LinearMappingFunctionTest.cpp

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/* *****************************************************************
    MESQUITE -- The Mesh Quality Improvement Toolkit

    Copyright 2006 Lawrence Livermore National Laboratory.  Under
    the terms of Contract B545069 with the University of Wisconsin --
    Madison, Lawrence Livermore National Laboratory retains certain
    rights in this software.

    This library 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.

    This library is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
    Lesser General Public License for more details.

    You should have received a copy of the GNU Lesser General Public License
    (lgpl.txt) along with this library; if not, write to the Free Software
    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

    (2006) kraftche@cae.wisc.edu

  ***************************************************************** */

/** \file LinearMappingFunctionTest.cpp
 *  \brief
 *  \author Jason Kraftcheck
 */

#include "Mesquite.hpp"
#include "MappingFunction.hpp"
#include "LinearHexahedron.hpp"
#include "LinearQuadrilateral.hpp"
#include "LinearTetrahedron.hpp"
#include "LinearTriangle.hpp"
#include "LinearPrism.hpp"
#include "LinearPyramid.hpp"
#include "TopologyInfo.hpp"
#include "MsqError.hpp"
#include "JacobianCalculator.hpp"
#include "IdealElements.hpp"

#include "UnitUtil.hpp"

#include <vector>
#include <algorithm>

using namespace MBMesquite;
using namespace std;

class LinearMappingFunctionTest : public CppUnit::TestFixture
{
  private:
    CPPUNIT_TEST_SUITE( LinearMappingFunctionTest );

    CPPUNIT_TEST( test_linear_hex_coeff_corners );
    CPPUNIT_TEST( test_linear_hex_coeff_edges );
    CPPUNIT_TEST( test_linear_hex_coeff_faces );
    CPPUNIT_TEST( test_linear_hex_coeff_center );

    CPPUNIT_TEST( test_linear_quad_coeff_corners );
    CPPUNIT_TEST( test_linear_quad_coeff_edges );
    //    CPPUNIT_TEST(test_linear_quad_coeff_faces);
    CPPUNIT_TEST( test_linear_quad_coeff_center );

    CPPUNIT_TEST( test_linear_tet_coeff_corners );
    CPPUNIT_TEST( test_linear_tet_coeff_edges );
    CPPUNIT_TEST( test_linear_tet_coeff_faces );
    CPPUNIT_TEST( test_linear_tet_coeff_center );

    CPPUNIT_TEST( test_linear_tri_coeff_corners );
    CPPUNIT_TEST( test_linear_tri_coeff_edges );
    CPPUNIT_TEST( test_linear_tri_coeff_faces );
    CPPUNIT_TEST( test_linear_tri_coeff_center );

    CPPUNIT_TEST( test_linear_prism_coeff_corners );
    CPPUNIT_TEST( test_linear_prism_coeff_edges );
    CPPUNIT_TEST( test_linear_prism_coeff_faces );
    CPPUNIT_TEST( test_linear_prism_coeff_center );

    CPPUNIT_TEST( test_linear_pyr_coeff_corners );
    CPPUNIT_TEST( test_linear_pyr_coeff_edges );
    CPPUNIT_TEST( test_linear_pyr_coeff_faces );
    CPPUNIT_TEST( test_linear_pyr_coeff_center );

    CPPUNIT_TEST( test_linear_hex_deriv_corners );
    CPPUNIT_TEST( test_linear_hex_deriv_edges );
    CPPUNIT_TEST( test_linear_hex_deriv_faces );
    CPPUNIT_TEST( test_linear_hex_deriv_center );

    CPPUNIT_TEST( test_linear_quad_deriv_corners );
    CPPUNIT_TEST( test_linear_quad_deriv_edges );
    //    CPPUNIT_TEST(test_linear_quad_deriv_faces);
    CPPUNIT_TEST( test_linear_quad_deriv_center );

    CPPUNIT_TEST( test_linear_tet_deriv_corners );
    CPPUNIT_TEST( test_linear_tet_deriv_edges );
    CPPUNIT_TEST( test_linear_tet_deriv_faces );
    CPPUNIT_TEST( test_linear_tet_deriv_center );

    CPPUNIT_TEST( test_linear_tri_deriv_corners );
    CPPUNIT_TEST( test_linear_tri_deriv_edges );
    //    CPPUNIT_TEST(test_linear_tri_deriv_faces);
    CPPUNIT_TEST( test_linear_tri_deriv_center );

    CPPUNIT_TEST( test_linear_prism_deriv_corners );
    CPPUNIT_TEST( test_linear_prism_deriv_edges );
    CPPUNIT_TEST( test_linear_prism_deriv_faces );
    CPPUNIT_TEST( test_linear_prism_deriv_center );

    CPPUNIT_TEST( test_linear_pyr_deriv_corners );
    CPPUNIT_TEST( test_linear_pyr_deriv_edges );
    CPPUNIT_TEST( test_linear_pyr_deriv_faces );
    CPPUNIT_TEST( test_linear_pyr_deriv_center );

    CPPUNIT_TEST( test_linear_hex_ideal );
    CPPUNIT_TEST( test_linear_quad_ideal );
    CPPUNIT_TEST( test_linear_tet_ideal );
    CPPUNIT_TEST( test_linear_tri_ideal );
    CPPUNIT_TEST( test_linear_prism_ideal );

    CPPUNIT_TEST_SUITE_END();

