int
KrylovAccelerator2::accelerate(Vector &vStar, LinearSOE &theSOE,
IncrementalIntegrator &theIntegrator)
{
const Vector &R = theSOE.getB();
int k = dimension;
// Store residual for differencing at next iteration
*(Av[k]) = R;
// If subspace is not empty
if (dimension > 0) {
// Compute Av_k = f(y_{k-1}) - f(y_k) = r_{k-1} - r_k
Av[k-1]->addVector(1.0, R, -1.0);
int i,j;
// Put subspace vectors into AvData
Matrix A(AvData, numEqns, k);
for (i = 0; i < k; i++) {
Vector &Ai = *(Av[i]);
for (j = 0; j < numEqns; j++)
A(j,i) = Ai(j);
}
for (i = 0; i < k; i++) {
for (int j = i+1; j < k; j++) {
double sum = 0.0;
double sumi = 0.0;
double sumj = 0.0;
for (int ii = 0; ii < numEqns; ii++) {
sum += A(ii,i)*A(ii,j);
sumi += A(ii,i)*A(ii,i);
sumj += A(ii,j)*A(ii,j);
}
sumi = sqrt(sumi);
sumj = sqrt(sumj);
sum = sum/(sumi*sumj);
//if (fabs(sum) > 0.99)
//opserr << sum << ' ' << i << ' ' << j << " ";
}
}
// Put residual vector into rData (need to save r for later!)
Vector B(rData, numEqns);
B = R;
// No transpose
char *trans = "N";
// The number of right hand side vectors
int nrhs = 1;
// Leading dimension of the right hand side vector
int ldb = (numEqns > k) ? numEqns : k;
// Subroutine error flag
int info = 0;
// Call the LAPACK least squares subroutine
#ifdef _WIN32
unsigned int sizeC = 1;
DGELS(trans, &sizeC, &numEqns, &k, &nrhs, AvData, &numEqns,
rData, &ldb, work, &lwork, &info);
#else
//SUBROUTINE DGELS( TRANS, M, N, NRHS, A, LDA, B, LDB, WORK, LWORK,
// $ INFO )
dgels_(trans, &numEqns, &k, &nrhs, AvData, &numEqns,
rData, &ldb, work, &lwork, &info);
#endif
// Check for error returned by subroutine
if (info < 0) {
opserr << "WARNING KrylovAccelerator2::accelerate() - \n";
opserr << "error code " << info << " returned by LAPACK dgels\n";
return info;
}
Vector Q(numEqns);
Q = R;
// Compute the correction vector
double cj;
for (j = 0; j < k; j++) {
// Solution to least squares is written to rData
cj = rData[j];
// Compute w_{k+1} = c_1 v_1 + ... + c_k v_k
vStar.addVector(1.0, *(v[j]), cj);
// Compute least squares residual
// q_{k+1} = r_k - (c_1 Av_1 + ... + c_k Av_k)
Q.addVector(1.0, *(Av[j]), -cj);
}
theSOE.setB(Q);
//opserr << "Q: " << Q << endln;
}
theSOE.solve();
vStar.addVector(1.0, theSOE.getX(), 1.0);
// Put accelerated vector into storage for next iteration
*(v[k]) = vStar;
dimension++;
return 0;
}
/* return 0 if ok
* otherwise return !=0
*/
int solveLeastSquareProblem(LinearSystemProblem* problem, double *z , SolverOptions* options)
{
/* Checks inputs */
if (problem == NULL || z == NULL)
numericsError("EqualityProblem", "null input for EqualityProblem and/or unknowns (z)");
/* Output info. : 0: ok - >0: problem (depends on solver) */
int info = -1;
int n = problem->size;
int n2 = n * n;
double * Maux = 0;
int * ipiv = 0;
if (options && options->dWork)
Maux = options->dWork;
else
Maux = (double *) malloc(LinearSystem_getNbDwork(problem, options) * sizeof(double));
if (options && options->iWork)
ipiv = options->iWork;
else
ipiv = (int *) malloc(LinearSystem_getNbIwork(problem, options) * sizeof(int));
int LAinfo = 0;
//displayLS(problem);
assert(problem->M->matrix0);
assert(problem->q);
memcpy(Maux, problem->M->matrix0, n2 * sizeof(double));
// memcpy(z,problem->q,n*sizeof(double));
for (int ii = 0; ii < n; ii++)
z[ii] = -problem->q[ii];
printf("LinearSystem : solveLeastSquareProblem LWORK is :%d\n", LWORK);
DGELS(LA_NOTRANS,n, n, 1, Maux, n, z, n, &LAinfo);
if (LAinfo)
{
printf("LinearSystem_driver: DGELS failed:\n");
goto __fin;
}
int ii;
for (ii = 0; ii < n; ii++)
{
if (isnan(z[ii]) || isinf(z[ii]))
{
printf("DGELS FAILED\n");
goto __fin;
}
}
info = 0;
printf("LinearSystem_driver: computeError of LinearSystem : %e\n", LinearSystem_computeError(problem, z));
__fin:
if (!(options && options->dWork))
free(Maux);
if (!(options && options->iWork))
free(ipiv);
return info;
}