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-rw-r--r--eigen/test/sparse_solver.h386
1 files changed, 278 insertions, 108 deletions
diff --git a/eigen/test/sparse_solver.h b/eigen/test/sparse_solver.h
index e1619d6..5145bc3 100644
--- a/eigen/test/sparse_solver.h
+++ b/eigen/test/sparse_solver.h
@@ -9,68 +9,123 @@
#include "sparse.h"
#include <Eigen/SparseCore>
+#include <sstream>
+
+template<typename Solver, typename Rhs, typename Guess,typename Result>
+void solve_with_guess(IterativeSolverBase<Solver>& solver, const MatrixBase<Rhs>& b, const Guess& g, Result &x) {
+ if(internal::random<bool>())
+ {
+ // With a temporary through evaluator<SolveWithGuess>
+ x = solver.derived().solveWithGuess(b,g) + Result::Zero(x.rows(), x.cols());
+ }
+ else
+ {
+ // direct evaluation within x through Assignment<Result,SolveWithGuess>
+ x = solver.derived().solveWithGuess(b.derived(),g);
+ }
+}
+
+template<typename Solver, typename Rhs, typename Guess,typename Result>
+void solve_with_guess(SparseSolverBase<Solver>& solver, const MatrixBase<Rhs>& b, const Guess& , Result& x) {
+ if(internal::random<bool>())
+ x = solver.derived().solve(b) + Result::Zero(x.rows(), x.cols());
+ else
+ x = solver.derived().solve(b);
+}
+
+template<typename Solver, typename Rhs, typename Guess,typename Result>
+void solve_with_guess(SparseSolverBase<Solver>& solver, const SparseMatrixBase<Rhs>& b, const Guess& , Result& x) {
+ x = solver.derived().solve(b);
+}
template<typename Solver, typename Rhs, typename DenseMat, typename DenseRhs>
void check_sparse_solving(Solver& solver, const typename Solver::MatrixType& A, const Rhs& b, const DenseMat& dA, const DenseRhs& db)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
+ typedef typename Mat::StorageIndex StorageIndex;
- DenseRhs refX = dA.lu().solve(db);
+ DenseRhs refX = dA.householderQr().solve(db);
{
- Rhs x(b.rows(), b.cols());
+ Rhs x(A.cols(), b.cols());
Rhs oldb = b;
solver.compute(A);
if (solver.info() != Success)
{
- std::cerr << "sparse solver testing: factorization failed (check_sparse_solving)\n";
- exit(0);
- return;
+ std::cerr << "ERROR | sparse solver testing, factorization failed (" << typeid(Solver).name() << ")\n";
+ VERIFY(solver.info() == Success);
}
x = solver.solve(b);
if (solver.info() != Success)
{
- std::cerr << "sparse solver testing: solving failed\n";
+ std::cerr << "WARNING | sparse solver testing: solving failed (" << typeid(Solver).name() << ")\n";
return;
}
VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
+ VERIFY(x.isApprox(refX,test_precision<Scalar>()));
+ x.setZero();
+ solve_with_guess(solver, b, x, x);
+ VERIFY(solver.info() == Success && "solving failed when using analyzePattern/factorize API");
+ VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
VERIFY(x.isApprox(refX,test_precision<Scalar>()));
+
x.setZero();
// test the analyze/factorize API
solver.analyzePattern(A);
solver.factorize(A);
- if (solver.info() != Success)
- {
- std::cerr << "sparse solver testing: factorization failed (check_sparse_solving)\n";
- exit(0);
- return;
- }
+ VERIFY(solver.info() == Success && "factorization failed when using analyzePattern/factorize API");
x = solver.solve(b);
- if (solver.info() != Success)
- {
- std::cerr << "sparse solver testing: solving failed\n";
- return;
- }
+ VERIFY(solver.info() == Success && "solving failed when using analyzePattern/factorize API");
VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
-
VERIFY(x.isApprox(refX,test_precision<Scalar>()));
- }
-
- // test dense Block as the result and rhs:
- {
- DenseRhs x(db.rows(), db.cols());
- DenseRhs oldb(db);
+
x.setZero();
- x.block(0,0,x.rows(),x.cols()) = solver.solve(db.block(0,0,db.rows(),db.cols()));
- VERIFY(oldb.isApprox(db) && "sparse solver testing: the rhs should not be modified!");
- VERIFY(x.isApprox(refX,test_precision<Scalar>()));
+ // test with Map
+ MappedSparseMatrix<Scalar,Mat::Options,StorageIndex> Am(A.rows(), A.cols(), A.nonZeros(), const_cast<StorageIndex*>(A.outerIndexPtr()), const_cast<StorageIndex*>(A.innerIndexPtr()), const_cast<Scalar*>(A.valuePtr()));
+ solver.compute(Am);
+ VERIFY(solver.info() == Success && "factorization failed when using Map");
+ DenseRhs dx(refX);
+ dx.setZero();
+ Map<DenseRhs> xm(dx.data(), dx.rows(), dx.cols());
+ Map<const DenseRhs> bm(db.data(), db.rows(), db.cols());
+ xm = solver.solve(bm);
+ VERIFY(solver.info() == Success && "solving failed when using Map");
+ VERIFY(oldb.isApprox(bm) && "sparse solver testing: the rhs should not be modified!");
+ VERIFY(xm.isApprox(refX,test_precision<Scalar>()));
}
-
+
// if not too large, do some extra check:
if(A.rows()<2000)
{
+ // test initialization ctor
+ {
+ Rhs x(b.rows(), b.cols());
+ Solver solver2(A);
+ VERIFY(solver2.info() == Success);
+ x = solver2.solve(b);
+ VERIFY(x.isApprox(refX,test_precision<Scalar>()));
+ }
+
+ // test dense Block as the result and rhs:
+ {
+ DenseRhs x(refX.rows(), refX.cols());
+ DenseRhs oldb(db);
+ x.setZero();
+ x.block(0,0,x.rows(),x.cols()) = solver.solve(db.block(0,0,db.rows(),db.cols()));
+ VERIFY(oldb.isApprox(db) && "sparse solver testing: the rhs should not be modified!");
+ VERIFY(x.isApprox(refX,test_precision<Scalar>()));
+ }
+
+ // test uncompressed inputs
+ {
+ Mat A2 = A;
+ A2.reserve((ArrayXf::Random(A.outerSize())+2).template cast<typename Mat::StorageIndex>().eval());
+ solver.compute(A2);
+ Rhs x = solver.solve(b);
+ VERIFY(x.isApprox(refX,test_precision<Scalar>()));
+ }
// test expression as input
{
@@ -86,41 +141,35 @@ void check_sparse_solving(Solver& solver, const typename Solver::MatrixType& A,
}
template<typename Solver, typename Rhs>
-void check_sparse_solving_real_cases(Solver& solver, const typename Solver::MatrixType& A, const Rhs& b, const Rhs& refX)
+void check_sparse_solving_real_cases(Solver& solver, const typename Solver::MatrixType& A, const Rhs& b, const typename Solver::MatrixType& fullA, const Rhs& refX)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
typedef typename Mat::RealScalar RealScalar;
- Rhs x(b.rows(), b.cols());
-
+ Rhs x(A.cols(), b.cols());
+
solver.compute(A);
if (solver.info() != Success)
{
- std::cerr << "sparse solver testing: factorization failed (check_sparse_solving_real_cases)\n";
- exit(0);
- return;
+ std::cerr << "ERROR | sparse solver testing, factorization failed (" << typeid(Solver).name() << ")\n";
+ VERIFY(solver.info() == Success);
}
x = solver.solve(b);
+
if (solver.info() != Success)
{
- std::cerr << "sparse solver testing: solving failed\n";
+ std::cerr << "WARNING | sparse solver testing, solving failed (" << typeid(Solver).name() << ")\n";
return;
}
- RealScalar res_error;
- // Compute the norm of the relative error
- if(refX.size() != 0)
- res_error = (refX - x).norm()/refX.norm();
- else
- {
- // Compute the relative residual norm
