void Tikhonov
( Orientation orientation,
const SparseMatrix<F>& A,
const Matrix<F>& B,
const SparseMatrix<F>& G,
Matrix<F>& X,
const LeastSquaresCtrl<Base<F>>& ctrl )
{
DEBUG_CSE
// Explicitly form W := op(A)
// ==========================
SparseMatrix<F> W;
if( orientation == NORMAL )
W = A;
else if( orientation == TRANSPOSE )
Transpose( A, W );
else
Adjoint( A, W );
const Int m = W.Height();
const Int n = W.Width();
const Int numRHS = B.Width();
// Embed into a higher-dimensional problem via appending regularization
// ====================================================================
SparseMatrix<F> WEmb;
if( m >= n )
VCat( W, G, WEmb );
else
HCat( W, G, WEmb );
Matrix<F> BEmb;
Zeros( BEmb, WEmb.Height(), numRHS );
if( m >= n )
{
auto BEmbT = BEmb( IR(0,m), IR(0,numRHS) );
BEmbT = B;
}
else
BEmb = B;
// Solve the higher-dimensional problem
// ====================================
Matrix<F> XEmb;
LeastSquares( NORMAL, WEmb, BEmb, XEmb, ctrl );
// Extract the solution
// ====================
if( m >= n )
X = XEmb;
else
X = XEmb( IR(0,n), IR(0,numRHS) );
}
void StackedRuizEquil
( SparseMatrix<Field>& A,
SparseMatrix<Field>& B,
Matrix<Base<Field>>& dRowA,
Matrix<Base<Field>>& dRowB,
Matrix<Base<Field>>& dCol,
bool progress )
{
EL_DEBUG_CSE
typedef Base<Field> Real;
const Int mA = A.Height();
const Int mB = B.Height();
const Int n = A.Width();
Ones( dRowA, mA, 1 );
Ones( dRowB, mB, 1 );
Ones( dCol, n, 1 );
// TODO(poulson): Expose these as control parameters
// For now, simply hard-code the number of iterations
const Int maxIter = 4;
Matrix<Real> scales, maxAbsValsB;
const Int indent = PushIndent();
for( Int iter=0; iter<maxIter; ++iter )
{
// Rescale the columns
// -------------------
ColumnMaxNorms( A, scales );
ColumnMaxNorms( B, maxAbsValsB );
for( Int j=0; j<n; ++j )
scales(j) = Max(scales(j),maxAbsValsB(j));
EntrywiseMap( scales, MakeFunction(DampScaling<Real>) );
DiagonalScale( LEFT, NORMAL, scales, dCol );
DiagonalSolve( RIGHT, NORMAL, scales, A );
DiagonalSolve( RIGHT, NORMAL, scales, B );
// Rescale the rows
// ----------------
RowMaxNorms( A, scales );
EntrywiseMap( scales, MakeFunction(DampScaling<Real>) );
DiagonalScale( LEFT, NORMAL, scales, dRowA );
DiagonalSolve( LEFT, NORMAL, scales, A );
RowMaxNorms( B, scales );
EntrywiseMap( scales, MakeFunction(DampScaling<Real>) );
DiagonalScale( LEFT, NORMAL, scales, dRowB );
DiagonalSolve( LEFT, NORMAL, scales, B );
}
SetIndent( indent );
}
void ShiftDiagonal
( SparseMatrix<T>& A, S alphaPre, Int offset, bool existingDiag )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const T alpha = T(alphaPre);
if( existingDiag )
{
T* valBuf = A.ValueBuffer();
for( Int i=Max(0,-offset); i<Min(m,n-offset); ++i )
{
const Int e = A.Offset( i, i+offset );
valBuf[e] += alpha;
}
}
else
{
const Int diagLength = Min(m,n-offset) - Max(0,-offset);
A.Reserve( diagLength );
for( Int i=Max(0,-offset); i<Min(m,n-offset); ++i )
A.QueueUpdate( i, i+offset, alpha );
A.ProcessQueues();
}
}
void LAV
( const SparseMatrix<Real>& A,
const Matrix<Real>& b,
Matrix<Real>& x,
const lp::affine::Ctrl<Real>& ctrl )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const Range<Int> xInd(0,n), uInd(n,n+m), vInd(n+m,n+2*m);
SparseMatrix<Real> AHat, G;
Matrix<Real> c, h;
// c := [0;1;1]
// ============
Zeros( c, n+2*m, 1 );
auto cuv = c( IR(n,n+2*m), ALL );
Fill( cuv, Real(1) );
// \hat A := [A, I, -I]
// ====================
Zeros( AHat, m, n+2*m );
const Int numEntriesA = A.NumEntries();
AHat.Reserve( numEntriesA + 2*m );
for( Int e=0; e<numEntriesA; ++e )
AHat.QueueUpdate( A.Row(e), A.Col(e), A.Value(e) );
for( Int i=0; i<m; ++i )
{
AHat.QueueUpdate( i, i+n, Real( 1) );
AHat.QueueUpdate( i, i+n+m, Real(-1) );
}
AHat.ProcessQueues();
// G := | 0 -I 0 |
// | 0 0 -I |
// ================
Zeros( G, 2*m, n+2*m );
G.Reserve( G.Height() );
for( Int i=0; i<2*m; ++i )
G.QueueUpdate( i, i+n, Real(-1) );
G.ProcessQueues();
// h := | 0 |
// | 0 |
// ==========
Zeros( h, 2*m, 1 );
// Solve the affine linear program
// ===============================
Matrix<Real> xHat, y, z, s;
LP( AHat, G, b, c, h, xHat, y, z, s, ctrl );
// Extract x
// =========
x = xHat( xInd, ALL );
}
void Fill( SparseMatrix<T>& A, T alpha )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
A.Resize( m, n );
Zero( A );
if( alpha != T(0) )
{
A.Reserve( m*n );
for( Int i=0; i<m; ++i )
for( Int j=0; j<n; ++j )
A.QueueUpdate( i, j, alpha );
A.ProcessQueues();
}
}
void MatrixMarket( const SparseMatrix<T>& A, string basename="matrix" )
{
EL_DEBUG_CSE
string filename = basename + "." + FileExtension(MATRIX_MARKET);
ofstream file( filename.c_str(), std::ios::binary );
if( !file.is_open() )
RuntimeError("Could not open ",filename);
// Write the header
// ================
{
ostringstream os;
os << "%%MatrixMarket matrix coordinate ";
if( IsComplex<T>::value )
os << "complex ";
else
os << "real ";
os << "general\n";
file << os.str();
}
// Write the size line
// ===================
const Int m = A.Height();
const Int n = A.Width();
const Int numNonzeros = A.NumEntries();
file << BuildString(m," ",n," ",numNonzeros,"\n");
// Write the entries
// =================
for( Int e=0; e<numNonzeros; ++e )
{
const Int i = A.Row(e);
const Int j = A.Col(e);
const T value = A.Value(e);
if( IsComplex<T>::value )
{
file <<
BuildString(i," ",j," ",RealPart(value)," ",ImagPart(value),"\n");
}
else
{
file << BuildString(i," ",j," ",RealPart(value),"\n");
}
}
}
void Lanczos
( const SparseMatrix<F>& A,
Matrix<Base<F>>& T,
Int basisSize )
{
DEBUG_CSE
const Int n = A.Height();
if( n != A.Width() )
LogicError("A was not square");
auto applyA =
[&]( const Matrix<F>& X, Matrix<F>& Y )
{
Zeros( Y, n, X.Width() );
Multiply( NORMAL, F(1), A, X, F(0), Y );
};
Lanczos<F>( n, applyA, T, basisSize );
}
bool WriteMatrixMarketFile(const std::string& file_path,
const SparseMatrix<T>& A,
const unsigned int precision)
{
// Write a MatrixMarket file with no comments. Note that the
// MatrixMarket format uses 1-based indexing for rows and columns.
