UblasCustomFunctions.hpp

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#ifndef UBLASCUSTOMFUNCTIONS_HPP_
#define UBLASCUSTOMFUNCTIONS_HPP_

#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/vector.hpp>

#include <boost/numeric/ublas/matrix_proxy.hpp>
#include <boost/numeric/ublas/io.hpp>
#include <boost/numeric/ublas/matrix_expression.hpp>

#include "petsc.h"
#include "petscblaslapack.h"
//Promote universal LAPACK name if it's an old version of PETSc
#if (PETSC_VERSION_MAJOR == 2 && PETSC_VERSION_MINOR == 2) //PETSc 2.2
#define LAPACKgeev_ LAgeev_
#endif

#include "Exception.hpp"
#include "MathsCustomFunctions.hpp"

using namespace boost::numeric::ublas;

// COMMON DETERMINANTS - SQUARE

template<class T>
T Determinant(const boost::numeric::ublas::c_matrix<T, 1, 1>& rM)
{
    using namespace boost::numeric::ublas;

    return rM(0,0);
}

template<class T>
T Determinant(const boost::numeric::ublas::c_matrix<T,2,2>& rM)
{
    using namespace boost::numeric::ublas;

    return rM(0,0)*rM(1,1) - rM(1,0)*rM(0,1);
}

template<class T>
T Determinant(const boost::numeric::ublas::c_matrix<T, 3, 3>& rM)
{
    using namespace boost::numeric::ublas;

    return    rM(0,0) * (rM(1,1)*rM(2,2) - rM(1,2)*rM(2,1))
            - rM(0,1) * (rM(1,0)*rM(2,2) - rM(1,2)*rM(2,0))
            + rM(0,2) * (rM(1,0)*rM(2,1) - rM(1,1)*rM(2,0));
}

// COMMON GENERALIZED DETERMINANTS - NOT SQUARE

template<class T>
T Determinant(const boost::numeric::ublas::c_matrix<T, 3, 2>& rM)
{
    using namespace boost::numeric::ublas;
    c_matrix<T,2,2> product = prod(trans(rM), rM);
    return std::sqrt(Determinant(product));
}

template<class T>
T Determinant(const boost::numeric::ublas::c_matrix<T, 3, 1>& rM)
{
    using namespace boost::numeric::ublas;
    return std::sqrt(rM(0,0)*rM(0,0) + rM(1,0)*rM(1,0) + rM(2,0)*rM(2,0));
}

template<class T>
T Determinant(const boost::numeric::ublas::c_matrix<T, 2, 1>& rM)
{
    using namespace boost::numeric::ublas;
    return   std::sqrt(rM(0,0) * rM(0,0) + rM(1,0) * rM(1,0));
}

template<class T>
T Determinant(const boost::numeric::ublas::c_matrix<T, 3, 0>& rM)
{
    NEVER_REACHED;
}

template<class T>
T Determinant(const boost::numeric::ublas::c_matrix<T, 2, 0>& rM)
{
    NEVER_REACHED;
}

template<class T>
T Determinant(const boost::numeric::ublas::c_matrix<T, 1, 0>& rM)
{
    NEVER_REACHED;
}

// COMMON SUBDETERMINANTS - SQUARE

template<class T>
T SubDeterminant(const boost::numeric::ublas::c_matrix<T, 1, 1>& rM, const unsigned missrow, const unsigned misscol)
{
    using namespace boost::numeric::ublas;

    assert(missrow == 0);
    assert(misscol == 0);
    return 1.0;
}

template<class T>
T SubDeterminant(const boost::numeric::ublas::c_matrix<T, 2, 2>& rM, const unsigned missrow, const unsigned misscol)
{
    using namespace boost::numeric::ublas;

    assert(missrow < 2);
    assert(misscol < 2);

    unsigned row = (missrow==1) ? 0 : 1;
    unsigned col = (misscol==1) ? 0 : 1;
    return rM(row,col);
}

template<class T>
T SubDeterminant(const boost::numeric::ublas::c_matrix<T, 3, 3>& rM, const unsigned missrow, const unsigned misscol)
{
    using namespace boost::numeric::ublas;

    assert(missrow < 3);
    assert(misscol < 3);

    unsigned lorow = (missrow==0) ? 1 : 0;
    unsigned hirow = (missrow==2) ? 1 : 2;
    unsigned locol = (misscol==0) ? 1 : 0;
    unsigned hicol = (misscol==2) ? 1 : 2;
    return rM(lorow,locol)*rM(hirow,hicol) - rM(lorow,hicol)*rM(hirow,locol);
}

