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 // This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2006-2008 Benoit Jacob // // 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/. #include "main.h" #include template bool areNotApprox(const MatrixBase& m1, const MatrixBase& m2, typename Derived1::RealScalar epsilon = NumTraits::dummy_precision()) { return !((m1-m2).cwiseAbs2().maxCoeff() < epsilon * epsilon * (std::max)(m1.cwiseAbs2().maxCoeff(), m2.cwiseAbs2().maxCoeff())); } template void product(const MatrixType& m) { /* this test covers the following files: Identity.h Product.h */ typedef typename MatrixType::Scalar Scalar; typedef Matrix RowVectorType; typedef Matrix ColVectorType; typedef Matrix RowSquareMatrixType; typedef Matrix ColSquareMatrixType; typedef Matrix OtherMajorMatrixType; Index rows = m.rows(); Index cols = m.cols(); // this test relies a lot on Random.h, and there's not much more that we can do // to test it, hence I consider that we will have tested Random.h MatrixType m1 = MatrixType::Random(rows, cols), m2 = MatrixType::Random(rows, cols), m3(rows, cols); RowSquareMatrixType identity = RowSquareMatrixType::Identity(rows, rows), square = RowSquareMatrixType::Random(rows, rows), res = RowSquareMatrixType::Random(rows, rows); ColSquareMatrixType square2 = ColSquareMatrixType::Random(cols, cols), res2 = ColSquareMatrixType::Random(cols, cols); RowVectorType v1 = RowVectorType::Random(rows); ColVectorType vc2 = ColVectorType::Random(cols), vcres(cols); OtherMajorMatrixType tm1 = m1; Scalar s1 = internal::random(); Index r = internal::random(0, rows-1), c = internal::random(0, cols-1), c2 = internal::random(0, cols-1); // begin testing Product.h: only associativity for now // (we use Transpose.h but this doesn't count as a test for it) VERIFY_IS_APPROX((m1*m1.transpose())*m2, m1*(m1.transpose()*m2)); m3 = m1; m3 *= m1.transpose() * m2; VERIFY_IS_APPROX(m3, m1 * (m1.transpose()*m2)); VERIFY_IS_APPROX(m3, m1 * (m1.transpose()*m2)); // continue testing Product.h: distributivity VERIFY_IS_APPROX(square*(m1 + m2), square*m1+square*m2); VERIFY_IS_APPROX(square*(m1 - m2), square*m1-square*m2); // continue testing Product.h: compatibility with ScalarMultiple.h VERIFY_IS_APPROX(s1*(square*m1), (s1*square)*m1); VERIFY_IS_APPROX(s1*(square*m1), square*(m1*s1)); // test Product.h together with Identity.h VERIFY_IS_APPROX(v1, identity*v1); VERIFY_IS_APPROX(v1.transpose(), v1.transpose() * identity); // again, test operator() to check const-qualification VERIFY_IS_APPROX(MatrixType::Identity(rows, cols)(r,c), static_cast(r==c)); if (rows!=cols) VERIFY_RAISES_ASSERT(m3 = m1*m1); // test the previous tests were not screwed up because operator* returns 0 // (we use the more accurate default epsilon) if (!NumTraits::IsInteger && (std::min)(rows,cols)>1) { VERIFY(areNotApprox(m1.transpose()*m2,m2.transpose()*m1)); } // test optimized operator+= path res = square; res.noalias() += m1 * m2.transpose(); VERIFY_IS_APPROX(res, square + m1 * m2.transpose()); if (!NumTraits::IsInteger && (std::min)(rows,cols)>1) { VERIFY(areNotApprox(res,square + m2 * m1.transpose())); } vcres = vc2; vcres.noalias() += m1.transpose() * v1; VERIFY_IS_APPROX(vcres, vc2 + m1.transpose() * v1); // test optimized operator-= path res = square; res.noalias() -= m1 * m2.transpose(); VERIFY_IS_APPROX(res, square - (m1 * m2.transpose())); if (!NumTraits::IsInteger && (std::min)(rows,cols)>1) { VERIFY(areNotApprox(res,square - m2 * m1.transpose())); } vcres = vc2; vcres.noalias() -= m1.transpose() * v1; VERIFY_IS_APPROX(vcres, vc2 - m1.transpose() * v1); // test scaled products res = square; res.noalias() = s1 * m1 * m2.transpose(); VERIFY_IS_APPROX(res, ((s1*m1).eval() * m2.transpose())); res = square; res.noalias() += s1 * m1 * m2.transpose(); VERIFY_IS_APPROX(res, square + ((s1*m1).eval() * m2.transpose())); res = square; res.noalias() -= s1 * m1 * m2.transpose(); VERIFY_IS_APPROX(res, square - ((s1*m1).eval() * m2.transpose())); // test d ?= a+b*c rules res.noalias() = square + m1 * m2.transpose(); VERIFY_IS_APPROX(res, square + m1 * m2.transpose()); res.noalias() += square + m1 * m2.transpose(); VERIFY_IS_APPROX(res, 2*(square + m1 * m2.transpose())); res.noalias() -= square + m1 * m2.transpose(); VERIFY_IS_APPROX(res, square + m1 * m2.transpose()); // test d ?