std::ofstream outfile(file_path);
if (!outfile)
return false;
unsigned int height = A.Height();
unsigned int width = A.Width();
unsigned int nnz = A.Size();
// write the 'banner'
outfile << MM_BANNER << " matrix coordinate real general" << std::endl;
// write matrix dimensions and number of nonzeros
outfile << height << " " << width << " " << nnz << std::endl;
outfile << std::fixed;
outfile.precision(precision);
const unsigned int* cols_a = A.LockedColBuffer();
const unsigned int* rows_a = A.LockedRowBuffer();
const T* data_a = A.LockedDataBuffer();
unsigned int width_a = A.Width();
for (unsigned int c=0; c != width_a; ++c)
{
unsigned int start = cols_a[c];
unsigned int end = cols_a[c+1];
for (unsigned int offset=start; offset != end; ++offset)
{
unsigned int r = rows_a[offset];
T val = data_a[offset];
outfile << r+1 << " " << c+1 << " " << val << std::endl;
}
}
outfile.close();
return true;
}
void RowMaxNorms( const SparseMatrix<F>& A, Matrix<Base<F>>& norms )
{
DEBUG_CSE
typedef Base<F> Real;
const Int m = A.Height();
const F* valBuf = A.LockedValueBuffer();
const Int* offsetBuf = A.LockedOffsetBuffer();
norms.Resize( m, 1 );
for( Int i=0; i<m; ++i )
{
Real rowMax = 0;
const Int offset = offsetBuf[i];
const Int numConn = offsetBuf[i+1] - offset;
for( Int e=offset; e<offset+numConn; ++e )
rowMax = Max(rowMax,Abs(valBuf[e]));
norms(i) = rowMax;
}
}
Base<Field> ProductLanczosDecomp
( const SparseMatrix<Field>& A,
Matrix<Field>& V,
Matrix<Base<Field>>& T,
Matrix<Field>& v,
Int basisSize )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
Matrix<Field> S;
// Cache the adjoint
// -----------------
SparseMatrix<Field> AAdj;
Adjoint( A, AAdj );
if( m >= n )
{
auto applyA =
[&]( const Matrix<Field>& X, Matrix<Field>& Y )
{
Zeros( S, m, X.Width() );
Multiply( NORMAL, Field(1), A, X, Field(0), S );
Zeros( Y, n, X.Width() );
Multiply( NORMAL, Field(1), AAdj, S, Field(0), Y );
};
return LanczosDecomp( n, applyA, V, T, v, basisSize );
}
else
{
auto applyA =
[&]( const Matrix<Field>& X, Matrix<Field>& Y )
{
Zeros( S, n, X.Width() );
Multiply( NORMAL, Field(1), AAdj, X, Field(0), S );
Zeros( Y, m, X.Width() );
Multiply( NORMAL, Field(1), A, S, Field(0), Y );
};
return LanczosDecomp( m, applyA, V, T, v, basisSize );
}
}
Base<Field> LanczosDecomp
( const SparseMatrix<Field>& A,
Matrix<Field>& V,
Matrix<Base<Field>>& T,
Matrix<Field>& v,
Int basisSize )
{
EL_DEBUG_CSE
const Int n = A.Height();
if( n != A.Width() )
LogicError("A was not square");
auto applyA =
[&]( const Matrix<Field>& X, Matrix<Field>& Y )
{
Zeros( Y, n, X.Width() );
Multiply( NORMAL, Field(1), A, X, Field(0), Y );
};
return LanczosDecomp( n, applyA, V, T, v, basisSize );
}
void RowTwoNorms( const SparseMatrix<F>& A, Matrix<Base<F>>& norms )
{
DEBUG_CSE
typedef Base<F> Real;
const Int m = A.Height();
const F* valBuf = A.LockedValueBuffer();
const Int* offsetBuf = A.LockedOffsetBuffer();
norms.Resize( m, 1 );
for( Int i=0; i<m; ++i )
{
Real scale = 0;
Real scaledSquare = 1;
const Int offset = offsetBuf[i];
const Int numConn = offsetBuf[i+1] - offset;
for( Int e=offset; e<offset+numConn; ++e )
UpdateScaledSquare( valBuf[e], scale, scaledSquare );
norms(i) = scale*Sqrt(scaledSquare);
}
}
void GetMappedDiagonal
( const SparseMatrix<T>& A,
Matrix<S>& d,
function<S(const T&)> func,
Int offset )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const T* valBuf = A.LockedValueBuffer();
const Int* colBuf = A.LockedTargetBuffer();
const Int iStart = Max(-offset,0);
const Int jStart = Max( offset,0);
const Int diagLength = El::DiagonalLength(m,n,offset);
d.Resize( diagLength, 1 );
Zero( d );
S* dBuf = d.Buffer();
for( Int k=0; k<diagLength; ++k )
{
const Int i = iStart + k;
const Int j = jStart + k;
const Int thisOff = A.RowOffset(i);
const Int nextOff = A.RowOffset(i+1);
auto it = std::lower_bound( colBuf+thisOff, colBuf+nextOff, j );
if( *it == j )
{
const Int e = it-colBuf;
dBuf[Min(i,j)] = func(valBuf[e]);
}
else
dBuf[Min(i,j)] = func(0);
}
}
void SymmetricRuizEquil
( SparseMatrix<F>& A,
Matrix<Base<F>>& d,
Int maxIter, bool progress )
{
DEBUG_CSE
typedef Base<F> Real;
const Int n = A.Height();
Ones( d, n, 1 );
Matrix<Real> scales;
const Int indent = PushIndent();
for( Int iter=0; iter<maxIter; ++iter )
{
// Rescale the columns (and rows)
// ------------------------------
ColumnMaxNorms( A, scales );
EntrywiseMap( scales, function<Real(Real)>(DampScaling<Real>) );
EntrywiseMap( scales, function<Real(Real)>(SquareRootScaling<Real>) );
DiagonalScale( LEFT, NORMAL, scales, d );
SymmetricDiagonalSolve( scales, A );
}
SetIndent( indent );
}
int main(int argc, char *argv[])
{
// 1. Parse command-line options.
