static Rcpp::NumericMatrix refit_model(Rcpp::NumericMatrix X,
Rcpp::NumericVector y,
Rcpp::NumericMatrix beta_new,
Rcpp::IntegerVector nk,
int model,
double eps,
int maxiter)
{
int K = nk.size();
int p = X.ncol();
int n;
Rcpp::NumericMatrix Xtmp(X.nrow(),p);
Rcpp::NumericMatrix beta_refit(p,K);
Rcpp::NumericVector lasso_result;
int idx = 0;
for (int k = 0; k < K; k++) {
n = nk[k];
for (int i = 0; i < n; i++) {
for (int j = 0; j < p; j++) {
Xtmp(idx+i,j) = X(idx+i,j) * nz(beta_new(j,k),eps);
}
}
idx += n;
}
idx = 0;
for (int k = 0; k < K; k++) {
n = nk[k];
lasso_result = lasso(Xtmp(Rcpp::Range(idx,idx+n-1),Rcpp::_), y[Rcpp::Range(idx,idx+n-1)], 0.0, model, false, eps, maxiter);
for(int j = 0; j < p; j++){
beta_refit(j,k) = lasso_result[j];
}
idx += n;
}
return beta_refit;
}
int BlockDACG::reSolve(int numEigen, Epetra_MultiVector &Q, double *lambda, int startingEV) {
// Computes the smallest eigenvalues and the corresponding eigenvectors
// of the generalized eigenvalue problem
//
// K X = M X Lambda
//
// using a Block Deflation Accelerated Conjugate Gradient algorithm.
//
// Note that if M is not specified, then K X = X Lambda is solved.
//
// Ref: P. Arbenz & R. Lehoucq, "A comparison of algorithms for modal analysis in the
// absence of a sparse direct method", SNL, Technical Report SAND2003-1028J
// With the notations of this report, the coefficient beta is defined as
// diag( H^T_{k} G_{k} ) / diag( H^T_{k-1} G_{k-1} )
//
// Input variables:
//
// numEigen (integer) = Number of eigenmodes requested
//
// Q (Epetra_MultiVector) = Converged eigenvectors
// The number of columns of Q must be equal to numEigen + blockSize.
// The rows of Q are distributed across processors.
// At exit, the first numEigen columns contain the eigenvectors requested.
//
// lambda (array of doubles) = Converged eigenvalues
// At input, it must be of size numEigen + blockSize.
// At exit, the first numEigen locations contain the eigenvalues requested.
//
// startingEV (integer) = Number of existing converged eigenmodes
//
// Return information on status of computation
//
// info >= 0 >> Number of converged eigenpairs at the end of computation
//
// // Failure due to input arguments
//
// info = - 1 >> The stiffness matrix K has not been specified.
// info = - 2 >> The maps for the matrix K and the matrix M differ.
// info = - 3 >> The maps for the matrix K and the preconditioner P differ.
// info = - 4 >> The maps for the vectors and the matrix K differ.
// info = - 5 >> Q is too small for the number of eigenvalues requested.
// info = - 6 >> Q is too small for the computation parameters.
