/usr/include/madness/mra/mra.h is in libmadness-dev 0.10-3.
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This file is part of MADNESS.
Copyright (C) 2007,2010 Oak Ridge National Laboratory
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
For more information please contact:
Robert J. Harrison
Oak Ridge National Laboratory
One Bethel Valley Road
P.O. Box 2008, MS-6367
email: harrisonrj@ornl.gov
tel: 865-241-3937
fax: 865-572-0680
*/
#ifndef MADNESS_MRA_MRA_H__INCLUDED
#define MADNESS_MRA_MRA_H__INCLUDED
/*!
\file mra/mra.h
\brief Main include file for MADNESS and defines \c Function interface
\addtogroup mra
*/
#include <madness/world/MADworld.h>
#include <madness/misc/misc.h>
#include <madness/tensor/tensor.h>
#define FUNCTION_INSTANTIATE_1
#define FUNCTION_INSTANTIATE_2
#define FUNCTION_INSTANTIATE_3
#if !defined(HAVE_IBMBGP) || !defined(HAVE_IBMBGQ)
#define FUNCTION_INSTANTIATE_4
#define FUNCTION_INSTANTIATE_5
#define FUNCTION_INSTANTIATE_6
#endif
static const bool VERIFY_TREE = false; //true
namespace madness {
void startup(World& world, int argc, char** argv);
}
#include <madness/mra/key.h>
#include <madness/mra/twoscale.h>
#include <madness/mra/legendre.h>
#include <madness/mra/indexit.h>
#include <madness/world/parallel_archive.h>
#include <madness/world/worlddc.h>
#include <madness/mra/funcdefaults.h>
#include <madness/mra/function_factory.h>
#include <madness/mra/lbdeux.h>
#include <madness/mra/funcimpl.h>
// some forward declarations
namespace madness {
template<typename T, std::size_t NDIM>
class FunctionImpl;
template<typename T, std::size_t NDIM>
class Function;
template<typename T, std::size_t NDIM>
class FunctionNode;
template<typename T, std::size_t NDIM>
class FunctionFactory;
template<typename T, std::size_t NDIM>
class FunctionFunctorInterface;
template<typename T, std::size_t NDIM>
struct leaf_op;
template<typename T, std::size_t NDIM>
struct mul_leaf_op;
template<typename T, std::size_t NDIM>
struct hartree_leaf_op;
template<typename T, std::size_t NDIM, std::size_t LDIM, typename opT>
struct hartree_convolute_leaf_op;
template<typename T, std::size_t NDIM, typename opT>
struct op_leaf_op;
template<typename T, std::size_t NDIM>
struct error_leaf_op;
}
namespace madness {
/// \ingroup mra
/// \addtogroup function
/// A multiresolution adaptive numerical function
template <typename T, std::size_t NDIM>
class Function : public archive::ParallelSerializableObject {
// We make all of the content of Function and FunctionImpl
// public with the intent of avoiding the cumbersome forward
// and friend declarations. However, this open access should
// not be abused.
private:
std::shared_ptr< FunctionImpl<T,NDIM> > impl;
public:
typedef FunctionImpl<T,NDIM> implT;
typedef FunctionNode<T,NDIM> nodeT;
typedef FunctionFactory<T,NDIM> factoryT;
typedef Vector<double,NDIM> coordT; ///< Type of vector holding coordinates
/// Asserts that the function is initialized
inline void verify() const {
MADNESS_ASSERT(impl);
}
/// Returns true if the function is initialized
bool is_initialized() const {
return impl.get();
}
/// Default constructor makes uninitialized function. No communication.
/// An unitialized function can only be assigned to. Any other operation will throw.
Function() : impl() {}
/// Constructor from FunctionFactory provides named parameter idiom. Possible non-blocking communication.
Function(const factoryT& factory)
: impl(new FunctionImpl<T,NDIM>(factory)) {
PROFILE_MEMBER_FUNC(Function);
}
/// Copy constructor is \em shallow. No communication, works in either basis.
Function(const Function<T,NDIM>& f)
: impl(f.impl) {
}
/// Assignment is \em shallow. No communication, works in either basis.
Function<T,NDIM>& operator=(const Function<T,NDIM>& f) {
PROFILE_MEMBER_FUNC(Function);
if (this != &f) impl = f.impl;
return *this;
}
/// Destruction of any underlying implementation is deferred to next global fence.
~Function() {}
/// Evaluates the function at a point in user coordinates. Possible non-blocking comm.
/// Only the invoking process will receive the result via the future
/// though other processes may be involved in the evaluation.
///
/// Throws if function is not initialized.
Future<T> eval(const coordT& xuser) const {
PROFILE_MEMBER_FUNC(Function);
const double eps=1e-15;
verify();
MADNESS_ASSERT(!is_compressed());
coordT xsim;
user_to_sim(xuser,xsim);
// If on the boundary, move the point just inside the
// volume so that the evaluation logic does not fail
for (std::size_t d=0; d<NDIM; ++d) {
if (xsim[d] < -eps) {
MADNESS_EXCEPTION("eval: coordinate lower-bound error in dimension", d);
}
else if (xsim[d] < eps) {
xsim[d] = eps;
}
if (xsim[d] > 1.0+eps) {
MADNESS_EXCEPTION("eval: coordinate upper-bound error in dimension", d);
}
else if (xsim[d] > 1.0-eps) {
xsim[d] = 1.0-eps;
}
}
Future<T> result;
impl->eval(xsim, impl->key0(), result.remote_ref(impl->world));
return result;
}
/// Evaluate function only if point is local returning (true,value); otherwise return (false,0.0)
/// maxlevel is the maximum depth to search down to --- the max local depth can be
/// computed with max_local_depth();
std::pair<bool,T> eval_local_only(const Vector<double,NDIM>& xuser, Level maxlevel) const {
const double eps=1e-15;
verify();
MADNESS_ASSERT(!is_compressed());
coordT xsim;
user_to_sim(xuser,xsim);
// If on the boundary, move the point just inside the
// volume so that the evaluation logic does not fail
for (std::size_t d=0; d<NDIM; ++d) {
if (xsim[d] < -eps) {
MADNESS_EXCEPTION("eval: coordinate lower-bound error in dimension", d);
}
else if (xsim[d] < eps) {
xsim[d] = eps;
}
if (xsim[d] > 1.0+eps) {
MADNESS_EXCEPTION("eval: coordinate upper-bound error in dimension", d);
}
else if (xsim[d] > 1.0-eps) {
xsim[d] = 1.0-eps;
}
}
return impl->eval_local_only(xsim,maxlevel);
}
/// Only the invoking process will receive the result via the future
/// though other processes may be involved in the evaluation.
///
/// Throws if function is not initialized.
///
/// This function is a minimally-modified version of eval()
Future<Level> evaldepthpt(const coordT& xuser) const {
PROFILE_MEMBER_FUNC(Function);
const double eps=1e-15;
verify();
MADNESS_ASSERT(!is_compressed());
coordT xsim;
user_to_sim(xuser,xsim);
// If on the boundary, move the point just inside the
// volume so that the evaluation logic does not fail
for (std::size_t d=0; d<NDIM; ++d) {
if (xsim[d] < -eps) {
MADNESS_EXCEPTION("eval: coordinate lower-bound error in dimension", d);
}
else if (xsim[d] < eps) {
xsim[d] = eps;
}
if (xsim[d] > 1.0+eps) {
MADNESS_EXCEPTION("eval: coordinate upper-bound error in dimension", d);
}
else if (xsim[d] > 1.0-eps) {
xsim[d] = 1.0-eps;
}
}
Future<Level> result;
impl->evaldepthpt(xsim, impl->key0(), result.remote_ref(impl->world));
return result;
}
/// Evaluates the function rank at a point in user coordinates. Possible non-blocking comm.
/// Only the invoking process will receive the result via the future
/// though other processes may be involved in the evaluation.
///
/// Throws if function is not initialized.
Future<long> evalR(const coordT& xuser) const {
PROFILE_MEMBER_FUNC(Function);
const double eps=1e-15;
verify();
MADNESS_ASSERT(!is_compressed());
coordT xsim;
user_to_sim(xuser,xsim);
// If on the boundary, move the point just inside the
// volume so that the evaluation logic does not fail
for (std::size_t d=0; d<NDIM; ++d) {
if (xsim[d] < -eps) {
MADNESS_EXCEPTION("eval: coordinate lower-bound error in dimension", d);
}
else if (xsim[d] < eps) {
xsim[d] = eps;
}
if (xsim[d] > 1.0+eps) {
MADNESS_EXCEPTION("eval: coordinate upper-bound error in dimension", d);
}
else if (xsim[d] > 1.0-eps) {
xsim[d] = 1.0-eps;
}
}
Future<long> result;
impl->evalR(xsim, impl->key0(), result.remote_ref(impl->world));
return result;
}
/// Evaluates a cube/slice of points (probably for plotting) ... collective but no fence necessary
/// All processes recieve the entire result (which is a rather severe limit
/// on the size of the cube that is possible).
/// Set eval_refine=true to return the refinment levels of
/// the given function.
/// @param[in] cell A Tensor describe the cube where the function to be evaluated in
/// @param[in] npt How many points to evaluate in each dimension
/// @param[in] eval_refine Wether to return the refinment levels of the given function
Tensor<T> eval_cube(const Tensor<double>& cell,
const std::vector<long>& npt,
bool eval_refine = false) const {
MADNESS_ASSERT(static_cast<std::size_t>(cell.dim(0))>=NDIM && cell.dim(1)==2 && npt.size()>=NDIM);
PROFILE_MEMBER_FUNC(Function);
const double eps=1e-14;
verify();
reconstruct();
coordT simlo, simhi;
for (std::size_t d=0; d<NDIM; ++d) {
simlo[d] = cell(d,0);
simhi[d] = cell(d,1);
}
user_to_sim(simlo, simlo);
user_to_sim(simhi, simhi);
// Move the bounding box infintesimally inside dyadic
// points so that the evaluation logic does not fail
for (std::size_t d=0; d<NDIM; ++d) {
MADNESS_ASSERT(simhi[d] >= simlo[d]);
MADNESS_ASSERT(simlo[d] >= 0.0);
MADNESS_ASSERT(simhi[d] <= 1.0);
double delta = eps*(simhi[d]-simlo[d]);
simlo[d] += delta;
simhi[d] -= 2*delta; // deliberate asymmetry
}
return impl->eval_plot_cube(simlo, simhi, npt, eval_refine);
}
/// Evaluates the function at a point in user coordinates. Collective operation.
