Rasmus Munk LarsenandRasmus Munk Larsen
ddd2165ab4
libeigen/eigen!2814 Co-authored-by: Rasmus Munk Larsen <rmlarsen@gmail.com>
588 lines
24 KiB
C++
588 lines
24 KiB
C++
// This file is triangularView of Eigen, a lightweight C++ template library
|
|
// for linear algebra.
|
|
//
|
|
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
|
|
//
|
|
// 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
|
|
|
|
#if defined(EIGEN_TEST_PART_100) || defined(EIGEN_TEST_PART_ALL)
|
|
#define EIGEN_NO_DEPRECATED_WARNING
|
|
#endif
|
|
|
|
#include "main.h"
|
|
|
|
template <typename ViewType, typename = void>
|
|
struct has_left_scalar_multiply : std::false_type {};
|
|
|
|
template <typename ViewType>
|
|
struct has_left_scalar_multiply<
|
|
ViewType, internal::void_t<decltype(std::declval<typename ViewType::Scalar>() * std::declval<const ViewType&>())>>
|
|
: std::true_type {};
|
|
|
|
template <typename ViewType, typename = void>
|
|
struct has_right_scalar_multiply : std::false_type {};
|
|
|
|
template <typename ViewType>
|
|
struct has_right_scalar_multiply<
|
|
ViewType, internal::void_t<decltype(std::declval<const ViewType&>() * std::declval<typename ViewType::Scalar>())>>
|
|
: std::true_type {};
|
|
|
|
template <typename ViewType, typename = void>
|
|
struct has_structured_sum : std::false_type {};
|
|
|
|
template <typename ViewType>
|
|
struct has_structured_sum<ViewType,
|
|
internal::void_t<decltype(std::declval<const ViewType&>() + std::declval<const ViewType&>())>>
|
|
: std::true_type {};
|
|
|
|
template <unsigned int Mode, typename MatrixType>
|
|
void triangular_scalar_multiply(const MatrixType& m) {
|
|
typedef typename MatrixType::Scalar Scalar;
|
|
|
|
const Index rows = m.rows();
|
|
const Index cols = m.cols();
|
|
|
|
const Scalar s = internal::random<Scalar>();
|
|
const MatrixType triangular = MatrixType::Random(rows, cols);
|
|
|
|
VERIFY_IS_APPROX((s * triangular.template triangularView<Mode>()).toDenseMatrix(),
|
|
(s * triangular).template triangularView<Mode>().toDenseMatrix());
|
|
VERIFY_IS_APPROX((triangular.template triangularView<Mode>() * s).toDenseMatrix(),
|
|
(triangular * s).template triangularView<Mode>().toDenseMatrix());
|
|
}
|
|
|
|
template <unsigned int Mode, typename MatrixType, bool IsSelfAdjointMode = Mode == Upper || Mode == Lower>
|
|
struct selfadjoint_structured_sum_impl {
|
|
typedef typename MatrixType::Scalar Scalar;
|
|
|
|
static void run(const Scalar&, const MatrixType&, const MatrixType&, MatrixType&, MatrixType&) {}
|
|
};
|
|
|
|
template <unsigned int Mode, typename MatrixType>
|
|
struct selfadjoint_structured_sum_impl<Mode, MatrixType, true> {
|
|
typedef typename MatrixType::Scalar Scalar;
|
|
|
|
static void run(const Scalar& s, const MatrixType& a, const MatrixType& b, MatrixType& result,
|
|
MatrixType& reference) {
|
|
if (a.rows() != a.cols()) return;
|
|
|
|
result.setRandom();
|
|
result.template selfadjointView<Mode>() =
|
|
s * a.template selfadjointView<Mode>() + b.template selfadjointView<Mode>();
|
|
reference = (s * a + b).template selfadjointView<Mode>().toDenseMatrix();
|
|
VERIFY_IS_APPROX(result, reference);
|
|
|
|