    LinearHexahedron hex;
    LinearQuadrilateral quad;
    LinearTetrahedron tet;
    LinearTriangle tri;
    LinearPrism prism;
    LinearPyramid pyr;

    static void hex_coeff( double xi[3], double coeff[8] );
    static void tet_coeff( double xi[3], double coeff[4] );
    static void quad_coeff( double xi[2], double coeff[4] );
    static void tri_coeff( double xi[2], double coeff[3] );
    static void prism_coeff( double xi[3], double coeff[6] );
    static void pyr_coeff( double xi[3], double coeff[5] );

    static void hex_deriv( double xi[3], double coeff_deriv[24] );
    static void tet_deriv( double xi[3], double coeff_deriv[12] );
    static void quad_deriv( double xi[2], double coeff_deriv[8] );
    static void tri_deriv( double xi[2], double coeff_deriv[6] );
    static void prism_deriv( double xi[3], double coeff_deriv[18] );
    static void pyr_deriv( double xi[3], double coeff_deriv[15] );

    typedef void ( *map_func )( double*, double* );

    void do_coeff_test( MappingFunction& mf, unsigned subdim, map_func mf2, unsigned count, double* xi );
    void do_deriv_test( MappingFunction2D& mf, unsigned subdim, map_func mf2, unsigned count, double* xi );
    void do_deriv_test( MappingFunction3D& mf, unsigned subdim, map_func mf2, unsigned count, double* xi );
    void do_ideal_test( MappingFunction2D& mf );
    void do_ideal_test( MappingFunction3D& mf );

    void test_coeff_fail( MappingFunction& mf, unsigned subdim );
    void test_deriv_fail( MappingFunction2D& mf, unsigned subdim );
    void test_deriv_fail( MappingFunction3D& mf, unsigned subdim );

    void xi_at_corners( EntityTopology type, double* xi, const int* corners );
    void xi_at_edges( EntityTopology type, double* xi, const int* corners );
    void xi_at_faces( EntityTopology type, double* xi, const int* corners );

  public:
    void setUp();
    void tearDown();

    void test_linear_hex_coeff_corners();
    void test_linear_hex_coeff_edges();
    void test_linear_hex_coeff_faces();
    void test_linear_hex_coeff_center();

    void test_linear_quad_coeff_corners();
    void test_linear_quad_coeff_edges();
    //    void test_linear_quad_coeff_faces();
    void test_linear_quad_coeff_center();

    void test_linear_tet_coeff_corners();
    void test_linear_tet_coeff_edges();
    void test_linear_tet_coeff_faces();
    void test_linear_tet_coeff_center();

    void test_linear_tri_coeff_corners();
    void test_linear_tri_coeff_edges();
    void test_linear_tri_coeff_faces();
    void test_linear_tri_coeff_center();

    void test_linear_prism_coeff_corners();
    void test_linear_prism_coeff_edges();
    void test_linear_prism_coeff_faces();
    void test_linear_prism_coeff_center();

    void test_linear_pyr_coeff_corners();
    void test_linear_pyr_coeff_edges();
    void test_linear_pyr_coeff_faces();
    void test_linear_pyr_coeff_center();

    void test_linear_hex_deriv_corners();
    void test_linear_hex_deriv_edges();
    void test_linear_hex_deriv_faces();
    void test_linear_hex_deriv_center();

    void test_linear_quad_deriv_corners();
    void test_linear_quad_deriv_edges();
    //    void test_linear_quad_deriv_faces();
    void test_linear_quad_deriv_center();

    void test_linear_tet_deriv_corners();
    void test_linear_tet_deriv_edges();
    void test_linear_tet_deriv_faces();
    void test_linear_tet_deriv_center();

    void test_linear_tri_deriv_corners();
    void test_linear_tri_deriv_edges();
    //    void test_linear_tri_deriv_faces();
    void test_linear_tri_deriv_center();

    void test_linear_prism_deriv_corners();
    void test_linear_prism_deriv_edges();
    void test_linear_prism_deriv_faces();
    void test_linear_prism_deriv_center();

    void test_linear_pyr_deriv_corners();
    void test_linear_pyr_deriv_edges();
    void test_linear_pyr_deriv_faces();
    void test_linear_pyr_deriv_center();

    void test_linear_hex_ideal()
    {
        do_ideal_test( hex );
    }
    void test_linear_quad_ideal()
    {
        do_ideal_test( quad );
    }
    void test_linear_tet_ideal()
    {
        do_ideal_test( tet );
    }
    void test_linear_tri_ideal()
    {
        do_ideal_test( tri );
    }
    void test_linear_prism_ideal()
    {
        do_ideal_test( prism );
    }
};

CPPUNIT_TEST_SUITE_NAMED_REGISTRATION( LinearMappingFunctionTest, "LinearMappingFunctionTest" );
CPPUNIT_TEST_SUITE_NAMED_REGISTRATION( LinearMappingFunctionTest, "Unit" );

void LinearMappingFunctionTest::setUp() {}
void LinearMappingFunctionTest::tearDown() {}

/*******************************************************************************
 *                             Xi values at element corners
 *******************************************************************************/

const int HexCorners[8][3] = { { 0, 0, 0 }, { 1, 0, 0 }, { 1, 1, 0 }, { 0, 1, 0 },
                               { 0, 0, 1 }, { 1, 0, 1 }, { 1, 1, 1 }, { 0, 1, 1 } };

const int QuadCorners[4][2] = { { 0, 0 }, { 1, 0 }, { 1, 1 }, { 0, 1 } };

const int TetCorners[12] = { 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1 };

const int TriCorners[6] = { 0, 0, 1, 0, 0, 1 };

const int PrismCorners[18] = { 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 1 };

