/usr/include/madness/mra/vmra.h is in libmadness-dev 0.10.1~gite4aa500e-10.
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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
$Id$
*/
#ifndef MADNESS_MRA_VMRA_H__INCLUDED
#define MADNESS_MRA_VMRA_H__INCLUDED
/*!
\file vmra.h
\brief Defines operations on vectors of Functions
\ingroup mra
This file defines a number of operations on vectors of functions.
Assume v is a vector of NDIM-D functions of a certain type.
Operations on array of functions
*) copying: deep copying of vectors of functions to vector of functions
\code
vector2 = copy(world, vector1,fence);
\endcode
*) compress: convert multiwavelet representation to legendre representation
\code
compress(world, vector, fence);
\endcode
*) reconstruct: convert representation to multiwavelets
\code
reconstruct(world, vector, fence);
\endcode
*) nonstandard: convert to non-standard form
\code
nonstandard(world, v, fence);
\endcode
*) standard: convert to standard form
\code
standard(world, v, fence);
\endcode
*) truncate: truncating vectors of functions to desired precision
\code
truncate(world, v, tolerance, fence);
\endcode
*) zero function: create a vector of zero functions of length n
\code
v=zero(world, n);
\endcode
*) transform: transform a representation from one basis to another
\code
transform(world, vector, tensor, tolerance, fence )
\endcode
Setting thresh-hold for precision
*) set_thresh: setting a finite thresh-hold for a vector of functions
\code
void set_thresh(World& world, std::vector< Function<T,NDIM> >& v, double thresh, bool fence=true);
\endcode
Arithmetic Operations on arrays of functions
*) conjugation: conjugate a vector of complex functions
*) add
*) sub
*) mul
- mul_sparse
*) square
*) gaxpy
*) apply
Norms, inner-products, blas-1 like operations on vectors of functions
*) inner
*) matrix_inner
*) norm_tree
*) normalize
*) norm2
- norm2s
*) scale(world, v, alpha);
*/
#include <madness/mra/mra.h>
#include <madness/mra/derivative.h>
#include <madness/tensor/distributed_matrix.h>
#include <cstdio>
namespace madness {
/// Compress a vector of functions
template <typename T, std::size_t NDIM>
void compress(World& world,
const std::vector< Function<T,NDIM> >& v,
bool fence=true) {
PROFILE_BLOCK(Vcompress);
bool must_fence = false;
for (unsigned int i=0; i<v.size(); ++i) {
if (!v[i].is_compressed()) {
v[i].compress(false);
must_fence = true;
}
}
if (fence && must_fence) world.gop.fence();
}
/// Reconstruct a vector of functions
template <typename T, std::size_t NDIM>
void reconstruct(World& world,
const std::vector< Function<T,NDIM> >& v,
bool fence=true) {
PROFILE_BLOCK(Vreconstruct);
bool must_fence = false;
for (unsigned int i=0; i<v.size(); ++i) {
if (v[i].is_compressed()) {
v[i].reconstruct(false);
must_fence = true;
}
}
if (fence && must_fence) world.gop.fence();
}
/// refine the functions according to the autorefine criteria
template <typename T, std::size_t NDIM>
void refine(World& world, const std::vector<Function<T,NDIM> >& vf,
bool fence=true) {
for (const auto& f : vf) f.refine(false);
if (fence) world.gop.fence();
}
/// refine all functions to a common (finest) level
/// if functions are not initialized (impl==NULL) they are ignored
template <typename T, std::size_t NDIM>
void refine_to_common_level(World& world, std::vector<Function<T,NDIM> >& vf,
bool fence=true) {
reconstruct(world,vf);
Key<NDIM> key0(0, Vector<Translation, NDIM> (0));
std::vector<FunctionImpl<T,NDIM>*> v_ptr;
