627 lines
16 KiB
C++
627 lines
16 KiB
C++
# ifndef CPPAD_CORE_REV_SPARSE_JAC_HPP
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# define CPPAD_CORE_REV_SPARSE_JAC_HPP
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/* --------------------------------------------------------------------------
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CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-17 Bradley M. Bell
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CppAD is distributed under multiple licenses. This distribution is under
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the terms of the
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Eclipse Public License Version 1.0.
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A copy of this license is included in the COPYING file of this distribution.
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Please visit http://www.coin-or.org/CppAD/ for information on other licenses.
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-------------------------------------------------------------------------- */
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/*
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$begin RevSparseJac$$
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$spell
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optimizer
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nz
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CondExpRel
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std
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VecAD
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var
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Jacobian
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Jac
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const
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Bool
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Dep
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proportional
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$$
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$section Jacobian Sparsity Pattern: Reverse Mode$$
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$mindex RevSparseJac sparse$$
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$head Syntax$$
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$icode%s% = %f%.RevSparseJac(%q%, %r%)
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%$$
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$icode%s% = %f%.RevSparseJac(%q%, %r%, %transpose%, %dependency%)%$$
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$head Purpose$$
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We use $latex F : B^n \rightarrow B^m$$ to denote the
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$cref/AD function/glossary/AD Function/$$ corresponding to $icode f$$.
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For a fixed matrix $latex R \in B^{q \times m}$$,
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the Jacobian of $latex R * F( x )$$
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with respect to $latex x$$ is
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$latex \[
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S(x) = R * F^{(1)} ( x )
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\] $$
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Given a
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$cref/sparsity pattern/glossary/Sparsity Pattern/$$
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for $latex R$$,
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$code RevSparseJac$$ returns a sparsity pattern for the $latex S(x)$$.
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$head f$$
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The object $icode f$$ has prototype
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$codei%
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ADFun<%Base%> %f%
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%$$
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$head x$$
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If the operation sequence in $icode f$$ is
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$cref/independent/glossary/Operation/Independent/$$ of
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the independent variables in $latex x \in B^n$$,
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the sparsity pattern is valid for all values of
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(even if it has $cref CondExp$$ or $cref VecAD$$ operations).
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$head q$$
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The argument $icode q$$ has prototype
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$codei%
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size_t %q%
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%$$
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It specifies the number of rows in
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$latex R \in B^{q \times m}$$ and the
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Jacobian $latex S(x) \in B^{q \times n}$$.
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$head transpose$$
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The argument $icode transpose$$ has prototype
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$codei%
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bool %transpose%
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%$$
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The default value $code false$$ is used when $icode transpose$$ is not present.
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$head dependency$$
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The argument $icode dependency$$ has prototype
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$codei%
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bool %dependency%
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%$$
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If $icode dependency$$ is true,
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the $cref/dependency pattern/dependency.cpp/Dependency Pattern/$$
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(instead of sparsity pattern) is computed.
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$head r$$
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The argument $icode s$$ has prototype
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$codei%
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const %VectorSet%& %r%
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%$$
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see $cref/VectorSet/RevSparseJac/VectorSet/$$ below.
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$subhead transpose false$$
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If $icode r$$ has elements of type $code bool$$,
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its size is $latex q * m$$.
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If it has elements of type $code std::set<size_t>$$,
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its size is $icode q$$ and all its set elements are between
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zero and $latex m - 1$$.
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It specifies a
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$cref/sparsity pattern/glossary/Sparsity Pattern/$$
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for the matrix $latex R \in B^{q \times m}$$.
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$subhead transpose true$$
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If $icode r$$ has elements of type $code bool$$,
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its size is $latex m * q$$.
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If it has elements of type $code std::set<size_t>$$,
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its size is $icode m$$ and all its set elements are between
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zero and $latex q - 1$$.
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It specifies a
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$cref/sparsity pattern/glossary/Sparsity Pattern/$$
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for the matrix $latex R^\R{T} \in B^{m \times q}$$.