const char *mesh_file = "../data/beam-tri.mesh";
int order = 1;
bool static_cond = false;
bool visualization = 1;
OptionsParser args(argc, argv);
args.AddOption(&mesh_file, "-m", "--mesh",
"Mesh file to use.");
args.AddOption(&order, "-o", "--order",
"Finite element order (polynomial degree).");
args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
"--no-static-condensation", "Enable static condensation.");
args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
"--no-visualization",
"Enable or disable GLVis visualization.");
args.Parse();
if (!args.Good())
{
args.PrintUsage(cout);
return 1;
}
args.PrintOptions(cout);
// 2. Read the mesh from the given mesh file. We can handle triangular,
// quadrilateral, tetrahedral or hexahedral elements with the same code.
Mesh *mesh = new Mesh(mesh_file, 1, 1);
int dim = mesh->Dimension();
if (mesh->attributes.Max() < 2 || mesh->bdr_attributes.Max() < 2)
{
cerr << "\nInput mesh should have at least two materials and "
<< "two boundary attributes! (See schematic in ex2.cpp)\n"
<< endl;
return 3;
}
// 3. Select the order of the finite element discretization space. For NURBS
// meshes, we increase the order by degree elevation.
if (mesh->NURBSext)
{
mesh->DegreeElevate(order, order);
}
// 4. Refine the mesh to increase the resolution. In this example we do
// 'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
// largest number that gives a final mesh with no more than 5,000
// elements.
{
int ref_levels =
(int)floor(log(5000./mesh->GetNE())/log(2.)/dim);
for (int l = 0; l < ref_levels; l++)
{
mesh->UniformRefinement();
}
}
// 5. Define a finite element space on the mesh. Here we use vector finite
// elements, i.e. dim copies of a scalar finite element space. The vector
// dimension is specified by the last argument of the FiniteElementSpace
// constructor. For NURBS meshes, we use the (degree elevated) NURBS space
// associated with the mesh nodes.
FiniteElementCollection *fec;
FiniteElementSpace *fespace;
if (mesh->NURBSext)
{
fec = NULL;
fespace = mesh->GetNodes()->FESpace();
}
else
{
fec = new H1_FECollection(order, dim);
fespace = new FiniteElementSpace(mesh, fec, dim);
}
cout << "Number of finite element unknowns: " << fespace->GetTrueVSize()
<< endl << "Assembling: " << flush;
// 6. Determine the list of true (i.e. conforming) essential boundary dofs.
// In this example, the boundary conditions are defined by marking only
// boundary attribute 1 from the mesh as essential and converting it to a
// list of true dofs.
Array<int> ess_tdof_list, ess_bdr(mesh->bdr_attributes.Max());
ess_bdr = 0;
ess_bdr[0] = 1;
fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
// 7. Set up the linear form b(.) which corresponds to the right-hand side of
// the FEM linear system. In this case, b_i equals the boundary integral
// of f*phi_i where f represents a "pull down" force on the Neumann part
// of the boundary and phi_i are the basis functions in the finite element
// fespace. The force is defined by the VectorArrayCoefficient object f,
// which is a vector of Coefficient objects. The fact that f is non-zero
// on boundary attribute 2 is indicated by the use of piece-wise constants
// coefficient for its last component.
VectorArrayCoefficient f(dim);
for (int i = 0; i < dim-1; i++)
{
f.Set(i, new ConstantCoefficient(0.0));
}
{
Vector pull_force(mesh->bdr_attributes.Max());
pull_force = 0.0;
pull_force(1) = -1.0e-2;
f.Set(dim-1, new PWConstCoefficient(pull_force));
}
LinearForm *b = new LinearForm(fespace);
b->AddBoundaryIntegrator(new VectorBoundaryLFIntegrator(f));
cout << "r.h.s. ... " << flush;
b->Assemble();
// 8. Define the solution vector x as a finite element grid function
// corresponding to fespace. Initialize x with initial guess of zero,
// which satisfies the boundary conditions.
GridFunction x(fespace);
x = 0.0;
// 9. Set up the bilinear form a(.,.) on the finite element space
// corresponding to the linear elasticity integrator with piece-wise
// constants coefficient lambda and mu.
