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Build QP Constraint Matrix and Target Vector

Source: R/daly_resistance_profiles.R
build_constraint_matrix.Rd

Constructs the constraint matrix M and target vector v used in the simplex-constrained weighted least-squares QP:

Usage

build_constraint_matrix(profiles_enum, r_marg, co_mat = NULL)

Arguments

profiles_enum

Tibble from enumerate_binary_profiles(). The profile_delta column is ignored; only the binary class columns are used.

r_marg

Named numeric vector. Marginal resistance rates, one per class. Names must match column names in profiles_enum.

co_mat

Numeric matrix or NULL. Square symmetric pairwise co-resistance prevalence matrix with row/column names matching names(r_marg). NA cells trigger independence fallback. Default NULL.

Value

Named list:

M

Numeric matrix \((n + n(n-1)/2) \times 2^n\).

v

Numeric vector of constraint targets.

constraint_names

Character vector labelling each row of M.

fallback_pairs

Character vector of class pairs that used the independence fallback.

capped_pairs

Named numeric vector of pairs whose pairwise value was capped, showing original and capped values.

Details

$$\min_p \|Mp - v\|^2_W \quad \text{s.t.} \quad p \ge 0,\; \sum p = 1$$

Marginal rows: \(M_{d,\delta} = 1\) iff class \(d\) is resistant in profile \(\delta\). Pairwise rows: \(M_{d_1 d_2,\delta} = 1\) iff both classes are resistant. When a pairwise value is unavailable (too few co-tested isolates), the product of marginals (independence assumption) is substituted. Pairwise values that exceed \(\min(P(A), P(B))\) are capped.