape[0])
        )

        # States
        for state_idx, state in enumerate(expanded_states):
            row = (state_idx // n_state_cols) + 1
            col = (state_idx % n_state_cols) + 1
            idx = state["idx"]

            # Multi-shot propagation lines
            if X_prop_history and iter_idx < len(X_prop_history):
                pos_traj = X_prop_history[iter_idx]
                for j in range(pos_traj.shape[1]):
                    segment_times = pos_traj[:, j, time_slice].flatten()
                    segment_states = pos_traj[:, j, idx]
                    fig.add_trace(
                        go.Scatter(
                            x=segment_times,
                            y=segment_states,
                            mode="lines",
                            line={"color": color, "width": 1.5},
                            legendgroup=legend_group,
                            showlegend=show_legend_for_iter,
                            name=f"Iter {iter_idx}" if show_legend_for_iter else None,
                            hoverinfo="skip",
                        ),
                        row=row,
                        col=col,
                    )
                    show_legend_for_iter = False

            # Nodes
            fig.add_trace(
                go.Scatter(
                    x=t_nodes,
                    y=X_nodes[:, idx],
                    mode="markers",
                    marker={"color": color, "size": 5},
                    legendgroup=legend_group,
                    showlegend=show_legend_for_iter,
                    name=f"Iter {iter_idx}" if show_legend_for_iter else None,
                    hovertemplate=f"iter {iter_idx}<br>t=%{{x:.2f}}<br>y=%{{y:.3g}}<extra></extra>",
                ),
                row=row,
                col=col,
            )
            show_legend_for_iter = False

        # Controls
        for control_idx, control in enumerate(expanded_controls):
            row = n_state_rows + (control_idx // n_control_cols) + 1
            col = (control_idx % n_control_cols) + 1
            idx = control["idx"]

            fig.add_trace(
                go.Scatter(
                    x=t_nodes,
                    y=U_iter[:, idx],
                    mode="markers",
                    marker={"color": color, "size": 5},
                    legendgroup=legend_group,
                    showlegend=show_legend_for_iter,
                    name=f"Iter {iter_idx}" if show_legend_for_iter else None,
                    hovertemplate=f"iter {iter_idx}<br>t=%{{x:.2f}}<br>y=%{{y:.3g}}<extra></extra>",
                ),
                row=row,
                col=col,
            )
            show_legend_for_iter = False

    # Add bounds (once, using final iteration's time range)
    t_nodes_final = (
        result.X[-1][:, time_slice].flatten()
        if time_slice is not None
        else np.linspace(0, result.t_final, result.X[-1].shape[0])
    )
    t_min, t_max = t_nodes_final.min(), t_nodes_final.max()

    for state_idx, state in enumerate(expanded_states):
        row = (state_idx // n_state_cols) + 1
        col = (state_idx % n_state_cols) + 1
        parent = _get_var(result, state["parent"], result._states)
        comp_idx = state["comp"]

        for bound_val, bound_attr in [(parent.min, "min"), (parent.max, "max")]:
            if bound_val is not None and np.isfinite(bound_val[comp_idx]):
                fig.add_trace(
                    go.Scatter(
                        x=[t_min, t_max],
                        y=[bound_val[comp_idx], bound_val[comp_idx]],
                        mode="lines",
                        line={"color": "red", "width": 1.5, "dash": "dot"},
                        showlegend=False,
                        hoverinfo="skip",
                    ),
                    row=row,
                    col=col,
                )

    for control_idx, control in enumerate(expanded_controls):
        row = n_state_rows + (control_idx // n_control_cols) + 1
        col = (control_idx % n_control_cols) + 1
        parent = _get_var(result, control["parent"], result._controls)
        comp_idx = control["comp"]

        for bound_val in [parent.min, parent.max]:
            if bound_val is not None and np.isfinite(bound_val[comp_idx]):
                fig.add_trace(
                    go.Scatter(
                        x=[t_min, t_max],
                        y=[bound_val[comp_idx], bound_val[comp_idx]],
                        mode="lines",
                        line={"color": "red", "width": 1.5, "dash": "dot"},
                        showlegend=False,
                        hoverinfo="skip",
                    ),
                    row=row,
                    col=col,
                )

    # Layout
    if publication:
        apply_publication_plotly_layout(
            fig,
            n_rows=total_rows,
            n_cols=max_cols,
            extra_legend_width=PUBLICATION_LEGEND_EXTRA_W,
            dark=style == "publication_dark",
        )
        fig.update_layout(
            showlegend=True,
            legend={
                "title": "Iterations",
                "yanchor": "top",
                "y": 0.99,
                "xanchor": "left",
                "x": 1.02,
                "bgcolor": "rgba(255, 255, 255, 0.8)",
                "itemclick": "toggle",
                "itemdoubleclick": "toggleothers",
            },
        )

        for state_idx, state in enumerate(expanded_states):
            row = (state_idx // n_state_cols) + 1
            col = (state_idx % n_state_cols) + 1
            parent = _get_var(result, state["parent"], result._states)
            dim = (parent._slice.stop or 1) - (parent._slice.start or 0)
            fig.update_yaxes(
                title_text=latex_component_label(state["parent"], state["comp"], dim=dim),
                row=row,
                col=col,
            )

        for control_idx, control in enumerate(expanded_controls):
            row = n_state_rows + (control_idx // n_control_cols) + 1
            col = (control_idx % n_control_cols) + 1
            parent = _get_var(result, control["parent"], result._controls)
            dim = (parent._slice.stop or 1) - (parent._slice.start or 0)
            fig.update_yaxes(
                title_text=latex_component_label(control["parent"], control["comp"], dim=dim),
                row=row,
                col=col,
            )
    else:
        fig.update_layout(
            title_text="SCP Iterations",
            template="plotly_dark",
            showlegend=True,
            legend={
                "title": "Iterations",
                "yanchor": "top",
                "y": 0.99,
                "xanchor": "left",
                "x": 1.02,
                "bgcolor": "rgba(0, 0, 0, 0.5)",
                "itemclick": "toggle",
                "itemdoubleclick": "toggleothers",
            },
        )

    x_label = r"$t\,\mathrm{(s)}$" if publication else "Time (s)"
    for col_idx in range(1, max_cols + 1):
        fig.update_xaxes(title_text=x_label, row=total_rows, col=col_idx)

    if publication:

        def _save(path: str | Path) -> None:
            save_scp_iterations_pdf(
                result,
                expanded_states=expanded_states,
                expanded_controls=expanded_controls,
                n_state_cols=n_state_cols,
                n_control_cols=n_control_cols,
                n_state_rows=n_state_rows,
                n_control_rows=n_control_rows,
                n_iterations=n_iterations,
                time_slice=time_slice,
                X_prop_history=X_prop_history if show_propagation else None,
                path=path,
                cmap_name=cmap_name,
            )

        return wrap_publication_figure(
            fig,
            pdf_path=pdf_path,
            default_pdf_name="scp_iterations.pdf",
            save_fn=_save,
        )

    return fig