compute the hessian of f in the forward mode of AD

Compute the matrix exponential using a fixed-order Pade approximation.

i and j multi-indices

Notation is from Yang and Nielsen 2008. The first group of args consists of precomputed ndarrays. The second group is only the fixation f

computes the Hessian H = self.hessian(x) Parameters ---------- x: array_like x.ndim == 1 Return

computes the Householder vector v and twice its norm beta (v,beta) = house(x) Parameters ---------- x: array_like l

computes y = hyp0f1(b, x) in UTP arithmetic

computes y = hyp2f0(a1, a2, x) in UTP arithmetic

this is a helper function for a summation of the type :math:`sum_{0 <= k <= i}`, where i and k are multi-indices. Parameters

univariate Taylor arithmetic of scipy.linalg.lu

generic implementation of numpy.ones_like

computes QR decomposition using Householder relections (Q,R) = qr_house(A) such that 0 = Q R - A 0 = dot(Q.T,Q) - eye(M)

UTPM implementation of numpy.tile(A, reps)

vectorized dot z = vdot(x,y) Rationale: given two iteratable containers (list,array,...) x and y this function compute

computes the Jacobian-vector product w^T*J of a function F:R^N --> R^M in the reverse mode wJ = self.vec_jac(w, x) Paramete

generic implementation of numpy.zeros_like

this is the objective function

prototypical OED objective function

prototypical OED objective function

human readable output of the UTPS object or debugging UTPS([1,2,3]).__repr__()

In this function the args are permuted w.r.t numpy.

compute the choleksy decomposition in Taylor arithmetic of a symmetric positive definite matrix A i.e. ..math:

Compare alpha/beta/rc/final.

Compare major.minor.bugfix

computes tr(ybar.T, dy) = tr(xbar.T,dx) where y = diag(x)

z = dot(x,y)

z = dot(x,y)

computes the eigenvalue decompositon L,Q = eig(A) for symmetric matrix A with possibly repeated eigenvalues, i.e. w

Helper function for Pade approximation of expm.

Helper function for Pade approximation of expm.

Helper function for Pade approximation of expm.

Helper function for Pade approximation of expm.

Helper function for Pade approximation of expm.

z = x // y use L'Hospital's rule when leading coefficients of y_data are zero