inline typename Base<F>::type
internal::FrobeniusNorm( const DistMatrix<F,MC,MR>& A )
{
#ifndef RELEASE
PushCallStack("internal::FrobeniusNorm");
#endif
typedef typename Base<F>::type R;
R localScale = 0;
R localScaledSquare = 1;
for( int jLocal=0; jLocal<A.LocalWidth(); ++jLocal )
{
for( int iLocal=0; iLocal<A.LocalHeight(); ++iLocal )
{
const R alphaAbs = Abs(A.GetLocalEntry(iLocal,jLocal));
if( alphaAbs != 0 )
{
if( alphaAbs <= localScale )
{
const R relScale = alphaAbs/localScale;
localScaledSquare += relScale*relScale;
}
else
{
const R relScale = localScale/alphaAbs;
localScaledSquare = localScaledSquare*relScale*relScale + 1;
localScale = alphaAbs;
}
}
}
}
// Find the maximum relative scale
R scale;
mpi::AllReduce( &localScale, &scale, 1, mpi::MAX, A.Grid().VCComm() );
R norm = 0;
if( scale != 0 )
{
// Equilibrate our local scaled sum to the maximum scale
R relScale = localScale/scale;
localScaledSquare *= relScale*relScale;
// The scaled square is now simply the sum of the local contributions
R scaledSquare;
mpi::AllReduce
( &localScaledSquare, &scaledSquare, 1, mpi::SUM, A.Grid().VCComm() );
norm = scale*Sqrt(scaledSquare);
}
#ifndef RELEASE
PopCallStack();
#endif
return norm;
}
inline typename Base<F>::type
internal::InfinityNorm( const DistMatrix<F,MC,MR>& A )
{
#ifndef RELEASE
PushCallStack("internal::InfinityNorm");
#endif
typedef typename Base<F>::type R;
// Compute the partial row sums defined by our local matrix, A[MC,MR]
std::vector<R> myPartialRowSums(A.LocalHeight());
for( int iLocal=0; iLocal<A.LocalHeight(); ++iLocal )
{
myPartialRowSums[iLocal] = 0;
for( int jLocal=0; jLocal<A.LocalWidth(); ++jLocal )
myPartialRowSums[iLocal] += Abs(A.GetLocalEntry(iLocal,jLocal));
}
// Sum our partial row sums to get the row sums over A[MC,* ]
std::vector<R> myRowSums(A.LocalHeight());
mpi::AllReduce
( &myPartialRowSums[0], &myRowSums[0], A.LocalHeight(), mpi::SUM,
A.Grid().RowComm() );
// Find the maximum out of the row sums
R myMaxRowSum = 0;
for( int iLocal=0; iLocal<A.LocalHeight(); ++iLocal )
myMaxRowSum = std::max( myMaxRowSum, myRowSums[iLocal] );
// Find the global maximum row sum by searching over the MC team
R maxRowSum = 0;
mpi::AllReduce( &myMaxRowSum, &maxRowSum, 1, mpi::MAX, A.Grid().ColComm() );
#ifndef RELEASE
PopCallStack();
#endif
return maxRowSum;
}
inline void
internal::PanelLU
( DistMatrix<F, STAR,STAR>& A,
DistMatrix<F, MC, STAR>& B,
DistMatrix<int,STAR,STAR>& p,
int pivotOffset )
{
#ifndef RELEASE
PushCallStack("internal::PanelLU");
if( A.Grid() != p.Grid() || p.Grid() != B.Grid() )
throw std::logic_error
("Matrices must be distributed over the same grid");
if( A.Width() != B.Width() )
throw std::logic_error("A and B must be the same width");
if( A.Height() != p.Height() || p.Width() != 1 )
throw std::logic_error("p must be a vector that conforms with A");
#endif
const Grid& g = A.Grid();
const int r = g.Height();
const int colShift = B.ColShift();
const int colAlignment = B.ColAlignment();
// Matrix views
DistMatrix<F,STAR,STAR>
ATL(g), ATR(g), A00(g), a01(g), A02(g),
ABL(g), ABR(g), a10(g), alpha11(g), a12(g),
A20(g), a21(g), A22(g);
DistMatrix<F,MC,STAR>
BL(g), BR(g),
B0(g), b1(g), B2(g);
DistMatrix<int,STAR,STAR>
pT(g), p0(g),
pB(g), psi1(g),
p2(g);
const int width = A.Width();
const int numBytes = (width+1)*sizeof(F)+sizeof(int);
std::vector<byte> sendData(numBytes);
std::vector<byte> recvData(numBytes);
// Extract pointers to send and recv data
F* sendBufFloat = (F*) &sendData[0];
F* recvBufFloat = (F*) &recvData[0];
int* sendBufInt = (int*) &sendData[(width+1)*sizeof(F)];
int* recvBufInt = (int*) &recvData[(width+1)*sizeof(F)];
