/usr/include/deal.II/lac/packaged_operation.h is in libdeal.ii-dev 8.4.2-2+b1.
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//
// Copyright (C) 2014 - 2016 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef dealii__packaged_operation_h
#define dealii__packaged_operation_h
#include <deal.II/base/config.h>
#include <deal.II/base/exceptions.h>
#include <deal.II/lac/vector_memory.h>
#ifdef DEAL_II_WITH_CXX11
#include <functional>
DEAL_II_NAMESPACE_OPEN
// Forward declarations:
template <typename Number> class Vector;
template <typename Range, typename Domain> class LinearOperator;
template <typename Range = Vector<double> > class PackagedOperation;
/**
* A class to store a computation.
*
* The PackagedOperation class allows lazy evaluation of expressions involving
* vectors and linear operators. This is done by storing the computational
* expression and only performing the computation when either the object is
* implicitly converted to a vector object, or <code>apply</code> (or
* <code>apply_add</code>) is invoked by hand. This avoids unnecessary
* temporary storage of intermediate results.
*
* The class essentially consists of <code>std::function</code> objects that
* store the knowledge of how to generate the result of a computation and
* store it in a vector:
* @code
* std::function<void(Range &)> apply;
* std::function<void(Range &)> apply_add;
* @endcode
*
* Similar to the LinearOperator class it also has knowledge about how to
* initialize a vector of the @p Range space:
* @code
* std::function<void(Range &, bool)> reinit_vector;
* @endcode
*
* As an example consider the addition of multiple vectors
* @code
* dealii::Vector<double> a, b, c, d;
* // ..
* dealii::Vector<double> result = a + b - c + d;
* @endcode
* or the computation of a residual $b-Ax$:
* @code
* dealii::SparseMatrix<double> A;
* dealii::Vector<double> b, x;
* // ..
* const auto op_a = linear_operator(A);
*
* dealii::Vector<double> residual = b - op_a * x;
* @endcode
* The expression <code>residual</code> is of type
* <code>PackagedOperation<dealii::Vector<double>></code>. It stores
* references to <code>A</code>, <code>b</code> and <code>x</code> and defers
* the actual computation until <code>apply</code>, or <code>apply_add</code>
* are explicitly invoked,
* @code
* dealii::Vector<double> y;
* residual.reinit_vector(y);
* residual.apply(y);
* residual.apply_add(y);
* @endcode
* or until the @p PackagedOperation object is implicitly converted:
* @code
* dealii::Vector<double> y;
* y = residual;
* y += residual;
* y -= residual;
* @endcode
*
* @author Matthias Maier, 2015
*
* @ingroup LAOperators
*/
template <typename Range> class PackagedOperation
{
public:
/**
* Create an empty PackagedOperation object. All <code>std::function</code>
* member objects are initialized with default variants that throw an
* exception upon invocation.
*/
PackagedOperation ()
{
apply = [](Range &)
{
Assert(false,
ExcMessage("Uninitialized PackagedOperation<Range>::apply called"));
};
apply_add = [](Range &)
{
Assert(false,
ExcMessage("Uninitialized PackagedOperation<Range>::apply_add called"));
};
reinit_vector = [](Range &, bool)
{
Assert(false,
ExcMessage("Uninitialized PackagedOperation<Range>::reinit_vector "
"method called"));
};
}
/**
* Default copy constructor.
*/
PackagedOperation (const PackagedOperation<Range> &) = default;
/**
* Constructor that creates a PackagedOperation object from a reference
* vector @p u. The PackagedOperation returns @p u.
*
* The PackagedOperation object that is created stores a reference to @p u.
* Thus, the vector must remain a valid reference for the whole lifetime of
* the PackagedOperation object. All changes made on @p u after the creation
* of the PackagedOperation object are reflected by the operator object.
*/
PackagedOperation (const Range &u)
{
*this = u;
}
/**
* Default copy assignment operator.
*/
PackagedOperation<Range> &operator=(const PackagedOperation<Range> &) = default;
/**
* Copy assignment operator that creates a PackagedOperation object from a
* reference vector @p u. The PackagedOperation returns @p u.
