void dotproduct(DistMatrix<R> &A,DistMatrix<R> &B){
if(A.Height() != B.Height()){
//ERROR!
}
if(A.Width() != B.Width()){
//ERROR!
}
double temp,temp1;
const int colShift = A.ColShift(); // first row we own
const int rowShift = A.RowShift(); // first col we own
const int colStride = A.ColStride();
const int rowStride = A.RowStride();
const int localHeight = A.LocalHeight();
const int localWidth = A.LocalWidth();
for( int iLocal=0; iLocal<localHeight; ++iLocal ){
for( int jLocal=0; jLocal<localWidth; ++jLocal ){
const int i = colShift + iLocal*colStride;
const int j = rowShift + jLocal*rowStride;
temp = A.GetLocal(iLocal, jLocal);
temp1 = B.GetLocal(iLocal,jLocal);
B.SetLocal(iLocal, jLocal, (temp*temp1));
}
}
}
void calc_x_else(const R alpha, const R beta,const R c, const R delta, DistMatrix<R> &x, DistMatrix<R> &phi,DistMatrix<R> &w){
R bphi;
R temp;
R temp2;
const R pi = 4*atan(1);
const int colShift = x.ColShift(); // first row we own
const int rowShift = x.RowShift(); // first col we own
const int colStride = x.ColStride();
const int rowStride = x.RowStride();
const int localHeight = x.LocalHeight();
const int localWidth = x.LocalWidth();
for( int iLocal=0; iLocal<localHeight; ++iLocal ){
for( int jLocal=0; jLocal<localWidth; ++jLocal ){
const int i = colShift + iLocal*colStride;
const int j = rowShift + jLocal*rowStride;
temp = phi.GetLocal(0,jLocal);//phi
temp2 = w.GetLocal(0,jLocal); //w
bphi = (pi/2) + beta * temp;
//cout<< (delta + c * (((2/pi) * (bphi * tan(temp) - beta * log((pi/2) * temp2 * cos(temp) / bphi))) + (beta * tan (pi *alpha/2))))<<endl;
x.SetLocal(iLocal, jLocal, (-1* sqrt(abs(delta + c * (((2/pi) * (bphi * tan(temp) - beta * log((pi/2) * temp2 * cos(temp) / bphi))) + (beta * tan (pi *alpha/2)))))));
}
}
}
inline typename Base<F>::type
HermitianEntrywiseOneNorm( UpperOrLower uplo, const DistMatrix<F>& A )
{
#ifndef RELEASE
PushCallStack("HermitianEntrywiseOneNorm");
#endif
if( A.Height() != A.Width() )
throw std::logic_error("Hermitian matrices must be square.");
const int r = A.Grid().Height();
const int c = A.Grid().Width();
const int colShift = A.ColShift();
const int rowShift = A.RowShift();
typedef typename Base<F>::type R;
R localSum = 0;
const int localWidth = A.LocalWidth();
if( uplo == UPPER )
{
for( int jLocal=0; jLocal<localWidth; ++jLocal )
{
int j = rowShift + jLocal*c;
int numUpperRows = Length(j+1,colShift,r);
for( int iLocal=0; iLocal<numUpperRows; ++iLocal )
{
int i = colShift + iLocal*r;
const R alpha = Abs(A.GetLocal(iLocal,jLocal));
if( i ==j )
localSum += alpha;
else
localSum += 2*alpha;
}
}
}
else
{
for( int jLocal=0; jLocal<localWidth; ++jLocal )
{
int j = rowShift + jLocal*c;
int numStrictlyUpperRows = Length(j,colShift,r);
for( int iLocal=numStrictlyUpperRows;
iLocal<A.LocalHeight(); ++iLocal )
{
int i = colShift + iLocal*r;
const R alpha = Abs(A.GetLocal(iLocal,jLocal));
if( i ==j )
localSum += alpha;
else
localSum += 2*alpha;
}
}
}
R norm;
mpi::AllReduce( &localSum, &norm, 1, mpi::SUM, A.Grid().VCComm() );
#ifndef RELEASE
PopCallStack();
#endif
return norm;
}
void calc_x_if(const R alpha,const R beta,const R c, const R delta,DistMatrix<R> &x, DistMatrix<R> &phi,DistMatrix<R> &w){
R temp; // phi
R temp2; // w
R aphi;
R a1phi;
const R pi = 4*atan(1);
const R zeta = beta * tan(pi * alpha/2);
const int colShift = x.ColShift(); // first row we own
const int rowShift = x.RowShift(); // first col we own
const int colStride = x.ColStride();
const int rowStride = x.RowStride();
const int localHeight = x.LocalHeight();
const int localWidth = x.LocalWidth();
for( int iLocal=0; iLocal<localHeight; ++iLocal ){
for( int jLocal=0; jLocal<localWidth; ++jLocal ){
const int i = colShift + iLocal*colStride;
const int j = rowShift + jLocal*rowStride;
temp = phi.GetLocal(iLocal,jLocal);//phi
temp2 = w.GetLocal(iLocal,jLocal); //w
aphi = alpha * temp;
a1phi = (1-alpha)*temp;
x.SetLocal(iLocal, jLocal, (-1 * sqrt(abs(delta + c *( ( (sin(aphi)+zeta * cos(aphi))/ cos(temp)) * -1 * pow( abs( ((cos(a1phi) + zeta * sin(a1phi))/ (temp2 * cos(temp))) ) ,((1-alpha)/alpha) ) + beta * tan(pi * alpha/2) )))) );
}
}
}
inline typename Base<F>::type
HermitianMaxNorm( UpperOrLower uplo, const DistMatrix<F>& A )
{
#ifndef RELEASE
PushCallStack("internal::HermitianMaxNorm");
#endif
typedef typename Base<F>::type R;
if( A.Height() != A.Width() )
throw std::logic_error("Hermitian matrices must be square.");
const int r = A.Grid().Height();
const int c = A.Grid().Width();
const int colShift = A.ColShift();
const int rowShift = A.RowShift();
R localMaxAbs = 0;
const int localWidth = A.LocalWidth();
if( uplo == UPPER )
{
for( int jLocal=0; jLocal<localWidth; ++jLocal )
{
int j = rowShift + jLocal*c;
int numUpperRows = LocalLength(j+1,colShift,r);
for( int iLocal=0; iLocal<numUpperRows; ++iLocal )
{
const R thisAbs = Abs(A.GetLocal(iLocal,jLocal));
localMaxAbs = std::max( localMaxAbs, thisAbs );
}
}
}
else
{
for( int jLocal=0; jLocal<localWidth; ++jLocal )
{
int j = rowShift + jLocal*c;
int numStrictlyUpperRows = LocalLength(j,colShift,r);
for( int iLocal=numStrictlyUpperRows;
iLocal<A.LocalHeight(); ++iLocal )
{
const R thisAbs = Abs(A.GetLocal(iLocal,jLocal));
localMaxAbs = std::max( localMaxAbs, thisAbs );
}
}
}
R maxAbs;
mpi::AllReduce( &localMaxAbs, &maxAbs, 1, mpi::MAX, A.Grid().VCComm() );
#ifndef RELEASE
PopCallStack();
#endif
return maxAbs;
}
void GetMappedDiagonal
( const DistMatrix<T,U,V,BLOCK>& A,
AbstractDistMatrix<S>& d,
function<S(const T&)> func,
Int offset )
{
EL_DEBUG_CSE
EL_DEBUG_ONLY(AssertSameGrids( A, d ))
// TODO(poulson): Make this more efficient
const Int diagLength = A.DiagonalLength(offset);
d.Resize( diagLength, 1 );
Zero( d );
if( d.Participating() && A.RedundantRank() == 0 )
{
const Int iStart = Max(-offset,0);
const Int jStart = Max( offset,0);
for( Int k=0; k<diagLength; ++k )
{
if( A.IsLocal(iStart+k,jStart+k) )
{
const Int iLoc = A.LocalRow(iStart+k);
const Int jLoc = A.LocalCol(jStart+k);
d.QueueUpdate(k,0,func(A.GetLocal(iLoc,jLoc)));
}
}
}
d.ProcessQueues();
}
InfinityNorm( const DistMatrix<F,U,V>& A )
{
#ifndef RELEASE
CallStackEntry entry("InfinityNorm");
#endif
// Compute the partial row sums defined by our local matrix, A[U,V]
typedef BASE(F) R;
const Int localHeight = A.LocalHeight();
const Int localWidth = A.LocalWidth();
