Add conditional alpha capping, PolarPhase line-search scaling, and optimizer options

[Fuwsusu]

Motivation

• Stabilize gradient-based updates and avoid over-clipping by introducing a conditional alpha cap that only triggers under identified risk conditions.
• Correct the line-search scaling mismatch when using the PolarPhase misfit by applying a lightweight denominator scaling tied to the phase/amplitude weight.
• Expose optimizer-related parameters for reproducibility and saving so runs can be replayed and post-analysed.

Description

• Added optimizer options enableConditionalAlphaCap and alpha_cap_percentile and adjusted comments to clarify alpha_ls/alpha_cap behavior and target_dv_per_iter semantics.
• Implemented PolarPhase line-search denominator correction by computing a weighted squared term and replacing the L2 denominator when misfitType == 'PolarPhase'.
• Introduced risk-detection flags (bad_fit_flag, tau_rise_flag, ring_rise_flag) and enabled conditional application of the hard step-size cap using a quantile-based sd_ref instead of max(abs(search_dir)).
• Rewired the trust-gate logic to reuse the new risk flags and persist the new optimizer variables (optimizerType, target_dv_per_iter, enableConditionalAlphaCap, alpha_cap_percentile) into the results file, and made the three-stage reference saves conditional with exist checks.

Testing

• Performed a smoke integration run of MultiFrequencyWaveformInvkWave_fws20260409_2new.m on a small sample frequency set and confirmed the script completes without runtime errors and produces filename_results.
• Verified that the saved results file contains the newly persisted optimizer variables and that the updated alpha computation path is exercised when misfitType is set to PolarPhase.

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Codex Task