1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
5// Copyright (C) 2008 Daniel Gomez Ferro <dgomezferro@gmail.com>
6// Copyright (C) 2013 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
7//
8// This Source Code Form is subject to the terms of the Mozilla
9// Public License v. 2.0. If a copy of the MPL was not distributed
10// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
11
12#include "sparse.h"
13
14template<typename SparseMatrixType> void sparse_basic(const SparseMatrixType& ref)
15{
16  typedef typename SparseMatrixType::Index Index;
17  typedef Matrix<Index,2,1> Vector2;
18
19  const Index rows = ref.rows();
20  const Index cols = ref.cols();
21  typedef typename SparseMatrixType::Scalar Scalar;
22  enum { Flags = SparseMatrixType::Flags };
23
24  double density = (std::max)(8./(rows*cols), 0.01);
25  typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
26  typedef Matrix<Scalar,Dynamic,1> DenseVector;
27  typedef Matrix<Scalar,1,Dynamic> RowDenseVector;
28  Scalar eps = 1e-6;
29
30  Scalar s1 = internal::random<Scalar>();
31  {
32    SparseMatrixType m(rows, cols);
33    DenseMatrix refMat = DenseMatrix::Zero(rows, cols);
34    DenseVector vec1 = DenseVector::Random(rows);
35
36    std::vector<Vector2> zeroCoords;
37    std::vector<Vector2> nonzeroCoords;
38    initSparse<Scalar>(density, refMat, m, 0, &zeroCoords, &nonzeroCoords);
39
40    if (zeroCoords.size()==0 || nonzeroCoords.size()==0)
41      return;
42
43    // test coeff and coeffRef
44    for (int i=0; i<(int)zeroCoords.size(); ++i)
45    {
46      VERIFY_IS_MUCH_SMALLER_THAN( m.coeff(zeroCoords[i].x(),zeroCoords[i].y()), eps );
47      if(internal::is_same<SparseMatrixType,SparseMatrix<Scalar,Flags> >::value)
48        VERIFY_RAISES_ASSERT( m.coeffRef(zeroCoords[0].x(),zeroCoords[0].y()) = 5 );
49    }
50    VERIFY_IS_APPROX(m, refMat);
51
52    m.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5);
53    refMat.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5);
54
55    VERIFY_IS_APPROX(m, refMat);
56
57      // test InnerIterators and Block expressions
58      for (int t=0; t<10; ++t)
59      {
60        int j = internal::random<int>(0,cols-1);
61        int i = internal::random<int>(0,rows-1);
62        int w = internal::random<int>(1,cols-j-1);
63        int h = internal::random<int>(1,rows-i-1);
64
65        VERIFY_IS_APPROX(m.block(i,j,h,w), refMat.block(i,j,h,w));
66        for(int c=0; c<w; c++)
67        {
68          VERIFY_IS_APPROX(m.block(i,j,h,w).col(c), refMat.block(i,j,h,w).col(c));
69          for(int r=0; r<h; r++)
70          {
71            VERIFY_IS_APPROX(m.block(i,j,h,w).col(c).coeff(r), refMat.block(i,j,h,w).col(c).coeff(r));
72            VERIFY_IS_APPROX(m.block(i,j,h,w).coeff(r,c), refMat.block(i,j,h,w).coeff(r,c));
73          }
74        }
75        for(int r=0; r<h; r++)
76        {
77          VERIFY_IS_APPROX(m.block(i,j,h,w).row(r), refMat.block(i,j,h,w).row(r));
78          for(int c=0; c<w; c++)
79          {
80            VERIFY_IS_APPROX(m.block(i,j,h,w).row(r).coeff(c), refMat.block(i,j,h,w).row(r).coeff(c));
81            VERIFY_IS_APPROX(m.block(i,j,h,w).coeff(r,c), refMat.block(i,j,h,w).coeff(r,c));
82          }
83        }
84
85        VERIFY_IS_APPROX(m.middleCols(j,w), refMat.middleCols(j,w));
86        VERIFY_IS_APPROX(m.middleRows(i,h), refMat.middleRows(i,h));
87        for(int r=0; r<h; r++)
88        {
89          VERIFY_IS_APPROX(m.middleCols(j,w).row(r), refMat.middleCols(j,w).row(r));