// push initialized function pointers into the vector v_ptr
for (unsigned int i=0; i<vf.size(); ++i) {
if (vf[i].is_initialized()) v_ptr.push_back(vf[i].get_impl().get());
}
// sort and remove duplicates to not confuse the refining function
std::sort(v_ptr.begin(),v_ptr.end());
typename std::vector<FunctionImpl<T, NDIM>*>::iterator it;
it = std::unique(v_ptr.begin(), v_ptr.end());
v_ptr.resize( std::distance(v_ptr.begin(),it) );
std::vector< Tensor<T> > c(v_ptr.size());
v_ptr[0]->refine_to_common_level(v_ptr, c, key0);
if (fence) v_ptr[0]->world.gop.fence();
if (VERIFY_TREE)
for (unsigned int i=0; i<vf.size(); i++) vf[i].verify_tree();
}
/// Generates non-standard form of a vector of functions
template <typename T, std::size_t NDIM>
void nonstandard(World& world,
std::vector< Function<T,NDIM> >& v,
bool fence=true) {
PROFILE_BLOCK(Vnonstandard);
reconstruct(world, v);
for (unsigned int i=0; i<v.size(); ++i) {
v[i].nonstandard(false,false);
}
if (fence) world.gop.fence();
}
/// Generates standard form of a vector of functions
template <typename T, std::size_t NDIM>
void standard(World& world,
std::vector< Function<T,NDIM> >& v,
bool fence=true) {
PROFILE_BLOCK(Vstandard);
for (unsigned int i=0; i<v.size(); ++i) {
v[i].standard(false);
}
if (fence) world.gop.fence();
}
/// Truncates a vector of functions
template <typename T, std::size_t NDIM>
void truncate(World& world,
std::vector< Function<T,NDIM> >& v,
double tol=0.0,
bool fence=true) {
PROFILE_BLOCK(Vtruncate);
compress(world, v);
for (unsigned int i=0; i<v.size(); ++i) {
v[i].truncate(tol, false);
}
if (fence) world.gop.fence();
}
/// Applies a derivative operator to a vector of functions
template <typename T, std::size_t NDIM>
std::vector< Function<T,NDIM> >
apply(World& world,
const Derivative<T,NDIM>& D,
const std::vector< Function<T,NDIM> >& v,
bool fence=true)
{
reconstruct(world, v);
std::vector< Function<T,NDIM> > df(v.size());
for (unsigned int i=0; i<v.size(); ++i) {
df[i] = D(v[i],false);
}
if (fence) world.gop.fence();
return df;
}
/// Generates a vector of zero functions (reconstructed)
template <typename T, std::size_t NDIM>
std::vector< Function<T,NDIM> >
zero_functions(World& world, int n, bool fence=true) {
PROFILE_BLOCK(Vzero_functions);
std::vector< Function<T,NDIM> > r(n);
for (int i=0; i<n; ++i)
r[i] = Function<T,NDIM>(FunctionFactory<T,NDIM>(world).fence(false));
if (n && fence) world.gop.fence();
return r;
}
/// Generates a vector of zero functions (compressed)
template <typename T, std::size_t NDIM>
std::vector< Function<T,NDIM> >
zero_functions_compressed(World& world, int n, bool fence=true) {
PROFILE_BLOCK(Vzero_functions);
std::vector< Function<T,NDIM> > r(n);
for (int i=0; i<n; ++i)
r[i] = Function<T,NDIM>(FunctionFactory<T,NDIM>(world).fence(false).compressed(true).initial_level(1));
if (n && fence) world.gop.fence();
return r;
}
/// Transforms a vector of functions according to new[i] = sum[j] old[j]*c[j,i]
/// Uses sparsity in the transformation matrix --- set small elements to
/// zero to take advantage of this.
template <typename T, typename R, std::size_t NDIM>
std::vector< Function<TENSOR_RESULT_TYPE(T,R),NDIM> >
transform(World& world,
const std::vector< Function<T,NDIM> >& v,
const Tensor<R>& c,
bool fence=true) {
PROFILE_BLOCK(Vtransformsp);
typedef TENSOR_RESULT_TYPE(T,R) resultT;
int n = v.size(); // n is the old dimension
int m = c.dim(1); // m is the new dimension
MADNESS_ASSERT(n==c.dim(0));
