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eigen/test/product_small.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 "product.h"
#include <Eigen/LU>
// regression test for bug 447
template <int>
void product1x1() {
Matrix<float, 1, 3> matAstatic;
Matrix<float, 3, 1> matBstatic;
matAstatic.setRandom();
matBstatic.setRandom();
VERIFY_IS_APPROX((matAstatic * matBstatic).coeff(0, 0), matAstatic.cwiseProduct(matBstatic.transpose()).sum());
MatrixXf matAdynamic(1, 3);
MatrixXf matBdynamic(3, 1);
matAdynamic.setRandom();
matBdynamic.setRandom();
VERIFY_IS_APPROX((matAdynamic * matBdynamic).coeff(0, 0), matAdynamic.cwiseProduct(matBdynamic.transpose()).sum());
}
template <typename TC, typename TA, typename TB>
const TC &ref_prod(TC &C, const TA &A, const TB &B) {
for (Index i = 0; i < C.rows(); ++i)
for (Index j = 0; j < C.cols(); ++j)
for (Index k = 0; k < A.cols(); ++k) C.coeffRef(i, j) += A.coeff(i, k) * B.coeff(k, j);
return C;
}
template <typename T, int Rows, int Cols, int Depth, int OC, int OA, int OB>
std::enable_if_t<!((Rows == 1 && Depth != 1 && OA == ColMajor) || (Depth == 1 && Rows != 1 && OA == RowMajor) ||
(Cols == 1 && Depth != 1 && OB == RowMajor) || (Depth == 1 && Cols != 1 && OB == ColMajor) ||
(Rows == 1 && Cols != 1 && OC == ColMajor) || (Cols == 1 && Rows != 1 && OC == RowMajor)),
void>
test_lazy_single(int rows, int cols, int depth) {
Matrix<T, Rows, Depth, OA> A(rows, depth);
A.setRandom();
Matrix<T, Depth, Cols, OB> B(depth, cols);
B.setRandom();
Matrix<T, Rows, Cols, OC> C(rows, cols);
C.setRandom();
Matrix<T, Rows, Cols, OC> D(C);
VERIFY_IS_APPROX(C += A.lazyProduct(B), ref_prod(D, A, B));
}
void test_dynamic_bool() {
int rows = internal::random<int>(1, 64);
int cols = internal::random<int>(1, 64);
int depth = internal::random<int>(1, 65);
typedef Matrix<bool, Dynamic, Dynamic> MatrixX;
MatrixX A(rows, depth);
A.setRandom();
MatrixX B(depth, cols);
B.setRandom();
MatrixX C(rows, cols);
C.setRandom();
MatrixX D(C);
for (Index i = 0; i < C.rows(); ++i)
for (Index j = 0; j < C.cols(); ++j)
for (Index k = 0; k < A.cols(); ++k) D.coeffRef(i, j) |= (A.coeff(i, k) && B.coeff(k, j));
C += A * B;
VERIFY_IS_EQUAL(C, D);
MatrixX E = B.transpose();
for (Index i = 0; i < B.rows(); ++i)
for (Index j = 0; j < B.cols(); ++j) VERIFY_IS_EQUAL(B(i, j), E(j, i));
}
template <typename T, int Rows, int Cols, int Depth, int OC, int OA, int OB>
std::enable_if_t<((Rows == 1 && Depth != 1 && OA == ColMajor) || (Depth == 1 && Rows != 1 && OA == RowMajor) ||
(Cols == 1 && Depth != 1 && OB == RowMajor) || (Depth == 1 && Cols != 1 && OB == ColMajor) ||
(Rows == 1 && Cols != 1 && OC == ColMajor) || (Cols == 1 && Rows != 1 && OC == RowMajor)),
void>
test_lazy_single(int, int, int) {}
template <typename T, int Rows, int Cols, int Depth>
void test_lazy_all_layout(int rows = Rows, int cols = Cols, int depth = Depth) {
CALL_SUBTEST((test_lazy_single<T, Rows, Cols, Depth, ColMajor, ColMajor, ColMajor>(rows, cols, depth)));
CALL_SUBTEST((test_lazy_single<T, Rows, Cols, Depth, RowMajor, ColMajor, ColMajor>(rows, cols, depth)));
CALL_SUBTEST((test_lazy_single<T, Rows, Cols, Depth, ColMajor, RowMajor, ColMajor>(rows, cols, depth)));
