void Contract
( const ElementalMatrix<T>& A,
ElementalMatrix<T>& B )
{
DEBUG_ONLY(CSE cse("Contract"))
AssertSameGrids( A, B );
const Dist U = B.ColDist();
const Dist V = B.RowDist();
// TODO: Shorten this implementation?
if( A.ColDist() == U && A.RowDist() == V )
{
Copy( A, B );
}
else if( A.ColDist() == U && A.RowDist() == Partial(V) )
{
B.AlignAndResize
( A.ColAlign(), A.RowAlign(), A.Height(), A.Width(), false, false );
Zeros( B.Matrix(), B.LocalHeight(), B.LocalWidth() );
AxpyContract( T(1), A, B );
}
else if( A.ColDist() == Partial(U) && A.RowDist() == V )
{
B.AlignAndResize
( A.ColAlign(), A.RowAlign(), A.Height(), A.Width(), false, false );
Zeros( B.Matrix(), B.LocalHeight(), B.LocalWidth() );
AxpyContract( T(1), A, B );
}
else if( A.ColDist() == U && A.RowDist() == Collect(V) )
{
B.AlignColsAndResize
( A.ColAlign(), A.Height(), A.Width(), false, false );
Zeros( B.Matrix(), B.LocalHeight(), B.LocalWidth() );
AxpyContract( T(1), A, B );
}
else if( A.ColDist() == Collect(U) && A.RowDist() == V )
{
B.AlignRowsAndResize
( A.RowAlign(), A.Height(), A.Width(), false, false );
Zeros( B.Matrix(), B.LocalHeight(), B.LocalWidth() );
AxpyContract( T(1), A, B );
}
else if( A.ColDist() == Collect(U) && A.RowDist() == Collect(V) )
{
Zeros( B, A.Height(), A.Width() );
AxpyContract( T(1), A, B );
}
else
LogicError("Incompatible distributions");
}
void UniformHelmholtzGreens
( ElementalMatrix<Complex<Real>>& A, Int n, Real lambda )
{
EL_DEBUG_CSE
typedef Complex<Real> C;
const Real pi = 4*Atan( Real(1) );
const Real k0 = 2*pi/lambda;
const Grid& g = A.Grid();
// Generate a list of n uniform samples from the 3D unit ball
DistMatrix<Real,STAR,VR> X_STAR_VR(3,n,g);
for( Int jLoc=0; jLoc<X_STAR_VR.LocalWidth(); ++jLoc )
{
Real x0, x1, x2;
// Sample uniformly from [-1,+1]^3 until a point is drawn from the ball
while( true )
{
x0 = SampleUniform( Real(-1), Real(1) );
x1 = SampleUniform( Real(-1), Real(1) );
x2 = SampleUniform( Real(-1), Real(1) );
const Real radiusSq = x0*x0 + x1*x1 + x2*x2;
if( radiusSq > 0 && radiusSq <= 1 )
break;
}
X_STAR_VR.SetLocal( 0, jLoc, x0 );
X_STAR_VR.SetLocal( 1, jLoc, x1 );
X_STAR_VR.SetLocal( 2, jLoc, x2 );
}
DistMatrix<Real,STAR,STAR> X_STAR_STAR( X_STAR_VR );
A.Resize( n, n );
for( Int jLoc=0; jLoc<A.LocalWidth(); ++jLoc )
{
const Int j = A.GlobalCol(jLoc);
const Real xj0 = X_STAR_STAR.GetLocal(0,j);
const Real xj1 = X_STAR_STAR.GetLocal(1,j);
const Real xj2 = X_STAR_STAR.GetLocal(2,j);
for( Int iLoc=0; iLoc<A.LocalHeight(); ++iLoc )
{
const Int i = A.GlobalRow(iLoc);
if( i == j )
{
A.SetLocal( iLoc, jLoc, 0 );
}
else
{
const Real d0 = X_STAR_STAR.GetLocal(0,i)-xj0;
const Real d1 = X_STAR_STAR.GetLocal(1,i)-xj1;
const Real d2 = X_STAR_STAR.GetLocal(2,i)-xj2;
const Real gamma = k0*Sqrt(d0*d0+d1*d1+d2*d2);
const Real realPart = Cos(gamma)/gamma;
const Real imagPart = Sin(gamma)/gamma;
A.SetLocal( iLoc, jLoc, C(realPart,imagPart) );
}
}
}
}
void PartialRowScatter
( T alpha,
const ElementalMatrix<T>& A,
ElementalMatrix<T>& B )
{
DEBUG_ONLY(CSE cse("axpy_contract::PartialRowScatter"))
AssertSameGrids( A, B );