/// Throws if function is not initialized.
///
/// This function calls eval, blocks until the result is
/// available and then broadcasts the result to everyone.
/// Therefore, if you are evaluating many points in parallel
/// it is \em vastly less efficient than calling eval
/// directly, saving the futures, and then forcing all of the
/// results.
T operator()(const coordT& xuser) const {
PROFILE_MEMBER_FUNC(Function);
verify();
if (is_compressed()) reconstruct();
T result;
if (impl->world.rank() == 0) result = eval(xuser).get();
impl->world.gop.broadcast(result);
//impl->world.gop.fence();
return result;
}
/// Evaluates the function at a point in user coordinates. Collective operation.
/// See "operator()(const coordT& xuser)" for more info
T operator()(double x, double y=0, double z=0, double xx=0, double yy=0, double zz=0) const {
coordT r;
r[0] = x;
if (NDIM>=2) r[1] = y;
if (NDIM>=3) r[2] = z;
if (NDIM>=4) r[3] = xx;
if (NDIM>=5) r[4] = yy;
if (NDIM>=6) r[5] = zz;
return (*this)(r);
}
/// Throws if function is not initialized.
///
/// This function mimics operator() by going through the
/// tree looking for the depth of the tree at the point.
/// It blocks until the result is
/// available and then broadcasts the result to everyone.
/// Therefore, if you are evaluating many points in parallel
/// it is \em vastly less efficient than calling evaldepthpt
/// directly, saving the futures, and then forcing all of the
/// results.
Level depthpt(const coordT& xuser) const {
PROFILE_MEMBER_FUNC(Function);
verify();
if (is_compressed()) reconstruct();
Level result;
if (impl->world.rank() == 0) result = evaldepthpt(xuser).get();
impl->world.gop.broadcast(result);
//impl->world.gop.fence();
return result;
}
/// Returns an estimate of the difference ||this-func||^2 from local data
/// No communication is performed. If the function is not
/// reconstructed, it throws an exception. To get the global
/// value either do a global sum of the local values or call
/// errsq
/// @param[in] func Templated interface to the a user specified function
template <typename funcT>
double errsq_local(const funcT& func) const {
PROFILE_MEMBER_FUNC(Function);
verify();
if (is_compressed()) MADNESS_EXCEPTION("Function:errsq_local:not reconstructed",0);
return impl->errsq_local(func);
}
/// Returns an estimate of the difference ||this-func|| ... global sum performed
/// If the function is compressed, it is reconstructed first. For efficient use
/// especially with many functions, reconstruct them all first, and use errsq_local
/// instead so you can perform a global sum on all at the same time.
/// @param[in] func Templated interface to the a user specified function
template <typename funcT>
double err(const funcT& func) const {
PROFILE_MEMBER_FUNC(Function);
verify();
if (VERIFY_TREE) verify_tree();
if (is_compressed()) reconstruct();
if (VERIFY_TREE) verify_tree();
double local = impl->errsq_local(func);
impl->world.gop.sum(local);
impl->world.gop.fence();
return sqrt(local);
}
/// Verifies the tree data structure ... global sync implied
void verify_tree() const {
PROFILE_MEMBER_FUNC(Function);
if (impl) impl->verify_tree();
}
/// Returns true if compressed, false otherwise. No communication.
/// If the function is not initialized, returns false.
bool is_compressed() const {
PROFILE_MEMBER_FUNC(Function);
if (impl)
return impl->is_compressed();
else
return false;
}
/// Returns the number of nodes in the function tree ... collective global sum
std::size_t tree_size() const {
PROFILE_MEMBER_FUNC(Function);
if (!impl) return 0;
return impl->tree_size();
}
/// print some info about this
void print_size(const std::string name) const {
if (!impl) print("function",name,"not assigned yet");
impl->print_size(name);
}
/// Returns the maximum depth of the function tree ... collective global sum
std::size_t max_depth() const {
PROFILE_MEMBER_FUNC(Function);
if (!impl) return 0;
return impl->max_depth();
}
/// Returns the maximum local depth of the function tree ... no communications
std::size_t max_local_depth() const {
PROFILE_MEMBER_FUNC(Function);
if (!impl) return 0;
return impl->max_local_depth();
}
/// Returns the max number of nodes on a processor
std::size_t max_nodes() const {
PROFILE_MEMBER_FUNC(Function);
if (!impl) return 0;
return impl->max_nodes();
}
/// Returns the min number of nodes on a processor
std::size_t min_nodes() const {
PROFILE_MEMBER_FUNC(Function);
if (!impl) return 0;
return impl->min_nodes();
}
/// Returns the number of coefficients in the function ... collective global sum
std::size_t size() const {
PROFILE_MEMBER_FUNC(Function);
if (!impl) return 0;
return impl->size();
}
/// Returns value of autorefine flag. No communication.
bool autorefine() const {
PROFILE_MEMBER_FUNC(Function);
if (!impl) return true;
return impl->get_autorefine();
}
/// Sets the value of the autorefine flag. Optional global fence.
/// A fence is required to ensure consistent global state.
void set_autorefine(bool value, bool fence = true) {
PROFILE_MEMBER_FUNC(Function);
verify();
impl->set_autorefine(value);
if (fence) impl->world.gop.fence();
}
/// Returns value of truncation threshold. No communication.
double thresh() const {
PROFILE_MEMBER_FUNC(Function);
if (!impl) return 0.0;
return impl->get_thresh();
}
/// Sets the vaule of the truncation threshold. Optional global fence.
/// A fence is required to ensure consistent global state.
void set_thresh(double value, bool fence = true) {
PROFILE_MEMBER_FUNC(Function);
verify();
impl->set_thresh(value);
if (fence) impl->world.gop.fence();
}
/// Returns the number of multiwavelets (k). No communication.
int k() const {
PROFILE_MEMBER_FUNC(Function);
verify();
return impl->get_k();
}
/// Truncate the function with optional fence. Compresses with fence if not compressed.
/// If the truncation threshold is less than or equal to zero the default value
/// specified when the function was created is used.
/// If the function is not initialized, it just returns.
///
/// Returns this for chaining.
/// @param[in] tol Tolerance for truncating the coefficients. Default 0.0 means use the implimentation's member value \c thresh instead.
/// @param[in] fence Do fence
Function<T,NDIM>& truncate(double tol = 0.0, bool fence = true) {
PROFILE_MEMBER_FUNC(Function);
if (!impl) return *this;
verify();
// if (!is_compressed()) compress();
impl->truncate(tol,fence);
if (VERIFY_TREE) verify_tree();
return *this;
}
/// Returns a shared-pointer to the implementation
const std::shared_ptr< FunctionImpl<T,NDIM> >& get_impl() const {
PROFILE_MEMBER_FUNC(Function);
verify();
return impl;
}
/// Replace current FunctionImpl with provided new one
void set_impl(const std::shared_ptr< FunctionImpl<T,NDIM> >& impl) {
PROFILE_MEMBER_FUNC(Function);
this->impl = impl;
}
/// Replace the current functor with the provided new one
/// presumably the new functor will be a CompositeFunctor, which will
/// change the behavior of the function: multiply the functor with the function
void set_functor(const std::shared_ptr<FunctionFunctorInterface<T, NDIM> > functor) {
this->impl->set_functor(functor);
print("set functor in mra.h");
}
bool is_on_demand() const {return this->impl->is_on_demand();}
/// Replace current FunctionImpl with a new one using the same parameters & map as f
/// If zero is true the function is initialized to zero, otherwise it is empty
template <typename R>
void set_impl(const Function<R,NDIM>& f, bool zero = true) {
impl = std::shared_ptr<implT>(new implT(*f.get_impl(), f.get_pmap(), zero));
}
/// Returns the world
World& world() const {
PROFILE_MEMBER_FUNC(Function);
verify();
return impl->world;
}
/// Returns a shared pointer to the process map
const std::shared_ptr< WorldDCPmapInterface< Key<NDIM> > >& get_pmap() const {
PROFILE_MEMBER_FUNC(Function);
verify();
return impl->get_pmap();
}
/// Returns the square of the norm of the local function ... no communication
/// Works in either basis
double norm2sq_local() const {
PROFILE_MEMBER_FUNC(Function);
verify();
return impl->norm2sq_local();
}
/// Returns the 2-norm of the function ... global sum ... works in either basis
/// See comments for err() w.r.t. applying to many functions.
double norm2() const {
PROFILE_MEMBER_FUNC(Function);
verify();
if (VERIFY_TREE) verify_tree();
double local = impl->norm2sq_local();
impl->world.gop.sum(local);
impl->world.gop.fence();
return sqrt(local);
}
/// Initializes information about the function norm at all length scales
void norm_tree(bool fence = true) const {
PROFILE_MEMBER_FUNC(Function);
verify();
if (VERIFY_TREE) verify_tree();
if (is_compressed()) reconstruct();
const_cast<Function<T,NDIM>*>(this)->impl->norm_tree(fence);
}
/// Compresses the function, transforming into wavelet basis. Possible non-blocking comm.
/// By default fence=true meaning that this operation completes before returning,
/// otherwise if fence=false it returns without fencing and the user must invoke
/// world.gop.fence() to assure global completion before using the function
/// for other purposes.
///
/// Noop if already compressed or if not initialized.
///
/// Since reconstruction/compression do not discard information we define them
/// as const ... "logical constness" not "bitwise constness".
const Function<T,NDIM>& compress(bool fence = true) const {
PROFILE_MEMBER_FUNC(Function);
if (!impl || is_compressed()) return *this;
if (VERIFY_TREE) verify_tree();
const_cast<Function<T,NDIM>*>(this)->impl->compress(false, false, false, fence);
return *this;
}
/// Compresses the function retaining scaling function coeffs. Possible non-blocking comm.
