Compressed Differentiation

The package differentiates symbolic multivariate functions fast and efficiently

Differentiating a function of many variables a large number of times can be very slow and memory consuming. The Matlab function jacobian.m differentiates symbolic functions, but it does so without exploiting the sparse structure of the derivatives (how many nonzero derivatives there are), and the symmetry of mixed derivatives.
The new function compderivs.m performs the differentiation in a compressed manner. With each differentiation, only the nonzero unique derivatives are differentiated. The function returns compressed vectors (collected in a cell array) that contain only the nonzero unique derivatives, and matrices (collected in a cell array) that uncompress the compressed vectors.
A test file shows that compderivs.m is faster than using jacobian.m iteratively, especially if one has to evaluate the symbolic derivatives numerically. Also, memory consumption is much lower, because only the nonzero unique derivatives are stored.

Details are provided in the paper Levintal, Oren, "Fifth Order Perturbation Solution to DSGE Models".