if( A.Height() != B.Height() || A.Width() != B.Width() )
LogicError("Matrix sizes did not match");
if( !B.Participating() )
return;
if( B.RowAlign() % A.RowStride() == A.RowAlign() )
{
const Int rowStride = B.RowStride();
const Int rowStridePart = B.PartialRowStride();
const Int rowStrideUnion = B.PartialUnionRowStride();
const Int rowRankPart = B.PartialRowRank();
const Int height = B.Height();
const Int width = B.Width();
const Int maxLocalWidth = MaxLength( width, rowStride );
const Int recvSize = mpi::Pad( height*maxLocalWidth );
const Int sendSize = rowStrideUnion*recvSize;
//vector<T> buffer( sendSize );
vector<T> buffer;
buffer.reserve( sendSize );
// Pack
copy::util::PartialRowStridedPack
( height, width,
B.RowAlign(), rowStride,
rowStrideUnion, rowStridePart, rowRankPart,
A.RowShift(),
A.LockedBuffer(), A.LDim(),
buffer.data(), recvSize );
// Communicate
mpi::ReduceScatter( buffer.data(), recvSize, B.PartialUnionRowComm() );
// Unpack our received data
axpy::util::InterleaveMatrixUpdate
( alpha, height, B.LocalWidth(),
buffer.data(), 1, height,
B.Buffer(), 1, B.LDim() );
}
else
LogicError("Unaligned PartialRowScatter not implemented");
}
void Scatter
( T alpha,
const ElementalMatrix<T>& A,
ElementalMatrix<T>& B )
{
DEBUG_ONLY(CSE cse("axpy_contract::Scatter"))
AssertSameGrids( A, B );
if( A.Height() != B.Height() || A.Width() != B.Width() )
LogicError("Sizes of A and B must match");
if( !B.Participating() )
return;
const Int colStride = B.ColStride();
const Int rowStride = B.RowStride();
const Int colAlign = B.ColAlign();
const Int rowAlign = B.RowAlign();
const Int height = B.Height();
const Int width = B.Width();
const Int localHeight = B.LocalHeight();
const Int localWidth = B.LocalWidth();
const Int maxLocalHeight = MaxLength(height,colStride);
const Int maxLocalWidth = MaxLength(width,rowStride);
const Int recvSize = mpi::Pad( maxLocalHeight*maxLocalWidth );
const Int sendSize = colStride*rowStride*recvSize;
//vector<T> buffer( sendSize );
vector<T> buffer;
buffer.reserve( sendSize );
// Pack
copy::util::StridedPack
( height, width,
colAlign, colStride,
rowAlign, rowStride,
A.LockedBuffer(), A.LDim(),
buffer.data(), recvSize );
// Communicate
mpi::ReduceScatter( buffer.data(), recvSize, B.DistComm() );
// Unpack our received data
axpy::util::InterleaveMatrixUpdate
( alpha, localHeight, localWidth,
buffer.data(), 1, localHeight,
B.Buffer(), 1, B.LDim() );
}
void MakeExtendedKahan
( ElementalMatrix<F>& A, Base<F> phi, Base<F> mu )
{
EL_DEBUG_CSE
typedef Base<F> Real;
if( A.Height() != A.Width() )
LogicError("Extended Kahan matrices must be square");
const Int n = A.Height();
if( n % 3 != 0 )
LogicError("Dimension must be an integer multiple of 3");
const Int l = n / 3;
if( !l || (l & (l-1)) )
LogicError("n/3 is not a power of two");
Int k=0;
while( Int(1u<<k) < l )
++k;
if( phi <= Real(0) || phi >= Real(1) )
LogicError("phi must be in (0,1)");
if( mu <= Real(0) || mu >= Real(1) )
LogicError("mu must be in (0,1)");
// Start by setting A to the identity, and then modify the necessary
// l x l blocks of its 3 x 3 partitioning.