Vector lambda(mesh->attributes.Max());
lambda = 1.0;
lambda(0) = lambda(1)*50;
PWConstCoefficient lambda_func(lambda);
Vector mu(mesh->attributes.Max());
mu = 1.0;
mu(0) = mu(1)*50;
PWConstCoefficient mu_func(mu);
BilinearForm *a = new BilinearForm(fespace);
a->AddDomainIntegrator(new ElasticityIntegrator(lambda_func,mu_func));
// 10. Assemble the bilinear form and the corresponding linear system,
// applying any necessary transformations such as: eliminating boundary
// conditions, applying conforming constraints for non-conforming AMR,
// static condensation, etc.
cout << "matrix ... " << flush;
if (static_cond) { a->EnableStaticCondensation(); }
a->Assemble();
SparseMatrix A;
Vector B, X;
a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
cout << "done." << endl;
cout << "Size of linear system: " << A.Height() << endl;
#ifndef MFEM_USE_SUITESPARSE
// 11. Define a simple symmetric Gauss-Seidel preconditioner and use it to
// solve the system Ax=b with PCG.
GSSmoother M(A);
PCG(A, M, B, X, 1, 500, 1e-8, 0.0);
#else
// 11. If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
UMFPackSolver umf_solver;
umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
umf_solver.SetOperator(A);
umf_solver.Mult(B, X);
#endif
// 12. Recover the solution as a finite element grid function.
a->RecoverFEMSolution(X, *b, x);
// 13. For non-NURBS meshes, make the mesh curved based on the finite element
// space. This means that we define the mesh elements through a fespace
// based transformation of the reference element. This allows us to save
// the displaced mesh as a curved mesh when using high-order finite
// element displacement field. We assume that the initial mesh (read from
// the file) is not higher order curved mesh compared to the chosen FE
// space.
if (!mesh->NURBSext)
{
mesh->SetNodalFESpace(fespace);
}
// 14. Save the displaced mesh and the inverted solution (which gives the
// backward displacements to the original grid). This output can be
// viewed later using GLVis: "glvis -m displaced.mesh -g sol.gf".
{
GridFunction *nodes = mesh->GetNodes();
*nodes += x;
x *= -1;
ofstream mesh_ofs("displaced.mesh");
mesh_ofs.precision(8);
mesh->Print(mesh_ofs);
ofstream sol_ofs("sol.gf");
sol_ofs.precision(8);
x.Save(sol_ofs);
}
// 15. Send the above data by socket to a GLVis server. Use the "n" and "b"
// keys in GLVis to visualize the displacements.
if (visualization)
{
char vishost[] = "localhost";
int visport = 19916;
socketstream sol_sock(vishost, visport);
sol_sock.precision(8);
sol_sock << "solution\n" << *mesh << x << flush;
}
// 16. Free the used memory.
delete a;
delete b;
if (fec)
{
delete fespace;
delete fec;
}
delete mesh;
return 0;
}
void IPM
( const SparseMatrix<Real>& A,
const Matrix<Real>& b,
Real lambda,
Matrix<Real>& x,
const qp::affine::Ctrl<Real>& ctrl )
{
DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const Range<Int> uInd(0,n), vInd(n,2*n), rInd(2*n,2*n+m);
SparseMatrix<Real> Q, AHat, G;
Matrix<Real> c, h;
// Q := | 0 0 0 |
// | 0 0 0 |
// | 0 0 I |
// ==============
Zeros( Q, 2*n+m, 2*n+m );
Q.Reserve( m );
for( Int e=0; e<m; ++e )
Q.QueueUpdate( 2*n+e, 2*n+e, Real(1) );
Q.ProcessQueues();
// c := lambda*[1;1;0]
// ===================
Zeros( c, 2*n+m, 1 );
auto cuv = c( IR(0,2*n), ALL );
Fill( cuv, lambda );
// \hat A := [A, -A, I]
// ====================
const Int numEntriesA = A.NumEntries();
Zeros( AHat, m, 2*n+m );
AHat.Reserve( 2*numEntriesA+m );
for( Int e=0; e<numEntriesA; ++e )
{
AHat.QueueUpdate( A.Row(e), A.Col(e), A.Value(e) );
AHat.QueueUpdate( A.Row(e), A.Col(e)+n, -A.Value(e) );
}
for( Int e=0; e<m; ++e )
AHat.QueueUpdate( e, e+2*n, Real(1) );
AHat.ProcessQueues();
// G := | -I 0 0 |
// | 0 -I 0 |
// ================
Zeros( G, 2*n, 2*n+m );
G.Reserve( 2*m );
for( Int e=0; e<2*m; ++e )
G.QueueUpdate( e, e, Real(-1) );
G.ProcessQueues();
// h := 0
// ======
Zeros( h, 2*n, 1 );
// Solve the affine QP
// ===================
Matrix<Real> xHat, y, z, s;
QP( Q, AHat, G, b, c, h, xHat, y, z, s, ctrl );
// x := u - v
// ==========
x = xHat( uInd, ALL );
x -= xHat( vInd, ALL );
}
//-----------------------------------------------------------------------------
void Nmf(const unsigned int kval,
const Algorithm algorithm,
const std::string& csv_file_w,
const std::string& csv_file_h)
{
if (!matrix_loaded)
throw std::logic_error("smallk error (NMF): no matrix has been loaded.");
if (max_iter < min_iter)
throw std::logic_error("smallk error (NMF): min_iterations exceeds max_iterations.");
if (0 == kval)
throw std::logic_error("smallk error (NMF): k must be greater than 0.");
// Check the sizes of matrix W(m, k) and matrix H(k, n) and make sure
// they don't overflow Elemental's default signed int index type.
