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Up-> cppad_py library py_lib py_sparse py_jac_sparsity

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_jac_sparsity-> sparse_jac_pattern_xam.py

Headings-> Syntax Purpose ---..for_jac_sparsity ---..rev_jac_sparsity x f pattern_in pattern_out Sparsity for Entire Jacobian Example

@(@\newcommand{\B}[1]{ {\bf #1} } \newcommand{\R}[1]{ {\rm #1} }@)@Jacobian Sparsity Patterns
Syntax
f.for_jac_sparsity(pattern_in, pattern_out)
f.rev_jac_sparsity(pattern_in, pattern_out)

Purpose
We use @(@ F : \B{R}^n \rightarrow \B{R}^m @)@ to denote the function corresponding to the operation sequence stored in f .

for_jac_sparsity
Fix @(@ R \in \B{R}^{n \times \ell} @)@ and define the function @[@ J(x) = F^{(1)} ( x ) * R @]@ Given a sparsity pattern for @(@ R @)@, for_jac_sparsity computes a sparsity pattern for @(@ J(x) @)@.

rev_jac_sparsity
Fix @(@ R \in \B{R}^{\ell \times m} @)@ and define the function @[@ J(x) = R * F^{(1)} ( x ) @]@ Given a sparsity pattern for @(@ R @)@, rev_jac_sparsity computes a sparsity pattern for @(@ J(x) @)@.

x
Note that a sparsity pattern for @(@ J(x) @)@ corresponds to the operation sequence stored in f and does not depend on the argument x .

f
This object must have been returned by a previous call to the python d_fun constructor. The object f is not constant when using for_jac_sparsity. After a call to for_jac_sparsity, a sparsity pattern for each of the variables in the operation sequence is held in f for possible later use during reverse Hessian sparsity calculations.

pattern_in
This argument must have be a pattern returned by the sparse_rc constructor. It specifies the sparsity pattern for @(@ R @)@.

pattern_out
This argument must have be a pattern returned by the sparse_rc constructor. This input value of pattern_out does not matter. Upon return pattern_out is a sparsity pattern for @(@ J(x) @)@.

Sparsity for Entire Jacobian
Suppose that @(@ R @)@ is the identity matrix. In this case, pattern_out is a sparsity pattern for @(@ F^{(1)} ( x ) @)@.

Example
Python

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Input File: lib/python/jac_sparsity.omh