sparse_solver.h File Reference

#include "sparse.h"
#include <Eigen/SparseCore>
#include <Eigen/SparseLU>
#include <sstream>

Go to the source code of this file.

Classes
struct	prune_column

Functions
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)
template<typename Solver , typename Rhs , typename Guess , typename Result >
void	solve_with_guess (SparseSolverBase< Solver > &solver, const MatrixBase< Rhs > &b, const Guess &, Result &x)
template<typename Solver , typename Rhs , typename Guess , typename Result >
void	solve_with_guess (SparseSolverBase< Solver > &solver, const SparseMatrixBase< Rhs > &b, const Guess &, Result &x)
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)
template<typename Scalar , typename Rhs , typename DenseMat , typename DenseRhs >
void	check_sparse_solving (Eigen::SparseLU< Eigen::SparseMatrix< Scalar >> &solver, const typename Eigen::SparseMatrix< Scalar > &A, const Rhs &b, const DenseMat &dA, const DenseRhs &db)
template<typename Solver , typename Rhs >
void	check_sparse_solving_real_cases (Solver &solver, const typename Solver::MatrixType &A, const Rhs &b, const typename Solver::MatrixType &fullA, const Rhs &refX)
template<typename Solver , typename DenseMat >
void	check_sparse_determinant (Solver &solver, const typename Solver::MatrixType &A, const DenseMat &dA)
template<typename Solver , typename DenseMat >
void	check_sparse_abs_determinant (Solver &solver, const typename Solver::MatrixType &A, const DenseMat &dA)
template<typename Solver , typename DenseMat >
int	generate_sparse_spd_problem (Solver &, typename Solver::MatrixType &A, typename Solver::MatrixType &halfA, DenseMat &dA, int maxSize=300)
template<typename Solver >
void	check_sparse_spd_solving (Solver &solver, int maxSize=(std::min)(300, EIGEN_TEST_MAX_SIZE), int maxRealWorldSize=100000)
template<typename Solver >
void	check_sparse_spd_determinant (Solver &solver)
template<typename Solver , typename DenseMat >
int	generate_sparse_nonhermitian_problem (Solver &, typename Solver::MatrixType &A, typename Solver::MatrixType &halfA, DenseMat &dA, int maxSize=300)
template<typename Solver >
void	check_sparse_nonhermitian_solving (Solver &solver, int maxSize=(std::min)(300, EIGEN_TEST_MAX_SIZE), int maxRealWorldSize=100000)
template<typename Solver >
void	check_sparse_nonhermitian_determinant (Solver &solver)
template<typename Solver >
void	check_sparse_zero_matrix (Solver &solver)
template<typename Solver , typename DenseMat >
Index	generate_sparse_square_problem (Solver &, typename Solver::MatrixType &A, DenseMat &dA, int maxSize=300, int options=ForceNonZeroDiag)
template<typename Solver >
void	check_sparse_square_solving (Solver &solver, int maxSize=300, int maxRealWorldSize=100000, bool checkDeficient=false)
template<typename Solver >
void	check_sparse_square_determinant (Solver &solver)
template<typename Solver >
void	check_sparse_square_abs_determinant (Solver &solver)
template<typename Solver , typename DenseMat >
void	generate_sparse_leastsquare_problem (Solver &, typename Solver::MatrixType &A, DenseMat &dA, int maxSize=300, int options=ForceNonZeroDiag)
template<typename Solver >
void	check_sparse_leastsquare_solving (Solver &solver)

Function Documentation

check_sparse_abs_determinant()

template<typename Solver , typename DenseMat >

void check_sparse_abs_determinant	(	Solver &	solver,
		const typename Solver::MatrixType &	A,
		const DenseMat &	dA
	)

                                                                                                          {
  using std::abs;
  typedef typename Solver::MatrixType Mat;
  typedef typename Mat::Scalar Scalar;
 
  solver.compute(A);
  if (solver.info() != Success) {
    std::cerr << "WARNING | sparse solver testing: factorization failed (check_sparse_abs_determinant)\n";
    return;
  }
 
  Scalar refDet = abs(dA.determinant());
  VERIFY_IS_APPROX(refDet, solver.absDeterminant());
}

References abs(), solver, Eigen::Success, and VERIFY_IS_APPROX.

