| // This file is part of Eigen, a lightweight C++ template library |
| // for linear algebra. |
| // |
| // Copyright (C) 2008-2011 Gael Guennebaud <gael.guennebaud@inria.fr> |
| // |
| // This Source Code Form is subject to the terms of the Mozilla |
| // Public License v. 2.0. If a copy of the MPL was not distributed |
| // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. |
| |
| #if defined(_MSC_VER) && (_MSC_VER == 1800) |
| // This unit test takes forever to compile in Release mode with MSVC 2013, |
| // multiple hours. So let's switch off optimization for this one. |
| #pragma optimize("", off) |
| #endif |
| |
| static long int nb_temporaries; |
| |
| inline void on_temporary_creation() { |
| // here's a great place to set a breakpoint when debugging failures in this test! |
| nb_temporaries++; |
| } |
| |
| #define EIGEN_SPARSE_CREATE_TEMPORARY_PLUGIN \ |
| { on_temporary_creation(); } |
| |
| #include "sparse.h" |
| |
| #define VERIFY_EVALUATION_COUNT(XPR, N) \ |
| { \ |
| nb_temporaries = 0; \ |
| CALL_SUBTEST(XPR); \ |
| if (nb_temporaries != N) std::cerr << "nb_temporaries == " << nb_temporaries << "\n"; \ |
| VERIFY((#XPR) && nb_temporaries == N); \ |
| } |
| |
| template <typename SparseMatrixType> |
| void sparse_product() { |
| typedef typename SparseMatrixType::StorageIndex StorageIndex; |
| Index n = 100; |
| const Index rows = internal::random<Index>(1, n); |
| const Index cols = internal::random<Index>(1, n); |
| const Index depth = internal::random<Index>(1, n); |
| typedef typename SparseMatrixType::Scalar Scalar; |
| enum { Flags = SparseMatrixType::Flags }; |
| |
| double density = (std::max)(8. / (rows * cols), 0.2); |
| typedef Matrix<Scalar, Dynamic, Dynamic> DenseMatrix; |
| typedef Matrix<Scalar, Dynamic, 1> DenseVector; |
| typedef Matrix<Scalar, 1, Dynamic> RowDenseVector; |
| typedef SparseVector<Scalar, 0, StorageIndex> ColSpVector; |
| typedef SparseVector<Scalar, RowMajor, StorageIndex> RowSpVector; |
| |
| Scalar s1 = internal::random<Scalar>(); |
| Scalar s2 = internal::random<Scalar>(); |
| |
| // test matrix-matrix product |
| { |
| DenseMatrix refMat2 = DenseMatrix::Zero(rows, depth); |
| DenseMatrix refMat2t = DenseMatrix::Zero(depth, rows); |
| DenseMatrix refMat3 = DenseMatrix::Zero(depth, cols); |
| DenseMatrix refMat3t = DenseMatrix::Zero(cols, depth); |
| DenseMatrix refMat4 = DenseMatrix::Zero(rows, cols); |
| DenseMatrix refMat4t = DenseMatrix::Zero(cols, rows); |
| DenseMatrix refMat5 = DenseMatrix::Random(depth, cols); |
| DenseMatrix refMat6 = DenseMatrix::Random(rows, rows); |
| DenseMatrix dm4 = DenseMatrix::Zero(rows, rows); |
| // DenseVector dv1 = DenseVector::Random(rows); |
| SparseMatrixType m2(rows, depth); |
| SparseMatrixType m2t(depth, rows); |
| SparseMatrixType m3(depth, cols); |
| SparseMatrixType m3t(cols, depth); |
| SparseMatrixType m4(rows, cols); |
| SparseMatrixType m4t(cols, rows); |
| SparseMatrixType m6(rows, rows); |
| initSparse(density, refMat2, m2); |
| initSparse(density, refMat2t, m2t); |
| initSparse(density, refMat3, m3); |
| initSparse(density, refMat3t, m3t); |
| initSparse(density, refMat4, m4); |
| initSparse(density, refMat4t, m4t); |
| initSparse(density, refMat6, m6); |
| |
| // int c = internal::random<int>(0,depth-1); |
| |
| // sparse * sparse |
| VERIFY_IS_APPROX(m4 = m2 * m3, refMat4 = refMat2 * refMat3); |
| VERIFY_IS_APPROX(m4 = m2t.transpose() * m3, refMat4 = refMat2t.transpose() * refMat3); |
| VERIFY_IS_APPROX(m4 = m2t.transpose() * m3t.transpose(), refMat4 = refMat2t.transpose() * refMat3t.transpose()); |