std::vector< Function<resultT,NDIM> > vc = zero_functions_compressed<resultT,NDIM>(world, m);
compress(world, v);
for (int i=0; i<m; ++i) {
for (int j=0; j<n; ++j) {
if (c(j,i) != R(0.0)) vc[i].gaxpy(1.0,v[j],c(j,i),false);
}
}
if (fence) world.gop.fence();
return vc;
}
template <typename L, typename R, std::size_t NDIM>
std::vector< Function<TENSOR_RESULT_TYPE(L,R),NDIM> >
transform(World& world, const std::vector< Function<L,NDIM> >& v,
const Tensor<R>& c, double tol, bool fence) {
PROFILE_BLOCK(Vtransform);
MADNESS_ASSERT(v.size() == (unsigned int)(c.dim(0)));
std::vector< Function<TENSOR_RESULT_TYPE(L,R),NDIM> > vresult
= zero_functions_compressed<TENSOR_RESULT_TYPE(L,R),NDIM>(world, c.dim(1));
compress(world, v, true);
vresult[0].vtransform(v, c, vresult, tol, fence);
return vresult;
}
template <typename T, typename R, std::size_t NDIM>
std::vector< Function<TENSOR_RESULT_TYPE(T,R),NDIM> >
transform(World& world,
const std::vector< Function<T,NDIM> >& v,
const DistributedMatrix<R>& c,
bool fence=true) {
PROFILE_FUNC;
typedef TENSOR_RESULT_TYPE(T,R) resultT;
long n = v.size(); // n is the old dimension
long m = c.rowdim(); // m is the new dimension
MADNESS_ASSERT(n==c.coldim());
// new(i) = sum(j) old(j) c(j,i)
Tensor<T> tmp(n,m);
c.copy_to_replicated(tmp); // for debugging
tmp = transpose(tmp);
std::vector< Function<resultT,NDIM> > vc = zero_functions_compressed<resultT,NDIM>(world, m);
compress(world, v);
for (int i=0; i<m; ++i) {
for (int j=0; j<n; ++j) {
if (tmp(j,i) != R(0.0)) vc[i].gaxpy(1.0,v[j],tmp(j,i),false);
}
}
if (fence) world.gop.fence();
return vc;
}
/// Scales inplace a vector of functions by distinct values
template <typename T, typename Q, std::size_t NDIM>
void scale(World& world,
std::vector< Function<T,NDIM> >& v,
const std::vector<Q>& factors,
bool fence=true) {
PROFILE_BLOCK(Vscale);
for (unsigned int i=0; i<v.size(); ++i) v[i].scale(factors[i],false);
if (fence) world.gop.fence();
}
/// Scales inplace a vector of functions by the same
template <typename T, typename Q, std::size_t NDIM>
void scale(World& world,
std::vector< Function<T,NDIM> >& v,
const Q factor,
bool fence=true) {
PROFILE_BLOCK(Vscale);
for (unsigned int i=0; i<v.size(); ++i) v[i].scale(factor,false);
if (fence) world.gop.fence();
}
/// Computes the 2-norms of a vector of functions
template <typename T, std::size_t NDIM>
std::vector<double> norm2s(World& world,
const std::vector< Function<T,NDIM> >& v) {
PROFILE_BLOCK(Vnorm2);
std::vector<double> norms(v.size());
for (unsigned int i=0; i<v.size(); ++i) norms[i] = v[i].norm2sq_local();
world.gop.sum(&norms[0], norms.size());
for (unsigned int i=0; i<v.size(); ++i) norms[i] = sqrt(norms[i]);
world.gop.fence();
return norms;
}
/// Computes the 2-norm of a vector of functions
template <typename T, std::size_t NDIM>
double norm2(World& world,
const std::vector< Function<T,NDIM> >& v) {
PROFILE_BLOCK(Vnorm2);
std::vector<double> norms(v.size());
for (unsigned int i=0; i<v.size(); ++i) norms[i] = v[i].norm2sq_local();
world.gop.sum(&norms[0], norms.size());
for (unsigned int i=1; i<v.size(); ++i) norms[0] += norms[i];
world.gop.fence();
return sqrt(norms[0]);
}
inline double conj(double x) {
return x;
}
inline double conj(float x) {
return x;
}
// !!! FIXME: this task is broken because FunctionImpl::inner_local forces a
// future on return from WorldTaskQueue::reduce, which will causes a deadlock if
// run inside a task. This behavior must be changed before this task can be used
// again.
