test/mapped_matrix.cpp - eigen - Git at Google


            
            // This file is part of Eigen, a lightweight C++ template library

            
            // for linear algebra.

            
            //

            
            // Copyright (C) 2006-2010 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/.

            
            // SPDX-License-Identifier: MPL-2.0


            #include "main.h"

            
            #include "random_for_arithmetic.h"


            #define EIGEN_TESTMAP_MAX_SIZE 256


            template <typename VectorType>

            
            void map_class_vector(const VectorType& m) {

            
              typedef typename VectorType::Scalar Scalar;


              Index size = m.size();


              Scalar* array1 = internal::aligned_new<Scalar>(size);

            
              Scalar* array2 = internal::aligned_new<Scalar>(size);

            
              Scalar* array3 = new Scalar[size + 1];

            
              // In case of no alignment, avoid division by zero.

            
              constexpr int alignment = (std::max<int>)(EIGEN_MAX_ALIGN_BYTES, 1);

            
              Scalar* array3unaligned = (std::uintptr_t(array3) % alignment) == 0 ? array3 + 1 : array3;

            
              Scalar array4[EIGEN_TESTMAP_MAX_SIZE];


              Map<VectorType, AlignedMax>(array1, size) = VectorType::Random(size);

            
              Map<VectorType, AlignedMax>(array2, size) = Map<VectorType, AlignedMax>(array1, size);

            
              Map<VectorType>(array3unaligned, size) = Map<VectorType>(array1, size);

            
              Map<VectorType>(array4, size) = Map<VectorType, AlignedMax>(array1, size);

            
              VectorType ma1 = Map<VectorType, AlignedMax>(array1, size);

            
              VectorType ma2 = Map<VectorType, AlignedMax>(array2, size);

            
              VectorType ma3 = Map<VectorType>(array3unaligned, size);

            
              VectorType ma4 = Map<VectorType>(array4, size);

            
              VERIFY_IS_EQUAL(ma1, ma2);

            
              VERIFY_IS_EQUAL(ma1, ma3);

            
              VERIFY_IS_EQUAL(ma1, ma4);

            
            #ifdef EIGEN_VECTORIZE

            
              if (internal::packet_traits<Scalar>::Vectorizable && size >= AlignedMax)

            
                VERIFY_RAISES_ASSERT((Map<VectorType, AlignedMax>(array3unaligned, size)))

            
            #endif


              internal::aligned_delete(array1, size);

            
              internal::aligned_delete(array2, size);

            
              delete[] array3;

            
            }


            template <typename MatrixType>

            
            void map_class_matrix(const MatrixType& m) {

            
              typedef typename MatrixType::Scalar Scalar;


              Index rows = m.rows(), cols = m.cols(), size = rows * cols;

            
              Scalar s1 = random_scalar_for_arithmetic<Scalar>();


              // array1 and array2 -> aligned heap allocation

            
              Scalar* array1 = internal::aligned_new<Scalar>(size);

            
              for (int i = 0; i < size; i++) array1[i] = Scalar(1);

            
              Scalar* array2 = internal::aligned_new<Scalar>(size);

            
              for (int i = 0; i < size; i++) array2[i] = Scalar(1);

            
              // array3unaligned -> unaligned pointer to heap

            
              Scalar* array3 = new Scalar[size + 1];

            
              Index sizep1 = size + 1;  // <- without this temporary MSVC 2103 generates bad code

            
              for (Index i = 0; i < sizep1; i++) array3[i] = Scalar(1);

            
              // In case of no alignment, avoid division by zero.

            
              constexpr int alignment = (std::max<int>)(EIGEN_MAX_ALIGN_BYTES, 1);

            
              Scalar* array3unaligned = (std::uintptr_t(array3) % alignment) == 0 ? array3 + 1 : array3;

            
              Scalar array4[256];

            
              if (size <= 256)

            
                for (int i = 0; i < size; i++) array4[i] = Scalar(1);


              Map<MatrixType> map1(array1, rows, cols);

            
              Map<MatrixType, AlignedMax> map2(array2, rows, cols);

            
              Map<MatrixType> map3(array3unaligned, rows, cols);

            
              Map<MatrixType> map4(array4, rows, cols);


              VERIFY_IS_EQUAL(map1, MatrixType::Ones(rows, cols));