- res_error = (b - A * x).norm()/b.norm();
- }
- if (res_error > test_precision<Scalar>() ){
- std::cerr << "Test " << g_test_stack.back() << " failed in "EI_PP_MAKE_STRING(__FILE__)
- << " (" << EI_PP_MAKE_STRING(__LINE__) << ")" << std::endl << std::endl;
- abort();
+ RealScalar res_error = (fullA*x-b).norm()/b.norm();
+ VERIFY( (res_error <= test_precision<Scalar>() ) && "sparse solver failed without noticing it");
+
+
+ if(refX.size() != 0 && (refX - x).norm()/refX.norm() > test_precision<Scalar>())
+ {
+ std::cerr << "WARNING | found solution is different from the provided reference one\n";
}
}
@@ -133,7 +182,7 @@ void check_sparse_determinant(Solver& solver, const typename Solver::MatrixType&
solver.compute(A);
if (solver.info() != Success)
{
- std::cerr << "sparse solver testing: factorization failed (check_sparse_determinant)\n";
+ std::cerr << "WARNING | sparse solver testing: factorization failed (check_sparse_determinant)\n";
return;
}
@@ -150,7 +199,7 @@ void check_sparse_abs_determinant(Solver& solver, const typename Solver::MatrixT
solver.compute(A);
if (solver.info() != Success)
{
- std::cerr << "sparse solver testing: factorization failed (check_sparse_abs_determinant)\n";
+ std::cerr << "WARNING | sparse solver testing: factorization failed (check_sparse_abs_determinant)\n";
return;
}
@@ -197,13 +246,33 @@ inline std::string get_matrixfolder()
mat_folder = mat_folder + static_cast<std::string>("/real/");
return mat_folder;
}
+std::string sym_to_string(int sym)
+{
+ if(sym==Symmetric) return "Symmetric ";
+ if(sym==SPD) return "SPD ";
+ return "";
+}
+template<typename Derived>
+std::string solver_stats(const IterativeSolverBase<Derived> &solver)
+{
+ std::stringstream ss;
+ ss << solver.iterations() << " iters, error: " << solver.error();
+ return ss.str();
+}
+template<typename Derived>
+std::string solver_stats(const SparseSolverBase<Derived> &/*solver*/)
+{
+ return "";
+}
#endif
-template<typename Solver> void check_sparse_spd_solving(Solver& solver)
+template<typename Solver> void check_sparse_spd_solving(Solver& solver, int maxSize = 300, int maxRealWorldSize = 100000)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
- typedef SparseMatrix<Scalar,ColMajor> SpMat;
+ typedef typename Mat::StorageIndex StorageIndex;
+ typedef SparseMatrix<Scalar,ColMajor, StorageIndex> SpMat;
+ typedef SparseVector<Scalar, 0, StorageIndex> SpVec;
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
typedef Matrix<Scalar,Dynamic,1> DenseVector;
@@ -211,7 +280,7 @@ template<typename Solver> void check_sparse_spd_solving(Solver& solver)
Mat A, halfA;
DenseMatrix dA;
for (int i = 0; i < g_repeat; i++) {
- int size = generate_sparse_spd_problem(solver, A, halfA, dA);
+ int size = generate_sparse_spd_problem(solver, A, halfA, dA, maxSize);
// generate the right hand sides
int rhsCols = internal::random<int>(1,16);
@@ -220,13 +289,17 @@ template<typename Solver> void check_sparse_spd_solving(Solver& solver)
DenseVector b = DenseVector::Random(size);
DenseMatrix dB(size,rhsCols);
initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);
+ SpVec c = B.col(0);
+ DenseVector dc = dB.col(0);
- check_sparse_solving(solver, A, b, dA, b);
- check_sparse_solving(solver, halfA, b, dA, b);
- check_sparse_solving(solver, A, dB, dA, dB);
- check_sparse_solving(solver, halfA, dB, dA, dB);
- check_sparse_solving(solver, A, B, dA, dB);
- check_sparse_solving(solver, halfA, B, dA, dB);
