DOFMatrix.cc 19.2 KB
Newer Older
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
#include "DOFMatrix.h"
#include <algorithm>
#include <png.h>
#include "QPsiPhi.h"
#include "BasisFunction.h"
#include "Boundary.h"
#include "DOFAdmin.h"
#include "ElInfo.h"
#include "FiniteElemSpace.h"
#include "Mesh.h"
#include "DOFVector.h"
#include "Operator.h"
#include "BoundaryCondition.h"
#include "BoundaryManager.h"
#include "ElementMatrix.h"
#include "Assembler.h"

namespace AMDiS {

  DOFMatrix *DOFMatrix::traversePtr = NULL;

  DOFMatrix::DOFMatrix()
  {
    rowFESpace = NULL;
    colFESpace = NULL;
    elementMatrix = NULL;
  }

  DOFMatrix::DOFMatrix(const FiniteElemSpace* rowFESpace_,
		       const FiniteElemSpace* colFESpace_,
		       ::std::string name_)
    : rowFESpace(rowFESpace_),
      colFESpace(colFESpace_),
      name(name_), 
      elementMatrix(NULL),
      coupleMatrix(false)
  {
    TEST_EXIT(rowFESpace)("no rowFESpace\n");
  
    if(!colFESpace) {
      colFESpace = rowFESpace;
    }

    if (rowFESpace && rowFESpace->getAdmin())
      (const_cast<DOFAdmin*>( rowFESpace->getAdmin()))->addDOFIndexed(this);

    boundaryManager = NEW BoundaryManager;
  }

  DOFMatrix::DOFMatrix(const DOFMatrix& rhs)
    : name(rhs.name+"copy")
  {
    *this=rhs;
    elementMatrix = NULL;
    if (rowFESpace && rowFESpace->getAdmin())
      (const_cast<DOFAdmin*>( rowFESpace->getAdmin()))->addDOFIndexed(this);
  }

  DOFMatrix::~DOFMatrix()
  {
    FUNCNAME("DOFMatrix::~DOFMatrix");
    if(rowFESpace && rowFESpace->getAdmin()) {
      (const_cast<DOFAdmin*>(rowFESpace->getAdmin()))->removeDOFIndexed(this);
    }  
    if(elementMatrix != NULL) {
      DELETE elementMatrix;
    }
    //DELETE boundaryManager;
  }

  void DOFMatrix::print() const
  {
    FUNCNAME("DOFMatrix::print()");
    int  i, j, jcol;
    DOFMatrix::MatrixRow row;

    int sizeUsed = rowFESpace->getAdmin()->getUsedSize();

    if (static_cast<int>(matrix.size()) < sizeUsed) {
      WARNING("DOFMatrix not yet initialized\n");
      return;
    }

    for (i = 0; i < sizeUsed; i++) { 
      row = matrix[i];
      MSG("row %3d:",i);
      int rowSize = static_cast<int>( row.size());
      for (j = 0; j < rowSize; j++) {
	jcol = row[j].col;
	if (entryUsed(i,j)) {
	  Msg::print(" (%3d,%20.17lf)", jcol, row[j].entry);
	}
      }
      Msg::print("\n");
    }
    return;
  }

  void DOFMatrix::printRow(int i) const
  {
    FUNCNAME("DOFMatrix::printRow()");

    int sizeUsed = rowFESpace->getAdmin()->getUsedSize();

    if (static_cast<int>(matrix.size()) < sizeUsed) {
      WARNING("DOFMatrix not yet initialized\n");
      return;
    }

    DOFMatrix::MatrixRow row = matrix[i];
    MSG("row %3d:",i);
    int rowSize = static_cast<int>( row.size());
    for (int j = 0; j < rowSize; j++) {
      int jcol = row[j].col;
      if (entryUsed(i,j)) {
	Msg::print(" (%3d,%20.17lf)", jcol, row[j].entry);
      }
    }
    Msg::print("\n");   
  }

  /****************************************************************************/
  /*  clear: remove all entries from dof_matrix                               */
  /****************************************************************************/

  void DOFMatrix::clear()
  {
128 129
    int mSize = static_cast<int>(matrix.size());
    for (int i = 0; i < mSize; i++) {
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
      matrix[i].resize(0);
    }
    return;
  }

  bool DOFMatrix::symmetric()
  {
    FUNCNAME("DOFMatrix::symmetric()");

