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Thu, Feb 20, 22:17

adjoint.cpp
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// 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/.
#define EIGEN_NO_STATIC_ASSERT
#include "main.h"
template<bool IsInteger> struct adjoint_specific;
template<> struct adjoint_specific<true> {
template<typename Vec, typename Mat, typename Scalar>
static void run(const Vec& v1, const Vec& v2, Vec& v3, const Mat& square, Scalar s1, Scalar s2) {
VERIFY(test_isApproxWithRef((s1 * v1 + s2 * v2).dot(v3), numext::conj(s1) * v1.dot(v3) + numext::conj(s2) * v2.dot(v3), 0));
VERIFY(test_isApproxWithRef(v3.dot(s1 * v1 + s2 * v2), s1*v3.dot(v1)+s2*v3.dot(v2), 0));
// check compatibility of dot and adjoint
VERIFY(test_isApproxWithRef(v1.dot(square * v2), (square.adjoint() * v1).dot(v2), 0));
}
};
template<> struct adjoint_specific<false> {
template<typename Vec, typename Mat, typename Scalar>
static void run(const Vec& v1, const Vec& v2, Vec& v3, const Mat& square, Scalar s1, Scalar s2) {
typedef typename NumTraits<Scalar>::Real RealScalar;
using std::abs;
RealScalar ref = NumTraits<Scalar>::IsInteger ? RealScalar(0) : (std::max)((s1 * v1 + s2 * v2).norm(),v3.norm());
VERIFY(test_isApproxWithRef((s1 * v1 + s2 * v2).dot(v3), numext::conj(s1) * v1.dot(v3) + numext::conj(s2) * v2.dot(v3), ref));
VERIFY(test_isApproxWithRef(v3.dot(s1 * v1 + s2 * v2), s1*v3.dot(v1)+s2*v3.dot(v2), ref));
VERIFY_IS_APPROX(v1.squaredNorm(), v1.norm() * v1.norm());
// check normalized() and normalize()
VERIFY_IS_APPROX(v1, v1.norm() * v1.normalized());
v3 = v1;
v3.normalize();
VERIFY_IS_APPROX(v1, v1.norm() * v3);
VERIFY_IS_APPROX(v3, v1.normalized());
VERIFY_IS_APPROX(v3.norm(), RealScalar(1));
// check null inputs
VERIFY_IS_APPROX((v1*0).normalized(), (v1*0));
#if (!EIGEN_ARCH_i386) || defined(EIGEN_VECTORIZE)
RealScalar very_small = (std::numeric_limits<RealScalar>::min)();
VERIFY( (v1*very_small).norm() == 0 );
VERIFY_IS_APPROX((v1*very_small).normalized(), (v1*very_small));
v3 = v1*very_small;
v3.normalize();
VERIFY_IS_APPROX(v3, (v1*very_small));
#endif
// check compatibility of dot and adjoint
ref = NumTraits<Scalar>::IsInteger ? 0 : (std::max)((std::max)(v1.norm(),v2.norm()),(std::max)((square * v2).norm(),(square.adjoint() * v1).norm()));
VERIFY(internal::isMuchSmallerThan(abs(v1.dot(square * v2) - (square.adjoint() * v1).dot(v2)), ref, test_precision<Scalar>()));
// check that Random().normalized() works: tricky as the random xpr must be evaluated by
// normalized() in order to produce a consistent result.
VERIFY_IS_APPROX(Vec::Random(v1.size()).normalized().norm(), RealScalar(1));
}
};
template<typename MatrixType> void adjoint(const MatrixType& m)
{
/* this test covers the following files:
Transpose.h Conjugate.h Dot.h
*/
using std::abs;
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
const Index PacketSize = internal::packet_traits<Scalar>::size;
Index rows = m.rows();
Index cols = m.cols();
MatrixType m1 = MatrixType::Random(rows, cols),
m2 = MatrixType::Random(rows, cols),
m3(rows, cols),
square = SquareMatrixType::Random(rows, rows);
VectorType v1 = VectorType::Random(rows),
v2 = VectorType::Random(rows),
v3 = VectorType::Random(rows),
vzero = VectorType::Zero(rows);
Scalar s1 = internal::random<Scalar>(),
s2 = internal::random<Scalar>();
// check basic compatibility of adjoint, transpose, conjugate
VERIFY_IS_APPROX(m1.transpose().conjugate().adjoint(), m1);
VERIFY_IS_APPROX(m1.adjoint().conjugate().transpose(), m1);
// check multiplicative behavior
VERIFY_IS_APPROX((m1.adjoint() * m2).adjoint(), m2.adjoint() * m1);
VERIFY_IS_APPROX((s1 * m1).adjoint(), numext::conj(s1) * m1.adjoint());
// check basic properties of dot, squaredNorm
VERIFY_IS_APPROX(numext::conj(v1.dot(v2)), v2.dot(v1));