| VERIFY_IS_APPROX(m4 = m2 * m3t.transpose(), refMat4 = refMat2 * refMat3t.transpose()); |
| |
| VERIFY_IS_APPROX(m4 = m2 * m3 / s1, refMat4 = refMat2 * refMat3 / s1); |
| VERIFY_IS_APPROX(m4 = m2 * m3 * s1, refMat4 = refMat2 * refMat3 * s1); |
| VERIFY_IS_APPROX(m4 = s2 * m2 * m3 * s1, refMat4 = s2 * refMat2 * refMat3 * s1); |
| VERIFY_IS_APPROX(m4 = (m2 + m2) * m3, refMat4 = (refMat2 + refMat2) * refMat3); |
| VERIFY_IS_APPROX(m4 = m2 * m3.leftCols(cols / 2), refMat4 = refMat2 * refMat3.leftCols(cols / 2)); |
| VERIFY_IS_APPROX(m4 = m2 * (m3 + m3).leftCols(cols / 2), |
| refMat4 = refMat2 * (refMat3 + refMat3).leftCols(cols / 2)); |
| |
| VERIFY_IS_APPROX(m4 = (m2 * m3).pruned(0), refMat4 = refMat2 * refMat3); |
| VERIFY_IS_APPROX(m4 = (m2t.transpose() * m3).pruned(0), refMat4 = refMat2t.transpose() * refMat3); |
| VERIFY_IS_APPROX(m4 = (m2t.transpose() * m3t.transpose()).pruned(0), |
| refMat4 = refMat2t.transpose() * refMat3t.transpose()); |
| VERIFY_IS_APPROX(m4 = (m2 * m3t.transpose()).pruned(0), refMat4 = refMat2 * refMat3t.transpose()); |
| |
| #ifndef EIGEN_SPARSE_PRODUCT_IGNORE_TEMPORARY_COUNT |
| // make sure the right product implementation is called: |
| if ((!SparseMatrixType::IsRowMajor) && m2.rows() <= m3.cols()) { |
| VERIFY_EVALUATION_COUNT(m4 = m2 * m3, 2); // 2 for transposing and get a sorted result. |
| VERIFY_EVALUATION_COUNT(m4 = (m2 * m3).pruned(0), 1); |
| VERIFY_EVALUATION_COUNT(m4 = (m2 * m3).eval().pruned(0), 4); |
| } |
| #endif |
| |
| // and that pruning is effective: |
| { |
| DenseMatrix Ad(2, 2); |
| Ad << -1, 1, 1, 1; |
| SparseMatrixType As(Ad.sparseView()), B(2, 2); |
| VERIFY_IS_EQUAL((As * As.transpose()).eval().nonZeros(), 4); |
| VERIFY_IS_EQUAL((Ad * Ad.transpose()).eval().sparseView().eval().nonZeros(), 2); |
| VERIFY_IS_EQUAL((As * As.transpose()).pruned(1e-6).eval().nonZeros(), 2); |
| } |
| |
| // dense ?= sparse * sparse |
| VERIFY_IS_APPROX(dm4 = m2 * m3, refMat4 = refMat2 * refMat3); |
| VERIFY_IS_APPROX(dm4 += m2 * m3, refMat4 += refMat2 * refMat3); |
| VERIFY_IS_APPROX(dm4 -= m2 * m3, refMat4 -= refMat2 * refMat3); |
| VERIFY_IS_APPROX(dm4 = m2t.transpose() * m3, refMat4 = refMat2t.transpose() * refMat3); |
| VERIFY_IS_APPROX(dm4 += m2t.transpose() * m3, refMat4 += refMat2t.transpose() * refMat3); |
| VERIFY_IS_APPROX(dm4 -= m2t.transpose() * m3, refMat4 -= refMat2t.transpose() * refMat3); |
| VERIFY_IS_APPROX(dm4 = m2t.transpose() * m3t.transpose(), refMat4 = refMat2t.transpose() * refMat3t.transpose()); |
| VERIFY_IS_APPROX(dm4 += m2t.transpose() * m3t.transpose(), refMat4 += refMat2t.transpose() * refMat3t.transpose()); |
| VERIFY_IS_APPROX(dm4 -= m2t.transpose() * m3t.transpose(), refMat4 -= refMat2t.transpose() * refMat3t.transpose()); |
| VERIFY_IS_APPROX(dm4 = m2 * m3t.transpose(), refMat4 = refMat2 * refMat3t.transpose()); |
| VERIFY_IS_APPROX(dm4 += m2 * m3t.transpose(), refMat4 += refMat2 * refMat3t.transpose()); |
| VERIFY_IS_APPROX(dm4 -= m2 * m3t.transpose(), refMat4 -= refMat2 * refMat3t.transpose()); |
| VERIFY_IS_APPROX(dm4 = m2 * m3 * s1, refMat4 = refMat2 * refMat3 * s1); |
| |
| // test aliasing |
| m4 = m2; |
| refMat4 = refMat2; |
| VERIFY_IS_APPROX(m4 = m4 * m3, refMat4 = refMat4 * refMat3); |
| |
| // sparse * dense matrix |
| VERIFY_IS_APPROX(dm4 = m2 * refMat3, refMat4 = refMat2 * refMat3); |
| VERIFY_IS_APPROX(dm4 = m2 * refMat3t.transpose(), refMat4 = refMat2 * refMat3t.transpose()); |
| VERIFY_IS_APPROX(dm4 = m2t.transpose() * refMat3, refMat4 = refMat2t.transpose() * refMat3); |