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$head s$$
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The return value $icode s$$ has prototype
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$codei%
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%VectorSet% %s%
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%$$
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see $cref/VectorSet/RevSparseJac/VectorSet/$$ below.
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$subhead transpose false$$
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If it has elements of type $code bool$$,
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its size is $latex q * n$$.
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If it has elements of type $code std::set<size_t>$$,
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its size is $icode q$$ and all its set elements are between
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zero and $latex n - 1$$.
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It specifies a
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$cref/sparsity pattern/glossary/Sparsity Pattern/$$
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for the matrix $latex S(x) \in {q \times n}$$.
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$subhead transpose true$$
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If it has elements of type $code bool$$,
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its size is $latex n * q$$.
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If it has elements of type $code std::set<size_t>$$,
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its size is $icode n$$ and all its set elements are between
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zero and $latex q - 1$$.
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It specifies a
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$cref/sparsity pattern/glossary/Sparsity Pattern/$$
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for the matrix $latex S(x)^\R{T} \in {n \times q}$$.
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$head VectorSet$$
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The type $icode VectorSet$$ must be a $cref SimpleVector$$ class with
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$cref/elements of type/SimpleVector/Elements of Specified Type/$$
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$code bool$$ or $code std::set<size_t>$$;
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see $cref/sparsity pattern/glossary/Sparsity Pattern/$$ for a discussion
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of the difference.
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$head Entire Sparsity Pattern$$
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Suppose that $latex q = m$$ and
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$latex R$$ is the $latex m \times m$$ identity matrix.
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In this case,
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the corresponding value for $icode s$$ is a
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sparsity pattern for the Jacobian $latex S(x) = F^{(1)} ( x )$$.
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$head Example$$
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$children%
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example/sparse/rev_sparse_jac.cpp
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%$$
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The file
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$cref rev_sparse_jac.cpp$$
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contains an example and test of this operation.
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It returns true if it succeeds and false otherwise.
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$end
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-----------------------------------------------------------------------------
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*/
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# include <cppad/local/std_set.hpp>
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namespace CppAD { // BEGIN_CPPAD_NAMESPACE
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/*!
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\file rev_sparse_jac.hpp
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Reverse mode Jacobian sparsity patterns.
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*/
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// =========================================================================
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// RevSparseJacCase
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/*!
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Private helper function for RevSparseJac(q, r, transpose) boolean sparsity.
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All of the description in the public member function
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\c RevSparseJac(q, r, transpose) apply.
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\param set_type
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is a \c bool value.
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This argument is used to dispatch to the proper source code
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depending on the value of \c VectorSet::value_type.
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\param transpose
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See \c RevSparseJac(q, r, transpose, dependency)
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\param dependency
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See \c RevSparseJac(q, r, transpose, dependency)
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\param q
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See \c RevSparseJac(q, r, transpose, dependency)
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\param r
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See \c RevSparseJac(q, r, transpose, dependency)
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\param s
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is the return value for the corresponding call to
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RevSparseJac(q, r, transpose).
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*/
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template <class Base>
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template <class VectorSet>
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void ADFun<Base>::RevSparseJacCase(
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bool set_type ,
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bool transpose ,
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bool dependency ,
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size_t q ,
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const VectorSet& r ,
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VectorSet& s )
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{ size_t n = Domain();
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size_t m = Range();
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// dimension of the result vector
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s.resize( q * n );
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// temporary indices
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size_t i, j;
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// check VectorSet is Simple Vector class with bool elements
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CheckSimpleVector<bool, VectorSet>();
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//
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CPPAD_ASSERT_KNOWN(
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q > 0,
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"RevSparseJac: q is not greater than zero"
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);
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CPPAD_ASSERT_KNOWN(
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size_t(r.size()) == q * m,
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"RevSparseJac: size of r is not equal to\n"
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"q times range dimension for ADFun object."