/// By default fence=true meaning that this operation completes before returning,
/// otherwise if fence=false it returns without fencing and the user must invoke
/// world.gop.fence() to assure global completion before using the function
/// for other purposes.
///
/// Noop if already compressed or if not initialized.
void nonstandard(bool keepleaves, bool fence=true) {
PROFILE_MEMBER_FUNC(Function);
verify();
if (impl->is_nonstandard()) return;
if (VERIFY_TREE) verify_tree();
if (is_compressed()) reconstruct();
impl->compress(true, keepleaves, false, fence);
}
/// Converts the function from nonstandard form to standard form. Possible non-blocking comm.
/// By default fence=true meaning that this operation completes before returning,
/// otherwise if fence=false it returns without fencing and the user must invoke
/// world.gop.fence() to assure global completion before using the function
/// for other purposes.
///
/// Must be already compressed.
void standard(bool fence = true) {
PROFILE_MEMBER_FUNC(Function);
verify();
MADNESS_ASSERT(is_compressed());
impl->standard(fence);
if (fence && VERIFY_TREE) verify_tree();
}
/// Reconstructs the function, transforming into scaling function basis. Possible non-blocking comm.
/// By default fence=true meaning that this operation completes before returning,
/// otherwise if fence=false it returns without fencing and the user must invoke
/// world.gop.fence() to assure global completion before using the function
/// for other purposes.
///
/// Noop if already reconstructed or if not initialized.
///
/// Since reconstruction/compression do not discard information we define them
/// as const ... "logical constness" not "bitwise constness".
void reconstruct(bool fence = true) const {
PROFILE_MEMBER_FUNC(Function);
if (!impl || !is_compressed()) return;
const_cast<Function<T,NDIM>*>(this)->impl->reconstruct(fence);
if (fence && VERIFY_TREE) verify_tree(); // Must be after in case nonstandard
}
/// Sums scaling coeffs down tree restoring state with coeffs only at leaves. Optional fence. Possible non-blocking comm.
void sum_down(bool fence = true) const {
PROFILE_MEMBER_FUNC(Function);
verify();
MADNESS_ASSERT(!is_compressed());
const_cast<Function<T,NDIM>*>(this)->impl->sum_down(fence);
if (fence && VERIFY_TREE) verify_tree(); // Must be after in case nonstandard
}
/// Inplace autorefines the function. Optional fence. Possible non-blocking comm.
template <typename opT>
void refine_general(const opT& op, bool fence = true) const {
PROFILE_MEMBER_FUNC(Function);
verify();
if (is_compressed()) reconstruct();
impl->refine(op, fence);
}
struct autorefine_square_op {
bool operator()(implT* impl, const Key<NDIM>& key, const nodeT& t) const {
return impl->autorefine_square_test(key, t);
}
template <typename Archive> void serialize (Archive& ar) {}
};
/// Inplace autorefines the function using same test as for squaring.
void refine(bool fence = true) {
refine_general(autorefine_square_op(), fence);
}
/// Inplace broadens support in scaling function basis
void broaden(const BoundaryConditions<NDIM>& bc=FunctionDefaults<NDIM>::get_bc(),
bool fence = true) const {
verify();
reconstruct();
impl->broaden(bc.is_periodic(), fence);
}
/// Get the scaling function coeffs at level n starting from NS form
Tensor<T> coeffs_for_jun(Level n, long mode=0) {
PROFILE_MEMBER_FUNC(Function);
nonstandard(true,true);
return impl->coeffs_for_jun(n,mode);
//return impl->coeffs_for_jun(n);
}
/// Clears the function as if constructed uninitialized. Optional fence.
/// Any underlying data will not be freed until the next global fence.
void clear(bool fence = true) {
PROFILE_MEMBER_FUNC(Function);
if (impl) {
World& world = impl->world;
impl.reset();
if (fence) world.gop.fence();
}
}
/// Process 0 prints a summary of all nodes in the tree (collective)
void print_tree(std::ostream& os = std::cout) const {
PROFILE_MEMBER_FUNC(Function);
if (impl) impl->print_tree(os);
}
/// Process 0 prints a graphviz-formatted output of all nodes in the tree (collective)
void print_tree_graphviz(std::ostream& os = std::cout) const {
PROFILE_MEMBER_FUNC(Function);
os << "digraph G {" << std::endl;
if (impl) impl->print_tree_graphviz(os);
os << "}" << std::endl;
}
/// Print a summary of the load balancing info
/// This is serial and VERY expensive
void print_info() const {
PROFILE_MEMBER_FUNC(Function);
if (impl) impl->print_info();
}
struct SimpleUnaryOpWrapper {
T (*f)(T);
SimpleUnaryOpWrapper(T (*f)(T)) : f(f) {}
void operator()(const Key<NDIM>& key, Tensor<T>& t) const {
UNARY_OPTIMIZED_ITERATOR(T, t, *_p0 = f(*_p0));
}
template <typename Archive> void serialize(Archive& ar) {}
};
/// Inplace unary operation on function values
void unaryop(T (*f)(T)) {
// Must fence here due to temporary object on stack
// stopping us returning before complete
this->unaryop(SimpleUnaryOpWrapper(f));
}
/// Inplace unary operation on function values
template <typename opT>
void unaryop(const opT& op, bool fence=true) {
PROFILE_MEMBER_FUNC(Function);
verify();
reconstruct();
impl->unary_op_value_inplace(op, fence);
}
/// Unary operation applied inplace to the coefficients
template <typename opT>
void unaryop_coeff(const opT& op,
bool fence = true) {
PROFILE_MEMBER_FUNC(Function);
verify();
impl->unary_op_coeff_inplace(op, fence);
}
/// Unary operation applied inplace to the nodes
template <typename opT>
void unaryop_node(const opT& op,
bool fence = true) {
PROFILE_MEMBER_FUNC(Function);
verify();
impl->unary_op_node_inplace(op, fence);
}
static void doconj(const Key<NDIM>, Tensor<T>& t) {
PROFILE_MEMBER_FUNC(Function);
t.conj();
}
/// Inplace complex conjugate. No communication except for optional fence.
/// Returns this for chaining. Works in either basis.
Function<T,NDIM> conj(bool fence = true) {
PROFILE_MEMBER_FUNC(Function);
unaryop_coeff(&Function<T,NDIM>::doconj, fence);
return *this;
}
/// Inplace, scale the function by a constant. No communication except for optional fence.
/// Works in either basis. Returns reference to this for chaining.
template <typename Q>
Function<T,NDIM>& scale(const Q q, bool fence=true) {
PROFILE_MEMBER_FUNC(Function);
verify();
if (VERIFY_TREE) verify_tree();
impl->scale_inplace(q,fence);
return *this;
}
/// Inplace add scalar. No communication except for optional fence.
Function<T,NDIM>& add_scalar(T t, bool fence=true) {
PROFILE_MEMBER_FUNC(Function);
verify();
if (VERIFY_TREE) verify_tree();
impl->add_scalar_inplace(t,fence);
return *this;
}
/// Inplace, general bi-linear operation in wavelet basis. No communication except for optional fence.
/// If the functions are not in the wavelet basis an exception is thrown since this routine
/// is intended to be fast and unexpected compression is assumed to be a performance bug.
///
/// Returns this for chaining.
///
/// this <-- this*alpha + other*beta
template <typename Q, typename R>
Function<T,NDIM>& gaxpy(const T& alpha,
const Function<Q,NDIM>& other, const R& beta, bool fence=true) {
PROFILE_MEMBER_FUNC(Function);
verify();
other.verify();
MADNESS_ASSERT(is_compressed() == other.is_compressed());
if (is_compressed()) impl->gaxpy_inplace(alpha,*other.get_impl(),beta,fence);
if (not is_compressed()) impl->gaxpy_inplace_reconstructed(alpha,*other.get_impl(),beta,fence);
return *this;
}
/// Inplace addition of functions in the wavelet basis
/// Using operator notation forces a global fence after every operation.
/// Functions don't need to be compressed, it's the caller's responsibility
/// to choose an appropriate state with performance, usually compressed for 3d,
/// reconstructed for 6d)
template <typename Q>
Function<T,NDIM>& operator+=(const Function<Q,NDIM>& other) {
PROFILE_MEMBER_FUNC(Function);
if (NDIM<=3) {
compress();
other.compress();
} else {
reconstruct();
other.reconstruct();
}
MADNESS_ASSERT(is_compressed() == other.is_compressed());
if (VERIFY_TREE) verify_tree();
if (VERIFY_TREE) other.verify_tree();
return gaxpy(T(1.0), other, Q(1.0), true);
}
/// Inplace subtraction of functions in the wavelet basis
/// Using operator notation forces a global fence after every operation
template <typename Q>
Function<T,NDIM>& operator-=(const Function<Q,NDIM>& other) {
PROFILE_MEMBER_FUNC(Function);
if (NDIM<=3) {
compress();
other.compress();
} else {
reconstruct();
other.reconstruct();
}
MADNESS_ASSERT(is_compressed() == other.is_compressed());
if (VERIFY_TREE) verify_tree();
if (VERIFY_TREE) other.verify_tree();
return gaxpy(T(1.0), other, Q(-1.0), true);
}
/// Inplace scaling by a constant
/// Using operator notation forces a global fence after every operation
template <typename Q>
typename IsSupported<TensorTypeData<Q>, Function<T,NDIM> >::type &
operator*=(const Q q) {
PROFILE_MEMBER_FUNC(Function);
scale(q,true);
return *this;
}
/// Inplace squaring of function ... global comm only if not reconstructed
/// Returns *this for chaining.
Function<T,NDIM>& square(bool fence = true) {
PROFILE_MEMBER_FUNC(Function);
if (is_compressed()) reconstruct();
if (VERIFY_TREE) verify_tree();
impl->square_inplace(fence);
return *this;
}
/// Returns *this for chaining.