std::vector<R> myPartialRowSums( localHeight );
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
myPartialRowSums[iLoc] = 0;
for( Int jLoc=0; jLoc<localWidth; ++jLoc )
myPartialRowSums[iLoc] += Abs(A.GetLocal(iLoc,jLoc));
}
// Sum our partial row sums to get the row sums over A[U,* ]
std::vector<R> myRowSums( localHeight );
mpi::Comm rowComm = ReduceRowComm<U,V>( A.Grid() );
mpi::AllReduce( &myPartialRowSums[0], &myRowSums[0], localHeight, rowComm );
// Find the maximum out of the row sums
R myMaxRowSum = 0;
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
myMaxRowSum = std::max( myMaxRowSum, myRowSums[iLoc] );
// Find the global maximum row sum by searching over the U team
mpi::Comm colComm = ReduceColComm<U,V>( A.Grid() );
return mpi::AllReduce( myMaxRowSum, mpi::MAX, colComm );
}
int Corrupt( DistMatrix<F>& A, double probCorrupt )
{
#ifndef RELEASE
CallStackEntry entry("Corrupt");
#endif
typedef BASE(F) Real;
Int numLocalCorrupt = 0;
const Int localHeight = A.LocalHeight();
const Int localWidth = A.LocalWidth();
for( Int jLocal=0; jLocal<localWidth; ++jLocal )
{
for( Int iLocal=0; iLocal<localHeight; ++iLocal )
{
if( Uniform<Real>() <= probCorrupt )
{
++numLocalCorrupt;
const F perturb = SampleBall<F>();
A.SetLocal( iLocal, jLocal, A.GetLocal(iLocal,jLocal)+perturb );
}
}
}
Int numCorrupt;
mpi::AllReduce
( &numLocalCorrupt, &numCorrupt, 1, mpi::SUM, A.Grid().VCComm() );
return numCorrupt;
}
inline bool
PivotParity( const DistMatrix<int,VC,STAR>& p, int pivotOffset )
{
#ifndef RELEASE
PushCallStack("PivotParity");
if( p.Width() != 1 )
throw std::logic_error("p must be a column vector");
if( pivotOffset < 0 )
throw std::logic_error("pivot offset cannot be negative");
#endif
const int mLocal = p.LocalHeight();
const Grid& g = p.Grid();
bool isLocallyOdd = false;
const int colShift = p.ColShift();
const int gridSize = g.Size();
for( int iLocal=0; iLocal<mLocal; ++iLocal )
{
const int i = colShift + iLocal*gridSize;
if( p.GetLocal(iLocal,0) != i+pivotOffset )
isLocallyOdd = !isLocallyOdd;
}
int localContribution = isLocallyOdd;
int globalContribution;
mpi::AllReduce
( &localContribution, &globalContribution, 1, MPI_SUM, g.VCComm() );
globalContribution = globalContribution % 2;
bool isOdd = globalContribution;
#ifndef RELEASE
PopCallStack();
#endif
return isOdd;
}
inline typename Base<F>::type
FrobeniusNorm( const DistMatrix<F,U,V>& A )
{
#ifndef RELEASE
PushCallStack("internal::FrobeniusNorm");
#endif
typedef typename Base<F>::type R;
mpi::Comm comm = NormComm( A );
R localScale = 0;
R localScaledSquare = 1;
const int localHeight = A.LocalHeight();
const int localWidth = A.LocalWidth();
for( int jLocal=0; jLocal<localWidth; ++jLocal )
{
for( int iLocal=0; iLocal<localHeight; ++iLocal )
{
const R alphaAbs = Abs(A.GetLocal(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, comm );
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, comm );
norm = scale*Sqrt(scaledSquare);
}
#ifndef RELEASE
PopCallStack();
#endif
return norm;
}
void NormalizeEntries( DistMatrix<F,U,V>& A )
{
const Int localHeight = A.LocalHeight();
const Int localWidth = A.LocalWidth();
for( Int jLocal=0; jLocal<localWidth; ++jLocal )
{
for( Int iLocal=0; iLocal<localHeight; ++iLocal )
{
const F alpha = A.GetLocal( iLocal, jLocal );
A.SetLocal( iLocal, jLocal, alpha/Abs(alpha) );
}
}
}
inline void HermitianSVD
( UpperOrLower uplo, DistMatrix<F>& A,
DistMatrix<BASE(F),VR,STAR>& s, DistMatrix<F>& U, DistMatrix<F>& V )
{
#ifndef RELEASE
CallStackEntry entry("HermitianSVD");
#endif
#ifdef HAVE_PMRRR
typedef BASE(F) R;
// Grab an eigenvalue decomposition of A
HermitianEig( uplo, A, s, V );
// Redistribute the singular values into an [MR,* ] distribution
const Grid& grid = A.Grid();
DistMatrix<R,MR,STAR> s_MR_STAR( grid );
s_MR_STAR.AlignWith( V.DistData() );
s_MR_STAR = s;
// Set the singular values to the absolute value of the eigenvalues
const Int numLocalVals = s.LocalHeight();
for( Int iLoc=0; iLoc<numLocalVals; ++iLoc )
{
const R sigma = s.GetLocal(iLoc,0);
s.SetLocal(iLoc,0,Abs(sigma));
}
// Copy V into U (flipping the sign as necessary)
U.AlignWith( V );
U.ResizeTo( V.Height(), V.Width() );
const Int localHeight = V.LocalHeight();
const Int localWidth = V.LocalWidth();
for( Int jLoc=0; jLoc<localWidth; ++jLoc )
{
const R sigma = s_MR_STAR.GetLocal( jLoc, 0 );
F* UCol = U.Buffer( 0, jLoc );
const F* VCol = V.LockedBuffer( 0, jLoc );
if( sigma >= 0 )
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
UCol[iLoc] = VCol[iLoc];
else
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
UCol[iLoc] = -VCol[iLoc];
}
#else
U = A;
MakeHermitian( uplo, U );
SVD( U, s, V );
#endif // ifdef HAVE_PMRRR
}
FrobeniusNorm( const DistMatrix<F,U,V>& A )
{
#ifndef RELEASE
CallStackEntry entry("FrobeniusNorm");
#endif
typedef BASE(F) R;
R localScale = 0;
R localScaledSquare = 1;
const Int localHeight = A.LocalHeight();
const Int localWidth = A.LocalWidth();
for( Int jLoc=0; jLoc<localWidth; ++jLoc )
{
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
const R alphaAbs = Abs(A.GetLocal(iLoc,jLoc));
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
mpi::Comm comm = ReduceComm<U,V>( A.Grid() );
const R scale = mpi::AllReduce( localScale, mpi::MAX, comm );
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
const R scaledSquare = mpi::AllReduce( localScaledSquare, comm );
norm = scale*Sqrt(scaledSquare);
}
return norm;
}
inline void HermitianSVD
( UpperOrLower uplo,
DistMatrix<F>& A, DistMatrix<typename Base<F>::type,VR,STAR>& s,
DistMatrix<F>& U, DistMatrix<F>& V )
{
#ifndef RELEASE
PushCallStack("HermitianSVD");
#endif
typedef typename Base<F>::type R;
// Grab an eigenvalue decomposition of A
HermitianEig( uplo, A, s, V );
// Redistribute the singular values into an [MR,* ] distribution
const Grid& grid = A.Grid();
DistMatrix<R,MR,STAR> s_MR_STAR( grid );
s_MR_STAR.AlignWith( V );
s_MR_STAR = s;
// Set the singular values to the absolute value of the eigenvalues
const int numLocalVals = s.LocalHeight();
for( int iLocal=0; iLocal<numLocalVals; ++iLocal )
{
const R sigma = s.GetLocal(iLocal,0);
s.SetLocal(iLocal,0,Abs(sigma));
}
// Copy V into U (flipping the sign as necessary)
U.AlignWith( V );
U.ResizeTo( V.Height(), V.Width() );
const int localHeight = V.LocalHeight();
const int localWidth = V.LocalWidth();
