From 44861dcbfeee041223c4aac1ee075e92fa4daa01 Mon Sep 17 00:00:00 2001
From: Stanislaw Halik <sthalik@misaki.pl>
Date: Sun, 18 Sep 2016 12:42:15 +0200
Subject: update

---
 eigen/test/triangular.cpp | 232 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 232 insertions(+)
 create mode 100644 eigen/test/triangular.cpp

(limited to 'eigen/test/triangular.cpp')

diff --git a/eigen/test/triangular.cpp b/eigen/test/triangular.cpp
new file mode 100644
index 0000000..5432039
--- /dev/null
+++ b/eigen/test/triangular.cpp
@@ -0,0 +1,232 @@
+// 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/.
+
+#include "main.h"
+
+
+
+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;
+
+  RealScalar largerEps = 10*test_precision<RealScalar>();
+
+  typename MatrixType::Index rows = m.rows();
+  typename MatrixType::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);
+
+  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)
+    while (numext::abs2(m1(i,i))<1e-1) m1(i,i) = internal::random<Scalar>();
+
+  Transpose<MatrixType> trm4(m4);
+  // test back and forward subsitution with a vector as the rhs
+  m3 = m1.template triangularView<Upper>();
+  VERIFY(v2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Lower>().solve(v2)), largerEps));
+  m3 = m1.template triangularView<Lower>();
+  VERIFY(v2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Upper>().solve(v2)), largerEps));
+  m3 = m1.template triangularView<Upper>();
+  VERIFY(v2.isApprox(m3 * (m1.template triangularView<Upper>().solve(v2)), largerEps));
+  m3 = m1.template triangularView<Lower>();
+  VERIFY(v2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Lower>().solve(v2)), largerEps));
+
+  // test back and forward subsitution with a matrix as the rhs
+  m3 = m1.template triangularView<Upper>();
+  VERIFY(m2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Lower>().solve(m2)), largerEps));
+  m3 = m1.template triangularView<Lower>();
+  VERIFY(m2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Upper>().solve(m2)), largerEps));
+  m3 = m1.template triangularView<Upper>();
+  VERIFY(m2.isApprox(m3 * (m1.template triangularView<Upper>().solve(m2)), largerEps));
+  m3 = m1.template triangularView<Lower>();
+  VERIFY(m2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Lower>().solve(m2)), 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);
+  m3.setZero();
+  m3.template triangularView<Upper>().setOnes();
+  VERIFY_IS_APPROX(m2,m3);
+
+}
+
+
+template<typename MatrixType> void triangular_rect(const MatrixType& m)
+{
+  typedef const typename MatrixType::Index Index;
+  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);
+  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);
+  m3.setZero();
+  m3.template triangularView<Upper>().setOnes();
+  VERIFY_IS_APPROX(m2,m3);
+}
+
+void bug_159()
+{
+  Matrix3d m = Matrix3d::Random().triangularView<Lower>();
+  EIGEN_UNUSED_VARIABLE(m)
+}
+
+void 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_1( bug_159() );
+}
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