if (!SizeCheck<int>(m, kval))
throw std::logic_error("smallk error (Nmf): mxk matrix W is too large.");
if (!SizeCheck<int>(kval, n))
throw std::logic_error("smallk error (Nmf): kxn matrix H is too large.");
k = kval;
// convert to the 'NmfAlgorithm' type in nmf.hpp
switch (algorithm)
{
case Algorithm::MU:
nmf_opts.algorithm = NmfAlgorithm::MU;
break;
case Algorithm::HALS:
nmf_opts.algorithm = NmfAlgorithm::HALS;
break;
case Algorithm::RANK2:
nmf_opts.algorithm = NmfAlgorithm::RANK2;
break;
case Algorithm::BPP:
nmf_opts.algorithm = NmfAlgorithm::BPP;
break;
default:
throw std::logic_error("smallk error (NMF): unknown NMF algorithm.");
}
// set k == 2 for Rank2 algorithm
if (NmfAlgorithm::RANK2 == nmf_opts.algorithm)
k = 2;
ldim_w = m;
ldim_h = k;
if (buf_w.size() < m*k)
buf_w.resize(m*k);
if (buf_h.size() < k*n)
buf_h.resize(k*n);
// initialize matrices W and H
bool ok;
unsigned int height_w = m, width_w = k, height_h = k, width_h = n;
cout << "Initializing matrix W..." << endl;
if (csv_file_w.empty())
ok = RandomMatrix(&buf_w[0], ldim_w, m, k, rng);
else
ok = LoadDelimitedFile(buf_w, height_w, width_w, csv_file_w);
if (!ok)
{
std::ostringstream msg;
msg << "smallk error (Nmf): load failed for file ";
msg << "\"" << csv_file_w << "\"";
throw std::runtime_error(msg.str());
}
if ( (height_w != m) || (width_w != k))
{
cerr << "\tdimensions of matrix W are " << height_w
<< " x " << width_w << endl;
cerr << "\texpected " << m << " x " << k << endl;
throw std::logic_error("smallk error (Nmf): non-conformant matrix W.");
}
cout << "Initializing matrix H..." << endl;
if (csv_file_h.empty())
ok = RandomMatrix(&buf_h[0], ldim_h, k, n, rng);
else
ok = LoadDelimitedFile(buf_h, height_h, width_h, csv_file_h);
if (!ok)
{
std::ostringstream msg;
msg << "smallk error (Nmf): load failed for file ";
msg << "\"" << csv_file_h << "\"";
throw std::runtime_error(msg.str());
}
if ( (height_h != k) || (width_h != n))
{
cerr << "\tdimensions of matrix H are " << height_h
<< " x " << width_h << endl;
cerr << "\texpected " << k << " x " << n << endl;
throw std::logic_error("smallk error (Nmf): non-conformant matrix H.");
}
// The ratio of projected gradient norms doesn't seem to work very well
// with MU. We frequently observe a 'leveling off' behavior and the
// convergence is even slower than usual. So for MU use the relative
// change in the Frobenius norm of W as the stopping criterion, which
// always seems to behave well, even though it is on shaky theoretical
// ground.
if (NmfAlgorithm::MU == nmf_opts.algorithm)
nmf_opts.prog_est_algorithm = NmfProgressAlgorithm::DELTA_FNORM;
else
nmf_opts.prog_est_algorithm = NmfProgressAlgorithm::PG_RATIO;
nmf_opts.tol = nmf_tolerance;
nmf_opts.height = m;
nmf_opts.width = n;
nmf_opts.k = k;
nmf_opts.min_iter = min_iter;
nmf_opts.max_iter = max_iter;
nmf_opts.tolcount = 1;
nmf_opts.max_threads = max_threads;
nmf_opts.verbose = true;
nmf_opts.normalize = true;
// display all params to user
PrintNmfOpts(nmf_opts);
NmfStats stats;
Result result;
if (is_sparse)
{
result = NmfSparse(nmf_opts,
A.Height(), A.Width(), A.Size(),
A.LockedColBuffer(),
A.LockedRowBuffer(),
A.LockedDataBuffer(),
&buf_w[0], ldim_w,
&buf_h[0], ldim_h,
stats);
}
else
{
result = Nmf(nmf_opts,
&buf_a[0], ldim_a,
&buf_w[0], ldim_w,
&buf_h[0], ldim_h,
stats);
}
cout << "Elapsed wall clock time: ";
cout << ElapsedTime(stats.elapsed_us) << endl;
cout << endl;
if (Result::OK != result)
throw std::runtime_error("smallk error (Nmf): NMF solver failure.");
// write the computed W and H factors to disk
std::string outfile_w, outfile_h;
if (outdir.empty())
{
outfile_w = DEFAULT_FILENAME_W;
outfile_h = DEFAULT_FILENAME_H;
}
else
{
outfile_w = outdir + DEFAULT_FILENAME_W;
outfile_h = outdir + DEFAULT_FILENAME_H;
}
cout << "Writing output files..." << endl;
if (!WriteDelimitedFile(&buf_w[0], ldim_w, m, k, outfile_w, outprecision))
throw std::runtime_error("smallk error (Nmf): could not write W result.");
if (!WriteDelimitedFile(&buf_h[0], ldim_h, k, n, outfile_h, outprecision))
throw std::runtime_error("smallk error (Nmf): could not write H result.");
}
void SparseMatrix<T>::SubMatrixColsCompact(SparseMatrix<T>& result,
const std::vector<unsigned int>& col_indices,
std::vector<unsigned int>& old_to_new_rows,
std::vector<unsigned int>& new_to_old_rows) const
{
const unsigned int UNUSED_ROW = 0xFFFFFFFF;
// extract entire columns from the source matrix to form the dest matrix
unsigned int new_width = col_indices.size();
if (0u == new_width)
throw std::logic_error("SparseMatrix::SubMatrixColsCompact: empty column set");
// need one entry per original row in the row_map
if (old_to_new_rows.size() < height_)
old_to_new_rows.resize(height_);
std::fill(old_to_new_rows.begin(), old_to_new_rows.begin() + height_, UNUSED_ROW);
// no need to fill 'new_to_old_rows'
// check the column indices for validty and count nonzeros
unsigned int new_size = 0;
for (auto it=col_indices.begin(); it != col_indices.end(); ++it)
{
// index of next source column
unsigned int c = *it;
if (c >= width_)
throw std::logic_error("SparseMatrix::SubMatrixColsCompact: column index out of range");
// number of nonzeros in source column c
new_size += (col_offsets_[c+1] - col_offsets_[c]);
}
if (0u == new_size)
throw std::logic_error("SparseMatrix::SubMatrixColsCompact: submatrix is the zero matrix");
// allocate memory in the result; won't allocate if sufficient memory available
result.Reserve(height_, new_width, new_size);
unsigned int* cols_b = result.ColBuffer();
unsigned int* rows_b = result.RowBuffer();
T* data_b = result.DataBuffer();
unsigned int c_dest = 0;
unsigned int elt_count = 0;
for (auto it=col_indices.begin(); it != col_indices.end(); ++it)
{
// index of the next source column
unsigned int c = *it;
// set element offset for the next dest column
cols_b[c_dest] = elt_count;
unsigned int start = col_offsets_[c];
unsigned int end = col_offsets_[c+1];
for (unsigned int offset = start; offset != end; ++offset)
{
unsigned int row = row_indices_[offset];