            
              map1.setConstant(s1);

            
              VERIFY_IS_EQUAL(map1, MatrixType::Constant(rows, cols, s1));

            
              map1.setZero();

            
              VERIFY_IS_EQUAL(map1, MatrixType::Zero(rows, cols));


              VERIFY_IS_EQUAL(map2, MatrixType::Ones(rows, cols));

            
              map2.setConstant(s1);

            
              VERIFY_IS_EQUAL(map2, MatrixType::Constant(rows, cols, s1));

            
              map2.setZero();

            
              VERIFY_IS_EQUAL(map2, MatrixType::Zero(rows, cols));


              VERIFY_IS_EQUAL(map3, MatrixType::Ones(rows, cols));

            
              map3.setConstant(s1);

            
              VERIFY_IS_EQUAL(map3, MatrixType::Constant(rows, cols, s1));

            
              map3.setZero();

            
              VERIFY_IS_EQUAL(map3, MatrixType::Zero(rows, cols));


              map1 = random_for_arithmetic<MatrixType>(rows, cols);

            
              map2 = map1;

            
              map3 = map1;

            
              MatrixType ma1 = map1;

            
              MatrixType ma2 = map2;

            
              MatrixType ma3 = map3;

            
              VERIFY_IS_EQUAL(map1, map2);

            
              VERIFY_IS_EQUAL(map1, map3);

            
              VERIFY_IS_EQUAL(ma1, ma2);

            
              VERIFY_IS_EQUAL(ma1, ma3);

            
              VERIFY_IS_EQUAL(ma1, map3);


              VERIFY_IS_APPROX(s1 * map1, s1 * map2);

            
              VERIFY_IS_APPROX(s1 * ma1, s1 * ma2);

            
              VERIFY_IS_EQUAL(s1 * ma1, s1 * ma3);

            
              VERIFY_IS_APPROX(s1 * map1, s1 * map3);


              map2 *= s1;

            
              map3 *= s1;

            
              VERIFY_IS_APPROX(s1 * map1, map2);

            
              VERIFY_IS_APPROX(s1 * map1, map3);


              if (size <= 256) {

            
                VERIFY_IS_EQUAL(map4, MatrixType::Ones(rows, cols));

            
                map4 = map1;

            
                MatrixType ma4 = map4;

            
                VERIFY_IS_EQUAL(map1, map4);

            
                VERIFY_IS_EQUAL(ma1, map4);

            
                VERIFY_IS_EQUAL(ma1, ma4);

            
                VERIFY_IS_APPROX(s1 * map1, s1 * map4);


                map4 *= s1;

            
                VERIFY_IS_APPROX(s1 * map1, map4);

            
              }


              internal::aligned_delete(array1, size);

            
              internal::aligned_delete(array2, size);

            
              delete[] array3;

            
            }


            template <typename VectorType>

            
            void map_static_methods(const VectorType& m) {

            
              typedef typename VectorType::Scalar Scalar;


              Index size = m.size();


              Scalar* array1 = internal::aligned_new<Scalar>(size);

            
              Scalar* array2 = internal::aligned_new<Scalar>(size);

            
              Scalar* array3 = new Scalar[size + 1];

            
              // In case of no alignment, avoid division by zero.

            
              constexpr int alignment = (std::max<int>)(EIGEN_MAX_ALIGN_BYTES, 1);

            
              Scalar* array3unaligned = (std::uintptr_t(array3) % alignment) == 0 ? array3 + 1 : array3;


              VectorType::MapAligned(array1, size) = VectorType::Random(size);

            
              VectorType::Map(array2, size) = VectorType::Map(array1, size);

            
              VectorType::Map(array3unaligned, size) = VectorType::Map(array1, size);

            
              VectorType ma1 = VectorType::Map(array1, size);

            
              VectorType ma2 = VectorType::MapAligned(array2, size);

            
              VectorType ma3 = VectorType::Map(array3unaligned, size);

            
              VERIFY_IS_EQUAL(ma1, ma2);

            
              VERIFY_IS_EQUAL(ma1, ma3);


              internal::aligned_delete(array1, size);

            
              internal::aligned_delete(array2, size);

            
              delete[] array3;

            
            }


            template <typename PlainObjectType>

            
            void check_const_correctness(const PlainObjectType&) {

            
              // there's a lot that we can't test here while still having this test compile!