result.setRandom();
|
|
result.template selfadjointView<Mode>() =
|
|
a.template selfadjointView<Mode>() - s * b.template selfadjointView<Mode>();
|
|
reference = (a - s * b).template selfadjointView<Mode>().toDenseMatrix();
|
|
VERIFY_IS_APPROX(result, reference);
|
|
}
|
|
};
|
|
|
|
template <unsigned int Mode, typename MatrixType>
|
|
void triangular_structured_sum(const MatrixType& m) {
|
|
typedef typename MatrixType::Scalar Scalar;
|
|
|
|
const Index rows = m.rows();
|
|
const Index cols = m.cols();
|
|
|
|
const Scalar s = internal::random<Scalar>();
|
|
const MatrixType a = MatrixType::Random(rows, cols);
|
|
const MatrixType b = MatrixType::Random(rows, cols);
|
|
|
|
MatrixType result = MatrixType::Random(rows, cols);
|
|
MatrixType reference = result;
|
|
|
|
result.template triangularView<Mode>() = s * a.template triangularView<Mode>() + b.template triangularView<Mode>();
|
|
reference.template triangularView<Mode>() = s * a + b;
|
|
VERIFY_IS_APPROX(result, reference);
|
|
|
|
result.setRandom();
|
|
reference = result;
|
|
result.template triangularView<Mode>() = a.template triangularView<Mode>() - s * b.template triangularView<Mode>();
|
|
reference.template triangularView<Mode>() = a - s * b;
|
|
VERIFY_IS_APPROX(result, reference);
|
|
|
|
selfadjoint_structured_sum_impl<Mode, MatrixType>::run(s, a, b, result, reference);
|
|
}
|
|
|
|
template <typename MatrixType>
|
|
void triangular_setters(const MatrixType& m) {
|
|
const Index rows = m.rows();
|
|
const Index cols = m.cols();
|
|
|
|
MatrixType result = MatrixType::Random(rows, cols);
|
|
MatrixType reference = result;
|
|
|
|
result.template triangularView<Upper>().setIdentity();
|
|
reference.template triangularView<Upper>() = MatrixType::Identity(rows, cols);
|
|
VERIFY_IS_APPROX(result, reference);
|
|
|
|
result.setRandom();
|
|
reference = result;
|
|
result.template triangularView<Lower>().setIdentity();
|
|
reference.template triangularView<Lower>() = MatrixType::Identity(rows, cols);
|
|
VERIFY_IS_APPROX(result, reference);
|
|
|
|
result.setRandom();
|
|
reference = result;
|
|
result.template triangularView<Upper>().setRandom();
|
|
VERIFY_IS_APPROX(result.template triangularView<StrictlyLower>().toDenseMatrix(),
|
|
reference.template triangularView<StrictlyLower>().toDenseMatrix());
|
|
|
|
result.setRandom();
|
|
reference = result;
|
|
result.template triangularView<StrictlyLower>().setRandom();
|
|
VERIFY_IS_APPROX(result.template triangularView<Upper>().toDenseMatrix(),
|
|
reference.template triangularView<Upper>().toDenseMatrix());
|
|
}
|
|
|
|
template <typename MatrixType>
|
|
void triangular_scalar_multiply_sfinae() {
|
|
typedef decltype(std::declval<MatrixType&>().template triangularView<Upper>()) UpperView;
|
|
typedef decltype(std::declval<MatrixType&>().template triangularView<Lower>()) LowerView;
|
|
typedef decltype(std::declval<MatrixType&>().template triangularView<StrictlyLower>()) StrictlyLowerView;
|
|
typedef decltype(std::declval<MatrixType&>().template triangularView<StrictlyUpper>()) StrictlyUpperView;
|
|
typedef decltype(std::declval<MatrixType&>().template triangularView<UnitLower>()) UnitLowerView;