//
// template <typename T, typename R, std::size_t NDIM>
// struct MatrixInnerTask : public TaskInterface {
// Tensor<TENSOR_RESULT_TYPE(T,R)> result; // Must be a copy
// const Function<T,NDIM>& f;
// const std::vector< Function<R,NDIM> >& g;
// long jtop;
//
// MatrixInnerTask(const Tensor<TENSOR_RESULT_TYPE(T,R)>& result,
// const Function<T,NDIM>& f,
// const std::vector< Function<R,NDIM> >& g,
// long jtop)
// : result(result), f(f), g(g), jtop(jtop) {}
//
// void run(World& world) {
// for (long j=0; j<jtop; ++j) {
// result(j) = f.inner_local(g[j]);
// }
// }
//
// private:
// /// Get the task id
//
// /// \param id The id to set for this task
// virtual void get_id(std::pair<void*,unsigned short>& id) const {
// PoolTaskInterface::make_id(id, *this);
// }
// }; // struct MatrixInnerTask
template <typename T, std::size_t NDIM>
DistributedMatrix<T> matrix_inner(const DistributedMatrixDistribution& d,
const std::vector< Function<T,NDIM> >& f,
const std::vector< Function<T,NDIM> >& g,
bool sym=false)
{
PROFILE_FUNC;
DistributedMatrix<T> A(d);
const int64_t n = A.coldim();
const int64_t m = A.rowdim();
MADNESS_ASSERT(int64_t(f.size()) == n && int64_t(g.size()) == m);
// Assume we can always create an ichunk*jchunk matrix locally
const int ichunk = 1000;
const int jchunk = 1000; // 1000*1000*8 = 8 MBytes
for (int64_t ilo=0; ilo<n; ilo+=ichunk) {
int64_t ihi = std::min(ilo + ichunk, n);
std::vector< Function<T,NDIM> > ivec(f.begin()+ilo, f.begin()+ihi);
for (int64_t jlo=0; jlo<m; jlo+=jchunk) {
int64_t jhi = std::min(jlo + jchunk, m);
std::vector< Function<T,NDIM> > jvec(g.begin()+jlo, g.begin()+jhi);
Tensor<T> P = matrix_inner(A.get_world(),ivec,jvec);
A.copy_from_replicated_patch(ilo, ihi-1, jlo, jhi-1, P);
}
}
return A;
}
/// Computes the matrix inner product of two function vectors - q(i,j) = inner(f[i],g[j])
/// For complex types symmetric is interpreted as Hermitian.
///
/// The current parallel loop is non-optimal but functional.
template <typename T, typename R, std::size_t NDIM>
Tensor< TENSOR_RESULT_TYPE(T,R) > matrix_inner(World& world,
const std::vector< Function<T,NDIM> >& f,
const std::vector< Function<R,NDIM> >& g,
bool sym=false)
{
world.gop.fence();
compress(world, f);
if ((void*)(&f) != (void*)(&g)) compress(world, g);
std::vector<const FunctionImpl<T,NDIM>*> left(f.size());
std::vector<const FunctionImpl<R,NDIM>*> right(g.size());
for (unsigned int i=0; i<f.size(); i++) left[i] = f[i].get_impl().get();
for (unsigned int i=0; i<g.size(); i++) right[i]= g[i].get_impl().get();
Tensor< TENSOR_RESULT_TYPE(T,R) > r= FunctionImpl<T,NDIM>::inner_local(left, right, sym);
world.gop.fence();
world.gop.sum(r.ptr(),f.size()*g.size());
return r;
}
/// Computes the matrix inner product of two function vectors - q(i,j) = inner(f[i],g[j])
/// For complex types symmetric is interpreted as Hermitian.
///
/// The current parallel loop is non-optimal but functional.
template <typename T, typename R, std::size_t NDIM>
Tensor< TENSOR_RESULT_TYPE(T,R) > matrix_inner_old(World& world,
const std::vector< Function<T,NDIM> >& f,
const std::vector< Function<R,NDIM> >& g,
bool sym=false) {
PROFILE_BLOCK(Vmatrix_inner);
long n=f.size(), m=g.size();
Tensor< TENSOR_RESULT_TYPE(T,R) > r(n,m);
if (sym) MADNESS_ASSERT(n==m);
world.gop.fence();
compress(world, f);
if ((void*)(&f) != (void*)(&g)) compress(world, g);
for (long i=0; i<n; ++i) {
long jtop = m;
if (sym) jtop = i+1;
for (long j=0; j<jtop; ++j) {
r(i,j) = f[i].inner_local(g[j]);
if (sym) r(j,i) = conj(r(i,j));
}
}
// for (long i=n-1; i>=0; --i) {
// long jtop = m;
// if (sym) jtop = i+1;
// world.taskq.add(new MatrixInnerTask<T,R,NDIM>(r(i,_), f[i], g, jtop));
// }
world.gop.fence();
world.gop.sum(r.ptr(),n*m);
// if (sym) {
// for (int i=0; i<n; ++i) {
// for (int j=0; j<i; ++j) {
// r(j,i) = conj(r(i,j));