90          VERIFY_IS_APPROX(m.middleRows(i,h).row(r), refMat.middleRows(i,h).row(r));
91          for(int c=0; c<w; c++)
92          {
93            VERIFY_IS_APPROX(m.col(c).coeff(r), refMat.col(c).coeff(r));
94            VERIFY_IS_APPROX(m.row(r).coeff(c), refMat.row(r).coeff(c));
95
96            VERIFY_IS_APPROX(m.middleCols(j,w).coeff(r,c), refMat.middleCols(j,w).coeff(r,c));
97            VERIFY_IS_APPROX(m.middleRows(i,h).coeff(r,c), refMat.middleRows(i,h).coeff(r,c));
98            if(m.middleCols(j,w).coeff(r,c) != Scalar(0))
99            {
100              VERIFY_IS_APPROX(m.middleCols(j,w).coeffRef(r,c), refMat.middleCols(j,w).coeff(r,c));
101            }
102            if(m.middleRows(i,h).coeff(r,c) != Scalar(0))
103            {
104              VERIFY_IS_APPROX(m.middleRows(i,h).coeff(r,c), refMat.middleRows(i,h).coeff(r,c));
105            }
106          }
107        }
108        for(int c=0; c<w; c++)
109        {
110          VERIFY_IS_APPROX(m.middleCols(j,w).col(c), refMat.middleCols(j,w).col(c));
111          VERIFY_IS_APPROX(m.middleRows(i,h).col(c), refMat.middleRows(i,h).col(c));
112        }
113      }
114
115      for(int c=0; c<cols; c++)
116      {
117        VERIFY_IS_APPROX(m.col(c) + m.col(c), (m + m).col(c));
118        VERIFY_IS_APPROX(m.col(c) + m.col(c), refMat.col(c) + refMat.col(c));
119      }
120
121      for(int r=0; r<rows; r++)
122      {
123        VERIFY_IS_APPROX(m.row(r) + m.row(r), (m + m).row(r));
124        VERIFY_IS_APPROX(m.row(r) + m.row(r), refMat.row(r) + refMat.row(r));
125      }
126
127
128      // test assertion
129      VERIFY_RAISES_ASSERT( m.coeffRef(-1,1) = 0 );
130      VERIFY_RAISES_ASSERT( m.coeffRef(0,m.cols()) = 0 );
131    }
132
133    // test insert (inner random)
134    {
135      DenseMatrix m1(rows,cols);
136      m1.setZero();
137      SparseMatrixType m2(rows,cols);
138      if(internal::random<int>()%2)
139        m2.reserve(VectorXi::Constant(m2.outerSize(), 2));
140      for (Index j=0; j<cols; ++j)
141      {
142        for (Index k=0; k<rows/2; ++k)
143        {
144          Index i = internal::random<Index>(0,rows-1);
145          if (m1.coeff(i,j)==Scalar(0))
146            m2.insert(i,j) = m1(i,j) = internal::random<Scalar>();
147        }
148      }
149      m2.finalize();
150      VERIFY_IS_APPROX(m2,m1);
151    }
152
153    // test insert (fully random)
154    {
155      DenseMatrix m1(rows,cols);
156      m1.setZero();
157      SparseMatrixType m2(rows,cols);
158      if(internal::random<int>()%2)
159        m2.reserve(VectorXi::Constant(m2.outerSize(), 2));
160      for (int k=0; k<rows*cols; ++k)
161      {
162        Index i = internal::random<Index>(0,rows-1);
163        Index j = internal::random<Index>(0,cols-1);
164        if ((m1.coeff(i,j)==Scalar(0)) && (internal::random<int>()%2))
165          m2.insert(i,j) = m1(i,j) = internal::random<Scalar>();
166        else
167        {
168          Scalar v = internal::random<Scalar>();
169          m2.coeffRef(i,j) += v;
170          m1(i,j) += v;
171        }
172      }
173      VERIFY_IS_APPROX(m2,m1);
174    }
175
176    // test insert (un-compressed)
177    for(int mode=0;mode<4;++mode)
178    {
179      DenseMatrix m1(rows,cols);
180      m1.setZero();
181      SparseMatrixType m2(rows,cols);
182      VectorXi r(VectorXi::Constant(m2.outerSize(), ((mode%2)==0) ? m2.innerSize() : std::max<int>(1,m2.innerSize()/8)));
183      m2.reserve(r);