// COMMON SUBDETERMINANTS - NOT SQUARE

template<class T>
T SubDeterminant(const boost::numeric::ublas::c_matrix<T, 3, 2>& rM, const unsigned missrow, const unsigned misscol)
{
    using namespace boost::numeric::ublas;

    assert(missrow < 3);
    //assert(misscol < 2); //Don't assert this since it is used

    unsigned lorow = (missrow==0) ? 1 : 0;
    unsigned hirow = (missrow==2) ? 1 : 2;
    unsigned locol = (misscol==0) ? 1 : 0;
    unsigned hicol = (misscol==2) ? 1 : 2;
    return rM(lorow,locol)*rM(hirow,hicol) - rM(lorow,hicol)*rM(hirow,locol);
}

template<class T>
T SubDeterminant(const boost::numeric::ublas::c_matrix<T, 3, 1>& rM, const unsigned missrow, const unsigned misscol)
{
    using namespace boost::numeric::ublas;

    assert(missrow < 3);
    assert(misscol < 1);

    unsigned lorow = (missrow==0) ? 1 : 0;
    unsigned hirow = (missrow==2) ? 1 : 2;
    unsigned locol = (misscol==0) ? 1 : 0;
    unsigned hicol = (misscol==2) ? 1 : 2;
    return rM(lorow,locol)*rM(hirow,hicol) - rM(lorow,hicol)*rM(hirow,locol);
}

template<class T>
T SubDeterminant(const boost::numeric::ublas::c_matrix<T, 2, 1>& rM, const unsigned missrow, const unsigned misscol)
{
    using namespace boost::numeric::ublas;

    assert(missrow < 2);
    assert(misscol < 1);

    unsigned row = (missrow==1) ? 0 : 1;
    unsigned col = (misscol==1) ? 0 : 1;
    return rM(row,col);
}

#if defined(__xlC__)
/* IBM compiler doesn't support zero-sized arrays*/
#else //#if defined(__xlC__)

template<class T>
T SubDeterminant(const boost::numeric::ublas::c_matrix<T, 3, 0>& rM, const unsigned missrow, const unsigned misscol)
{
    NEVER_REACHED;
}

template<class T>
T SubDeterminant(const boost::numeric::ublas::c_matrix<T, 2, 0>& rM, const unsigned missrow, const unsigned misscol)
{
    NEVER_REACHED;
}

template<class T>
T SubDeterminant(const boost::numeric::ublas::c_matrix<T, 1, 0>& rM, const unsigned missrow, const unsigned misscol)
{
    NEVER_REACHED;
}
#endif //#if defined(__xlC__)

// COMMON INVERSES - SQUARE

template<class T>
boost::numeric::ublas::c_matrix<T, 1, 1> Inverse(const boost::numeric::ublas::c_matrix<T, 1, 1>& rM)
{
    using namespace boost::numeric::ublas;

    c_matrix<T,1,1> inverse;
    T det = Determinant(rM);
    assert(fabs(det) > DBL_EPSILON); // else it is a singular matrix
    inverse(0,0) =  1.0/det;
    return inverse;
}

template<class T>
boost::numeric::ublas::c_matrix<T, 2, 2> Inverse(const boost::numeric::ublas::c_matrix<T, 2, 2>& rM)
{
    using namespace boost::numeric::ublas;

    c_matrix<T, 2, 2> inverse;
    T det = Determinant(rM);

    assert( fabs(det) > DBL_EPSILON ); // else it is a singular matrix
    inverse(0,0)  =  rM(1,1)/det;
    inverse(0,1)  = -rM(0,1)/det;
    inverse(1,0)  = -rM(1,0)/det;
    inverse(1,1)  =  rM(0,0)/det;
    return inverse;
}

template<class T>
boost::numeric::ublas::c_matrix<T, 3, 3> Inverse(const boost::numeric::ublas::c_matrix<T, 3, 3>& rM)
{
    using namespace boost::numeric::ublas;

    c_matrix<T, 3, 3> inverse;
    T det = Determinant(rM);
    assert(fabs(det) > DBL_EPSILON); // else it is a singular matrix

    inverse(0,0) =  (rM(1,1)*rM(2,2) - rM(1,2)*rM(2,1))/det;
    inverse(1,0) = -(rM(1,0)*rM(2,2) - rM(1,2)*rM(2,0))/det;
    inverse(2,0) =  (rM(1,0)*rM(2,1) - rM(1,1)*rM(2,0))/det;
    inverse(0,1) = -(rM(0,1)*rM(2,2) - rM(0,2)*rM(2,1))/det;
    inverse(1,1) =  (rM(0,0)*rM(2,2) - rM(0,2)*rM(2,0))/det;
    inverse(2,1) = -(rM(0,0)*rM(2,1) - rM(0,1)*rM(2,0))/det;
    inverse(0,2) =  (rM(0,1)*rM(1,2) - rM(0,2)*rM(1,1))/det;
    inverse(1,2) = -(rM(0,0)*rM(1,2) - rM(0,2)*rM(1,0))/det;
    inverse(2,2) =  (rM(0,0)*rM(1,1) - rM(0,1)*rM(1,0))/det;

    return inverse;
}

// COMMON PSEUDO-INVERSES - NOT SQUARE

template<class T>
boost::numeric::ublas::c_matrix<T, 2, 3> Inverse(const boost::numeric::ublas::c_matrix<T, 3, 2>& rM)
{
    using namespace boost::numeric::ublas;

    c_matrix<T, 2, 3> inverse;