for( int jLocal=0; jLocal<localWidth; ++jLocal )
{
const R sigma = s_MR_STAR.GetLocal( jLocal, 0 );
F* UCol = U.LocalBuffer( 0, jLocal );
const F* VCol = V.LockedLocalBuffer( 0, jLocal );
if( sigma >= 0 )
for( int iLocal=0; iLocal<localHeight; ++iLocal )
UCol[iLocal] = VCol[iLocal];
else
for( int iLocal=0; iLocal<localHeight; ++iLocal )
UCol[iLocal] = -VCol[iLocal];
}
#ifndef RELEASE
PopCallStack();
#endif
}
void repmat_as2(DistMatrix<R> &vector, DistMatrix<R> &repmatrix){
//old 1 x d
//new nSim x d
//Must set dimensions of New before being passed to function
double temp;
const int colShift = repmatrix.ColShift(); // first row we own
const int rowShift = repmatrix.RowShift(); // first col we own
const int colStride = repmatrix.ColStride();
const int rowStride = repmatrix.RowStride();
const int localHeight = repmatrix.LocalHeight();
const int localWidth = repmatrix.LocalWidth();
for( int iLocal=0; iLocal<localHeight; ++iLocal ){
for( int jLocal=0; jLocal<localWidth; ++jLocal ){
const int i = colShift + iLocal*colStride;
const int j = rowShift + jLocal*rowStride;
temp = vector.GetLocal(jLocal, 0);
repmatrix.SetLocal(iLocal, jLocal, temp);
}
}
}
inline typename Base<F>::type
OneNorm( const DistMatrix<F,U,V>& A )
{
#ifndef RELEASE
PushCallStack("internal::OneNorm");
#endif
typedef typename Base<F>::type R;
mpi::Comm colComm = NormColComm( A );
mpi::Comm rowComm = NormRowComm( A );
// Compute the partial column sums defined by our local matrix, A[U,V]
const int localHeight = A.LocalHeight();
const int localWidth = A.LocalWidth();
std::vector<R> myPartialColSums( localWidth );
for( int jLocal=0; jLocal<localWidth; ++jLocal )
{
myPartialColSums[jLocal] = 0;
for( int iLocal=0; iLocal<localHeight; ++iLocal )
myPartialColSums[jLocal] += Abs(A.GetLocal(iLocal,jLocal));
}
// Sum our partial column sums to get the column sums over A[* ,V]
std::vector<R> myColSums( localWidth );
mpi::AllReduce
( &myPartialColSums[0], &myColSums[0], localWidth, mpi::SUM, colComm );
// Find the maximum out of the column sums
R myMaxColSum = 0;
for( int jLocal=0; jLocal<localWidth; ++jLocal )
myMaxColSum = std::max( myMaxColSum, myColSums[jLocal] );
// Find the global maximum column sum by searching over the MR team
R maxColSum = 0;
mpi::AllReduce( &myMaxColSum, &maxColSum, 1, mpi::MAX, rowComm );
#ifndef RELEASE
PopCallStack();
#endif
return maxColSum;
}
inline typename Base<F>::type
EntrywiseOneNorm( const DistMatrix<F,U,V>& A )
{
#ifndef RELEASE
PushCallStack("EntrywiseOneNorm");
#endif
typedef typename Base<F>::type R;
R localSum = 0;
const int localHeight = A.LocalHeight();
const int localWidth = A.LocalWidth();
for( int jLocal=0; jLocal<localWidth; ++jLocal )
for( int iLocal=0; iLocal<localHeight; ++iLocal )
localSum += Abs(A.GetLocal(iLocal,jLocal));
R norm;
mpi::Comm comm = ReduceComm<U,V>( A.Grid() );
mpi::AllReduce( &localSum, &norm, 1, mpi::SUM, comm );
#ifndef RELEASE
PopCallStack();
#endif
return norm;
}
inline void HermitianSingularValues
( UpperOrLower uplo,
DistMatrix<F>& A, DistMatrix<typename Base<F>::type,VR,STAR>& s )
{
#ifndef RELEASE
PushCallStack("HermitianSingularValues");
#endif
typedef typename Base<F>::type R;
// Grab an eigenvalue decomposition of A
HermitianEig( uplo, A, s );
// Replace the eigenvalues with their absolute values
const int numLocalVals = s.LocalHeight();
for( int iLocal=0; iLocal<numLocalVals; ++iLocal )
{
const R sigma = s.GetLocal(iLocal,0);
s.SetLocal(iLocal,0,Abs(sigma));
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void HermitianSVD
( UpperOrLower uplo, DistMatrix<F>& A, DistMatrix<BASE(F),VR,STAR>& s )
{
#ifndef RELEASE
CallStackEntry entry("HermitianSVD");
#endif
#ifdef HAVE_PMRRR
typedef BASE(F) R;
// Grab the eigenvalues of A
HermitianEig( uplo, A, s );
// Replace the eigenvalues with their absolute values
const Int numLocalVals = s.LocalHeight();
for( Int iLoc=0; iLoc<numLocalVals; ++iLoc )
{
const R sigma = s.GetLocal(iLoc,0);
s.SetLocal(iLoc,0,Abs(sigma));
}
#else
MakeHermitian( uplo, A );
SVD( A, s );
#endif // ifdef HAVE_PMRRR
}
inline typename Base<F>::type
HermitianFrobeniusNorm
( UpperOrLower uplo, const DistMatrix<F>& A )
{
#ifndef RELEASE
PushCallStack("internal::HermitianFrobeniusNorm");
#endif
typedef typename Base<F>::type R;
if( A.Height() != A.Width() )
throw std::logic_error("Hermitian matrices must be square.");
const int r = A.Grid().Height();
const int c = A.Grid().Width();
const int colShift = A.ColShift();
const int rowShift = A.RowShift();
R localScale = 0;
R localScaledSquare = 1;
const int localWidth = A.LocalWidth();
if( uplo == UPPER )
{
for( int jLocal=0; jLocal<localWidth; ++jLocal )
{
int j = rowShift + jLocal*c;
int numUpperRows = LocalLength(j+1,colShift,r);
for( int iLocal=0; iLocal<numUpperRows; ++iLocal )
{
int i = colShift + iLocal*r;
const R alphaAbs = Abs(A.GetLocal(iLocal,jLocal));
if( alphaAbs != 0 )
{
if( alphaAbs <= localScale )
{
const R relScale = alphaAbs/localScale;
if( i != j )
localScaledSquare += 2*relScale*relScale;
else
localScaledSquare += relScale*relScale;
}
else
{
const R relScale = localScale/alphaAbs;
if( i != j )
localScaledSquare =
localScaledSquare*relScale*relScale + 2;
else
localScaledSquare =
localScaledSquare*relScale*relScale + 1;
localScale = alphaAbs;
}
}
}
}
}
else
{
for( int jLocal=0; jLocal<localWidth; ++jLocal )
{
int j = rowShift + jLocal*c;
int numStrictlyUpperRows = LocalLength(j,colShift,r);
for( int iLocal=numStrictlyUpperRows;
iLocal<A.LocalHeight(); ++iLocal )
{
int i = colShift + iLocal*r;
const R alphaAbs = Abs(A.GetLocal(iLocal,jLocal));
if( alphaAbs != 0 )
{
if( alphaAbs <= localScale )
{
const R relScale = alphaAbs/localScale;
if( i != j )
localScaledSquare += 2*relScale*relScale;
else
localScaledSquare += relScale*relScale;
}
else
{
const R relScale = localScale/alphaAbs;
if( i != j )
localScaledSquare =
localScaledSquare*relScale*relScale + 2;
else
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;
}
const DistMatrix<T,STAR,STAR>&
DistMatrix<T,STAR,STAR>::operator=( const DistMatrix<T,STAR,STAR>& A )
{
#ifndef RELEASE
CallStackEntry entry("[* ,* ] = [* ,* ]");
this->AssertNotLocked();
#endif
this->ResizeTo( A.Height(), A.Width() );
if( this->Grid() == A.Grid() )
{
this->matrix_ = A.LockedMatrix();
}
else
{
// TODO: Remember why I wrote this...