// }
// }
// }
return r;
}
/// Computes the element-wise inner product of two function vectors - q(i) = inner(f[i],g[i])
template <typename T, typename R, std::size_t NDIM>
Tensor< TENSOR_RESULT_TYPE(T,R) > inner(World& world,
const std::vector< Function<T,NDIM> >& f,
const std::vector< Function<R,NDIM> >& g) {
PROFILE_BLOCK(Vinnervv);
long n=f.size(), m=g.size();
MADNESS_ASSERT(n==m);
Tensor< TENSOR_RESULT_TYPE(T,R) > r(n);
compress(world, f);
compress(world, g);
for (long i=0; i<n; ++i) {
r(i) = f[i].inner_local(g[i]);
}
world.taskq.fence();
world.gop.sum(r.ptr(),n);
world.gop.fence();
return r;
}
/// Computes the inner product of a function with a function vector - q(i) = inner(f,g[i])
template <typename T, typename R, std::size_t NDIM>
Tensor< TENSOR_RESULT_TYPE(T,R) > inner(World& world,
const Function<T,NDIM>& f,
const std::vector< Function<R,NDIM> >& g) {
PROFILE_BLOCK(Vinner);
long n=g.size();
Tensor< TENSOR_RESULT_TYPE(T,R) > r(n);
f.compress();
compress(world, g);
for (long i=0; i<n; ++i) {
r(i) = f.inner_local(g[i]);
}
world.taskq.fence();
world.gop.sum(r.ptr(),n);
world.gop.fence();
return r;
}
/// Multiplies a function against a vector of functions --- q[i] = a * v[i]
template <typename T, typename R, std::size_t NDIM>
std::vector< Function<TENSOR_RESULT_TYPE(T,R), NDIM> >
mul(World& world,
const Function<T,NDIM>& a,
const std::vector< Function<R,NDIM> >& v,
bool fence=true) {
PROFILE_BLOCK(Vmul);
a.reconstruct(false);
reconstruct(world, v, false);
world.gop.fence();
return vmulXX(a, v, 0.0, fence);
}
/// Multiplies a function against a vector of functions using sparsity of a and v[i] --- q[i] = a * v[i]
template <typename T, typename R, std::size_t NDIM>
std::vector< Function<TENSOR_RESULT_TYPE(T,R), NDIM> >
mul_sparse(World& world,
const Function<T,NDIM>& a,
const std::vector< Function<R,NDIM> >& v,
double tol,
bool fence=true) {
PROFILE_BLOCK(Vmulsp);
a.reconstruct(false);
reconstruct(world, v, false);
world.gop.fence();
for (unsigned int i=0; i<v.size(); ++i) {
v[i].norm_tree(false);
}
a.norm_tree();
return vmulXX(a, v, tol, fence);
}
/// Makes the norm tree for all functions in a vector
template <typename T, std::size_t NDIM>
void norm_tree(World& world,
const std::vector< Function<T,NDIM> >& v,
bool fence=true)
{
PROFILE_BLOCK(Vnorm_tree);
for (unsigned int i=0; i<v.size(); ++i) {
v[i].norm_tree(false);
}
if (fence) world.gop.fence();
}
/// Multiplies two vectors of functions q[i] = a[i] * b[i]
template <typename T, typename R, std::size_t NDIM>
std::vector< Function<TENSOR_RESULT_TYPE(T,R), NDIM> >
mul(World& world,
const std::vector< Function<T,NDIM> >& a,
const std::vector< Function<R,NDIM> >& b,
bool fence=true) {
PROFILE_BLOCK(Vmulvv);
reconstruct(world, a, true);
if (&a != &b) reconstruct(world, b, true);
std::vector< Function<TENSOR_RESULT_TYPE(T,R),NDIM> > q(a.size());
for (unsigned int i=0; i<a.size(); ++i) {
q[i] = mul(a[i], b[i], false);
}
if (fence) world.gop.fence();
return q;
}
/// Computes the square of a vector of functions --- q[i] = v[i]**2
template <typename T, std::size_t NDIM>
std::vector< Function<T,NDIM> >
square(World& world,
const std::vector< Function<T,NDIM> >& v,
bool fence=true) {
return mul<T,T,NDIM>(world, v, v, fence);
// std::vector< Function<T,NDIM> > vsq(v.size());
// for (unsigned int i=0; i<v.size(); ++i) {
// vsq[i] = square(v[i], false);
// }
// if (fence) world.gop.fence();
// return vsq;
}
/// Sets the threshold in a vector of functions
template <typename T, std::size_t NDIM>
void set_thresh(World& world, std::vector< Function<T,NDIM> >& v, double thresh, bool fence=true) {
for (unsigned int j=0; j<v.size(); ++j) {
v[j].set_thresh(thresh,false);
}
if (fence) world.gop.fence();
}
/// Returns the complex conjugate of the vector of functions
template <typename T, std::size_t NDIM>
