dynare/mex/sources/libkorder/tl/stack_container.cc

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/*
* Copyright © 2004 Ondra Kamenik
* Copyright © 2019-2023 Dynare Team
*
* This file is part of Dynare.
*
* Dynare 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 3 of the License, or
* (at your option) any later version.
*
* Dynare 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 Dynare. If not, see <https://www.gnu.org/licenses/>.
*/
#include "stack_container.hh"
#include "ps_tensor.hh"
#include "pyramid_prod2.hh"
#include <memory>
// FoldedStackContainer::multAndAdd() sparse code
/* Here we multiply the sparse tensor with the FoldedStackContainer. We have
four implementations, multAndAddSparse1(), multAndAddSparse2(),
multAndAddSparse3(), and multAndAddSparse4(). The third is not threaded yet
and I expect that it is certainly the slowest. The multAndAddSparse4()
exploits the sparsity, however, it seems to be still worse than
multAndAddSparse2() even for really sparse matrices. On the other hand, it
can be more efficient than multAndAddSparse2() for large problems, since it
does not need that much of memory and can avoid much swapping. Very
preliminary examination shows that multAndAddSparse2() is the best in terms
of time. */
void
FoldedStackContainer::multAndAdd(const FSSparseTensor& t, FGSTensor& out) const
{
TL_RAISE_IF(t.nvar() != getAllSize(),
"Wrong number of variables of tensor for FoldedStackContainer::multAndAdd");
multAndAddSparse2(t, out);
}
// FoldedStackContainer::multAndAdd() dense code
/* Here we perform the Faà Di Bruno step for a given dimension dim, and for
the dense fully symmetric tensor which is scattered in the container
of general symmetric tensors. The implementation is pretty the same as
UnfoldedStackContainer::multAndAdd() dense code. */
void
FoldedStackContainer::multAndAdd(int dim, const FGSContainer& c, FGSTensor& out) const
{
TL_RAISE_IF(c.num() != numStacks(),
"Wrong symmetry length of container for FoldedStackContainer::multAndAdd");
sthread::detach_thread_group gr;
for (auto& si : SymmetrySet(dim, c.num()))
if (c.check(si))
gr.insert(std::make_unique<WorkerFoldMAADense>(*this, si, c, out));
gr.run();
}
/* This is analogous to WorkerUnfoldMAADense::operator()() code. */
void
WorkerFoldMAADense::operator()(std::mutex& mut)
{
Permutation iden(dense_cont.num());
IntSequence coor(iden.getMap().unfold(sym));
const FGSTensor& g = dense_cont.get(sym);
cont.multAndAddStacks(coor, g, out, mut);
}
WorkerFoldMAADense::WorkerFoldMAADense(const FoldedStackContainer& container, Symmetry s,
const FGSContainer& dcontainer, FGSTensor& outten) :
cont(container), sym(std::move(s)), dense_cont(dcontainer), out(outten)
{
}
/* This is analogous to UnfoldedStackContainer::multAndAddSparse1() code. */
void
FoldedStackContainer::multAndAddSparse1(const FSSparseTensor& t, FGSTensor& out) const
{
sthread::detach_thread_group gr;
UFSTensor dummy(0, numStacks(), t.dimen());
for (Tensor::index ui = dummy.begin(); ui != dummy.end(); ++ui)
gr.insert(std::make_unique<WorkerFoldMAASparse1>(*this, t, out, ui.getCoor()));
gr.run();
}
/* This is analogous to WorkerUnfoldMAASparse1::operator()() code.
The only difference is that instead of UPSTensor as a
result of multiplication of unfolded tensor and tensors from
containers, we have FPSTensor with partially folded permuted
symmetry.