| VERIFY_IS_APPROX(dm4 = m2t.transpose() * refMat3t.transpose(), |
| refMat4 = refMat2t.transpose() * refMat3t.transpose()); |
| |
| VERIFY_IS_APPROX(dm4 = m2 * refMat3, refMat4 = refMat2 * refMat3); |
| VERIFY_IS_APPROX(dm4 = dm4 + m2 * refMat3, refMat4 = refMat4 + refMat2 * refMat3); |
| VERIFY_IS_APPROX(dm4 += m2 * refMat3, refMat4 += refMat2 * refMat3); |
| VERIFY_IS_APPROX(dm4 -= m2 * refMat3, refMat4 -= refMat2 * refMat3); |
| VERIFY_IS_APPROX(dm4.noalias() += m2 * refMat3, refMat4 += refMat2 * refMat3); |
| VERIFY_IS_APPROX(dm4.noalias() -= m2 * refMat3, refMat4 -= refMat2 * refMat3); |
| VERIFY_IS_APPROX(dm4 = m2 * (refMat3 + refMat3), refMat4 = refMat2 * (refMat3 + refMat3)); |
| VERIFY_IS_APPROX(dm4 = m2t.transpose() * (refMat3 + refMat5) * 0.5, |
| refMat4 = refMat2t.transpose() * (refMat3 + refMat5) * 0.5); |
| |
| // sparse * dense vector |
| VERIFY_IS_APPROX(dm4.col(0) = m2 * refMat3.col(0), refMat4.col(0) = refMat2 * refMat3.col(0)); |
| VERIFY_IS_APPROX(dm4.col(0) = m2 * refMat3t.transpose().col(0), |
| refMat4.col(0) = refMat2 * refMat3t.transpose().col(0)); |
| VERIFY_IS_APPROX(dm4.col(0) = m2t.transpose() * refMat3.col(0), |
| refMat4.col(0) = refMat2t.transpose() * refMat3.col(0)); |
| VERIFY_IS_APPROX(dm4.col(0) = m2t.transpose() * refMat3t.transpose().col(0), |
| refMat4.col(0) = refMat2t.transpose() * refMat3t.transpose().col(0)); |
| |
| // dense * sparse |
| VERIFY_IS_APPROX(dm4 = refMat2 * m3, refMat4 = refMat2 * refMat3); |
| VERIFY_IS_APPROX(dm4 = dm4 + refMat2 * m3, refMat4 = refMat4 + refMat2 * refMat3); |
| VERIFY_IS_APPROX(dm4 += refMat2 * m3, refMat4 += refMat2 * refMat3); |
| VERIFY_IS_APPROX(dm4 -= refMat2 * m3, refMat4 -= refMat2 * refMat3); |
| VERIFY_IS_APPROX(dm4.noalias() += refMat2 * m3, refMat4 += refMat2 * refMat3); |
| VERIFY_IS_APPROX(dm4.noalias() -= refMat2 * m3, refMat4 -= refMat2 * refMat3); |
| VERIFY_IS_APPROX(dm4 = refMat2 * m3t.transpose(), refMat4 = refMat2 * refMat3t.transpose()); |
| VERIFY_IS_APPROX(dm4 = refMat2t.transpose() * m3, refMat4 = refMat2t.transpose() * refMat3); |
| VERIFY_IS_APPROX(dm4 = refMat2t.transpose() * m3t.transpose(), |
| refMat4 = refMat2t.transpose() * refMat3t.transpose()); |
| |
| // sparse * dense and dense * sparse outer product |
| { |
| Index c = internal::random<Index>(0, depth - 1); |
| Index r = internal::random<Index>(0, rows - 1); |
| Index c1 = internal::random<Index>(0, cols - 1); |
| Index r1 = internal::random<Index>(0, depth - 1); |
| DenseMatrix dm5 = DenseMatrix::Random(depth, cols); |
| |
| VERIFY_IS_APPROX(m4 = m2.col(c) * dm5.col(c1).transpose(), refMat4 = refMat2.col(c) * dm5.col(c1).transpose()); |
| VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array() != 0).count()); |
| VERIFY_IS_APPROX(m4 = m2.middleCols(c, 1) * dm5.col(c1).transpose(), |
| refMat4 = refMat2.col(c) * dm5.col(c1).transpose()); |
| VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array() != 0).count()); |
| VERIFY_IS_APPROX(dm4 = m2.col(c) * dm5.col(c1).transpose(), refMat4 = refMat2.col(c) * dm5.col(c1).transpose()); |
| |
| VERIFY_IS_APPROX(m4 = dm5.col(c1) * m2.col(c).transpose(), refMat4 = dm5.col(c1) * refMat2.col(c).transpose()); |
| VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array() != 0).count()); |
| VERIFY_IS_APPROX(m4 = dm5.col(c1) * m2.middleCols(c, 1).transpose(), |
| refMat4 = dm5.col(c1) * refMat2.col(c).transpose()); |
| VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array() != 0).count()); |