std::vector< Function<T,NDIM> >
conj(World& world,
const std::vector< Function<T,NDIM> >& v,
bool fence=true) {
PROFILE_BLOCK(Vconj);
std::vector< Function<T,NDIM> > r = copy(world, v); // Currently don't have oop conj
for (unsigned int i=0; i<v.size(); ++i) {
r[i].conj(false);
}
if (fence) world.gop.fence();
return r;
}
/// Returns a deep copy of a vector of functions
template <typename T, std::size_t NDIM>
std::vector< Function<T,NDIM> >
copy(World& world,
const std::vector< Function<T,NDIM> >& v,
bool fence=true) {
PROFILE_BLOCK(Vcopy);
std::vector< Function<T,NDIM> > r(v.size());
for (unsigned int i=0; i<v.size(); ++i) {
r[i] = copy(v[i], false);
}
if (fence) world.gop.fence();
return r;
}
/// Returns a vector of deep copies of of a function
template <typename T, std::size_t NDIM>
std::vector< Function<T,NDIM> >
copy(World& world,
const Function<T,NDIM>& v,
const unsigned int n,
bool fence=true) {
PROFILE_BLOCK(Vcopy1);
std::vector< Function<T,NDIM> > r(n);
for (unsigned int i=0; i<n; ++i) {
r[i] = copy(v, false);
}
if (fence) world.gop.fence();
return r;
}
/// Returns new vector of functions --- q[i] = a[i] + b[i]
template <typename T, typename R, std::size_t NDIM>
std::vector< Function<TENSOR_RESULT_TYPE(T,R), NDIM> >
add(World& world,
const std::vector< Function<T,NDIM> >& a,
const std::vector< Function<R,NDIM> >& b,
bool fence=true) {
PROFILE_BLOCK(Vadd);
MADNESS_ASSERT(a.size() == b.size());
compress(world, a);
compress(world, b);
std::vector< Function<TENSOR_RESULT_TYPE(T,R),NDIM> > r(a.size());
for (unsigned int i=0; i<a.size(); ++i) {
r[i] = add(a[i], b[i], false);
}
if (fence) world.gop.fence();
return r;
}
/// Returns new vector of functions --- q[i] = a + b[i]
template <typename T, typename R, std::size_t NDIM>
std::vector< Function<TENSOR_RESULT_TYPE(T,R), NDIM> >
add(World& world,
const Function<T,NDIM> & a,
const std::vector< Function<R,NDIM> >& b,
bool fence=true) {
PROFILE_BLOCK(Vadd1);
a.compress();
compress(world, b);
std::vector< Function<TENSOR_RESULT_TYPE(T,R),NDIM> > r(b.size());
for (unsigned int i=0; i<b.size(); ++i) {
r[i] = add(a, b[i], false);
}
if (fence) world.gop.fence();
return r;
}
template <typename T, typename R, std::size_t NDIM>
inline std::vector< Function<TENSOR_RESULT_TYPE(T,R), NDIM> >
add(World& world,
const std::vector< Function<R,NDIM> >& b,
const Function<T,NDIM> & a,
bool fence=true) {
return add(world, a, b, fence);
}
/// Returns new vector of functions --- q[i] = a[i] - b[i]
template <typename T, typename R, std::size_t NDIM>
std::vector< Function<TENSOR_RESULT_TYPE(T,R), NDIM> >
sub(World& world,
const std::vector< Function<T,NDIM> >& a,
const std::vector< Function<R,NDIM> >& b,
bool fence=true) {
PROFILE_BLOCK(Vsub);
MADNESS_ASSERT(a.size() == b.size());
compress(world, a);
compress(world, b);
std::vector< Function<TENSOR_RESULT_TYPE(T,R),NDIM> > r(a.size());
for (unsigned int i=0; i<a.size(); ++i) {
r[i] = sub(a[i], b[i], false);
}
if (fence) world.gop.fence();
return r;
}
/// Returns new function --- q = sum_i f[i]
template <typename T, std::size_t NDIM>
Function<T, NDIM> sum(World& world, const std::vector<Function<T,NDIM> >& f,
bool fence=true) {
compress(world, f);
Function<T,NDIM> r=real_factory_3d(world).compressed();
for (unsigned int i=0; i<f.size(); ++i) r.gaxpy(1.0,f[i],1.0,false);
if (fence) world.gop.fence();
return r;
}
/// Multiplies and sums two vectors of functions r = \sum_i a[i] * b[i]
template <typename T, typename R, std::size_t NDIM>
Function<TENSOR_RESULT_TYPE(T,R), NDIM>
dot(World& world,
const std::vector< Function<T,NDIM> >& a,
const std::vector< Function<R,NDIM> >& b,
bool fence=true) {
return sum(world,mul(world,a,b,true),fence);
}
/// Generalized A*X+Y for vectors of functions ---- a[i] = alpha*a[i] + beta*b[i]
template <typename T, typename Q, typename R, std::size_t NDIM>