|
|
|
|
STATIC_CHECK((has_left_scalar_multiply<UpperView>::value));
|
|
STATIC_CHECK((has_right_scalar_multiply<UpperView>::value));
|
|
STATIC_CHECK((has_left_scalar_multiply<LowerView>::value));
|
|
STATIC_CHECK((has_right_scalar_multiply<LowerView>::value));
|
|
STATIC_CHECK((has_left_scalar_multiply<StrictlyLowerView>::value));
|
|
STATIC_CHECK((has_right_scalar_multiply<StrictlyLowerView>::value));
|
|
STATIC_CHECK((has_left_scalar_multiply<StrictlyUpperView>::value));
|
|
STATIC_CHECK((has_right_scalar_multiply<StrictlyUpperView>::value));
|
|
STATIC_CHECK((!has_left_scalar_multiply<UnitLowerView>::value));
|
|
STATIC_CHECK((!has_right_scalar_multiply<UnitLowerView>::value));
|
|
|
|
STATIC_CHECK((has_structured_sum<UpperView>::value));
|
|
STATIC_CHECK((has_structured_sum<LowerView>::value));
|
|
STATIC_CHECK((has_structured_sum<StrictlyLowerView>::value));
|
|
STATIC_CHECK((has_structured_sum<StrictlyUpperView>::value));
|
|
STATIC_CHECK((!has_structured_sum<UnitLowerView>::value));
|
|
}
|
|
|
|
template <typename MatrixType>
|
|
void triangular_deprecated(const MatrixType& m) {
|
|
Index rows = m.rows();
|
|
Index cols = m.cols();
|
|
MatrixType m1, m2, m3, m4;
|
|
m1.setRandom(rows, cols);
|
|
m2.setRandom(rows, cols);
|
|
m3 = m1;
|
|
m4 = m2;
|
|
// deprecated method:
|
|
m1.template triangularView<Eigen::Upper>().swap(m2);
|
|
// use this method instead:
|
|
m3.template triangularView<Eigen::Upper>().swap(m4.template triangularView<Eigen::Upper>());
|
|
VERIFY_IS_APPROX(m1, m3);
|
|
VERIFY_IS_APPROX(m2, m4);
|
|
// deprecated method:
|
|
m1.template triangularView<Eigen::Lower>().swap(m4);
|
|
// use this method instead:
|
|
m3.template triangularView<Eigen::Lower>().swap(m2.template triangularView<Eigen::Lower>());
|
|
VERIFY_IS_APPROX(m1, m3);
|
|
VERIFY_IS_APPROX(m2, m4);
|
|
}
|
|
|
|
template <typename MatrixType>
|
|
void triangular_square(const MatrixType& m) {
|
|
typedef typename MatrixType::Scalar Scalar;
|
|
typedef typename NumTraits<Scalar>::Real RealScalar;
|
|
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
|
|
|
|
triangular_scalar_multiply_sfinae<MatrixType>();
|
|
triangular_structured_sum<Upper>(m);
|
|
triangular_structured_sum<Lower>(m);
|
|
triangular_structured_sum<StrictlyUpper>(m);
|
|
triangular_structured_sum<StrictlyLower>(m);
|
|
triangular_setters(m);
|
|
|
|
RealScalar largerEps = 10 * test_precision<RealScalar>();
|
|
|
|
Index rows = m.rows();
|
|
Index cols = m.cols();
|
|
|
|
MatrixType m1 = MatrixType::Random(rows, cols), m2 = MatrixType::Random(rows, cols), m3(rows, cols), m4(rows, cols),
|
|
r1(rows, cols), r2(rows, cols);
|
|
VectorType v2 = VectorType::Random(rows);
|
|
VectorType v3 = VectorType::Zero(rows);
|
|
|
|
MatrixType m1up = m1.template triangularView<Upper>();
|
|
MatrixType m2up = m2.template triangularView<Upper>();
|
|
|
|
if (rows * cols > 1) {
|
|
VERIFY(m1up.isUpperTriangular());
|
|
VERIFY(m2up.transpose().isLowerTriangular());
|
|
VERIFY(!m2.isLowerTriangular());
|
|
}
|
|
|
|
// VERIFY_IS_APPROX(m1up.transpose() * m2, m1.upper().transpose().lower() * m2);
|
|
|
|
// test overloaded operator+=
|
|