CALL_SUBTEST((test_lazy_single<T, Rows, Cols, Depth, RowMajor, RowMajor, ColMajor>(rows, cols, depth)));
CALL_SUBTEST((test_lazy_single<T, Rows, Cols, Depth, ColMajor, ColMajor, RowMajor>(rows, cols, depth)));
CALL_SUBTEST((test_lazy_single<T, Rows, Cols, Depth, RowMajor, ColMajor, RowMajor>(rows, cols, depth)));
CALL_SUBTEST((test_lazy_single<T, Rows, Cols, Depth, ColMajor, RowMajor, RowMajor>(rows, cols, depth)));
CALL_SUBTEST((test_lazy_single<T, Rows, Cols, Depth, RowMajor, RowMajor, RowMajor>(rows, cols, depth)));
}
template <typename T>
void test_lazy_l1() {
int rows = internal::random<int>(1, 12);
int cols = internal::random<int>(1, 12);
int depth = internal::random<int>(1, 12);
// Inner
CALL_SUBTEST((test_lazy_all_layout<T, 1, 1, 1>()));
CALL_SUBTEST((test_lazy_all_layout<T, 1, 1, 2>()));
CALL_SUBTEST((test_lazy_all_layout<T, 1, 1, 3>()));
CALL_SUBTEST((test_lazy_all_layout<T, 1, 1, 8>()));
CALL_SUBTEST((test_lazy_all_layout<T, 1, 1, 9>()));
CALL_SUBTEST((test_lazy_all_layout<T, 1, 1, -1>(1, 1, depth)));
// Outer
CALL_SUBTEST((test_lazy_all_layout<T, 2, 1, 1>()));
CALL_SUBTEST((test_lazy_all_layout<T, 1, 2, 1>()));
CALL_SUBTEST((test_lazy_all_layout<T, 2, 2, 1>()));
CALL_SUBTEST((test_lazy_all_layout<T, 3, 3, 1>()));
CALL_SUBTEST((test_lazy_all_layout<T, 4, 4, 1>()));
CALL_SUBTEST((test_lazy_all_layout<T, 4, 8, 1>()));
CALL_SUBTEST((test_lazy_all_layout<T, 4, -1, 1>(4, cols)));
CALL_SUBTEST((test_lazy_all_layout<T, 7, -1, 1>(7, cols)));
CALL_SUBTEST((test_lazy_all_layout<T, -1, 8, 1>(rows)));
CALL_SUBTEST((test_lazy_all_layout<T, -1, 3, 1>(rows)));
CALL_SUBTEST((test_lazy_all_layout<T, -1, -1, 1>(rows, cols)));
}
template <typename T>
void test_lazy_l2() {
int rows = internal::random<int>(1, 12);
int cols = internal::random<int>(1, 12);
int depth = internal::random<int>(1, 12);
// mat-vec
CALL_SUBTEST((test_lazy_all_layout<T, 2, 1, 2>()));
CALL_SUBTEST((test_lazy_all_layout<T, 2, 1, 4>()));
CALL_SUBTEST((test_lazy_all_layout<T, 4, 1, 2>()));
CALL_SUBTEST((test_lazy_all_layout<T, 4, 1, 4>()));
CALL_SUBTEST((test_lazy_all_layout<T, 5, 1, 4>()));
CALL_SUBTEST((test_lazy_all_layout<T, 4, 1, 5>()));
CALL_SUBTEST((test_lazy_all_layout<T, 4, 1, 6>()));
CALL_SUBTEST((test_lazy_all_layout<T, 6, 1, 4>()));
CALL_SUBTEST((test_lazy_all_layout<T, 8, 1, 8>()));
CALL_SUBTEST((test_lazy_all_layout<T, -1, 1, 4>(rows)));
CALL_SUBTEST((test_lazy_all_layout<T, 4, 1, -1>(4, 1, depth)));
CALL_SUBTEST((test_lazy_all_layout<T, -1, 1, -1>(rows, 1, depth)));
// vec-mat
CALL_SUBTEST((test_lazy_all_layout<T, 1, 2, 2>()));
CALL_SUBTEST((test_lazy_all_layout<T, 1, 2, 4>()));
CALL_SUBTEST((test_lazy_all_layout<T, 1, 4, 2>()));
CALL_SUBTEST((test_lazy_all_layout<T, 1, 4, 4>()));
CALL_SUBTEST((test_lazy_all_layout<T, 1, 5, 4>()));
CALL_SUBTEST((test_lazy_all_layout<T, 1, 4, 5>()));
CALL_SUBTEST((test_lazy_all_layout<T, 1, 4, 6>()));
CALL_SUBTEST((test_lazy_all_layout<T, 1, 6, 4>()));
CALL_SUBTEST((test_lazy_all_layout<T, 1, 8, 8>()));
CALL_SUBTEST((test_lazy_all_layout<T, 1, -1, 4>(1, cols)));
CALL_SUBTEST((test_lazy_all_layout<T, 1, 4, -1>(1, 4, depth)));
CALL_SUBTEST((test_lazy_all_layout<T, 1, -1, -1>(1, cols, depth)));
}
template <typename T>
void test_lazy_l3() {