Function<T,NDIM>& abs(bool fence = true) {
PROFILE_MEMBER_FUNC(Function);
if (is_compressed()) reconstruct();
if (VERIFY_TREE) verify_tree();
impl->abs_inplace(fence);
return *this;
}
/// Returns *this for chaining.
Function<T,NDIM>& abs_square(bool fence = true) {
PROFILE_MEMBER_FUNC(Function);
if (is_compressed()) reconstruct();
if (VERIFY_TREE) verify_tree();
impl->abs_square_inplace(fence);
return *this;
}
/// Returns local contribution to \c int(f(x),x) ... no communication
/// In the wavelet basis this is just the coefficient of the first scaling
/// function which is a constant. In the scaling function basis we
/// must add up contributions from each box.
T trace_local() const {
PROFILE_MEMBER_FUNC(Function);
if (!impl) return 0.0;
if (VERIFY_TREE) verify_tree();
return impl->trace_local();
}
/// Returns global value of \c int(f(x),x) ... global comm required
T trace() const {
PROFILE_MEMBER_FUNC(Function);
if (!impl) return 0.0;
T sum = impl->trace_local();
impl->world.gop.sum(sum);
impl->world.gop.fence();
return sum;
}
/// Returns local part of inner product ... throws if both not compressed
template <typename R>
TENSOR_RESULT_TYPE(T,R) inner_local(const Function<R,NDIM>& g) const {
PROFILE_MEMBER_FUNC(Function);
MADNESS_ASSERT(is_compressed());
MADNESS_ASSERT(g.is_compressed());
if (VERIFY_TREE) verify_tree();
if (VERIFY_TREE) g.verify_tree();
return impl->inner_local(*(g.get_impl()));
}
/// With this being an on-demand function, fill the MRA tree according to different criteria
/// @param[in] g the function after which the MRA structure is modeled (any basis works)
template<typename R>
Function<T,NDIM>& fill_tree(const Function<R,NDIM>& g, bool fence=true) {
MADNESS_ASSERT(g.is_initialized());
MADNESS_ASSERT(is_on_demand());
// clear what we have
impl->get_coeffs().clear();
leaf_op<T,NDIM> gnode_is_leaf(g.get_impl().get());
impl->make_Vphi(gnode_is_leaf,fence);
return *this;
}
/// With this being an on-demand function, fill the MRA tree according to different criteria
/// @param[in] op the convolution operator for screening
template<typename opT>
Function<T,NDIM>& fill_tree(const opT& op, bool fence=true) {
MADNESS_ASSERT(is_on_demand());
// clear what we have
impl->get_coeffs().clear();
op_leaf_op<T,NDIM,opT> leaf_op(&op,this->get_impl().get());
impl->make_Vphi(leaf_op,fence);
return *this;
}
/// With this being an on-demand function, fill the MRA tree according to different criteria
Function<T,NDIM>& fill_tree(bool fence=true) {
MADNESS_ASSERT(is_on_demand());
// clear what we have
impl->get_coeffs().clear();
error_leaf_op<T,NDIM> leaf_op(this->get_impl().get());
impl->make_Vphi(leaf_op,fence);
return *this;
}
/// perform the hartree product of f*g, invoked by result
template<size_t LDIM, size_t KDIM, typename opT>
void do_hartree_product(const FunctionImpl<T,LDIM>* left, const FunctionImpl<T,KDIM>* right,
const opT* op) {
// get the right leaf operator
hartree_convolute_leaf_op<T,KDIM+LDIM,LDIM,opT> leaf_op(impl.get(),left,op);
impl->hartree_product(left,right,leaf_op,true);
this->truncate(0.0,false);
}
/// perform the hartree product of f*g, invoked by result
template<size_t LDIM, size_t KDIM>
void do_hartree_product(const FunctionImpl<T,LDIM>* left, const FunctionImpl<T,KDIM>* right) {
// hartree_leaf_op<T,KDIM+LDIM> leaf_op(impl.get(),cdata.s0);
hartree_leaf_op<T,KDIM+LDIM> leaf_op(impl.get(),k());
impl->hartree_product(left,right,leaf_op,true);
this->truncate(0.0,false);
}
/// Returns the inner product
/// Not efficient for computing multiple inner products
/// @param[in] g Function, optionally on-demand
template <typename R>
TENSOR_RESULT_TYPE(T,R) inner(const Function<R,NDIM>& g) const {
PROFILE_MEMBER_FUNC(Function);
// fast return if possible
if (not this->is_initialized()) return 0.0;
if (not g.is_initialized()) return 0.0;
// if this and g are the same, use norm2()
if (this->get_impl()==g.get_impl()) {
double norm=this->norm2();
return norm*norm;
}
// do it case-by-case
if (this->is_on_demand()) return g.inner_on_demand(*this);
if (g.is_on_demand()) return this->inner_on_demand(g);
if (VERIFY_TREE) verify_tree();
if (VERIFY_TREE) g.verify_tree();
// compression is more efficient for 3D
if (NDIM==3) {
if (!is_compressed()) compress(false);
if (!g.is_compressed()) g.compress(false);
impl->world.gop.fence();
}
if (this->is_compressed() and g.is_compressed()) {
} else {
if (not this->get_impl()->is_redundant()) this->get_impl()->make_redundant(false);
if (not g.get_impl()->is_redundant()) g.get_impl()->make_redundant(false);
impl->world.gop.fence();
}
TENSOR_RESULT_TYPE(T,R) local = impl->inner_local(*g.get_impl());
impl->world.gop.sum(local);
impl->world.gop.fence();
if (this->get_impl()->is_redundant()) this->get_impl()->undo_redundant(false);
if (g.get_impl()->is_redundant()) g.get_impl()->undo_redundant(false);
impl->world.gop.fence();
return local;
}
/// Return the local part of inner product with external function ... no communication.
/// If you are going to be doing a bunch of inner_ext calls, set
/// keep_redundant to true and then manually undo_redundant when you
/// are finished.
/// @param[in] f Pointer to function of type T that take coordT arguments. This is the externally provided function
/// @param[in] leaf_refine boolean switch to turn on/off refinement past leaf nodes
/// @param[in] keep_redundant boolean switch to turn on/off undo_redundant
/// @return Returns local part of the inner product, i.e. over the domain of all function nodes on this compute node.
T inner_ext_local(const std::shared_ptr< FunctionFunctorInterface<T,NDIM> > f, const bool leaf_refine=true, const bool keep_redundant=false) const {
PROFILE_MEMBER_FUNC(Function);
if (not impl->is_redundant()) impl->make_redundant(true);
T local = impl->inner_ext_local(f, leaf_refine);
if (not keep_redundant) impl->undo_redundant(true);
return local;
}
/// Return the inner product with external function ... requires communication.
/// If you are going to be doing a bunch of inner_ext calls, set
/// keep_redundant to true and then manually undo_redundant when you
/// are finished.
/// @param[in] f Reference to FunctionFunctorInterface. This is the externally provided function
/// @param[in] leaf_refine boolean switch to turn on/off refinement past leaf nodes
/// @param[in] keep_redundant boolean switch to turn on/off undo_redundant
/// @return Returns the inner product
T inner_ext(const std::shared_ptr< FunctionFunctorInterface<T,NDIM> > f, const bool leaf_refine=true, const bool keep_redundant=false) const {
PROFILE_MEMBER_FUNC(Function);
if (not impl->is_redundant()) impl->make_redundant(true);
T local = impl->inner_ext_local(f, leaf_refine);
impl->world.gop.sum(local);
impl->world.gop.fence();
if (not keep_redundant) impl->undo_redundant(true);
return local;
}
/// Return the inner product with external function ... requires communication.
/// If you are going to be doing a bunch of inner_ext calls, set
/// keep_redundant to true and then manually undo_redundant when you
/// are finished.
/// @param[in] f Reference to FunctionFunctorInterface. This is the externally provided function
/// @param[in] leaf_refine boolean switch to turn on/off refinement past leaf nodes
/// @return Returns the inner product
T inner_adaptive(const std::shared_ptr< FunctionFunctorInterface<T,NDIM> > f,
const bool leaf_refine=true) const {
PROFILE_MEMBER_FUNC(Function);
reconstruct();
T local = impl->inner_adaptive_local(f, leaf_refine);
impl->world.gop.sum(local);
impl->world.gop.fence();
return local;
}
/// Return the local part of gaxpy with external function, this*alpha + f*beta ... no communication.
/// @param[in] alpha prefactor for this Function
/// @param[in] f Pointer to function of type T that take coordT arguments. This is the externally provided function
/// @param[in] beta prefactor for f
template <typename L>
void gaxpy_ext(const Function<L,NDIM>& left, T (*f)(const coordT&), T alpha, T beta, double tol, bool fence=true) const {
PROFILE_MEMBER_FUNC(Function);
if (left.is_compressed()) left.reconstruct();
impl->gaxpy_ext(left.get_impl().get(), f, alpha, beta, tol, fence);
}
/// Returns the inner product for one on-demand function
/// It does work, but it might not give you the precision you expect.
/// The assumption is that the function g returns proper sum
/// coefficients on the MRA tree of this. This might not be the case if
/// g is constructed with an implicit multiplication, e.g.