TODO: make slice vertically narrowed according to the fill of t,
vertically narrow out accordingly. */
void
WorkerFoldMAASparse1::operator()(std::mutex& mut)
{
const EquivalenceSet& eset = TLStatic::getEquiv(out.dimen());
const PermutationSet& pset = TLStatic::getPerm(t.dimen());
Permutation iden(t.dimen());
UPSTensor slice(t, cont.getStackSizes(), coor, PerTensorDimens(cont.getStackSizes(), coor));
for (int iper = 0; iper < pset.getNum(); iper++)
{
const Permutation& per = pset.get(iper);
IntSequence percoor(coor.size());
per.apply(coor, percoor);
for (const auto& it : eset)
if (it.numClasses() == t.dimen())
{
StackProduct<FGSTensor> sp(cont, it, out.getSym());
if (!sp.isZero(percoor))
{
KronProdStack<FGSTensor> kp(sp, percoor);
kp.optimizeOrder();
const Permutation& oper = kp.getPer();
if (Permutation(oper, per) == iden)
{
FPSTensor fps(out.getDims(), it, slice, kp);
{
std::unique_lock<std::mutex> lk {mut};
fps.addTo(out);
}
}
}
}
}
}
WorkerFoldMAASparse1::WorkerFoldMAASparse1(const FoldedStackContainer& container,
const FSSparseTensor& ten, FGSTensor& outten,
IntSequence c) :
cont(container), t(ten), out(outten), coor(std::move(c))
{
}
/* Here is the second implementation of sparse folded multAndAdd(). It
is pretty similar to implementation of
UnfoldedStackContainer::multAndAddSparse2() code. We make a
dense folded slice, and then call folded multAndAddStacks(), which
multiplies all the combinations compatible with the slice. */
void
FoldedStackContainer::multAndAddSparse2(const FSSparseTensor& t, FGSTensor& out) const
{
sthread::detach_thread_group gr;
FFSTensor dummy_f(0, numStacks(), t.dimen());
for (Tensor::index fi = dummy_f.begin(); fi != dummy_f.end(); ++fi)
gr.insert(std::make_unique<WorkerFoldMAASparse2>(*this, t, out, fi.getCoor()));
gr.run();
}
/* Here we make a sparse slice first and then call multAndAddStacks()
if the slice is not empty. If the slice is really sparse, we call
sparse version of multAndAddStacks(). What means “really sparse” is
given by fill_threshold. It is not tuned yet, a practice shows that
it must be a really low number, since sparse multAndAddStacks() is
much slower than the dense version.
Further, we take only nonzero rows of the slice, and accordingly of
the out tensor. We jump over zero initial rows and drop zero tailing
rows. */
void
WorkerFoldMAASparse2::operator()(std::mutex& mut)
{
GSSparseTensor slice(t, cont.getStackSizes(), coor, TensorDimens(cont.getStackSizes(), coor));
if (slice.getNumNonZero())
{
if (slice.getUnfoldIndexFillFactor() > FoldedStackContainer::fill_threshold)
{
FGSTensor dense_slice(slice);
int r1 = slice.getFirstNonZeroRow();
int r2 = slice.getLastNonZeroRow();
FGSTensor dense_slice1(r1, r2 - r1 + 1, dense_slice);
FGSTensor out1(r1, r2 - r1 + 1, out);
cont.multAndAddStacks(coor, dense_slice1, out1, mut);
}
else
cont.multAndAddStacks(coor, slice, out, mut);
}
}
WorkerFoldMAASparse2::WorkerFoldMAASparse2(const FoldedStackContainer& container,
const FSSparseTensor& ten, FGSTensor& outten,
IntSequence c) :
cont(container), t(ten), out(outten), coor(std::move(c))
{
}
/* Here is the third implementation of the sparse folded
multAndAdd(). It is column-wise implementation, and thus is not a good
candidate for the best performer.
