logcondens: quadDeriv – R documentation

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quadDeriv

Gradient and Diagonal of Hesse Matrix of Quadratic Approximation to Log-Likelihood Function L

Computes gradient and diagonal of the Hesse matrix w.r.t. to η of a quadratic approximation to the reparametrized original log-likelihood function

L(φ) = ∑_{i=1}^m w_i φ(x_i) - int_{-∞}^{∞} exp(φ(t)) dt.

where L is parametrized via

η(φ) = (φ_1, (η_1 + ∑_{j=2}^i (x_i-x_{i-1}) η_i)_{i=2}^m).

φ: vector (φ(x_i))_{i=1}^m representing concave, piecewise linear function φ,
η: vector representing successive slopes of φ.

quadDeriv(dx, w, eta)

`dx`	Vector (0, x_i-x_{i-1})_{i=2}^m.
`w`	Vector of weights as in `activeSetLogCon`.
`eta`	Vector η.

m \times 2 matrix. First column contains gradient and second column diagonal of Hesse matrix.

This function is not intended to be invoked by the end user.