    DegreeOfFreedom row, col;
    double entry, tol = 1e-5;

    DOFMatrix::Iterator matrixRow(this, USED_DOFS);

    for (matrixRow.reset(); !matrixRow.end(); ++matrixRow) {
      row = matrixRow.getDOFIndex();
      int rowSize = matrixRow->size();
      for (int i = 0; i < rowSize; i++) {
	col = (*matrixRow)[i].col;
	entry = (*matrixRow)[i].entry;
	if (abs(entry - logAcc(col, row)) > tol) {
	  MSG("matrix[%d][%d] = %e, matrix[%d][%d] = %e\n",
	      row, col, entry, col, row, logAcc(col, row));

	  return false;
	}
      }
    }

    return true;
  }

  void DOFMatrix::test()
  {
    FUNCNAME("DOFMatrix::test()");

    int non_symmetric = 0, found = 0;

    /* test symmetry */
    for (int i = 0; i < static_cast<int>(matrix.size()); i++) { 
      double sum = 0.0;
      DOFMatrix::MatrixRow *row = &matrix[i];
      for (int j = 0; j < static_cast<int>(row->size()); j++) {
	int jcol = (*row)[j].col;
	if (entryUsed(i, j)) {
	  found = 0;
	  if ((*row)[j].entry != (*row)[j].entry) {
	    MSG("mat[%d,%d]=%10.5e ???\n", i, jcol, (*row)[j].entry);
	    WAIT;
	  }
	  DOFMatrix::MatrixRow *row2 = &matrix[jcol];
	  for (int k = 0; k < static_cast<int>(row->size()); k++) {
	    int kcol = (*row)[k].col;
	    if (entryUsed(jcol, k)) {
	      if (kcol == i) {
		found = 1;
		if (abs((*row2)[k].entry - (*row)[j].entry) > 1.E-5) {
		  non_symmetric = 1;
		  MSG("mat[%d,%d]=%10.5e != mat[%d,%d]=%10.5e\n",
		      i, jcol, (*row)[j].entry, jcol, i, (*row2)[k].entry);
		}
		row2 = NULL;
		break;
	      }
	    }
	  }
	  if (!found) {
	    non_symmetric = 1;
	    MSG("mat[%d,%d] not found\n", jcol, i);
	  }
	}
      }
      if (abs(sum) > 1.E-5) {
	MSG("Zeilensumme[%d] = %10.5e\n", i, sum);
      }
    }

    if (non_symmetric) {
      MSG("matrix `%s' not symmetric.\n", name.data());
    } else {
      MSG("matrix `%s' is symmetric.\n", name.data());
    }
  }


  DOFMatrix& DOFMatrix::operator=(const DOFMatrix& rhs)
  {
    rowFESpace = rhs.rowFESpace;
    colFESpace = rhs.colFESpace;
    operators = rhs.operators;
    operatorFactor = rhs.operatorFactor;
    matrix = rhs.matrix;
    if (rhs.boundaryManager) {
      boundaryManager = new BoundaryManager(*rhs.boundaryManager);
    } else {
      boundaryManager=NULL;
    }

    return *this;
  }


  void DOFMatrix::addElementMatrix(double sign, 
				   const ElementMatrix &elMat, 
				   const BoundaryType *bound,
				   bool add)
  {
    FUNCNAME("DOFMatrix::addElementMatrix");

    DegreeOfFreedom row, col;
    double entry;

    int n_row = elMat.rowIndices.getSize();
    int n_col = elMat.colIndices.getSize();

    for (int i = 0; i < n_row; i++)  {   // for all rows of element matrix
      row = elMat.rowIndices[i];

      BoundaryCondition *condition = 
	bound ? boundaryManager->getBoundaryCondition(bound[i]) : NULL;

      if (condition && condition->isDirichlet()) {
	MatrixRow *matrixRow = &(matrix[row]);
253
	if (coupleMatrix) {
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
	  matrixRow->resize(0);
	} else {
	  matrixRow->resize(1);
	  ((*matrixRow)[0]).col = row;
	  ((*matrixRow)[0]).entry = 1.0;
	}     
      } else {
	for (int j = 0; j < n_col; j++) {  // for all columns
	  col = elMat.colIndices[j];
	  entry = elMat[i][j];
	  addSparseDOFEntry(sign, row, col, entry, add); 
	}
      }
    }
  }