if( !mpi::CongruentComms( A.Grid().ViewingComm(),
this->Grid().ViewingComm() ) )
LogicError
("Redistributing between nonmatching grids currently requires"
" the viewing communicators to match.");
// Compute and allocate the amount of required memory
Int requiredMemory = 0;
if( A.Grid().VCRank() == 0 )
requiredMemory += A.Height()*A.Width();
if( this->Participating() )
requiredMemory += A.Height()*A.Width();
T* buffer = this->auxMemory_.Require( requiredMemory );
Int offset = 0;
T* sendBuf = &buffer[offset];
if( A.Grid().VCRank() == 0 )
offset += A.Height()*A.Width();
T* bcastBuffer = &buffer[offset];
// Send from the root of A to the root of this matrix's grid
mpi::Request sendRequest;
if( A.Grid().VCRank() == 0 )
{
for( Int j=0; j<A.Width(); ++j )
for( Int i=0; i<A.Height(); ++i )
sendBuf[i+j*A.Height()] = A.GetLocal(i,j);
const Int recvViewingRank = this->Grid().VCToViewingMap(0);
mpi::ISend
( sendBuf, A.Height()*A.Width(), recvViewingRank,
this->Grid().ViewingComm(), sendRequest );
}
// Receive on the root of this matrix's grid and then broadcast
// over this matrix's owning communicator
if( this->Participating() )
{
if( this->Grid().VCRank() == 0 )
{
const Int sendViewingRank = A.Grid().VCToViewingMap(0);
mpi::Recv
( bcastBuffer, A.Height()*A.Width(), sendViewingRank,
this->Grid().ViewingComm() );
}
mpi::Broadcast
( bcastBuffer, A.Height()*A.Width(), 0, this->Grid().VCComm() );
for( Int j=0; j<A.Width(); ++j )
for( Int i=0; i<A.Height(); ++i )
this->SetLocal(i,j,bcastBuffer[i+j*A.Height()]);
}
if( A.Grid().VCRank() == 0 )
mpi::Wait( sendRequest );
this->auxMemory_.Release();
}
return *this;
}
HermitianFrobeniusNorm( UpperOrLower uplo, const DistMatrix<F>& A )
{
#ifndef RELEASE
CallStackEntry entry("HermitianFrobeniusNorm");
#endif
if( A.Height() != A.Width() )
LogicError("Hermitian matrices must be square.");
const Int r = A.Grid().Height();
const Int c = A.Grid().Width();
const Int colShift = A.ColShift();
const Int rowShift = A.RowShift();
typedef BASE(F) R;
R localScale = 0;
R localScaledSquare = 1;
const Int localWidth = A.LocalWidth();
if( uplo == UPPER )
{
for( Int jLoc=0; jLoc<localWidth; ++jLoc )
{
Int j = rowShift + jLoc*c;
Int numUpperRows = Length(j+1,colShift,r);
for( Int iLoc=0; iLoc<numUpperRows; ++iLoc )
{
Int i = colShift + iLoc*r;
const R alphaAbs = Abs(A.GetLocal(iLoc,jLoc));
if( alphaAbs != 0 )
{
if( alphaAbs <= localScale )
{
const R relScale = alphaAbs/localScale;
if( i != j )
localScaledSquare += 2*relScale*relScale;
else
localScaledSquare += relScale*relScale;
}
else
{
const R relScale = localScale/alphaAbs;
if( i != j )
localScaledSquare =
localScaledSquare*relScale*relScale + 2;
else
localScaledSquare =
localScaledSquare*relScale*relScale + 1;
localScale = alphaAbs;
}
}
}
}
}
else
{
for( Int jLoc=0; jLoc<localWidth; ++jLoc )
{
Int j = rowShift + jLoc*c;
Int numStrictlyUpperRows = Length(j,colShift,r);
for( Int iLoc=numStrictlyUpperRows;
iLoc<A.LocalHeight(); ++iLoc )
{
Int i = colShift + iLoc*r;
const R alphaAbs = Abs(A.GetLocal(iLoc,jLoc));
if( alphaAbs != 0 )
{
if( alphaAbs <= localScale )
{
const R relScale = alphaAbs/localScale;
if( i != j )
localScaledSquare += 2*relScale*relScale;
else
localScaledSquare += relScale*relScale;
}
else
{
const R relScale = localScale/alphaAbs;
if( i != j )
localScaledSquare =
localScaledSquare*relScale*relScale + 2;
else
localScaledSquare =
localScaledSquare*relScale*relScale + 1;
localScale = alphaAbs;
}
}
}
}
}
// Find the maximum relative scale
const R scale = mpi::AllReduce( localScale, 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
const R scaledSquare =
mpi::AllReduce( localScaledSquare, A.Grid().VCComm() );
norm = scale*Sqrt(scaledSquare);
}
return norm;
}
int
main( int argc, char* argv[] )
{
Initialize( argc, argv );
try
{
const Int matType =
Input("--matType","0:uniform,1:Haar,2:Lotkin,3:Grcar,4:FoxLi,"
"5:HelmholtzPML1D,6:HelmholtzPML2D",5);
const Int n = Input("--size","height of matrix",100);
const Real realCenter = Input("--realCenter","real center",0.);
const Real imagCenter = Input("--imagCenter","imag center",0.);
const Real xWidth = Input("--xWidth","x width of image",0.);
const Real yWidth = Input("--yWidth","y width of image",0.);
const Int xSize = Input("--xSize","number of x samples",100);
const Int ySize = Input("--ySize","number of y samples",100);
const bool lanczos = Input("--lanczos","use Lanczos?",true);
const Int krylovSize = Input("--krylovSize","num Lanczos vectors",10);
const bool reorthog = Input("--reorthog","reorthog basis?",true);
const bool deflate = Input("--deflate","deflate converged?",true);
const Int maxIts = Input("--maxIts","maximum two-norm iter's",1000);
const Real tol = Input("--tol","tolerance for norm estimates",1e-6);
const Int numBands = Input("--numBands","num bands for Grcar",3);
const Real omega = Input("--omega","frequency for Fox-Li/Helm",16*M_PI);
const Int mx = Input("--mx","number of x points for HelmholtzPML",30);
const Int my = Input("--my","number of y points for HelmholtzPML",30);
const Int numPmlPoints = Input("--numPml","num PML points for Helm",5);
const double sigma = Input("--sigma","PML amplitude",1.5);
const double pmlExp = Input("--pmlExp","PML takeoff exponent",3.);
const bool progress = Input("--progress","print progress?",true);
const bool display = Input("--display","display matrices?",false);
const bool write = Input("--write","write matrices?",false);
const bool writePseudo = Input("--writePs","write pseudospec.",false);
const Int formatInt = Input("--format","write format",2);
