Function build_b_matrix 

fn build_b_matrix(errors: &[DVector<f64>]) -> DMatrix<f64>

Builds the B matrix for GDIIS optimization.

The B matrix is the core of the DIIS method, containing dot products of error vectors plus constraint equations. It has the structure:

B = [ e₁·e₁  e₁·e₂  ...  e₁·eₙ  1 ]
    [ e₂·e₁  e₂·e₂  ...  e₂·eₙ  1 ]
    [  ...    ...   ...   ...   1 ]
    [ eₙ·e₁  eₙ·e₂  ...  eₙ·eₙ  1 ]
    [   1      1    ...    1    0 ]

where eᵢ·eⱼ represents the dot product of error vectors i and j.

Arguments

• errors - Vector of error vectors from compute_error_vectors

Returns

Returns the (n+1) × (n+1) B matrix where n is the number of error vectors. The extra row and column enforce the constraint that coefficients sum to 1.

Mathematical Background

The B matrix is used in solving the DIIS equations:

B * c = [0, 0, ..., 0, 1]ᵀ

where c contains the interpolation coefficients and the Lagrange multiplier.