//
// info = - 10 >> Failure during the mass orthonormalization
//
// info = - 20 >> Error in LAPACK during the local eigensolve
//
// info = - 30 >> MEMORY
//
// Check the input parameters
if (numEigen <= startingEV) {
return startingEV;
}
int info = myVerify.inputArguments(numEigen, K, M, Prec, Q, numEigen + blockSize);
if (info < 0)
return info;
int myPid = MyComm.MyPID();
// Get the weight for approximating the M-inverse norm
Epetra_Vector *vectWeight = 0;
if (normWeight) {
vectWeight = new Epetra_Vector(View, Q.Map(), normWeight);
}
int knownEV = startingEV;
int localVerbose = verbose*(myPid==0);
// Define local block vectors
//
// MX = Working vectors (storing M*X if M is specified, else pointing to X)
// KX = Working vectors (storing K*X)
//
// R = Residuals
//
// H = Preconditioned residuals
//
// P = Search directions
// MP = Working vectors (storing M*P if M is specified, else pointing to P)
// KP = Working vectors (storing K*P)
int xr = Q.MyLength();
Epetra_MultiVector X(View, Q, numEigen, blockSize);
X.Random();
int tmp;
tmp = (M == 0) ? 5*blockSize*xr : 7*blockSize*xr;
double *work1 = new (nothrow) double[tmp];
if (work1 == 0) {
if (vectWeight)
delete vectWeight;
info = -30;
return info;
}
memRequested += sizeof(double)*tmp/(1024.0*1024.0);
highMem = (highMem > currentSize()) ? highMem : currentSize();
double *tmpD = work1;
Epetra_MultiVector KX(View, Q.Map(), tmpD, xr, blockSize);
tmpD = tmpD + xr*blockSize;
Epetra_MultiVector MX(View, Q.Map(), (M) ? tmpD : X.Values(), xr, blockSize);
tmpD = (M) ? tmpD + xr*blockSize : tmpD;
Epetra_MultiVector R(View, Q.Map(), tmpD, xr, blockSize);
tmpD = tmpD + xr*blockSize;
Epetra_MultiVector H(View, Q.Map(), tmpD, xr, blockSize);
tmpD = tmpD + xr*blockSize;
Epetra_MultiVector P(View, Q.Map(), tmpD, xr, blockSize);
tmpD = tmpD + xr*blockSize;
Epetra_MultiVector KP(View, Q.Map(), tmpD, xr, blockSize);
tmpD = tmpD + xr*blockSize;
Epetra_MultiVector MP(View, Q.Map(), (M) ? tmpD : P.Values(), xr, blockSize);
// Define arrays
//
// theta = Store the local eigenvalues (size: 2*blockSize)
// normR = Store the norm of residuals (size: blockSize)
//
// oldHtR = Store the previous H_i^T*R_i (size: blockSize)
// currentHtR = Store the current H_i^T*R_i (size: blockSize)
//
// MM = Local mass matrix (size: 2*blockSize x 2*blockSize)
// KK = Local stiffness matrix (size: 2*blockSize x 2*blockSize)
//
// S = Local eigenvectors (size: 2*blockSize x 2*blockSize)
int lwork2;
lwork2 = 5*blockSize + 12*blockSize*blockSize;
double *work2 = new (nothrow) double[lwork2];
if (work2 == 0) {
if (vectWeight)
delete vectWeight;
delete[] work1;
info = -30;
return info;
}
highMem = (highMem > currentSize()) ? highMem : currentSize();
tmpD = work2;
double *theta = tmpD;
tmpD = tmpD + 2*blockSize;
double *normR = tmpD;
tmpD = tmpD + blockSize;
double *oldHtR = tmpD;
tmpD = tmpD + blockSize;
double *currentHtR = tmpD;
tmpD = tmpD + blockSize;
memset(currentHtR, 0, blockSize*sizeof(double));
double *MM = tmpD;
tmpD = tmpD + 4*blockSize*blockSize;
double *KK = tmpD;
tmpD = tmpD + 4*blockSize*blockSize;
double *S = tmpD;
memRequested += sizeof(double)*lwork2/(1024.0*1024.0);
// Define an array to store the residuals history
if (localVerbose > 2) {
resHistory = new (nothrow) double[maxIterEigenSolve*blockSize];
if (resHistory == 0) {
if (vectWeight)
delete vectWeight;
delete[] work1;
delete[] work2;
info = -30;
return info;
}
historyCount = 0;