            
              // the only possible approach would be to run a script trying to compile stuff and checking that it fails.

            
              // CMake can help with that.


              // verify that map-to-const don't have LvalueBit

            
              typedef std::add_const_t<PlainObjectType> ConstPlainObjectType;

            
              VERIFY(!(internal::traits<Map<ConstPlainObjectType>>::Flags & LvalueBit));

            
              VERIFY(!(internal::traits<Map<ConstPlainObjectType, AlignedMax>>::Flags & LvalueBit));

            
              VERIFY(!(Map<ConstPlainObjectType>::Flags & LvalueBit));

            
              VERIFY(!(Map<ConstPlainObjectType, AlignedMax>::Flags & LvalueBit));

            
            }


            // Test Map with InnerStride at vectorization boundary sizes.

            
            // Strided Maps exercise different traversal paths (SliceVectorized or Default)

            
            // in assignment and reductions.

            
            template <typename Scalar>

            
            void map_inner_stride_boundary() {

            
              const Index PS = internal::packet_traits<Scalar>::size;

            
              const Index sizes[] = {1, 2, 3, PS - 1, PS, PS + 1, 2 * PS, 2 * PS + 1, 4 * PS, 4 * PS + 1};

            
              for (int si = 0; si < 10; ++si) {

            
                const Index n = sizes[si];

            
                if (n <= 0) continue;

            
                typedef Matrix<Scalar, Dynamic, 1> Vec;

            
                // InnerStride<2>: every other element

            
                Vec data = random_for_arithmetic<Vec>(2 * n);

            
                Map<Vec, 0, InnerStride<2>> strided(data.data(), n);


                // Test assignment to/from strided map

            
                Vec dense = strided;

            
                for (Index k = 0; k < n; ++k) VERIFY_IS_APPROX(dense(k), data(2 * k));


                // Test scalar operations on strided map

            
                Vec result = Scalar(2) * strided;

            
                for (Index k = 0; k < n; ++k) VERIFY_IS_APPROX(result(k), Scalar(2) * data(2 * k));


                // Test strided map + dense vector

            
                Vec other = random_for_arithmetic<Vec>(n);

            
                Vec sum_result = strided + other;

            
                for (Index k = 0; k < n; ++k) VERIFY_IS_APPROX(sum_result(k), data(2 * k) + other(k));


                // Test writing to strided map

            
                Map<Vec, 0, InnerStride<2>> strided_dst(data.data(), n);

            
                strided_dst = other;

            
                for (Index k = 0; k < n; ++k) VERIFY_IS_APPROX(data(2 * k), other(k));

            
              }

            
            }


            // Test Map with OuterStride on matrices at boundary sizes.

            
            template <typename Scalar>

            
            void map_outer_stride_boundary() {

            
              const Index PS = internal::packet_traits<Scalar>::size;

            
              typedef Matrix<Scalar, Dynamic, Dynamic> Mat;

            
              // Test various inner dimensions around packet size

            
              const Index inner_sizes[] = {1, PS - 1, PS, PS + 1, 2 * PS, 2 * PS + 1};

            
              const Index outer_stride = 64;  // large enough for any inner size

            
              const Index cols = 4;


              for (int si = 0; si < 6; ++si) {

            
                Index rows = inner_sizes[si];

            
                if (rows <= 0) continue;

            
                typedef Matrix<Scalar, Dynamic, 1> Vec;

            
                Vec data = random_for_arithmetic<Vec>(outer_stride * cols);

            
                Map<Mat, 0, OuterStride<>> mapped(data.data(), rows, cols, OuterStride<>(outer_stride));


                // Test that mapped values match expected layout

            
                Mat dense = mapped;

            
                for (Index j = 0; j < cols; ++j)

            
                  for (Index i = 0; i < rows; ++i) VERIFY_IS_APPROX(dense(i, j), data(j * outer_stride + i));


                // Test reduction on mapped matrix

            
                Scalar ref_sum(0);

            
                for (Index j = 0; j < cols; ++j)

            
                  for (Index i = 0; i < rows; ++i) ref_sum += data(j * outer_stride + i);

            
                VERIFY_IS_APPROX(mapped.sum(), ref_sum);