void gaxpy(World& world,
Q alpha,
std::vector< Function<T,NDIM> >& a,
Q beta,
const std::vector< Function<R,NDIM> >& b,
bool fence=true) {
PROFILE_BLOCK(Vgaxpy);
MADNESS_ASSERT(a.size() == b.size());
compress(world, a);
compress(world, b);
for (unsigned int i=0; i<a.size(); ++i) {
a[i].gaxpy(alpha, b[i], beta, false);
}
if (fence) world.gop.fence();
}
/// Applies a vector of operators to a vector of functions --- q[i] = apply(op[i],f[i])
template <typename opT, typename R, std::size_t NDIM>
std::vector< Function<TENSOR_RESULT_TYPE(typename opT::opT,R), NDIM> >
apply(World& world,
const std::vector< std::shared_ptr<opT> >& op,
const std::vector< Function<R,NDIM> > f) {
PROFILE_BLOCK(Vapplyv);
MADNESS_ASSERT(f.size()==op.size());
std::vector< Function<R,NDIM> >& ncf = *const_cast< std::vector< Function<R,NDIM> >* >(&f);
reconstruct(world, f);
nonstandard(world, ncf);
std::vector< Function<TENSOR_RESULT_TYPE(typename opT::opT,R), NDIM> > result(f.size());
for (unsigned int i=0; i<f.size(); ++i) {
MADNESS_ASSERT(not op[i]->is_slaterf12);
result[i] = apply_only(*op[i], f[i], false);
}
world.gop.fence();
standard(world, ncf, false); // restores promise of logical constness
world.gop.fence();
reconstruct(world, result);
return result;
}
/// Applies an operator to a vector of functions --- q[i] = apply(op,f[i])
template <typename T, typename R, std::size_t NDIM>
std::vector< Function<TENSOR_RESULT_TYPE(T,R), NDIM> >
apply(World& world,
const SeparatedConvolution<T,NDIM>& op,
const std::vector< Function<R,NDIM> > f) {
PROFILE_BLOCK(Vapply);
std::vector< Function<R,NDIM> >& ncf = *const_cast< std::vector< Function<R,NDIM> >* >(&f);
reconstruct(world, f);
nonstandard(world, ncf);
std::vector< Function<TENSOR_RESULT_TYPE(T,R), NDIM> > result(f.size());
for (unsigned int i=0; i<f.size(); ++i) {
result[i] = apply_only(op, f[i], false);
}
world.gop.fence();
standard(world, ncf, false); // restores promise of logical constness
reconstruct(world, result);
if (op.is_slaterf12) {
MADNESS_ASSERT(not op.destructive());
for (unsigned int i=0; i<f.size(); ++i) {
double trace=f[i].trace();
result[i]=(result[i]-trace).scale(-0.5/op.mu());
}
}
return result;
}
/// Normalizes a vector of functions --- v[i] = v[i].scale(1.0/v[i].norm2())
template <typename T, std::size_t NDIM>
void normalize(World& world, std::vector< Function<T,NDIM> >& v, bool fence=true) {
PROFILE_BLOCK(Vnormalize);
std::vector<double> nn = norm2s(world, v);
for (unsigned int i=0; i<v.size(); ++i) v[i].scale(1.0/nn[i],false);
if (fence) world.gop.fence();
}
template <typename T, std::size_t NDIM>
void print_size(World &world, const std::vector<Function<T,NDIM> > &v, const std::string &msg = "vectorfunction" ){
if(v.empty()){
if(world.rank()==0) std::cout << "print_size: " << msg << " is empty" << std::endl;
}else if(v.size()==1){
v.front().print_size(msg);
}else{
for(auto x:v){
x.print_size(msg);
}
}
}
// gives back the size in GB
template <typename T, std::size_t NDIM>
double get_size(World& world, const std::vector< Function<T,NDIM> >& v){
if (v.empty()) return 0.0;
const double d=sizeof(T);
const double fac=1024*1024*1024;
double size=0.0;
for(unsigned int i=0;i<v.size();i++){
if (v[i].is_initialized()) size+=v[i].size();
}
return size/fac*d;
}
// gives back the size in GB
template <typename T, std::size_t NDIM>
double get_size(const Function<T,NDIM> & f){
const double d=sizeof(T);
const double fac=1024*1024*1024;
double size=f.size();
return size/fac*d;
}
// convenience operators
template <typename T, std::size_t NDIM>
std::vector<Function<T,NDIM> > operator+(const std::vector<Function<T,NDIM> >& lhs,
const std::vector<Function<T,NDIM>>& rhs) {
return add(lhs[0].world(),lhs,rhs);
}
template <typename T, std::size_t NDIM>
std::vector<Function<T,NDIM> > operator-(const std::vector<Function<T,NDIM> >& lhs,
