Function gdiis_blend_step 

pub fn gdiis_blend_step(
    opt_state: &OptimizationState_blend,
    max_step: f64,
    thresh_rms_g: f64,
    print_level: usize,
    reduced_factor: f64,
    step_reduction_multiplier: f64,
) -> DVector<f64>

GDIIS_blend step: interpolate geometry, apply Newton correction via INVERTED mean true Hessian, with step control.

Algorithm

1. Build combined forces: F_i = g_vec_i + f_vec_i (Fhist)
2. Compute error vectors: e_i = H_mean^{-1} @ F_i
3. Build B-matrix: B[i,j] = e_i . e_j
4. Solve [B 1; 1^T 0] . c = [0,...,0, 1]^T
5. Interpolate: X_interp = sum(c_i . X_i) and F_interp = sum(c_i . F_i)
6. Newton correction: X_new = X_interp - H_mean^{-1} @ F_interp
7. Step reduction: factor = 0.5 if ||F_hist|| < thresh * 10
8. Step size cap via stepsize_blend

Arguments

• opt_state - Optimization state with history of geometries, combined forces (via grad + f_vec), and true Hessians.
• max_step - Maximum allowed step size (maxstep).
• thresh_rms_g - RMS gradient threshold for step reduction (conver[4]).
• reduced_factor - Step reduction factor when activated.

Returns

The new geometry after GDIIS_blend interpolation, Newton correction, and step control.