| VERIFY_IS_APPROX(dm4 = dm5.col(c1) * m2.col(c).transpose(), refMat4 = dm5.col(c1) * refMat2.col(c).transpose()); |
| |
| VERIFY_IS_APPROX(m4 = dm5.row(r1).transpose() * m2.col(c).transpose(), |
| refMat4 = dm5.row(r1).transpose() * refMat2.col(c).transpose()); |
| VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array() != 0).count()); |
| VERIFY_IS_APPROX(dm4 = dm5.row(r1).transpose() * m2.col(c).transpose(), |
| refMat4 = dm5.row(r1).transpose() * refMat2.col(c).transpose()); |
| |
| VERIFY_IS_APPROX(m4 = m2.row(r).transpose() * dm5.col(c1).transpose(), |
| refMat4 = refMat2.row(r).transpose() * dm5.col(c1).transpose()); |
| VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array() != 0).count()); |
| VERIFY_IS_APPROX(m4 = m2.middleRows(r, 1).transpose() * dm5.col(c1).transpose(), |
| refMat4 = refMat2.row(r).transpose() * dm5.col(c1).transpose()); |
| VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array() != 0).count()); |
| VERIFY_IS_APPROX(dm4 = m2.row(r).transpose() * dm5.col(c1).transpose(), |
| refMat4 = refMat2.row(r).transpose() * dm5.col(c1).transpose()); |
| |
| VERIFY_IS_APPROX(m4 = dm5.col(c1) * m2.row(r), refMat4 = dm5.col(c1) * refMat2.row(r)); |
| VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array() != 0).count()); |
| VERIFY_IS_APPROX(m4 = dm5.col(c1) * m2.middleRows(r, 1), refMat4 = dm5.col(c1) * refMat2.row(r)); |
| VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array() != 0).count()); |
| VERIFY_IS_APPROX(dm4 = dm5.col(c1) * m2.row(r), refMat4 = dm5.col(c1) * refMat2.row(r)); |
| |
| VERIFY_IS_APPROX(m4 = dm5.row(r1).transpose() * m2.row(r), refMat4 = dm5.row(r1).transpose() * refMat2.row(r)); |
| VERIFY_IS_EQUAL(m4.nonZeros(), (refMat4.array() != 0).count()); |
| VERIFY_IS_APPROX(dm4 = dm5.row(r1).transpose() * m2.row(r), refMat4 = dm5.row(r1).transpose() * refMat2.row(r)); |
| } |
| |
| VERIFY_IS_APPROX(m6 = m6 * m6, refMat6 = refMat6 * refMat6); |
| |
| // sparse matrix * sparse vector |
| ColSpVector cv0(cols), cv1; |
| DenseVector dcv0(cols), dcv1; |
| initSparse(2 * density, dcv0, cv0); |
| |
| RowSpVector rv0(depth), rv1; |
| RowDenseVector drv0(depth), drv1(rv1); |
| initSparse(2 * density, drv0, rv0); |
| |
| VERIFY_IS_APPROX(cv1 = m3 * cv0, dcv1 = refMat3 * dcv0); |
| VERIFY_IS_APPROX(rv1 = rv0 * m3, drv1 = drv0 * refMat3); |
| VERIFY_IS_APPROX(cv1 = m3t.adjoint() * cv0, dcv1 = refMat3t.adjoint() * dcv0); |
| VERIFY_IS_APPROX(cv1 = rv0 * m3, dcv1 = drv0 * refMat3); |
| VERIFY_IS_APPROX(rv1 = m3 * cv0, drv1 = refMat3 * dcv0); |
| } |
| |
| // test matrix - diagonal product |
| { |
| DenseMatrix refM2 = DenseMatrix::Zero(rows, cols); |
| DenseMatrix refM3 = DenseMatrix::Zero(rows, cols); |
| DenseMatrix d3 = DenseMatrix::Zero(rows, cols); |
| DiagonalMatrix<Scalar, Dynamic> d1(DenseVector::Random(cols)); |
| DiagonalMatrix<Scalar, Dynamic> d2(DenseVector::Random(rows)); |
| SparseMatrixType m2(rows, cols); |
| SparseMatrixType m3(rows, cols); |
| initSparse<Scalar>(density, refM2, m2); |
| initSparse<Scalar>(density, refM3, m3); |
| VERIFY_IS_APPROX(m3 = m2 * d1, refM3 = refM2 * d1); |
| VERIFY_IS_APPROX(m3 = m2.transpose() * d2, refM3 = refM2.transpose() * d2); |
| VERIFY_IS_APPROX(m3 = d2 * m2, refM3 = d2 * refM2); |
| VERIFY_IS_APPROX(m3 = d1 * m2.transpose(), refM3 = d1 * refM2.transpose()); |
| |
| // also check with a SparseWrapper: |
| DenseVector v1 = DenseVector::Random(cols); |
| DenseVector v2 = DenseVector::Random(rows); |
| DenseVector v3 = DenseVector::Random(rows); |
| VERIFY_IS_APPROX(m3 = m2 * v1.asDiagonal(), refM3 = refM2 * v1.asDiagonal()); |