old_to_new_rows[row] = row;
rows_b[elt_count] = row;
data_b[elt_count] = data_[offset];
++elt_count;
}
// have now completed another column
++c_dest;
}
cols_b[new_width] = elt_count;
assert(new_width == c_dest);
// set the size of the new matrix explicitly, since Load() has been bypassed
result.SetSize(elt_count);
// determine the new height of the submatrix
unsigned int new_height = 0;
for (unsigned int r=0; r != height_; ++r)
{
if (UNUSED_ROW != old_to_new_rows[r])
++new_height;
}
new_to_old_rows.resize(new_height);
// renumber the rows in the submatrix
unsigned int new_r = 0;
for (unsigned int r=0; r<height_; ++r)
{
if (UNUSED_ROW != old_to_new_rows[r])
{
old_to_new_rows[r] = new_r;
new_to_old_rows[new_r] = r;
++new_r;
}
}
// set the height of the new matrix explicitly
assert(new_r == new_height);
result.SetHeight(new_height);
// re-index the rows in the submatrix
for (unsigned int s=0; s != elt_count; ++s)
{
unsigned int old_row_index = rows_b[s];
rows_b[s] = old_to_new_rows[old_row_index];
}
assert(result.Height() == new_height);
assert(new_to_old_rows.size() == new_height);
assert(old_to_new_rows.size() == height_);
}
//-----------------------------------------------------------------------------
int main(int argc, char* argv[])
{
Timer timer;
double elapsed_s;
// print usage info if no command line args were specified
std::string prog_name(argv[0]);
if (1 == argc)
{
PrintUsage(prog_name);
return 0;
}
CommandLineOptions opts;
ParseCommandLine(argc, argv, opts);
if (!IsValid(opts))
return -1;
//
// Check to see if the specified directories exist.
//
if (!DirectoryExists(opts.indir))
{
cerr << "\npreprocessor: the specified input directory "
<< opts.indir << " does not exist." << endl;
return -1;
}
if (!opts.outdir.empty())
{
if (!DirectoryExists(opts.outdir))
{
cerr << "\npreprocessor: the specified output directory "
<< opts.outdir << " does not exist." << endl;
return -1;
}
}
// setup paths and filenames
std::string inputdir = EnsureTrailingPathSep(opts.indir);
std::string infile = inputdir + std::string("matrix.mtx");
std::string indict = inputdir + std::string("dictionary.txt");
std::string indocs = inputdir + std::string("documents.txt");
std::string outputdir, outfile, outdict, outdocs;
if (!opts.outdir.empty())
{
outputdir = EnsureTrailingPathSep(opts.outdir);
outfile = outputdir + std::string("reduced_matrix.mtx");
outdict = outputdir + std::string("reduced_dictionary.txt");
outdocs = outputdir + std::string("reduced_documents.txt");
}
else
{
outfile = std::string("reduced_matrix.mtx");
outdict = std::string("reduced_dictionary.txt");
outdocs = std::string("reduced_documents.txt");
}
//
// load the input dictionary and documents
//
std::vector<std::string> dictionary, documents;
if (!LoadStringsFromFile(indict, dictionary))
{
cerr << "\npreprocessor: could not open dictionary file "
<< indict << endl;
return -1;
}
unsigned int num_terms = dictionary.size();
if (!LoadStringsFromFile(indocs, documents))
{
cerr << "\npreprocessor: could not open documents file "
<< indocs << endl;
return -1;
}
unsigned int num_docs = documents.size();
// print options to screen prior to run
opts.indir = inputdir;
if (outputdir.empty())
opts.outdir = std::string("current directory");
else
opts.outdir = outputdir;
PrintOpts(opts);
bool boolean_mode = (0 != opts.boolean_mode);
SparseMatrix<double> A;
unsigned int height, width, nonzeros;
//
// load the input matrix
//
cout << "Loading input matrix " << infile << endl;
timer.Start();
if (!LoadMatrixMarketFile(infile, A, height, width, nonzeros))
{
cerr << "\npreprocessor: could not load file " << infile << endl;
return -1;
}
timer.Stop();
elapsed_s = static_cast<double>(timer.ReportMilliseconds() * 0.001);
cout << "\tInput file load time: " << elapsed_s << "s." << endl;
//
// check num_terms and num_docs
//
if (num_terms < A.Height())
{
cerr << "\npreprocessor error: expected " << A.Height()
<< " terms in the dictionary; found " << num_terms << "." << endl;
return -1;
}
if (num_docs < A.Width())
{
cerr << "\npreprocessor error: expected " << A.Width()
<< " strings in the documents file; found " << num_docs
<< "." << endl;
return -1;
}
//
// do the preprocessing
//
timer.Start();
TermFrequencyMatrix M(A, boolean_mode);
// allocate the index sets for the terms and docs
std::vector<unsigned int> term_indices(height);
std::vector<unsigned int> doc_indices(width);
std::vector<double> scores;
bool ok = preprocess_tf(M, term_indices, doc_indices, scores,
opts.max_iter, opts.docs_per_term, opts.terms_per_doc);
timer.Stop();
elapsed_s = static_cast<double>(timer.ReportMilliseconds() * 0.001);
cout << "Processing time: " << elapsed_s << "s." << endl;
cout << endl;
if (!ok)
{
cerr << "\npreprocessor: matrix has dimension zero." << endl;
cerr << "no output files will be written" << endl;
return false;
}
//
// write the result matrix to disk
//
cout << "Writing output matrix " << outfile << endl;
timer.Start();
if (!M.WriteMtxFile(outfile, &scores[0], opts.precision))
{
cerr << "\npreprocessor: could not write file "
<< outfile << endl;
return -1;
}
timer.Stop();
elapsed_s = static_cast<double>(timer.ReportMilliseconds() * 0.001);
cout << "Output file write time: " << elapsed_s << "s." << endl;
//
// write the reduced dictionary and documents to disk
//
cout << "Writing dictionary file " << outdict << endl;
timer.Start();
if (!WriteStringsToFile(outdict, dictionary, term_indices, M.Height()))
{
cerr << "\npreprocessor: could not write file "
<< outdict << endl;
}
timer.Stop();
elapsed_s = static_cast<double>(timer.ReportMilliseconds() * 0.001);
cout << "Writing documents file " << outdocs << endl;
timer.Start();
if (!WriteStringsToFile(outdocs, documents, doc_indices, M.Width()))
{
cerr << "\npreprocessor: could not write file "
<< outdocs << endl;
}
timer.Stop();
elapsed_s += static_cast<double>(timer.ReportMilliseconds() * 0.001);
cout << "Dictionary + documents write time: " << elapsed_s << "s." << endl;
return 0;
}
int main(int argc, char *argv[])
{
// 1. Parse command-line options.