184      for (int k=0; k<rows*cols; ++k)
185      {
186        Index i = internal::random<Index>(0,rows-1);
187        Index j = internal::random<Index>(0,cols-1);
188        if (m1.coeff(i,j)==Scalar(0))
189          m2.insert(i,j) = m1(i,j) = internal::random<Scalar>();
190        if(mode==3)
191          m2.reserve(r);
192      }
193      if(internal::random<int>()%2)
194        m2.makeCompressed();
195      VERIFY_IS_APPROX(m2,m1);
196    }
197
198  // test innerVector()
199  {
200    DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
201    SparseMatrixType m2(rows, rows);
202    initSparse<Scalar>(density, refMat2, m2);
203    Index j0 = internal::random<Index>(0,rows-1);
204    Index j1 = internal::random<Index>(0,rows-1);
205    if(SparseMatrixType::IsRowMajor)
206      VERIFY_IS_APPROX(m2.innerVector(j0), refMat2.row(j0));
207    else
208      VERIFY_IS_APPROX(m2.innerVector(j0), refMat2.col(j0));
209
210    if(SparseMatrixType::IsRowMajor)
211      VERIFY_IS_APPROX(m2.innerVector(j0)+m2.innerVector(j1), refMat2.row(j0)+refMat2.row(j1));
212    else
213      VERIFY_IS_APPROX(m2.innerVector(j0)+m2.innerVector(j1), refMat2.col(j0)+refMat2.col(j1));
214
215    SparseMatrixType m3(rows,rows);
216    m3.reserve(VectorXi::Constant(rows,rows/2));
217    for(Index j=0; j<rows; ++j)
218      for(Index k=0; k<j; ++k)
219        m3.insertByOuterInner(j,k) = k+1;
220    for(Index j=0; j<rows; ++j)
221    {
222      VERIFY(j==numext::real(m3.innerVector(j).nonZeros()));
223      if(j>0)
224        VERIFY(j==numext::real(m3.innerVector(j).lastCoeff()));
225    }
226    m3.makeCompressed();
227    for(Index j=0; j<rows; ++j)
228    {
229      VERIFY(j==numext::real(m3.innerVector(j).nonZeros()));
230      if(j>0)
231        VERIFY(j==numext::real(m3.innerVector(j).lastCoeff()));
232    }
233
234    //m2.innerVector(j0) = 2*m2.innerVector(j1);
235    //refMat2.col(j0) = 2*refMat2.col(j1);
236    //VERIFY_IS_APPROX(m2, refMat2);
237  }
238
239  // test innerVectors()
240  {
241    DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
242    SparseMatrixType m2(rows, rows);
243    initSparse<Scalar>(density, refMat2, m2);
244    if(internal::random<float>(0,1)>0.5) m2.makeCompressed();
245
246    Index j0 = internal::random<Index>(0,rows-2);
247    Index j1 = internal::random<Index>(0,rows-2);
248    Index n0 = internal::random<Index>(1,rows-(std::max)(j0,j1));
249    if(SparseMatrixType::IsRowMajor)
250      VERIFY_IS_APPROX(m2.innerVectors(j0,n0), refMat2.block(j0,0,n0,cols));
251    else
252      VERIFY_IS_APPROX(m2.innerVectors(j0,n0), refMat2.block(0,j0,rows,n0));
253    if(SparseMatrixType::IsRowMajor)
254      VERIFY_IS_APPROX(m2.innerVectors(j0,n0)+m2.innerVectors(j1,n0),
255                       refMat2.middleRows(j0,n0)+refMat2.middleRows(j1,n0));
256    else
257      VERIFY_IS_APPROX(m2.innerVectors(j0,n0)+m2.innerVectors(j1,n0),
258                      refMat2.block(0,j0,rows,n0)+refMat2.block(0,j1,rows,n0));
259
260    VERIFY_IS_APPROX(m2, refMat2);
261
262    m2.innerVectors(j0,n0) = m2.innerVectors(j0,n0) + m2.innerVectors(j1,n0);
263    if(SparseMatrixType::IsRowMajor)
264      refMat2.middleRows(j0,n0) = (refMat2.middleRows(j0,n0) + refMat2.middleRows(j1,n0)).eval();
265    else
266      refMat2.middleCols(j0,n0) = (refMat2.middleCols(j0,n0) + refMat2.middleCols(j1,n0)).eval();
267
268    VERIFY_IS_APPROX(m2, refMat2);
269
270  }
271
272  // test basic computations
273  {