| VERIFY_IS_APPROX(m3 = m2.transpose() * v2.asDiagonal(), refM3 = refM2.transpose() * v2.asDiagonal()); |
| VERIFY_IS_APPROX(m3 = v2.asDiagonal() * m2, refM3 = v2.asDiagonal() * refM2); |
| VERIFY_IS_APPROX(m3 = v1.asDiagonal() * m2.transpose(), refM3 = v1.asDiagonal() * refM2.transpose()); |
| |
| VERIFY_IS_APPROX(m3 = v2.asDiagonal() * m2 * v1.asDiagonal(), refM3 = v2.asDiagonal() * refM2 * v1.asDiagonal()); |
| |
| VERIFY_IS_APPROX(v2 = m2 * v1.asDiagonal() * v1, refM2 * v1.asDiagonal() * v1); |
| VERIFY_IS_APPROX(v3 = v2.asDiagonal() * m2 * v1, v2.asDiagonal() * refM2 * v1); |
| |
| // evaluate to a dense matrix to check the .row() and .col() iterator functions |
| VERIFY_IS_APPROX(d3 = m2 * d1, refM3 = refM2 * d1); |
| VERIFY_IS_APPROX(d3 = m2.transpose() * d2, refM3 = refM2.transpose() * d2); |
| VERIFY_IS_APPROX(d3 = d2 * m2, refM3 = d2 * refM2); |
| VERIFY_IS_APPROX(d3 = d1 * m2.transpose(), refM3 = d1 * refM2.transpose()); |
| } |
| |
| // test self-adjoint and triangular-view products |
| { |
| DenseMatrix b = DenseMatrix::Random(rows, rows); |
| DenseMatrix x = DenseMatrix::Random(rows, rows); |
| DenseMatrix refX = DenseMatrix::Random(rows, rows); |
| DenseMatrix refUp = DenseMatrix::Zero(rows, rows); |
| DenseMatrix refLo = DenseMatrix::Zero(rows, rows); |
| DenseMatrix refS = DenseMatrix::Zero(rows, rows); |
| DenseMatrix refA = DenseMatrix::Zero(rows, rows); |
| SparseMatrixType mUp(rows, rows); |
| SparseMatrixType mLo(rows, rows); |
| SparseMatrixType mS(rows, rows); |
| SparseMatrixType mA(rows, rows); |
| initSparse<Scalar>(density, refA, mA); |
| do { |
| initSparse<Scalar>(density, refUp, mUp, ForceRealDiag | /*ForceNonZeroDiag|*/ MakeUpperTriangular); |
| } while (refUp.isZero()); |
| refLo = refUp.adjoint(); |
| mLo = mUp.adjoint(); |
| refS = refUp + refLo; |
| refS.diagonal() *= 0.5; |
| mS = mUp + mLo; |
| // TODO be able to address the diagonal.... |
| for (int k = 0; k < mS.outerSize(); ++k) |
| for (typename SparseMatrixType::InnerIterator it(mS, k); it; ++it) |
| if (it.index() == k) it.valueRef() *= Scalar(0.5); |
| |
| VERIFY_IS_APPROX(refS.adjoint(), refS); |
| VERIFY_IS_APPROX(mS.adjoint(), mS); |
| VERIFY_IS_APPROX(mS, refS); |
| VERIFY_IS_APPROX(x = mS * b, refX = refS * b); |
| |
| // sparse selfadjointView with dense matrices |
| VERIFY_IS_APPROX(x = mUp.template selfadjointView<Upper>() * b, refX = refS * b); |
| VERIFY_IS_APPROX(x = mLo.template selfadjointView<Lower>() * b, refX = refS * b); |
| VERIFY_IS_APPROX(x = mS.template selfadjointView<Upper | Lower>() * b, refX = refS * b); |
| |
| VERIFY_IS_APPROX(x = b * mUp.template selfadjointView<Upper>(), refX = b * refS); |
| VERIFY_IS_APPROX(x = b * mLo.template selfadjointView<Lower>(), refX = b * refS); |
| VERIFY_IS_APPROX(x = b * mS.template selfadjointView<Upper | Lower>(), refX = b * refS); |
| |
| VERIFY_IS_APPROX(x.noalias() += mUp.template selfadjointView<Upper>() * b, refX += refS * b); |
| VERIFY_IS_APPROX(x.noalias() -= mLo.template selfadjointView<Lower>() * b, refX -= refS * b); |
| VERIFY_IS_APPROX(x.noalias() += mS.template selfadjointView<Upper | Lower>() * b, refX += refS * b); |
| |
| // sparse selfadjointView with sparse matrices |
| SparseMatrixType mSres(rows, rows); |
| VERIFY_IS_APPROX(mSres = mLo.template selfadjointView<Lower>() * mS, |
| refX = refLo.template selfadjointView<Lower>() * refS); |
| VERIFY_IS_APPROX(mSres = mS * mLo.template selfadjointView<Lower>(), |
| refX = refS * refLo.template selfadjointView<Lower>()); |
| |
| // sparse triangularView with dense matrices |