Referenced by check_sparse_square_abs_determinant().

check_sparse_determinant()

template<typename Solver , typename DenseMat >

void check_sparse_determinant	(	Solver &	solver,
		const typename Solver::MatrixType &	A,
		const DenseMat &	dA
	)

                                                                                                      {
  typedef typename Solver::MatrixType Mat;
  typedef typename Mat::Scalar Scalar;
 
  solver.compute(A);
  if (solver.info() != Success) {
    std::cerr << "WARNING | sparse solver testing: factorization failed (check_sparse_determinant)\n";
    return;
  }
 
  Scalar refDet = dA.determinant();
  VERIFY_IS_APPROX(refDet, solver.determinant());
}

References solver, Eigen::Success, and VERIFY_IS_APPROX.

Referenced by check_sparse_nonhermitian_determinant(), check_sparse_spd_determinant(), and check_sparse_square_determinant().

check_sparse_leastsquare_solving()

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);
    }
  }
}

References b, check_sparse_solving(), UniformPSDSelfTest::density, ForceNonZeroDiag, Eigen::g_repeat, generate_sparse_leastsquare_problem(), i, max, Eigen::PlainObjectBase< Derived >::rows(), solver, and oomph::PseudoSolidHelper::Zero.

Referenced by test_lscg_T().

check_sparse_nonhermitian_determinant()

template<typename Solver >

void check_sparse_nonhermitian_determinant

(

Solver &

solver

)

                                                           {
  typedef typename Solver::MatrixType Mat;
  typedef typename Mat::Scalar Scalar;
  typedef Matrix<Scalar, Dynamic, Dynamic> DenseMatrix;
 
  // generate the problem
  Mat A, halfA;
  DenseMatrix dA;
  generate_sparse_nonhermitian_problem(solver, A, halfA, dA, 30);
 
  for (int i = 0; i < g_repeat; i++) {
    check_sparse_determinant(solver, A, dA);
    check_sparse_determinant(solver, halfA, dA);
  }
}

References check_sparse_determinant(), Eigen::g_repeat, generate_sparse_nonhermitian_problem(), i, and solver.

Referenced by test_simplicial_cholesky_T().

check_sparse_nonhermitian_solving()

template<typename Solver >

void check_sparse_nonhermitian_solving	(	Solver &	solver,
		int	maxSize = (std::min)(300, EIGEN_TEST_MAX_SIZE),
		int	maxRealWorldSize = 100000
	)

                                                                      {
  typedef typename Solver::MatrixType Mat;
  typedef typename Mat::Scalar Scalar;
  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;
 
  // generate the problem
  Mat A, halfA;
  DenseMatrix dA;
  for (int i = 0; i < g_repeat; i++) {
    int size = generate_sparse_nonhermitian_problem(solver, A, halfA, dA, maxSize);
 
    // generate the right hand sides
    int rhsCols = internal::random<int>(1, 16);
    double density = (std::max)(8. / static_cast<double>(size * rhsCols), 0.1);
    SpMat B(size, rhsCols);
    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);
 
    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) {
      b = DenseVector::Zero(size);
      check_sparse_solving(solver, A, b, dA, b);
    }
  }
 
  EIGEN_UNUSED_VARIABLE(maxRealWorldSize);
}

References b, calibrate::c, CALL_SUBTEST, check_sparse_solving(), UniformPSDSelfTest::density, EIGEN_UNUSED_VARIABLE, ForceNonZeroDiag, Eigen::g_repeat, generate_sparse_nonhermitian_problem(), i, max, size, solver, and oomph::PseudoSolidHelper::Zero.

Referenced by test_simplicial_cholesky_T().

check_sparse_solving() [1/2]

template<typename Scalar , typename Rhs , typename DenseMat , typename DenseRhs >

void check_sparse_solving	(	Eigen::SparseLU< Eigen::SparseMatrix< Scalar >> &	solver,
		const typename Eigen::SparseMatrix< Scalar > &	A,
		const Rhs &	b,
		const DenseMat &	dA,
		const DenseRhs &	db
	)

                                              {
  typedef typename Eigen::SparseMatrix<Scalar> Mat;
  typedef typename Mat::StorageIndex StorageIndex;
  typedef typename Eigen::SparseLU<Eigen::SparseMatrix<Scalar>> Solver;
 
  // reference solutions computed by dense QR solver
  DenseRhs refX1 = dA.householderQr().solve(db);              // solution of A x = db
  DenseRhs refX2 = dA.transpose().householderQr().solve(db);  // solution of A^T * x = db (use transposed matrix A^T)
  DenseRhs refX3 = dA.adjoint().householderQr().solve(db);    // solution of A^* * x = db (use adjoint matrix A^*)
 
