openpilot/external/cppad/include/cppad/core/rev_sparse_jac.hpp

627 lines
16 KiB
C++

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