                // Test matrix product with mapped matrix

            
                Vec x = random_for_arithmetic<Vec>(cols);

            
                Vec y = mapped * x;

            
                Vec y_ref = dense * x;

            
                VERIFY_IS_APPROX(y, y_ref);

            
              }

            
            }


            EIGEN_DECLARE_TEST(mapped_matrix) {

            
              for (int i = 0; i < g_repeat; i++) {

            
                CALL_SUBTEST_1(map_class_vector(Matrix<float, 1, 1>()));

            
                CALL_SUBTEST_1(check_const_correctness(Matrix<float, 1, 1>()));

            
                CALL_SUBTEST_2(map_class_vector(Vector4d()));

            
                CALL_SUBTEST_2(map_class_vector(VectorXd(13)));

            
                CALL_SUBTEST_2(check_const_correctness(Matrix4d()));

            
                CALL_SUBTEST_3(map_class_vector(RowVector4f()));

            
                CALL_SUBTEST_4(map_class_vector(VectorXcf(8)));

            
                CALL_SUBTEST_5(map_class_vector(VectorXi(12)));

            
                CALL_SUBTEST_5(check_const_correctness(VectorXi(12)));


                CALL_SUBTEST_1(map_class_matrix(Matrix<float, 1, 1>()));

            
                CALL_SUBTEST_2(map_class_matrix(Matrix4d()));

            
                CALL_SUBTEST_11(map_class_matrix(Matrix<float, 3, 5>()));

            
                CALL_SUBTEST_4(map_class_matrix(MatrixXcf(internal::random<int>(1, 10), internal::random<int>(1, 10))));

            
                CALL_SUBTEST_5(map_class_matrix(MatrixXi(internal::random<int>(1, 10), internal::random<int>(1, 10))));


                CALL_SUBTEST_6(map_static_methods(Matrix<double, 1, 1>()));

            
                CALL_SUBTEST_7(map_static_methods(Vector3f()));

            
                CALL_SUBTEST_8(map_static_methods(RowVector3d()));

            
                CALL_SUBTEST_9(map_static_methods(VectorXcd(8)));

            
                CALL_SUBTEST_10(map_static_methods(VectorXf(12)));

            
              }


              // Strided map tests at vectorization boundaries (deterministic, outside g_repeat).

            
              CALL_SUBTEST_12(map_inner_stride_boundary<float>());

            
              CALL_SUBTEST_12(map_inner_stride_boundary<double>());

            
              CALL_SUBTEST_13(map_outer_stride_boundary<float>());

            
              CALL_SUBTEST_13(map_outer_stride_boundary<double>());

            
            }
	// This file is part of Eigen, a lightweight C++ template library
	// for linear algebra.
	//
	// Copyright (C) 2006-2010 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/.
	// SPDX-License-Identifier: MPL-2.0

	#include "main.h"
	#include "random_for_arithmetic.h"

	#define EIGEN_TESTMAP_MAX_SIZE 256

	template <typename VectorType>
	void map_class_vector(const VectorType& m) {
	typedef typename VectorType::Scalar Scalar;

	Index size = m.size();

	Scalar* array1 = internal::aligned_new<Scalar>(size);
	Scalar* array2 = internal::aligned_new<Scalar>(size);
	Scalar* array3 = new Scalar[size + 1];
	// In case of no alignment, avoid division by zero.
	constexpr int alignment = (std::max<int>)(EIGEN_MAX_ALIGN_BYTES, 1);
	Scalar* array3unaligned = (std::uintptr_t(array3) % alignment) == 0 ? array3 + 1 : array3;
	Scalar array4[EIGEN_TESTMAP_MAX_SIZE];