  {
    Rhs x1(A.cols(), b.cols());
    Rhs x2(A.cols(), b.cols());
    Rhs x3(A.cols(), b.cols());
    Rhs oldb = b;
 
    solver.compute(A);
    if (solver.info() != Success) {
      std::cerr << "ERROR | sparse solver testing, factorization failed (" << typeid(Solver).name() << ")\n";
      VERIFY(solver.info() == Success);
    }
    x1 = solver.solve(b);
    if (solver.info() != Success) {
      std::cerr << "WARNING | sparse solver testing: solving failed (" << typeid(Solver).name() << ")\n";
      return;
    }
    VERIFY(oldb.isApprox(b, 0.0) && "sparse solver testing: the rhs should not be modified!");
    VERIFY(x1.isApprox(refX1, test_precision<Scalar>()));
 
    // test solve with transposed
    x2 = solver.transpose().solve(b);
    VERIFY(oldb.isApprox(b) && "sparse solver testing: the rhs should not be modified!");
    VERIFY(x2.isApprox(refX2, test_precision<Scalar>()));
 
    // test solve with adjoint
    // solver.template _solve_impl_transposed<true>(b, x3);
    x3 = solver.adjoint().solve(b);
    VERIFY(oldb.isApprox(b, 0.0) && "sparse solver testing: the rhs should not be modified!");
    VERIFY(x3.isApprox(refX3, test_precision<Scalar>()));
 
    x1.setZero();
    solve_with_guess(solver, b, x1, x1);
    VERIFY(solver.info() == Success && "solving failed when using analyzePattern/factorize API");
    VERIFY(oldb.isApprox(b, 0.0) && "sparse solver testing: the rhs should not be modified!");
    VERIFY(x1.isApprox(refX1, test_precision<Scalar>()));
 
    x1.setZero();
    x2.setZero();
    x3.setZero();
    // test the analyze/factorize API
    solver.analyzePattern(A);
    solver.factorize(A);
    VERIFY(solver.info() == Success && "factorization failed when using analyzePattern/factorize API");
    x1 = solver.solve(b);
    x2 = solver.transpose().solve(b);
    x3 = solver.adjoint().solve(b);
 
    VERIFY(solver.info() == Success && "solving failed when using analyzePattern/factorize API");
    VERIFY(oldb.isApprox(b, 0.0) && "sparse solver testing: the rhs should not be modified!");
    VERIFY(x1.isApprox(refX1, test_precision<Scalar>()));
    VERIFY(x2.isApprox(refX2, test_precision<Scalar>()));
    VERIFY(x3.isApprox(refX3, test_precision<Scalar>()));
 
    x1.setZero();
    // test with Map
    Map<SparseMatrix<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(refX1);
    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, 0.0) && "sparse solver testing: the rhs should not be modified!");
    VERIFY(xm.isApprox(refX1, 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(refX1, test_precision<Scalar>()));
    }
 
    // test dense Block as the result and rhs:
    {
      DenseRhs x(refX1.rows(), refX1.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, 0.0) && "sparse solver testing: the rhs should not be modified!");
      VERIFY(x.isApprox(refX1, 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(refX1, test_precision<Scalar>()));
    }
 
    // test expression as input
    {
      solver.compute(0.5 * (A + A));
      Rhs x = solver.solve(b);
      VERIFY(x.isApprox(refX1, test_precision<Scalar>()));
 
      Solver solver2(0.5 * (A + A));
      Rhs x2 = solver2.solve(b);
      VERIFY(x2.isApprox(refX1, test_precision<Scalar>()));
    }
  }
}

References b, Eigen::PlainObjectBase< Derived >::cols(), plotDoE::name, Eigen::internal::Rhs, Eigen::PlainObjectBase< Derived >::rows(), Eigen::SparseSolverBase< Derived >::solve(), solve_with_guess(), solver, Eigen::Success, VERIFY, plotDoE::x, Global_parameters::x1(), and Global_parameters::x2().

check_sparse_solving() [2/2]