+ CALL_SUBTEST( check_sparse_solving(solver, A, b, dA, b) );
+ CALL_SUBTEST( check_sparse_solving(solver, halfA, b, dA, b) );
+ CALL_SUBTEST( check_sparse_solving(solver, A, dB, dA, dB) );
+ CALL_SUBTEST( check_sparse_solving(solver, halfA, dB, dA, dB) );
+ CALL_SUBTEST( check_sparse_solving(solver, A, B, dA, dB) );
+ CALL_SUBTEST( check_sparse_solving(solver, halfA, B, dA, dB) );
+ CALL_SUBTEST( check_sparse_solving(solver, A, c, dA, dc) );
+ CALL_SUBTEST( check_sparse_solving(solver, halfA, c, dA, dc) );
// check only once
if(i==0)
@@ -237,25 +310,44 @@ template<typename Solver> void check_sparse_spd_solving(Solver& solver)
}
// First, get the folder
-#ifdef TEST_REAL_CASES
- if (internal::is_same<Scalar, float>::value
- || internal::is_same<Scalar, std::complex<float> >::value)
- return ;
-
- std::string mat_folder = get_matrixfolder<Scalar>();
- MatrixMarketIterator<Scalar> it(mat_folder);
- for (; it; ++it)
+#ifdef TEST_REAL_CASES
+ // Test real problems with double precision only
+ if (internal::is_same<typename NumTraits<Scalar>::Real, double>::value)
{
- if (it.sym() == SPD){
- Mat halfA;
- PermutationMatrix<Dynamic, Dynamic, Index> pnull;
- halfA.template selfadjointView<Solver::UpLo>() = it.matrix().template triangularView<Eigen::Lower>().twistedBy(pnull);
-
- std::cout<< " ==== SOLVING WITH MATRIX " << it.matname() << " ==== \n";
- check_sparse_solving_real_cases(solver, it.matrix(), it.rhs(), it.refX());
- check_sparse_solving_real_cases(solver, halfA, it.rhs(), it.refX());
+ std::string mat_folder = get_matrixfolder<Scalar>();
+ MatrixMarketIterator<Scalar> it(mat_folder);
+ for (; it; ++it)
+ {
+ if (it.sym() == SPD){
+ A = it.matrix();
+ if(A.diagonal().size() <= maxRealWorldSize)
+ {
+ DenseVector b = it.rhs();
+ DenseVector refX = it.refX();
+ PermutationMatrix<Dynamic, Dynamic, StorageIndex> pnull;
+ halfA.resize(A.rows(), A.cols());
+ if(Solver::UpLo == (Lower|Upper))
+ halfA = A;
+ else
+ halfA.template selfadjointView<Solver::UpLo>() = A.template triangularView<Eigen::Lower>().twistedBy(pnull);
+
+ std::cout << "INFO | Testing " << sym_to_string(it.sym()) << "sparse problem " << it.matname()
+ << " (" << A.rows() << "x" << A.cols() << ") using " << typeid(Solver).name() << "..." << std::endl;
+ CALL_SUBTEST( check_sparse_solving_real_cases(solver, A, b, A, refX) );
+ std::string stats = solver_stats(solver);
+ if(stats.size()>0)
+ std::cout << "INFO | " << stats << std::endl;
+ CALL_SUBTEST( check_sparse_solving_real_cases(solver, halfA, b, A, refX) );
+ }
+ else
+ {
+ std::cout << "INFO | Skip sparse problem \"" << it.matname() << "\" (too large)" << std::endl;
+ }
+ }
}
}
+#else
+ EIGEN_UNUSED_VARIABLE(maxRealWorldSize);
#endif
}
@@ -277,37 +369,39 @@ template<typename Solver> void check_sparse_spd_determinant(Solver& solver)
}
template<typename Solver, typename DenseMat>
-int generate_sparse_square_problem(Solver&, typename Solver::MatrixType& A, DenseMat& dA, int maxSize = 300)
+Index generate_sparse_square_problem(Solver&, typename Solver::MatrixType& A, DenseMat& dA, int maxSize = 300, int options = ForceNonZeroDiag)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
- int size = internal::random<int>(1,maxSize);
+ Index size = internal::random<int>(1,maxSize);
double density = (std::max)(8./(size*size), 0.01);
A.resize(size,size);
dA.resize(size,size);
- initSparse<Scalar>(density, dA, A, ForceNonZeroDiag);