MakeIdentity( A );
unique_ptr<ElementalMatrix<F>> ABlock( A.Construct(A.Grid(),A.Root()) );
View( *ABlock, A, IR(2*l,3*l), IR(2*l,3*l) );
*ABlock *= mu;
View( *ABlock, A, IR(0,l), IR(l,2*l) );
Walsh( *ABlock, k );
*ABlock *= -phi;
View( *ABlock, A, IR(l,2*l), IR(2*l,3*l) );
Walsh( *ABlock, k );
*ABlock *= phi;
// Now scale A by S
const Real zeta = Sqrt(Real(1)-phi*phi);
auto& ALoc = A.Matrix();
for( Int iLoc=0; iLoc<A.LocalHeight(); ++iLoc )
{
const Int i = A.GlobalRow(iLoc);
const Real gamma = Pow(zeta,Real(i));
for( Int jLoc=0; jLoc<A.LocalWidth(); ++jLoc )
ALoc(iLoc,jLoc) *= gamma;
}
}
void IndexDependentMap
( const ElementalMatrix<S>& A,
ElementalMatrix<T>& B,
function<T(Int,Int,S)> func )
{
DEBUG_CSE
const Int mLoc = A.LocalHeight();
const Int nLoc = A.LocalWidth();
B.AlignWith( A.DistData() );
B.Resize( A.Height(), A.Width() );
auto& ALoc = A.LockedMatrix();
auto& BLoc = B.Matrix();
for( Int jLoc=0; jLoc<nLoc; ++jLoc )
{
const Int j = A.GlobalCol(jLoc);
for( Int iLoc=0; iLoc<mLoc; ++iLoc )
{
const Int i = A.GlobalRow(iLoc);
BLoc(iLoc,jLoc) = func(i,j,ALoc(iLoc,jLoc));
}
}
}
void Gather
( const ElementalMatrix<T>& A,
DistMatrix<T,CIRC,CIRC>& B )
{
DEBUG_ONLY(CSE cse("copy::Gather"))
AssertSameGrids( A, B );
if( A.DistSize() == 1 && A.CrossSize() == 1 )
{
B.Resize( A.Height(), A.Width() );
if( B.CrossRank() == B.Root() )
Copy( A.LockedMatrix(), B.Matrix() );
return;
}
const Int height = A.Height();
const Int width = A.Width();
B.SetGrid( A.Grid() );
B.Resize( height, width );
// Gather the colShifts and rowShifts
// ==================================
Int myShifts[2];
myShifts[0] = A.ColShift();
myShifts[1] = A.RowShift();
vector<Int> shifts;
const Int crossSize = B.CrossSize();
if( B.CrossRank() == B.Root() )
shifts.resize( 2*crossSize );
mpi::Gather( myShifts, 2, shifts.data(), 2, B.Root(), B.CrossComm() );
// Gather the payload data
// =======================
const bool irrelevant = ( A.RedundantRank()!=0 || A.CrossRank()!=A.Root() );
int totalSend = ( irrelevant ? 0 : A.LocalHeight()*A.LocalWidth() );
vector<int> recvCounts, recvOffsets;
if( B.CrossRank() == B.Root() )
recvCounts.resize( crossSize );
mpi::Gather( &totalSend, 1, recvCounts.data(), 1, B.Root(), B.CrossComm() );
int totalRecv = Scan( recvCounts, recvOffsets );
//vector<T> sendBuf(totalSend), recvBuf(totalRecv);
vector<T> sendBuf, recvBuf;
sendBuf.reserve( totalSend );
recvBuf.reserve( totalRecv );
if( !irrelevant )
copy::util::InterleaveMatrix
( A.LocalHeight(), A.LocalWidth(),
A.LockedBuffer(), 1, A.LDim(),
sendBuf.data(), 1, A.LocalHeight() );
mpi::Gather
( sendBuf.data(), totalSend,
recvBuf.data(), recvCounts.data(), recvOffsets.data(),
B.Root(), B.CrossComm() );
// Unpack
// ======
if( B.Root() == B.CrossRank() )
{
for( Int q=0; q<crossSize; ++q )
{
if( recvCounts[q] == 0 )
continue;
const Int colShift = shifts[2*q+0];
const Int rowShift = shifts[2*q+1];
const Int colStride = A.ColStride();