}
// Miscellaneous definitions
bool reStart = false;
numRestart = 0;
int localSize;
int twoBlocks = 2*blockSize;
int nFound = blockSize;
int i, j;
if (localVerbose > 0) {
cout << endl;
cout << " *|* Problem: ";
if (M)
cout << "K*Q = M*Q D ";
else
cout << "K*Q = Q D ";
if (Prec)
cout << " with preconditioner";
cout << endl;
cout << " *|* Algorithm = DACG (block version)" << endl;
cout << " *|* Size of blocks = " << blockSize << endl;
cout << " *|* Number of requested eigenvalues = " << numEigen << endl;
cout.precision(2);
cout.setf(ios::scientific, ios::floatfield);
cout << " *|* Tolerance for convergence = " << tolEigenSolve << endl;
cout << " *|* Norm used for convergence: ";
if (normWeight)
cout << "weighted L2-norm with user-provided weights" << endl;
else
cout << "L^2-norm" << endl;
if (startingEV > 0)
cout << " *|* Input converged eigenvectors = " << startingEV << endl;
cout << "\n -- Start iterations -- \n";
}
timeOuterLoop -= MyWatch.WallTime();
for (outerIter = 1; outerIter <= maxIterEigenSolve; ++outerIter) {
highMem = (highMem > currentSize()) ? highMem : currentSize();
if ((outerIter == 1) || (reStart == true)) {
reStart = false;
localSize = blockSize;
if (nFound > 0) {
Epetra_MultiVector X2(View, X, blockSize-nFound, nFound);
Epetra_MultiVector MX2(View, MX, blockSize-nFound, nFound);
Epetra_MultiVector KX2(View, KX, blockSize-nFound, nFound);
// Apply the mass matrix to X
timeMassOp -= MyWatch.WallTime();
if (M)
M->Apply(X2, MX2);
timeMassOp += MyWatch.WallTime();
massOp += nFound;
if (knownEV > 0) {
// Orthonormalize X against the known eigenvectors with Gram-Schmidt
// Note: Use R as a temporary work space
Epetra_MultiVector copyQ(View, Q, 0, knownEV);
timeOrtho -= MyWatch.WallTime();
info = modalTool.massOrthonormalize(X, MX, M, copyQ, nFound, 0, R.Values());
timeOrtho += MyWatch.WallTime();
// Exit the code if the orthogonalization did not succeed
if (info < 0) {
info = -10;
delete[] work1;
delete[] work2;
if (vectWeight)
delete vectWeight;
return info;
}
}
// Apply the stiffness matrix to X
timeStifOp -= MyWatch.WallTime();
K->Apply(X2, KX2);
timeStifOp += MyWatch.WallTime();
stifOp += nFound;
} // if (nFound > 0)
} // if ((outerIter == 1) || (reStart == true))
else {
// Apply the preconditioner on the residuals
if (Prec != 0) {
timePrecOp -= MyWatch.WallTime();
Prec->ApplyInverse(R, H);
timePrecOp += MyWatch.WallTime();
precOp += blockSize;
}
else {
memcpy(H.Values(), R.Values(), xr*blockSize*sizeof(double));
}
// Compute the product H^T*R
timeSearchP -= MyWatch.WallTime();
memcpy(oldHtR, currentHtR, blockSize*sizeof(double));
H.Dot(R, currentHtR);
// Define the new search directions
if (localSize == blockSize) {
P.Scale(-1.0, H);
localSize = twoBlocks;
} // if (localSize == blockSize)
else {
bool hasZeroDot = false;
for (j = 0; j < blockSize; ++j) {
if (oldHtR[j] == 0.0) {
hasZeroDot = true;
break;
}
callBLAS.SCAL(xr, currentHtR[j]/oldHtR[j], P.Values() + j*xr);
}
if (hasZeroDot == true) {
// Restart the computation when there is a null dot product
if (localVerbose > 0) {
cout << endl;
cout << " !! Null dot product -- Restart the search space !!\n";
cout << endl;
}
if (blockSize == 1) {
X.Random();
nFound = blockSize;
}
else {
Epetra_MultiVector Xinit(View, X, j, blockSize-j);
Xinit.Random();
nFound = blockSize - j;
} // if (blockSize == 1)
reStart = true;
numRestart += 1;
info = 0;
continue;
}
callBLAS.AXPY(xr*blockSize, -1.0, H.Values(), P.Values());