+ initSparse<Scalar>(density, dA, A, options);
return size;
}
struct prune_column {
- int m_col;
- prune_column(int col) : m_col(col) {}
+ Index m_col;
+ prune_column(Index col) : m_col(col) {}
template<class Scalar>
- bool operator()(int, int col, const Scalar&) const {
+ bool operator()(Index, Index col, const Scalar&) const {
return col != m_col;
}
};
-template<typename Solver> void check_sparse_square_solving(Solver& solver, bool checkDeficient = false)
+
+template<typename Solver> void check_sparse_square_solving(Solver& solver, int maxSize = 300, int maxRealWorldSize = 100000, bool checkDeficient = false)
{
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
- typedef SparseMatrix<Scalar,ColMajor> SpMat;
+ typedef SparseMatrix<Scalar,ColMajor, typename Mat::StorageIndex> SpMat;
+ typedef SparseVector<Scalar, 0, typename Mat::StorageIndex> SpVec;
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
typedef Matrix<Scalar,Dynamic,1> DenseVector;
@@ -316,7 +410,7 @@ template<typename Solver> void check_sparse_square_solving(Solver& solver, bool
Mat A;
DenseMatrix dA;
for (int i = 0; i < g_repeat; i++) {
- int size = generate_sparse_square_problem(solver, A, dA);
+ Index size = generate_sparse_square_problem(solver, A, dA, maxSize);
A.makeCompressed();
DenseVector b = DenseVector::Random(size);
@@ -325,9 +419,12 @@ template<typename Solver> void check_sparse_square_solving(Solver& solver, bool
double density = (std::max)(8./(size*rhsCols), 0.1);
initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);
B.makeCompressed();
- check_sparse_solving(solver, A, b, dA, b);
- check_sparse_solving(solver, A, dB, dA, dB);
- check_sparse_solving(solver, A, B, dA, dB);
+ SpVec c = B.col(0);
+ DenseVector dc = dB.col(0);
+ CALL_SUBTEST(check_sparse_solving(solver, A, b, dA, b));
+ CALL_SUBTEST(check_sparse_solving(solver, A, dB, dA, dB));
+ CALL_SUBTEST(check_sparse_solving(solver, A, B, dA, dB));
+ CALL_SUBTEST(check_sparse_solving(solver, A, c, dA, dc));
// check only once
if(i==0)
@@ -337,7 +434,7 @@ template<typename Solver> void check_sparse_square_solving(Solver& solver, bool
}
// regression test for Bug 792 (structurally rank deficient matrices):
if(checkDeficient && size>1) {
- int col = internal::random<int>(0,size-1);
+ Index col = internal::random<int>(0,int(size-1));
A.prune(prune_column(col));
solver.compute(A);
VERIFY_IS_EQUAL(solver.info(), NumericalIssue);
@@ -346,17 +443,33 @@ template<typename Solver> void check_sparse_square_solving(Solver& solver, bool
// First, get the folder
#ifdef TEST_REAL_CASES
- if (internal::is_same<Scalar, float>::value
- || internal::is_same<Scalar, std::complex<float> >::value)
- return ;
-
- std::string mat_folder = get_matrixfolder<Scalar>();
- MatrixMarketIterator<Scalar> it(mat_folder);
- for (; it; ++it)
+ // Test real problems with double precision only
+ if (internal::is_same<typename NumTraits<Scalar>::Real, double>::value)
{
- std::cout<< " ==== SOLVING WITH MATRIX " << it.matname() << " ==== \n";
- check_sparse_solving_real_cases(solver, it.matrix(), it.rhs(), it.refX());
+ std::string mat_folder = get_matrixfolder<Scalar>();
+ MatrixMarketIterator<Scalar> it(mat_folder);
+ for (; it; ++it)
+ {
+ A = it.matrix();
+ if(A.diagonal().size() <= maxRealWorldSize)
+ {
+ DenseVector b = it.rhs();
+ DenseVector refX = it.refX();
+ std::cout << "INFO | Testing " << sym_to_string(it.sym()) << "sparse problem " << it.matname()