/*******************************************************************************
 * Functions to calculate element xi at different locations, given the xi
 * at the corners.
 *******************************************************************************/

void LinearMappingFunctionTest::xi_at_corners( EntityTopology type, double* xi, const int* corners )
{
    unsigned d = TopologyInfo::dimension( type );
    unsigned c = TopologyInfo::corners( type );
    for( unsigned i = 0; i < c * d; ++i )
        xi[i] = corners[i];
}

void LinearMappingFunctionTest::xi_at_edges( EntityTopology type, double* xi, const int* corners )
{
    MsqError err;
    unsigned d = TopologyInfo::dimension( type );
    unsigned e = TopologyInfo::edges( type );
    for( unsigned i = 0; i < e; ++i )
    {
        const unsigned* vtx = TopologyInfo::edge_vertices( type, i, err );
        CPPUNIT_ASSERT( !err );
        for( unsigned j = 0; j < d; ++j )
            xi[d * i + j] = ( corners[d * vtx[0] + j] + corners[d * vtx[1] + j] ) / 2.0;
    }
}

void LinearMappingFunctionTest::xi_at_faces( EntityTopology type, double* xi, const int* corners )
{
    MsqError err;
    unsigned d = TopologyInfo::dimension( type );
    unsigned f = TopologyInfo::faces( type );
    for( unsigned i = 0; i < f; ++i )
    {
        unsigned c;
        const unsigned* vtx = TopologyInfo::face_vertices( type, i, c, err );
        CPPUNIT_ASSERT( !err );
        for( unsigned j = 0; j < d; ++j )
        {
            int sum = 0;
            for( unsigned k = 0; k < c; ++k )
                sum += corners[d * vtx[k] + j];
            xi[d * i + j] = (double)sum / c;
        }
    }
}

/*******************************************************************************
 *                 Test functions for mapping function coefficients
 *******************************************************************************/

void LinearMappingFunctionTest::test_linear_hex_coeff_corners()
{
    double xi[24];
    xi_at_corners( HEXAHEDRON, xi, &HexCorners[0][0] );
    do_coeff_test( hex, 0, hex_coeff, 8, xi );
}

void LinearMappingFunctionTest::test_linear_hex_coeff_edges()
{
    double xi[36];
    xi_at_edges( HEXAHEDRON, xi, &HexCorners[0][0] );
    do_coeff_test( hex, 1, hex_coeff, 12, xi );
}

void LinearMappingFunctionTest::test_linear_hex_coeff_faces()
{
    double xi[18];
    xi_at_faces( HEXAHEDRON, xi, &HexCorners[0][0] );
    do_coeff_test( hex, 2, hex_coeff, 6, xi );
}

void LinearMappingFunctionTest::test_linear_hex_coeff_center()
{
    double xi[3] = { 0.5, 0.5, 0.5 };
    do_coeff_test( hex, 3, hex_coeff, 1, xi );
}

void LinearMappingFunctionTest::test_linear_quad_coeff_corners()
{
    double xi[8];
    xi_at_corners( QUADRILATERAL, xi, &QuadCorners[0][0] );
    do_coeff_test( quad, 0, quad_coeff, 4, xi );
}

void LinearMappingFunctionTest::test_linear_quad_coeff_edges()
{
    double xi[8];
    xi_at_edges( QUADRILATERAL, xi, &QuadCorners[0][0] );
    do_coeff_test( quad, 1, quad_coeff, 4, xi );
}

// void LinearMappingFunctionTest::test_linear_quad_coeff_faces()
//{
//  test_coeff_fail( quad, 3 );
//}

void LinearMappingFunctionTest::test_linear_quad_coeff_center()
{
    double xi[2] = { 0.5, 0.5 };
    do_coeff_test( quad, 2, quad_coeff, 1, xi );
}

void LinearMappingFunctionTest::test_linear_tet_coeff_corners()
{
    double xi[12];
    xi_at_corners( TETRAHEDRON, xi, TetCorners );
    do_coeff_test( tet, 0, tet_coeff, 4, xi );
}

void LinearMappingFunctionTest::test_linear_tet_coeff_edges()
{
    double xi[18];
    xi_at_edges( TETRAHEDRON, xi, TetCorners );
    do_coeff_test( tet, 1, tet_coeff, 6, xi );
}

void LinearMappingFunctionTest::test_linear_tet_coeff_faces()
{
    double xi[12];
    xi_at_faces( TETRAHEDRON, xi, TetCorners );
    do_coeff_test( tet, 2, tet_coeff, 4, xi );
}

void LinearMappingFunctionTest::test_linear_tet_coeff_center()
{
    double xi[3] = { 0.25, 0.25, 0.25 };
    do_coeff_test( tet, 3, tet_coeff, 1, xi );
}

void LinearMappingFunctionTest::test_linear_tri_coeff_corners()
{
    double xi[12];
    xi_at_corners( TRIANGLE, xi, TriCorners );
    do_coeff_test( tri, 0, tri_coeff, 3, xi );
}

void LinearMappingFunctionTest::test_linear_tri_coeff_edges()
{
    double xi[18];
    xi_at_edges( TRIANGLE, xi, TriCorners );
    do_coeff_test( tri, 1, tri_coeff, 3, xi );
}

void LinearMappingFunctionTest::test_linear_tri_coeff_faces()
{
    test_coeff_fail( tri, 3 );
}

void LinearMappingFunctionTest::test_linear_tri_coeff_center()
{
    double xi[2] = { 1. / 3, 1. / 3 };
    do_coeff_test( tri, 2, tri_coeff, 1, xi );
}

void LinearMappingFunctionTest::test_linear_prism_coeff_corners()
{
    double xi[18];
    xi_at_corners( PRISM, xi, PrismCorners );
    do_coeff_test( prism, 0, prism_coeff, 6, xi );
}

void LinearMappingFunctionTest::test_linear_prism_coeff_edges()
{
    double xi[27];
    xi_at_edges( PRISM, xi, PrismCorners );
    do_coeff_test( prism, 1, prism_coeff, 9, xi );
}

void LinearMappingFunctionTest::test_linear_prism_coeff_faces()
{
    double xi[15];
    xi_at_faces( PRISM, xi, PrismCorners );
    do_coeff_test( prism, 2, prism_coeff, 5, xi );
}

void LinearMappingFunctionTest::test_linear_prism_coeff_center()
{
    double xi[3] = { 0.5, 1. / 3, 1. / 3 };
    do_coeff_test( prism, 3, prism_coeff, 1, xi );
}

void LinearMappingFunctionTest::test_linear_pyr_coeff_corners()
{
    double xi[15] = { 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1 };
    do_coeff_test( pyr, 0, pyr_coeff, 5, xi );
}