r1.setZero();
|
|
r2.setZero();
|
|
r1.template triangularView<Upper>() += m1;
|
|
r2 += m1up;
|
|
VERIFY_IS_APPROX(r1, r2);
|
|
|
|
// test overloaded operator=
|
|
m1.setZero();
|
|
m1.template triangularView<Upper>() = m2.transpose() + m2;
|
|
m3 = m2.transpose() + m2;
|
|
VERIFY_IS_APPROX(m3.template triangularView<Lower>().transpose().toDenseMatrix(), m1);
|
|
|
|
// test overloaded operator=
|
|
m1.setZero();
|
|
m1.template triangularView<Lower>() = m2.transpose() + m2;
|
|
VERIFY_IS_APPROX(m3.template triangularView<Lower>().toDenseMatrix(), m1);
|
|
|
|
VERIFY_IS_APPROX(m3.template triangularView<Lower>().conjugate().toDenseMatrix(),
|
|
m3.conjugate().template triangularView<Lower>().toDenseMatrix());
|
|
|
|
m1 = MatrixType::Random(rows, cols);
|
|
for (int i = 0; i < rows; ++i)
|
|
if (numext::abs2(m1(i, i)) < RealScalar(1e-1)) m1(i, i) = Scalar(1);
|
|
|
|
Transpose<MatrixType> trm4(m4);
|
|
// test back and forward substitution with a vector as the rhs
|
|
m3 = m1.template triangularView<Upper>();
|
|
v3 = m3.adjoint() * (m1.adjoint().template triangularView<Lower>().solve(v2));
|
|
VERIFY(v2.isApprox(v3, largerEps));
|
|
m3 = m1.template triangularView<Lower>();
|
|
v3 = m3.transpose() * (m1.transpose().template triangularView<Upper>().solve(v2));
|
|
VERIFY(v2.isApprox(v3, largerEps));
|
|
m3 = m1.template triangularView<Upper>();
|
|
v3 = m3 * (m1.template triangularView<Upper>().solve(v2));
|
|
VERIFY(v2.isApprox(v3, largerEps));
|
|
m3 = m1.template triangularView<Lower>();
|
|
v3 = m3.conjugate() * (m1.conjugate().template triangularView<Lower>().solve(v2));
|
|
VERIFY(v2.isApprox(v3, largerEps));
|
|
|
|
// test back and forward substitution with a matrix as the rhs
|
|
m3 = m1.template triangularView<Upper>();
|
|
m4 = m3.adjoint() * (m1.adjoint().template triangularView<Lower>().solve(m2));
|
|
VERIFY(m2.isApprox(m4, largerEps));
|
|
m3 = m1.template triangularView<Lower>();
|
|
m4 = m3.transpose() * (m1.transpose().template triangularView<Upper>().solve(m2));
|
|
VERIFY(m2.isApprox(m4, largerEps));
|
|
m3 = m1.template triangularView<Upper>();
|
|
m4 = m3 * (m1.template triangularView<Upper>().solve(m2));
|
|
VERIFY(m2.isApprox(m4, largerEps));
|
|
m3 = m1.template triangularView<Lower>();
|
|
m4 = m3.conjugate() * (m1.conjugate().template triangularView<Lower>().solve(m2));
|
|
VERIFY(m2.isApprox(m4, largerEps));
|
|
|
|
// check M * inv(L) using in place API
|
|
m4 = m3;
|
|
m1.transpose().template triangularView<Eigen::Upper>().solveInPlace(trm4);
|
|
VERIFY_IS_APPROX(m4 * m1.template triangularView<Eigen::Lower>(), m3);
|
|
|
|
// check M * inv(U) using in place API
|
|
m3 = m1.template triangularView<Upper>();
|
|
m4 = m3;
|
|
m3.transpose().template triangularView<Eigen::Lower>().solveInPlace(trm4);
|
|
VERIFY_IS_APPROX(m4 * m1.template triangularView<Eigen::Upper>(), m3);
|
|
|
|
// check solve with unit diagonal
|
|
m3 = m1.template triangularView<UnitUpper>();
|
|
VERIFY(m2.isApprox(m3 * (m1.template triangularView<UnitUpper>().solve(m2)), largerEps));
|
|
|
|
// VERIFY(( m1.template triangularView<Upper>()
|
|
// * m2.template triangularView<Upper>()).isUpperTriangular());
