double SpinAdapted::Linear::MinResMethod(Wavefunction& xi, double normtol, Davidson_functor& h_multiply, std::vector<Wavefunction>& lowerStates)
{
setbuf(stdout, NULL);
p3out.precision (12);
int iter = 0, maxIter = 100;
double levelshift = 0.0, overlap2 = 0.0, oldError=0.0, functional=0.0, Error=0.0;
Wavefunction& targetState = lowerStates[0];
if (mpigetrank() == 0) {
makeOrthogonalToLowerStates(targetState, lowerStates);
makeOrthogonalToLowerStates(xi, lowerStates);
}
#ifndef SERIAL
mpi::communicator world;
mpi::broadcast(world, xi, 0);
#endif
Wavefunction pi, ri;
ri=xi; ri.Clear();
h_multiply(xi, ri);
//Check if we should even perform CG or just exit with a zero vector.
bool doCG = true;
if (mpigetrank() == 0) {
Wavefunction ricopy = ri; ricopy.Clear(); ricopy.Randomise();
Wavefunction ricopy2 = ricopy;
makeOrthogonalToLowerStates(ricopy2, lowerStates);
if (abs(DotProduct(ricopy2, targetState)) < NUMERICAL_ZERO) {
pout << "The problem is ill posed or the initial guess is very bad "<<DotProduct(ricopy, targetState)<<endl;
doCG = false;
}
}
#ifndef SERIAL
mpi::broadcast(world, doCG, 0);
#endif
if (!doCG) {
xi.Clear();
int success = 0;
functional = 0.0;
return functional;
}
if (mpigetrank() == 0) {
ScaleAdd(-1.0, targetState, ri);
Scale(-1.0, ri);
makeOrthogonalToLowerStates(ri, lowerStates);
pi = ri;
oldError = DotProduct(ri, ri);
printf("\t\t\t %15s %15s %15s\n", "iter", "Functional", "Error");
}
#ifndef SERIAL
mpi::broadcast(world, oldError, 0);
#endif
if (oldError < normtol) {
if (mpigetrank() == 0) {
functional = -DotProduct(xi, ri) - DotProduct(xi, targetState);
printf("\t\t\t %15i %15.8e %15.8e\n", 0, functional, oldError);
}
#ifndef SERIAL
mpi::broadcast(world, functional, 0);
#endif
return functional;
}
#ifndef SERIAL
mpi::broadcast(world, ri, 0);
#endif
double betaNumerator = 0, betaDenominator = 0;
Wavefunction Hr = ri; Hr.Clear();
h_multiply(ri, Hr);
betaDenominator = DotProduct(ri, Hr);
Wavefunction Hp = Hr;
if (mpigetrank() == 0) {
makeOrthogonalToLowerStates(Hp, lowerStates);
makeOrthogonalToLowerStates(Hr, lowerStates);
}
while(true) {
if (mpigetrank() == 0) {
double alpha = DotProduct(ri, Hr)/DotProduct(Hp, Hp);
ScaleAdd(alpha, pi, xi);
ScaleAdd(-alpha, Hp, ri);
Error = DotProduct(ri, ri);
functional = -DotProduct(xi, targetState);
printf("\t\t\t %15i %15.8e %15.8e \n", iter, functional, Error);
}
#ifndef SERIAL
mpi::broadcast(world, Error, 0);
mpi::broadcast(world, functional, 0);
mpi::broadcast(world, ri, 0);
#endif
if (Error < normtol || iter >maxIter) {
return functional;
}
else {
Hr.Clear();
h_multiply(ri, Hr);
if (mpigetrank() == 0) {
makeOrthogonalToLowerStates(Hr, lowerStates);
betaNumerator = DotProduct(ri, Hr);
double beta = betaNumerator/betaDenominator;
betaDenominator = betaNumerator;
ScaleAdd(1./beta, ri, pi);
Scale(beta, pi);
ScaleAdd(1./beta, Hr, Hp);
Scale(beta, Hp);
}
iter ++;
}
}
}
//solves the equation (H-E)^T(H-E)|psi_1> = -(H-E)^TQV|\Psi_0> where lowerState[1] contains |\Psi_0> to enforce orthogonality (Q), and lowerState[0] contains V|\Psi_0> so we can calculate its projection in the krylov space
//the algorithm is taken from wikipedia page
//the algorithm is taken from wikipedia page
double SpinAdapted::Linear::ConjugateGradient(Wavefunction& xi, double normtol, Davidson_functor& h_multiply, std::vector<Wavefunction>& lowerStates)
{
setbuf(stdout, NULL);
p3out.precision (12);
int iter = 0, maxIter = 100;
double levelshift = 0.0, overlap2 = 0.0, oldError=0.0, functional=0.0, Error=0.0;
Wavefunction& targetState = lowerStates[0];
if (mpigetrank() == 0) {
for (int i=1; i<lowerStates.size(); i++) {
overlap2 = pow(DotProduct(lowerStates[i], lowerStates[i]), 0.5);
if (fabs(overlap2) > NUMERICAL_ZERO) {
ScaleAdd(-DotProduct(targetState, lowerStates[i])/overlap2,
lowerStates[i], targetState);
ScaleAdd(-DotProduct(xi, lowerStates[i])/overlap2,
lowerStates[i], xi);
}
}
}
#ifndef SERIAL
mpi::communicator world;
mpi::broadcast(world, xi, 0);
#endif
Wavefunction pi, ri;
ri=xi; ri.Clear();
h_multiply(xi, ri);
//Check if we should even perform CG or just exit with a zero vector.