  DegreeOfFreedom DOFMatrix::logToPhysIndex(DegreeOfFreedom a,
					    DegreeOfFreedom b) const
  {
    int j;

    for (j = 0; j < static_cast<int>(matrix[a].size()); j++) 
      if (b == matrix[a][j].col) 
	break;

    return (j == static_cast<int>(matrix[a].size())) ? -1 : j;
  }


  double DOFMatrix::logAcc(DegreeOfFreedom a,DegreeOfFreedom b) const
  {
    int j;

    for (j = 0; j < static_cast<int>(matrix[a].size()); j++) 
      if (b == matrix[a][j].col) 
	break;

    return (j == static_cast<int>(matrix[a].size())) ? 0.0 : matrix[a][j].entry;
  }

  void DOFMatrix::changeColOfEntry(DegreeOfFreedom a,
				   DegreeOfFreedom b,
				   DegreeOfFreedom c)
  {
    int j;

    for (j=0; j<static_cast<int>(matrix[a].size());j++) 
      if (b==matrix[a][j].col) break;
    if (j!=static_cast<int>(matrix[a].size())) matrix[a][j].col=c;
  }

  double *DOFMatrix::addSparseDOFEntry(double sign, int irow, 
				       int jcol, double entry,
				       bool add)
  {
    FUNCNAME("add_sparse_dof_entry");

    MatrixRow *row = &(matrix[irow]);

    if(add && !entry) return NULL;

    double *result = NULL;

    int i, freeCol = -1, rowSize = static_cast<int>( row->size());

321 322 323
    TEST_EXIT_DBG(jcol >= 0 && 
		  jcol < colFESpace->getAdmin()->getUsedSize())
      ("Column index %d out of range 0-%d\n", jcol, colFESpace->getAdmin()->getUsedSize() - 1);
324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451

    // first entry is diagonal entry
    if(rowFESpace==colFESpace)
      if (rowSize == 0) {
	MatEntry newEntry = {irow, 0.0};
	row->push_back(newEntry);
	rowSize = 1;
      }

    // search jcol
    for(i=0; i < rowSize; i++) {
      // jcol found ?
      if((*row)[i].col == jcol) {
	break;
      }
      // remember free entry
      if((*row)[i].col == UNUSED_ENTRY) {
	freeCol = i;
      }
      // no more entries
      if((*row)[i].col == NO_MORE_ENTRIES) {
	freeCol = i;
	if(rowSize > i+1) {
	  (*row)[i+1].entry = NO_MORE_ENTRIES;
	}
	break;
      }
    }

    // jcol found?
    if(i < rowSize) {
      if(!add) (*row)[i].entry = 0.0;
      (*row)[i].entry += sign * entry;
      result = &((*row)[i].entry);
    } else {
      if(freeCol == -1) {
	MatEntry newEntry = {jcol, sign * entry};
	row->push_back(newEntry);
	result = &((*row)[row->size() - 1].entry);
      } else {
	(*row)[freeCol].col = jcol;
	if(!add) (*row)[freeCol].entry = 0.0;
	(*row)[freeCol].entry += sign * entry;
	result = &((*row)[freeCol].entry);
      }
    }
  
    return result;
  }

  void DOFMatrix::addMatEntry(int row, MatEntry entry)
  {
    matrix[row].push_back(entry);
  }

  void DOFMatrix::addMatEntry(int row,  DegreeOfFreedom col, double value)
  {
    MatEntry entry;
    entry.col = col;
    entry.entry = value;
    matrix[row].push_back(entry);
  }

  void DOFMatrix::addRow(::std::vector<MatEntry> row)
  {
    matrix.push_back(row);
  }

  void DOFMatrix::compressDOFIndexed(int first, int last, 
				     ::std::vector<DegreeOfFreedom> &newDOF)
  {
    int i, j, k, col;
    ::std::vector<MatEntry> *row;

    for(i = first; i <= last; i++) {
      if((k = newDOF[i]) >= 0) {
	matrix[k].swap(matrix[i]);
	matrix[i].resize(0);
      }
    }
    int usedSize = rowFESpace->getAdmin()->getUsedSize();
    for(i=0; i < usedSize; i++) {
      row = reinterpret_cast< ::std::vector<MatEntry>*>(&(matrix[i])); 
      int rowSize = static_cast<int>(row->size());
      for (j=0; j < rowSize; j++) {
	col = (*row)[j].col;
	if (entryUsed(i,j)) (*row)[j].col = newDOF[col];
      }    
    }
  }