const char *mesh_file = "../../data/fichera.mesh";
int order = sol_p;
bool static_cond = false;
bool visualization = 1;
bool perf = true;
OptionsParser args(argc, argv);
args.AddOption(&mesh_file, "-m", "--mesh",
"Mesh file to use.");
args.AddOption(&order, "-o", "--order",
"Finite element order (polynomial degree) or -1 for"
" isoparametric space.");
args.AddOption(&perf, "-perf", "--hpc-version", "-std", "--standard-version",
"Enable high-performance, tensor-based, assembly.");
args.AddOption(&static_cond, "-sc", "--static-condensation", "-no-sc",
"--no-static-condensation", "Enable static condensation.");
args.AddOption(&visualization, "-vis", "--visualization", "-no-vis",
"--no-visualization",
"Enable or disable GLVis visualization.");
args.Parse();
if (!args.Good())
{
args.PrintUsage(cout);
return 1;
}
args.PrintOptions(cout);
// 2. Read the mesh from the given mesh file. We can handle triangular,
// quadrilateral, tetrahedral, hexahedral, surface and volume meshes with
// the same code.
Mesh *mesh = new Mesh(mesh_file, 1, 1);
int dim = mesh->Dimension();
// 3. Check if the optimized version matches the given mesh
if (perf)
{
cout << "High-performance version using integration rule with "
<< int_rule_t::qpts << " points ..." << endl;
if (!mesh_t::MatchesGeometry(*mesh))
{
cout << "The given mesh does not match the optimized 'geom' parameter.\n"
<< "Recompile with suitable 'geom' value." << endl;
delete mesh;
return 3;
}
else if (!mesh_t::MatchesNodes(*mesh))
{
cout << "Switching the mesh curvature to match the "
<< "optimized value (order " << mesh_p << ") ..." << endl;
mesh->SetCurvature(mesh_p, false, -1, Ordering::byNODES);
}
}
// 4. Refine the mesh to increase the resolution. In this example we do
// 'ref_levels' of uniform refinement. We choose 'ref_levels' to be the
// largest number that gives a final mesh with no more than 50,000
// elements.
{
int ref_levels =
(int)floor(log(50000./mesh->GetNE())/log(2.)/dim);
for (int l = 0; l < ref_levels; l++)
{
mesh->UniformRefinement();
}
}
// 5. Define a finite element space on the mesh. Here we use continuous
// Lagrange finite elements of the specified order. If order < 1, we
// instead use an isoparametric/isogeometric space.
FiniteElementCollection *fec;
if (order > 0)
{
fec = new H1_FECollection(order, dim);
}
else if (mesh->GetNodes())
{
fec = mesh->GetNodes()->OwnFEC();
cout << "Using isoparametric FEs: " << fec->Name() << endl;
}
else
{
fec = new H1_FECollection(order = 1, dim);
}
FiniteElementSpace *fespace = new FiniteElementSpace(mesh, fec);
cout << "Number of finite element unknowns: "
<< fespace->GetTrueVSize() << endl;
// 6. Check if the optimized version matches the given space
if (perf && !sol_fes_t::Matches(*fespace))
{
cout << "The given order does not match the optimized parameter.\n"
<< "Recompile with suitable 'sol_p' value." << endl;
delete fespace;
delete fec;
delete mesh;
return 4;
}
// 7. Determine the list of true (i.e. conforming) essential boundary dofs.
// In this example, the boundary conditions are defined by marking all
// the boundary attributes from the mesh as essential (Dirichlet) and
// converting them to a list of true dofs.
Array<int> ess_tdof_list;
if (mesh->bdr_attributes.Size())
{
Array<int> ess_bdr(mesh->bdr_attributes.Max());
ess_bdr = 1;
fespace->GetEssentialTrueDofs(ess_bdr, ess_tdof_list);
}
// 8. Set up the linear form b(.) which corresponds to the right-hand side of
// the FEM linear system, which in this case is (1,phi_i) where phi_i are
// the basis functions in the finite element fespace.
LinearForm *b = new LinearForm(fespace);
ConstantCoefficient one(1.0);
b->AddDomainIntegrator(new DomainLFIntegrator(one));
b->Assemble();
// 9. Define the solution vector x as a finite element grid function
// corresponding to fespace. Initialize x with initial guess of zero,
// which satisfies the boundary conditions.
GridFunction x(fespace);
x = 0.0;
// 10. Set up the bilinear form a(.,.) on the finite element space that will
// hold the matrix corresponding to the Laplacian operator -Delta.
BilinearForm *a = new BilinearForm(fespace);
// 11. Assemble the bilinear form and the corresponding linear system,
// applying any necessary transformations such as: eliminating boundary
// conditions, applying conforming constraints for non-conforming AMR,
// static condensation, etc.
if (static_cond) { a->EnableStaticCondensation(); }
cout << "Assembling the matrix ..." << flush;
tic_toc.Clear();
tic_toc.Start();
// Pre-allocate sparsity assuming dense element matrices
a->UsePrecomputedSparsity();
if (!perf)
{
// Standard assembly using a diffusion domain integrator
a->AddDomainIntegrator(new DiffusionIntegrator(one));
a->Assemble();
}
else
{
// High-performance assembly using the templated operator type
oper_t a_oper(integ_t(coeff_t(1.0)), *fespace);
a_oper.AssembleBilinearForm(*a);
}
tic_toc.Stop();
cout << " done, " << tic_toc.RealTime() << "s." << endl;
SparseMatrix A;
Vector B, X;
a->FormLinearSystem(ess_tdof_list, x, *b, A, X, B);
cout << "Size of linear system: " << A.Height() << endl;
#ifndef MFEM_USE_SUITESPARSE
// 12. Define a simple symmetric Gauss-Seidel preconditioner and use it to
// solve the system A X = B with PCG.