} // if (localSize == blockSize)
timeSearchP += MyWatch.WallTime();
// Apply the mass matrix on P
timeMassOp -= MyWatch.WallTime();
if (M)
M->Apply(P, MP);
timeMassOp += MyWatch.WallTime();
massOp += blockSize;
if (knownEV > 0) {
// Orthogonalize P against the known eigenvectors
// Note: Use R as a temporary work space
Epetra_MultiVector copyQ(View, Q, 0, knownEV);
timeOrtho -= MyWatch.WallTime();
modalTool.massOrthonormalize(P, MP, M, copyQ, blockSize, 1, R.Values());
timeOrtho += MyWatch.WallTime();
}
// Apply the stiffness matrix to P
timeStifOp -= MyWatch.WallTime();
K->Apply(P, KP);
timeStifOp += MyWatch.WallTime();
stifOp += blockSize;
} // if ((outerIter == 1) || (reStart == true))
// Form "local" mass and stiffness matrices
// Note: Use S as a temporary workspace
timeLocalProj -= MyWatch.WallTime();
modalTool.localProjection(blockSize, blockSize, xr, X.Values(), xr, KX.Values(), xr,
KK, localSize, S);
modalTool.localProjection(blockSize, blockSize, xr, X.Values(), xr, MX.Values(), xr,
MM, localSize, S);
if (localSize > blockSize) {
modalTool.localProjection(blockSize, blockSize, xr, X.Values(), xr, KP.Values(), xr,
KK + blockSize*localSize, localSize, S);
modalTool.localProjection(blockSize, blockSize, xr, P.Values(), xr, KP.Values(), xr,
KK + blockSize*localSize + blockSize, localSize, S);
modalTool.localProjection(blockSize, blockSize, xr, X.Values(), xr, MP.Values(), xr,
MM + blockSize*localSize, localSize, S);
modalTool.localProjection(blockSize, blockSize, xr, P.Values(), xr, MP.Values(), xr,
MM + blockSize*localSize + blockSize, localSize, S);
} // if (localSize > blockSize)
timeLocalProj += MyWatch.WallTime();
// Perform a spectral decomposition
timeLocalSolve -= MyWatch.WallTime();
int nevLocal = localSize;
info = modalTool.directSolver(localSize, KK, localSize, MM, localSize, nevLocal,
S, localSize, theta, localVerbose,
(blockSize == 1) ? 1: 0);
timeLocalSolve += MyWatch.WallTime();
if (info < 0) {
// Stop when spectral decomposition has a critical failure
break;
}
// Check for restarting
if ((theta[0] < 0.0) || (nevLocal < blockSize)) {
if (localVerbose > 0) {
cout << " Iteration " << outerIter;
cout << "- Failure for spectral decomposition - RESTART with new random search\n";
}
if (blockSize == 1) {
X.Random();
nFound = blockSize;
}
else {
Epetra_MultiVector Xinit(View, X, 1, blockSize-1);
Xinit.Random();
nFound = blockSize - 1;
} // if (blockSize == 1)
reStart = true;
numRestart += 1;
info = 0;
continue;
} // if ((theta[0] < 0.0) || (nevLocal < blockSize))
if ((localSize == twoBlocks) && (nevLocal == blockSize)) {
for (j = 0; j < nevLocal; ++j)
memcpy(S + j*blockSize, S + j*twoBlocks, blockSize*sizeof(double));
localSize = blockSize;
}
// Check the direction of eigenvectors
// Note: This sign check is important for convergence
for (j = 0; j < nevLocal; ++j) {
double coeff = S[j + j*localSize];
if (coeff < 0.0)
callBLAS.SCAL(localSize, -1.0, S + j*localSize);
}
// Compute the residuals
timeResidual -= MyWatch.WallTime();
callBLAS.GEMM('N', 'N', xr, blockSize, blockSize, 1.0, KX.Values(), xr,
S, localSize, 0.0, R.Values(), xr);
if (localSize == twoBlocks) {
callBLAS.GEMM('N', 'N', xr, blockSize, blockSize, 1.0, KP.Values(), xr,
S + blockSize, localSize, 1.0, R.Values(), xr);
}
for (j = 0; j < blockSize; ++j)
callBLAS.SCAL(localSize, theta[j], S + j*localSize);
callBLAS.GEMM('N', 'N', xr, blockSize, blockSize, -1.0, MX.Values(), xr,