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.householderQr().solve(db);
  {
    Rhs x(A.cols(), b.cols());
    Rhs oldb = b;
 
    solver.compute(A);
    if (solver.info() != Success) {
      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 << "WARNING: sparse solver testing: solving failed (" << typeid(Solver).name() << ")\n";
      // dump call stack:
      g_test_level++;
      VERIFY(solver.info() == Success);
      g_test_level--;
      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 solve_with_guess 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);
    VERIFY(solver.info() == Success && "factorization failed when using analyzePattern/factorize API");
    x = solver.solve(b);
    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 with Map
    Map<SparseMatrix<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>()));
 
    // Test with a Map and non-unit stride.
    Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> out(2 * xm.rows(), 2 * xm.cols());
    out.setZero();
    Eigen::Map<DenseRhs, 0, Stride<Eigen::Dynamic, 2>> outm(out.data(), xm.rows(), xm.cols(),
                                                            Stride<Eigen::Dynamic, 2>(2 * xm.rows(), 2));
    outm = solver.solve(bm);
    VERIFY(outm.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
    {
      solver.compute(0.5 * (A + A));
      Rhs x = solver.solve(b);
      VERIFY(x.isApprox(refX, test_precision<Scalar>()));
 
      Solver solver2(0.5 * (A + A));
      Rhs x2 = solver2.solve(b);
      VERIFY(x2.isApprox(refX, test_precision<Scalar>()));
    }
  }
}

References b, Eigen::PlainObjectBase< Derived >::cols(), Eigen::g_test_level, plotDoE::name, out(), Eigen::internal::Rhs, Eigen::PlainObjectBase< Derived >::rows(), solve_with_guess(), solver, Eigen::Success, VERIFY, plotDoE::x, and Global_parameters::x2().

Referenced by check_sparse_leastsquare_solving(), check_sparse_nonhermitian_solving(), check_sparse_spd_solving(), and check_sparse_square_solving().

check_sparse_solving_real_cases()

template<typename Solver , typename Rhs >

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(A.cols(), b.cols());
 
  solver.compute(A);
  if (solver.info() != Success) {
    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 << "WARNING | sparse solver testing, solving failed (" << typeid(Solver).name() << ")\n";
    return;
  }
 
  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";
  }
}

References b, Eigen::PlainObjectBase< Derived >::cols(), plotDoE::name, Eigen::internal::Rhs, solver, Eigen::Success, VERIFY, and plotDoE::x.

Referenced by check_sparse_spd_solving(), and check_sparse_square_solving().

check_sparse_spd_determinant()

template<typename Solver >

void check_sparse_spd_determinant

(

Solver &

solver

)

                                                  {
  typedef typename Solver::MatrixType Mat;
  typedef typename Mat::Scalar Scalar;
  typedef Matrix<Scalar, Dynamic, Dynamic> DenseMatrix;
 
  // generate the problem
  Mat A, halfA;
  DenseMatrix dA;
  generate_sparse_spd_problem(solver, A, halfA, dA, 30);
 
  for (int i = 0; i < g_repeat; i++) {
    check_sparse_determinant(solver, A, dA);
    check_sparse_determinant(solver, halfA, dA);
  }
}

References check_sparse_determinant(), Eigen::g_repeat, generate_sparse_spd_problem(), i, and solver.

Referenced by test_cholmod_ST(), and test_simplicial_cholesky_T().

check_sparse_spd_solving()

template<typename Solver >

void check_sparse_spd_solving	(	Solver &	solver,
		int	maxSize = (std::min)(300, EIGEN_TEST_MAX_SIZE),
		int	maxRealWorldSize = 100000
	)

                                                             {
  typedef typename Solver::MatrixType Mat;
  typedef typename Mat::Scalar Scalar;
  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;
 
  // generate the problem
  Mat A, halfA;
  DenseMatrix dA;
  for (int i = 0; i < g_repeat; i++) {
    int size = generate_sparse_spd_problem(solver, A, halfA, dA, maxSize);
 
    // generate the right hand sides
    int rhsCols = internal::random<int>(1, 16);
    double density = (std::max)(8. / static_cast<double>(size * rhsCols), 0.1);
    SpMat B(size, rhsCols);
    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);
 
    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) {
      b = DenseVector::Zero(size);
      check_sparse_solving(solver, A, b, dA, b);
    }
  }
 
  // First, get the folder
#ifdef TEST_REAL_CASES
  // Test real problems with double precision only
  if (internal::is_same<typename NumTraits<Scalar>::Real, double>::value) {
    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
}

