Reverse-mode automatic differentiation for closed-form scalar algebraic expressions, producing gradients and Hessians. Efficient sparse Hessian computation is implemented by using state-of-the-art graph coloring approaches, written in pure Julia (see src/coloring.jl). This package is primarily used by JuMP, but it works stand-alone as well.
Expressions are built around Placeholder objects (instead of symbols). These placeholders carry variable indices. The @processNLExpr macro is used to build expression trees. Examples:
using ReverseDiffSparse
x = placeholders(3)
ex = @processNLExpr sin(x[1])+sin(x[2])+sin(x[3])
# or, using the specialized sum{} syntax:
# ex = @processNLExpr sum{ sin(x[i]), i = 1:3 }
fg = genfgrad_simple(ex) # generates gradient evaluation function
out = zeros(3)
fval = fg([1.0,2.0,3.0], out) # evaluates the gradient at x = [1,2,3]
# fval = sin(1.0)+sin(2.0)+sin(3.0)
# out now stores [cos(1.0),cos(2.0),cos(3.0)]
# compute a sparse hessian matrix
x = placeholders(5)
ex = @processNLExpr sum{ x[i]^2, i =1:5 } + sin(x[1]*x[2])
sparsemat, sparsefunc = gen_hessian_sparse_mat(ex)
# sparsemat holds the structure of the Hessian matrix
# to evaluate the Hessian at a particular value [1,1,1,1,1], call
sparsefunc(ones(5), sparsemat)
# the values of the Hessian are now filled into sparsemat
For more examples of gradient and Hessian computations, see test/test_grad.jl and test/test_hessian.jl. More documentation is forthcoming. This package is experimental and still under development.