void LinearMappingFunctionTest::test_linear_pyr_coeff_edges()
{
    double xi[24] = { 0.5, 0.0, 0.0, 1.0, 0.5, 0.0, 0.5, 1.0, 0.0, 0.0, 0.5, 0.0,
                      0.0, 0.0, 0.5, 1.0, 0.0, 0.5, 1.0, 1.0, 0.5, 0.0, 1.0, 0.5 };
    do_coeff_test( pyr, 1, pyr_coeff, 8, xi );
}

void LinearMappingFunctionTest::test_linear_pyr_coeff_faces()
{
    double xi[15] = { 0.5, 0.0, 0.5, 1.0, 0.5, 0.5, 0.5, 1.0, 0.5, 0.0, 0.5, 0.5, 0.5, 0.5, 0.0 };
    do_coeff_test( pyr, 2, pyr_coeff, 5, xi );
}

void LinearMappingFunctionTest::test_linear_pyr_coeff_center()
{
    double xi[3] = { 0.5, 0.5, 0.5 };
    do_coeff_test( pyr, 3, pyr_coeff, 1, xi );
}

/*******************************************************************************
 *                 Test functions for mapping function derivatives
 *******************************************************************************/

void LinearMappingFunctionTest::test_linear_hex_deriv_corners()
{
    double xi[24];
    xi_at_corners( HEXAHEDRON, xi, &HexCorners[0][0] );
    do_deriv_test( hex, 0, hex_deriv, 8, xi );
}

void LinearMappingFunctionTest::test_linear_hex_deriv_edges()
{
    double xi[36];
    xi_at_edges( HEXAHEDRON, xi, &HexCorners[0][0] );
    do_deriv_test( hex, 1, hex_deriv, 12, xi );
}

void LinearMappingFunctionTest::test_linear_hex_deriv_faces()
{
    double xi[18];
    xi_at_faces( HEXAHEDRON, xi, &HexCorners[0][0] );
    do_deriv_test( hex, 2, hex_deriv, 6, xi );
}

void LinearMappingFunctionTest::test_linear_hex_deriv_center()
{
    double xi[3] = { 0.5, 0.5, 0.5 };
    do_deriv_test( hex, 3, hex_deriv, 1, xi );
}

void LinearMappingFunctionTest::test_linear_quad_deriv_corners()
{
    double xi[8];
    xi_at_corners( QUADRILATERAL, xi, &QuadCorners[0][0] );
    do_deriv_test( quad, 0, quad_deriv, 4, xi );
}

void LinearMappingFunctionTest::test_linear_quad_deriv_edges()
{
    double xi[8];
    xi_at_edges( QUADRILATERAL, xi, &QuadCorners[0][0] );
    do_deriv_test( quad, 1, quad_deriv, 4, xi );
}

// void LinearMappingFunctionTest::test_linear_quad_deriv_faces()
//{
//  test_deriv_fail( quad, 3 );
//}

void LinearMappingFunctionTest::test_linear_quad_deriv_center()
{
    double xi[2] = { 0.5, 0.5 };
    do_deriv_test( quad, 2, quad_deriv, 1, xi );
}

void LinearMappingFunctionTest::test_linear_tet_deriv_corners()
{
    double xi[12];
    xi_at_corners( TETRAHEDRON, xi, TetCorners );
    do_deriv_test( tet, 0, tet_deriv, 4, xi );
}

void LinearMappingFunctionTest::test_linear_tet_deriv_edges()
{
    double xi[18];
    xi_at_edges( TETRAHEDRON, xi, TetCorners );
    do_deriv_test( tet, 1, tet_deriv, 6, xi );
}

void LinearMappingFunctionTest::test_linear_tet_deriv_faces()
{
    double xi[12];
    xi_at_faces( TETRAHEDRON, xi, TetCorners );
    do_deriv_test( tet, 2, tet_deriv, 4, xi );
}

void LinearMappingFunctionTest::test_linear_tet_deriv_center()
{
    double xi[3] = { 0.25, 0.25, 0.25 };
    do_deriv_test( tet, 3, tet_deriv, 1, xi );
}

void LinearMappingFunctionTest::test_linear_tri_deriv_corners()
{
    double xi[12];
    xi_at_corners( TRIANGLE, xi, TriCorners );
    do_deriv_test( tri, 0, tri_deriv, 3, xi );
}

void LinearMappingFunctionTest::test_linear_tri_deriv_edges()
{
    double xi[18];
    xi_at_edges( TRIANGLE, xi, TriCorners );
    do_deriv_test( tri, 1, tri_deriv, 3, xi );
}

// void LinearMappingFunctionTest::test_linear_tri_deriv_faces()
//{
//  test_deriv_fail( tri, 3 );
//}

void LinearMappingFunctionTest::test_linear_tri_deriv_center()
{
    double xi[2] = { 1. / 3, 1. / 3 };
    do_deriv_test( tri, 2, tri_deriv, 1, xi );
}

void LinearMappingFunctionTest::test_linear_prism_deriv_corners()
{
    double xi[18];
    xi_at_corners( PRISM, xi, PrismCorners );
    do_deriv_test( prism, 0, prism_deriv, 6, xi );
}

void LinearMappingFunctionTest::test_linear_prism_deriv_edges()
{
    double xi[27];
    xi_at_edges( PRISM, xi, PrismCorners );
    do_deriv_test( prism, 1, prism_deriv, 9, xi );
}

void LinearMappingFunctionTest::test_linear_prism_deriv_faces()
{
    double xi[15];
    xi_at_faces( PRISM, xi, PrismCorners );
    do_deriv_test( prism, 2, prism_deriv, 5, xi );
}

void LinearMappingFunctionTest::test_linear_prism_deriv_center()
{
    double xi[3] = { 0.5, 1. / 3, 1. / 3 };
    do_deriv_test( prism, 3, prism_deriv, 1, xi );
}

void LinearMappingFunctionTest::test_linear_pyr_deriv_corners()
{
    double xi[15] = { 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0.5, 0.5, 1 };
    do_deriv_test( pyr, 0, pyr_deriv, 5, xi );
}