| VERIFY_IS_APPROX(x = mA.template triangularView<Upper>() * b, refX = refA.template triangularView<Upper>() * b); |
| VERIFY_IS_APPROX(x = mA.template triangularView<Lower>() * b, refX = refA.template triangularView<Lower>() * b); |
| VERIFY_IS_APPROX(x = b * mA.template triangularView<Upper>(), refX = b * refA.template triangularView<Upper>()); |
| VERIFY_IS_APPROX(x = b * mA.template triangularView<Lower>(), refX = b * refA.template triangularView<Lower>()); |
| |
| // sparse triangularView with sparse matrices |
| VERIFY_IS_APPROX(mSres = mA.template triangularView<Lower>() * mS, |
| refX = refA.template triangularView<Lower>() * refS); |
| VERIFY_IS_APPROX(mSres = mS * mA.template triangularView<Lower>(), |
| refX = refS * refA.template triangularView<Lower>()); |
| VERIFY_IS_APPROX(mSres = mA.template triangularView<Upper>() * mS, |
| refX = refA.template triangularView<Upper>() * refS); |
| VERIFY_IS_APPROX(mSres = mS * mA.template triangularView<Upper>(), |
| refX = refS * refA.template triangularView<Upper>()); |
| } |
| } |
| |
| // New test for Bug in SparseTimeDenseProduct |
| template <typename SparseMatrixType, typename DenseMatrixType> |
| void sparse_product_regression_test() { |
| // This code does not compile with afflicted versions of the bug |
| SparseMatrixType sm1(3, 2); |
| DenseMatrixType m2(2, 2); |
| sm1.setZero(); |
| m2.setZero(); |
| |
| DenseMatrixType m3 = sm1 * m2; |
| |
| // This code produces a segfault with afflicted versions of another SparseTimeDenseProduct |
| // bug |
| |
| SparseMatrixType sm2(20000, 2); |
| sm2.setZero(); |
| DenseMatrixType m4(sm2 * m2); |
| |
| VERIFY_IS_APPROX(m4(0, 0), 0.0); |
| } |
| |
| template <typename Scalar> |
| void bug_942() { |
| typedef Matrix<Scalar, Dynamic, 1> Vector; |
| typedef SparseMatrix<Scalar, ColMajor> ColSpMat; |
| typedef SparseMatrix<Scalar, RowMajor> RowSpMat; |
| ColSpMat cmA(1, 1); |
| cmA.insert(0, 0) = 1; |
| |
| RowSpMat rmA(1, 1); |
| rmA.insert(0, 0) = 1; |
| |
| Vector d(1); |
| d[0] = 2; |
| |
| double res = 2; |
| |
| VERIFY_IS_APPROX((cmA * d.asDiagonal()).eval().coeff(0, 0), res); |
| VERIFY_IS_APPROX((d.asDiagonal() * rmA).eval().coeff(0, 0), res); |
| VERIFY_IS_APPROX((rmA * d.asDiagonal()).eval().coeff(0, 0), res); |
| VERIFY_IS_APPROX((d.asDiagonal() * cmA).eval().coeff(0, 0), res); |
| } |
| |
| template <typename Real> |
| void test_mixing_types() { |
| typedef std::complex<Real> Cplx; |
| typedef SparseMatrix<Real> SpMatReal; |
| typedef SparseMatrix<Cplx> SpMatCplx; |
| typedef SparseMatrix<Cplx, RowMajor> SpRowMatCplx; |
| typedef Matrix<Real, Dynamic, Dynamic> DenseMatReal; |
| typedef Matrix<Cplx, Dynamic, Dynamic> DenseMatCplx; |
| |
| Index n = internal::random<Index>(1, 100); |
| double density = (std::max)(8. / static_cast<double>(n * n), 0.2); |
| |
| SpMatReal sR1(n, n); |
| SpMatCplx sC1(n, n), sC2(n, n), sC3(n, n); |
| SpRowMatCplx sCR(n, n); |
| DenseMatReal dR1(n, n); |
| DenseMatCplx dC1(n, n), dC2(n, n), dC3(n, n); |
| |
| initSparse<Real>(density, dR1, sR1); |
| initSparse<Cplx>(density, dC1, sC1); |
| initSparse<Cplx>(density, dC2, sC2); |
| |
| VERIFY_IS_APPROX(sC2 = (sR1 * sC1), dC3 = dR1.template cast<Cplx>() * dC1); |
| VERIFY_IS_APPROX(sC2 = (sC1 * sR1), dC3 = dC1 * dR1.template cast<Cplx>()); |
| VERIFY_IS_APPROX(sC2 = (sR1.transpose() * sC1), dC3 = dR1.template cast<Cplx>().transpose() * dC1); |
| VERIFY_IS_APPROX(sC2 = (sC1.transpose() * sR1), dC3 = dC1.transpose() * dR1.template cast<Cplx>()); |
