From a20a744adc5414f9a79ae0637de9c3227c3dd420 Mon Sep 17 00:00:00 2001
From: Benoit Jacob <jacob.benoit.1@gmail.com>
Date: Thu, 19 Nov 2009 17:07:55 -0500
Subject: TriangularMatrix: extend to rectangular matrices

---
 test/triangular.cpp | 183 ++++++++++++++++++++++++++++++++++++++++------------
 1 file changed, 143 insertions(+), 40 deletions(-)

(limited to 'test/triangular.cpp')

diff --git a/test/triangular.cpp b/test/triangular.cpp
index ee02c0022..3c89a8abb 100644
--- a/test/triangular.cpp
+++ b/test/triangular.cpp
@@ -24,7 +24,9 @@
 
 #include "main.h"
 
-template<typename MatrixType> void triangular(const MatrixType& m)
+
+
+template<typename MatrixType> void triangular_square(const MatrixType& m)
 {
   typedef typename MatrixType::Scalar Scalar;
   typedef typename NumTraits<Scalar>::Real RealScalar;
@@ -51,8 +53,8 @@ template<typename MatrixType> void triangular(const MatrixType& m)
              v2 = VectorType::Random(rows),
              vzero = VectorType::Zero(rows);
 
-  MatrixType m1up = m1.template triangularView<Eigen::UpperTriangular>();
-  MatrixType m2up = m2.template triangularView<Eigen::UpperTriangular>();
+  MatrixType m1up = m1.template triangularView<UpperTriangular>();
+  MatrixType m2up = m2.template triangularView<UpperTriangular>();
 
   if (rows*cols>1)
   {
@@ -66,20 +68,20 @@ template<typename MatrixType> void triangular(const MatrixType& m)
   // test overloaded operator+=
   r1.setZero();
   r2.setZero();
-  r1.template triangularView<Eigen::UpperTriangular>() +=  m1;
+  r1.template triangularView<UpperTriangular>() +=  m1;
   r2 += m1up;
   VERIFY_IS_APPROX(r1,r2);
 
   // test overloaded operator=
   m1.setZero();
-  m1.template triangularView<Eigen::UpperTriangular>() = m2.transpose() + m2;
+  m1.template triangularView<UpperTriangular>() = m2.transpose() + m2;
   m3 = m2.transpose() + m2;
-  VERIFY_IS_APPROX(m3.template triangularView<Eigen::LowerTriangular>().transpose().toDense(), m1);
+  VERIFY_IS_APPROX(m3.template triangularView<LowerTriangular>().transpose().toDenseMatrix(), m1);
 
   // test overloaded operator=
   m1.setZero();
-  m1.template triangularView<Eigen::LowerTriangular>() = m2.transpose() + m2;
-  VERIFY_IS_APPROX(m3.template triangularView<Eigen::LowerTriangular>().toDense(), m1);
+  m1.template triangularView<LowerTriangular>() = m2.transpose() + m2;
+  VERIFY_IS_APPROX(m3.template triangularView<LowerTriangular>().toDenseMatrix(), m1);
 
   m1 = MatrixType::Random(rows, cols);
   for (int i=0; i<rows; ++i)
@@ -87,49 +89,143 @@ template<typename MatrixType> void triangular(const MatrixType& m)
 
   Transpose<MatrixType> trm4(m4);
   // test back and forward subsitution with a vector as the rhs
-  m3 = m1.template triangularView<Eigen::UpperTriangular>();
-  VERIFY(v2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Eigen::LowerTriangular>().solve(v2)), largerEps));
-  m3 = m1.template triangularView<Eigen::LowerTriangular>();
-  VERIFY(v2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Eigen::UpperTriangular>().solve(v2)), largerEps));
-  m3 = m1.template triangularView<Eigen::UpperTriangular>();
-  VERIFY(v2.isApprox(m3 * (m1.template triangularView<Eigen::UpperTriangular>().solve(v2)), largerEps));
-  m3 = m1.template triangularView<Eigen::LowerTriangular>();
-  VERIFY(v2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Eigen::LowerTriangular>().solve(v2)), largerEps));
+  m3 = m1.template triangularView<UpperTriangular>();
+  VERIFY(v2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<LowerTriangular>().solve(v2)), largerEps));
+  m3 = m1.template triangularView<LowerTriangular>();
+  VERIFY(v2.isApprox(m3.transpose() * (m1.transpose().template triangularView<UpperTriangular>().solve(v2)), largerEps));
+  m3 = m1.template triangularView<UpperTriangular>();
+  VERIFY(v2.isApprox(m3 * (m1.template triangularView<UpperTriangular>().solve(v2)), largerEps));
+  m3 = m1.template triangularView<LowerTriangular>();
+  VERIFY(v2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<LowerTriangular>().solve(v2)), largerEps));
 