const Int rowStride = A.RowStride();
const Int localHeight = Length( height, colShift, colStride );
const Int localWidth = Length( width, rowShift, rowStride );
copy::util::InterleaveMatrix
( localHeight, localWidth,
&recvBuf[recvOffsets[q]], 1, localHeight,
B.Buffer(colShift,rowShift), colStride, rowStride*B.LDim() );
}
}
}
void Scatter
( const DistMatrix<T,CIRC,CIRC>& A,
ElementalMatrix<T>& B )
{
DEBUG_CSE
AssertSameGrids( A, B );
const Int m = A.Height();
const Int n = A.Width();
const Int colStride = B.ColStride();
const Int rowStride = B.RowStride();
B.Resize( m, n );
if( B.CrossSize() != 1 || B.RedundantSize() != 1 )
{
// TODO:
// Broadcast over the redundant communicator and use mpi::Translate
// rank to determine whether a process is the root of the broadcast.
GeneralPurpose( A, B );
return;
}
const Int pkgSize = mpi::Pad(MaxLength(m,colStride)*MaxLength(n,rowStride));
const Int recvSize = pkgSize;
const Int sendSize = B.DistSize()*pkgSize;
// Translate the root of A into the DistComm of B (if possible)
const Int root = A.Root();
const Int target = mpi::Translate( A.CrossComm(), root, B.DistComm() );
if( target == mpi::UNDEFINED )
return;
if( B.DistSize() == 1 )
{
Copy( A.LockedMatrix(), B.Matrix() );
return;
}
vector<T> buffer;
T* recvBuf=0; // some compilers (falsely) warn otherwise
if( A.CrossRank() == root )
{
FastResize( buffer, sendSize+recvSize );
T* sendBuf = &buffer[0];
recvBuf = &buffer[sendSize];
// Pack the send buffer
copy::util::StridedPack
( m, n,
B.ColAlign(), colStride,
B.RowAlign(), rowStride,
A.LockedBuffer(), A.LDim(),
sendBuf, pkgSize );
// Scatter from the root
mpi::Scatter
( sendBuf, pkgSize, recvBuf, pkgSize, target, B.DistComm() );
}
else
{
FastResize( buffer, recvSize );
recvBuf = &buffer[0];
// Perform the receiving portion of the scatter from the non-root
mpi::Scatter
( static_cast<T*>(0), pkgSize,
recvBuf, pkgSize, target, B.DistComm() );
}
// Unpack
copy::util::InterleaveMatrix
( B.LocalHeight(), B.LocalWidth(),
recvBuf, 1, B.LocalHeight(),
B.Buffer(), 1, B.LDim() );
}
void RowScatter
( T alpha,
const ElementalMatrix<T>& A,
ElementalMatrix<T>& B )
{
DEBUG_ONLY(CSE cse("axpy_contract::RowScatter"))
AssertSameGrids( A, B );
if( A.Height() != B.Height() || A.Width() != B.Width() )
LogicError("Matrix sizes did not match");
if( !B.Participating() )
return;
const Int width = B.Width();
const Int colDiff = B.ColAlign()-A.ColAlign();
if( colDiff == 0 )
{
if( width == 1 )
{
const Int localHeight = B.LocalHeight();
const Int portionSize = mpi::Pad( localHeight );
//vector<T> buffer( portionSize );
vector<T> buffer;
buffer.reserve( portionSize );
// Reduce to rowAlign
const Int rowAlign = B.RowAlign();
mpi::Reduce
( A.LockedBuffer(), buffer.data(), portionSize,
rowAlign, B.RowComm() );
if( B.RowRank() == rowAlign )
{
axpy::util::InterleaveMatrixUpdate
( alpha, localHeight, 1,
buffer.data(), 1, localHeight,
B.Buffer(), 1, B.LDim() );
}
}
else
{