References b, calibrate::c, CALL_SUBTEST, check_sparse_solving(), check_sparse_solving_real_cases(), Eigen::PlainObjectBase< Derived >::cols(), UniformPSDSelfTest::density, EIGEN_UNUSED_VARIABLE, ForceNonZeroDiag, Eigen::g_repeat, generate_sparse_spd_problem(), i, Eigen::Lower, Eigen::MatrixMarketIterator< Scalar >::matname(), Eigen::MatrixMarketIterator< Scalar >::matrix(), max, plotDoE::name, Eigen::MatrixMarketIterator< Scalar >::refX(), Eigen::PlainObjectBase< Derived >::resize(), Eigen::MatrixMarketIterator< Scalar >::rhs(), Eigen::PlainObjectBase< Derived >::rows(), size, solver, Eigen::SPD, oomph::Global_string_for_annotation::string(), Eigen::MatrixMarketIterator< Scalar >::sym(), Eigen::Upper, Eigen::value, and oomph::PseudoSolidHelper::Zero.

Referenced by test_cholmod_ST(), test_conjugate_gradient_T(), test_incomplete_cholesky_T(), test_minres_T(), test_pardiso_T(), test_pastix_T(), and test_simplicial_cholesky_T().

check_sparse_square_abs_determinant()

template<typename Solver >

void check_sparse_square_abs_determinant

(

Solver &

solver

)

                                                         {
  typedef typename Solver::MatrixType Mat;
  typedef typename Mat::Scalar Scalar;
  typedef Matrix<Scalar, Dynamic, Dynamic> DenseMatrix;
 
  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);
  }
}

References check_sparse_abs_determinant(), Eigen::g_repeat, generate_sparse_square_problem(), i, and solver.

Referenced by test_sparselu_T().

check_sparse_square_determinant()

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;
 
  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);
  }
}

References check_sparse_determinant(), Eigen::g_repeat, i, Eigen::PlainObjectBase< Derived >::setRandom(), size, and solver.

Referenced by EIGEN_DECLARE_TEST(), test_sparselu_T(), and test_umfpack_support_T().

check_sparse_square_solving()

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, typename Mat::StorageIndex> SpMat;
  typedef SparseVector<Scalar, 0, typename Mat::StorageIndex> SpVec;
  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++) {
    Index size = generate_sparse_square_problem(solver, A, dA, maxSize);
 
    A.makeCompressed();
    DenseVector b = DenseVector::Random(size);
    DenseMatrix dB(size, rhsCols);
    SpMat B(size, rhsCols);
    double density = (std::max)(8. / double(size * rhsCols), 0.1);
    initSparse<Scalar>(density, dB, B, ForceNonZeroDiag);
    B.makeCompressed();
    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) {
      CALL_SUBTEST(b = DenseVector::Zero(size); check_sparse_solving(solver, A, b, dA, b));
    }
    // regression test for Bug 792 (structurally rank deficient matrices):
    if (checkDeficient && 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);
    }
  }
 
  // First, get the folder
#ifdef TEST_REAL_CASES
  // Test real problems with double precision only
  if (internal::is_same<typename NumTraits<Scalar>::Real, double>::value) {
    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
}

References b, calibrate::c, CALL_SUBTEST, check_sparse_solving(), check_sparse_solving_real_cases(), col(), Eigen::PlainObjectBase< Derived >::cols(), UniformPSDSelfTest::density, EIGEN_UNUSED_VARIABLE, ForceNonZeroDiag, Eigen::g_repeat, generate_sparse_square_problem(), i, Eigen::MatrixMarketIterator< Scalar >::matname(), Eigen::MatrixMarketIterator< Scalar >::matrix(), max, plotDoE::name, Eigen::NumericalIssue, Eigen::MatrixMarketIterator< Scalar >::refX(), Eigen::MatrixMarketIterator< Scalar >::rhs(), Eigen::PlainObjectBase< Derived >::rows(), size, solver, oomph::Global_string_for_annotation::string(), Eigen::MatrixMarketIterator< Scalar >::sym(), Eigen::value, VERIFY_IS_EQUAL, and oomph::PseudoSolidHelper::Zero.