+ << " (" << A.rows() << "x" << A.cols() << ") using " << typeid(Solver).name() << "..." << std::endl;
+ CALL_SUBTEST(check_sparse_solving_real_cases(solver, A, b, A, refX));
+ std::string stats = solver_stats(solver);
+ if(stats.size()>0)
+ std::cout << "INFO | " << stats << std::endl;
+ }
+ else
+ {
+ std::cout << "INFO | SKIP sparse problem \"" << it.matname() << "\" (too large)" << std::endl;
+ }
+ }
}
+#else
+ EIGEN_UNUSED_VARIABLE(maxRealWorldSize);
#endif
}
@@ -366,13 +479,20 @@ template<typename Solver> void check_sparse_square_determinant(Solver& solver)
typedef typename Solver::MatrixType Mat;
typedef typename Mat::Scalar Scalar;
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
-
- // generate the problem
- Mat A;
- DenseMatrix dA;
- generate_sparse_square_problem(solver, A, dA, 30);
- A.makeCompressed();
+
for (int i = 0; i < g_repeat; i++) {
+ // generate the problem
+ Mat A;
+ DenseMatrix dA;
+
+ int size = internal::random<int>(1,30);
+ dA.setRandom(size,size);
+
+ dA = (dA.array().abs()<0.3).select(0,dA);
+ dA.diagonal() = (dA.diagonal().array()==0).select(1,dA.diagonal());
+ A = dA.sparseView();
+ A.makeCompressed();
+
check_sparse_determinant(solver, A, dA);
}
}
@@ -383,13 +503,63 @@ template<typename Solver> void check_sparse_square_abs_determinant(Solver& solve
typedef typename Mat::Scalar Scalar;
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
- // generate the problem
- Mat A;
- DenseMatrix dA;
- generate_sparse_square_problem(solver, A, dA, 30);
- A.makeCompressed();
for (int i = 0; i < g_repeat; i++) {
+ // generate the problem
+ Mat A;
+ DenseMatrix dA;
+ generate_sparse_square_problem(solver, A, dA, 30);
+ A.makeCompressed();
check_sparse_abs_determinant(solver, A, dA);
}
}
+template<typename Solver, typename DenseMat>
+void generate_sparse_leastsquare_problem(Solver&, typename Solver::MatrixType& A, DenseMat& dA, int maxSize = 300, int options = ForceNonZeroDiag)
+{
+ typedef typename Solver::MatrixType Mat;
+ typedef typename Mat::Scalar Scalar;
+
+ int rows = internal::random<int>(1,maxSize);
+ int cols = internal::random<int>(1,rows);
+ double density = (std::max)(8./(rows*cols), 0.01);
+
+ A.resize(rows,cols);
+ dA.resize(rows,cols);
+
+ initSparse<Scalar>(density, dA, A, options);
+}
+
+template<typename Solver> void check_sparse_leastsquare_solving(Solver& solver)
+{
+ typedef typename Solver::MatrixType Mat;
+ typedef typename Mat::Scalar Scalar;
+ typedef SparseMatrix<Scalar,ColMajor, typename Mat::StorageIndex> SpMat;
+ typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
+ typedef Matrix<Scalar,Dynamic,1> DenseVector;
+
+ int rhsCols = internal::random<int>(1,16);
+
+ Mat A;
+ DenseMatrix dA;
+ for (int i = 0; i < g_repeat; i++) {
+ generate_sparse_leastsquare_problem(solver, A, dA);
+
+ A.makeCompressed();
+ DenseVector b = DenseVector::Random(A.rows());
+ DenseMatrix dB(A.rows(),rhsCols);
+ SpMat B(A.rows(),rhsCols);
+ double density = (std::max)(8./(A.rows()*rhsCols), 0.1);
+ initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);
+ B.makeCompressed();
+ check_sparse_solving(solver, A, b, dA, b);
+ check_sparse_solving(solver, A, dB, dA, dB);
+ check_sparse_solving(solver, A, B, dA, dB);
+
+ // check only once
+ if(i==0)
+ {
+ b = DenseVector::Zero(A.rows());
+ check_sparse_solving(solver, A, b, dA, b);
+ }
+ }
+}
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