|
|
|
|
// test swap
|
|
m1.setOnes();
|
|
m2.setZero();
|
|
m2.template triangularView<Upper>().swap(m1.template triangularView<Eigen::Upper>());
|
|
m3.setZero();
|
|
m3.template triangularView<Upper>().setOnes();
|
|
VERIFY_IS_APPROX(m2, m3);
|
|
|
|
m1.setRandom();
|
|
m3 = m1.template triangularView<Upper>();
|
|
Matrix<Scalar, MatrixType::ColsAtCompileTime, Dynamic> m5(cols, internal::random<int>(1, 20));
|
|
m5.setRandom();
|
|
Matrix<Scalar, Dynamic, MatrixType::RowsAtCompileTime> m6(internal::random<int>(1, 20), rows);
|
|
m6.setRandom();
|
|
VERIFY_IS_APPROX(m1.template triangularView<Upper>() * m5, m3 * m5);
|
|
VERIFY_IS_APPROX(m6 * m1.template triangularView<Upper>(), m6 * m3);
|
|
triangular_scalar_multiply<Upper>(m1);
|
|
triangular_scalar_multiply<Lower>(m1);
|
|
triangular_scalar_multiply<StrictlyUpper>(m1);
|
|
triangular_scalar_multiply<StrictlyLower>(m1);
|
|
|
|
m1up = m1.template triangularView<Upper>();
|
|
VERIFY_IS_APPROX(m1.template selfadjointView<Upper>().template triangularView<Upper>().toDenseMatrix(), m1up);
|
|
VERIFY_IS_APPROX(m1up.template selfadjointView<Upper>().template triangularView<Upper>().toDenseMatrix(), m1up);
|
|
VERIFY_IS_APPROX(m1.template selfadjointView<Upper>().template triangularView<Lower>().toDenseMatrix(),
|
|
m1up.adjoint());
|
|
VERIFY_IS_APPROX(m1up.template selfadjointView<Upper>().template triangularView<Lower>().toDenseMatrix(),
|
|
m1up.adjoint());
|
|
|
|
VERIFY_IS_APPROX(m1.template selfadjointView<Upper>().diagonal(), m1.diagonal());
|
|
|
|
m3.setRandom();
|
|
const MatrixType& m3c(m3);
|
|
VERIFY(is_same_type(m3c.template triangularView<Lower>(),
|
|
m3.template triangularView<Lower>().template conjugateIf<false>()));
|
|
VERIFY(is_same_type(m3c.template triangularView<Lower>().conjugate(),
|
|
m3.template triangularView<Lower>().template conjugateIf<true>()));
|
|
VERIFY_IS_APPROX(m3.template triangularView<Lower>().template conjugateIf<true>().toDenseMatrix(),
|
|
m3.conjugate().template triangularView<Lower>().toDenseMatrix());
|
|
VERIFY_IS_APPROX(m3.template triangularView<Lower>().template conjugateIf<false>().toDenseMatrix(),
|
|
m3.template triangularView<Lower>().toDenseMatrix());
|
|
|
|
VERIFY(is_same_type(m3c.template selfadjointView<Lower>(),
|
|
m3.template selfadjointView<Lower>().template conjugateIf<false>()));
|
|
VERIFY(is_same_type(m3c.template selfadjointView<Lower>().conjugate(),
|
|
m3.template selfadjointView<Lower>().template conjugateIf<true>()));
|
|
VERIFY_IS_APPROX(m3.template selfadjointView<Lower>().template conjugateIf<true>().toDenseMatrix(),
|
|
m3.conjugate().template selfadjointView<Lower>().toDenseMatrix());
|
|
VERIFY_IS_APPROX(m3.template selfadjointView<Lower>().template conjugateIf<false>().toDenseMatrix(),
|
|
m3.template selfadjointView<Lower>().toDenseMatrix());
|
|
}
|
|
|
|
template <typename MatrixType>
|
|
void triangular_rect(const MatrixType& m) {
|
|
typedef typename MatrixType::Scalar Scalar;
|
|
typedef typename NumTraits<Scalar>::Real RealScalar;
|
|
enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
|
|
|
|
Index rows = m.rows();
|
|
Index cols = m.cols();
|