void LinearMappingFunctionTest::test_linear_pyr_deriv_edges()
{
    double xi[24] = { 0.5, 0.0, 0.0, 1.0, 0.5, 0.0, 0.5, 1.0, 0.0, 0.0, 0.5, 0.0,
                      0.0, 0.0, 0.5, 1.0, 0.0, 0.5, 1.0, 1.0, 0.5, 0.0, 1.0, 0.5 };
    do_deriv_test( pyr, 1, pyr_deriv, 8, xi );
}

void LinearMappingFunctionTest::test_linear_pyr_deriv_faces()
{
    double xi[15] = { 0.5, 0.0, 0.5, 1.0, 0.5, 0.5, 0.5, 1.0, 0.5, 0.0, 0.5, 0.5, 0.5, 0.5, 0.0 };
    do_deriv_test( pyr, 2, pyr_deriv, 5, xi );
}

void LinearMappingFunctionTest::test_linear_pyr_deriv_center()
{
    double xi[3] = { 0.5, 0.5, 0.5 };
    do_deriv_test( pyr, 3, pyr_deriv, 1, xi );
}

/*******************************************************************************
 *        Mapping function implementations to compare with
 *******************************************************************************/

void LinearMappingFunctionTest::hex_coeff( double xi[3], double coeff[8] )
{
    coeff[0] = ( 1 - xi[0] ) * ( 1 - xi[1] ) * ( 1 - xi[2] );
    coeff[1] = xi[0] * ( 1 - xi[1] ) * ( 1 - xi[2] );
    coeff[2] = xi[0] * xi[1] * ( 1 - xi[2] );
    coeff[3] = ( 1 - xi[0] ) * xi[1] * ( 1 - xi[2] );
    coeff[4] = ( 1 - xi[0] ) * ( 1 - xi[1] ) * xi[2];
    coeff[5] = xi[0] * ( 1 - xi[1] ) * xi[2];
    coeff[6] = xi[0] * xi[1] * xi[2];
    coeff[7] = ( 1 - xi[0] ) * xi[1] * xi[2];
}

void LinearMappingFunctionTest::tet_coeff( double xi[3], double coeff[4] )
{
    coeff[0] = 1 - xi[0] - xi[1] - xi[2];
    coeff[1] = xi[0];
    coeff[2] = xi[1];
    coeff[3] = xi[2];
}

void LinearMappingFunctionTest::quad_coeff( double xi[2], double coeff[4] )
{
    coeff[0] = ( 1 - xi[0] ) * ( 1 - xi[1] );
    coeff[1] = xi[0] * ( 1 - xi[1] );
    coeff[2] = xi[0] * xi[1];
    coeff[3] = ( 1 - xi[0] ) * xi[1];
}

void LinearMappingFunctionTest::tri_coeff( double xi[2], double coeff[3] )
{
    coeff[0] = 1 - xi[0] - xi[1];
    coeff[1] = xi[0];
    coeff[2] = xi[1];
}

void LinearMappingFunctionTest::prism_coeff( double xi[3], double coeff[6] )
{
    coeff[0] = ( 1 - xi[0] ) * ( 1 - xi[1] - xi[2] );
    coeff[1] = ( 1 - xi[0] ) * xi[1];
    coeff[2] = ( 1 - xi[0] ) * xi[2];
    coeff[3] = xi[0] * ( 1 - xi[1] - xi[2] );
    coeff[4] = xi[0] * xi[1];
    coeff[5] = xi[0] * xi[2];
}

void LinearMappingFunctionTest::pyr_coeff( double xi[3], double coeff[5] )
{
    coeff[0] = ( 1 - xi[0] ) * ( 1 - xi[1] ) * ( 1 - xi[2] );
    coeff[1] = xi[0] * ( 1 - xi[1] ) * ( 1 - xi[2] );
    coeff[2] = xi[0] * xi[1] * ( 1 - xi[2] );
    coeff[3] = ( 1 - xi[0] ) * xi[1] * ( 1 - xi[2] );
    coeff[4] = xi[2];
}

/*******************************************************************************
 *        Mapping function derivatives to compare with
 *******************************************************************************/

void LinearMappingFunctionTest::hex_deriv( double xi[3], double coeff[24] )
{
    coeff[3 * 0 + 0] = -( 1 - xi[1] ) * ( 1 - xi[2] );
    coeff[3 * 0 + 1] = -( 1 - xi[0] ) * ( 1 - xi[2] );
    coeff[3 * 0 + 2] = -( 1 - xi[0] ) * ( 1 - xi[1] );

    coeff[3 * 1 + 0] = ( 1 - xi[1] ) * ( 1 - xi[2] );
    coeff[3 * 1 + 1] = -xi[0] * ( 1 - xi[2] );
    coeff[3 * 1 + 2] = -xi[0] * ( 1 - xi[1] );

    coeff[3 * 2 + 0] = xi[1] * ( 1 - xi[2] );
    coeff[3 * 2 + 1] = xi[0] * ( 1 - xi[2] );
    coeff[3 * 2 + 2] = -xi[0] * xi[1];

    coeff[3 * 3 + 0] = -xi[1] * ( 1 - xi[2] );
    coeff[3 * 3 + 1] = ( 1 - xi[0] ) * ( 1 - xi[2] );
    coeff[3 * 3 + 2] = -( 1 - xi[0] ) * xi[1];

    coeff[3 * 4 + 0] = -( 1 - xi[1] ) * xi[2];
    coeff[3 * 4 + 1] = -( 1 - xi[0] ) * xi[2];
    coeff[3 * 4 + 2] = ( 1 - xi[0] ) * ( 1 - xi[1] );

    coeff[3 * 5 + 0] = ( 1 - xi[1] ) * xi[2];
    coeff[3 * 5 + 1] = -xi[0] * xi[2];
    coeff[3 * 5 + 2] = xi[0] * ( 1 - xi[1] );