*
* The PackagedOperation object that is created stores a reference to @p u.
* Thus, the vector must remain a valid reference for the whole lifetime of
* the PackagedOperation object. All changes made on @p u after the creation
* of the PackagedOperation object are reflected by the operator object.
*/
PackagedOperation<Range> &operator=(const Range &u)
{
apply = [&u](Range &v)
{
v = u;
};
apply_add = [&u](Range &v)
{
v += u;
};
reinit_vector = [&u](Range &v, bool omit_zeroing_entries)
{
v.reinit(u, omit_zeroing_entries);
};
return *this;
}
/**
* Convert a PackagedOperation to its result.
*
* This conversion operator creates a vector of the Range space and calls
* <code>apply()</code> on it.
*/
operator Range() const
{
Range result_vector;
reinit_vector(result_vector, /*bool omit_zeroing_entries=*/ true);
apply(result_vector);
return result_vector;
}
/**
* @name In-place vector space operations
*/
//@{
/**
* Addition with a PackagedOperation @p second_comp with the same @p Range.
*/
PackagedOperation<Range> &operator+=(const PackagedOperation<Range> &second_comp)
{
*this = *this + second_comp;
return *this;
}
/**
* Subtraction with a PackagedOperation @p second_comp with the same @p
* Range.
*/
PackagedOperation<Range> &operator-=(const PackagedOperation<Range> &second_comp)
{
*this = *this - second_comp;
return *this;
}
/**
* Add a constant @p offset (of the @p Range space) to the result of a
* PackagedOperation.
*/
PackagedOperation<Range> &operator+=(const Range &offset)
{
*this = *this + PackagedOperation<Range>(offset);
return *this;
}
/**
* Subtract a constant @p offset (of the @p Range space) from the result of
* a PackagedOperation.
*/
PackagedOperation<Range> &operator-=(const Range &offset)
{
*this = *this - PackagedOperation<Range>(offset);
return *this;
}
/**
* Scalar multiplication of the PackagedOperation with a @p number.
*/
PackagedOperation<Range> &operator*=(typename Range::value_type number)
{
*this = *this * number;
return *this;
}
//@}
/**
* Store the result of the PackagedOperation in a vector v of the @p Range
* space.
*/
std::function<void(Range &v)> apply;
/**
* Add the result of the PackagedOperation to a vector v of the @p Range
* space.
*/
std::function<void(Range &v)> apply_add;
/**
* Initializes a vector v of the Range space to be directly usable as the
* destination parameter in an application of apply, or apply_add. Similar
* to the reinit functions of the vector classes, the boolean determines
* whether a fast initialization is done, i.e., if it is set to false the
* content of the vector is set to 0.
*/
std::function<void(Range &v, bool omit_zeroing_entries)> reinit_vector;
};
/**
* @name Vector space operations
*/
//@{
/**
* @relates PackagedOperation
*
* Addition of two PackagedOperation objects @p first_comp and @p second_comp
* given by vector space addition of the corresponding results.
*
* @ingroup LAOperators
*/
template <typename Range>
PackagedOperation<Range>
operator+(const PackagedOperation<Range> &first_comp,
const PackagedOperation<Range> &second_comp)
{
PackagedOperation<Range> return_comp;
return_comp.reinit_vector = first_comp.reinit_vector;
// ensure to have valid PackagedOperation objects by catching first_comp and
// second_comp by value
return_comp.apply = [first_comp, second_comp](Range &v)
{
first_comp.apply(v);
second_comp.apply_add(v);
};
return_comp.apply_add = [first_comp, second_comp](Range &v)
{
first_comp.apply_add(v);
second_comp.apply_add(v);
};
return return_comp;
}
/**
* @relates PackagedOperation
*
* Subtraction of two PackagedOperation objects @p first_comp and @p
* second_comp given by vector space addition of the corresponding results.