VERIFY_IS_APPROX(numext::real(v1.dot(v1)), v1.squaredNorm());
adjoint_specific<NumTraits<Scalar>::IsInteger>::run(v1, v2, v3, square, s1, s2);
VERIFY_IS_MUCH_SMALLER_THAN(abs(vzero.dot(v1)), static_cast<RealScalar>(1));
// like in testBasicStuff, test operator() to check const-qualification
Index r = internal::random<Index>(0, rows-1),
c = internal::random<Index>(0, cols-1);
VERIFY_IS_APPROX(m1.conjugate()(r,c), numext::conj(m1(r,c)));
VERIFY_IS_APPROX(m1.adjoint()(c,r), numext::conj(m1(r,c)));
// check inplace transpose
m3 = m1;
m3.transposeInPlace();
VERIFY_IS_APPROX(m3,m1.transpose());
m3.transposeInPlace();
VERIFY_IS_APPROX(m3,m1);
if(PacketSize<m3.rows() && PacketSize<m3.cols())
{
m3 = m1;
Index i = internal::random<Index>(0,m3.rows()-PacketSize);
Index j = internal::random<Index>(0,m3.cols()-PacketSize);
m3.template block<PacketSize,PacketSize>(i,j).transposeInPlace();
VERIFY_IS_APPROX( (m3.template block<PacketSize,PacketSize>(i,j)), (m1.template block<PacketSize,PacketSize>(i,j).transpose()) );
m3.template block<PacketSize,PacketSize>(i,j).transposeInPlace();
VERIFY_IS_APPROX(m3,m1);
}
// check inplace adjoint
m3 = m1;
m3.adjointInPlace();
VERIFY_IS_APPROX(m3,m1.adjoint());
m3.transposeInPlace();
VERIFY_IS_APPROX(m3,m1.conjugate());
// check mixed dot product
typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType;
RealVectorType rv1 = RealVectorType::Random(rows);
VERIFY_IS_APPROX(v1.dot(rv1.template cast<Scalar>()), v1.dot(rv1));
VERIFY_IS_APPROX(rv1.template cast<Scalar>().dot(v1), rv1.dot(v1));
VERIFY( is_same_type(m1,m1.template conjugateIf<false>()) );
VERIFY( is_same_type(m1.conjugate(),m1.template conjugateIf<true>()) );
}
template<int>
void adjoint_extra()
{
MatrixXcf a(10,10), b(10,10);
VERIFY_RAISES_ASSERT(a = a.transpose());
VERIFY_RAISES_ASSERT(a = a.transpose() + b);
VERIFY_RAISES_ASSERT(a = b + a.transpose());
VERIFY_RAISES_ASSERT(a = a.conjugate().transpose());
VERIFY_RAISES_ASSERT(a = a.adjoint());
VERIFY_RAISES_ASSERT(a = a.adjoint() + b);
VERIFY_RAISES_ASSERT(a = b + a.adjoint());
// no assertion should be triggered for these cases:
a.transpose() = a.transpose();
a.transpose() += a.transpose();
a.transpose() += a.transpose() + b;
a.transpose() = a.adjoint();
a.transpose() += a.adjoint();
a.transpose() += a.adjoint() + b;
// regression tests for check_for_aliasing
MatrixXd c(10,10);
c = 1.0 * MatrixXd::Ones(10,10) + c;
c = MatrixXd::Ones(10,10) * 1.0 + c;
c = c + MatrixXd::Ones(10,10) .cwiseProduct( MatrixXd::Zero(10,10) );
c = MatrixXd::Ones(10,10) * MatrixXd::Zero(10,10);
// regression for bug 1646
for (int j = 0; j < 10; ++j) {
c.col(j).head(j) = c.row(j).head(j);
}
for (int j = 0; j < 10; ++j) {
c.col(j) = c.row(j);
}
a.conservativeResize(1,1);
a = a.transpose();
a.conservativeResize(0,0);
a = a.transpose();
}
EIGEN_DECLARE_TEST(adjoint)
{
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( adjoint(Matrix<float, 1, 1>()) );
CALL_SUBTEST_2( adjoint(Matrix3d()) );
CALL_SUBTEST_3( adjoint(Matrix4f()) );
CALL_SUBTEST_4( adjoint(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2), internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
CALL_SUBTEST_5( adjoint(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
CALL_SUBTEST_6( adjoint(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
// Complement for 128 bits vectorization:
CALL_SUBTEST_8( adjoint(Matrix2d()) );
CALL_SUBTEST_9( adjoint(Matrix<int,4,4>()) );
// 256 bits vectorization:
CALL_SUBTEST_10( adjoint(Matrix<float,8,8>()) );
CALL_SUBTEST_11( adjoint(Matrix<double,4,4>()) );
CALL_SUBTEST_12( adjoint(Matrix<int,8,8>()) );
}
// test a large static matrix only once
CALL_SUBTEST_7( adjoint(Matrix<float, 100, 100>()) );
CALL_SUBTEST_13( adjoint_extra<0>() );
}

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