This file is indexed.

/usr/include/trilinos/Galeri_HexQuadrature.h is in libtrilinos-galeri-dev 12.10.1-3.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
// @HEADER
// ************************************************************************
//
//           Galeri: Finite Element and Matrix Generation Package
//                 Copyright (2006) ETHZ/Sandia Corporation
//
// Under terms of Contract DE-AC04-94AL85000, there is a non-exclusive
// license for use of this work by or on behalf of the U.S. Government.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// 1. Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// 2. 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.
//
// 3. Neither the name of the Corporation nor the names of the
// contributors may be used to endorse or promote products derived from
// this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY SANDIA CORPORATION "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 SANDIA CORPORATION OR THE
// 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.
//
// Questions about Galeri? Contact Marzio Sala (marzio.sala _AT_ gmail.com)
//
// ************************************************************************
// @HEADER

#ifndef GALERI_HEXQUADRATURE_H
#define GALERI_HEXQUADRATURE_H

/*!
 * \file Galeri_HexQuadrature.h
 */

#include "Epetra_SerialDenseVector.h"
#include "Epetra_SerialDenseMatrix.h"
#include "Galeri_AbstractQuadrature.h"

namespace Galeri {
namespace FiniteElements {

/*!
 * \class HexQuadrature
 *
 * \brief Quadrature formula on hexahedra.
 *
 * \author Marzio Sala, SNL 9214.
 *
 * \author Last updated on 02-Apr-05.
 *
 */
class HexQuadrature : public AbstractQuadrature
{
    
public:

  //! Constructor.
  /*! 
   * \param NumQuadrNodes - (In) Number of quadrature nodes per element.
   *                             Valid choices are: 1.
   */
  HexQuadrature(const int NumQuadrNodes)
  {
    NumQuadrNodes_ = NumQuadrNodes;
    NumDimensions_ = 3;
    NumLocalNodes_ = 8;

    J_.Reshape(NumDimensions_,NumDimensions_);
    basis_rs_.Reshape(NumLocalNodes_,NumQuadrNodes_);
    basis_dr_.Reshape(NumLocalNodes_,NumQuadrNodes_);
    basis_ds_.Reshape(NumLocalNodes_,NumQuadrNodes_);
    basis_dt_.Reshape(NumLocalNodes_,NumQuadrNodes_);

    basis_xy_.Reshape(NumLocalNodes_, 1);
    basis_dx_.Reshape(NumLocalNodes_, 1);
    basis_dy_.Reshape(NumLocalNodes_, 1);
    basis_dz_.Reshape(NumLocalNodes_, 1);

    basis_rs_temp_.Reshape(NumLocalNodes_, 1);
    basis_dr_temp_.Reshape(NumLocalNodes_, 1);
    basis_ds_temp_.Reshape(NumLocalNodes_, 1);
    basis_dt_temp_.Reshape(NumLocalNodes_, 1);

    Weight_.Reshape(NumQuadrNodes_, 1);

    qr_.Reshape(NumQuadrNodes_, 1);
    qs_.Reshape(NumQuadrNodes_, 1);
    qt_.Reshape(NumQuadrNodes_, 1);

    switch (NumQuadrNodes_) {
    case 1:      
      qs_[0]    = 0.0;
      qr_[0]    = 0.0;
      qt_[0]    = 0.0;
      Weight_[0] = 8.0;
      break;

    case 8:

      qs_[0]     =  -0.57735026918963;
      qr_[0]     =  -0.57735026918963;
      qt_[0]     =  -0.57735026918963;
      Weight_[0] = 1;
      qs_[1]     =   0.57735026918963;
      qr_[1]     =  -0.57735026918963;
      qt_[1]     =  -0.57735026918963;
      Weight_[1] = 1;
      qs_[2]     =   0.57735026918963;
      qr_[2]     =   0.57735026918963;
      qt_[2]     =  -0.57735026918963;    
      Weight_[2] = 1;
      qs_[3]     =   0.57735026918963;
      qr_[3]     =  -0.57735026918963;
      qt_[3]     =  -0.57735026918963;
      Weight_[3] = 1;
      qs_[4]     =  -0.57735026918963;
      qr_[4]     =  -0.57735026918963;
      qt_[4]     =   0.57735026918963;
      Weight_[4] = 1;
      qs_[5]     =   0.57735026918963;
      qr_[5]     =  -0.57735026918963;
      qt_[5]     =   0.57735026918963;
      Weight_[5] = 1;
      qs_[6]     =   0.57735026918963;
      qr_[6]     =   0.57735026918963;
      qt_[6]     =   0.57735026918963;    
      Weight_[6] = 1;
      qs_[7]     =   0.57735026918963;
      qr_[7]     =  -0.57735026918963;
      qt_[7]     =   0.57735026918963;
      Weight_[7] = 1;
      break;