*
* @ingroup LAOperators
*/
template <typename Range>
PackagedOperation<Range>
operator-(const PackagedOperation<Range> &first_comp,
const PackagedOperation<Range> &second_comp)
{
PackagedOperation<Range> return_comp;
return_comp.reinit_vector = first_comp.reinit_vector;
// ensure to have valid PackagedOperation objects by catching first_comp and
// second_comp by value
return_comp.apply = [first_comp, second_comp](Range &v)
{
second_comp.apply(v);
v *= -1.;
first_comp.apply_add(v);
};
return_comp.apply_add = [first_comp, second_comp](Range &v)
{
first_comp.apply_add(v);
v *= -1.;
second_comp.apply_add(v);
v *= -1.;
};
return return_comp;
}
/**
* @relates PackagedOperation
*
* Scalar multiplication of a PackagedOperation objects @p comp with a scalar
* @p number given by a scaling PackagedOperation result with @p number.
*
* @ingroup LAOperators
*/
template <typename Range>
PackagedOperation<Range>
operator*(const PackagedOperation<Range> &comp,
typename Range::value_type number)
{
PackagedOperation<Range> return_comp;
return_comp.reinit_vector = comp.reinit_vector;
// the trivial case: number is zero
if (number == 0.)
{
return_comp.apply = [](Range &v)
{
v = 0.;
};
return_comp.apply_add = [](Range &)
{
};
}
else
{
return_comp.apply = [comp, number](Range &v)
{
comp.apply(v);
v *= number;
};
return_comp.apply_add = [comp, number](Range &v)
{
v /= number;
comp.apply_add(v);
v *= number;
};
}
return return_comp;
}
/**
* @relates PackagedOperation
*
* Scalar multiplication of a PackagedOperation objects @p comp with a scalar
* @p number given by a scaling PackagedOperation result with @p number.
*
* @ingroup LAOperators
*/
template <typename Range>
PackagedOperation<Range>
operator*(typename Range::value_type number,
const PackagedOperation<Range> &comp)
{
return comp * number;
}
/**
* @relates PackagedOperation
*
* Add a constant @p offset (of the @p Range space) to the result of a
* PackagedOperation.
*
* @ingroup LAOperators
*/
template <typename Range>
PackagedOperation<Range> operator+(const PackagedOperation<Range> &comp,
const Range &offset)
{
return comp + PackagedOperation<Range>(offset);
}
/**
* @relates PackagedOperation
*
* Add a constant @p offset (of the @p Range space) to the result of a
* PackagedOperation.
*
* @ingroup LAOperators
*/
template <typename Range>
PackagedOperation<Range> operator+(const Range &offset,
const PackagedOperation<Range> &comp)
{
return PackagedOperation<Range>(offset) + comp;
}
/**
* @relates PackagedOperation
*
* Subtract a constant @p offset (of the @p Range space) from the result of a
* PackagedOperation.
*
* @ingroup LAOperators
*/
template <typename Range>
PackagedOperation<Range> operator-(const PackagedOperation<Range> &comp,
const Range &offset)
{
return comp - PackagedOperation<Range>(offset);
}
/**
* @relates PackagedOperation
*
* Subtract a computational result from a constant @p offset (of the @p Range
* space). The result is a PackagedOperation object that applies this
* computation.
*
* @ingroup LAOperators
*/
template <typename Range>
PackagedOperation<Range> operator-(const Range &offset,
const PackagedOperation<Range> &comp)
{
return PackagedOperation<Range>(offset) - comp;
}
//@}
/**
* @name Creation of a PackagedOperation object
*/
//@{
namespace
{
// Poor man's trait class that determines whether type T is a vector:
// FIXME: Implement this as a proper type trait - similar to
// isBlockVector
template <typename T>
class has_vector_interface
{
template <typename C>
static std::false_type test(...);
template <typename C>
static std::true_type test(decltype(&C::operator+=),
decltype(&C::operator-=),
decltype(&C::l2_norm));
public:
// type is std::true_type if Matrix provides vmult_add and Tvmult_add,
// otherwise it is std::false_type
typedef decltype(test<T>(0, 0, 0)) type;
};
}
/**
* @relates PackagedOperation
*
* Create a PackagedOperation object that stores the addition of two vectors.
*
* The PackagedOperation object that is created stores a reference to @p u and
* @p v. Thus, the vectors must remain valid references for the whole lifetime
* of the PackagedOperation object. All changes made on @p u or @p v after the
* creation of the PackagedOperation object are reflected by the operator
* object.