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);
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//
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// vector of sets that will hold the results
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local::sparse_pack var_sparsity;
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var_sparsity.resize(num_var_tape_, q);
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// The sparsity pattern corresponding to the dependent variables
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for(i = 0; i < m; i++)
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{ CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ );
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if( transpose )
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{ for(j = 0; j < q; j++) if( r[ i * q + j ] )
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var_sparsity.add_element( dep_taddr_[i], j );
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}
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else
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{ for(j = 0; j < q; j++) if( r[ j * m + i ] )
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var_sparsity.add_element( dep_taddr_[i], j );
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}
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}
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// evaluate the sparsity patterns
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local::RevJacSweep(
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dependency,
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n,
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num_var_tape_,
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&play_,
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var_sparsity
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);
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// return values corresponding to dependent variables
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CPPAD_ASSERT_UNKNOWN( size_t(s.size()) == q * n );
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for(j = 0; j < n; j++)
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{ CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] == (j+1) );
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// ind_taddr_[j] is operator taddr for j-th independent variable
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CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[j] ) == local::InvOp );
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// extract the result from var_sparsity
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if( transpose )
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{ for(i = 0; i < q; i++)
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s[ j * q + i ] = false;
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}
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else
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{ for(i = 0; i < q; i++)
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s[ i * n + j ] = false;
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}
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CPPAD_ASSERT_UNKNOWN( var_sparsity.end() == q );
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local::sparse_pack::const_iterator itr(var_sparsity, j+1);
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i = *itr;
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while( i < q )
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{ if( transpose )
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s[ j * q + i ] = true;
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else s[ i * n + j ] = true;
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i = *(++itr);
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}
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}
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}
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/*!
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Private helper function for RevSparseJac(q, r, transpose) set sparsity
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All of the description in the public member function
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\c RevSparseJac(q, r, transpose) apply.
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\param set_type
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is a \c std::set<size_t> object.
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This argument is used to dispatch to the proper source code
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depending on the value of \c VectorSet::value_type.
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\param transpose
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See \c RevSparseJac(q, r, transpose, dependency)
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\param dependency
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See \c RevSparseJac(q, r, transpose, dependency)
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\param q
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See \c RevSparseJac(q, r, transpose, dependency)
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\param r
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See \c RevSparseJac(q, r, transpose, dependency)
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\param s
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is the return value for the corresponding call to RevSparseJac(q, r, transpose)
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*/
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template <class Base>
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template <class VectorSet>
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void ADFun<Base>::RevSparseJacCase(
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const std::set<size_t>& set_type ,
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bool transpose ,
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bool dependency ,
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size_t q ,
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const VectorSet& r ,
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VectorSet& s )
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{ // dimension of the result vector
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if( transpose )
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s.resize( Domain() );
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else s.resize( q );
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// temporary indices
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size_t i, j;
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std::set<size_t>::const_iterator itr_1;
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// check VectorSet is Simple Vector class with sets for elements
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CheckSimpleVector<std::set<size_t>, VectorSet>(
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local::one_element_std_set<size_t>(), local::two_element_std_set<size_t>()
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);
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// domain dimensions for F
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size_t n = ind_taddr_.size();
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size_t m = dep_taddr_.size();
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CPPAD_ASSERT_KNOWN(
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q > 0,
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"RevSparseJac: q is not greater than zero"
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);
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CPPAD_ASSERT_KNOWN(
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size_t(r.size()) == q || transpose,
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"RevSparseJac: size of r is not equal to q and transpose is false."
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);
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CPPAD_ASSERT_KNOWN(
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size_t(r.size()) == m || ! transpose,
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"RevSparseJac: size of r is not equal to m and transpose is true."
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);
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// vector of lists that will hold the results
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local::sparse_list var_sparsity;
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var_sparsity.resize(num_var_tape_, q);
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// The sparsity pattern corresponding to the dependent variables
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if( transpose )
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{ for(i = 0; i < m; i++)
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{ itr_1 = r[i].begin();
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while(itr_1 != r[i].end())
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{ j = *itr_1++;
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CPPAD_ASSERT_KNOWN(
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j < q,
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"RevSparseJac: transpose is true and element of the set\n"
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"r[i] has value greater than or equal q."
