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cppad_py-> setup.py library whats_new_2018

library-> py_lib cpp_lib

py_lib-> py_fun py_sparse py_utility more_py

py_sparse-> py_sparse_rc py_sparse_rcv py_jac_sparsity py_hes_sparsity py_sparse_jac py_sparse_hes

py_sparse_jac-> sparse_jac_xam.py

Headings-> Syntax Purpose sparse_jac_for sparse_jac_rev f subset x pattern work n_sweep Uses Forward Example

@(@\newcommand{\B}[1]{ {\bf #1} } \newcommand{\R}[1]{ {\rm #1} }@)@Computing Sparse Jacobians
Syntax
work = cppad_py.sparse_jac_work()
n_sweep = f.sparse_jac_for(subset, x, pattern, work)
n_sweep = f.sparse_jac_rev(subset, x, pattern, work)

Purpose
We use @(@ F : \B{R}^n \rightarrow \B{R}^m @)@ to denote the function corresponding to f . The syntax above takes advantage of sparsity when computing the Jacobian @[@ J(x) = F^{(1)} (x) @]@ In the sparse case, this should be faster and take less memory than py_fun_jacobian . We use the notation @(@ J_{i,j} (x) @)@ to denote the partial of @(@ F_i (x) @)@ with respect to @(@ x_j @)@.

sparse_jac_for
This function uses first order forward mode sweeps py_fun_forward to compute multiple columns of the Jacobian at the same time.

sparse_jac_rev
This function uses first order reverse mode sweeps py_fun_reverse to compute multiple rows of the Jacobian at the same time.

f
This object must have been returned by a previous call to the python d_fun constructor. Note that the Taylor coefficients stored in f are affected by this operation; see uses forward below.

subset
This argument must have be a matrix returned by the sparse_rcv constructor. Its row size is subset.nr() == m , and its column size is subset.nc() == n . It specifies which elements of the Jacobian are computed. The input value of its value vector subset.val() does not matter. Upon return it contains the value of the corresponding elements of the Jacobian. All of the row, column pairs in subset must also appear in pattern ; i.e., they must be possibly non-zero.

x
This argument is a numpy vector with float elements and size n . It specifies the point at which to evaluate the Jacobian @(@ J(x) @)@.

pattern
This argument must have be a pattern returned by the sparse_rc constructor. Its row size is pattern.nr() == m , and its column size is pattern.nc() == n . It is a sparsity pattern for the Jacobian @(@ J(x) @)@. This argument is not used (and need not satisfy any conditions), when work is non-empty.

work
This argument must have been constructed by the call
     work = cppad_py.sparse_jac_work()
We refer to its initial value, and its value after work.clear() , as empty. If it is empty, information is stored in work . This can be used to reduce computation when a future call is for the same object f , the same member function sparse_jac_for or sparse_jac_rev, and the same subset of the Jacobian. If any of these values change, use work.clear() to empty this structure.

n_sweep
This return value is and int. If sparse_jac_for (sparse_jac_rev) is used, n_sweep is the number of first order forward (reverse) sweeps used to compute the requested Jacobian values. This is proportional to the total computational work, not counting the zero order forward sweep, or combining multiple columns (rows) into a single sweep.

Uses Forward
After each call to py_fun_forward , the object f contains the corresponding Taylor coefficients for all the variables in the operation sequence.. After a call to sparse_jac_forward or sparse_jac_rev, the zero order coefficients correspond to
     f.forward(0, x)
All the other forward mode coefficients are unspecified.

Example
sparse_jac_xam.py

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Input File: lib/python/sparse_jac.py