= a-b*c rules res.noalias() = square - m1 * m2.transpose(); VERIFY_IS_APPROX(res, square - m1 * m2.transpose()); res.noalias() += square - m1 * m2.transpose(); VERIFY_IS_APPROX(res, 2*(square - m1 * m2.transpose())); res.noalias() -= square - m1 * m2.transpose(); VERIFY_IS_APPROX(res, square - m1 * m2.transpose()); tm1 = m1; VERIFY_IS_APPROX(tm1.transpose() * v1, m1.transpose() * v1); VERIFY_IS_APPROX(v1.transpose() * tm1, v1.transpose() * m1); // test submatrix and matrix/vector product for (int i=0; i::IsInteger && (std::min)(rows,cols)>1) { VERIFY(areNotApprox(res2,square2 + m2.transpose() * m1)); } VERIFY_IS_APPROX(res.col(r).noalias() = square.adjoint() * square.col(r), (square.adjoint() * square.col(r)).eval()); VERIFY_IS_APPROX(res.col(r).noalias() = square * square.col(r), (square * square.col(r)).eval()); // vector at runtime (see bug 1166) { RowSquareMatrixType ref(square); ColSquareMatrixType ref2(square2); ref = res = square; VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.col(0).transpose() * square.transpose(), (ref.row(0) = m1.col(0).transpose() * square.transpose())); VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.block(0,0,rows,1).transpose() * square.transpose(), (ref.row(0) = m1.col(0).transpose() * square.transpose())); VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.col(0).transpose() * square, (ref.row(0) = m1.col(0).transpose() * square)); VERIFY_IS_APPROX(res.block(0,0,1,rows).noalias() = m1.block(0,0,rows,1).transpose() * square, (ref.row(0) = m1.col(0).transpose() * square)); ref2 = res2 = square2; VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2.transpose(), (ref2.row(0) = m1.row(0) * square2.transpose())); VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.block(0,0,1,cols) * square2.transpose(), (ref2.row(0) = m1.row(0) * square2.transpose())); VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.row(0) * square2, (ref2.row(0) = m1.row(0) * square2)); VERIFY_IS_APPROX(res2.block(0,0,1,cols).noalias() = m1.block(0,0,1,cols) * square2, (ref2.row(0) = m1.row(0) * square2)); } // vector.block() (see bug 1283) { RowVectorType w1(rows); VERIFY_IS_APPROX(square * v1.block(0,0,rows,1), square * v1); VERIFY_IS_APPROX(w1.noalias() = square * v1.block(0,0,rows,1), square * v1); VERIFY_IS_APPROX(w1.block(0,0,rows,1).noalias() = square * v1.block(0,0,rows,1), square * v1); Matrix w2(cols); VERIFY_IS_APPROX(vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2); VERIFY_IS_APPROX(w2.noalias() = vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2); VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = vc2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2); vc2 = square2.block(0,0,1,cols).transpose(); VERIFY_IS_APPROX(square2.block(0,0,1,cols) * square2, vc2.transpose() * square2); VERIFY_IS_APPROX(w2.noalias() = square2.block(0,0,1,cols) * square2, vc2.transpose() * square2); VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = square2.block(0,0,1,cols) * square2, vc2.transpose() * square2); vc2 = square2.block(0,0,cols,1); VERIFY_IS_APPROX(square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2); VERIFY_IS_APPROX(w2.noalias() = square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2); VERIFY_IS_APPROX(w2.block(0,0,1,cols).noalias() = square2.block(0,0,cols,1).transpose() * square2, vc2.transpose() * square2); } // inner product { Scalar x = square2.row(c) * square2.col(c2); VERIFY_IS_APPROX(x, square2.row(c).transpose().cwiseProduct(square2.col(c2)).sum()); } // outer product { VERIFY_IS_APPROX(m1.col(c) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols)); VERIFY_IS_APPROX(m1.row(r).transpose() * m1.col(c).transpose(), m1.block(r,0,1,cols).transpose() * m1.block(0,c,rows,1).transpose()); VERIFY_IS_APPROX(m1.block(0,c,rows,1) * m1.row(r), m1.block(0,c,rows,1) * m1.block(r,0,1,cols)); VERIFY_IS_APPROX(m1.col(c) * m1.block(r,0,1,cols), m1.block(0,c,rows,1) * m1.block(r,0,1,cols)); VERIFY_IS_APPROX(m1.leftCols(1) * m1.row(r), m1.block(0,0,rows,1) * m1.block(r,0,1,cols)); VERIFY_IS_APPROX(m1.col(c) * m1.topRows(1), m1.block(0,c,rows,1) * m1.block(0,0,1,cols)); } // Aliasing { ColVectorType x(cols); x.setRandom(); ColVectorType z(x); ColVectorType y(cols); y.setZero(); ColSquareMatrixType A(cols,cols); A.setRandom(); // CwiseBinaryOp VERIFY_IS_APPROX(x = y + A*x, A*z); x = z; // CwiseUnaryOp VERIFY_IS_APPROX(x = Scalar(1.)*(A*x), A*z); } // regression for blas_trais { VERIFY_IS_APPROX(square * (square*square).transpose(), square * square.transpose() * square.transpose()); VERIFY_IS_APPROX(square * (-(square*square)), -square * square * square); VERIFY_IS_APPROX(square * (s1*(square*square)), s1 * square * square * square); VERIFY_IS_APPROX(square * (square*square).conjugate(), square * square.conjugate() * square.conjugate()); } // destination with a non-default inner-stride // see bug 1741 if(!MatrixType::IsRowMajor) { typedef Matrix MatrixX; MatrixX buffer(2*rows,2*rows); Map > map1(buffer.data(),rows,rows,Stride(2*rows,2)); buffer.setZero(); VERIFY_IS_APPROX(map1 = m1 * m2.transpose(), (m1 * m2.transpose()).eval()); buffer.setZero(); VERIFY_IS_APPROX(map1.noalias() = m1 * m2.transpose(), (m1 * m2.transpose()).eval()); buffer.setZero(); VERIFY_IS_APPROX(map1.noalias() += m1 * m2.transpose(), (m1 * m2.transpose()).eval()); } }