| VERIFY_IS_APPROX(sC2 = (sR1 * sC1.transpose()), dC3 = dR1.template cast<Cplx>() * dC1.transpose()); |
| VERIFY_IS_APPROX(sC2 = (sC1 * sR1.transpose()), dC3 = dC1 * dR1.template cast<Cplx>().transpose()); |
| VERIFY_IS_APPROX(sC2 = (sR1.transpose() * sC1.transpose()), |
| dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose()); |
| VERIFY_IS_APPROX(sC2 = (sC1.transpose() * sR1.transpose()), |
| dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose()); |
| |
| VERIFY_IS_APPROX(sCR = (sR1 * sC1), dC3 = dR1.template cast<Cplx>() * dC1); |
| VERIFY_IS_APPROX(sCR = (sC1 * sR1), dC3 = dC1 * dR1.template cast<Cplx>()); |
| VERIFY_IS_APPROX(sCR = (sR1.transpose() * sC1), dC3 = dR1.template cast<Cplx>().transpose() * dC1); |
| VERIFY_IS_APPROX(sCR = (sC1.transpose() * sR1), dC3 = dC1.transpose() * dR1.template cast<Cplx>()); |
| VERIFY_IS_APPROX(sCR = (sR1 * sC1.transpose()), dC3 = dR1.template cast<Cplx>() * dC1.transpose()); |
| VERIFY_IS_APPROX(sCR = (sC1 * sR1.transpose()), dC3 = dC1 * dR1.template cast<Cplx>().transpose()); |
| VERIFY_IS_APPROX(sCR = (sR1.transpose() * sC1.transpose()), |
| dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose()); |
| VERIFY_IS_APPROX(sCR = (sC1.transpose() * sR1.transpose()), |
| dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose()); |
| |
| VERIFY_IS_APPROX(sC2 = (sR1 * sC1).pruned(), dC3 = dR1.template cast<Cplx>() * dC1); |
| VERIFY_IS_APPROX(sC2 = (sC1 * sR1).pruned(), dC3 = dC1 * dR1.template cast<Cplx>()); |
| VERIFY_IS_APPROX(sC2 = (sR1.transpose() * sC1).pruned(), dC3 = dR1.template cast<Cplx>().transpose() * dC1); |
| VERIFY_IS_APPROX(sC2 = (sC1.transpose() * sR1).pruned(), dC3 = dC1.transpose() * dR1.template cast<Cplx>()); |
| VERIFY_IS_APPROX(sC2 = (sR1 * sC1.transpose()).pruned(), dC3 = dR1.template cast<Cplx>() * dC1.transpose()); |
| VERIFY_IS_APPROX(sC2 = (sC1 * sR1.transpose()).pruned(), dC3 = dC1 * dR1.template cast<Cplx>().transpose()); |
| VERIFY_IS_APPROX(sC2 = (sR1.transpose() * sC1.transpose()).pruned(), |
| dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose()); |
| VERIFY_IS_APPROX(sC2 = (sC1.transpose() * sR1.transpose()).pruned(), |
| dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose()); |
| |
| VERIFY_IS_APPROX(sCR = (sR1 * sC1).pruned(), dC3 = dR1.template cast<Cplx>() * dC1); |
| VERIFY_IS_APPROX(sCR = (sC1 * sR1).pruned(), dC3 = dC1 * dR1.template cast<Cplx>()); |
| VERIFY_IS_APPROX(sCR = (sR1.transpose() * sC1).pruned(), dC3 = dR1.template cast<Cplx>().transpose() * dC1); |
| VERIFY_IS_APPROX(sCR = (sC1.transpose() * sR1).pruned(), dC3 = dC1.transpose() * dR1.template cast<Cplx>()); |
| VERIFY_IS_APPROX(sCR = (sR1 * sC1.transpose()).pruned(), dC3 = dR1.template cast<Cplx>() * dC1.transpose()); |
| VERIFY_IS_APPROX(sCR = (sC1 * sR1.transpose()).pruned(), dC3 = dC1 * dR1.template cast<Cplx>().transpose()); |
| VERIFY_IS_APPROX(sCR = (sR1.transpose() * sC1.transpose()).pruned(), |
| dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose()); |
| VERIFY_IS_APPROX(sCR = (sC1.transpose() * sR1.transpose()).pruned(), |
| dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose()); |
| |
| VERIFY_IS_APPROX(dC2 = (sR1 * sC1), dC3 = dR1.template cast<Cplx>() * dC1); |
| VERIFY_IS_APPROX(dC2 = (sC1 * sR1), dC3 = dC1 * dR1.template cast<Cplx>()); |
| VERIFY_IS_APPROX(dC2 = (sR1.transpose() * sC1), dC3 = dR1.template cast<Cplx>().transpose() * dC1); |
| VERIFY_IS_APPROX(dC2 = (sC1.transpose() * sR1), dC3 = dC1.transpose() * dR1.template cast<Cplx>()); |
| VERIFY_IS_APPROX(dC2 = (sR1 * sC1.transpose()), dC3 = dR1.template cast<Cplx>() * dC1.transpose()); |