const Int colorMapInt = Input("--colorMap","color map",0);
ProcessInput();
PrintInputReport();
if( formatInt < 1 || formatInt >= FileFormat_MAX )
LogicError("Invalid file format integer, should be in [1,",
FileFormat_MAX,")");
FileFormat format = static_cast<FileFormat>(formatInt);
ColorMap colorMap = static_cast<ColorMap>(colorMapInt);
SetColorMap( colorMap );
C center(realCenter,imagCenter);
DistMatrix<C> A;
switch( matType )
{
case 0: Uniform( A, n, n ); break;
case 1: Haar( A, n ); break;
case 2: Lotkin( A, n ); break;
case 3: Grcar( A, n, numBands ); break;
case 4: FoxLi( A, n, omega ); break;
case 5: HelmholtzPML
( A, n, C(omega), numPmlPoints, sigma, pmlExp ); break;
case 6: HelmholtzPML
( A, mx, my, C(omega), numPmlPoints, sigma, pmlExp ); break;
default: LogicError("Invalid matrix type");
}
if( display )
Display( A, "A" );
if( write )
Write( A, "A", format );
// Visualize the pseudospectrum by evaluating ||inv(A-sigma I)||_2
// for a grid of complex sigma's.
DistMatrix<Real> invNormMap;
DistMatrix<Int> itCountMap;
if( xWidth != 0. && yWidth != 0. )
itCountMap = Pseudospectrum
( A, invNormMap, center, xWidth, yWidth, xSize, ySize,
lanczos, krylovSize, reorthog, deflate, maxIts, tol, progress );
else
itCountMap = Pseudospectrum
( A, invNormMap, center, xSize, ySize,
lanczos, krylovSize, reorthog, deflate, maxIts, tol, progress );
const Int numIts = MaxNorm( itCountMap );
if( mpi::WorldRank() == 0 )
std::cout << "num iterations=" << numIts << std::endl;
if( display )
{
Display( invNormMap, "invNormMap" );
Display( itCountMap, "itCountMap" );
}
if( write || writePseudo )
{
Write( invNormMap, "invNormMap", format );
Write( itCountMap, "itCountMap", format );
}
// Take the element-wise log
const Int mLocal = invNormMap.LocalHeight();
const Int nLocal = invNormMap.LocalWidth();
for( Int jLoc=0; jLoc<nLocal; ++jLoc )
for( Int iLoc=0; iLoc<mLocal; ++iLoc )
invNormMap.SetLocal
( iLoc, jLoc, Log(invNormMap.GetLocal(iLoc,jLoc)) );
if( display )
{
Display( invNormMap, "logInvNormMap" );
if( GetColorMap() != GRAYSCALE_DISCRETE )
{
auto colorMap = GetColorMap();
SetColorMap( GRAYSCALE_DISCRETE );
Display( invNormMap, "discreteLogInvNormMap" );
SetColorMap( colorMap );
}
}
if( write || writePseudo )
{
Write( invNormMap, "logInvNormMap", format );
if( GetColorMap() != GRAYSCALE_DISCRETE )
{
auto colorMap = GetColorMap();
SetColorMap( GRAYSCALE_DISCRETE );
Write( invNormMap, "discreteLogInvNormMap", format );
SetColorMap( colorMap );
}
}
}
catch( exception& e ) { ReportException(e); }
Finalize();
return 0;
}
void TestCorrectness
( bool print,
UpperOrLower uplo,
const DistMatrix<F>& A,
const DistMatrix<Base<F>,VR,STAR>& w,
const DistMatrix<F>& Z,
const DistMatrix<F>& AOrig )
{
typedef Base<F> Real;
const Grid& g = A.Grid();
const Int n = Z.Height();
const Int k = Z.Width();
if( g.Rank() == 0 )
{
cout << " Gathering computed eigenvalues...";
cout.flush();
}
DistMatrix<Real,MR,STAR> w_MR_STAR(true,Z.RowAlign(),g);
w_MR_STAR = w;
if( g.Rank() == 0 )
cout << "DONE" << endl;
if( g.Rank() == 0 )
cout << " Testing orthogonality of eigenvectors..." << endl;
DistMatrix<F> X(g);
Identity( X, k, k );
Herk( uplo, ADJOINT, F(-1), Z, F(1), X );
Real oneNormOfError = OneNorm( X );
Real infNormOfError = InfinityNorm( X );
Real frobNormOfError = FrobeniusNorm( X );
if( g.Rank() == 0 )
{
cout << " ||Z^H Z - I||_1 = " << oneNormOfError << "\n"
<< " ||Z^H Z - I||_oo = " << infNormOfError << "\n"
<< " ||Z^H Z - I||_F = " << frobNormOfError << "\n\n"
<< " Testing for deviation of AZ from ZW..." << endl;
}
// X := AZ
X.AlignWith( Z );
Zeros( X, n, k );
Hemm( LEFT, uplo, F(1), AOrig, Z, F(0), X );
// Find the residual ||X-ZW||_oo = ||AZ-ZW||_oo
for( Int jLoc=0; jLoc<X.LocalWidth(); ++jLoc )
{
const Real omega = w_MR_STAR.GetLocal(jLoc,0);
for( Int iLoc=0; iLoc<X.LocalHeight(); ++iLoc )
{
const F chi = X.GetLocal(iLoc,jLoc);
const F zeta = Z.GetLocal(iLoc,jLoc);
X.SetLocal(iLoc,jLoc,chi-omega*zeta);
}
}
// Find the infinity norms of A, Z, and AZ-ZW
Real infNormOfA = HermitianInfinityNorm( uplo, AOrig );
Real frobNormOfA = HermitianFrobeniusNorm( uplo, AOrig );
Real oneNormOfZ = OneNorm( Z );
Real infNormOfZ = InfinityNorm( Z );
Real frobNormOfZ = FrobeniusNorm( Z );
oneNormOfError = OneNorm( X );
infNormOfError = InfinityNorm( X );
frobNormOfError = FrobeniusNorm( X );
if( g.Rank() == 0 )
{
cout << " ||A||_1 = ||A||_oo = " << infNormOfA << "\n"
<< " ||A||_F = " << frobNormOfA << "\n"
<< " ||Z||_1 = " << oneNormOfZ << "\n"
<< " ||Z||_oo = " << infNormOfZ << "\n"
<< " ||Z||_F = " << frobNormOfZ << "\n"
<< " ||A Z - Z W||_1 = " << oneNormOfError << "\n"
<< " ||A Z - Z W||_oo = " << infNormOfError << "\n"
<< " ||A Z - Z W||_F = " << frobNormOfError << endl;
}
}
int
main( int argc, char* argv[] )
{
Initialize( argc, argv );
mpi::Comm comm = mpi::COMM_WORLD;
const int commRank = mpi::CommRank( comm );
try
{
const int n = Input("--size","size of matrix",10);
const bool print = Input("--print","print matrices?",true);
#ifdef HAVE_QT5
const bool display = Input("--display","display matrices?",true);
#endif
ProcessInput();
PrintInputReport();
// Create a circulant matrix
DistMatrix<Complex<double> > A;
std::vector<Complex<double> > a( n );
for( int j=0; j<n; ++j )
a[j] = j;
Circulant( A, a );
if( print )
A.Print("Circulant matrix:");
#ifdef HAVE_QT5
if( display )
Display( A, "Circulant" );
#endif
// Create a discrete Fourier matrix, which can be used to diagonalize
// circulant matrices
DistMatrix<Complex<double> > F;
DiscreteFourier( F, n );
if( print )
F.Print("DFT matrix (F):");
#ifdef HAVE_QT5