   // test back and forward subsitution with a matrix as the rhs
-  m3 = m1.template triangularView<Eigen::UpperTriangular>();
-  VERIFY(m2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<Eigen::LowerTriangular>().solve(m2)), largerEps));
-  m3 = m1.template triangularView<Eigen::LowerTriangular>();
-  VERIFY(m2.isApprox(m3.transpose() * (m1.transpose().template triangularView<Eigen::UpperTriangular>().solve(m2)), largerEps));
-  m3 = m1.template triangularView<Eigen::UpperTriangular>();
-  VERIFY(m2.isApprox(m3 * (m1.template triangularView<Eigen::UpperTriangular>().solve(m2)), largerEps));
-  m3 = m1.template triangularView<Eigen::LowerTriangular>();
-  VERIFY(m2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<Eigen::LowerTriangular>().solve(m2)), largerEps));
+  m3 = m1.template triangularView<UpperTriangular>();
+  VERIFY(m2.isApprox(m3.adjoint() * (m1.adjoint().template triangularView<LowerTriangular>().solve(m2)), largerEps));
+  m3 = m1.template triangularView<LowerTriangular>();
+  VERIFY(m2.isApprox(m3.transpose() * (m1.transpose().template triangularView<UpperTriangular>().solve(m2)), largerEps));
+  m3 = m1.template triangularView<UpperTriangular>();
+  VERIFY(m2.isApprox(m3 * (m1.template triangularView<UpperTriangular>().solve(m2)), largerEps));
+  m3 = m1.template triangularView<LowerTriangular>();
+  VERIFY(m2.isApprox(m3.conjugate() * (m1.conjugate().template triangularView<LowerTriangular>().solve(m2)), largerEps));
 
   // check M * inv(L) using in place API
   m4 = m3;
-  m3.transpose().template triangularView<Eigen::UpperTriangular>().solveInPlace(trm4);
+  m3.transpose().template triangularView<UpperTriangular>().solveInPlace(trm4);
   VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>()));
 
   // check M * inv(U) using in place API
-  m3 = m1.template triangularView<Eigen::UpperTriangular>();
+  m3 = m1.template triangularView<UpperTriangular>();
   m4 = m3;
-  m3.transpose().template triangularView<Eigen::LowerTriangular>().solveInPlace(trm4);
+  m3.transpose().template triangularView<LowerTriangular>().solveInPlace(trm4);
   VERIFY(m4.cwise().abs().isIdentity(test_precision<RealScalar>()));
 
   // check solve with unit diagonal
-  m3 = m1.template triangularView<Eigen::UnitUpperTriangular>();
-  VERIFY(m2.isApprox(m3 * (m1.template triangularView<Eigen::UnitUpperTriangular>().solve(m2)), largerEps));
+  m3 = m1.template triangularView<UnitUpperTriangular>();
+  VERIFY(m2.isApprox(m3 * (m1.template triangularView<UnitUpperTriangular>().solve(m2)), largerEps));
+
+//   VERIFY((  m1.template triangularView<UpperTriangular>()
+//           * m2.template triangularView<UpperTriangular>()).isUpperTriangular());
+
+  // test swap
+  m1.setOnes();
+  m2.setZero();
+  m2.template triangularView<UpperTriangular>().swap(m1);
+  m3.setZero();
+  m3.template triangularView<UpperTriangular>().setOnes();
+  VERIFY_IS_APPROX(m2,m3);
+
+}
+
+
+template<typename MatrixType> void triangular_rect(const MatrixType& m)
+{
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
+
+  int rows = m.rows();
+  int 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),
+             mzero = MatrixType::Zero(rows, cols),
+             mones = MatrixType::Ones(rows, cols),
+             identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+                              ::Identity(rows, rows),
+             square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>
+                              ::Random(rows, rows);
+  VectorType v1 = VectorType::Random(rows),
+             v2 = VectorType::Random(rows),
+             vzero = VectorType::Zero(rows);
+
+  MatrixType m1up = m1.template triangularView<UpperTriangular>();
+  MatrixType m2up = m2.template triangularView<UpperTriangular>();
+
+  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);
 
-//   VERIFY((  m1.template triangularView<Eigen::UpperTriangular>()
-//           * m2.template triangularView<Eigen::UpperTriangular>()).isUpperTriangular());
+  // test overloaded operator+=
+  r1.setZero();
+  r2.setZero();
+  r1.template triangularView<UpperTriangular>() +=  m1;
+  r2 += m1up;
+  VERIFY_IS_APPROX(r1,r2);
 