	Map<VectorType, AlignedMax>(array1, size) = VectorType::Random(size);
	Map<VectorType, AlignedMax>(array2, size) = Map<VectorType, AlignedMax>(array1, size);
	Map<VectorType>(array3unaligned, size) = Map<VectorType>(array1, size);
	Map<VectorType>(array4, size) = Map<VectorType, AlignedMax>(array1, size);
	VectorType ma1 = Map<VectorType, AlignedMax>(array1, size);
	VectorType ma2 = Map<VectorType, AlignedMax>(array2, size);
	VectorType ma3 = Map<VectorType>(array3unaligned, size);
	VectorType ma4 = Map<VectorType>(array4, size);
	VERIFY_IS_EQUAL(ma1, ma2);
	VERIFY_IS_EQUAL(ma1, ma3);
	VERIFY_IS_EQUAL(ma1, ma4);
	#ifdef EIGEN_VECTORIZE
	if (internal::packet_traits<Scalar>::Vectorizable && size >= AlignedMax)
	VERIFY_RAISES_ASSERT((Map<VectorType, AlignedMax>(array3unaligned, size)))
	#endif

	internal::aligned_delete(array1, size);
	internal::aligned_delete(array2, size);
	delete[] array3;
	}

	template <typename MatrixType>
	void map_class_matrix(const MatrixType& m) {
	typedef typename MatrixType::Scalar Scalar;

	Index rows = m.rows(), cols = m.cols(), size = rows * cols;
	Scalar s1 = random_scalar_for_arithmetic<Scalar>();

	// array1 and array2 -> aligned heap allocation
	Scalar* array1 = internal::aligned_new<Scalar>(size);
	for (int i = 0; i < size; i++) array1[i] = Scalar(1);
	Scalar* array2 = internal::aligned_new<Scalar>(size);
	for (int i = 0; i < size; i++) array2[i] = Scalar(1);
	// array3unaligned -> unaligned pointer to heap
	Scalar* array3 = new Scalar[size + 1];
	Index sizep1 = size + 1; // <- without this temporary MSVC 2103 generates bad code
	for (Index i = 0; i < sizep1; i++) array3[i] = Scalar(1);
	// In case of no alignment, avoid division by zero.
	constexpr int alignment = (std::max<int>)(EIGEN_MAX_ALIGN_BYTES, 1);
	Scalar* array3unaligned = (std::uintptr_t(array3) % alignment) == 0 ? array3 + 1 : array3;
	Scalar array4[256];
	if (size <= 256)
	for (int i = 0; i < size; i++) array4[i] = Scalar(1);

	Map<MatrixType> map1(array1, rows, cols);
	Map<MatrixType, AlignedMax> map2(array2, rows, cols);
	Map<MatrixType> map3(array3unaligned, rows, cols);
	Map<MatrixType> map4(array4, rows, cols);

	VERIFY_IS_EQUAL(map1, MatrixType::Ones(rows, cols));
	map1.setConstant(s1);
	VERIFY_IS_EQUAL(map1, MatrixType::Constant(rows, cols, s1));
	map1.setZero();
	VERIFY_IS_EQUAL(map1, MatrixType::Zero(rows, cols));

	VERIFY_IS_EQUAL(map2, MatrixType::Ones(rows, cols));
	map2.setConstant(s1);
	VERIFY_IS_EQUAL(map2, MatrixType::Constant(rows, cols, s1));
	map2.setZero();
	VERIFY_IS_EQUAL(map2, MatrixType::Zero(rows, cols));

	VERIFY_IS_EQUAL(map3, MatrixType::Ones(rows, cols));
	map3.setConstant(s1);
	VERIFY_IS_EQUAL(map3, MatrixType::Constant(rows, cols, s1));
	map3.setZero();
	VERIFY_IS_EQUAL(map3, MatrixType::Zero(rows, cols));

	map1 = random_for_arithmetic<MatrixType>(rows, cols);
	map2 = map1;
	map3 = map1;
	MatrixType ma1 = map1;
	MatrixType ma2 = map2;
	MatrixType ma3 = map3;
	VERIFY_IS_EQUAL(map1, map2);
	VERIFY_IS_EQUAL(map1, map3);
	VERIFY_IS_EQUAL(ma1, ma2);
	VERIFY_IS_EQUAL(ma1, ma3);
	VERIFY_IS_EQUAL(ma1, map3);