    coeff[3 * 6 + 0] = xi[1] * xi[2];
    coeff[3 * 6 + 1] = xi[0] * xi[2];
    coeff[3 * 6 + 2] = xi[0] * xi[1];

    coeff[3 * 7 + 0] = -xi[1] * xi[2];
    coeff[3 * 7 + 1] = ( 1 - xi[0] ) * xi[2];
    coeff[3 * 7 + 2] = ( 1 - xi[0] ) * xi[1];
}

void LinearMappingFunctionTest::tet_deriv( double*, double coeff[12] )
{
    static const double derivs[] = { -1, -1, -1, 1, 0, 0, 0, 1, 0, 0, 0, 1 };
    memcpy( coeff, derivs, sizeof( derivs ) );
}

void LinearMappingFunctionTest::quad_deriv( double xi[2], double coeff[8] )
{
    coeff[2 * 0 + 0] = xi[1] - 1;
    coeff[2 * 0 + 1] = xi[0] - 1;

    coeff[2 * 1 + 0] = 1 - xi[1];
    coeff[2 * 1 + 1] = -xi[0];

    coeff[2 * 2 + 0] = xi[1];
    coeff[2 * 2 + 1] = xi[0];

    coeff[2 * 3 + 0] = -xi[1];
    coeff[2 * 3 + 1] = 1 - xi[0];
}

void LinearMappingFunctionTest::tri_deriv( double*, double coeff[6] )
{
    static const double derivs[] = { -1, -1, 1, 0, 0, 1 };
    memcpy( coeff, derivs, sizeof( derivs ) );
}

void LinearMappingFunctionTest::prism_deriv( double xi[3], double coeff[18] )
{
    coeff[0] = xi[1] + xi[2] - 1.0;
    ;
    coeff[1] = xi[0] - 1.0;
    coeff[2] = xi[0] - 1.0;

    coeff[3] = -xi[1];
    coeff[4] = 1.0 - xi[0];
    coeff[5] = 0.0;

    coeff[6] = -xi[2];
    coeff[7] = 0.0;
    coeff[8] = 1.0 - xi[0];

    coeff[9]  = 1.0 - xi[1] - xi[2];
    coeff[10] = -xi[0];
    coeff[11] = -xi[0];

    coeff[12] = xi[1];
    coeff[13] = xi[0];
    coeff[14] = 0.0;

    coeff[15] = xi[2];
    coeff[16] = 0.0;
    coeff[17] = xi[0];
}

void LinearMappingFunctionTest::pyr_deriv( double xi[3], double coeff[15] )
{
    coeff[3 * 0 + 0] = -( 1 - xi[1] ) * ( 1 - xi[2] );
    coeff[3 * 0 + 1] = -( 1 - xi[0] ) * ( 1 - xi[2] );
    coeff[3 * 0 + 2] = -( 1 - xi[0] ) * ( 1 - xi[1] );

    coeff[3 * 1 + 0] = ( 1 - xi[1] ) * ( 1 - xi[2] );
    coeff[3 * 1 + 1] = -xi[0] * ( 1 - xi[2] );
    coeff[3 * 1 + 2] = -xi[0] * ( 1 - xi[1] );

    coeff[3 * 2 + 0] = xi[1] * ( 1 - xi[2] );
    coeff[3 * 2 + 1] = xi[0] * ( 1 - xi[2] );
    coeff[3 * 2 + 2] = -xi[0] * xi[1];

    coeff[3 * 3 + 0] = -xi[1] * ( 1 - xi[2] );
    coeff[3 * 3 + 1] = ( 1 - xi[0] ) * ( 1 - xi[2] );
    coeff[3 * 3 + 2] = -xi[1] * ( 1 - xi[0] );

    coeff[3 * 4 + 0] = 0.0;
    coeff[3 * 4 + 1] = 0.0;
    coeff[3 * 4 + 2] = 1.0;
}

/*******************************************************************************
 *         Some utlity functions for creating CppUnit error messages
 *******************************************************************************/

static string itostr( int i )
{
    char buffer[32];
    sprintf( buffer, "%d", i );
    return buffer;
}

static string dtostr( double i )
{
    char buffer[32];
    sprintf( buffer, "%g", i );
    return buffer;
}

/*******************************************************************************
 *         Actual test imlplementation (common code for many tests)
 *******************************************************************************/

void LinearMappingFunctionTest::do_coeff_test( MappingFunction& mf, unsigned subdim, map_func mf2, unsigned count,
                                               double* xi )
{
    // make sure it fails if passed a nonlinear element
    MsqError err;
    double coeff[100];
    size_t indices[100];
    size_t num_coeff = 100;
    NodeSet tmp_set;
    tmp_set.set_mid_edge_node( 1 );
    mf.coefficients( Sample( 0, 1 ), tmp_set, coeff, indices, num_coeff, err );
    CPPUNIT_ASSERT( err );
    err.clear();

    // get number of vertices in element
    const unsigned n = TopologyInfo::corners( mf.element_topology() );
    const unsigned d = TopologyInfo::dimension( mf.element_topology() );

    // compare coefficients at each location
    vector< double > comp( n );
    for( unsigned i = 0; i < count; ++i )
    {
        num_coeff = 101;
        mf.coefficients( Sample( subdim, i ), NodeSet(), coeff, indices, num_coeff, err );
        CPPUNIT_ASSERT( !err );

        mf2( xi, &comp[0] );
        string xi_str;
        for( unsigned j = 0; j < d; ++j )
        {
            xi_str += !j ? "(" : ", ";
            xi_str += dtostr( xi[j] );
        }
        xi_str += ")";
        xi += d;

        for( unsigned j = 0; j < n; ++j )
        {
            double mf_val = 0.0;
            size_t idx    = std::find( indices, indices + num_coeff, j ) - indices;
            if( idx < num_coeff ) mf_val = coeff[idx];