  void DOFMatrix::freeDOFContent(int index)
  {
    int        i, j, col=0, col2;

    if (0 < matrix[index].size()) {
      // for all columns in this row
      int size = static_cast<int>(matrix[index].size());
      for (i=0; i<size; i++) {
	// if entry is used
	if (entryUsed(index,i)) {
	  // get column of this entry
	  col = matrix[index][i].col;
	  if (col != index) {  // remove symmetric entry if exists
	    int colsize = static_cast<int>(matrix[col].size());
	    for (j=0; j< colsize; j++) {
	      col2 = matrix[col][j].col;
	      if (col2 == index) {
		matrix[col][j].col = DOFMatrix::UNUSED_ENTRY;
	      }
	      else if (col2 == DOFMatrix::NO_MORE_ENTRIES) {
		break;
	      }
	    }
	  }
	}
	else if (col == DOFMatrix::NO_MORE_ENTRIES) {
	  break;
	}
      }
      matrix[index].resize(0);	
    }
  }


  ElementMatrix *DOFMatrix::assemble(double factor, ElInfo *elInfo, 
				     const BoundaryType *bound, Operator *op)
  {
452
    FUNCNAME("DOFMatrix::assemble()");
453

454
    if (!op && operators.size() == 0) {
455 456
      return NULL;
    }
Thomas Witkowski's avatar
Thomas Witkowski committed
457
    
458
    Operator *operat = op ? op : operators[0];
Thomas Witkowski's avatar
Thomas Witkowski committed
459
    
460 461
    elementMatrix = 
      operat->getAssembler()->initElementMatrix(elementMatrix, elInfo);
Thomas Witkowski's avatar
Thomas Witkowski committed
462
    
463
    if (op) {
464 465 466 467
      op->getElementMatrix(elInfo, elementMatrix);
    } else {
      ::std::vector<Operator*>::iterator it;
      ::std::vector<double*>::iterator factorIt;
468
      for (it = operators.begin(), factorIt = operatorFactor.begin();	
469 470 471 472 473 474 475
	  it != operators.end(); 
	  ++it, ++factorIt) 
	{
	  (*it)->getElementMatrix(elInfo, 
				  elementMatrix, 
				  *factorIt ? **factorIt : 1.0);
	}
Thomas Witkowski's avatar
Thomas Witkowski committed
476
      
477
    }
Thomas Witkowski's avatar
Thomas Witkowski committed
478
    
479
    addElementMatrix(factor, *elementMatrix, bound);
Thomas Witkowski's avatar
Thomas Witkowski committed
480
    
481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502
    return elementMatrix;
  }

  Flag DOFMatrix::getAssembleFlag()
  {
    Flag fillFlag(0);
    ::std::vector<Operator*>::iterator op;
    for(op = operators.begin(); op != operators.end(); ++op) {
      fillFlag |= (*op)->getFillFlag();
    }
    return fillFlag;
  }

  void DOFMatrix::mm(MatrixTranspose aTranspose,
		     DOFMatrix& a, 
		     MatrixTranspose bTranspose,
		     DOFMatrix& b)
  {
    FUNCNAME("DOFMatrix::mm()");

    WARNING("implementation not finished!!!\n");

503
    TEST_EXIT_DBG(a.getColFESpace() == b.getRowFESpace())
504
      ("a.colFESpace != b.rowFESpace\n");
505
    TEST_EXIT_DBG(rowFESpace == a.getRowFESpace())
506
      ("rowFESpace != a.rowFESpace\n");  
507
    TEST_EXIT_DBG(colFESpace == b.getColFESpace())
508 509 510 511
      ("colFESpace != b.colFESpace\n");  

    clear();

512
    int i, j;
513

514
    if (aTranspose == NoTranspose && bTranspose == NoTranspose) {
515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573
      int cols  = b.getColFESpace()->getAdmin()->getUsedSize();
      DOFMatrix::Iterator rowIterator(this, USED_DOFS);