We go through all columns from the output. For each column we
calculate folded sumcol which is a sum of all appropriate columns
for all suitable equivalences. So we go through all suitable
equivalences, for each we construct a StackProduct object and
construct IrregTensor for a corresponding column of z. The
IrregTensor is an abstraction for Kronecker multiplication of
stacked columns of the two containers without zeros. Then the column
is added to sumcol. Finally, the sumcol is multiplied by the
sparse tensor. */
void
FoldedStackContainer::multAndAddSparse3(const FSSparseTensor& t, FGSTensor& out) const
{
const EquivalenceSet& eset = TLStatic::getEquiv(out.dimen());
for (Tensor::index run = out.begin(); run != out.end(); ++run)
{
Vector outcol {out.getCol(*run)};
FRSingleTensor sumcol(t.nvar(), t.dimen());
sumcol.zeros();
for (const auto& it : eset)
if (it.numClasses() == t.dimen())
{
StackProduct<FGSTensor> sp(*this, it, out.getSym());
IrregTensorHeader header(sp, run.getCoor());
IrregTensor irten(header);
irten.addTo(sumcol);
}
t.multColumnAndAdd(sumcol, outcol);
}
}
/* Here is the fourth implementation of sparse
FoldedStackContainer::multAndAdd(). It is almost equivalent to
multAndAddSparse2() with the exception that the FPSTensor as a
result of a product of a slice and Kronecker product of the stack
derivatives is calculated in the sparse fashion. For further details, see
FoldedStackContainer::multAndAddStacks() sparse code and
FPSTensor| sparse constructor. */
void
FoldedStackContainer::multAndAddSparse4(const FSSparseTensor& t, FGSTensor& out) const
{
sthread::detach_thread_group gr;
FFSTensor dummy_f(0, numStacks(), t.dimen());
for (Tensor::index fi = dummy_f.begin(); fi != dummy_f.end(); ++fi)
gr.insert(std::make_unique<WorkerFoldMAASparse4>(*this, t, out, fi.getCoor()));
gr.run();
}
/* The WorkerFoldMAASparse4 is the same as WorkerFoldMAASparse2
with the exception that we call a sparse version of
multAndAddStacks(). */
void
WorkerFoldMAASparse4::operator()(std::mutex& mut)
{
GSSparseTensor slice(t, cont.getStackSizes(), coor, TensorDimens(cont.getStackSizes(), coor));
if (slice.getNumNonZero())
cont.multAndAddStacks(coor, slice, out, mut);
}
WorkerFoldMAASparse4::WorkerFoldMAASparse4(const FoldedStackContainer& container,
const FSSparseTensor& ten, FGSTensor& outten,
IntSequence c) :
cont(container), t(ten), out(outten), coor(std::move(c))
{
}
// FoldedStackContainer::multAndAddStacks() dense code
/* This is almost the same as UnfoldedStackContainer::multAndAddStacks() code.
The only difference is that we do not construct a UPSTensor from
KronProdStack, but we construct partially folded permuted symmetry
FPSTensor. Note that the tensor g must be unfolded in order to be able to
multiply with unfolded rows of Kronecker product. However, columns of such a
product are partially folded giving a rise to the FPSTensor. */
void
FoldedStackContainer::multAndAddStacks(const IntSequence& coor, const FGSTensor& g, FGSTensor& out,
std::mutex& mut) const
{
const EquivalenceSet& eset = TLStatic::getEquiv(out.dimen());
UGSTensor ug(g);
UFSTensor dummy_u(0, numStacks(), g.dimen());
for (Tensor::index ui = dummy_u.begin(); ui != dummy_u.end(); ++ui)
{
IntSequence tmp(ui.getCoor());
tmp.sort();
if (tmp == coor)
{
Permutation sort_per(ui.getCoor());
sort_per.inverse();
for (const auto& it : eset)
if (it.numClasses() == g.dimen())
{
StackProduct<FGSTensor> sp(*this, it, sort_per, out.getSym());
if (!sp.isZero(coor))
{
KronProdStack<FGSTensor> kp(sp, coor);
if (ug.getSym().isFull())
kp.optimizeOrder();
FPSTensor fps(out.getDims(), it, sort_per, ug, kp);
{
std::unique_lock<std::mutex> lk {mut};
fps.addTo(out);
}
}
}
}
}
}
// FoldedStackContainer::multAndAddStacks() sparse code
/* This is almost the same as FoldedStackContainer::multAndAddStacks() dense code. The only
difference is that the Kronecker product of the stacks is multiplied