+  // test overloaded operator=
+  m1.setZero();
+  m1.template triangularView<UpperTriangular>() = 3 * m2;
+  m3 = 3 * m2;
+  VERIFY_IS_APPROX(m3.template triangularView<UpperTriangular>().toDenseMatrix(), m1);
+
+  m1.setZero();
+  m1.template triangularView<LowerTriangular>() = 3 * m2;
+  VERIFY_IS_APPROX(m3.template triangularView<LowerTriangular>().toDenseMatrix(), m1);
+
+  m1.setZero();
+  m1.template triangularView<StrictlyUpperTriangular>() = 3 * m2;
+  VERIFY_IS_APPROX(m3.template triangularView<StrictlyUpperTriangular>().toDenseMatrix(), m1);
+
+  m1.setZero();
+  m1.template triangularView<StrictlyLowerTriangular>() = 3 * m2;
+  VERIFY_IS_APPROX(m3.template triangularView<StrictlyLowerTriangular>().toDenseMatrix(), m1);
+
+  m1.setRandom();
+  m2 = m1.template triangularView<UpperTriangular>();
+  VERIFY(m2.isUpperTriangular());
+  VERIFY(!m2.isLowerTriangular());
+  m2 = m1.template triangularView<StrictlyUpperTriangular>();
+  VERIFY(m2.isUpperTriangular());
+  VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
+  m2 = m1.template triangularView<UnitUpperTriangular>();
+  VERIFY(m2.isUpperTriangular());
+  m2.diagonal().cwise() -= Scalar(1);
+  VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
+  m2 = m1.template triangularView<LowerTriangular>();
+  VERIFY(m2.isLowerTriangular());
+  VERIFY(!m2.isUpperTriangular());
+  m2 = m1.template triangularView<StrictlyLowerTriangular>();
+  VERIFY(m2.isLowerTriangular());
+  VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
+  m2 = m1.template triangularView<UnitLowerTriangular>();
+  VERIFY(m2.isLowerTriangular());
+  m2.diagonal().cwise() -= Scalar(1);
+  VERIFY(m2.diagonal().isMuchSmallerThan(RealScalar(1)));
   // test swap
   m1.setOnes();
   m2.setZero();
-  m2.template triangularView<Eigen::UpperTriangular>().swap(m1);
+  m2.template triangularView<UpperTriangular>().swap(m1);
   m3.setZero();
-  m3.template triangularView<Eigen::UpperTriangular>().setOnes();
+  m3.template triangularView<UpperTriangular>().setOnes();
   VERIFY_IS_APPROX(m2,m3);
 
 }
@@ -137,12 +233,19 @@ template<typename MatrixType> void triangular(const MatrixType& m)
 void test_triangular()
 {
   for(int i = 0; i < g_repeat ; i++) {
-    CALL_SUBTEST_1( triangular(Matrix<float, 1, 1>()) );
-    CALL_SUBTEST_2( triangular(Matrix<float, 2, 2>()) );
-    CALL_SUBTEST_3( triangular(Matrix3d()) );
-    CALL_SUBTEST_4( triangular(MatrixXcf(4, 4)) );
-    CALL_SUBTEST_5( triangular(Matrix<std::complex<float>,8, 8>()) );
-    CALL_SUBTEST_6( triangular(MatrixXcd(17,17)) );
-    CALL_SUBTEST_7( triangular(Matrix<float,Dynamic,Dynamic,RowMajor>(5, 5)) );
+    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(MatrixXcf(4, 4)) );
+    CALL_SUBTEST_5( triangular_square(Matrix<std::complex<float>,8, 8>()) );
+    CALL_SUBTEST_6( triangular_square(MatrixXcd(17,17)) );
+    CALL_SUBTEST_7( triangular_square(Matrix<float,Dynamic,Dynamic,RowMajor>(5, 5)) );
+
+    CALL_SUBTEST_8( triangular_rect(Matrix<float, 4, 5>()) );
+    CALL_SUBTEST_9( triangular_rect(Matrix<double, 6, 2>()) );
+    CALL_SUBTEST_4( triangular_rect(MatrixXcf(4, 10)) );
+    CALL_SUBTEST_6( triangular_rect(MatrixXcd(11, 3)) );
+    CALL_SUBTEST_7( triangular_rect(Matrix<float,Dynamic,Dynamic,RowMajor>(7, 6)) );
+
   }
 }
-- 
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