*
* @ingroup LAOperators
*/
template <typename Range,
typename = typename std::enable_if<has_vector_interface<Range>::type::value>::type>
PackagedOperation<Range> operator+(const Range &u, const Range &v)
{
PackagedOperation<Range> return_comp;
// ensure to have valid PackagedOperation objects by catching op by value
// u is caught by reference
return_comp.reinit_vector = [&u](Range &x, bool omit_zeroing_entries)
{
x.reinit(u, omit_zeroing_entries);
};
return_comp.apply = [&u, &v](Range &x)
{
x = u;
x += v;
};
return_comp.apply_add = [&u, &v](Range &x)
{
x += u;
x += v;
};
return return_comp;
}
/**
* @relates PackagedOperation
*
* Create a PackagedOperation object that stores the subtraction of two
* vectors.
*
* The PackagedOperation object that is created stores a reference to @p u and
* @p v. Thus, the vectors must remain valid references for the whole lifetime
* of the PackagedOperation object. All changes made on @p u or @p v after the
* creation of the PackagedOperation object are reflected by the operator
* object.
*
* @ingroup LAOperators
*/
template <typename Range,
typename = typename std::enable_if<has_vector_interface<Range>::type::value>::type>
PackagedOperation<Range> operator-(const Range &u, const Range &v)
{
PackagedOperation<Range> return_comp;
// ensure to have valid PackagedOperation objects by catching op by value
// u is catched by reference
return_comp.reinit_vector = [&u](Range &x, bool omit_zeroing_entries)
{
x.reinit(u, omit_zeroing_entries);
};
return_comp.apply = [&u, &v](Range &x)
{
x = u;
x -= v;
};
return_comp.apply_add = [&u, &v](Range &x)
{
x += u;
x -= v;
};
return return_comp;
}
/**
* @relates PackagedOperation
*
* Create a PackagedOperation object that stores the scaling of a vector with
* a @p number.
*
* The PackagedOperation object that is created stores a reference to @p u.
* Thus, the vectors must remain valid references for the whole lifetime of
* the PackagedOperation object. All changes made on @p u or @p v after the
* creation of the PackagedOperation object are reflected by the operator
* object.
*
* @ingroup LAOperators
*/
template <typename Range,
typename = typename std::enable_if<has_vector_interface<Range>::type::value>::type>
PackagedOperation<Range> operator*(const Range &u,
typename Range::value_type number)
{
return PackagedOperation<Range>(u) * number;
}
/**
* @relates PackagedOperation
*
* Create a PackagedOperation object that stores the scaling of a vector with
* a @p number.
*
* The PackagedOperation object that is created stores a reference to @p u.
* Thus, the vectors must remain valid references for the whole lifetime of
* the PackagedOperation object. All changes made on @p u or @p v after the
* creation of the PackagedOperation object are reflected by the operator
* object.
*
* @ingroup LAOperators
*/
template <typename Range,
typename = typename std::enable_if<has_vector_interface<Range>::type::value>::type>
PackagedOperation<Range> operator*(typename Range::value_type number,
const Range &u)
{
return number * PackagedOperation<Range>(u);
}
/**
* @relates PackagedOperation
*
* Create a PackagedOperation object from a LinearOperator and a reference to
* a vector @p u of the Domain space. The object stores the PackagedOperation
* $\text{op} \,u$ (in matrix notation). <code>return</code>
* (<code>return_add</code>) are implemented with <code>vmult(__1,u)</code>
* (<code>vmult_add(__1,u)</code>).
*
* The PackagedOperation object that is created stores a reference to @p u.
* Thus, the vector must remain a valid reference for the whole lifetime of
* the PackagedOperation object. All changes made on @p u after the creation
* of the PackagedOperation object are reflected by the operator object.