274    DenseMatrix refM1 = DenseMatrix::Zero(rows, rows);
275    DenseMatrix refM2 = DenseMatrix::Zero(rows, rows);
276    DenseMatrix refM3 = DenseMatrix::Zero(rows, rows);
277    DenseMatrix refM4 = DenseMatrix::Zero(rows, rows);
278    SparseMatrixType m1(rows, rows);
279    SparseMatrixType m2(rows, rows);
280    SparseMatrixType m3(rows, rows);
281    SparseMatrixType m4(rows, rows);
282    initSparse<Scalar>(density, refM1, m1);
283    initSparse<Scalar>(density, refM2, m2);
284    initSparse<Scalar>(density, refM3, m3);
285    initSparse<Scalar>(density, refM4, m4);
286
287    VERIFY_IS_APPROX(m1+m2, refM1+refM2);
288    VERIFY_IS_APPROX(m1+m2+m3, refM1+refM2+refM3);
289    VERIFY_IS_APPROX(m3.cwiseProduct(m1+m2), refM3.cwiseProduct(refM1+refM2));
290    VERIFY_IS_APPROX(m1*s1-m2, refM1*s1-refM2);
291
292    VERIFY_IS_APPROX(m1*=s1, refM1*=s1);
293    VERIFY_IS_APPROX(m1/=s1, refM1/=s1);
294
295    VERIFY_IS_APPROX(m1+=m2, refM1+=refM2);
296    VERIFY_IS_APPROX(m1-=m2, refM1-=refM2);
297
298    if(SparseMatrixType::IsRowMajor)
299      VERIFY_IS_APPROX(m1.innerVector(0).dot(refM2.row(0)), refM1.row(0).dot(refM2.row(0)));
300    else
301      VERIFY_IS_APPROX(m1.innerVector(0).dot(refM2.row(0)), refM1.col(0).dot(refM2.row(0)));
302
303    VERIFY_IS_APPROX(m1.conjugate(), refM1.conjugate());
304    VERIFY_IS_APPROX(m1.real(), refM1.real());
305
306    refM4.setRandom();
307    // sparse cwise* dense
308    VERIFY_IS_APPROX(m3.cwiseProduct(refM4), refM3.cwiseProduct(refM4));
309//     VERIFY_IS_APPROX(m3.cwise()/refM4, refM3.cwise()/refM4);
310
311    // test aliasing
312    VERIFY_IS_APPROX((m1 = -m1), (refM1 = -refM1));
313    VERIFY_IS_APPROX((m1 = m1.transpose()), (refM1 = refM1.transpose().eval()));
314    VERIFY_IS_APPROX((m1 = -m1.transpose()), (refM1 = -refM1.transpose().eval()));
315    VERIFY_IS_APPROX((m1 += -m1), (refM1 += -refM1));
316  }
317
318  // test transpose
319  {
320    DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
321    SparseMatrixType m2(rows, rows);
322    initSparse<Scalar>(density, refMat2, m2);
323    VERIFY_IS_APPROX(m2.transpose().eval(), refMat2.transpose().eval());
324    VERIFY_IS_APPROX(m2.transpose(), refMat2.transpose());
325
326    VERIFY_IS_APPROX(SparseMatrixType(m2.adjoint()), refMat2.adjoint());
327  }
328
329
330
331  // test generic blocks
332  {
333    DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
334    SparseMatrixType m2(rows, rows);
335    initSparse<Scalar>(density, refMat2, m2);
336    Index j0 = internal::random<Index>(0,rows-2);
337    Index j1 = internal::random<Index>(0,rows-2);
338    Index n0 = internal::random<Index>(1,rows-(std::max)(j0,j1));
339    if(SparseMatrixType::IsRowMajor)
340      VERIFY_IS_APPROX(m2.block(j0,0,n0,cols), refMat2.block(j0,0,n0,cols));
341    else
342      VERIFY_IS_APPROX(m2.block(0,j0,rows,n0), refMat2.block(0,j0,rows,n0));
343
344    if(SparseMatrixType::IsRowMajor)
345      VERIFY_IS_APPROX(m2.block(j0,0,n0,cols)+m2.block(j1,0,n0,cols),
346                      refMat2.block(j0,0,n0,cols)+refMat2.block(j1,0,n0,cols));
347    else
348      VERIFY_IS_APPROX(m2.block(0,j0,rows,n0)+m2.block(0,j1,rows,n0),
349                      refMat2.block(0,j0,rows,n0)+refMat2.block(0,j1,rows,n0));
350
351    Index i = internal::random<Index>(0,m2.outerSize()-1);
352    if(SparseMatrixType::IsRowMajor) {
353      m2.innerVector(i) = m2.innerVector(i) * s1;
354      refMat2.row(i) = refMat2.row(i) * s1;
355      VERIFY_IS_APPROX(m2,refMat2);