      // for every row ...
      for(rowIterator.reset(); !rowIterator.end(); ++rowIterator) {
	int rowIndex = rowIterator.getDOFIndex();
	// and every column of result   
	for(i=0; i < cols; i++) {
	  double entry = 0.0;
	  // for every entry in a[i] ...
	  for(j=0; j < static_cast<int>( a[rowIndex].size()); j++) {
	    int logIndex = a[rowIndex][j].col;
	    int physIndex = b.logToPhysIndex(logIndex, i);
	    if(physIndex != -1) {
	      entry += a[rowIndex][j].entry * b[logIndex][physIndex].entry;
	    }
	  }
	  if(entry != 0.0) {
	    addSparseDOFEntry(1.0, rowIndex, i, entry);
	  }
	}
      }
    } else if(aTranspose == Transpose && bTranspose == NoTranspose) {
      DOFMatrix::Iterator aIterator(&a, USED_DOFS);
      DOFMatrix::Iterator bIterator(&b, USED_DOFS);
      for(aIterator.reset(), bIterator.reset(); 
	  !aIterator.end(); 
	  ++aIterator, ++bIterator) 
	{
	  ::std::vector<MatEntry>::const_iterator aRowIt;
	  ::std::vector<MatEntry>::const_iterator bRowIt;
	  for(aRowIt = aIterator->begin(); aRowIt != aIterator->end(); ++aRowIt) {
	    int aCol = aRowIt->col;
	    if(aCol == UNUSED_ENTRY) continue;
	    if(aCol == NO_MORE_ENTRIES) break;
	    for(bRowIt = bIterator->begin(); bRowIt !=bIterator->end(); ++bRowIt) {
	      int bCol = bRowIt->col;
	      if(bCol == UNUSED_ENTRY) continue;
	      if(bCol == NO_MORE_ENTRIES) break;

	      double entry = aRowIt->entry * bRowIt->entry;

	      if(entry != 0.0) {
		addSparseDOFEntry(1.0, aCol, bCol, entry);	    
	      }
	    }
	  }
	}
    } else if(aTranspose == NoTranspose && bTranspose == Transpose) {
      ERROR_EXIT("not yet\n");
    } else if(aTranspose == Transpose && bTranspose == Transpose) {
      ERROR_EXIT("not yet\n");
    }
  }

  void DOFMatrix::axpy(double a, 
		       const DOFMatrix& x,
		       const DOFMatrix& y)
  {
574 575 576 577
    FUNCNAME("DOFMatrix::axpy()");

    TEST_EXIT_DBG(x.getRowFESpace() == y.getRowFESpace() &&
		  rowFESpace == x.getRowFESpace())
578
      ("row fe-spaces not equal\n");
579 580
    TEST_EXIT_DBG(x.getColFESpace() == y.getColFESpace() &&
		  colFESpace == x.getColFESpace())
581
      ("col fe-spaces not equal\n");
582
    
583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667
    DOFMatrix::Iterator rowIterator(this, USED_DOFS);
    DOFMatrix::Iterator xIterator(const_cast<DOFMatrix*>(&x), USED_DOFS);
    DOFMatrix::Iterator yIterator(const_cast<DOFMatrix*>(&y), USED_DOFS);

    int i, rowIndex, colIndex;

    for(rowIterator.reset(), xIterator.reset(), yIterator.reset();
	!rowIterator.end();
	++rowIterator, ++xIterator, ++yIterator)
      {
	rowIndex = rowIterator.getDOFIndex();
	// add x contributions to this row
	for(i=0; i < static_cast<int>((*xIterator).size()); i++) {
	  colIndex = (*xIterator)[i].col;
	  if(colIndex >= 0) {
	    addSparseDOFEntry(a, rowIndex, colIndex, (*xIterator)[i].entry);
	  }
	}
	// add y contributions to this row
	for(i=0; i < static_cast<int>((*yIterator).size()); i++) {
	  colIndex = (*yIterator)[i].col;
	  if(colIndex >= 0) {
	    addSparseDOFEntry(1.0, rowIndex, colIndex, (*yIterator)[i].entry);
	  }
	}
      }
  }

  void DOFMatrix::scal(double b) 
  {
    int i;
    DOFMatrix::Iterator rowIterator(this, USED_DOFS);
    for(rowIterator.reset(); !rowIterator.end(); ++rowIterator) {
      for(i=0; i < static_cast<int>((*rowIterator).size()); i++) {
	if((*rowIterator)[i].col >= 0) {
	  (*rowIterator)[i].entry *= b;
	}
      }
    }
  }