*
* @ingroup LAOperators
*/
template <typename Range, typename Domain>
PackagedOperation<Range>
operator*(const LinearOperator<Range, Domain> &op,
const Domain &u)
{
PackagedOperation<Range> return_comp;
return_comp.reinit_vector = op.reinit_range_vector;
// ensure to have valid PackagedOperation objects by catching op by value
// u is caught by reference
return_comp.apply = [op, &u](Range &v)
{
op.vmult(v, u);
};
return_comp.apply_add = [op, &u](Range &v)
{
op.vmult_add(v, u);
};
return return_comp;
}
/**
* @relates PackagedOperation
*
* Create a PackagedOperation object from a LinearOperator and a reference to
* a vector @p u of the Range space. The object stores the PackagedOperation
* $\text{op}^T \,u$ (in matrix notation). <code>return</code>
* (<code>return_add</code>) are implemented with <code>Tvmult(__1,u)</code>
* (<code>Tvmult_add(__1,u)</code>).
*
* The PackagedOperation object that is created stores a reference to @p u.
* Thus, the vector must remain a valid reference for the whole lifetime of
* the PackagedOperation object. All changes made on @p u after the creation
* of the PackagedOperation object are reflected by the operator object.
*
* @ingroup LAOperators
*/
template <typename Range, typename Domain>
PackagedOperation<Domain>
operator*(const Range &u,
const LinearOperator<Range, Domain> &op)
{
PackagedOperation<Range> return_comp;
return_comp.reinit_vector = op.reinit_domain_vector;
// ensure to have valid PackagedOperation objects by catching op by value
// u is caught by reference
return_comp.apply = [op, &u](Domain &v)
{
op.Tvmult(v, u);
};
return_comp.apply_add = [op, &u](Domain &v)
{
op.Tvmult_add(v, u);
};
return return_comp;
}
/**
* @relates PackagedOperation
*
* Composition of a PackagedOperation object with a LinearOperator. The object
* stores the computation $\text{op} \,comp$ (in matrix notation).
*
* @ingroup LAOperators
*/
template <typename Range, typename Domain>
PackagedOperation<Range>
operator*(const LinearOperator<Range, Domain> &op,
const PackagedOperation<Domain> &comp)
{
PackagedOperation<Range> return_comp;
return_comp.reinit_vector = op.reinit_range_vector;
// ensure to have valid PackagedOperation objects by catching op by value
// u is caught by reference
return_comp.apply = [op, comp](Domain &v)
{
static GrowingVectorMemory<Range> vector_memory;
Range *i = vector_memory.alloc();
op.reinit_domain_vector(*i, /*bool omit_zeroing_entries =*/ true);
comp.apply(*i);
op.vmult(v, *i);
vector_memory.free(i);
};
return_comp.apply_add = [op, comp](Domain &v)
{
static GrowingVectorMemory<Range> vector_memory;
Range *i = vector_memory.alloc();
op.reinit_range_vector(*i, /*bool omit_zeroing_entries =*/ true);
comp.apply(*i);
op.vmult_add(v, *i);
vector_memory.free(i);
};
return return_comp;
}
/**
* @relates PackagedOperation
*
* Composition of a PackagedOperation object with a LinearOperator. The object
* stores the computation $\text{op}^T \,comp$ (in matrix notation).
*
* @ingroup LAOperators
*/
template <typename Range, typename Domain>
PackagedOperation<Domain>
operator*(const PackagedOperation<Range> &comp,
const LinearOperator<Range, Domain> &op)
{
PackagedOperation<Range> return_comp;
return_comp.reinit_vector = op.reinit_domain_vector;
// ensure to have valid PackagedOperation objects by catching op by value
// u is caught by reference
return_comp.apply = [op, comp](Domain &v)
{
static GrowingVectorMemory<Range> vector_memory;
Range *i = vector_memory.alloc();
op.reinit_range_vector(*i, /*bool omit_zeroing_entries =*/ true);
comp.apply(*i);
op.Tvmult(v, *i);
vector_memory.free(i);
};
return_comp.apply_add = [op, comp](Domain &v)
{
static GrowingVectorMemory<Range> vector_memory;
Range *i = vector_memory.alloc();
op.reinit_range_vector(*i, /*bool omit_zeroing_entries =*/ true);
comp.apply(*i);
op.Tvmult_add(v, *i);
vector_memory.free(i);
};
return return_comp;
}
//@}
DEAL_II_NAMESPACE_CLOSE
#endif // DEAL_II_WITH_CXX11
#endif
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