if( display )
Display( F, "Discrete Fourier" );
#endif
// Form B := A F
DistMatrix<Complex<double> > B;
Zeros( B, n, n );
Gemm( NORMAL, NORMAL,
Complex<double>(1), A, F, Complex<double>(0), B );
// Form A := F^H B = F^H \hat A F
Gemm( ADJOINT, NORMAL,
Complex<double>(1), F, B, Complex<double>(0), A );
if( print )
A.Print("A := F^H A F");
#ifdef HAVE_QT5
if( display )
Display( A, "F^H A F" );
#endif
// Form the thresholded result
const int localHeight = A.LocalHeight();
const int localWidth = A.LocalWidth();
for( int jLocal=0; jLocal<localWidth; ++jLocal )
{
for( int iLocal=0; iLocal<localHeight; ++iLocal )
{
const double absValue = Abs(A.GetLocal(iLocal,jLocal));
if( absValue < 1e-13 )
A.SetLocal(iLocal,jLocal,0);
}
}
if( print )
A.Print("A with values below 1e-13 removed");
#ifdef HAVE_QT5
if( display )
Display( A, "Thresholded (1e-13) A" );
#endif
}
catch( ArgException& e )
{
// There is nothing to do
}
catch( std::exception& e )
{
std::ostringstream os;
os << "Process " << commRank << " caught error message:\n" << e.what()
<< std::endl;
std::cerr << os.str();
#ifndef RELEASE
DumpCallStack();
#endif
}
Finalize();
return 0;
}
inline R
Row( DistMatrix<R>& chi, DistMatrix<R>& x )
{
#ifndef RELEASE
PushCallStack("reflector::Row");
if( chi.Grid() != x.Grid() )
throw std::logic_error
("chi and x must be distributed over the same grid");
if( chi.Height() != 1 || chi.Width() != 1 )
throw std::logic_error("chi must be a scalar");
if( x.Height() != 1 )
throw std::logic_error("x must be a row vector");
if( chi.Grid().Row() != chi.ColAlignment() )
throw std::logic_error("Reflecting with incorrect row of processes");
if( x.Grid().Row() != x.ColAlignment() )
throw std::logic_error("Reflecting with incorrect row of processes");
#endif
const Grid& grid = x.Grid();
mpi::Comm rowComm = grid.RowComm();
const int gridCol = grid.Col();
const int gridWidth = grid.Width();
const int rowAlignment = chi.RowAlignment();
std::vector<R> localNorms(gridWidth);
R localNorm = Nrm2( x.LockedMatrix() );
mpi::AllGather( &localNorm, 1, &localNorms[0], 1, rowComm );
R norm = blas::Nrm2( gridWidth, &localNorms[0], 1 );
if( norm == 0 )
{
if( gridCol == rowAlignment )
chi.SetLocal(0,0,-chi.GetLocal(0,0));
#ifndef RELEASE
PopCallStack();
#endif
return R(2);
}
R alpha;
if( gridCol == rowAlignment )
alpha = chi.GetLocal(0,0);
mpi::Broadcast( &alpha, 1, rowAlignment, rowComm );
R beta;
if( alpha <= 0 )
beta = lapack::SafeNorm( alpha, norm );
else
beta = -lapack::SafeNorm( alpha, norm );
const R one = 1;
const R safeMin = lapack::MachineSafeMin<R>();
const R epsilon = lapack::MachineEpsilon<R>();
const R safeInv = safeMin/epsilon;
int count = 0;
if( Abs(beta) < safeInv )
{
R invOfSafeInv = one/safeInv;
do
{
++count;
Scale( invOfSafeInv, x );
alpha *= invOfSafeInv;
beta *= invOfSafeInv;
} while( Abs(beta) < safeInv );
localNorm = Nrm2( x.LockedMatrix() );
mpi::AllGather( &localNorm, 1, &localNorms[0], 1, rowComm );
norm = blas::Nrm2( gridWidth, &localNorms[0], 1 );
if( alpha <= 0 )
beta = lapack::SafeNorm( alpha, norm );
else
beta = -lapack::SafeNorm( alpha, norm );
}
R tau = (beta-alpha)/beta;
Scale( one/(alpha-beta), x );
for( int j=0; j<count; ++j )
beta *= safeInv;
if( gridCol == rowAlignment )
chi.SetLocal(0,0,beta);
#ifndef RELEASE
PopCallStack();
#endif
return tau;
}
inline void
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);
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
// TODO: Think of how to make this safer with respect to alignment issues
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 );
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 );
//--------------------------------------------------------------------//
const int currentRow = a01.Height();
// Store the index/value of the pivot candidate in A
F pivot = alpha11.GetLocal(0,0);
int pivotRow = currentRow;
for( int i=0; i<a21.Height(); ++i )
{
F value = a21.GetLocal(i,0);
if( FastAbs(value) > FastAbs(pivot) )
{
pivot = value;
pivotRow = currentRow + i + 1;
}
}
// Update the pivot candidate to include local data from B
for( int i=0; i<B.LocalHeight(); ++i )
{
F value = b1.GetLocal(i,0);
if( FastAbs(value) > FastAbs(pivot) )
{
pivot = value;
pivotRow = A.Height() + colShift + i*r;
}
}
// Fill the send buffer with:
// [ pivotValue | pivot row data | pivotRow ]
if( pivotRow < A.Height() )
{
sendBufFloat[0] = A.GetLocal(pivotRow,a10.Width());
const int ALDim = A.LocalLDim();
const F* ABuffer = A.LocalBuffer(pivotRow,0);
for( int j=0; j<width; ++j )
sendBufFloat[j+1] = ABuffer[j*ALDim];
}
else
{
const int localRow = ((pivotRow-A.Height())-colShift)/r;
sendBufFloat[0] = b1.GetLocal(localRow,0);
const int BLDim = B.LocalLDim();
const F* BBuffer = B.LocalBuffer(localRow,0);
for( int j=0; j<width; ++j )
sendBufFloat[j+1] = BBuffer[j*BLDim];
}
*sendBufInt = pivotRow;
// Communicate to establish the pivot information
mpi::AllReduce
( &sendData[0], &recvData[0], numBytes, PivotOp<F>(), g.ColComm() );
// Update the pivot vector
pivotRow = *recvBufInt;
p.SetLocal(currentRow,0,pivotRow+pivotOffset);
// Copy the current row into the pivot row
if( pivotRow < A.Height() )
{
const int ALDim = A.LocalLDim();
F* ASetBuffer = A.LocalBuffer(pivotRow,0);
const F* AGetBuffer = A.LocalBuffer(currentRow,0);
for( int j=0; j<width; ++j )
ASetBuffer[j*ALDim] = AGetBuffer[j*ALDim];
}
else
{
const int ownerRank = (colAlignment+(pivotRow-A.Height())) % r;
if( g.Row() == ownerRank )
{
const int localRow = ((pivotRow-A.Height())-colShift) / r;
const int ALDim = A.LocalLDim();
const int BLDim = B.LocalLDim();