Referenced by EIGEN_DECLARE_TEST(), test_bicgstab_T(), test_bicgstabl_T(), test_dgmres_T(), test_gmres_T(), test_idrs_T(), test_idrstabl_T(), test_klu_support_T(), test_lscg_T(), test_metis_T(), test_pardiso_T(), test_pastix_T(), test_pastix_T_LU(), test_sparselu_T(), and test_umfpack_support_T().

check_sparse_zero_matrix()

template<typename Solver >

void check_sparse_zero_matrix

(

Solver &

solver

)

                                              {
  typedef typename Solver::MatrixType Mat;
 
  Mat A(1, 1);
  solver.compute(A);
  VERIFY_IS_EQUAL(solver.info(), NumericalIssue);
}

References Eigen::NumericalIssue, solver, and VERIFY_IS_EQUAL.

Referenced by test_cholmod_ST().

generate_sparse_leastsquare_problem()

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);
}

References cols, UniformPSDSelfTest::density, max, Eigen::PlainObjectBase< Derived >::resize(), and rows.

Referenced by check_sparse_leastsquare_solving().

generate_sparse_nonhermitian_problem()

template<typename Solver , typename DenseMat >

int generate_sparse_nonhermitian_problem	(	Solver &	,
		typename Solver::MatrixType &	A,
		typename Solver::MatrixType &	halfA,
		DenseMat &	dA,
		int	maxSize = 300
	)

                                                                          {
  typedef typename Solver::MatrixType Mat;
  typedef typename Mat::Scalar Scalar;
  typedef Matrix<Scalar, Dynamic, Dynamic> DenseMatrix;
 
  int size = internal::random<int>(1, maxSize);
  double density = (std::max)(8. / static_cast<double>(size * size), 0.01);
 
  Mat M(size, size);
  DenseMatrix dM(size, size);
 
  initSparse<Scalar>(density, dM, M, ForceNonZeroDiag);
 
  A = M * M.transpose();
  dA = dM * dM.transpose();
 
  halfA.resize(size, size);
  if (Solver::UpLo == (Lower | Upper))
    halfA = A;
  else
    halfA = A.template triangularView<Solver::UpLo>();
 
  return size;
}

References UniformPSDSelfTest::density, ForceNonZeroDiag, Eigen::Lower, max, Eigen::PlainObjectBase< Derived >::resize(), size, and Eigen::Upper.

Referenced by check_sparse_nonhermitian_determinant(), and check_sparse_nonhermitian_solving().

generate_sparse_spd_problem()

template<typename Solver , typename DenseMat >

int generate_sparse_spd_problem	(	Solver &	,
		typename Solver::MatrixType &	A,
		typename Solver::MatrixType &	halfA,
		DenseMat &	dA,
		int	maxSize = 300
	)

                                                                 {
  typedef typename Solver::MatrixType Mat;
  typedef typename Mat::Scalar Scalar;
  typedef Matrix<Scalar, Dynamic, Dynamic> DenseMatrix;
 
  int size = internal::random<int>(1, maxSize);
  double density = (std::max)(8. / static_cast<double>(size * size), 0.01);
 
  Mat M(size, size);
  DenseMatrix dM(size, size);
 
  initSparse<Scalar>(density, dM, M, ForceNonZeroDiag);
 
  A = M * M.adjoint();
  dA = dM * dM.adjoint();
 
  halfA.resize(size, size);
  if (Solver::UpLo == (Lower | Upper))
    halfA = A;
  else
    halfA.template selfadjointView<Solver::UpLo>().rankUpdate(M);
 
  return size;
}

References UniformPSDSelfTest::density, ForceNonZeroDiag, Eigen::Lower, max, Eigen::PlainObjectBase< Derived >::resize(), size, and Eigen::Upper.

Referenced by check_sparse_spd_determinant(), and check_sparse_spd_solving().

generate_sparse_square_problem()

template<typename Solver , typename DenseMat >

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;
 
  Index size = internal::random<int>(1, maxSize);
  double density = (std::max)(8. / static_cast<double>(size * size), 0.01);
 
  A.resize(size, size);
  dA.resize(size, size);
 
  initSparse<Scalar>(density, dA, A, options);
 
  return size;
}

References UniformPSDSelfTest::density, max, Eigen::PlainObjectBase< Derived >::resize(), and size.

Referenced by check_sparse_square_abs_determinant(), and check_sparse_square_solving().

solve_with_guess() [1/3]

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);
  }
}

References b, solver, plotDoE::x, and oomph::PseudoSolidHelper::Zero.

Referenced by check_sparse_solving().

solve_with_guess() [2/3]

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);
}

References b, solver, plotDoE::x, and oomph::PseudoSolidHelper::Zero.

solve_with_guess() [3/3]

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);
}

References b, solver, and plotDoE::x.