/// result = <this|g>, with g = 1/r12 | gg>
/// @param[in] g on-demand function
template <typename R>
TENSOR_RESULT_TYPE(T,R) inner_on_demand(const Function<R,NDIM>& g) const {
MADNESS_ASSERT(g.is_on_demand() and (not this->is_on_demand()));
this->reconstruct();
// save for later, will be removed by make_Vphi
std::shared_ptr< FunctionFunctorInterface<T,NDIM> > func=g.get_impl()->get_functor();
leaf_op<T,NDIM> fnode_is_leaf(this->get_impl().get());
g.get_impl()->make_Vphi(fnode_is_leaf,true); // fence here
if (VERIFY_TREE) verify_tree();
TENSOR_RESULT_TYPE(T,R) local = impl->inner_local(*g.get_impl());
impl->world.gop.sum(local);
impl->world.gop.fence();
// restore original state
g.get_impl()->set_functor(func);
g.get_impl()->get_coeffs().clear();
g.get_impl()->is_on_demand()=true;
return local;
}
/// project this on the low-dim function g: h(x) = <f(x,y) | g(y)>
/// @param[in] g low-dim function
/// @param[in] dim over which dimensions to be integrated: 0..LDIM-1 or LDIM..NDIM-1
/// @return new function of dimension NDIM-LDIM
template <typename R, size_t LDIM>
Function<TENSOR_RESULT_TYPE(T,R),NDIM-LDIM> project_out(const Function<R,LDIM>& g, const int dim) const {
if (NDIM<=LDIM) MADNESS_EXCEPTION("confused dimensions in project_out?",1);
MADNESS_ASSERT(dim==0 or dim==1);
verify();
typedef TENSOR_RESULT_TYPE(T,R) resultT;
static const size_t KDIM=NDIM-LDIM;
FunctionFactory<resultT,KDIM> factory=FunctionFactory<resultT,KDIM>(world())
.k(g.k()).thresh(g.thresh());
Function<resultT,KDIM> result=factory; // no empty() here!
FunctionImpl<R,LDIM>* gimpl = const_cast< FunctionImpl<R,LDIM>* >(g.get_impl().get());
this->reconstruct();
gimpl->make_redundant(true);
this->get_impl()->project_out(result.get_impl().get(),gimpl,dim,true);
// result.get_impl()->project_out2(this->get_impl().get(),gimpl,dim);
result.world().gop.fence();
result.get_impl()->trickle_down(true);
gimpl->undo_redundant(true);
return result;
}
/// Replaces this function with one loaded from an archive using the default processor map
/// Archive can be sequential or parallel.
///
/// The & operator for serializing will only work with parallel archives.
template <typename Archive>
void load(World& world, Archive& ar) {
PROFILE_MEMBER_FUNC(Function);
// Type checking since we are probably circumventing the archive's own type checking
long magic = 0l, id = 0l, ndim = 0l, k = 0l;
ar & magic & id & ndim & k;
MADNESS_ASSERT(magic == 7776768); // Mellow Mushroom Pizza tel.# in Knoxville
MADNESS_ASSERT(id == TensorTypeData<T>::id);
MADNESS_ASSERT(ndim == NDIM);
impl.reset(new implT(FunctionFactory<T,NDIM>(world).k(k).empty()));
impl->load(ar);
}
/// Stores the function to an archive
/// Archive can be sequential or parallel.
///
/// The & operator for serializing will only work with parallel archives.
template <typename Archive>
void store(Archive& ar) const {
PROFILE_MEMBER_FUNC(Function);
verify();
// For type checking, etc.
ar & long(7776768) & long(TensorTypeData<T>::id) & long(NDIM) & long(k());
impl->store(ar);
}
/// change the tensor type of the coefficients in the FunctionNode
/// @param[in] targs target tensor arguments (threshold and full/low rank)
void change_tensor_type(const TensorArgs& targs, bool fence=true) {
if (not impl) return;
impl->change_tensor_type1(targs,fence);
}
/// This is replaced with left*right ... private
template <typename Q, typename opT>
Function<typename opT::resultT,NDIM>& unary_op_coeffs(const Function<Q,NDIM>& func,
const opT& op, bool fence) {
PROFILE_MEMBER_FUNC(Function);
func.verify();
MADNESS_ASSERT(!(func.is_compressed()));
if (VERIFY_TREE) func.verify_tree();
impl.reset(new implT(*func.get_impl(), func.get_pmap(), false));
impl->unaryXX(func.get_impl().get(), op, fence);
return *this;
}
/// Returns vector of FunctionImpl pointers corresponding to vector of functions
template <typename Q, std::size_t D>
static std::vector< std::shared_ptr< FunctionImpl<Q,D> > > vimpl(const std::vector< Function<Q,D> >& v) {
PROFILE_MEMBER_FUNC(Function);
std::vector< std::shared_ptr< FunctionImpl<Q,D> > > r(v.size());
for (unsigned int i=0; i<v.size(); ++i) r[i] = v[i].get_impl();
return r;
}
/// Refine vector of functions down to common finest level (reconstructs as necessary, optional fence)
void refine_to_common_level(std::vector< Function<T,NDIM> >& vf, bool fence=true) {
Key<NDIM> key0(0, Vector<Translation, NDIM> (0));
std::vector< Tensor<T> > c(vf.size());
std::vector<implT*> v(vf.size());
bool mustfence = false;
for (unsigned int i=0; i<v.size(); ++i) {
if (vf[i].is_compressed()) {
vf[i].reconstruct(false);
mustfence = true;
}
v[i] = vf[i].get_impl().get();
}
vf[0].impl->refine_to_common_level(v, c, key0);
if (mustfence) vf[0].world().gop.fence();
if (fence) vf[0].world().gop.fence();
if (VERIFY_TREE)
for (unsigned int i=0; i<vf.size(); i++) vf[i].verify_tree();
}
/// This is replaced with op(vector of functions) ... private
template <typename opT>
Function<T,NDIM>& multiop_values(const opT& op, const std::vector< Function<T,NDIM> >& vf) {
std::vector<implT*> v(vf.size());
for (unsigned int i=0; i<v.size(); ++i) {
v[i] = vf[i].get_impl().get();
}
impl->multiop_values(op, v);
world().gop.fence();
if (VERIFY_TREE) verify_tree();
return *this;
}
/// Multiplication of function * vector of functions using recursive algorithm of mulxx
template <typename L, typename R>
void vmulXX(const Function<L,NDIM>& left,
const std::vector< Function<R,NDIM> >& right,
std::vector< Function<T,NDIM> >& result,
double tol,
bool fence) {
PROFILE_MEMBER_FUNC(Function);
std::vector<FunctionImpl<T,NDIM>*> vresult(right.size());
std::vector<const FunctionImpl<R,NDIM>*> vright(right.size());
for (unsigned int i=0; i<right.size(); ++i) {
result[i].set_impl(left,false);
vresult[i] = result[i].impl.get();
vright[i] = right[i].impl.get();
}
left.world().gop.fence(); // Is this still essential? Yes.
vresult[0]->mulXXvec(left.get_impl().get(), vright, vresult, tol, fence);
}
/// Same as \c operator* but with optional fence and no automatic reconstruction
/// f or g are on-demand functions
template<typename L, typename R>
void mul_on_demand(const Function<L,NDIM>& f, const Function<R,NDIM>& g, bool fence=true) {
const FunctionImpl<L,NDIM>* fimpl=f.get_impl().get();
const FunctionImpl<R,NDIM>* gimpl=g.get_impl().get();
if (fimpl->is_on_demand() and gimpl->is_on_demand()) {
MADNESS_EXCEPTION("can't multiply two on-demand functions",1);
}
if (fimpl->is_on_demand()) {
leaf_op<R,NDIM> leaf_op1(gimpl);
impl->multiply(leaf_op1,gimpl,fimpl,fence);
} else {
leaf_op<L,NDIM> leaf_op1(fimpl);
impl->multiply(leaf_op1,fimpl,gimpl,fence);
}
}
/// sparse transformation of a vector of functions ... private
template <typename R, typename Q>
void vtransform(const std::vector< Function<R,NDIM> >& v,
const Tensor<Q>& c,
std::vector< Function<T,NDIM> >& vresult,
double tol,
bool fence=true) {
PROFILE_MEMBER_FUNC(Function);
vresult[0].impl->vtransform(vimpl(v), c, vimpl(vresult), tol, fence);
}
/// This is replaced with alpha*left + beta*right ... private
template <typename L, typename R>
Function<T,NDIM>& gaxpy_oop(T alpha, const Function<L,NDIM>& left,
T beta, const Function<R,NDIM>& right, bool fence) {
PROFILE_MEMBER_FUNC(Function);
left.verify();
right.verify();
MADNESS_ASSERT(left.is_compressed() && right.is_compressed());
if (VERIFY_TREE) left.verify_tree();
if (VERIFY_TREE) right.verify_tree();
impl.reset(new implT(*left.get_impl(), left.get_pmap(), false));
impl->gaxpy(alpha,*left.get_impl(),beta,*right.get_impl(),fence);
return *this;
}
/// This is replaced with mapdim(f) ... private
Function<T,NDIM>& mapdim(const Function<T,NDIM>& f, const std::vector<long>& map, bool fence) {
PROFILE_MEMBER_FUNC(Function);
f.verify();
if (VERIFY_TREE) f.verify_tree();
for (std::size_t i=0; i<NDIM; ++i) MADNESS_ASSERT(map[i]>=0 && static_cast<std::size_t>(map[i])<NDIM);
impl.reset(new implT(*f.impl, f.get_pmap(), false));
impl->mapdim(*f.impl,map,fence);
return *this;
}
/// check symmetry of a function by computing the 2nd derivative
double check_symmetry() const {
impl->make_redundant(true);
if (VERIFY_TREE) verify_tree();
double local = impl->check_symmetry_local();
impl->world.gop.sum(local);
impl->world.gop.fence();
double asy=sqrt(local);
if (this->world().rank()==0) print("asymmetry wrt particle",asy);
impl->undo_redundant(true);
return asy;
}
/// reduce the rank of the coefficient tensors
Function<T,NDIM>& reduce_rank(const bool fence=true) {
verify();
impl->reduce_rank(impl->get_tensor_args(),fence);
return *this;
}
};
template <typename T, typename opT, int NDIM>
Function<T,NDIM> multiop_values(const opT& op, const std::vector< Function<T,NDIM> >& vf) {
Function<T,NDIM> r;
r.set_impl(vf[0], false);
r.multiop_values(op, vf);
return r;
}
/// Returns new function equal to alpha*f(x) with optional fence
template <typename Q, typename T, std::size_t NDIM>
Function<TENSOR_RESULT_TYPE(Q,T),NDIM>
mul(const Q alpha, const Function<T,NDIM>& f, bool fence=true) {
PROFILE_FUNC;
f.verify();
if (VERIFY_TREE) f.verify_tree();
Function<TENSOR_RESULT_TYPE(Q,T),NDIM> result;
result.set_impl(f, false);
result.get_impl()->scale_oop(alpha,*f.get_impl(),fence);
return result;
}
/// Returns new function equal to f(x)*alpha with optional fence
template <typename Q, typename T, std::size_t NDIM>
Function<TENSOR_RESULT_TYPE(Q,T),NDIM>
mul(const Function<T,NDIM>& f, const Q alpha, bool fence=true) {
PROFILE_FUNC;
return mul(alpha,f,fence);
}
/// Returns new function equal to f(x)*alpha
/// Using operator notation forces a global fence after each operation
template <typename Q, typename T, std::size_t NDIM>
Function<TENSOR_RESULT_TYPE(Q,T),NDIM>
operator*(const Function<T,NDIM>& f, const Q alpha) {
return mul(alpha, f, true);
}
/// Returns new function equal to alpha*f(x)
/// Using operator notation forces a global fence after each operation
template <typename Q, typename T, std::size_t NDIM>
Function<TENSOR_RESULT_TYPE(Q,T),NDIM>
operator*(const Q alpha, const Function<T,NDIM>& f) {
return mul(alpha, f, true);
}
/// Sparse multiplication --- left and right must be reconstructed and if tol!=0 have tree of norms already created