F* BBuffer = B.LocalBuffer(localRow,0);
const F* ABuffer = A.LocalBuffer(currentRow,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(currentRow,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
const F alpha = alpha11.GetLocal(0,0);
if( alpha == F(0) )
throw SingularMatrixException();
const F alpha11Inv = F(1) / alpha;
Scale( alpha11Inv, a21.LocalMatrix() );
Scale( 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 );
}
PopBlocksizeStack();
#ifndef RELEASE
PopCallStack();
#endif
}
int
main( int argc, char* argv[] )
{
Initialize( argc, argv );
try
{
const Int matType =
Input("--matType","0:uniform,1:Haar,2:Lotkin,3:Grcar,4:FoxLi"
"5:HelmholtzPML1D,6:HelmholtzPML2D",5);
const Int n = Input("--size","height of matrix",100);
const Real realCenter = Input("--realCenter","real center",0.);
const Real imagCenter = Input("--imagCenter","imag center",0.);
Real xWidth = Input("--xWidth","x width of image",0.);
Real yWidth = Input("--yWidth","y width of image",0.);
const Real nx = Input("--nx","num x chunks",2);
const Real ny = Input("--ny","num y chunks",2);
const Int xSize = Input("--xSize","number of x samples",100);
const Int ySize = Input("--ySize","number of y samples",100);
const bool lanczos = Input("--lanczos","use Lanczos?",true);
const Int krylovSize = Input("--krylovSize","num Lanczos vectors",10);
const bool reorthog = Input("--reorthog","reorthog basis?",true);
const bool deflate = Input("--deflate","deflate converged?",true);
const Int maxIts = Input("--maxIts","maximum two-norm iter's",1000);
const Real tol = Input("--tol","tolerance for norm estimates",1e-6);
const Int cutoff = Input("--cutoff","problem size for QR",256);
const Int maxInnerIts = Input("--maxInnerIts","SDC limit",2);
const Int maxOuterIts = Input("--maxOuterIts","SDC limit",10);
const bool random = Input("--random","Random RRQR in SDC",true);
const Real signTol = Input("--signTol","Sign tolerance for SDC",1e-9);
const Real relTol = Input("--relTol","Rel. tol. for SDC",1e-6);
const Real spreadFactor = Input("--spreadFactor","median pert.",1e-6);
const Int numBands = Input("--numBands","num bands for Grcar",3);
const Real omega = Input("--omega","frequency for Fox-Li/Helm",16*M_PI);
const Int mx = Input("--mx","number of x points for HelmholtzPML",30);
const Int my = Input("--my","number of y points for HelmholtzPML",30);
const Int numPmlPoints = Input("--numPml","num PML points for Helm",5);
const double sigma = Input("--sigma","PML amplitude",1.5);
const double pmlExp = Input("--pmlExp","PML takeoff exponent",3.);
const bool progress = Input("--progress","print progress?",true);
const bool display = Input("--display","display matrices?",false);
const bool write = Input("--write","write matrices?",false);
const bool writePseudo = Input("--writePs","write pseudospec.",false);
const Int formatInt = Input("--format","write format",2);
const Int colorMapInt = Input("--colorMap","color map",0);
ProcessInput();
PrintInputReport();
if( formatInt < 1 || formatInt >= FileFormat_MAX )
LogicError("Invalid file format integer, should be in [1,",
FileFormat_MAX,")");
FileFormat format = static_cast<FileFormat>(formatInt);
ColorMap colorMap = static_cast<ColorMap>(colorMapInt);
SetColorMap( colorMap );
C center(realCenter,imagCenter);
DistMatrix<C> A;
switch( matType )
{
case 0: Uniform( A, n, n ); break;
case 1: Haar( A, n ); break;
case 2: Lotkin( A, n ); break;
case 3: Grcar( A, n, numBands ); break;
case 4: FoxLi( A, n, omega ); break;
case 5: HelmholtzPML
( A, n, C(omega), numPmlPoints, sigma, pmlExp ); break;
case 6: HelmholtzPML
( A, mx, my, C(omega), numPmlPoints, sigma, pmlExp ); break;
default: LogicError("Invalid matrix type");
}
if( display )
Display( A, "A" );
if( write )
Write( A, "A", format );
// Begin by computing the Schur decomposition
Timer timer;
DistMatrix<C> X;
DistMatrix<C,VR,STAR> w;
mpi::Barrier( mpi::COMM_WORLD );
timer.Start();
const bool formATR = true;
schur::SDC
( A, w, X, formATR, cutoff, maxInnerIts, maxOuterIts, signTol, relTol,
spreadFactor, random, progress );
mpi::Barrier( mpi::COMM_WORLD );
const double sdcTime = timer.Stop();
if( mpi::WorldRank() == 0 )
std::cout << "SDC took " << sdcTime << " seconds" << std::endl;
// Find a window if none is specified
if( xWidth == 0. || yWidth == 0. )
{
const Real radius = MaxNorm( w );
const Real oneNorm = OneNorm( A );
Real width;
if( oneNorm == 0. && radius == 0. )
{
width = 1;
if( mpi::WorldRank() == 0 )
std::cout << "Setting width to 1 to handle zero matrix"
<< std::endl;
}
else if( radius >= 0.2*oneNorm )
{
width = 2.5*radius;
if( mpi::WorldRank() == 0 )
std::cout << "Setting width to " << width
<< " based on the spectral radius, "
<< radius << std::endl;
}
else
{
width = 0.8*oneNorm;
if( mpi::WorldRank() == 0 )
std::cout << "Setting width to " << width
<< " based on the one norm, " << oneNorm
<< std::endl;
}
xWidth = width;
yWidth = width;
}
// Visualize/write the pseudospectrum within each window
DistMatrix<Real> invNormMap;
DistMatrix<Int> itCountMap;
const Int xBlock = xSize / nx;
const Int yBlock = ySize / ny;
const Int xLeftover = xSize - (nx-1)*xBlock;
const Int yLeftover = ySize - (ny-1)*yBlock;
const Real xStep = xWidth/(xSize-1);
const Real yStep = yWidth/(ySize-1);
const C corner = center - C(xWidth/2,yWidth/2);
for( Int xChunk=0; xChunk<nx; ++xChunk )
{
const Int xChunkSize = ( xChunk==nx-1 ? xLeftover : xBlock );
const Real xChunkWidth = xStep*xChunkSize;
for( Int yChunk=0; yChunk<ny; ++yChunk )
{
const Int yChunkSize = ( yChunk==ny-1 ? yLeftover : yBlock );
const Real yChunkWidth = yStep*yChunkSize;