GSSmoother M(A);
PCG(A, M, B, X, 1, 500, 1e-12, 0.0);
#else
// 12. If MFEM was compiled with SuiteSparse, use UMFPACK to solve the system.
UMFPackSolver umf_solver;
umf_solver.Control[UMFPACK_ORDERING] = UMFPACK_ORDERING_METIS;
umf_solver.SetOperator(A);
umf_solver.Mult(B, X);
#endif
// 13. Recover the solution as a finite element grid function.
a->RecoverFEMSolution(X, *b, x);
// 14. Save the refined mesh and the solution. This output can be viewed later
// using GLVis: "glvis -m refined.mesh -g sol.gf".
ofstream mesh_ofs("refined.mesh");
mesh_ofs.precision(8);
mesh->Print(mesh_ofs);
ofstream sol_ofs("sol.gf");
sol_ofs.precision(8);
x.Save(sol_ofs);
// 15. Send the solution by socket to a GLVis server.
if (visualization)
{
char vishost[] = "localhost";
int visport = 19916;
socketstream sol_sock(vishost, visport);
sol_sock.precision(8);
sol_sock << "solution\n" << *mesh << x << flush;
}
// 16. Free the used memory.
delete a;
delete b;
delete fespace;
if (order > 0) { delete fec; }
delete mesh;
return 0;
}
void RLS
( const SparseMatrix<Real>& A,
const Matrix<Real>& b,
Real rho,
Matrix<Real>& x,
const socp::affine::Ctrl<Real>& ctrl )
{
DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
Matrix<Int> orders, firstInds;
Zeros( orders, m+n+3, 1 );
Zeros( firstInds, m+n+3, 1 );
for( Int i=0; i<m+1; ++i )
{
orders.Set( i, 0, m+1 );
firstInds.Set( i, 0, 0 );
}
for( Int i=0; i<n+2; ++i )
{
orders.Set( i+m+1, 0, n+2 );
firstInds.Set( i+m+1, 0, m+1 );
}
// G := | -1 0 0 |
// | 0 0 A |
// | 0 -1 0 |
// | 0 0 -I |
// | 0 0 0 |
SparseMatrix<Real> G;
{
const Int numEntriesA = A.NumEntries();
Zeros( G, m+n+3, n+2 );
G.Reserve( numEntriesA+n+2 );
G.QueueUpdate( 0, 0, -1 );
for( Int e=0; e<numEntriesA; ++e )
G.QueueUpdate( A.Row(e)+1, A.Col(e)+2, A.Value(e) );
G.QueueUpdate( m+1, 1, -1 );
for( Int j=0; j<n; ++j )
G.QueueUpdate( j+m+2, j+2, -1 );
G.ProcessQueues();
}
// h := | 0 |
// | b |
// | 0 |
// | 0 |
// | 1 |
Matrix<Real> h;
Zeros( h, m+n+3, 1 );
auto hb = h( IR(1,m+1), ALL );
hb = b;
h.Set( END, 0, 1 );
// c := [1; rho; 0]
Matrix<Real> c;
Zeros( c, n+2, 1 );
c.Set( 0, 0, 1 );
c.Set( 1, 0, rho );
SparseMatrix<Real> AHat;
Zeros( AHat, 0, n+2 );
Matrix<Real> bHat;
Zeros( bHat, 0, 1 );
Matrix<Real> xHat, y, z, s;
SOCP( AHat, G, bHat, c, h, orders, firstInds, xHat, y, z, s, ctrl );
x = xHat( IR(2,END), ALL );
}
void IPM
( const SparseMatrix<Real>& A,
const Matrix<Real>& d,
Real lambda,
Matrix<Real>& x,
const qp::affine::Ctrl<Real>& ctrl )
{
EL_DEBUG_CSE
const Int m = A.Height();
const Int n = A.Width();
const Range<Int> wInd(0,n), betaInd(n,n+1), zInd(n+1,n+m+1);
SparseMatrix<Real> Q, AHat, G;
Matrix<Real> c, b, h;
// Q := | I 0 0 |
// | 0 0 0 |
// | 0 0 0 |
// ==============
Zeros( Q, n+m+1, n+m+1 );
Q.Reserve( n );
for( Int e=0; e<n; ++e )
Q.QueueUpdate( e, e, Real(1) );
Q.ProcessQueues();
// c := [0;0;lambda]
// =================
Zeros( c, n+m+1, 1 );
auto cz = c( zInd, ALL );
Fill( cz, lambda );
// AHat = []
// =========
Zeros( AHat, 0, n+m+1 );
// b = []
// ======
Zeros( b, 0, 1 );
// G := |-diag(d) A, -d, -I|
// | 0, 0, -I|
// =========================
Zeros( G, 2*m, n+m+1 );
const Int numEntriesA = A.NumEntries();
G.Reserve( numEntriesA+3*m );
for( Int e=0; e<numEntriesA; ++e )
G.QueueUpdate( A.Row(e), A.Col(e), -d(A.Row(e))*A.Value(e) );
for( Int e=0; e<m; ++e )
G.QueueUpdate( e, n, -d(e) );
for( Int e=0; e<m; ++e )
{
G.QueueUpdate( e, e+n+1, Real(-1) );
G.QueueUpdate( e+m, e+n+1, Real(-1) );
}
G.ProcessQueues();
// h := [-ones(m,1); zeros(m,1)]
// =============================
Zeros( h, 2*m, 1 );
auto h0 = h( IR(0,m), ALL );
Fill( h0, Real(-1) );
// Solve the affine QP
// ===================
Matrix<Real> y, z, s;
QP( Q, AHat, G, b, c, h, x, y, z, s, ctrl );
}