NatafProbabilityTransformation.h

//----------------------------------------------------------------------------
//  XC program; finite element analysis code
//  for structural analysis and design.
//
//  Copyright (C)  Luis Claudio Pérez Tato
//
//  This program derives from OpenSees <http://opensees.berkeley.edu>
//  developed by the  «Pacific earthquake engineering research center».
//
//  Except for the restrictions that may arise from the copyright
//  of the original program (see copyright_opensees.txt)
//  XC is free software: you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation, either version 3 of the License, or 
//  (at your option) any later version.
//
//  This software is distributed in the hope that it will be useful, but 
//  WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details. 
//
//
// You should have received a copy of the GNU General Public License 
// along with this program.
// If not, see <http://www.gnu.org/licenses/>.
//----------------------------------------------------------------------------
/* ****************************************************************** **
**    OpenSees - Open System for Earthquake Engineering Simulation    **
**          Pacific Earthquake Engineering Research Center            **
**                                                                    **
**                                                                    **
** (C) Copyright 2001, The Regents of the University of California    **
** All Rights Reserved.                                               **
**                                                                    **
** Commercial use of this program without express permission of the   **
** University of California, Berkeley, is strictly prohibited.  See   **
** file 'COPYRIGHT'  in main directory for information on usage and   **
** redistribution,  and for a DISCLAIMER OF ALL WARRANTIES.           **
**                                                                    **
** Developed by:                                                      **
**   Frank McKenna (fmckenna@ce.berkeley.edu)                         **
**   Gregory L. Fenves (fenves@ce.berkeley.edu)                       **
**   Filip C. Filippou (filippou@ce.berkeley.edu)                     **
**                                                                    **
** Reliability module developed by:                                   **
**   Terje Haukaas (haukaas@ce.berkeley.edu)                          **
**   Armen Der Kiureghian (adk@ce.berkeley.edu)                       **
**                                                                    **
** ****************************************************************** */
                                                                        
// $Revision: 1.2 $
// $Date: 2003/10/27 23:45:45 $
// $Source: /usr/local/cvs/OpenSees/SRC/reliability/analysis/transformation/NatafProbabilityTransformation.h,v $


//
// Written by Terje Haukaas (haukaas@ce.berkeley.edu)
//

#ifndef NatafProbabilityTransformation_h
#define NatafProbabilityTransformation_h

#include <utility/matrix/Vector.h>
#include <utility/matrix/Matrix.h>
#include <reliability/domain/components/ReliabilityDomain.h>
#include <reliability/analysis/misc/MatrixOperations.h>

namespace XC {
class NatafProbabilityTransformation : public ProbabilityTransformation
{

public:
    NatafProbabilityTransformation(ReliabilityDomain *passedReliabilityDomain,
                          int printFlag);
    ~NatafProbabilityTransformation();

    int set_x(Vector x);
    int set_u(Vector u);

    int transform_x_to_u();
    int transform_u_to_x();
    int transform_u_to_x_andComputeJacobian();

    Vector get_x();
    Vector get_u();
    Matrix getJacobian_x_u();
    Matrix getJacobian_u_x();

    Vector meanSensitivityOf_x_to_u(Vector &x, int gradNumber);
    Vector stdvSensitivityOf_x_to_u(Vector &x, int gradNumber);

protected:

private:

    // Private data members
    Vector *x;
    Vector *u;
    Matrix *jacobian_x_u;
    Matrix *jacobian_u_x;
    ReliabilityDomain *theReliabilityDomain;
    MatrixOperations *theMatrixOperations;
    int nrv;
    Matrix *correlationMatrix;
    Matrix *lowerCholesky;
    Matrix *inverseLowerCholesky;
    int printFlag;

    // Private member functions
    void setCorrelationMatrix(int pertMeanOfThisRV, int pertStdvOfThisRV, double h);
    Matrix getJacobian_z_x(Vector x, Vector z);
    Vector z_to_x(Vector z);
    Vector x_to_z(Vector x);

    // Auxiliary member functions for manual evaluation of 
    // the integral equation to find Nataf correlation
    double phi2(double z_i, 
                double z_j, 
                double rho);
    double integrand(int rv_i,
                     double z_i, 
                     double mean_i,
                     double stdv_i, 
                     int rv_j,
                     double z_j,
                     double mean_j, 
                     double stdv_j,
                     double rho);
    double doubleIntegral(int rv_i,
                          double mean_i,
                          double stdv_i, 
                          int rv_j,
                          double mean_j, 
                          double stdv_j,
                          double rho);
    double residualFunction(double rho_original, 
                            double rho,
                            double rv_i, 
                            double mean_i, 
                            double stdv_i, 
                            double rv_j, 
                            double mean_j, 
                            double stdv_j);
    double solveForCorrelation(int rv_i, int rv_j, double rho_original);
};
} // end of XC namespace

#endif