const Int rowStride = B.RowStride();
const Int rowAlign = B.RowAlign();
const Int localHeight = B.LocalHeight();
const Int localWidth = B.LocalWidth();
const Int maxLocalWidth = MaxLength(width,rowStride);
const Int portionSize = mpi::Pad( localHeight*maxLocalWidth );
const Int sendSize = rowStride*portionSize;
// Pack
//vector<T> buffer( sendSize );
vector<T> buffer;
buffer.reserve( sendSize );
copy::util::RowStridedPack
( localHeight, width,
rowAlign, rowStride,
A.LockedBuffer(), A.LDim(),
buffer.data(), portionSize );
// Communicate
mpi::ReduceScatter( buffer.data(), portionSize, B.RowComm() );
// Update with our received data
axpy::util::InterleaveMatrixUpdate
( alpha, localHeight, localWidth,
buffer.data(), 1, localHeight,
B.Buffer(), 1, B.LDim() );
}
}
else
{
#ifdef EL_UNALIGNED_WARNINGS
if( B.Grid().Rank() == 0 )
cerr << "Unaligned RowScatter" << endl;
#endif
const Int colRank = B.ColRank();
const Int colStride = B.ColStride();
const Int sendRow = Mod( colRank+colDiff, colStride );
const Int recvRow = Mod( colRank-colDiff, colStride );
const Int localHeight = B.LocalHeight();
const Int localHeightA = A.LocalHeight();
if( width == 1 )
{
//vector<T> buffer( localHeight+localHeightA );
vector<T> buffer;
buffer.reserve( localHeight+localHeightA );
T* sendBuf = &buffer[0];
T* recvBuf = &buffer[localHeightA];
// Reduce to rowAlign
const Int rowAlign = B.RowAlign();
mpi::Reduce
( A.LockedBuffer(), sendBuf, localHeightA, rowAlign, B.RowComm() );
if( B.RowRank() == rowAlign )
{
// Perform the realignment
mpi::SendRecv
( sendBuf, localHeightA, sendRow,
recvBuf, localHeight, recvRow, B.ColComm() );
axpy::util::InterleaveMatrixUpdate
( alpha, localHeight, 1,
recvBuf, 1, localHeight,
B.Buffer(), 1, B.LDim() );
}
}
else
{
const Int rowStride = B.RowStride();
const Int rowAlign = B.RowAlign();
const Int localWidth = B.LocalWidth();
const Int maxLocalWidth = MaxLength(width,rowStride);
const Int recvSize_RS = mpi::Pad( localHeightA*maxLocalWidth );
const Int sendSize_RS = rowStride * recvSize_RS;
const Int recvSize_SR = localHeight * localWidth;
//vector<T> buffer( recvSize_RS + Max(sendSize_RS,recvSize_SR) );
vector<T> buffer;
buffer.reserve( recvSize_RS + Max(sendSize_RS,recvSize_SR) );
T* firstBuf = &buffer[0];
T* secondBuf = &buffer[recvSize_RS];
// Pack
copy::util::RowStridedPack
( localHeightA, width,
rowAlign, rowStride,
A.LockedBuffer(), A.LDim(),
secondBuf, recvSize_RS );
// Reduce-scatter over each process row
mpi::ReduceScatter( secondBuf, firstBuf, recvSize_RS, B.RowComm() );
// Trade reduced data with the appropriate process row
mpi::SendRecv
( firstBuf, localHeightA*localWidth, sendRow,
secondBuf, localHeight*localWidth, recvRow, B.ColComm() );
// Update with our received data
axpy::util::InterleaveMatrixUpdate
( alpha, localHeight, localWidth,
secondBuf, 1, localHeight,
B.Buffer(), 1, B.LDim() );
}
}
}
void ColScatter
( T alpha,
const ElementalMatrix<T>& A,
ElementalMatrix<T>& B )
