sp_mathematics.h

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/******************************************************************************
SP_Mathematics.h

Include all mathematics constants and functions

Sukitti Punak   (11/02/2003)
Latest Update   (07/14/2007)
******************************************************************************/
#ifndef SP_MATHEMATICS_H
#define SP_MATHEMATICS_H

#include <iostream>
#include <cmath>
using std::cout;
using std::cerr;
using std::endl;
//using namespace std;

#include <complex>

#include "SP_MatrixOperations.h"
#include "SPT_Matrix3x3.h"

namespace SP_Maths {

    // CONSTANT VALUES  *******************************************************
    const double PI = 3.141592654;
    //-------------------------------------------------------------------------
    // FN:  CrossProduct()
    // DESC:    Find C = A^B
    void CrossProduct( const double A[3], const double B[3], double C[3] );
    //-------------------------------------------------------------------------
    // FN:  DotProduct()
    // DESC:    Return double = A*B
    double DotProduct( const double A[3], const double B[3] );
    //-------------------------------------------------------------------------
    // FN:  FindAnEigenVector()
    // DESC:    Find an eigen vector of a 3x3 symmetric matrix
    void FindAnEigenVector( 
        double &m11,    double &m12,    double &m13,
                        double &m22,    double &m23,
                                        double &m33,    // I/P: 3x3 Symmetric Matrix
        double l1,      // O/P: eigen value
        double v1[3]    // O/P: eigen vector
    );
    //-------------------------------------------------------------------------
    // FN:  FindOrthogonalVectors()
    // DESC:    Find other two vectors (oB and oC) that are orthogonal to iA
    void FindOrthogonalVectors( const double iA[3], double oB[3], double oC[3] );
    //-------------------------------------------------------------------------
    void rootsOfCubicPolynomialCodeGeneratedByMaple(    
        double a, double b, double c, double d , 
        std::complex<double> &r1, 
        std::complex<double> &r2, 
        std::complex<double> &r3 
    );
    //-------------------------------------------------------------------------
    // FN:  rootsOfCubicPolynomial()  *****************************************
    // DESC:    Find all three roots of a cubic polynomial in this form;
    //          a*x^3 + b*x^2 + c*x + d = 0;
    //          The formula is adapted from "Mathematical Handbook of Formulas and Tables"
    // I/P:  a, b, c, and d
    // O/P:  r1, r2, and r3     ( r1 is the real root)
    //       r2 and r3 are only the real parts of the other two roots
    double rootsOfCubicPolynomial(  
        double a, double b, double c, double d , 
        //double &r1, double &r2, double &r3 )
        std::complex<double> &r1, 
        std::complex<double> &r2, 
        std::complex<double> &r3 
    );
    //-------------------------------------------------------------------------
    // Overloaded Function
    double rootsOfCubicPolynomial(  double a, double b, double c, double d , 
                                    double &r1, double &r2, double &r3 );
    //-------------------------------------------------------------------------
    // MARK: FIX IT!!!!!!!!!!!!!!!!
    // FN:  rootOfCubicPolynomial()  ******************************************
    // DESC:    Find all three roots of a cubic polynomial in this form;
    //          a*x^3 + b*x^2 + c*x + d = 0;
    // The formula is adapted from "Mathematical Handbook of Formulas and Tables"
    // I/P:  a, b, c, d, and rootNo
    // O/P:  a double value of the rootNo (1, 2, or 3)
    //       r1 is the real root
    //       r2 and r3 are only the real parts of the other two roots
    double rootOfCubicPolynomial( double a, double b, double c, double d , int rootNo );
    //-------------------------------------------------------------------------
    // FN:  eigenValsOf3by3SymMatrix()      ***********************************
    // DESC:    Find eigen values of a 3x3 symmetric matrix
    // I/P:  (double) m11, m12, m13, m22, m23, m33
    // O/P:  (double) lamda1, lamda2, lamda3
    double eigenValsOf3by3SymMatrix(    
        double m11, double m12, double m13, 
                    double m22, double m23, 
                                double m33, 
        double &lamda1, double &lamda2, double &lamda3 
    );
    //-------------------------------------------------------------------------
    // FN:  eigenValsOf3by3SymMatrixSmith1961()     ***************************
    // DESC:    Find eigen values of a 3x3 symmetric matrix
    // I/P:  (double) m11, m12, m13, m22, m23, m33
    // O/P:  (double) lamda1, lamda2, lamda3
    double eigenValsOf3by3SymMatrixSmith1961(   
        double m11, double m12, double m13, 
                    double m22, double m23, 
                                double m33, 
        double &lamda1,     double &lamda2,     double &lamda3 
    );
    //-------------------------------------------------------------------------
    // FN:  eigenValsAndVecsOf3by3SymMatrix()  ********************************
    // DESC:    Find eigen vectors of a 3x3 symmetric matrix which has all real eigen values
    // I/P:  (double) m11, m12, m13, m22, m23, m33
    // O/P:  (double) lamda1, lamda2, lamda3
    void eigenValsAndVecsOf3by3SymMatrix(   
        double m11, double m12, double m13, 
                    double m22, double m23, 
                                double m33, 
        double &l1, double &l2, double &l3,
        double v1[3], double v2[3], double v3[3] 
    );
    //-------------------------------------------------------------------------
    // FN:  eigenValsAndVecsOf3by3SymMatrixUsingQRFactor()  *******************
    // DESC:    Find eigen vectors of a 3x3 symmetric matrix which has all real eigen values
    // I/P:  (double) m11, m12, m13, m22, m23, m33
    // O/P:  (double) lamda1, lamda2, lamda3
    void eigenValsAndVecsOf3by3SymMatrixUsingQRFactor(  
        double m11, double m12, double m13, 
                    double m22, double m23, 
                                double m33, 
        double &l1, double &l2, double &l3,
        double v1[3], double v2[3], double v3[3] 
    );
    //-------------------------------------------------------------------------
    // FN:  RootFindingByNewtonRaphsonMethod()  *******************************
    // ADAPTED FROM:    "Numerical Recipes in C: The Art of Scientific Computing" (1988)
    //                  by W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling
    // DESC:  Using the Newton-Raphson method to find the root of a function known to lie in the 
    //        interval (x1,x2).  The root rtnewt will be refined until its accuracy is known within 
    //        +/-xacc.  funcd is a user-supplied routine that provides both the funciton value and 
    //        the first derivative of the function at the point x.
    double RootFindingByNewtonRaphsonMethod( 
        void (*funcd)( double x, double *fx, double *dfx ), // A user-supplied routine that provides both the function value and the first derivative of the function at the point x.
        double x1, double x2,                               // The root of a function must lies in the interval (x1,x2).
        double xacc                                         // The root will be refined until its accuracy is known within +/-xacc.
    );
    //--------------------------------------------------------------------------------------------
} // END: namespace SP_Maths
//-----------------------------------------------------------------------------
// Include definition if TAPs_USE_EXPORT is not defined
#if !defined( TAPs_USE_EXPORT )
    #include "SP_Mathematics.cpp"
#endif
//-----------------------------------------------------------------------------
#endif // #ifndef SP_MATHEMATICS_H