	VERIFY_IS_APPROX(s1 * map1, s1 * map2);
	VERIFY_IS_APPROX(s1 * ma1, s1 * ma2);
	VERIFY_IS_EQUAL(s1 * ma1, s1 * ma3);
	VERIFY_IS_APPROX(s1 * map1, s1 * map3);

	map2 *= s1;
	map3 *= s1;
	VERIFY_IS_APPROX(s1 * map1, map2);
	VERIFY_IS_APPROX(s1 * map1, map3);

	if (size <= 256) {
	VERIFY_IS_EQUAL(map4, MatrixType::Ones(rows, cols));
	map4 = map1;
	MatrixType ma4 = map4;
	VERIFY_IS_EQUAL(map1, map4);
	VERIFY_IS_EQUAL(ma1, map4);
	VERIFY_IS_EQUAL(ma1, ma4);
	VERIFY_IS_APPROX(s1 * map1, s1 * map4);

	map4 *= s1;
	VERIFY_IS_APPROX(s1 * map1, map4);
	}

	internal::aligned_delete(array1, size);
	internal::aligned_delete(array2, size);
	delete[] array3;
	}

	template <typename VectorType>
	void map_static_methods(const VectorType& m) {
	typedef typename VectorType::Scalar Scalar;

	Index size = m.size();

	Scalar* array1 = internal::aligned_new<Scalar>(size);
	Scalar* array2 = internal::aligned_new<Scalar>(size);
	Scalar* array3 = new Scalar[size + 1];
	// In case of no alignment, avoid division by zero.
	constexpr int alignment = (std::max<int>)(EIGEN_MAX_ALIGN_BYTES, 1);
	Scalar* array3unaligned = (std::uintptr_t(array3) % alignment) == 0 ? array3 + 1 : array3;

	VectorType::MapAligned(array1, size) = VectorType::Random(size);
	VectorType::Map(array2, size) = VectorType::Map(array1, size);
	VectorType::Map(array3unaligned, size) = VectorType::Map(array1, size);
	VectorType ma1 = VectorType::Map(array1, size);
	VectorType ma2 = VectorType::MapAligned(array2, size);
	VectorType ma3 = VectorType::Map(array3unaligned, size);
	VERIFY_IS_EQUAL(ma1, ma2);
	VERIFY_IS_EQUAL(ma1, ma3);

	internal::aligned_delete(array1, size);
	internal::aligned_delete(array2, size);
	delete[] array3;
	}

	template <typename PlainObjectType>
	void check_const_correctness(const PlainObjectType&) {
	// there's a lot that we can't test here while still having this test compile!
	// the only possible approach would be to run a script trying to compile stuff and checking that it fails.
	// CMake can help with that.

	// verify that map-to-const don't have LvalueBit
	typedef std::add_const_t<PlainObjectType> ConstPlainObjectType;
	VERIFY(!(internal::traits<Map<ConstPlainObjectType>>::Flags & LvalueBit));
	VERIFY(!(internal::traits<Map<ConstPlainObjectType, AlignedMax>>::Flags & LvalueBit));
	VERIFY(!(Map<ConstPlainObjectType>::Flags & LvalueBit));
	VERIFY(!(Map<ConstPlainObjectType, AlignedMax>::Flags & LvalueBit));
	}

	// Test Map with InnerStride at vectorization boundary sizes.
	// Strided Maps exercise different traversal paths (SliceVectorized or Default)
	// in assignment and reductions.
	template <typename Scalar>
	void map_inner_stride_boundary() {
	const Index PS = internal::packet_traits<Scalar>::size;
	const Index sizes[] = {1, 2, 3, PS - 1, PS, PS + 1, 2 * PS, 2 * PS + 1, 4 * PS, 4 * PS + 1};
	for (int si = 0; si < 10; ++si) {
	const Index n = sizes[si];
	if (n <= 0) continue;
	typedef Matrix<Scalar, Dynamic, 1> Vec;
	// InnerStride<2>: every other element
	Vec data = random_for_arithmetic<Vec>(2 * n);
	Map<Vec, 0, InnerStride<2>> strided(data.data(), n);

	// Test assignment to/from strided map
	Vec dense = strided;
	for (Index k = 0; k < n; ++k) VERIFY_IS_APPROX(dense(k), data(2 * k));

	// Test scalar operations on strided map
	Vec result = Scalar(2) * strided;
	for (Index k = 0; k < n; ++k) VERIFY_IS_APPROX(result(k), Scalar(2) * data(2 * k));

	// Test strided map + dense vector
	Vec other = random_for_arithmetic<Vec>(n);
	Vec sum_result = strided + other;
	for (Index k = 0; k < n; ++k) VERIFY_IS_APPROX(sum_result(k), data(2 * k) + other(k));