|
|
|
MatrixType m1 = MatrixType::Random(rows, cols), m2 = MatrixType::Random(rows, cols), m3(rows, cols), m4(rows, cols),
|
|
r1(rows, cols), r2(rows, cols);
|
|
|
|
MatrixType m1up = m1.template triangularView<Upper>();
|
|
MatrixType m2up = m2.template triangularView<Upper>();
|
|
|
|
if (rows > 1 && cols > 1) {
|
|
VERIFY(m1up.isUpperTriangular());
|
|
VERIFY(m2up.transpose().isLowerTriangular());
|
|
VERIFY(!m2.isLowerTriangular());
|
|
}
|
|
|
|
// test overloaded operator+=
|
|
r1.setZero();
|
|
r2.setZero();
|
|
r1.template triangularView<Upper>() += m1;
|
|
r2 += m1up;
|
|
VERIFY_IS_APPROX(r1, r2);
|
|
|
|
// test overloaded operator=
|
|
m1.setZero();
|
|
m1.template triangularView<Upper>() = 3 * m2;
|
|
m3 = 3 * m2;
|
|
VERIFY_IS_APPROX(m3.template triangularView<Upper>().toDenseMatrix(), m1);
|
|
|
|
m1.setZero();
|
|
m1.template triangularView<Lower>() = 3 * m2;
|
|
VERIFY_IS_APPROX(m3.template triangularView<Lower>().toDenseMatrix(), m1);
|
|
|
|
m1.setZero();
|
|
m1.template triangularView<StrictlyUpper>() = 3 * m2;
|
|
VERIFY_IS_APPROX(m3.template triangularView<StrictlyUpper>().toDenseMatrix(), m1);
|
|
|
|
m1.setZero();
|
|
m1.template triangularView<StrictlyLower>() = 3 * m2;
|
|
VERIFY_IS_APPROX(m3.template triangularView<StrictlyLower>().toDenseMatrix(), m1);
|
|
triangular_scalar_multiply<Upper>(m1);
|
|
triangular_scalar_multiply<Lower>(m1);
|
|
triangular_scalar_multiply<StrictlyUpper>(m1);
|
|
triangular_scalar_multiply<StrictlyLower>(m1);
|
|
triangular_structured_sum<Upper>(m1);
|
|
triangular_structured_sum<Lower>(m1);
|
|
triangular_structured_sum<StrictlyUpper>(m1);
|
|
triangular_structured_sum<StrictlyLower>(m1);
|
|
triangular_setters(m1);
|
|
m1.setRandom();
|
|
m2 = m1.template triangularView<Upper>();
|
|
VERIFY(m2.isUpperTriangular());
|
|
VERIFY(!m2.isLowerTriangular());
|
|
m2 = m1.template triangularView<StrictlyUpper>();
|
|
VERIFY(m2.isUpperTriangular());
|
|
VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
|
|
m2 = m1.template triangularView<UnitUpper>();
|
|
VERIFY(m2.isUpperTriangular());
|
|
m2.diagonal().array() -= Scalar(1);
|
|
VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
|
|
m2 = m1.template triangularView<Lower>();
|
|
VERIFY(m2.isLowerTriangular());
|
|
VERIFY(!m2.isUpperTriangular());
|
|
m2 = m1.template triangularView<StrictlyLower>();
|
|
VERIFY(m2.isLowerTriangular());
|
|
VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
|
|
m2 = m1.template triangularView<UnitLower>();
|
|
VERIFY(m2.isLowerTriangular());
|
|
m2.diagonal().array() -= Scalar(1);
|
|
VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
|
|
// test swap
|
|
m1.setOnes();
|
|
m2.setZero();
|
|
m2.template triangularView<Upper>().swap(m1.template triangularView<Eigen::Upper>());
|
|
m3.setZero();
|
|
m3.template triangularView<Upper>().setOnes();
|
|
VERIFY_IS_APPROX(m2, m3);
|
|
}
|
|
|
|
// isLowerTriangular() and isUpperTriangular() must inspect every off-diagonal coefficient. In a wide matrix the
|
|
// columns past the diagonal block are strictly upper down to their last row, which an off-by-one row bound in
|
|
// isLowerTriangular() used to skip.
