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eigen/test/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/.
#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(numext::is_exactly_zero((v1 * very_small).norm()));
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, typename Scalar = typename MatrixType::Scalar>
MatrixType RandomMatrix(Index rows, Index cols, Scalar min, Scalar max) {
MatrixType M = MatrixType(rows, cols);
for (Index i = 0; i < rows; ++i) {
for (Index j = 0; j < cols; ++j) {
M(i, j) = Eigen::internal::random<Scalar>(min, max);
}
}
return M;
}
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();
// Avoid integer overflow by limiting input values.
RealScalar rmin = static_cast<RealScalar>(NumTraits<Scalar>::IsInteger ? NumTraits<Scalar>::IsSigned ? -100 : 0 : -1);
RealScalar rmax = static_cast<RealScalar>(NumTraits<Scalar>::IsInteger ? 100 : 1);
MatrixType m1 = RandomMatrix<MatrixType>(rows, cols, rmin, rmax),
m2 = RandomMatrix<MatrixType>(rows, cols, rmin, rmax), m3(rows, cols),
square = RandomMatrix<SquareMatrixType>(rows, rows, rmin, rmax);
VectorType v1 = RandomMatrix<VectorType>(rows, 1, rmin, rmax), v2 = RandomMatrix<VectorType>(rows, 1, rmin, rmax),
v3 = RandomMatrix<VectorType>(rows, 1, rmin, rmax), vzero = VectorType::Zero(rows);
Scalar s1 = internal::random<Scalar>(rmin, rmax), s2 = internal::random<Scalar>(rmin, rmax);
// 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 = RandomMatrix<RealVectorType>(rows, 1, rmin, rmax);
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();
}
template <typename Scalar>
void inner_product_boundary_sizes() {
const Index PS = internal::packet_traits<Scalar>::size;
// Sizes that exercise every branch in the 4-way unrolled vectorized inner product:
// scalar fallback (< PS), 1-3 packets, quad loop entry/exit, remainder packets, scalar cleanup
const Index sizes[] = {0,
1,
PS - 1,
PS,
PS + 1,
2 * PS - 1,
2 * PS,
2 * PS + 1,
3 * PS - 1,
3 * PS,
3 * PS + 1,
4 * PS - 1,
4 * PS,
4 * PS + 1,
8 * PS,
8 * PS + 1,
8 * PS + PS,
8 * PS + 2 * PS,
8 * PS + 3 * PS,
8 * PS + 3 * PS + 1};
for (int si = 0; si < 20; ++si) {
const Index n = sizes[si];
if (n <= 0) continue;
typedef Matrix<Scalar, Dynamic, 1> Vec;
Vec v1 = Vec::Random(n);
Vec v2 = Vec::Random(n);
// Reference: scalar loop
Scalar expected(0);
for (Index k = 0; k < n; ++k) expected += numext::conj(v1(k)) * v2(k);
VERIFY_IS_APPROX(v1.dot(v2), expected);
// Also test squaredNorm
Scalar sq_expected(0);
for (Index k = 0; k < n; ++k) sq_expected += numext::conj(v1(k)) * v1(k);
VERIFY_IS_APPROX(v1.squaredNorm(), numext::real(sq_expected));
}
}
// Test transposeInPlace at vectorization boundary sizes.
// BlockedInPlaceTranspose uses PacketSize-blocked loops with a scalar remainder (line 273),
// exercising off-by-one-prone transitions.
template <typename Scalar>
void transposeInPlace_boundary() {
const Index PS = internal::packet_traits<Scalar>::size;
// Sizes around packet boundaries where the blocked path's remainder handling is exercised.
const Index sizes[] = {1, 2, 3, PS - 1, PS, PS + 1, 2 * PS - 1,
2 * PS, 2 * PS + 1, 3 * PS, 3 * PS + 1, 4 * PS, 4 * PS + 1};
for (int si = 0; si < 13; ++si) {
Index n = sizes[si];
if (n <= 0) continue;
typedef Matrix<Scalar, Dynamic, Dynamic> Mat;
// Square transposeInPlace
Mat m1 = Mat::Random(n, n);
Mat m2 = m1;
m2.transposeInPlace();
VERIFY_IS_APPROX(m2, m1.transpose());
// Double transpose should return to original
m2.transposeInPlace();
VERIFY_IS_APPROX(m2, m1);
}
// Non-square transposeInPlace (resizable dynamic matrices)
const Index rect_sizes[][2] = {{2, 5}, {PS, 2 * PS + 1}, {3, 1}, {1, 7}, {2 * PS, PS + 1}};
for (int si = 0; si < 5; ++si) {
Index r = rect_sizes[si][0], c = rect_sizes[si][1];
if (r <= 0 || c <= 0) continue;
typedef Matrix<Scalar, Dynamic, Dynamic> Mat;
Mat m1 = Mat::Random(r, c);
Mat expected = m1.transpose();
Mat m2 = m1;
m2.transposeInPlace();
VERIFY_IS_APPROX(m2, expected);
VERIFY(m2.rows() == c && m2.cols() == r);
}
}
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>());
// Inner product vectorization boundary tests (deterministic, outside g_repeat)
CALL_SUBTEST_14(inner_product_boundary_sizes<float>());
CALL_SUBTEST_15(inner_product_boundary_sizes<double>());
CALL_SUBTEST_16(inner_product_boundary_sizes<std::complex<float>>());
CALL_SUBTEST_17(inner_product_boundary_sizes<std::complex<double>>());
// transposeInPlace at vectorization boundaries (deterministic, outside g_repeat).
CALL_SUBTEST_18(transposeInPlace_boundary<float>());
CALL_SUBTEST_18(transposeInPlace_boundary<double>());
CALL_SUBTEST_18(transposeInPlace_boundary<std::complex<float>>());
}
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