            CppUnit::Message message( "Coefficients do not match." );
            message.addDetail( string( "Entity:             " ) + itostr( i ) );
            message.addDetail( string( "Coefficient number: " ) + itostr( j ) );
            message.addDetail( string( "Xi:             " ) + xi_str );
            message.addDetail( string( "Expected value: " ) + dtostr( comp[j] ) );
            message.addDetail( string( "Actual value:   " ) + dtostr( mf_val ) );
            ASSERT_MESSAGE( message, fabs( comp[j] - mf_val ) < DBL_EPSILON );
        }
    }
}

void LinearMappingFunctionTest::do_deriv_test( MappingFunction2D& mf, unsigned subdim, map_func mf2, unsigned count,
                                               double* xi )
{
    // make sure it fails if passed a nonlinear element
    MsqError err;
    MsqVector< 2 > derivs[100];
    size_t verts[100], num_vtx = 37;
    NodeSet tmp_set;
    tmp_set.set_mid_edge_node( 1 );
    mf.derivatives( Sample( subdim, 0 ), tmp_set, verts, derivs, num_vtx, err );
    CPPUNIT_ASSERT( err );
    err.clear();

    // get number of vertices in element
    const unsigned n = TopologyInfo::corners( mf.element_topology() );

    // compare coefficients at each location
    vector< double > comp( 2 * n );
    for( unsigned i = 0; i < count; ++i )
    {
        num_vtx = 33;
        mf.derivatives( Sample( subdim, i ), NodeSet(), verts, derivs, num_vtx, err );
        CPPUNIT_ASSERT( !err );
        CPPUNIT_ASSERT( num_vtx > 0 );
        CPPUNIT_ASSERT( num_vtx <= n );

        mf2( xi, &comp[0] );
        string xi_str;
        for( unsigned j = 0; j < 2; ++j )
        {
            xi_str += !j ? "(" : ", ";
            xi_str += dtostr( xi[j] );
        }
        xi_str += ")";
        xi += 2;

        for( unsigned j = 0; j < num_vtx; ++j )
        {
            bool all_zero = true;
            for( unsigned k = 0; k < 2; ++k )
            {
                CppUnit::Message message( "Coefficient derivatives do not match." );
                message.addDetail( string( "Entity:             " ) + itostr( i ) );
                message.addDetail( string( "Coefficient number: " ) + itostr( j ) );
                message.addDetail( string( "Xi:             " ) + xi_str );
                message.addDetail( string( "Axis:           " ) + itostr( k ) );
                message.addDetail( string( "Expected value: " ) + dtostr( comp[2 * verts[j] + k] ) );
                message.addDetail( string( "Actual value:   " ) + dtostr( derivs[j][k] ) );
                ASSERT_MESSAGE( message, fabs( comp[2 * verts[j] + k] - derivs[j][k] ) < DBL_EPSILON );
                if( fabs( derivs[j][k] ) > DBL_EPSILON ) all_zero = false;
            }

            // if vertex has all zero values, it shouldn't have been in the
            // vertex list at all, as the Jacobian will not depend on that vertex.
            CPPUNIT_ASSERT( !all_zero );
        }

        // If any vertex is not in the list, then its values must be zero.
        sort( verts, verts + num_vtx );
        for( unsigned j = 0; j < num_vtx; ++j )
        {
            if( !binary_search( verts, verts + num_vtx, j ) )
            {
                for( unsigned k = 0; k < 2; ++k )
                {
                    CppUnit::Message message( "Missing coefficient derivatives." );
                    message.addDetail( string( "Entity:              " ) + itostr( i ) );
                    message.addDetail( string( "Coefficient number:  " ) + itostr( j ) );
                    message.addDetail( string( "Axis:                " ) + itostr( k ) );
                    message.addDetail( string( "Expected derivative: " ) + dtostr( comp[2 * j + k] ) );
                    ASSERT_MESSAGE( message, fabs( comp[2 * j + k] ) < DBL_EPSILON );
                }
            }
        }
    }
}

void LinearMappingFunctionTest::do_deriv_test( MappingFunction3D& mf, unsigned subdim, map_func mf2, unsigned count,
                                               double* xi )
{
    // make sure it fails if passed a nonlinear element
    MsqError err;
    MsqVector< 3 > derivs[100];
    size_t verts[100], num_vtx = 37;
    NodeSet tmp_set;
    tmp_set.set_mid_edge_node( 1 );
    mf.derivatives( Sample( subdim, 0 ), tmp_set, verts, derivs, num_vtx, err );
    CPPUNIT_ASSERT( err );
    err.clear();

    // get number of vertices in element
    const unsigned n = TopologyInfo::corners( mf.element_topology() );

    // compare coefficients at each location
    vector< double > comp( 3 * n );
    for( unsigned i = 0; i < count; ++i )
    {
        num_vtx = 33;
        mf.derivatives( Sample( subdim, i ), NodeSet(), verts, derivs, num_vtx, err );
        CPPUNIT_ASSERT( !err );
        CPPUNIT_ASSERT( num_vtx > 0 );
        CPPUNIT_ASSERT( num_vtx <= n );

        mf2( xi, &comp[0] );
        string xi_str;
        for( unsigned j = 0; j < 3; ++j )
        {
            xi_str += !j ? "(" : ", ";
            xi_str += dtostr( xi[j] );
        }
        xi_str += ")";
        xi += 3;

        for( unsigned j = 0; j < num_vtx; ++j )
        {
            bool all_zero = true;
            for( unsigned k = 0; k < 3; ++k )
            {
                CppUnit::Message message( "Coefficient derivatives do not match." );
                message.addDetail( string( "Entity:             " ) + itostr( i ) );
                message.addDetail( string( "Coefficient number: " ) + itostr( j ) );
                message.addDetail( string( "Xi:             " ) + xi_str );
                message.addDetail( string( "Axis:           " ) + itostr( k ) );
                message.addDetail( string( "Expected value: " ) + dtostr( comp[3 * verts[j] + k] ) );
                message.addDetail( string( "Actual value:   " ) + dtostr( derivs[j][k] ) );
                ASSERT_MESSAGE( message, fabs( comp[3 * verts[j] + k] - derivs[j][k] ) < DBL_EPSILON );
                if( fabs( derivs[j][k] ) > DBL_EPSILON ) all_zero = false;
            }

