UblasCustomFunctions.hpp

Go to the documentation of this file.

/*
 
Copyright (c) 2005-2024, University of Oxford.
All rights reserved.
 
University of Oxford means the Chancellor, Masters and Scholars of the
University of Oxford, having an administrative office at Wellington
Square, Oxford OX1 2JD, UK.
 
This file is part of Chaste.
 
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
 * Redistributions of source code must retain the above copyright notice,
   this list of conditions and the following disclaimer.
 * Redistributions in binary form must reproduce the above copyright notice,
   this list of conditions and the following disclaimer in the documentation
   and/or other materials provided with the distribution.
 * Neither the name of the University of Oxford nor the names of its
   contributors may be used to endorse or promote products derived from this
   software without specific prior written permission.
 
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 
*/
 
#ifndef UBLASCUSTOMFUNCTIONS_HPP_
#define UBLASCUSTOMFUNCTIONS_HPP_
 
#include "UblasIncludes.hpp"
 
#include "Exception.hpp"
#include "MathsCustomFunctions.hpp"
 
// COMMON DETERMINANTS - SQUARE
 
template<class T>
inline 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>
inline T Trace(const c_matrix<T, 1, 1>& rM)
{
    return rM(0,0);
}
 
template<class T>
inline T Trace(const c_matrix<T, 2, 2>& rM)
{
    return rM(0,0) + rM(1,1);
}
 
template<class T>
inline T Trace(const c_matrix<T, 3, 3>& rM)
{
    return rM(0,0) + rM(1,1) + rM(2,2);
}
 
template<class T>
inline 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);
 
double CalculateMaxEigenpair(c_matrix<double, 3, 3>& rA, c_vector<double, 3>& rEigenvector);
 
                             //COMMON VECTOR FUNCTIONS
 
 
template<class T>
c_vector<T, 1> VectorProduct(const c_vector<T, 1>& rA, const c_vector<T, 1>& rB)
{
    NEVER_REACHED;
}
template<class T>
c_vector<T, 2> VectorProduct(const c_vector<T, 2>& rA, const c_vector<T, 2>& rB)
{
    NEVER_REACHED;
}
 
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;
 
    result(0) = rA(1)*rB(2) - rA(2)*rB(1);
    result(1) = rA(2)*rB(0) - rA(0)*rB(2);
    result(2) = rA(0)*rB(1) - rA(1)*rB(0);
 
    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_*/