{
DEBUG_ONLY(CSE cse("axpy_contract::ColScatter"))
AssertSameGrids( A, B );
if( A.Height() != B.Height() || A.Width() != B.Width() )
LogicError("A and B must be the same size");
#ifdef EL_VECTOR_WARNINGS
if( A.Width() == 1 && B.Grid().Rank() == 0 )
{
cerr <<
"The vector version of ColScatter does not"
" yet have a vector version implemented, but it would only "
"require a modification of the vector version of RowScatter"
<< endl;
}
#endif
#ifdef EL_CACHE_WARNINGS
if( A.Width() != 1 && B.Grid().Rank() == 0 )
{
cerr <<
"axpy_contract::ColScatter potentially causes a large "
"amount of cache-thrashing. If possible, avoid it by forming the "
"(conjugate-)transpose of the [* ,V] matrix instead." << endl;
}
#endif
if( !B.Participating() )
return;
const Int height = B.Height();
const Int localHeight = B.LocalHeight();
const Int localWidth = B.LocalWidth();
const Int colAlign = B.ColAlign();
const Int colStride = B.ColStride();
const Int rowDiff = B.RowAlign()-A.RowAlign();
// TODO: Allow for modular equivalence if possible
if( rowDiff == 0 )
{
const Int maxLocalHeight = MaxLength(height,colStride);
const Int recvSize = mpi::Pad( maxLocalHeight*localWidth );
const Int sendSize = colStride*recvSize;
//vector<T> buffer( sendSize );
vector<T> buffer;
buffer.reserve( sendSize );
// Pack
copy::util::ColStridedPack
( height, localWidth,
colAlign, colStride,
A.LockedBuffer(), A.LDim(),
buffer.data(), recvSize );
// Communicate
mpi::ReduceScatter( buffer.data(), recvSize, B.ColComm() );
// Update with our received data
axpy::util::InterleaveMatrixUpdate
( alpha, localHeight, localWidth,
buffer.data(), 1, localHeight,
B.Buffer(), 1, B.LDim() );
}
else
{
#ifdef EL_UNALIGNED_WARNINGS
if( B.Grid().Rank() == 0 )
cerr << "Unaligned ColScatter" << endl;
#endif
const Int localWidthA = A.LocalWidth();
const Int maxLocalHeight = MaxLength(height,colStride);
const Int recvSize_RS = mpi::Pad( maxLocalHeight*localWidthA );
const Int sendSize_RS = colStride*recvSize_RS;
const Int recvSize_SR = localHeight*localWidth;
//vector<T> buffer( recvSize_RS + Max(sendSize_RS,recvSize_SR) );
vector<T> buffer;
buffer.reserve( recvSize_RS + Max(sendSize_RS,recvSize_SR) );
T* firstBuf = &buffer[0];
T* secondBuf = &buffer[recvSize_RS];
// Pack
copy::util::ColStridedPack
( height, localWidth,
colAlign, colStride,
A.LockedBuffer(), A.LDim(),
secondBuf, recvSize_RS );
// Reduce-scatter over each col
mpi::ReduceScatter( secondBuf, firstBuf, recvSize_RS, B.ColComm() );
// Trade reduced data with the appropriate col
const Int sendCol = Mod( B.RowRank()+rowDiff, B.RowStride() );
const Int recvCol = Mod( B.RowRank()-rowDiff, B.RowStride() );
mpi::SendRecv
( firstBuf, localHeight*localWidthA, sendCol,
secondBuf, localHeight*localWidth, recvCol, B.RowComm() );
// Update with our received data
axpy::util::InterleaveMatrixUpdate
( alpha, localHeight, localWidth,
secondBuf, 1, localHeight,
B.Buffer(), 1, B.LDim() );
}
}