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);
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CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ );
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var_sparsity.add_element( dep_taddr_[i], j );
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}
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}
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}
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else
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{ for(i = 0; i < q; i++)
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{ itr_1 = r[i].begin();
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while(itr_1 != r[i].end())
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{ j = *itr_1++;
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CPPAD_ASSERT_KNOWN(
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j < m,
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"RevSparseJac: transpose is false and element of the set\n"
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"r[i] has value greater than or equal range dimension."
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);
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CPPAD_ASSERT_UNKNOWN( dep_taddr_[j] < num_var_tape_ );
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var_sparsity.add_element( dep_taddr_[j], i );
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}
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}
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}
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// evaluate the sparsity patterns
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local::RevJacSweep(
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dependency,
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n,
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num_var_tape_,
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&play_,
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var_sparsity
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);
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// return values corresponding to dependent variables
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CPPAD_ASSERT_UNKNOWN( size_t(s.size()) == q || transpose );
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CPPAD_ASSERT_UNKNOWN( size_t(s.size()) == n || ! transpose );
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for(j = 0; j < n; j++)
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{ CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] == (j+1) );
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// ind_taddr_[j] is operator taddr for j-th independent variable
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CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[j] ) == local::InvOp );
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CPPAD_ASSERT_UNKNOWN( var_sparsity.end() == q );
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local::sparse_list::const_iterator itr_2(var_sparsity, j+1);
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i = *itr_2;
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while( i < q )
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{ if( transpose )
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s[j].insert(i);
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else s[i].insert(j);
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i = *(++itr_2);
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}
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}
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}
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// =========================================================================
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// RevSparseJac
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/*!
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User API for Jacobian sparsity patterns using reverse mode.
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The C++ source code corresponding to this operation is
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\verbatim
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s = f.RevSparseJac(q, r, transpose, dependency)
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\endverbatim
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\tparam Base
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is the base type for this recording.
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\tparam VectorSet
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is a simple vector with elements of type \c bool.
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or \c std::set<size_t>.
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\param q
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is the number of rows in the matrix \f$ R \f$.
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\param r
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is a sparsity pattern for the matrix \f$ R \f$.
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\param transpose
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are the sparsity patterns for \f$ R \f$ and \f$ S(x) \f$ transposed.
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\param dependency
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Are the derivatives with respect to left and right of the expression below
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considered to be non-zero:
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\code
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CondExpRel(left, right, if_true, if_false)
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\endcode
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This is used by the optimizer to obtain the correct dependency relations.
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\return
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If \c transpose is false (true), the return value is a sparsity pattern
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for \f$ S(x) \f$ (\f$ S(x)^T \f$) where
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\f[
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S(x) = R * F^{(1)} (x)
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\f]
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and \f$ F \f$ is the function corresponding to the operation sequence
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and \a x is any argument value.
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If \c VectorSet::value_type is \c bool,
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the return value has size \f$ q * n \f$ ( \f$ n * q \f$).
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If \c VectorSet::value_type is \c std::set<size_t>,
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the return value has size \f$ q \f$ ( \f$ n \f$)
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and with all its elements between zero and \f$ n - 1 \f$ (\f$ q - 1 \f$).
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*/
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template <class Base>
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template <class VectorSet>
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VectorSet ADFun<Base>::RevSparseJac(
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size_t q ,
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const VectorSet& r ,
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bool transpose ,
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bool dependency )
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{
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VectorSet s;
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typedef typename VectorSet::value_type Set_type;
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RevSparseJacCase(
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Set_type() ,
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transpose ,
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dependency ,
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q ,
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r ,
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s
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);
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return s;
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}
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// ===========================================================================
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// RevSparseJacCheckpoint
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/*!
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Reverse mode Jacobian sparsity calculation used by checkpoint functions.
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\tparam Base
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is the base type for this recording.