with sparse slice GSSparseTensor (not dense slice FGSTensor). The
multiplication is done in FPSTensor sparse constructor. */
void
FoldedStackContainer::multAndAddStacks(const IntSequence& coor, const GSSparseTensor& g,
FGSTensor& out, std::mutex& mut) const
{
const EquivalenceSet& eset = TLStatic::getEquiv(out.dimen());
UFSTensor dummy_u(0, numStacks(), g.dimen());
for (Tensor::index ui = dummy_u.begin(); ui != dummy_u.end(); ++ui)
{
IntSequence tmp(ui.getCoor());
tmp.sort();
if (tmp == coor)
{
Permutation sort_per(ui.getCoor());
sort_per.inverse();
for (const auto& it : eset)
if (it.numClasses() == g.dimen())
{
StackProduct<FGSTensor> sp(*this, it, sort_per, out.getSym());
if (!sp.isZero(coor))
{
KronProdStack<FGSTensor> kp(sp, coor);
FPSTensor fps(out.getDims(), it, sort_per, g, kp);
{
std::unique_lock<std::mutex> lk {mut};
fps.addTo(out);
}
}
}
}
}
}
// UnfoldedStackContainer::multAndAdd() sparse code
/* Here we simply call either multAndAddSparse1() or
multAndAddSparse2(). The first one allows for optimization of
Kronecker products, so it seems to be more efficient. */
void
UnfoldedStackContainer::multAndAdd(const FSSparseTensor& t, UGSTensor& out) const
{
TL_RAISE_IF(t.nvar() != getAllSize(),
"Wrong number of variables of tensor for UnfoldedStackContainer::multAndAdd");
multAndAddSparse2(t, out);
}
// UnfoldedStackContainer::multAndAdd() dense code
/* Here we implement the formula for stacks for fully symmetric tensor
scattered in a number of general symmetry tensors contained in a given
container. The implementations is pretty the same as in
multAndAddSparse2() but we do not do the slices of sparse tensor, but
only a lookup to the container.
This means that we do not iterate through a dummy folded tensor to
obtain folded coordinates of stacks, rather we iterate through all
symmetries contained in the container and the coordinates of stacks
are obtained as unfolded identity sequence via the symmetry. The
reason of doing this is that we are unable to calculate symmetry from
stack coordinates as easily as stack coordinates from the symmetry. */
void
UnfoldedStackContainer::multAndAdd(int dim, const UGSContainer& c, UGSTensor& out) const
{
TL_RAISE_IF(c.num() != numStacks(),
"Wrong symmetry length of container for UnfoldedStackContainer::multAndAdd");
sthread::detach_thread_group gr;
for (auto& si : SymmetrySet(dim, c.num()))
if (c.check(si))
gr.insert(std::make_unique<WorkerUnfoldMAADense>(*this, si, c, out));
gr.run();
}
void
WorkerUnfoldMAADense::operator()(std::mutex& mut)
{
Permutation iden(dense_cont.num());
IntSequence coor(iden.getMap().unfold(sym));
const UGSTensor& g = dense_cont.get(sym);
cont.multAndAddStacks(coor, g, out, mut);
}
WorkerUnfoldMAADense::WorkerUnfoldMAADense(const UnfoldedStackContainer& container, Symmetry s,
const UGSContainer& dcontainer, UGSTensor& outten) :
cont(container), sym(std::move(s)), dense_cont(dcontainer), out(outten)
{
}
/* Here we implement the formula for unfolded tensors. If, for instance,
a coordinate z of a tensor [f_z²] is partitioned as
z=(a, b), then we perform the following:
⎛a_c(x)⎞ ⎛a_c(y)⎞
[f_z²] · ∑ ⎢ ⎥⊗⎢ ⎥ = [f_aa] · ∑ a_c(x)⊗a_c(y) + [f_ab] · ∑ a_c(x)⊗b_c(y)
ᶜ ⎝b_c(x)⎠ ⎝b_c(y)⎠ ᶜ ᶜ
+ [f_ba] · ∑ b_c(x)⊗a_c(y) + [f_bb] · ∑ b_c(x)⊗b_c(y)
This is exactly what happens here. The code is clear. It goes through
all combinations of stacks, and each thread is responsible for
operation for the slice corresponding to the combination of the stacks. */
void
UnfoldedStackContainer::multAndAddSparse1(const FSSparseTensor& t, UGSTensor& out) const
{
sthread::detach_thread_group gr;
UFSTensor dummy(0, numStacks(), t.dimen());
for (Tensor::index ui = dummy.begin(); ui != dummy.end(); ++ui)
gr.insert(std::make_unique<WorkerUnfoldMAASparse1>(*this, t, out, ui.getCoor()));
gr.run();
}
/* This does a step of UnfoldedStackContainer::multAndAddSparse1() for
a given coordinates. First it makes the slice of the given stack coordinates.