    default:
      cerr << "The selected number of quadrature nodes ("
           << NumQuadrNodes_ << " is not available" << endl;
      cerr << "Valid choices are: 1, 8." << endl;
      throw(-1);
    }

    double x[8], y[8], z[8];

    x[0] = -1.0;
    x[1] =  1.0;
    x[2] =  1.0;
    x[3] = -1.0;
    x[4] = -1.0;
    x[5] =  1.0;
    x[6] =  1.0;
    x[7] = -1.0;

    y[0] = -1.0;
    y[1] = -1.0;
    y[2] =  1.0;
    y[3] =  1.0;
    y[4] = -1.0;
    y[5] = -1.0;
    y[6] =  1.0;
    y[7] =  1.0;

    z[0] = -1.0;
    z[1] = -1.0;
    z[2] = -1.0;
    z[3] = -1.0;
    z[4] =  1.0;
    z[5] =  1.0;
    z[6] =  1.0;
    z[7] =  1.0;

    for (int k = 0 ; k < NumQuadrNodes_ ; k++) 
    {
      for (int i = 0 ; i < 8 ; i++) 
      { 
        basis_rs_(i,k) = 0.125 * (1+x[i] * qr_[k]) * (1+y[i] * qs_[k]) * (1+z[i] * qt_[k]);
        basis_dr_(i,k) = 0.125*     x[i]           * (1+y[i] * qs_[k]) * (1+z[i] * qt_[k]);
        basis_ds_(i,k) = 0.125 * (1+x[i] * qr_[k]) *   y[i]            * (1+z[i] * qt_[k]);
        basis_dt_(i,k) = 0.125 * (1+x[i] * qr_[k]) * (1+y[i] * qs_[k]) *    z[i]          ;
      }
    }
  }

  ~HexQuadrature()
  {}

  void ComputeJacobian(const int QuadrNode, 
                       const double* x_hex, 
                       const double* y_hex,
                       const double* z_hex) const
  {
    double a = 0.0, b = 0.0, c = 0.0;
    double d = 0.0, e = 0.0, f = 0.0;
    double g = 0.0, h = 0.0, l = 0.0;
    double divide_by;

    /* jacobian^{-1} is the matrix

                   [ a b c ]
       jacobian =  [ d e f ]
                   [ g h l ]
     */

    double x[8], y[8], z[8];

    x[0] = -1.0;
    x[1] =  1.0;
    x[2] =  1.0;
    x[3] = -1.0;
    x[4] = -1.0;
    x[5] =  1.0;
    x[6] =  1.0;
    x[7] = -1.0;

    y[0] = -1.0;
    y[1] = -1.0;
    y[2] =  1.0;
    y[3] =  1.0;
    y[4] = -1.0;
    y[5] = -1.0;
    y[6] =  1.0;
    y[7] =  1.0;

    z[0] = -1.0;
    z[1] = -1.0;
    z[2] = -1.0;
    z[3] = -1.0;
    z[4] =  1.0;
    z[5] =  1.0;
    z[6] =  1.0;
    z[7] =  1.0;

    double qr = qr_[QuadrNode];
    double qs = qs_[QuadrNode];
    double qt = qt_[QuadrNode];

    for (int i = 0 ; i < 8 ; i++) 
    {
      a += 0.125 * x_hex[i] *    x[i]     * (1+y[i]*qs) * (1+z[i]*qt);
      b += 0.125 * x_hex[i] * (1+x[i]*qr) *    y[i]     * (1+z[i]*qt);
      c += 0.125 * x_hex[i] * (1+x[i]*qr) * (1+y[i]*qs) *    z[i]    ;

      d += 0.125 * y_hex[i] *    x[i]     * (1+y[i]*qs) * (1+z[i]*qt);
      e += 0.125 * y_hex[i] * (1+x[i]*qr) *    y[i]     * (1+z[i]*qt);
      f += 0.125 * y_hex[i] * (1+x[i]*qr) * (1+y[i]*qs) *    z[i]    ;

      g += 0.125 * z_hex[i] *    x[i]     * (1+y[i]*qs) * (1+z[i]*qt);
      h += 0.125 * z_hex[i] * (1+x[i]*qr) *    y[i]     * (1+z[i]*qt);
      l += 0.125 * z_hex[i] * (1+x[i]*qr) * (1+y[i]*qs) *    z[i]    ;
    }

    det_J_ = ( a * e * l - a * f * h - d * b * l + d * c * h +
              g * b * f - g * c * e );

    if (det_J_ < 0) det_J_ = - det_J_;

    divide_by = - 1.0 / (det_J_);

