void calculateJacobian(const arma::Mat<std::complex<double> >& myOffsets,
arma::Mat<double>& myJacobian,
arma::Col<std::complex<double> >& myTargetsCalculated,
arma::Col<std::complex<double> >& myCurrentGuess,
void myCalculateDependentVariables(const arma::Mat<std::complex<double> >&, const arma::Col<std::complex<double> >&, arma::Col<std::complex<double> >&))
{
//Calculate a temporary, unperturbed target evaluation, such as is needed for solving for the updated guess
//formula
arma::Col<std::complex<double> > unperturbedTargetsCalculated(NUMDIMENSIONS);
unperturbedTargetsCalculated.fill(0.0);
myCalculateDependentVariables(myOffsets, myCurrentGuess, unperturbedTargetsCalculated);
std::complex<double> oldGuessValue(0.0, 0.0);
//Each iteration fills a column in the Jacobian
//The Jacobian takes this form:
//
// dF0/dx0 dF0/dx1
// dF1/dx0 dF1/dx1
//
for(int j = 0; j< NUMDIMENSIONS; j++)
{
//Store old element value, perturb the current value
oldGuessValue = myCurrentGuess[j];
myCurrentGuess[j] += std::complex<double>(0.0, PROBEDISTANCE);
//Evaluate functions for perturbed guess
myCalculateDependentVariables(myOffsets, myCurrentGuess, myTargetsCalculated);
//The column of the Jacobian that goes with the independent variable we perturbed
//can be determined using the finite-difference formula
//The arma::Col allows this to be expressed as a single vector operation
//note slice works as: std::slice(start_index, number_of_elements_to_access, index_interval_between_selections)
//std::cout << "Jacobian column " << j << " with:" << std::endl;
//std::cout << "myTargetsCalculated" << std::endl;
//std::cout << myTargetsCalculated << std::endl;
//std::cout << "unperturbedTargetsCalculated" << std::endl;
//std::cout << unperturbedTargetsCalculated << std::endl;
myJacobian.col(j) = arma::imag(myTargetsCalculated);
myJacobian.col(j) *= pow(PROBEDISTANCE, -1.0);
//std::cout << "The jacobian: " << std::endl;
//std::cout << myJacobian << std::endl;
myCurrentGuess[j] = oldGuessValue;
}
//Reset to unperturbed, so we dont waste a function evaluation
myTargetsCalculated = unperturbedTargetsCalculated;
}
int main(int argc, char* argv[])
{
//--This first declaration is included for software engineering reasons: allow main method to control flow of data
//create function pointer for calculateDependentVariable
//We want to do this so that calculateJacobian can call calculateDependentVariables as it needs to,
//but we explicitly give it this authority from the main method
void (*yourCalculateDependentVariables)(const Teuchos::SerialDenseMatrix<int, std::complex<double> >&, const Teuchos::SerialDenseVector<int, std::complex<double> >&, Teuchos::SerialDenseVector<int, std::complex<double> >&);
yourCalculateDependentVariables = &calculateDependentVariables;
//Create an object to allow access to LAPACK using a library found in Trilinos
//
Teuchos::LAPACK<int, std::complex<double> > Teuchos_LAPACK_Object;
//The problem being solved is to find the intersection of three infinite paraboloids:
//(x-1)^2 + y^2 + z = 0
//x^2 + y^2 -(z+1) = 0
//x^2 + y^2 +(z-1) = 0
//
//They should intersect at the point (1, 0, 0)
Teuchos::SerialDenseMatrix<int, std::complex<double> > offsets(NUMDIMENSIONS, NUMDIMENSIONS);
offsets(0,0) = 1.0;
offsets(1,2) = 1.0;
offsets(2,2) = 1.0;
//We need to initialize the target vectors and provide an initial guess
Teuchos::SerialDenseVector<int, std::complex<double> > targetsDesired(NUMDIMENSIONS);
Teuchos::SerialDenseVector<int, std::complex<double> > targetsCalculated(NUMDIMENSIONS);
Teuchos::SerialDenseVector<int, std::complex<double> > unperturbedTargetsCalculated(NUMDIMENSIONS);
Teuchos::SerialDenseVector<int, std::complex<double> > currentGuess(NUMDIMENSIONS);
Teuchos::SerialDenseVector<int, std::complex<double> > guessAdjustment(NUMDIMENSIONS);
currentGuess[0] = 2.0;
currentGuess[1] = 1.0;
currentGuess[2] = 1.0;
//Place to store our tangent-stiffness matrix or Jacobian
//One element for every combination of dependent variable with independent variable
Teuchos::SerialDenseMatrix<int, std::complex<double> > jacobian(NUMDIMENSIONS, NUMDIMENSIONS);
int count = 0;
double error = 1.0E5;
std::cout << "Running Forward Difference Example" << std::endl;
while(count < MAXITERATIONS and error > ERRORTOLLERANCE)
{
//Calculate Jacobian tangent to currentGuess point
//at the same time, an unperturbed targetsCalculated is, well, calculated
calculateJacobian(offsets,
jacobian,
targetsCalculated,
unperturbedTargetsCalculated,
currentGuess,
yourCalculateDependentVariables);
//Compute a guessChange and immediately set the currentGuess equal to the guessChange
updateGuess(currentGuess,
targetsCalculated,
jacobian,
Teuchos_LAPACK_Object);
//Compute F(x) with the updated, currentGuess
calculateDependentVariables(offsets,
currentGuess,
targetsCalculated);
//Calculate the L2 norm of Ftarget - F(xCurrentGuess)
calculateResidual(targetsDesired,
targetsCalculated,
error);
count ++;
//If we have converged, or if we have exceeded our alloted number of iterations, discontinue the loop
std::cout << "Residual Error: " << error << std::endl;
}
std::cout << "******************************************" << std::endl;
std::cout << "Number of iterations: " << count << std::endl;
std::cout << "Final guess:\n x, y, z\n " << currentGuess[0] << ", " << currentGuess[1] << ", " << currentGuess[2] << std::endl;
std::cout << "Error tollerance: " << ERRORTOLLERANCE << std::endl;
std::cout << "Final error: " << error << std::endl;
std::cout << "--program complete--" << std::endl;
return 0;
}