BumpFuncs
This package delivers bump functions, i.e. functions on the unit sphere that have infinitely many derivatives. Included functions cover the univariate and multivariate cases, gradients, and Hessians, with and without scale and location normalization. For further information, see e.g. a paper by Steven Johnson.
The formula used for the bump function without scale and location normalizations is simply
exp( 1 / ( ||x||^2 - 1 ) ) if ||x||<1
and zero otherwise.
BumpFuncs.bump
BumpFuncs.bump
BumpFuncs.bump
BumpFuncs.bump
BumpFuncs.dbump
BumpFuncs.dbump
BumpFuncs.dbump
BumpFuncs.dbump
BumpFuncs.ddbump
BumpFuncs.ddbump
BumpFuncs.ddbump
BumpFuncs.ddbump
BumpFuncs.bump
— Methodbump(x::Vector{Real}, x0::Vector{Real}, r::Vector{Real})
Compute a vector bump function at x centered at x0 scaled by r (element-wise)
BumpFuncs.bump
— Methodbump(x::Vector{Real})
Compute a bump function at the vector x.
BumpFuncs.bump
— Methodbump(x::Real, x0::Real, r::Real)
Compute a bump function at (x-x0) / r.
BumpFuncs.bump
— Methodbump(x::Real)
Compute a bump function at x.
BumpFuncs.dbump
— Methoddbump(x::Vector{Real}, x0::Vector{Real}, r::Vector{Real})
Compute the gradient of a vector bump function at x centered at x0 scaled by r (element-wise)
BumpFuncs.dbump
— Methoddbump(x::Vector{Real})
Compute the first derivative of a bump function at the vector x.
BumpFuncs.dbump
— Methoddbump(x::Real, x0::Real, r::Real)
Compute the first derivative of a bump function at (x-x0) / r.
BumpFuncs.dbump
— Methoddbump(x::Real)
Compute the first derivative of a bump function at x.
BumpFuncs.ddbump
— Methodddbump(x::Vector{Real}, x0::Vector{Real}, r::Vector{Real})
Compute the Hessian of a vector bump function at x centered at x0 scaled by r (element-wise)
BumpFuncs.ddbump
— Methodddbump(x::Vector{Real})
Compute the second derivative of a bump function at the vector x.
BumpFuncs.ddbump
— Methodddbump(x::Real, x0::Real, r::Real)
Compute the second derivative of a bump function at (x-x0) / r.
BumpFuncs.ddbump
— Methodddbump(x::Real)
Compute the second derivative of a bump function at x.