    J_(0,0) = divide_by * (-e * l + f * h);
    J_(0,1) = divide_by * ( b * l - c * h); 
    J_(0,2) = divide_by * (-b * f + c * e);

    J_(1,0) = divide_by * ( d * l - f * g);
    J_(1,1) = divide_by * (-a * l + c * g);
    J_(1,2) = divide_by * ( a * f - c * d);

    J_(2,0) = divide_by * (-d * h + e * g);
    J_(2,1) = divide_by * ( a * h - b * g);
    J_(2,2) = divide_by * (-a * e + b * d);
  }

  void ComputeQuadrNodes(const int ii,
                         const double* x, const double* y, const double* z,
                         double& xq, double& yq, double& zq) const
  {
    xq = 0.0;
    yq = 0.0;
    zq = 0.0;

    for (int k = 0 ; k < NumLocalNodes_ ; k++) 
    {
      xq += basis_rs_(k,ii) * x[k];
      yq += basis_rs_(k,ii) * y[k];
      zq += basis_rs_(k,ii) * z[k];
      basis_dr_temp_[k] = basis_dr_(k,ii);
      basis_ds_temp_[k] = basis_ds_(k,ii);
      basis_dt_temp_[k] = basis_dt_(k,ii);
      basis_xy_[k] = basis_rs_(k,ii);
    }
  }

  void ComputeDerivatives(const int QuadrNode) const
  {
    for (int i = 0 ; i < NumLocalNodes_ ; i++) 
    {
      basis_dx_(i) = basis_dr_(i,QuadrNode) * J_(0,0) +
                     basis_ds_(i,QuadrNode) * J_(0,1) +
                     basis_dt_(i,QuadrNode) * J_(0,2);
      basis_dy_(i) = basis_dr_(i,QuadrNode) * J_(1,0) +
                     basis_ds_(i,QuadrNode) * J_(1,1) +
                     basis_dt_(i,QuadrNode) * J_(1,2);
      basis_dz_(i) = basis_dr_(i,QuadrNode) * J_(2,0) +
                     basis_ds_(i,QuadrNode) * J_(2,1) +
                     basis_dt_(i,QuadrNode) * J_(2,2);
    }
  }

  inline double QuadrWeight(const int QuadrNode) const
  {
    return(Weight_[QuadrNode]);    
  }

  inline double DetJacobian(const int QuadrNode) const
  {
    return(det_J_);
  }

  inline double Phi(const int i) const
  {
    return(basis_xy_(i));
  }

  inline double PhiX(const int i) const
  {
    return(basis_dx_(i));
  }

  inline double PhiY(const int i) const
  {
    return(basis_dy_(i));
  }

  inline double PhiZ(const int i) const
  {
    return(basis_dz_(i));
  }

  inline double Psi(const int i) const
  {
    return(basis_xy_(i));
  }

  inline double PsiX(const int i) const
  {
    return(basis_dx_(i));
  }

  inline double PsiY(const int i) const
  {
    return(basis_dy_(i));
  }

  inline double PsiZ(const int i) const
  {
    return(basis_dz_(i));
  }

  inline int NumQuadrNodes() const
  {
    return(NumQuadrNodes_);
  }

  inline int NumPhiFunctions() const 
  {
    return(8);
  }

  inline int NumPsiFunctions() const 
  {
    return(8);
  }

protected:

  int NumQuadrNodes_;
  int NumDimensions_;
  int NumLocalNodes_;

  mutable double det_J_;

  mutable Epetra_SerialDenseMatrix J_;

  mutable Epetra_SerialDenseMatrix basis_rs_;
  mutable Epetra_SerialDenseMatrix basis_dr_;
  mutable Epetra_SerialDenseMatrix basis_ds_;
  mutable Epetra_SerialDenseMatrix basis_dt_;

  mutable Epetra_SerialDenseVector basis_xy_;
  mutable Epetra_SerialDenseVector basis_dx_;
  mutable Epetra_SerialDenseVector basis_dy_;
  mutable Epetra_SerialDenseVector basis_dz_;

  mutable Epetra_SerialDenseVector basis_rs_temp_;
  mutable Epetra_SerialDenseVector basis_dr_temp_;
  mutable Epetra_SerialDenseVector basis_ds_temp_;
  mutable Epetra_SerialDenseVector basis_dt_temp_;

  mutable Epetra_SerialDenseVector Weight_;

  mutable Epetra_SerialDenseVector qr_;
  mutable Epetra_SerialDenseVector qs_;
  mutable Epetra_SerialDenseVector qt_;

};

} // namespace FiniteElements
} // namespace Galeri
#endif