template <typename L, typename R,std::size_t NDIM>
Function<TENSOR_RESULT_TYPE(L,R),NDIM>
mul_sparse(const Function<L,NDIM>& left, const Function<R,NDIM>& right, double tol, bool fence=true) {
PROFILE_FUNC;
left.verify();
right.verify();
MADNESS_ASSERT(!(left.is_compressed() || right.is_compressed()));
if (VERIFY_TREE) left.verify_tree();
if (VERIFY_TREE) right.verify_tree();
Function<TENSOR_RESULT_TYPE(L,R),NDIM> result;
result.set_impl(left, false);
result.get_impl()->mulXX(left.get_impl().get(), right.get_impl().get(), tol, fence);
return result;
}
/// Same as \c operator* but with optional fence and no automatic reconstruction
template <typename L, typename R,std::size_t NDIM>
Function<TENSOR_RESULT_TYPE(L,R),NDIM>
mul(const Function<L,NDIM>& left, const Function<R,NDIM>& right, bool fence=true) {
return mul_sparse(left,right,0.0,fence);
}
/// Generate new function = op(left,right) where op acts on the function values
template <typename L, typename R, typename opT, std::size_t NDIM>
Function<TENSOR_RESULT_TYPE(L,R),NDIM>
binary_op(const Function<L,NDIM>& left, const Function<R,NDIM>& right, const opT& op, bool fence=true) {
PROFILE_FUNC;
if (left.is_compressed()) left.reconstruct();
if (right.is_compressed()) right.reconstruct();
Function<TENSOR_RESULT_TYPE(L,R),NDIM> result;
result.set_impl(left, false);
result.get_impl()->binaryXX(left.get_impl().get(), right.get_impl().get(), op, fence);
return result;
}
/// Out of place application of unary operation to function values with optional fence
template <typename Q, typename opT, std::size_t NDIM>
Function<typename opT::resultT, NDIM>
unary_op(const Function<Q,NDIM>& func, const opT& op, bool fence=true) {
if (func.is_compressed()) func.reconstruct();
Function<typename opT::resultT, NDIM> result;
if (VERIFY_TREE) func.verify_tree();
result.set_impl(func, false);
result.get_impl()->unaryXXvalues(func.get_impl().get(), op, fence);
return result;
}
/// Out of place application of unary operation to scaling function coefficients with optional fence
template <typename Q, typename opT, std::size_t NDIM>
Function<typename opT::resultT, NDIM>
unary_op_coeffs(const Function<Q,NDIM>& func, const opT& op, bool fence=true) {
if (func.is_compressed()) func.reconstruct();
Function<typename opT::resultT, NDIM> result;
return result.unary_op_coeffs(func,op,fence);
}
/// Use the vmra/mul(...) interface instead
/// This so that we don't have to have friend functions in a different header.
///
/// If using sparsity (tol != 0) you must have created the tree of norms
/// already for both left and right.
template <typename L, typename R, std::size_t D>
std::vector< Function<TENSOR_RESULT_TYPE(L,R),D> >
vmulXX(const Function<L,D>& left, const std::vector< Function<R,D> >& vright, double tol, bool fence=true) {
if (vright.size() == 0) return std::vector< Function<TENSOR_RESULT_TYPE(L,R),D> >();
std::vector< Function<TENSOR_RESULT_TYPE(L,R),D> > vresult(vright.size());
vresult[0].vmulXX(left, vright, vresult, tol, fence);
return vresult;
}
/// Multiplies two functions with the new result being of type TensorResultType<L,R>
/// Using operator notation forces a global fence after each operation but also
/// enables us to automatically reconstruct the input functions as required.
template <typename L, typename R, std::size_t NDIM>
Function<TENSOR_RESULT_TYPE(L,R), NDIM>
operator*(const Function<L,NDIM>& left, const Function<R,NDIM>& right) {
if (left.is_compressed()) left.reconstruct();
if (right.is_compressed()) right.reconstruct();
MADNESS_ASSERT(not (left.is_on_demand() or right.is_on_demand()));
return mul(left,right,true);
}
/// Performs a Hartree product on the two given low-dimensional functions
template<typename T, std::size_t KDIM, std::size_t LDIM>
Function<T,KDIM+LDIM>
hartree_product(const Function<T,KDIM>& left2, const Function<T,LDIM>& right2) {
// we need both sum and difference coeffs for error estimation
Function<T,KDIM>& left = const_cast< Function<T,KDIM>& >(left2);
Function<T,LDIM>& right = const_cast< Function<T,LDIM>& >(right2);
const double thresh=FunctionDefaults<KDIM+LDIM>::get_thresh();
FunctionFactory<T,KDIM+LDIM> factory=FunctionFactory<T,KDIM+LDIM>(left.world())
.k(left.k()).thresh(thresh);
Function<T,KDIM+LDIM> result=factory.empty();
bool same=(left2.get_impl()==right2.get_impl());
// some prep work
left.nonstandard(true,true);
right.nonstandard(true,true);
result.do_hartree_product(left.get_impl().get(),right.get_impl().get());
left.standard(false);
if (not same) right.standard(false);
left2.world().gop.fence();
return result;
}
/// Performs a Hartree product on the two given low-dimensional functions
template<typename T, std::size_t KDIM, std::size_t LDIM, typename opT>
Function<T,KDIM+LDIM>
hartree_product(const Function<T,KDIM>& left2, const Function<T,LDIM>& right2,
const opT& op) {
// we need both sum and difference coeffs for error estimation
Function<T,KDIM>& left = const_cast< Function<T,KDIM>& >(left2);
Function<T,LDIM>& right = const_cast< Function<T,LDIM>& >(right2);
const double thresh=FunctionDefaults<KDIM+LDIM>::get_thresh();
FunctionFactory<T,KDIM+LDIM> factory=FunctionFactory<T,KDIM+LDIM>(left.world())
.k(left.k()).thresh(thresh);
Function<T,KDIM+LDIM> result=factory.empty();
if (result.world().rank()==0) {
print("incomplete FunctionFactory in Function::hartree_product");
print("thresh: ", thresh);
}
bool same=(left2.get_impl()==right2.get_impl());
// some prep work
left.nonstandard(true,true);
right.nonstandard(true,true);
result.do_hartree_product(left.get_impl().get(),right.get_impl().get(),&op);
left.standard(false);
if (not same) right.standard(false);
left2.world().gop.fence();
return result;
}
/// Returns new function alpha*left + beta*right optional fence and no automatic compression
template <typename L, typename R,std::size_t NDIM>
Function<TENSOR_RESULT_TYPE(L,R),NDIM>
gaxpy_oop(TENSOR_RESULT_TYPE(L,R) alpha, const Function<L,NDIM>& left,
TENSOR_RESULT_TYPE(L,R) beta, const Function<R,NDIM>& right, bool fence=true) {
PROFILE_FUNC;
Function<TENSOR_RESULT_TYPE(L,R),NDIM> result;
return result.gaxpy_oop(alpha, left, beta, right, fence);
}
/// Same as \c operator+ but with optional fence and no automatic compression
template <typename L, typename R,std::size_t NDIM>
Function<TENSOR_RESULT_TYPE(L,R),NDIM>
add(const Function<L,NDIM>& left, const Function<R,NDIM>& right, bool fence=true) {
return gaxpy_oop(TENSOR_RESULT_TYPE(L,R)(1.0), left,
TENSOR_RESULT_TYPE(L,R)(1.0), right, fence);
}
/// Returns new function alpha*left + beta*right optional fence, having both addends reconstructed
template<typename T, std::size_t NDIM>
Function<T,NDIM> gaxpy_oop_reconstructed(const double alpha, const Function<T,NDIM>& left,
const double beta, const Function<T,NDIM>& right, const bool fence=true) {
Function<T,NDIM> result;
result.set_impl(right,false);
MADNESS_ASSERT(not left.is_compressed());
MADNESS_ASSERT(not right.is_compressed());
result.get_impl()->gaxpy_oop_reconstructed(alpha,*left.get_impl(),beta,*right.get_impl(),fence);
return result;
}
/// Adds two functions with the new result being of type TensorResultType<L,R>
/// Using operator notation forces a global fence after each operation
template <typename L, typename R, std::size_t NDIM>
Function<TENSOR_RESULT_TYPE(L,R), NDIM>
operator+(const Function<L,NDIM>& left, const Function<R,NDIM>& right) {
if (VERIFY_TREE) left.verify_tree();
if (VERIFY_TREE) right.verify_tree();
// no compression for high-dimensional functions
if (NDIM==6) {
left.reconstruct();
right.reconstruct();
return gaxpy_oop_reconstructed(1.0,left,1.0,right,true);
} else {
if (!left.is_compressed()) left.compress();
if (!right.is_compressed()) right.compress();
return add(left,right,true);
}
}
/// Same as \c operator- but with optional fence and no automatic compression
template <typename L, typename R,std::size_t NDIM>
Function<TENSOR_RESULT_TYPE(L,R),NDIM>
sub(const Function<L,NDIM>& left, const Function<R,NDIM>& right, bool fence=true) {
return gaxpy_oop(TENSOR_RESULT_TYPE(L,R)(1.0), left,
TENSOR_RESULT_TYPE(L,R)(-1.0), right, fence);
}
/// Subtracts two functions with the new result being of type TensorResultType<L,R>
/// Using operator notation forces a global fence after each operation
template <typename L, typename R, std::size_t NDIM>
Function<TENSOR_RESULT_TYPE(L,R), NDIM>
operator-(const Function<L,NDIM>& left, const Function<R,NDIM>& right) {
PROFILE_FUNC;
// no compression for high-dimensional functions
if (NDIM==6) {
left.reconstruct();
right.reconstruct();
return gaxpy_oop_reconstructed(1.0,left,-1.0,right,true);
} else {
if (!left.is_compressed()) left.compress();
if (!right.is_compressed()) right.compress();
return sub(left,right,true);
}
}
/// Create a new function that is the square of f - global comm only if not reconstructed
template <typename T, std::size_t NDIM>
Function<T,NDIM> square(const Function<T,NDIM>& f, bool fence=true) {
PROFILE_FUNC;
Function<T,NDIM> result = copy(f,true); // !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
return result.square(true); //fence); // !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
}
/// Create a new function that is the abs of f - global comm only if not reconstructed
template <typename T, int NDIM>
Function<T,NDIM> abs(const Function<T,NDIM>& f, bool fence=true) {
PROFILE_FUNC;
Function<T,NDIM> result = copy(f,true); // !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
return result.abs(true); //fence); // !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
}
/// Create a new function that is the abs_square of f - global comm only if not reconstructed
template <typename T, int NDIM>
Function<T,NDIM> abs_square(const Function<T,NDIM>& f, bool fence=true) {
PROFILE_FUNC;
Function<T,NDIM> result = copy(f,true); // !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
return result.abs_square(true); //fence); // !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
}
/// Create a new copy of the function with different distribution and optional fence
/// Works in either basis. Different distributions imply
/// asynchronous communication and the optional fence is
/// collective.