|
|
template <typename MatrixType>
|
|
void triangular_predicates(const MatrixType& m) {
|
|
typedef typename MatrixType::Scalar Scalar;
|
|
|
|
const Index rows = m.rows();
|
|
const Index cols = m.cols();
|
|
|
|
const MatrixType m1 = MatrixType::Random(rows, cols);
|
|
const MatrixType lower = m1.template triangularView<Lower>();
|
|
const MatrixType upper = m1.template triangularView<Upper>();
|
|
VERIFY(lower.isLowerTriangular());
|
|
VERIFY(upper.isUpperTriangular());
|
|
|
|
MatrixType diag = MatrixType::Zero(rows, cols);
|
|
diag.diagonal().setConstant(Scalar(1));
|
|
VERIFY(diag.isLowerTriangular());
|
|
VERIFY(diag.isUpperTriangular());
|
|
|
|
// A single large coefficient off the diagonal must be caught by exactly one of the two predicates, wherever it sits.
|
|
const Scalar offending = Scalar(100);
|
|
for (Index j = 0; j < cols; ++j)
|
|
for (Index i = 0; i < rows; ++i) {
|
|
if (i == j) continue;
|
|
MatrixType m2 = diag;
|
|
m2(i, j) = offending;
|
|
if (i < j) {
|
|
VERIFY(!m2.isLowerTriangular());
|
|
VERIFY(m2.isUpperTriangular());
|
|
} else {
|
|
VERIFY(!m2.isUpperTriangular());
|
|
VERIFY(m2.isLowerTriangular());
|
|
}
|
|
}
|
|
}
|
|
|
|
// Test triangular solve and product at sizes that exercise GEBP blocking.
|
|
// The standard test caps at maxsize=20, which never triggers the blocked code paths
|
|
// in TriangularSolverMatrix.h (requires size >= 48 with EIGEN_DEBUG_SMALL_PRODUCT_BLOCKS).
|
|
template <int>
|
|
void triangular_at_blocking_boundaries() {
|
|
typedef double Scalar;
|
|
typedef Matrix<Scalar, Dynamic, Dynamic> Mat;
|
|
typedef Matrix<Scalar, Dynamic, 1> Vec;
|
|
|
|
const int sizes[] = {47, 48, 49, 64, 96, 128};
|
|
for (int si = 0; si < 6; ++si) {
|
|
int n = sizes[si];
|
|
Mat m1 = Mat::Random(n, n);
|
|
// Make well-conditioned: dominant diagonal
|
|
for (int i = 0; i < n; ++i) m1(i, i) += Scalar(n);
|
|
|
|
Vec v = Vec::Random(n);
|
|
Mat rhs = Mat::Random(n, 5);
|
|
|
|
// Upper triangular solve with vector
|
|
Mat U = m1.triangularView<Upper>();
|
|
Vec x = m1.triangularView<Upper>().solve(v);
|
|
VERIFY_IS_APPROX(U * x, v);
|
|
|
|
// Lower triangular solve with vector
|
|
Mat L = m1.triangularView<Lower>();
|
|
x = m1.triangularView<Lower>().solve(v);
|
|
VERIFY_IS_APPROX(L * x, v);
|
|
|
|
// Upper triangular solve with matrix rhs
|
|
Mat X = m1.triangularView<Upper>().solve(rhs);
|
|
VERIFY_IS_APPROX(U * X, rhs);
|
|
|
|
// Lower triangular solve with matrix rhs
|
|
X = m1.triangularView<Lower>().solve(rhs);
|
|
VERIFY_IS_APPROX(L * X, rhs);
|
|
|
|
// Triangular product
|
|
Mat prod = m1.triangularView<Upper>() * rhs;
|
|
VERIFY_IS_APPROX(prod, U * rhs);
|
|
prod = rhs.transpose() * m1.triangularView<Upper>();
|
|
VERIFY_IS_APPROX(prod, rhs.transpose() * U);
|
|
}
|
|
|
|
// Also test with float and RowMajor
|
|
{
|
|
typedef Matrix<float, Dynamic, Dynamic, RowMajor> RMat;
|
|
typedef Matrix<float, Dynamic, 1> FVec;
|
|