// Start the algorithm
PushBlocksizeStack( 1 );
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
PartitionRight( B, BL, BR, 0 );
PartitionDown
( p, pT,
pB, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ a01, A02,
/*************/ /**********************/
/**/ a10, /**/ alpha11, a12,
ABL, /**/ ABR, A20, /**/ a21, A22 );
RepartitionRight
( BL, /**/ BR,
B0, /**/ b1, B2 );
RepartitionDown
( pT, p0,
/**/ /****/
psi1,
pB, p2 );
//--------------------------------------------------------------------//
// Store the index/value of the pivot candidate in A
F pivotValue = alpha11.GetLocalEntry(0,0);
int pivotIndex = a01.Height();
for( int i=0; i<a21.Height(); ++i )
{
F value = a21.GetLocalEntry(i,0);
if( FastAbs(value) > FastAbs(pivotValue) )
{
pivotValue = value;
pivotIndex = a01.Height() + i + 1;
}
}
// Update the pivot candidate to include local data from B
for( int i=0; i<B.LocalHeight(); ++i )
{
F value = b1.GetLocalEntry(i,0);
if( FastAbs(value) > FastAbs(pivotValue) )
{
pivotValue = value;
pivotIndex = A.Height() + colShift + i*r;
}
}
// Fill the send buffer with:
// [ pivotValue | pivotRow | pivotIndex ]
if( pivotIndex < A.Height() )
{
sendBufFloat[0] = A.GetLocalEntry(pivotIndex,a10.Width());
const int ALDim = A.LocalLDim();
const F* ABuffer = A.LocalBuffer(pivotIndex,0);
for( int j=0; j<width; ++j )
sendBufFloat[j+1] = ABuffer[j*ALDim];
}
else
{
const int localIndex = ((pivotIndex-A.Height())-colShift)/r;
sendBufFloat[0] = b1.GetLocalEntry(localIndex,0);
const int BLDim = B.LocalLDim();
const F* BBuffer = B.LocalBuffer(localIndex,0);
for( int j=0; j<width; ++j )
sendBufFloat[j+1] = BBuffer[j*BLDim];
}
*sendBufInt = pivotIndex;
// Communicate to establish the pivot information
mpi::AllReduce
( &sendData[0], &recvData[0], numBytes, PivotOp<F>(), g.ColComm() );
// Update the pivot vector
const int maxIndex = *recvBufInt;
p.SetLocalEntry(a01.Height(),0,maxIndex+pivotOffset);
// Copy the current row into the pivot row
if( maxIndex < A.Height() )
{
const int ALDim = A.LocalLDim();
F* ASetBuffer = A.LocalBuffer(maxIndex,0);
const F* AGetBuffer = A.LocalBuffer(A00.Height(),0);
for( int j=0; j<width; ++j )
ASetBuffer[j*ALDim] = AGetBuffer[j*ALDim];
}
else
{
const int ownerRank = (colAlignment+(maxIndex-A.Height())) % r;
if( g.Row() == ownerRank )
{
const int localIndex = ((maxIndex-A.Height())-colShift) / r;
const int ALDim = A.LocalLDim();
const int BLDim = B.LocalLDim();
F* BBuffer = B.LocalBuffer(localIndex,0);
const F* ABuffer = A.LocalBuffer(A00.Height(),0);
for( int j=0; j<width; ++j )
BBuffer[j*BLDim] = ABuffer[j*ALDim];
}
}
// Copy the pivot row into the current row
{
F* ABuffer = A.LocalBuffer(A00.Height(),0);
const int ALDim = A.LocalLDim();
for( int j=0; j<width; ++j )
ABuffer[j*ALDim] = recvBufFloat[j+1];
}
// Now we can perform the update of the current panel
F alpha = alpha11.GetLocalEntry(0,0);
if( alpha == (F)0 )
throw SingularMatrixException();
F alpha11Inv = ((F)1) / alpha;
Scal( alpha11Inv, a21.LocalMatrix() );
Scal( alpha11Inv, b1.LocalMatrix() );
Geru( (F)-1, a21.LocalMatrix(), a12.LocalMatrix(), A22.LocalMatrix() );
Geru( (F)-1, b1.LocalMatrix(), a12.LocalMatrix(), B2.LocalMatrix() );
//--------------------------------------------------------------------//
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, a01, /**/ A02,
/**/ a10, alpha11, /**/ a12,
/*************/ /**********************/
ABL, /**/ ABR, A20, a21, /**/ A22 );
SlidePartitionRight
( BL, /**/ BR,
B0, b1, /**/ B2 );
SlidePartitionDown
( pT, p0,
psi1,
/**/ /****/
pB, p2 );
}
PopBlocksizeStack();
#ifndef RELEASE
PopCallStack();
#endif
}