const std::vector<Function<T,NDIM> >& rhs) {
return sub(lhs[0].world(),lhs,rhs);
}
template <typename T, std::size_t NDIM>
std::vector<Function<T,NDIM> > operator*(const double fac,
const std::vector<Function<T,NDIM> >& rhs) {
std::vector<Function<T,NDIM> > tmp=copy(rhs[0].world(),rhs);
scale(tmp[0].world(),tmp,fac);
return tmp;
}
template <typename T, std::size_t NDIM>
std::vector<Function<T,NDIM> > operator*(const std::vector<Function<T,NDIM> >& rhs,
const double fac) {
std::vector<Function<T,NDIM> > tmp=copy(rhs[0].world(),rhs);
scale(tmp[0].world(),tmp,fac);
return tmp;
}
/// multiply a vector of functions with a function: r[i] = v[i] * a
template <typename T, std::size_t NDIM>
std::vector<Function<T,NDIM> > operator*(const Function<T,NDIM>& a,
const std::vector<Function<T,NDIM> >& v) {
return mul(v[0].world(),a,v,true);
}
/// multiply a vector of functions with a function: r[i] = a * v[i]
template <typename T, std::size_t NDIM>
std::vector<Function<T,NDIM> > operator*(const std::vector<Function<T,NDIM> >& v,
const Function<T,NDIM>& a) {
return mul(v[0].world(),a,v,true);
}
template <typename T, std::size_t NDIM>
std::vector<Function<T,NDIM> > operator+=(std::vector<Function<T,NDIM> >& rhs,
const std::vector<Function<T,NDIM> >& lhs) {
rhs=add(rhs[0].world(),rhs,lhs);
return rhs;
}
template <typename T, std::size_t NDIM>
std::vector<Function<T,NDIM> > operator-=(std::vector<Function<T,NDIM> >& rhs,
const std::vector<Function<T,NDIM> >& lhs) {
rhs=sub(rhs[0].world(),rhs,lhs);
return rhs;
}
/// shorthand gradient operator
/// returns the differentiated function f in all NDIM directions
/// @param[in] f the function on which the grad operator works on
/// @param[in] refine refinement before diff'ing makes the result more accurate
/// @param[in] fence fence after completion; if reconstruction is needed always fence
/// @return the vector \frac{\partial}{\partial x_i} f
template <typename T, std::size_t NDIM>
std::vector<Function<T,NDIM> > grad(const Function<T,NDIM>& f,
bool refine=false, bool fence=true) {
World& world=f.world();
f.reconstruct();
if (refine) f.refine(); // refine to make result more precise
std::vector< std::shared_ptr< Derivative<T,NDIM> > > grad=
gradient_operator<T,NDIM>(world);
std::vector<Function<T,NDIM> > result(NDIM);
for (int i=0; i<NDIM; ++i) result[i]=apply(*(grad[i]),f,false);
if (fence) world.gop.fence();
return result;
}
/// shorthand div operator
/// returns the dot product of nabla with a vector f
/// @param[in] f the vector of functions on which the div operator works on
/// @param[in] refine refinement before diff'ing makes the result more accurate
/// @param[in] fence fence after completion; currently always fences
/// @return the vector \frac{\partial}{\partial x_i} f
/// TODO: add this to operator fusion
template <typename T, std::size_t NDIM>
Function<T,NDIM> div(const std::vector<Function<T,NDIM> >& v,
bool do_refine=false, bool fence=true) {
MADNESS_ASSERT(v.size()>0);
World& world=v[0].world();
reconstruct(world,v);
if (do_refine) refine(world,v); // refine to make result more precise
std::vector< std::shared_ptr< Derivative<T,NDIM> > > grad=
gradient_operator<T,NDIM>(world);
std::vector<Function<T,NDIM> > result(NDIM);
for (int i=0; i<NDIM; ++i) result[i]=apply(*(grad[i]),v[i],false);
world.gop.fence();
return sum(world,result,fence);
}
/// load a vector of functions
template<typename T, size_t NDIM>
void load_function(World& world, std::vector<Function<T,NDIM> >& f,
const std::string name) {
if (world.rank()==0) print("loading vector of functions",name);
archive::ParallelInputArchive ar(world, name.c_str(), 1);
std::size_t fsize=0;
ar & fsize;
f.resize(fsize);
for (std::size_t i=0; i<fsize; ++i) ar & f[i];
}
}
#endif // MADNESS_MRA_VMRA_H__INCLUDED
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