S, localSize, 1.0, R.Values(), xr);
if (localSize == twoBlocks) {
callBLAS.GEMM('N', 'N', xr, blockSize, blockSize, -1.0, MP.Values(), xr,
S + blockSize, localSize, 1.0, R.Values(), xr);
}
for (j = 0; j < blockSize; ++j)
callBLAS.SCAL(localSize, 1.0/theta[j], S + j*localSize);
timeResidual += MyWatch.WallTime();
// Compute the norms of the residuals
timeNorm -= MyWatch.WallTime();
if (vectWeight)
R.NormWeighted(*vectWeight, normR);
else
R.Norm2(normR);
// Scale the norms of residuals with the eigenvalues
// Count the converged eigenvectors
nFound = 0;
for (j = 0; j < blockSize; ++j) {
normR[j] = (theta[j] == 0.0) ? normR[j] : normR[j]/theta[j];
if (normR[j] < tolEigenSolve)
nFound += 1;
}
timeNorm += MyWatch.WallTime();
// Store the residual history
if (localVerbose > 2) {
memcpy(resHistory + historyCount*blockSize, normR, blockSize*sizeof(double));
historyCount += 1;
}
// Print information on current iteration
if (localVerbose > 0) {
cout << " Iteration " << outerIter << " - Number of converged eigenvectors ";
cout << knownEV + nFound << endl;
}
if (localVerbose > 1) {
cout << endl;
cout.precision(2);
cout.setf(ios::scientific, ios::floatfield);
for (i=0; i<blockSize; ++i) {
cout << " Iteration " << outerIter << " - Scaled Norm of Residual " << i;
cout << " = " << normR[i] << endl;
}
cout << endl;
cout.precision(2);
for (i=0; i<blockSize; ++i) {
cout << " Iteration " << outerIter << " - Ritz eigenvalue " << i;
cout.setf((fabs(theta[i]) < 0.01) ? ios::scientific : ios::fixed, ios::floatfield);
cout << " = " << theta[i] << endl;
}
cout << endl;
}
if (nFound == 0) {
// Update the spaces
// Note: Use H as a temporary work space
timeLocalUpdate -= MyWatch.WallTime();
memcpy(H.Values(), X.Values(), xr*blockSize*sizeof(double));
callBLAS.GEMM('N', 'N', xr, blockSize, blockSize, 1.0, H.Values(), xr, S, localSize,
0.0, X.Values(), xr);
memcpy(H.Values(), KX.Values(), xr*blockSize*sizeof(double));
callBLAS.GEMM('N', 'N', xr, blockSize, blockSize, 1.0, H.Values(), xr, S, localSize,
0.0, KX.Values(), xr);
if (M) {
memcpy(H.Values(), MX.Values(), xr*blockSize*sizeof(double));
callBLAS.GEMM('N', 'N', xr, blockSize, blockSize, 1.0, H.Values(), xr, S, localSize,
0.0, MX.Values(), xr);
}
if (localSize == twoBlocks) {
callBLAS.GEMM('N', 'N', xr, blockSize, blockSize, 1.0, P.Values(), xr,
S + blockSize, localSize, 1.0, X.Values(), xr);
callBLAS.GEMM('N', 'N', xr, blockSize, blockSize, 1.0, KP.Values(), xr,
S + blockSize, localSize, 1.0, KX.Values(), xr);
if (M) {
callBLAS.GEMM('N', 'N', xr, blockSize, blockSize, 1.0, MP.Values(), xr,
S + blockSize, localSize, 1.0, MX.Values(), xr);
}
} // if (localSize == twoBlocks)
timeLocalUpdate += MyWatch.WallTime();
// When required, monitor some orthogonalities
if (verbose > 2) {
if (knownEV == 0) {
accuracyCheck(&X, &MX, &R, 0, (localSize>blockSize) ? &P : 0);
}
else {
Epetra_MultiVector copyQ(View, Q, 0, knownEV);
accuracyCheck(&X, &MX, &R, ©Q, (localSize>blockSize) ? &P : 0);
}
} // if (verbose > 2)
continue;
} // if (nFound == 0)
// Order the Ritz eigenvectors by putting the converged vectors at the beginning
int firstIndex = blockSize;
for (j = 0; j < blockSize; ++j) {
if (normR[j] >= tolEigenSolve) {
firstIndex = j;
break;
}
} // for (j = 0; j < blockSize; ++j)
while (firstIndex < nFound) {
for (j = firstIndex; j < blockSize; ++j) {
if (normR[j] < tolEigenSolve) {
// Swap the j-th and firstIndex-th position