template <typename T, std::size_t NDIM>
Function<T,NDIM> copy(const Function<T,NDIM>& f,
const std::shared_ptr< WorldDCPmapInterface< Key<NDIM> > >& pmap,
bool fence = true) {
PROFILE_FUNC;
f.verify();
Function<T,NDIM> result;
typedef FunctionImpl<T,NDIM> implT;
result.set_impl(std::shared_ptr<implT>(new implT(*f.get_impl(), pmap, false)));
result.get_impl()->copy_coeffs(*f.get_impl(), fence);
if (VERIFY_TREE) result.verify_tree();
return result;
}
/// Create a new copy of the function with the same distribution and optional fence
template <typename T, std::size_t NDIM>
Function<T,NDIM> copy(const Function<T,NDIM>& f, bool fence = true) {
PROFILE_FUNC;
return copy(f, f.get_pmap(), fence);
}
/// Type conversion implies a deep copy. No communication except for optional fence.
/// Works in either basis but any loss of precision may result in different errors
/// in applied in a different basis.
///
/// The new function is formed with the options from the default constructor.
///
/// There is no automatic type conversion since this is generally a rather dangerous
/// thing and because there would be no way to make the fence optional.
template <typename T, typename Q, std::size_t NDIM>
Function<Q,NDIM> convert(const Function<T,NDIM>& f, bool fence = true) {
PROFILE_FUNC;
f.verify();
Function<Q,NDIM> result;
result.set_impl(f, false);
result.get_impl()->copy_coeffs(*f.get_impl(), fence);
return result;
}
/// Return the complex conjugate of the input function with the same distribution and optional fence
/// !!! The fence is actually not optional in the current implementation !!!
template <typename T, std::size_t NDIM>
Function<T,NDIM> conj(const Function<T,NDIM>& f, bool fence = true) {
PROFILE_FUNC;
Function<T,NDIM> result = copy(f,true);
return result.conj(fence);
}
/// Apply operator on a hartree product of two low-dimensional functions
/// Supposed to be something like result= G( f(1)*f(2))
/// the hartree product is never constructed explicitly, but its coeffs are
/// constructed on the fly and processed immediately.
/// @param[in] op the operator
/// @param[in] f1 function of particle 1
/// @param[in] f2 function of particle 2
/// @param[in] fence if we shall fence
/// @return a function of dimension NDIM=LDIM+LDIM
template <typename opT, typename T, std::size_t LDIM>
Function<TENSOR_RESULT_TYPE(typename opT::opT,T), LDIM+LDIM>
apply(const opT& op, const Function<T,LDIM>& f1, const Function<T,LDIM>& f2, bool fence=true) {
typedef TENSOR_RESULT_TYPE(T,typename opT::opT) resultT;
Function<T,LDIM>& ff1 = const_cast< Function<T,LDIM>& >(f1);
Function<T,LDIM>& ff2 = const_cast< Function<T,LDIM>& >(f2);
bool same=(ff1.get_impl()==ff2.get_impl());
// keep the leaves! They are assumed to be there later
// even for modified op we need NS form for the hartree_leaf_op
if (not same) ff1.nonstandard(true,false);
ff2.nonstandard(true,true);
FunctionFactory<T,LDIM+LDIM> factory=FunctionFactory<resultT,LDIM+LDIM>(f1.world())
.k(f1.k()).thresh(FunctionDefaults<LDIM+LDIM>::get_thresh());
Function<resultT,LDIM+LDIM> result=factory.empty().fence();
result.get_impl()->reset_timer();
op.reset_timer();
// will fence here
result.get_impl()->recursive_apply(op, f1.get_impl().get(),f2.get_impl().get(),true);
result.get_impl()->print_timer();
op.print_timer();
result.get_impl()->finalize_apply(true); // need fence before reconstruct
if (op.modified()) {
result.get_impl()->trickle_down(true);
} else {
result.reconstruct();
}
if (not same) ff1.standard(false);
ff2.standard(false);
return result;
}
/// Apply operator ONLY in non-standard form - required other steps missing !!
template <typename opT, typename R, std::size_t NDIM>
Function<TENSOR_RESULT_TYPE(typename opT::opT,R), NDIM>
apply_only(const opT& op, const Function<R,NDIM>& f, bool fence=true) {
Function<TENSOR_RESULT_TYPE(typename opT::opT,R), NDIM> result;
// specialized version for 3D
if (NDIM <= 3) {
result.set_impl(f, true);
result.get_impl()->apply(op, *f.get_impl(), fence);
} else { // general version for higher dimension
Function<TENSOR_RESULT_TYPE(typename opT::opT,R), NDIM> r1;
result.set_impl(f, true);
r1.set_impl(f, true);
result.get_impl()->reset_timer();
op.reset_timer();
result.get_impl()->apply_source_driven(op, *f.get_impl(), fence);
// recursive_apply is about 20% faster than apply_source_driven
//result.get_impl()->recursive_apply(op, f.get_impl().get(),
// r1.get_impl().get(),true); // will fence here
double time=result.get_impl()->finalize_apply(fence); // need fence before reconstruction
result.world().gop.fence();
if (opT::opdim==6) {
result.get_impl()->print_timer();
op.print_timer();
if (result.world().rank()==0) print("time in finlize_apply", time);
}
}
return result;
}
/// Apply operator in non-standard form
/// Returns a new function with the same distribution
///
/// !!! For the moment does NOT respect fence option ... always fences
template <typename opT, typename R, std::size_t NDIM>
Function<TENSOR_RESULT_TYPE(typename opT::opT,R), NDIM>
apply(const opT& op, const Function<R,NDIM>& f, bool fence=true) {
typedef TENSOR_RESULT_TYPE(typename opT::opT,R) resultT;
Function<R,NDIM>& ff = const_cast< Function<R,NDIM>& >(f);
Function<resultT, NDIM> result;
MADNESS_ASSERT(not f.is_on_demand());
if (VERIFY_TREE) ff.verify_tree();
ff.reconstruct();
if (opT::opdim==6) ff.print_size("ff in apply after reconstruct");
if (op.modified()) {
MADNESS_ASSERT(not op.is_slaterf12);
ff.get_impl()->make_redundant(true);
result = apply_only(op, ff, fence);
ff.get_impl()->undo_redundant(false);
result.get_impl()->trickle_down(true);
} else {
// the slaterf12 function is
// 1/(2 mu) \int d1 (1 - exp(- mu r12)) f(1)
// = 1/(2 mu) (f.trace() - \int d1 exp(-mu r12) f(1) )
// f.trace() is just a number
R ftrace=0.0;
if (op.is_slaterf12) ftrace=f.trace();
// saves the standard() step, which is very expensive in 6D
// Function<R,NDIM> fff=copy(ff);
Function<R,NDIM> fff=(ff);
fff.nonstandard(op.doleaves, true);
if (opT::opdim==6) fff.print_size("ff in apply after nonstandard");
if ((opT::opdim==6) and (f.world().rank()==0)) {
fff.get_impl()->timer_filter.print("filter");
fff.get_impl()->timer_compress_svd.print("compress_svd");
}
result = apply_only(op, fff, fence);
result.reconstruct();
// fff.clear();
if (op.destructive()) {
ff.world().gop.fence();
ff.clear();
} else {
ff.standard();
}
if (op.is_slaterf12) result=(result-ftrace).scale(-0.5/op.mu());
}
if (opT::opdim==6) result.print_size("result after reconstruction");
return result;
}
template <typename opT, typename R, std::size_t NDIM>
Function<TENSOR_RESULT_TYPE(typename opT::opT,R), NDIM>
apply_1d_realspace_push(const opT& op, const Function<R,NDIM>& f, int axis, bool fence=true) {
PROFILE_FUNC;
Function<R,NDIM>& ff = const_cast< Function<R,NDIM>& >(f);
if (VERIFY_TREE) ff.verify_tree();
ff.reconstruct();
Function<TENSOR_RESULT_TYPE(typename opT::opT,R), NDIM> result;
result.set_impl(ff, false);
result.get_impl()->apply_1d_realspace_push(op, ff.get_impl().get(), axis, fence);
return result;
}
/// Generate a new function by reordering dimensions ... optional fence
/// You provide an array of dimension NDIM that maps old to new dimensions
/// according to
/// \code
/// newdim = mapdim[olddim]
/// \endcode
/// Works in either scaling function or wavelet basis.