Then it multiplies everything what should be multiplied with the slice.
That is it goes through all equivalences, creates StackProduct, then
KronProdStack, which is added to out. So far everything is clear.
However, we want to use optimized KronProdAllOptim to minimize a number of
flops and memory needed in the Kronecker product. So we go through all
permutations per, permute the coordinates to get percoor, go through all
equivalences, and make KronProdStack and optimize it. The result of
optimization is a permutation oper. Now, we multiply the Kronecker product
with the slice, only if the slice has the same ordering of coordinates as
the Kronecker product KronProdStack. However, it is not perfectly true.
Since we go through *all* permutations per, there might be two different
permutations leading to the same ordering in KronProdStack and thus the same
ordering in the optimized KronProdStack. The two cases would be counted
twice, which is wrong. That is why we do not condition on
coor∘oper∘per = coor, but we condition on oper∘per = id. In this way, we
rule out permutations per leading to the same ordering of stacks when
applied on coor.
TODO: vertically narrow slice and out according to the fill in t. */
void
WorkerUnfoldMAASparse1::operator()(std::mutex& mut)
{
const EquivalenceSet& eset = TLStatic::getEquiv(out.dimen());
const PermutationSet& pset = TLStatic::getPerm(t.dimen());
Permutation iden(t.dimen());
UPSTensor slice(t, cont.getStackSizes(), coor, PerTensorDimens(cont.getStackSizes(), coor));
for (int iper = 0; iper < pset.getNum(); iper++)
{
const Permutation& per = pset.get(iper);
IntSequence percoor(coor.size());
per.apply(coor, percoor);
for (const auto& it : eset)
if (it.numClasses() == t.dimen())
{
StackProduct<UGSTensor> sp(cont, it, out.getSym());
if (!sp.isZero(percoor))
{
KronProdStack<UGSTensor> kp(sp, percoor);
kp.optimizeOrder();
const Permutation& oper = kp.getPer();
if (Permutation(oper, per) == iden)
{
UPSTensor ups(out.getDims(), it, slice, kp);
{
std::unique_lock<std::mutex> lk {mut};
ups.addTo(out);
}
}
}
}
}
}
WorkerUnfoldMAASparse1::WorkerUnfoldMAASparse1(const UnfoldedStackContainer& container,
const FSSparseTensor& ten, UGSTensor& outten,
IntSequence c) :
cont(container), t(ten), out(outten), coor(std::move(c))
{
}
/* In here we implement the formula by a bit different way. We use the
fact, using notation of UnfoldedStackContainer::multAndAddSparse2(),
that
⎛ ⎞
[f_ba] · ∑ b_c(x)⊗a_c(y) = [f_ba] ·⎢∑ a_c(y)⊗b_c(x)⎥· P
ᶜ ⎝ᶜ ⎠
where P is a suitable permutation of columns. The permutation
corresponds to (in this example) a swap of a and b. An advantage
of this approach is that we do not need UPSTensor for [f_ba], and
thus we decrease the number of needed slices.