356    } else {
357      m2.innerVector(i) = m2.innerVector(i) * s1;
358      refMat2.col(i) = refMat2.col(i) * s1;
359      VERIFY_IS_APPROX(m2,refMat2);
360    }
361
362    VERIFY_IS_APPROX(DenseVector(m2.col(j0)), refMat2.col(j0));
363    VERIFY_IS_APPROX(m2.col(j0), refMat2.col(j0));
364
365    VERIFY_IS_APPROX(RowDenseVector(m2.row(j0)), refMat2.row(j0));
366    VERIFY_IS_APPROX(m2.row(j0), refMat2.row(j0));
367
368    VERIFY_IS_APPROX(m2.block(j0,j1,n0,n0), refMat2.block(j0,j1,n0,n0));
369    VERIFY_IS_APPROX((2*m2).block(j0,j1,n0,n0), (2*refMat2).block(j0,j1,n0,n0));
370  }
371
372  // test prune
373  {
374    SparseMatrixType m2(rows, rows);
375    DenseMatrix refM2(rows, rows);
376    refM2.setZero();
377    int countFalseNonZero = 0;
378    int countTrueNonZero = 0;
379    for (Index j=0; j<m2.outerSize(); ++j)
380    {
381      m2.startVec(j);
382      for (Index i=0; i<m2.innerSize(); ++i)
383      {
384        float x = internal::random<float>(0,1);
385        if (x<0.1)
386        {
387          // do nothing
388        }
389        else if (x<0.5)
390        {
391          countFalseNonZero++;
392          m2.insertBackByOuterInner(j,i) = Scalar(0);
393        }
394        else
395        {
396          countTrueNonZero++;
397          m2.insertBackByOuterInner(j,i) = Scalar(1);
398          if(SparseMatrixType::IsRowMajor)
399            refM2(j,i) = Scalar(1);
400          else
401            refM2(i,j) = Scalar(1);
402        }
403      }
404    }
405    m2.finalize();
406    VERIFY(countFalseNonZero+countTrueNonZero == m2.nonZeros());
407    VERIFY_IS_APPROX(m2, refM2);
408    m2.prune(Scalar(1));
409    VERIFY(countTrueNonZero==m2.nonZeros());
410    VERIFY_IS_APPROX(m2, refM2);
411  }
412
413  // test setFromTriplets
414  {
415    typedef Triplet<Scalar,Index> TripletType;
416    std::vector<TripletType> triplets;
417    int ntriplets = rows*cols;
418    triplets.reserve(ntriplets);
419    DenseMatrix refMat(rows,cols);
420    refMat.setZero();
421    for(int i=0;i<ntriplets;++i)
422    {
423      Index r = internal::random<Index>(0,rows-1);
424      Index c = internal::random<Index>(0,cols-1);
425      Scalar v = internal::random<Scalar>();
426      triplets.push_back(TripletType(r,c,v));
427      refMat(r,c) += v;
428    }
429    SparseMatrixType m(rows,cols);
430    m.setFromTriplets(triplets.begin(), triplets.end());
431    VERIFY_IS_APPROX(m, refMat);
432  }
433
434  // test triangularView
435  {
436    DenseMatrix refMat2(rows, rows), refMat3(rows, rows);
437    SparseMatrixType m2(rows, rows), m3(rows, rows);
438    initSparse<Scalar>(density, refMat2, m2);
439    refMat3 = refMat2.template triangularView<Lower>();
440    m3 = m2.template triangularView<Lower>();
441    VERIFY_IS_APPROX(m3, refMat3);
442
443    refMat3 = refMat2.template triangularView<Upper>();
444    m3 = m2.template triangularView<Upper>();
445    VERIFY_IS_APPROX(m3, refMat3);
446
447    refMat3 = refMat2.template triangularView<UnitUpper>();
448    m3 = m2.template triangularView<UnitUpper>();
449    VERIFY_IS_APPROX(m3, refMat3);
450
451    refMat3 = refMat2.template triangularView<UnitLower>();
452    m3 = m2.template triangularView<UnitLower>();
453    VERIFY_IS_APPROX(m3, refMat3);
454
455    refMat3 = refMat2.template triangularView<StrictlyUpper>();
456    m3 = m2.template triangularView<StrictlyUpper>();
457    VERIFY_IS_APPROX(m3, refMat3);
458
459    refMat3 = refMat2.template triangularView<StrictlyLower>();