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\param transpose
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is true (false) s is equal to \f$ S(x) \f$ (\f$ S(x)^T \f$)
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where
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\f[
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S(x) = R * F^{(1)} (x)
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\f]
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where \f$ F \f$ is the function corresponding to the operation sequence
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and \f$ x \f$ is any argument value.
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\param q
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is the number of rows in the matrix \f$ R \f$.
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\param r
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is a sparsity pattern for the matrix \f$ R \f$.
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\param transpose
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are the sparsity patterns for \f$ R \f$ and \f$ S(x) \f$ transposed.
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\param dependency
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Are the derivatives with respect to left and right of the expression below
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considered to be non-zero:
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\code
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CondExpRel(left, right, if_true, if_false)
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\endcode
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This is used by the optimizer to obtain the correct dependency relations.
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\param s
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The input size and elements of s do not matter.
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On output, s is the sparsity pattern for the matrix \f$ S(x) \f$
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or \f$ S(x)^T \f$ depending on transpose.
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*/
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template <class Base>
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void ADFun<Base>::RevSparseJacCheckpoint(
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size_t q ,
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const local::sparse_list& r ,
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bool transpose ,
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bool dependency ,
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local::sparse_list& s )
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{ size_t n = Domain();
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size_t m = Range();
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# ifndef NDEBUG
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if( transpose )
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{ CPPAD_ASSERT_UNKNOWN( r.n_set() == m );
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CPPAD_ASSERT_UNKNOWN( r.end() == q );
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}
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else
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{ CPPAD_ASSERT_UNKNOWN( r.n_set() == q );
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CPPAD_ASSERT_UNKNOWN( r.end() == m );
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}
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for(size_t i = 0; i < m; i++)
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CPPAD_ASSERT_UNKNOWN( dep_taddr_[i] < num_var_tape_ );
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# endif
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|
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// holds reverse Jacobian sparsity pattern for all variables
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local::sparse_list var_sparsity;
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var_sparsity.resize(num_var_tape_, q);
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|
|
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// set sparsity pattern for dependent variables
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if( transpose )
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{ for(size_t i = 0; i < m; i++)
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{ local::sparse_list::const_iterator itr(r, i);
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size_t j = *itr;
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while( j < q )
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{ var_sparsity.add_element( dep_taddr_[i], j );
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j = *(++itr);
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}
|
|
}
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|
}
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|
else
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|
{ for(size_t j = 0; j < q; j++)
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{ local::sparse_list::const_iterator itr(r, j);
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size_t i = *itr;
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while( i < m )
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{ var_sparsity.add_element( dep_taddr_[i], j );
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i = *(++itr);
|
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}
|
|
}
|
|
}
|
|
|
|
// evaluate the sparsity pattern for all variables
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|
local::RevJacSweep(
|
|
dependency,
|
|
n,
|
|
num_var_tape_,
|
|
&play_,
|
|
var_sparsity
|
|
);
|
|
|
|
// dimension the return value
|
|
if( transpose )
|
|
s.resize(n, m);
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|
else
|
|
s.resize(m, n);
|
|
|
|
// return values corresponding to independent variables
|
|
for(size_t j = 0; j < n; j++)
|
|
{ CPPAD_ASSERT_UNKNOWN( ind_taddr_[j] == (j+1) );
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|
|
|
// ind_taddr_[j] is operator taddr for j-th independent variable
|
|
CPPAD_ASSERT_UNKNOWN( play_.GetOp( ind_taddr_[j] ) == local::InvOp );
|
|
|
|
// extract the result from var_sparsity
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|
CPPAD_ASSERT_UNKNOWN( var_sparsity.end() == q );
|
|
local::sparse_list::const_iterator itr(var_sparsity, j+1);
|
|
size_t i = *itr;
|
|
while( i < q )
|
|
{ if( transpose )
|
|
s.add_element(j, i);
|
|
else
|
|
s.add_element(i, j);
|
|
i = *(++itr);
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
} // END_CPPAD_NAMESPACE
|
|
# endif
|