bool doCG = true;
if (mpigetrank() == 0) {
Wavefunction ricopy = ri; ricopy.Clear(); ricopy.Randomise();
Wavefunction ricopy2 = ricopy;
for (int i=1; i<lowerStates.size(); i++) {
overlap2 = pow(DotProduct(lowerStates[i], lowerStates[i]), 0.5);
if (fabs(overlap2) > NUMERICAL_ZERO) {
ScaleAdd(-DotProduct(ricopy, lowerStates[i])/overlap2,
lowerStates[i], ricopy2);
}
}
if (abs(DotProduct(ricopy2, targetState)) < NUMERICAL_ZERO) {
pout << "The problem is ill posed or the initial guess is very bad "<<DotProduct(ricopy, targetState)<<endl;
doCG = false;
}
}
#ifndef SERIAL
mpi::broadcast(world, doCG, 0);
#endif
if (!doCG) {
xi.Clear();
int success = 0;
functional = 0.0;
return functional;
}
if (mpigetrank() == 0) {
ScaleAdd(-1.0, targetState, ri);
Scale(-1.0, ri);
for (int i=1; i<lowerStates.size(); i++) {
overlap2 = pow(DotProduct(lowerStates[i], lowerStates[i]),0.5);
if (fabs(overlap2) > NUMERICAL_ZERO) {
ScaleAdd(-DotProduct(ri, lowerStates[i])/overlap2,
lowerStates[i], ri);
}
}
pi = ri;
oldError = DotProduct(ri, ri);
printf("\t\t\t %15s %15s %15s\n", "iter", "Functional", "Error");
}
#ifndef SERIAL
mpi::broadcast(world, Error, 0);
mpi::broadcast(world, oldError, 0);
mpi::broadcast(world, functional, 0);
#endif
if (oldError < normtol) {
if (mpigetrank() == 0) {
functional = -DotProduct(xi, ri) - DotProduct(xi, targetState);
printf("\t\t\t %15i %15.8e %15.8e\n", 0, functional, oldError);
}
#ifndef SERIAL
mpi::broadcast(world, functional, 0);
#endif
return functional;
}
while(true) {
#ifndef SERIAL
mpi::communicator world;
mpi::broadcast(world, pi, 0);
#endif
Wavefunction Hp = pi; Hp.Clear();
h_multiply(pi, Hp);
if (mpigetrank() == 0) {
for (int i=1; i<lowerStates.size(); i++) {
overlap2 = pow(DotProduct(lowerStates[i], lowerStates[i]),0.5);
if (fabs(overlap2) > NUMERICAL_ZERO) {
ScaleAdd(-DotProduct(Hp, lowerStates[i])/overlap2,
lowerStates[i], Hp);
}
}
double alpha = oldError/DotProduct(pi, Hp);
ScaleAdd(alpha, pi, xi);
ScaleAdd(-alpha, Hp, ri);
Error = DotProduct(ri, ri);
functional = -DotProduct(xi, ri) - DotProduct(xi, targetState);
printf("\t\t\t %15i %15.8e %15.8e\n", iter, functional, Error);
}
#ifndef SERIAL
mpi::broadcast(world, Error, 0);
mpi::broadcast(world, functional, 0);
#endif
if (Error < normtol || iter >maxIter) {
return functional;
}
else {
if (mpigetrank() == 0) {
double beta = Error/oldError;
oldError = Error;
ScaleAdd(1.0/beta, ri, pi);
Scale(beta, pi);
for (int i=1; i<lowerStates.size(); i++) {
overlap2 = pow(DotProduct(lowerStates[i], lowerStates[i]),0.5);
if (fabs(overlap2) > NUMERICAL_ZERO) {
ScaleAdd(-DotProduct(pi, lowerStates[i])/overlap2,
lowerStates[i], pi);
}
}
}
iter ++;
}
}
}