            // if vertex has all zero values, it shouldn't have been in the
            // vertex list at all, as the Jacobian will not depend on that vertex.
            CPPUNIT_ASSERT( !all_zero );
        }

        // If any vertex is not in the list, then its values must be zero.
        sort( verts, verts + num_vtx );
        for( unsigned j = 0; j < num_vtx; ++j )
        {
            if( !binary_search( verts, verts + num_vtx, j ) )
            {
                for( unsigned k = 0; k < 3; ++k )
                {
                    CppUnit::Message message( "Missing coefficient derivatives." );
                    message.addDetail( string( "Entity:              " ) + itostr( i ) );
                    message.addDetail( string( "Coefficient number:  " ) + itostr( j ) );
                    message.addDetail( string( "Axis:                " ) + itostr( k ) );
                    message.addDetail( string( "Expected derivative: " ) + dtostr( comp[3 * j + k] ) );
                    ASSERT_MESSAGE( message, fabs( comp[3 * j + k] ) < DBL_EPSILON );
                }
            }
        }
    }
}

void LinearMappingFunctionTest::do_ideal_test( MappingFunction2D& mf )
{
    MsqError err;
    MsqMatrix< 3, 2 > W_prime;
    mf.ideal( Sample( 2, 0 ), W_prime, err );
    ASSERT_NO_ERROR( err );

    // for this test that everything is in the xy-plane
    CPPUNIT_ASSERT_DOUBLES_EQUAL( 0.0, W_prime( 2, 0 ), 1e-12 );
    CPPUNIT_ASSERT_DOUBLES_EQUAL( 0.0, W_prime( 2, 1 ), 1e-12 );
    MsqMatrix< 2, 2 > W( W_prime.data() );
    CPPUNIT_ASSERT_DOUBLES_EQUAL( 1.0, det( W ), 1e-6 );

    const Vector3D* verts = unit_edge_element( mf.element_topology() );
    CPPUNIT_ASSERT( verts );

    JacobianCalculator jc;
    jc.get_Jacobian_2D( &mf, NodeSet(), Sample( 2, 0 ), verts, TopologyInfo::corners( mf.element_topology() ), W_prime,
                        err );
    ASSERT_NO_ERROR( err );

    // for this test that everything is in the xy-plane
    CPPUNIT_ASSERT_DOUBLES_EQUAL( 0.0, W_prime( 2, 0 ), 1e-12 );
    CPPUNIT_ASSERT_DOUBLES_EQUAL( 0.0, W_prime( 2, 1 ), 1e-12 );
    MsqMatrix< 2, 2 > W_exp( W_prime.data() );
    W_exp /= sqrt( det( W_exp ) );

    // Matrices should be a rotation of each other.
    // First, calculate tentative rotation matrix
    MsqMatrix< 2, 2 > R = inverse( W_exp ) * W;
    // next check that it is a rotation
    CPPUNIT_ASSERT_DOUBLES_EQUAL( 1.0, det( R ), 1e-6 );          // no scaling
    ASSERT_MATRICES_EQUAL( transpose( R ), inverse( R ), 1e-6 );  // orthogonal
}

void LinearMappingFunctionTest::do_ideal_test( MappingFunction3D& mf )
{
    MsqError err;
    MsqMatrix< 3, 3 > W, I( 1.0 );
    mf.ideal( Sample( 3, 0 ), W, err );
    ASSERT_NO_ERROR( err );
    CPPUNIT_ASSERT_DOUBLES_EQUAL( 1.0, det( W ), 1e-6 );

    const Vector3D* verts = unit_edge_element( mf.element_topology() );
    CPPUNIT_ASSERT( verts );

    JacobianCalculator jc;
    MsqMatrix< 3, 3 > W_exp;
    jc.get_Jacobian_3D( &mf, NodeSet(), Sample( 3, 0 ), verts, TopologyInfo::corners( mf.element_topology() ), W_exp,
                        err );
    ASSERT_NO_ERROR( err );
    W_exp /= MBMesquite::cbrt( det( W_exp ) );

    // Matrices should be a rotation of each other.
    // First, calculate tentative rotation matrix
    MsqMatrix< 3, 3 > R = W * inverse( W_exp );
    // next check that it is a rotation
    CPPUNIT_ASSERT_DOUBLES_EQUAL( 1.0, det( R ), 1e-6 );   // no scaling
    ASSERT_MATRICES_EQUAL( I, transpose( R ) * R, 1e-6 );  // orthogonal
}

void LinearMappingFunctionTest::test_coeff_fail( MappingFunction& mf, unsigned subdim )
{
    // make sure it fails if called
    MsqError err;
    double coeff[100];
    size_t num_coeff, indices[100];
    mf.coefficients( Sample( subdim, 0 ), NodeSet(), coeff, indices, num_coeff, err );
    CPPUNIT_ASSERT( err );
    err.clear();
}

void LinearMappingFunctionTest::test_deriv_fail( MappingFunction2D& mf, unsigned subdim )
{
    // make sure it fails if called
    MsqError err;
    MsqVector< 2 > coeff[100];
    size_t verts[100], num_coeff;
    mf.derivatives( Sample( subdim, 0 ), NodeSet(), verts, coeff, num_coeff, err );
    CPPUNIT_ASSERT( err );
    err.clear();
}

void LinearMappingFunctionTest::test_deriv_fail( MappingFunction3D& mf, unsigned subdim )
{
    // make sure it fails if called
    MsqError err;
    MsqVector< 3 > coeff[100];
    size_t verts[100], num_coeff;
    mf.derivatives( Sample( subdim, 0 ), NodeSet(), verts, coeff, num_coeff, err );
    CPPUNIT_ASSERT( err );
    err.clear();
}