///
/// Would be easy to modify this to also change the procmap here
/// if desired but presently it uses the same procmap as f.
template <typename T, std::size_t NDIM>
Function<T,NDIM>
mapdim(const Function<T,NDIM>& f, const std::vector<long>& map, bool fence=true) {
PROFILE_FUNC;
Function<T,NDIM> result;
return result.mapdim(f,map,fence);
}
/// symmetrize a function
/// @param[in] symmetry possibilities are:
/// (anti-) symmetric particle permutation ("sy_particle", "antisy_particle")
/// symmetric mirror plane ("xy", "xz", "yz")
/// @return a new function symmetrized according to the input parameter
template <typename T, std::size_t NDIM>
Function<T,NDIM>
symmetrize(const Function<T,NDIM>& f, const std::string symmetry, bool fence=true) {
Function<T,NDIM> result;
MADNESS_ASSERT(NDIM==6); // works only for pair functions
std::vector<long> map(NDIM);
// symmetric particle permutation
if (symmetry=="sy_particle") {
map[0]=3; map[1]=4; map[2]=5;
map[3]=0; map[4]=1; map[5]=2;
} else if (symmetry=="cx") {
map[0]=0; map[1]=2; map[2]=1;
map[3]=3; map[4]=5; map[5]=4;
} else if (symmetry=="cy") {
map[0]=2; map[1]=1; map[2]=0;
map[3]=5; map[4]=4; map[5]=3;
} else if (symmetry=="cz") {
map[0]=1; map[1]=0; map[2]=2;
map[3]=4; map[4]=3; map[5]=5;
} else {
if (f.world().rank()==0) {
print("unknown parameter in symmetrize:",symmetry);
}
MADNESS_EXCEPTION("unknown parameter in symmetrize",1);
}
result.mapdim(f,map,true); // need to fence here
result.get_impl()->average(*f.get_impl());
return result;
}
/// multiply a high-dimensional function with a low-dimensional function
/// @param[in] f NDIM function of 2 particles: f=f(1,2)
/// @param[in] g LDIM function of 1 particle: g=g(1) or g=g(2)
/// @param[in] particle if g=g(1) or g=g(2)
/// @return h(1,2) = f(1,2) * g(p)
template<typename T, std::size_t NDIM, std::size_t LDIM>
Function<T,NDIM> multiply(const Function<T,NDIM> f, const Function<T,LDIM> g, const int particle, const bool fence=true) {
MADNESS_ASSERT(LDIM+LDIM==NDIM);
MADNESS_ASSERT(particle==1 or particle==2);
Function<T,NDIM> result;
result.set_impl(f, true);
Function<T,NDIM>& ff = const_cast< Function<T,NDIM>& >(f);
Function<T,LDIM>& gg = const_cast< Function<T,LDIM>& >(g);
if (0) {
gg.nonstandard(true,false);
ff.nonstandard(true,false);
result.world().gop.fence();
result.get_impl()->multiply(ff.get_impl().get(),gg.get_impl().get(),particle);
result.world().gop.fence();
gg.standard(false);
ff.standard(false);
result.world().gop.fence();
} else {
FunctionImpl<T,NDIM>* fimpl=ff.get_impl().get();
FunctionImpl<T,LDIM>* gimpl=gg.get_impl().get();
gimpl->make_redundant(true);
fimpl->make_redundant(false);
result.world().gop.fence();
result.get_impl()->multiply(fimpl,gimpl,particle);
result.world().gop.fence();
fimpl->undo_redundant(false);
gimpl->undo_redundant(fence);
}
// if (particle==1) result.print_size("finished multiplication f(1,2)*g(1)");
// if (particle==2) result.print_size("finished multiplication f(1,2)*g(2)");
return result;
}
template <typename T, std::size_t NDIM>
Function<T,NDIM>
project(const Function<T,NDIM>& other,
int k=FunctionDefaults<NDIM>::get_k(),
double thresh=FunctionDefaults<NDIM>::get_thresh(),
bool fence=true)
{
PROFILE_FUNC;
Function<T,NDIM> result = FunctionFactory<T,NDIM>(other.world()).k(k).thresh(thresh).empty();
other.reconstruct();
result.get_impl()->project(*other.get_impl(),fence);
return result;
}
/// Computes the scalar/inner product between two functions
/// In Maple this would be \c int(conjugate(f(x))*g(x),x=-infinity..infinity)
template <typename T, typename R, std::size_t NDIM>
TENSOR_RESULT_TYPE(T,R) inner(const Function<T,NDIM>& f, const Function<R,NDIM>& g) {
PROFILE_FUNC;
return f.inner(g);
}
/// Computes the scalar/inner product between an MRA function and an external functor
/// Currently this defaults to inner_adaptive, which might be more expensive
/// than inner_ext since it loops over all leaf nodes. If you feel inner_ext
/// is more efficient you need to call it directly
/// @param[in] f MRA function
/// @param[in] g functor
/// @result inner(f,g)
template <typename T, typename opT, std::size_t NDIM>
TENSOR_RESULT_TYPE(T,typename opT::value_type) inner(const Function<T,NDIM>& f, const opT& g) {
PROFILE_FUNC;
std::shared_ptr< FunctionFunctorInterface<double,3> > func(new opT(g));
return f.inner_adaptive(func);
}
/// Computes the scalar/inner product between an MRA function and an external functor
/// Currently this defaults to inner_adaptive, which might be more expensive
/// than inner_ext since it loops over all leaf nodes. If you feel inner_ext
/// is more efficient you need to call it directly
/// @param[in] g functor
/// @param[in] f MRA function
/// @result inner(f,g)
template <typename T, typename opT, std::size_t NDIM>
TENSOR_RESULT_TYPE(T,typename opT::value_type) inner(const opT& g, const Function<T,NDIM>& f) {
return inner(f,g);
}
template <typename T, typename R, std::size_t NDIM>
typename IsSupported<TensorTypeData<R>, Function<TENSOR_RESULT_TYPE(T,R),NDIM> >::type
operator+(const Function<T,NDIM>& f, R r) {
return (f*R(1.0)).add_scalar(r);
}
template <typename T, typename R, std::size_t NDIM>
typename IsSupported<TensorTypeData<R>, Function<TENSOR_RESULT_TYPE(T,R),NDIM> >::type
operator+(R r, const Function<T,NDIM>& f) {
return (f*R(1.0)).add_scalar(r);
}
template <typename T, typename R, std::size_t NDIM>
typename IsSupported<TensorTypeData<R>, Function<TENSOR_RESULT_TYPE(T,R),NDIM> >::type
operator-(const Function<T,NDIM>& f, R r) {
return (f*R(1.0)).add_scalar(-r);
}
template <typename T, typename R, std::size_t NDIM>
typename IsSupported<TensorTypeData<R>, Function<TENSOR_RESULT_TYPE(T,R),NDIM> >::type
operator-(R r, const Function<T,NDIM>& f) {
return (f*R(-1.0)).add_scalar(r);
}
namespace detail {
template <std::size_t NDIM>
struct realop {
typedef double resultT;
Tensor<double> operator()(const Key<NDIM>& key, const Tensor<double_complex>& t) const {
return real(t);
}
template <typename Archive> void serialize (Archive& ar) {}
};
template <std::size_t NDIM>
struct imagop {
typedef double resultT;
Tensor<double> operator()(const Key<NDIM>& key, const Tensor<double_complex>& t) const {
return imag(t);
}
template <typename Archive> void serialize (Archive& ar) {}
};
template <std::size_t NDIM>
struct abssqop {
typedef double resultT;
Tensor<double> operator()(const Key<NDIM>& key, const Tensor<double_complex>& t) const {
Tensor<double> r = abs(t);
return r.emul(r);
}
template <typename Archive> void serialize (Archive& ar) {}
};
}
/// Returns a new function that is the real part of the input
template <std::size_t NDIM>
Function<double,NDIM> real(const Function<double_complex,NDIM>& z, bool fence=true) {
return unary_op_coeffs(z, detail::realop<NDIM>(), fence);
}
/// Returns a new function that is the imaginary part of the input
template <std::size_t NDIM>
Function<double,NDIM> imag(const Function<double_complex,NDIM>& z, bool fence=true) {
return unary_op_coeffs(z, detail::imagop<NDIM>(), fence);
}
/// Returns a new function that is the square of the absolute value of the input
template <std::size_t NDIM>
Function<double,NDIM> abssq(const Function<double_complex,NDIM>& z, bool fence=true) {
return unary_op(z, detail::abssqop<NDIM>(), fence);
}
}
#include <madness/mra/funcplot.h>
namespace madness {
namespace archive {
template <class T, std::size_t NDIM>
struct ArchiveLoadImpl< ParallelInputArchive, Function<T,NDIM> > {
static inline void load(const ParallelInputArchive& ar, Function<T,NDIM>& f) {
f.load(*ar.get_world(), ar);
}
};
template <class T, std::size_t NDIM>
struct ArchiveStoreImpl< ParallelOutputArchive, Function<T,NDIM> > {
static inline void store(const ParallelOutputArchive& ar, const Function<T,NDIM>& f) {
f.store(ar);
}
};
}
}
/* @} */
#include <madness/mra/derivative.h>
#include <madness/mra/operator.h>
#include <madness/mra/functypedefs.h>
#include <madness/mra/vmra.h>
// #include <madness/mra/mraimpl.h> !!!!!!!!!!!!! NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO !!!!!!!!!!!!!!!!!!
#endif // MADNESS_MRA_MRA_H__INCLUDED
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