  void DOFMatrix::copy(const DOFMatrix& rhs) 
  {
    clear();
    DOFMatrix::Iterator rhsIterator(const_cast<DOFMatrix*>(&rhs), USED_DOFS);
    DOFMatrix::Iterator thisIterator(this, USED_DOFS);
    ::std::vector<MatEntry>::const_iterator colIt;
    ::std::vector<MatEntry>::const_iterator colBegin;
    ::std::vector<MatEntry>::const_iterator colEnd;
    for(rhsIterator.reset(), thisIterator.reset();
	!rhsIterator.end(); 
	++rhsIterator, ++thisIterator) 
      {
	colBegin = rhsIterator->begin();
	colEnd = rhsIterator->end();
	for(colIt = colBegin; colIt != colEnd; ++colIt) {
	  MatEntry matEntry;
	  matEntry.col = colIt->col;
	  matEntry.entry = colIt->entry;
	  thisIterator->push_back(matEntry);
	}
      }
  }

  void DOFMatrix::createPictureFile(const char* filename, int dim)
  {
    png_structp png_ptr = png_create_write_struct(PNG_LIBPNG_VER_STRING, NULL, NULL, NULL);

    if (!png_ptr)
       return;

    png_bytep rowPointers[dim];
    for (int i = 0; i < dim; i++) {
      rowPointers[i] = (png_byte*)png_malloc(png_ptr, dim);

      for (int j = 0; j < dim; j++) {
	rowPointers[i][j] = 255;
      }
    }

    double scalFactor = static_cast<double>(dim) / static_cast<double>(matrix.size());

    for (int i = 0; i < static_cast<int>(matrix.size()); i++) {    
      int pi = static_cast<int>(static_cast<double>(i) * scalFactor);

668
      TEST_EXIT_DBG((pi >= 0) && (pi < dim))("PI");
669 670 671 672 673

      for (int j = 0; j < static_cast<int>(matrix[i].size()); j++) {
	
	int pj = static_cast<int>(static_cast<double>(matrix[i][j].col) * scalFactor);

674
	TEST_EXIT_DBG((pj >= 0) && (pj < dim))("PJ");
675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765

	rowPointers[pi][pj] = 0;
      }
    }
   
    FILE *fp = fopen(filename, "wb");
    TEST_EXIT(fp)("Cannot open file for writing matrix picture file!\n");

    png_infop info_ptr = png_create_info_struct(png_ptr);

    if (!info_ptr) {
       png_destroy_write_struct(&png_ptr, (png_infopp)NULL);
       return;
    }

    png_init_io(png_ptr, fp);

    png_set_IHDR(png_ptr, info_ptr, dim, dim, 8,
		 PNG_COLOR_TYPE_GRAY, 
		 PNG_INTERLACE_NONE,
		 PNG_COMPRESSION_TYPE_DEFAULT,
		 PNG_FILTER_TYPE_DEFAULT);

    png_set_rows(png_ptr, info_ptr, rowPointers);

    png_write_png(png_ptr, info_ptr, PNG_TRANSFORM_IDENTITY, NULL);

    png_destroy_write_struct(&png_ptr, &info_ptr);

    fclose(fp);
  }


  int DOFMatrix::memsize() 
  {   
    int sizeDOFMatrix = sizeof(DOFMatrix);   
    int sizeMatrix = sizeof(::std::vector<MatrixRow>);
    for (int i = 0; i < static_cast<int>(matrix.size()); i++) {
      sizeMatrix += sizeof(MatrixRow) + matrix[i].size() * sizeof(MatEntry);
    }
    
    return sizeDOFMatrix + sizeMatrix;
  }


  double norm(::std::vector<MatEntry> *row)
  {
    double result = 0.0;
    ::std::vector<MatEntry>::iterator it;
    for (it = row->begin(); it < row->end(); ++it) {
      result += (*it).entry * (*it).entry;
    }

    return(sqrt(result));
  }

  double min(::std::vector<MatEntry> *row)
  {
    double result = 0.0;
    if (row->size() > 0) {
      result = (*row)[0].entry;
    }

    ::std::vector<MatEntry>::iterator it;
    for (it = row->begin(); it < row->end(); ++it) {
      if ((*it).entry < result) {
	result = (*it).entry;
      }
    }

    return(result);
  }

  double max(::std::vector<MatEntry> *row)
  {
    double result = 0.0;
    if (row->size() > 0) {
      result = (*row)[0].entry;
    }

    ::std::vector<MatEntry>::iterator it;
    for (it = row->begin(); it < row->end(); ++it) {
      if ((*it).entry > result) {
	result = (*it).entry;
      }
    }

    return(result);
  }

}