So we go through all folded indices of stack coordinates, then for
each such index fi we make a slice and call multAndAddStacks(). This
goes through all corresponding unfolded indices to perform the
formula. Each unsorted (unfold) index implies a sorting permutation
sort_per which must be used to permute stacks in StackProduct, and
permute equivalence classes when UPSTensor is formed. In this way
the column permutation P from the formula is factored to the
permutation of UPSTensor. */
void
UnfoldedStackContainer::multAndAddSparse2(const FSSparseTensor& t, UGSTensor& out) const
{
sthread::detach_thread_group gr;
FFSTensor dummy_f(0, numStacks(), t.dimen());
for (Tensor::index fi = dummy_f.begin(); fi != dummy_f.end(); ++fi)
gr.insert(std::make_unique<WorkerUnfoldMAASparse2>(*this, t, out, fi.getCoor()));
gr.run();
}
/* This does a step of UnfoldedStackContainer::multAndAddSparse2() for a given
coordinates.
TODO: implement multAndAddStacks() for sparse slice as
FoldedStackContainer::multAndAddStacks() sparse code and do this method as
WorkerFoldMAASparse2::operator()(). */
void
WorkerUnfoldMAASparse2::operator()(std::mutex& mut)
{
GSSparseTensor slice(t, cont.getStackSizes(), coor, TensorDimens(cont.getStackSizes(), coor));
if (slice.getNumNonZero())
{
FGSTensor fslice(slice);
UGSTensor dense_slice(fslice);
int r1 = slice.getFirstNonZeroRow();
int r2 = slice.getLastNonZeroRow();
UGSTensor dense_slice1(r1, r2 - r1 + 1, dense_slice);
UGSTensor out1(r1, r2 - r1 + 1, out);
cont.multAndAddStacks(coor, dense_slice1, out1, mut);
}
}
WorkerUnfoldMAASparse2::WorkerUnfoldMAASparse2(const UnfoldedStackContainer& container,
const FSSparseTensor& ten, UGSTensor& outten,
IntSequence c) :
cont(container), t(ten), out(outten), coor(std::move(c))
{
}
/* For a given unfolded coordinates of stacks fi, and appropriate
tensor g, whose symmetry is a symmetry of fi, the method
contributes to out all tensors in unfolded stack formula involving
stacks chosen by fi.
We go through all ui coordinates which yield fi after sorting. We
construct a permutation sort_per which sorts ui to fi. We go
through all appropriate equivalences, and construct StackProduct
from equivalence classes permuted by sort_per, then UPSTensor with
implied permutation of columns by the permuted equivalence by
sort_per. The UPSTensor is then added to out.
We cannot use here the optimized KronProdStack, since the symmetry
of UGSTensor& g prescribes the ordering of the stacks. However, if
g is fully symmetric, we can do the optimization harmlessly. */
void
UnfoldedStackContainer::multAndAddStacks(const IntSequence& fi, const UGSTensor& g, UGSTensor& out,
std::mutex& mut) const
{
const EquivalenceSet& eset = TLStatic::getEquiv(out.dimen());
UFSTensor dummy_u(0, numStacks(), g.dimen());
for (Tensor::index ui = dummy_u.begin(); ui != dummy_u.end(); ++ui)
{
IntSequence tmp(ui.getCoor());
tmp.sort();
if (tmp == fi)
{
Permutation sort_per(ui.getCoor());
sort_per.inverse();
for (const auto& it : eset)
if (it.numClasses() == g.dimen())
{
StackProduct<UGSTensor> sp(*this, it, sort_per, out.getSym());
if (!sp.isZero(fi))
{
KronProdStack<UGSTensor> kp(sp, fi);
if (g.getSym().isFull())
kp.optimizeOrder();
UPSTensor ups(out.getDims(), it, sort_per, g, kp);
{
std::unique_lock<std::mutex> lk {mut};
ups.addTo(out);
}
}
}
}
}
}