for (int si = 0; si < 6; ++si) {
|
|
int n = sizes[si];
|
|
RMat m1 = RMat::Random(n, n);
|
|
for (int i = 0; i < n; ++i) m1(i, i) += float(n);
|
|
|
|
FVec v = FVec::Random(n);
|
|
RMat U = m1.triangularView<Upper>();
|
|
FVec x = m1.triangularView<Upper>().solve(v);
|
|
VERIFY_IS_APPROX(U * x, v);
|
|
|
|
RMat L = m1.triangularView<Lower>();
|
|
x = m1.triangularView<Lower>().solve(v);
|
|
VERIFY_IS_APPROX(L * x, v);
|
|
}
|
|
}
|
|
}
|
|
|
|
void bug_159() {
|
|
Matrix3d m = Matrix3d::Random().triangularView<Lower>();
|
|
EIGEN_UNUSED_VARIABLE(m);
|
|
}
|
|
|
|
EIGEN_DECLARE_TEST(triangular) {
|
|
int maxsize = (std::min)(EIGEN_TEST_MAX_SIZE, 20);
|
|
for (int i = 0; i < g_repeat; i++) {
|
|
int r = internal::random<int>(2, maxsize);
|
|
TEST_SET_BUT_UNUSED_VARIABLE(r);
|
|
int c = internal::random<int>(2, maxsize);
|
|
TEST_SET_BUT_UNUSED_VARIABLE(c);
|
|
|
|
CALL_SUBTEST_1(triangular_square(Matrix<float, 1, 1>()));
|
|
CALL_SUBTEST_2(triangular_square(Matrix<float, 2, 2>()));
|
|
CALL_SUBTEST_3(triangular_square(Matrix3d()));
|
|
CALL_SUBTEST_4(triangular_square(Matrix<std::complex<float>, 8, 8>()));
|
|
CALL_SUBTEST_5(triangular_square(MatrixXcd(r, r)));
|
|
CALL_SUBTEST_6(triangular_square(Matrix<float, Dynamic, Dynamic, RowMajor>(r, r)));
|
|
|
|
CALL_SUBTEST_7(triangular_rect(Matrix<float, 4, 5>()));
|
|
CALL_SUBTEST_8(triangular_rect(Matrix<double, 6, 2>()));
|
|
CALL_SUBTEST_9(triangular_rect(MatrixXcf(r, c)));
|
|
CALL_SUBTEST_5(triangular_rect(MatrixXcd(r, c)));
|
|
CALL_SUBTEST_6(triangular_rect(Matrix<float, Dynamic, Dynamic, RowMajor>(r, c)));
|
|
|
|
CALL_SUBTEST_100(triangular_deprecated(Matrix<float, 5, 7>()));
|
|
CALL_SUBTEST_100(triangular_deprecated(MatrixXd(r, c)));
|
|
|
|
// isLowerTriangular()/isUpperTriangular() on wide, tall and square shapes, including the 1xN and Nx1 edges.
|
|
CALL_SUBTEST_12(triangular_predicates(MatrixXd(2, 3)));
|
|
CALL_SUBTEST_12(triangular_predicates(MatrixXd(3, 2)));
|
|
CALL_SUBTEST_12(triangular_predicates(MatrixXd(3, 3)));
|
|
CALL_SUBTEST_12(triangular_predicates(MatrixXd(1, 4)));
|
|
CALL_SUBTEST_12(triangular_predicates(MatrixXd(4, 1)));
|
|
CALL_SUBTEST_12(triangular_predicates(MatrixXd(1, 1)));
|
|
CALL_SUBTEST_12(triangular_predicates(Matrix<float, 2, 5>()));
|
|
CALL_SUBTEST_12(triangular_predicates(Matrix<double, 5, 2>()));
|
|
CALL_SUBTEST_12(triangular_predicates(Matrix<std::complex<float>, 3, 7>()));
|
|
CALL_SUBTEST_12(triangular_predicates(MatrixXcd(r, c)));
|
|
CALL_SUBTEST_12(triangular_predicates(MatrixXcd(c, r)));
|
|
CALL_SUBTEST_12(triangular_predicates(Matrix<float, Dynamic, Dynamic, RowMajor>(2, 5)));
|
|
CALL_SUBTEST_12(triangular_predicates(Matrix<float, Dynamic, Dynamic, RowMajor>(r, c)));
|
|
}
|
|
|
|
CALL_SUBTEST_1(bug_159());
|
|
|
|
// Triangular solve/product at blocking boundaries (deterministic, outside g_repeat).
|
|
CALL_SUBTEST_11(triangular_at_blocking_boundaries<0>());
|
|
}
|