z = x * y

z = outer(x,y)

z = outer(x,y) where y is UTPM and x is ndarray

z = outer(x,y) where x is UTPM and y is ndarray

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

pullback of the linear form of the cholesky decomposition

pullback function of y = pow(x,r)

computes the qr decomposition (Q,R) = qr(A) <===> QR = A INPUTS: A_data (D,P,M,N) array regular m

computation of QR = A INPUTS: A (M,N) UTPM instance with A.data[0,:] have all rank N, M >= N OUTP

computes the pullback of the qr decomposition (Q,R) = qr(A) <===> QR = A A_data (D,P,M,N) array regular m

computes the pullback of the qr decomposition (Q,R) = qr(A) <===> QR = A A_data (D,P,M,N) array regular m

solves the linear system of equations for y:: A y = x when A is a simple (N,N) float array

solves the linear system of equations for y:: A y = x where x is simple (N,K) float array

computes one element of the sum in the evaluation of gamma, i.e. the equation below 13.13 in Griewanks Book

build lower triangular matrix with all ones, i.e. PL = [[0,0,0], [1,0,0], [1,1,0]]

operation to extract UTP coefficients of x defined by the slice sl creates a new UTPM instance where the coefficients have th

given a multi-index this function returns at to which position in the derivative tensor this mult-index points to. It is used to populate a

Use hypergeometric functions. Note that d = 2*h - 1 following Kimura 1957. The rate mu is a catch-all scaling factor. The finite dist

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This glues together the analytical solution. This is a second attempt, and this time it is with respect to the mpmath hypergeometric func

function as sent in the email by alex

compute the gradient of f in the forward mode of AD

compute the hessian of f in the forward mode of AD

compute the hessian of f in the forward mode of AD