	// Test writing to strided map
	Map<Vec, 0, InnerStride<2>> strided_dst(data.data(), n);
	strided_dst = other;
	for (Index k = 0; k < n; ++k) VERIFY_IS_APPROX(data(2 * k), other(k));
	}
	}

	// Test Map with OuterStride on matrices at boundary sizes.
	template <typename Scalar>
	void map_outer_stride_boundary() {
	const Index PS = internal::packet_traits<Scalar>::size;
	typedef Matrix<Scalar, Dynamic, Dynamic> Mat;
	// Test various inner dimensions around packet size
	const Index inner_sizes[] = {1, PS - 1, PS, PS + 1, 2 * PS, 2 * PS + 1};
	const Index outer_stride = 64; // large enough for any inner size
	const Index cols = 4;

	for (int si = 0; si < 6; ++si) {
	Index rows = inner_sizes[si];
	if (rows <= 0) continue;
	typedef Matrix<Scalar, Dynamic, 1> Vec;
	Vec data = random_for_arithmetic<Vec>(outer_stride * cols);
	Map<Mat, 0, OuterStride<>> mapped(data.data(), rows, cols, OuterStride<>(outer_stride));

	// Test that mapped values match expected layout
	Mat dense = mapped;
	for (Index j = 0; j < cols; ++j)
	for (Index i = 0; i < rows; ++i) VERIFY_IS_APPROX(dense(i, j), data(j * outer_stride + i));

	// Test reduction on mapped matrix
	Scalar ref_sum(0);
	for (Index j = 0; j < cols; ++j)
	for (Index i = 0; i < rows; ++i) ref_sum += data(j * outer_stride + i);
	VERIFY_IS_APPROX(mapped.sum(), ref_sum);

	// Test matrix product with mapped matrix
	Vec x = random_for_arithmetic<Vec>(cols);
	Vec y = mapped * x;
	Vec y_ref = dense * x;
	VERIFY_IS_APPROX(y, y_ref);
	}
	}

	EIGEN_DECLARE_TEST(mapped_matrix) {
	for (int i = 0; i < g_repeat; i++) {
	CALL_SUBTEST_1(map_class_vector(Matrix<float, 1, 1>()));
	CALL_SUBTEST_1(check_const_correctness(Matrix<float, 1, 1>()));
	CALL_SUBTEST_2(map_class_vector(Vector4d()));
	CALL_SUBTEST_2(map_class_vector(VectorXd(13)));
	CALL_SUBTEST_2(check_const_correctness(Matrix4d()));
	CALL_SUBTEST_3(map_class_vector(RowVector4f()));
	CALL_SUBTEST_4(map_class_vector(VectorXcf(8)));
	CALL_SUBTEST_5(map_class_vector(VectorXi(12)));
	CALL_SUBTEST_5(check_const_correctness(VectorXi(12)));

	CALL_SUBTEST_1(map_class_matrix(Matrix<float, 1, 1>()));
	CALL_SUBTEST_2(map_class_matrix(Matrix4d()));
	CALL_SUBTEST_11(map_class_matrix(Matrix<float, 3, 5>()));
	CALL_SUBTEST_4(map_class_matrix(MatrixXcf(internal::random<int>(1, 10), internal::random<int>(1, 10))));
	CALL_SUBTEST_5(map_class_matrix(MatrixXi(internal::random<int>(1, 10), internal::random<int>(1, 10))));

	CALL_SUBTEST_6(map_static_methods(Matrix<double, 1, 1>()));
	CALL_SUBTEST_7(map_static_methods(Vector3f()));
	CALL_SUBTEST_8(map_static_methods(RowVector3d()));
	CALL_SUBTEST_9(map_static_methods(VectorXcd(8)));
	CALL_SUBTEST_10(map_static_methods(VectorXf(12)));
	}

	// Strided map tests at vectorization boundaries (deterministic, outside g_repeat).
	CALL_SUBTEST_12(map_inner_stride_boundary<float>());
	CALL_SUBTEST_12(map_inner_stride_boundary<double>());
	CALL_SUBTEST_13(map_outer_stride_boundary<float>());
	CALL_SUBTEST_13(map_outer_stride_boundary<double>());
	}