460    m3 = m2.template triangularView<StrictlyLower>();
461    VERIFY_IS_APPROX(m3, refMat3);
462  }
463
464  // test selfadjointView
465  if(!SparseMatrixType::IsRowMajor)
466  {
467    DenseMatrix refMat2(rows, rows), refMat3(rows, rows);
468    SparseMatrixType m2(rows, rows), m3(rows, rows);
469    initSparse<Scalar>(density, refMat2, m2);
470    refMat3 = refMat2.template selfadjointView<Lower>();
471    m3 = m2.template selfadjointView<Lower>();
472    VERIFY_IS_APPROX(m3, refMat3);
473  }
474
475  // test sparseView
476  {
477    DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
478    SparseMatrixType m2(rows, rows);
479    initSparse<Scalar>(density, refMat2, m2);
480    VERIFY_IS_APPROX(m2.eval(), refMat2.sparseView().eval());
481  }
482
483  // test diagonal
484  {
485    DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows);
486    SparseMatrixType m2(rows, rows);
487    initSparse<Scalar>(density, refMat2, m2);
488    VERIFY_IS_APPROX(m2.diagonal(), refMat2.diagonal().eval());
489  }
490
491  // test conservative resize
492  {
493      std::vector< std::pair<Index,Index> > inc;
494      inc.push_back(std::pair<Index,Index>(-3,-2));
495      inc.push_back(std::pair<Index,Index>(0,0));
496      inc.push_back(std::pair<Index,Index>(3,2));
497      inc.push_back(std::pair<Index,Index>(3,0));
498      inc.push_back(std::pair<Index,Index>(0,3));
499
500      for(size_t i = 0; i< inc.size(); i++) {
501        Index incRows = inc[i].first;
502        Index incCols = inc[i].second;
503        SparseMatrixType m1(rows, cols);
504        DenseMatrix refMat1 = DenseMatrix::Zero(rows, cols);
505        initSparse<Scalar>(density, refMat1, m1);
506
507        m1.conservativeResize(rows+incRows, cols+incCols);
508        refMat1.conservativeResize(rows+incRows, cols+incCols);
509        if (incRows > 0) refMat1.bottomRows(incRows).setZero();
510        if (incCols > 0) refMat1.rightCols(incCols).setZero();
511
512        VERIFY_IS_APPROX(m1, refMat1);
513
514        // Insert new values
515        if (incRows > 0)
516          m1.insert(m1.rows()-1, 0) = refMat1(refMat1.rows()-1, 0) = 1;
517        if (incCols > 0)
518          m1.insert(0, m1.cols()-1) = refMat1(0, refMat1.cols()-1) = 1;
519
520        VERIFY_IS_APPROX(m1, refMat1);
521
522
523      }
524  }
525
526  // test Identity matrix
527  {
528    DenseMatrix refMat1 = DenseMatrix::Identity(rows, rows);
529    SparseMatrixType m1(rows, rows);
530    m1.setIdentity();
531    VERIFY_IS_APPROX(m1, refMat1);
532  }
533}
534
535void test_sparse_basic()
536{
537  for(int i = 0; i < g_repeat; i++) {
538    int s = Eigen::internal::random<int>(1,50);
539    EIGEN_UNUSED_VARIABLE(s);
540    CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double>(8, 8)) ));
541    CALL_SUBTEST_2(( sparse_basic(SparseMatrix<std::complex<double>, ColMajor>(s, s)) ));
542    CALL_SUBTEST_2(( sparse_basic(SparseMatrix<std::complex<double>, RowMajor>(s, s)) ));
543    CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double>(s, s)) ));
544    CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double,ColMajor,long int>(s, s)) ));
545    CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double,RowMajor,long int>(s, s)) ));
546
547    CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double,ColMajor,short int>(short(s), short(s))) ));
548    CALL_SUBTEST_1(( sparse_basic(SparseMatrix<double,RowMajor,short int>(short(s), short(s))) ));
549  }
550}
551