int rows = internal::random<int>(1, 12);
int cols = internal::random<int>(1, 12);
int depth = internal::random<int>(1, 12);
// mat-mat
CALL_SUBTEST((test_lazy_all_layout<T, 2, 4, 2>()));
CALL_SUBTEST((test_lazy_all_layout<T, 2, 6, 4>()));
CALL_SUBTEST((test_lazy_all_layout<T, 4, 3, 2>()));
CALL_SUBTEST((test_lazy_all_layout<T, 4, 8, 4>()));
CALL_SUBTEST((test_lazy_all_layout<T, 5, 6, 4>()));
CALL_SUBTEST((test_lazy_all_layout<T, 4, 2, 5>()));
CALL_SUBTEST((test_lazy_all_layout<T, 4, 7, 6>()));
CALL_SUBTEST((test_lazy_all_layout<T, 6, 8, 4>()));
CALL_SUBTEST((test_lazy_all_layout<T, 8, 3, 8>()));
CALL_SUBTEST((test_lazy_all_layout<T, -1, 6, 4>(rows)));
CALL_SUBTEST((test_lazy_all_layout<T, 4, 3, -1>(4, 3, depth)));
CALL_SUBTEST((test_lazy_all_layout<T, -1, 6, -1>(rows, 6, depth)));
CALL_SUBTEST((test_lazy_all_layout<T, 8, 2, 2>()));
CALL_SUBTEST((test_lazy_all_layout<T, 5, 2, 4>()));
CALL_SUBTEST((test_lazy_all_layout<T, 4, 4, 2>()));
CALL_SUBTEST((test_lazy_all_layout<T, 8, 4, 4>()));
CALL_SUBTEST((test_lazy_all_layout<T, 6, 5, 4>()));
CALL_SUBTEST((test_lazy_all_layout<T, 4, 4, 5>()));
CALL_SUBTEST((test_lazy_all_layout<T, 3, 4, 6>()));
CALL_SUBTEST((test_lazy_all_layout<T, 2, 6, 4>()));
CALL_SUBTEST((test_lazy_all_layout<T, 7, 8, 8>()));
CALL_SUBTEST((test_lazy_all_layout<T, 8, -1, 4>(8, cols)));
CALL_SUBTEST((test_lazy_all_layout<T, 3, 4, -1>(3, 4, depth)));
CALL_SUBTEST((test_lazy_all_layout<T, 4, -1, -1>(4, cols, depth)));
}
template <typename T, int N, int M, int K>
void test_linear_but_not_vectorizable() {
// Check tricky cases for which the result of the product is a vector and thus must exhibit the LinearBit flag,
// but is not vectorizable along the linear dimension.
Index n = N == Dynamic ? internal::random<Index>(1, 32) : N;
Index m = M == Dynamic ? internal::random<Index>(1, 32) : M;
Index k = K == Dynamic ? internal::random<Index>(1, 32) : K;
{
Matrix<T, N, M + 1> A;
A.setRandom(n, m + 1);
Matrix<T, M * 2, K> B;
B.setRandom(m * 2, k);
Matrix<T, 1, K> C;
Matrix<T, 1, K> R;
C.noalias() = A.template topLeftCorner<1, M>() * (B.template topRows<M>() + B.template bottomRows<M>());
R.noalias() = A.template topLeftCorner<1, M>() * (B.template topRows<M>() + B.template bottomRows<M>()).eval();
VERIFY_IS_APPROX(C, R);
}
{
Matrix<T, M + 1, N, RowMajor> A;
A.setRandom(m + 1, n);
Matrix<T, K, M * 2, RowMajor> B;
B.setRandom(k, m * 2);
Matrix<T, K, 1> C;
Matrix<T, K, 1> R;
C.noalias() = (B.template leftCols<M>() + B.template rightCols<M>()) * A.template topLeftCorner<M, 1>();
R.noalias() = (B.template leftCols<M>() + B.template rightCols<M>()).eval() * A.template topLeftCorner<M, 1>();
VERIFY_IS_APPROX(C, R);
}
}
template <int Rows>
void bug_1311() {
Matrix<double, Rows, 2> A;
A.setRandom();
Vector2d b = Vector2d::Random();
Matrix<double, Rows, 1> res;
res.noalias() = 1. * (A * b);
VERIFY_IS_APPROX(res, A * b);
res.noalias() = 1. * A * b;
VERIFY_IS_APPROX(res, A * b);
res.noalias() = (1. * A).lazyProduct(b);
VERIFY_IS_APPROX(res, A * b);
res.noalias() = (1. * A).lazyProduct(1. * b);
VERIFY_IS_APPROX(res, A * b);
res.noalias() = (A).lazyProduct(1. * b);
VERIFY_IS_APPROX(res, A * b);
}
template <int>
void product_small_regressions() {
{