const C chunkCorner = corner +
C(xStep*xChunk*xBlock,yStep*yChunk*yBlock);
const C chunkCenter = chunkCorner +
0.5*C(xStep*xChunkSize,yStep*yChunkSize);
mpi::Barrier( mpi::COMM_WORLD );
timer.Start();
itCountMap = TriangularPseudospectrum
( A, invNormMap, chunkCenter, xChunkWidth, yChunkWidth,
xChunkSize, yChunkSize, lanczos, krylovSize, reorthog,
deflate, maxIts, tol, progress );
mpi::Barrier( mpi::COMM_WORLD );
const double pseudoTime = timer.Stop();
const Int numIts = MaxNorm( itCountMap );
if( mpi::WorldRank() == 0 )
{
std::cout << "num seconds=" << pseudoTime << "\n"
<< "num iterations=" << numIts << std::endl;
}
std::ostringstream chunkStream;
chunkStream << "_" << xChunk << "_" << yChunk;
const std::string chunkTag = chunkStream.str();
if( display )
{
Display( invNormMap, "invNormMap"+chunkTag );
Display( itCountMap, "itCountMap"+chunkTag );
}
if( write || writePseudo )
{
Write( invNormMap, "invNormMap"+chunkTag, format );
Write( itCountMap, "itCountMap"+chunkTag, format );
}
// Take the element-wise log
const Int mLocal = invNormMap.LocalHeight();
const Int nLocal = invNormMap.LocalWidth();
for( Int jLoc=0; jLoc<nLocal; ++jLoc )
for( Int iLoc=0; iLoc<mLocal; ++iLoc )
invNormMap.SetLocal
( iLoc, jLoc, Log(invNormMap.GetLocal(iLoc,jLoc)) );
if( display )
{
Display( invNormMap, "logInvNormMap"+chunkTag );
if( GetColorMap() != GRAYSCALE_DISCRETE )
{
auto colorMap = GetColorMap();
SetColorMap( GRAYSCALE_DISCRETE );
Display( invNormMap, "discreteLogInvNormMap"+chunkTag );
SetColorMap( colorMap );
}
}
if( write || writePseudo )
{
Write( invNormMap, "logInvNormMap"+chunkTag, format );
if( GetColorMap() != GRAYSCALE_DISCRETE )
{
auto colorMap = GetColorMap();
SetColorMap( GRAYSCALE_DISCRETE );
Write
( invNormMap, "discreteLogInvNormMap"+chunkTag,
format );
SetColorMap( colorMap );
}
}
}
}
}
catch( exception& e ) { ReportException(e); }
Finalize();
return 0;
}
int
main( int argc, char* argv[] )
{
Environment env( argc, argv );
try
{
const Int n = Input("--size","size of matrix",10);
const bool display = Input("--display","display matrices?",false);
const bool print = Input("--print","print matrices?",true);
ProcessInput();
PrintInputReport();
// Create a circulant matrix
vector<C> a( n );
for( Int j=0; j<n; ++j )
a[j] = j;
DistMatrix<C> A;
Circulant( A, a );
if( display )
Display( A, "Circulant" );
if( print )
Print( A, "Circulant matrix:" );
// Create a Fourier matrix, which can be used to diagonalize circulant
// matrices
DistMatrix<C> F;
Fourier( F, n );
if( display )
Display( F, "DFT matrix" );
if( print )
Print( F, "DFT matrix:" );
// Form B := A F
DistMatrix<C> B;
Zeros( B, n, n );
Gemm( NORMAL, NORMAL, C(1), A, F, C(0), B );
// Form A := F^H B = F^H \hat A F
Gemm( ADJOINT, NORMAL, C(1), F, B, C(0), A );
if( display )
Display( A, "F^H A F" );
if( print )
Print( A, "A := F^H A F" );
// Form the thresholded result
const Int localHeight = A.LocalHeight();
const Int localWidth = A.LocalWidth();
for( Int jLoc=0; jLoc<localWidth; ++jLoc )
{
for( Int iLoc=0; iLoc<localHeight; ++iLoc )
{
const double absValue = Abs(A.GetLocal(iLoc,jLoc));
if( absValue < 1e-13 )
A.SetLocal(iLoc,jLoc,0);
}
}
if( display )
Display( A, "Thresholded (1e-13) A" );
if( print )
Print( A, "A with values below 1e-13 removed" );
}
catch( exception& e ) { ReportException(e); }
return 0;
}
void TestCorrectness
( bool print,
UpperOrLower uplo,
const DistMatrix<double>& A,
const DistMatrix<double,VR,STAR>& w,
const DistMatrix<double>& Z,
const DistMatrix<double>& AOrig )
{
const Grid& g = A.Grid();
const int n = Z.Height();
const int k = Z.Width();
if( g.Rank() == 0 )
{
cout << " Gathering computed eigenvalues...";
cout.flush();
}
DistMatrix<double,MR,STAR> w_MR_STAR(g);
w_MR_STAR.AlignWith( Z );
w_MR_STAR = w;
if( g.Rank() == 0 )
cout << "DONE" << endl;
if( g.Rank() == 0 )
cout << " Testing orthogonality of eigenvectors..." << endl;
DistMatrix<double> X(g);
Identity( X, k, k );
Herk( uplo, ADJOINT, -1., Z, 1., X );
double oneNormOfError = OneNorm( X );
double infNormOfError = InfinityNorm( X );
double frobNormOfError = FrobeniusNorm( X );
if( g.Rank() == 0 )
{
cout << " ||Z^H Z - I||_1 = " << oneNormOfError << "\n"
<< " ||Z^H Z - I||_oo = " << infNormOfError << "\n"
<< " ||Z^H Z - I||_F = " << frobNormOfError << "\n\n"
<< " Testing for deviation of AZ from ZW..." << endl;
}
// Set X := AZ
X.AlignWith( Z );
Zeros( X, n, k );
Hemm( LEFT, uplo, 1., AOrig, Z, 0., X );
// Set X := X - ZW = AZ - ZW
for( int jLocal=0; jLocal<X.LocalWidth(); ++jLocal )
{
const double omega = w_MR_STAR.GetLocal(jLocal,0);
for( int iLocal=0; iLocal<X.LocalHeight(); ++iLocal )
{
const double chi = X.GetLocal(iLocal,jLocal);
const double zeta = Z.GetLocal(iLocal,jLocal);
X.SetLocal(iLocal,jLocal,chi-omega*zeta);
}
}
// Find the infinity norms of A, Z, and AZ-ZW
double infNormOfA = HermitianInfinityNorm( uplo, AOrig );
double frobNormOfA = HermitianFrobeniusNorm( uplo, AOrig );
double oneNormOfZ = OneNorm( Z );
double infNormOfZ = InfinityNorm( Z );
double frobNormOfZ = FrobeniusNorm( Z );
oneNormOfError = OneNorm( X );
infNormOfError = InfinityNorm( X );
frobNormOfError = FrobeniusNorm( X );
if( g.Rank() == 0 )
{
cout << " ||A||_1 = ||A||_oo = " << infNormOfA << "\n"
<< " ||A||_F = " << frobNormOfA << "\n"
<< " ||Z||_1 = " << oneNormOfZ << "\n"
<< " ||Z||_oo = " << infNormOfZ << "\n"
<< " ||Z||_F = " << frobNormOfZ << "\n"
<< " ||A Z - Z W||_1 = " << oneNormOfError << "\n"
<< " ||A Z - Z W||_oo = " << infNormOfError << "\n"
<< " ||A Z - Z W||_F = " << frobNormOfError << endl;
}
}
