UblasCustomFunctions.cpp

00001 /*
00002 
00003 Copyright (C) University of Oxford, 2005-2010
00004 
00005 University of Oxford means the Chancellor, Masters and Scholars of the
00006 University of Oxford, having an administrative office at Wellington
00007 Square, Oxford OX1 2JD, UK.
00008 
00009 This file is part of Chaste.
00010 
00011 Chaste is free software: you can redistribute it and/or modify it
00012 under the terms of the GNU Lesser General Public License as published
00013 by the Free Software Foundation, either version 2.1 of the License, or
00014 (at your option) any later version.
00015 
00016 Chaste is distributed in the hope that it will be useful, but WITHOUT
00017 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
00018 FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
00019 License for more details. The offer of Chaste under the terms of the
00020 License is subject to the License being interpreted in accordance with
00021 English Law and subject to any action against the University of Oxford
00022 being under the jurisdiction of the English Courts.
00023 
00024 You should have received a copy of the GNU Lesser General Public License
00025 along with Chaste. If not, see <http://www.gnu.org/licenses/>.
00026 
00027 */
00028 
00029 
00030 #include "UblasCustomFunctions.hpp"
00031 
00032 
00033 c_vector<double, 1> Create_c_vector(double x)
00034 {
00035     c_vector<double, 1> v;
00036     v[0] = x;
00037     return v;
00038 }
00039 
00040 c_vector<double, 2> Create_c_vector(double x, double y)
00041 {
00042     c_vector<double, 2> v;
00043     v[0] = x;
00044     v[1] = y;
00045     return v;
00046 }
00047 
00048 c_vector<double, 3> Create_c_vector(double x, double y, double z)
00049 {
00050     c_vector<double, 3> v;
00051     v[0] = x;
00052     v[1] = y;
00053     v[2] = z;
00054     return v;
00055 }
00056 
00057 c_vector<double,3> CalculateEigenvectorForSmallestNonzeroEigenvalue(c_matrix<double, 3, 3>& rA)
00058 {
00059     int info;
00060     c_vector<double, 3> eigenvalues_real_part;
00061     c_vector<double, 3> eigenvalues_imaginary_part;
00062     c_vector<double, 4*3 > workspace;
00063     c_matrix<double, 3, 3> right_eigenvalues;
00064 
00065     char dont_compute_left_evectors = 'N';
00066     char compute_right_evectors = 'V';
00067 
00068     int matrix_size = 3;
00069     int matrix_ld = matrix_size;
00070     int workspace_size = 4*matrix_size;
00071 
00072     c_matrix<double, 3, 3> a_transpose;
00073     noalias(a_transpose) = trans(rA);
00074 
00075     //PETSc alias for dgeev or dgeev_
00076     LAPACKgeev_(&dont_compute_left_evectors, &compute_right_evectors,
00077            &matrix_size, a_transpose.data(),&matrix_ld,
00078            eigenvalues_real_part.data(), eigenvalues_imaginary_part.data(),
00079            NULL, &matrix_ld,
00080            right_eigenvalues.data(),&matrix_ld,
00081            workspace.data(),&workspace_size,
00082            &info);
00083     assert(info==0);
00084 
00085     // if this fails a complex eigenvalue was found
00086     assert(norm_2(eigenvalues_imaginary_part) < DBL_EPSILON);
00087 
00088     unsigned index_of_smallest=UINT_MAX;
00089     double min_eigenvalue = DBL_MAX;
00090 
00091     for (unsigned i=0; i<3; i++)
00092     {
00093         double eigen_magnitude = fabs(eigenvalues_real_part(i));
00094         if (eigen_magnitude < DBL_EPSILON)
00095         {
00096             //A zero eigenvalue is ignored
00098             continue;
00099         }
00100         if (eigen_magnitude < min_eigenvalue)
00101         {
00102             min_eigenvalue = eigen_magnitude;
00103             index_of_smallest = i;
00104         }
00105     }
00106     assert (min_eigenvalue != DBL_MAX);
00107     assert (index_of_smallest != UINT_MAX);
00108     assert (min_eigenvalue >= DBL_EPSILON);
00109 
00110     c_vector<double, 3> output;
00111     output(0) = right_eigenvalues(index_of_smallest, 0);
00112     output(1) = right_eigenvalues(index_of_smallest, 1);
00113     output(2) = right_eigenvalues(index_of_smallest, 2);
00114 
00115     return output;
00116 }
00117 
00118 double SmallPow(double x, unsigned exponent)
00119 {
00120     switch (exponent)
00121     {
00122         case 0:
00123         {
00124             return 1.0;
00125         }
00126         case 1:
00127         {
00128             return x;
00129         }
00130         case 2:
00131         {
00132             return x*x;
00133         }
00134         case 3:
00135         {
00136             return x*x*x;
00137         }
00138         default:
00139         {
00140             if (exponent % 2 == 0)
00141             {
00142                 //Even power
00143                 double partial_answer=SmallPow(x, exponent/2);
00144                 return partial_answer*partial_answer;
00145             }
00146             else
00147             {   //Odd power
00148                 return SmallPow(x, exponent-1)*x;
00149             }
00150         }
00151 
00152     }
00153 }
00154 
00155 

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