callFortran.SWAP(localSize, S + j*localSize, 1, S + firstIndex*localSize, 1);
callFortran.SWAP(1, theta + j, 1, theta + firstIndex, 1);
callFortran.SWAP(1, normR + j, 1, normR + firstIndex, 1);
break;
}
} // for (j = firstIndex; j < blockSize; ++j)
for (j = 0; j < blockSize; ++j) {
if (normR[j] >= tolEigenSolve) {
firstIndex = j;
break;
}
} // for (j = 0; j < blockSize; ++j)
} // while (firstIndex < nFound)
// Copy the converged eigenvalues
memcpy(lambda + knownEV, theta, nFound*sizeof(double));
// Convergence test
if (knownEV + nFound >= numEigen) {
callBLAS.GEMM('N', 'N', xr, nFound, blockSize, 1.0, X.Values(), xr,
S, localSize, 0.0, R.Values(), xr);
if (localSize > blockSize) {
callBLAS.GEMM('N', 'N', xr, nFound, blockSize, 1.0, P.Values(), xr,
S + blockSize, localSize, 1.0, R.Values(), xr);
}
memcpy(Q.Values() + knownEV*xr, R.Values(), nFound*xr*sizeof(double));
knownEV += nFound;
if (localVerbose == 1) {
cout << endl;
cout.precision(2);
cout.setf(ios::scientific, ios::floatfield);
for (i=0; i<blockSize; ++i) {
cout << " Iteration " << outerIter << " - Scaled Norm of Residual " << i;
cout << " = " << normR[i] << endl;
}
cout << endl;
}
break;
}
// Store the converged eigenvalues and eigenvectors
callBLAS.GEMM('N', 'N', xr, nFound, blockSize, 1.0, X.Values(), xr,
S, localSize, 0.0, Q.Values() + knownEV*xr, xr);
if (localSize == twoBlocks) {
callBLAS.GEMM('N', 'N', xr, nFound, blockSize, 1.0, P.Values(), xr,
S + blockSize, localSize, 1.0, Q.Values() + knownEV*xr, xr);
}
knownEV += nFound;
// Define the restarting vectors
timeRestart -= MyWatch.WallTime();
int leftOver = (nevLocal < blockSize + nFound) ? nevLocal - nFound : blockSize;
double *Snew = S + nFound*localSize;
memcpy(H.Values(), X.Values(), blockSize*xr*sizeof(double));
callBLAS.GEMM('N', 'N', xr, leftOver, blockSize, 1.0, H.Values(), xr,
Snew, localSize, 0.0, X.Values(), xr);
memcpy(H.Values(), KX.Values(), blockSize*xr*sizeof(double));
callBLAS.GEMM('N', 'N', xr, leftOver, blockSize, 1.0, H.Values(), xr,
Snew, localSize, 0.0, KX.Values(), xr);
if (M) {
memcpy(H.Values(), MX.Values(), blockSize*xr*sizeof(double));
callBLAS.GEMM('N', 'N', xr, leftOver, blockSize, 1.0, H.Values(), xr,
Snew, localSize, 0.0, MX.Values(), xr);
}
if (localSize == twoBlocks) {
callBLAS.GEMM('N', 'N', xr, leftOver, blockSize, 1.0, P.Values(), xr,
Snew+blockSize, localSize, 1.0, X.Values(), xr);
callBLAS.GEMM('N', 'N', xr, leftOver, blockSize, 1.0, KP.Values(), xr,
Snew+blockSize, localSize, 1.0, KX.Values(), xr);
if (M) {
callBLAS.GEMM('N', 'N', xr, leftOver, blockSize, 1.0, MP.Values(), xr,
Snew+blockSize, localSize, 1.0, MX.Values(), xr);
}
} // if (localSize == twoBlocks)
if (nevLocal < blockSize + nFound) {
// Put new random vectors at the end of the block
Epetra_MultiVector Xtmp(View, X, leftOver, blockSize - leftOver);
Xtmp.Random();
}
else {
nFound = 0;
} // if (nevLocal < blockSize + nFound)
reStart = true;
timeRestart += MyWatch.WallTime();
} // for (outerIter = 1; outerIter <= maxIterEigenSolve; ++outerIter)
timeOuterLoop += MyWatch.WallTime();
highMem = (highMem > currentSize()) ? highMem : currentSize();
// Clean memory
delete[] work1;
delete[] work2;
if (vectWeight)
delete vectWeight;
// Sort the eigenpairs
timePostProce -= MyWatch.WallTime();
if ((info == 0) && (knownEV > 0)) {
mySort.sortScalars_Vectors(knownEV, lambda, Q.Values(), Q.MyLength());
}
timePostProce += MyWatch.WallTime();
return (info == 0) ? knownEV : info;
}