// test compilation of (outer_product) * vector
Vector3f v = Vector3f::Random();
VERIFY_IS_APPROX((v * v.transpose()) * v, (v * v.transpose()).eval() * v);
}
{
// regression test for pull-request #93
Eigen::Matrix<double, 1, 1> A;
A.setRandom();
Eigen::Matrix<double, 18, 1> B;
B.setRandom();
Eigen::Matrix<double, 1, 18> C;
C.setRandom();
VERIFY_IS_APPROX(B * A.inverse(), B * A.inverse()[0]);
VERIFY_IS_APPROX(A.inverse() * C, A.inverse()[0] * C);
}
{
Eigen::Matrix<double, 10, 10> A, B, C;
A.setRandom();
C = A;
for (int k = 0; k < 79; ++k) C = C * A;
B.noalias() =
(((A * A) * (A * A)) * ((A * A) * (A * A)) * ((A * A) * (A * A)) * ((A * A) * (A * A)) * ((A * A) * (A * A)) *
((A * A) * (A * A)) * ((A * A) * (A * A)) * ((A * A) * (A * A)) * ((A * A) * (A * A)) * ((A * A) * (A * A))) *
(((A * A) * (A * A)) * ((A * A) * (A * A)) * ((A * A) * (A * A)) * ((A * A) * (A * A)) * ((A * A) * (A * A)) *
((A * A) * (A * A)) * ((A * A) * (A * A)) * ((A * A) * (A * A)) * ((A * A) * (A * A)) * ((A * A) * (A * A)));
VERIFY_IS_APPROX(B, C);
}
}
template <typename T>
void product_sweep(int max_m, int max_k, int max_n) {
using Matrix = Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>;
for (int m = 1; m < max_m; ++m) {
for (int n = 1; n < max_n; ++n) {
Matrix C = Matrix::Zero(m, n);
Matrix Cref = Matrix::Zero(m, n);
for (int k = 1; k < max_k; ++k) {
Matrix A = Matrix::Random(m, k);
Matrix B = Matrix::Random(k, n);
C = A * B;
Cref.setZero();
ref_prod(Cref, A, B);
VERIFY_IS_APPROX(C, Cref);
}
}
}
}
EIGEN_DECLARE_TEST(product_small) {
for (int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1(product(Matrix<float, 3, 2>()));
CALL_SUBTEST_2(product(Matrix<int, 3, 17>()));
CALL_SUBTEST_8(product(Matrix<double, 3, 17>()));
CALL_SUBTEST_3(product(Matrix3d()));
CALL_SUBTEST_4(product(Matrix4d()));
CALL_SUBTEST_5(product(Matrix4f()));
CALL_SUBTEST_10(product(Matrix<bfloat16, 3, 2>()));
CALL_SUBTEST_6(product1x1<0>());
CALL_SUBTEST_11(test_lazy_l1<float>());
CALL_SUBTEST_12(test_lazy_l2<float>());
CALL_SUBTEST_13(test_lazy_l3<float>());
CALL_SUBTEST_21(test_lazy_l1<double>());
CALL_SUBTEST_22(test_lazy_l2<double>());
CALL_SUBTEST_23(test_lazy_l3<double>());
CALL_SUBTEST_31(test_lazy_l1<std::complex<float> >());
CALL_SUBTEST_32(test_lazy_l2<std::complex<float> >());
CALL_SUBTEST_33(test_lazy_l3<std::complex<float> >());
CALL_SUBTEST_41(test_lazy_l1<std::complex<double> >());
CALL_SUBTEST_42(test_lazy_l2<std::complex<double> >());
CALL_SUBTEST_43(test_lazy_l3<std::complex<double> >());
CALL_SUBTEST_7((test_linear_but_not_vectorizable<float, 2, 1, Dynamic>()));
CALL_SUBTEST_7((test_linear_but_not_vectorizable<float, 3, 1, Dynamic>()));
CALL_SUBTEST_7((test_linear_but_not_vectorizable<float, 2, 1, 16>()));
CALL_SUBTEST_6(bug_1311<3>());
CALL_SUBTEST_6(bug_1311<5>());
CALL_SUBTEST_9(test_dynamic_bool());
// Commonly specialized vectorized types.
CALL_SUBTEST_50(product_sweep<float>(10, 10, 10));
CALL_SUBTEST_51(product_sweep<double>(10, 10, 10));
CALL_SUBTEST_52(product_sweep<Eigen::half>(10, 10, 10));
CALL_SUBTEST_53(product_sweep<Eigen::bfloat16>(10, 10, 10));
}
CALL_SUBTEST_6(product_small_regressions<0>());
}
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