UblasCustomFunctions.hpp

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/*

Copyright (C) University of Oxford, 2005-2011

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University of Oxford, having an administrative office at Wellington
Square, Oxford OX1 2JD, UK.

This file is part of Chaste.

Chaste is free software: you can redistribute it and/or modify it
under the terms of the GNU Lesser General Public License as published
by the Free Software Foundation, either version 2.1 of the License, or
(at your option) any later version.

Chaste is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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License for more details. The offer of Chaste under the terms of the
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being under the jurisdiction of the English Courts.

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along with Chaste. If not, see <http://www.gnu.org/licenses/>.

*/

#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_*/