    //
    // calculate (T'T)^-1, where T'T = (a b)
    //                                 (c d)

    T a = rM(0,0)*rM(0,0) + rM(1,0)*rM(1,0) + rM(2,0)*rM(2,0);
    T b = rM(0,0)*rM(0,1) + rM(1,0)*rM(1,1) + rM(2,0)*rM(2,1);
    T c = b;
    T d = rM(0,1)*rM(0,1) + rM(1,1)*rM(1,1) + rM(2,1)*rM(2,1);

    T det = a*d - b*c;

    T a_inv =  d/det;
    T b_inv = -b/det;
    T c_inv = -c/det;
    T d_inv =  a/det;

    inverse(0,0) = a_inv*rM(0,0) + b_inv*rM(0,1);
    inverse(1,0) = c_inv*rM(0,0) + d_inv*rM(0,1);
    inverse(0,1) = a_inv*rM(1,0) + b_inv*rM(1,1);
    inverse(1,1) = c_inv*rM(1,0) + d_inv*rM(1,1);
    inverse(0,2) = a_inv*rM(2,0) + b_inv*rM(2,1);
    inverse(1,2) = c_inv*rM(2,0) + d_inv*rM(2,1);

    return inverse;
}

template<class T>
boost::numeric::ublas::c_matrix<T, 1, 2> Inverse(const boost::numeric::ublas::c_matrix<T, 2, 1>& rM)
{
    using namespace boost::numeric::ublas;

    c_matrix<T, 1, 2> inverse;
    T det = Determinant(rM);

    inverse(0,0) = rM(0,0)/det/det;
    inverse(0,1) = rM(1,0)/det/det;

    return inverse;
}

template<class T>
boost::numeric::ublas::c_matrix<T, 1, 3> Inverse(const boost::numeric::ublas::c_matrix<T, 3, 1>& rM)
{
    using namespace boost::numeric::ublas;

    c_matrix<T, 1, 3> inverse;
    T det = Determinant(rM);

    inverse(0,0) = rM(0,0)/det/det;
    inverse(0,1) = rM(1,0)/det/det;
    inverse(0,2) = rM(2,0)/det/det;

    return inverse;
}

// COMMON MATRIX TRACES

template<class T>
T Trace(const c_matrix<T, 1, 1>& rM)
{
    return rM(0,0);
}

template<class T>
T Trace(const c_matrix<T, 2, 2>& rM)
{
    return rM(0,0) + rM(1,1);
}

template<class T>
T Trace(const c_matrix<T, 3, 3>& rM)
{
    return rM(0,0) + rM(1,1) + rM(2,2);
}

template<class T>
T Trace(const c_matrix<T, 4, 4>& rM)
{
    return rM(0,0) + rM(1,1) + rM(2,2) + rM(3,3);
}

// OTHER MATRIX FUNCTIONS (INVARIANTS, EIGENVECTORS)

template<class T>
T SecondInvariant(const c_matrix<T, 3, 3>& rM)
{
    return    rM(0,0)*rM(1,1) + rM(1,1)*rM(2,2) + rM(2,2)*rM(0,0)
            - rM(1,0)*rM(1,0) - rM(2,1)*rM(2,1) - rM(2,0)*rM(2,0);
}

template<class T>
T SecondInvariant(const c_matrix<T, 2, 2>& rM)
{
    return Determinant(rM);
}

c_vector<double,3> CalculateEigenvectorForSmallestNonzeroEigenvalue(c_matrix<double, 3, 3>& rA);

//COMMON VECTOR FUNCTIONS

template<class T>
c_vector<T, 3> VectorProduct(const c_vector<T, 3>& rA, const c_vector<T, 3>& rB)
{

    c_vector<T, 3> result;

    double x1 = rA(0);
    double y1 = rA(1);
    double z1 = rA(2);
    double x2 = rB(0);
    double y2 = rB(1);
    double z2 = rB(2);

    result(0) = y1*z2 - z1*y2;
    result(1) = z1*x2 - x1*z2;
    result(2) = x1*y2 - y1*x2;

    return result;
}

c_vector<double, 1> Create_c_vector(double x);

c_vector<double, 2> Create_c_vector(double x, double y);

c_vector<double, 3> Create_c_vector(double x, double y, double z);

#endif /*UBLASCUSTOMFUNCTIONS_HPP_*/