| VERIFY_IS_APPROX(dC2 = (sC1 * sR1.transpose()), dC3 = dC1 * dR1.template cast<Cplx>().transpose()); |
| VERIFY_IS_APPROX(dC2 = (sR1.transpose() * sC1.transpose()), |
| dC3 = dR1.template cast<Cplx>().transpose() * dC1.transpose()); |
| VERIFY_IS_APPROX(dC2 = (sC1.transpose() * sR1.transpose()), |
| dC3 = dC1.transpose() * dR1.template cast<Cplx>().transpose()); |
| |
| VERIFY_IS_APPROX(dC2 = dR1 * sC1, dC3 = dR1.template cast<Cplx>() * sC1); |
| VERIFY_IS_APPROX(dC2 = sR1 * dC1, dC3 = sR1.template cast<Cplx>() * dC1); |
| VERIFY_IS_APPROX(dC2 = dC1 * sR1, dC3 = dC1 * sR1.template cast<Cplx>()); |
| VERIFY_IS_APPROX(dC2 = sC1 * dR1, dC3 = sC1 * dR1.template cast<Cplx>()); |
| |
| VERIFY_IS_APPROX(dC2 = dR1.row(0) * sC1, dC3 = dR1.template cast<Cplx>().row(0) * sC1); |
| VERIFY_IS_APPROX(dC2 = sR1 * dC1.col(0), dC3 = sR1.template cast<Cplx>() * dC1.col(0)); |
| VERIFY_IS_APPROX(dC2 = dC1.row(0) * sR1, dC3 = dC1.row(0) * sR1.template cast<Cplx>()); |
| VERIFY_IS_APPROX(dC2 = sC1 * dR1.col(0), dC3 = sC1 * dR1.template cast<Cplx>().col(0)); |
| } |
| |
| // Test mixed storage types |
| template <int OrderA, int OrderB, int OrderC> |
| void test_mixed_storage_imp() { |
| typedef float Real; |
| typedef Matrix<Real, Dynamic, Dynamic> DenseMat; |
| |
| // Case: Large inputs but small result |
| { |
| SparseMatrix<Real, OrderA> A(8, 512); |
| SparseMatrix<Real, OrderB> B(512, 8); |
| DenseMat refA(8, 512); |
| DenseMat refB(512, 8); |
| |
| initSparse<Real>(0.1, refA, A); |
| initSparse<Real>(0.1, refB, B); |
| |
| SparseMatrix<Real, OrderC, std::int8_t> result; |
| SparseMatrix<Real, OrderC> result_large; |
| DenseMat refResult; |
| |
| VERIFY_IS_APPROX(result = (A * B), refResult = refA * refB); |
| } |
| |
| // Case: Small input but large result |
| { |
| SparseMatrix<Real, OrderA, std::int8_t> A(127, 8); |
| SparseMatrix<Real, OrderB, std::int8_t> B(8, 127); |
| DenseMat refA(127, 8); |
| DenseMat refB(8, 127); |
| |
| initSparse<Real>(0.01, refA, A); |
| initSparse<Real>(0.01, refB, B); |
| |
| SparseMatrix<Real, OrderC> result; |
| SparseMatrix<Real, OrderC> result_large; |
| DenseMat refResult; |
| |
| VERIFY_IS_APPROX(result = (A * B), refResult = refA * refB); |
| } |
| } |
| |
| void test_mixed_storage() { |
| test_mixed_storage_imp<RowMajor, RowMajor, RowMajor>(); |
| test_mixed_storage_imp<RowMajor, RowMajor, ColMajor>(); |
| test_mixed_storage_imp<RowMajor, ColMajor, RowMajor>(); |
| test_mixed_storage_imp<RowMajor, ColMajor, ColMajor>(); |
| test_mixed_storage_imp<ColMajor, RowMajor, RowMajor>(); |
| test_mixed_storage_imp<ColMajor, RowMajor, ColMajor>(); |
| test_mixed_storage_imp<ColMajor, ColMajor, RowMajor>(); |
| test_mixed_storage_imp<ColMajor, ColMajor, ColMajor>(); |
| } |
| |
| EIGEN_DECLARE_TEST(sparse_product) { |
| for (int i = 0; i < g_repeat; i++) { |
| CALL_SUBTEST_1((sparse_product<SparseMatrix<double, ColMajor> >())); |
| CALL_SUBTEST_1((sparse_product<SparseMatrix<double, RowMajor> >())); |
| CALL_SUBTEST_1((bug_942<double>())); |
| CALL_SUBTEST_2((sparse_product<SparseMatrix<std::complex<double>, ColMajor> >())); |
| CALL_SUBTEST_2((sparse_product<SparseMatrix<std::complex<double>, RowMajor> >())); |
| CALL_SUBTEST_3((sparse_product<SparseMatrix<float, ColMajor, long int> >())); |
| CALL_SUBTEST_4(( |
| sparse_product_regression_test<SparseMatrix<double, RowMajor>, Matrix<double, Dynamic, Dynamic, RowMajor> >())); |
| |
| CALL_SUBTEST_5((test_mixing_types<float>())); |
| CALL_SUBTEST_5((test_mixed_storage())); |
| } |
| } |
