eigen/test/product_trmm.cpp

// This file is part 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 T>
int get_random_size() {
  const int factor = NumTraits<T>::ReadCost;
  const int max_test_size = EIGEN_TEST_MAX_SIZE > 2 * factor ? EIGEN_TEST_MAX_SIZE / factor : EIGEN_TEST_MAX_SIZE;
  return internal::random<int>(1, max_test_size);
}

template <typename Scalar, int Mode, int TriOrder, int OtherOrder, int ResOrder, int OtherCols>
void trmm(int rows = get_random_size<Scalar>(), int cols = get_random_size<Scalar>(),
          int otherCols = OtherCols == Dynamic ? get_random_size<Scalar>() : OtherCols) {
  typedef Matrix<Scalar, Dynamic, Dynamic, TriOrder> TriMatrix;
  typedef Matrix<Scalar, Dynamic, OtherCols, OtherCols == 1 ? ColMajor : OtherOrder> OnTheRight;
  typedef Matrix<Scalar, OtherCols, Dynamic, OtherCols == 1 ? RowMajor : OtherOrder> OnTheLeft;

  typedef Matrix<Scalar, Dynamic, OtherCols, OtherCols == 1 ? ColMajor : ResOrder> ResXS;
  typedef Matrix<Scalar, OtherCols, Dynamic, OtherCols == 1 ? RowMajor : ResOrder> ResSX;

  TriMatrix mat(rows, cols), tri(rows, cols), triTr(cols, rows), s1tri(rows, cols), s1triTr(cols, rows);

  OnTheRight ge_right(cols, otherCols);
  OnTheLeft ge_left(otherCols, rows);
  ResSX ge_sx, ge_sx_save;
  ResXS ge_xs, ge_xs_save;

  Scalar s1 = internal::random<Scalar>(), s2 = internal::random<Scalar>();

  mat.setRandom();
  tri = mat.template triangularView<Mode>();
  triTr = mat.transpose().template triangularView<Mode>();
  s1tri = (s1 * mat).template triangularView<Mode>();
  s1triTr = (s1 * mat).transpose().template triangularView<Mode>();
  ge_right.setRandom();
  ge_left.setRandom();

  VERIFY_IS_APPROX(ge_xs = mat.template triangularView<Mode>() * ge_right, tri * ge_right);
  VERIFY_IS_APPROX(ge_sx = ge_left * mat.template triangularView<Mode>(), ge_left * tri);

  VERIFY_IS_APPROX(ge_xs.noalias() = mat.template triangularView<Mode>() * ge_right, tri * ge_right);
  VERIFY_IS_APPROX(ge_sx.noalias() = ge_left * mat.template triangularView<Mode>(), ge_left * tri);

  if ((Mode & UnitDiag) == 0)
    VERIFY_IS_APPROX(
        ge_xs.noalias() = (s1 * mat.adjoint()).template triangularView<Mode>() * (s2 * ge_left.transpose()),
        s1 * triTr.conjugate() * (s2 * ge_left.transpose()));

  VERIFY_IS_APPROX(
      ge_xs.noalias() = (s1 * mat.transpose()).template triangularView<Mode>() * (s2 * ge_left.transpose()),
      s1triTr * (s2 * ge_left.transpose()));
  VERIFY_IS_APPROX(ge_sx.noalias() = (s2 * ge_left) * (s1 * mat).template triangularView<Mode>(),
                   (s2 * ge_left) * s1tri);

  VERIFY_IS_APPROX(ge_sx.noalias() = ge_right.transpose() * mat.adjoint().template triangularView<Mode>(),
                   ge_right.transpose() * triTr.conjugate());
  VERIFY_IS_APPROX(ge_sx.noalias() = ge_right.adjoint() * mat.adjoint().template triangularView<Mode>(),
                   ge_right.adjoint() * triTr.conjugate());

  ge_xs_save = ge_xs;
  if ((Mode & UnitDiag) == 0)
    VERIFY_IS_APPROX(
        (ge_xs_save + s1 * triTr.conjugate() * (s2 * ge_left.adjoint())).eval(),
        ge_xs.noalias() += (s1 * mat.adjoint()).template triangularView<Mode>() * (s2 * ge_left.adjoint()));
  ge_xs_save = ge_xs;
  VERIFY_IS_APPROX(
      (ge_xs_save + s1triTr * (s2 * ge_left.adjoint())).eval(),
      ge_xs.noalias() += (s1 * mat.transpose()).template triangularView<Mode>() * (s2 * ge_left.adjoint()));
  ge_sx.setRandom();
  ge_sx_save = ge_sx;
  if ((Mode & UnitDiag) == 0)
    VERIFY_IS_APPROX(
        ge_sx_save - (ge_right.adjoint() * (-s1 * triTr).conjugate()).eval(),
        ge_sx.noalias() -= (ge_right.adjoint() * (-s1 * mat).adjoint().template triangularView<Mode>()).eval());

  if ((Mode & UnitDiag) == 0)
    VERIFY_IS_APPROX(ge_xs = (s1 * mat).adjoint().template triangularView<Mode>() * ge_left.adjoint(),
                     numext::conj(s1) * triTr.conjugate() * ge_left.adjoint());
  VERIFY_IS_APPROX(ge_xs = (s1 * mat).transpose().template triangularView<Mode>() * ge_left.adjoint(),
                   s1triTr * ge_left.adjoint());

  // TODO check with sub-matrix expressions ?

  // destination with a non-default inner-stride
  // see bug 1741
  {
    VERIFY_IS_APPROX(ge_xs.noalias() = mat.template triangularView<Mode>() * ge_right, tri * ge_right);
    typedef Matrix<Scalar, Dynamic, Dynamic> MatrixX;
    MatrixX buffer(2 * ge_xs.rows(), 2 * ge_xs.cols());
    Map<ResXS, 0, Stride<Dynamic, 2> > map1(buffer.data(), ge_xs.rows(), ge_xs.cols(),
                                            Stride<Dynamic, 2>(2 * ge_xs.outerStride(), 2));
    buffer.setZero();
    VERIFY_IS_APPROX(map1.noalias() = mat.template triangularView<Mode>() * ge_right, tri * ge_right);
  }
}

template <typename Scalar, int Mode, int TriOrder>
void trmv(int rows = get_random_size<Scalar>(), int cols = get_random_size<Scalar>()) {
  trmm<Scalar, Mode, TriOrder, ColMajor, ColMajor, 1>(rows, cols, 1);
}

template <typename Scalar, int Mode, int TriOrder, int OtherOrder, int ResOrder>
void trmm(int rows = get_random_size<Scalar>(), int cols = get_random_size<Scalar>(),
          int otherCols = get_random_size<Scalar>()) {
  trmm<Scalar, Mode, TriOrder, OtherOrder, ResOrder, Dynamic>(rows, cols, otherCols);
}

#define CALL_ALL_ORDERS(NB, SCALAR, MODE)                                             \
  EIGEN_CAT(CALL_SUBTEST_, NB)((trmm<SCALAR, MODE, ColMajor, ColMajor, ColMajor>())); \
  EIGEN_CAT(CALL_SUBTEST_, NB)((trmm<SCALAR, MODE, ColMajor, ColMajor, RowMajor>())); \
  EIGEN_CAT(CALL_SUBTEST_, NB)((trmm<SCALAR, MODE, ColMajor, RowMajor, ColMajor>())); \
  EIGEN_CAT(CALL_SUBTEST_, NB)((trmm<SCALAR, MODE, ColMajor, RowMajor, RowMajor>())); \
  EIGEN_CAT(CALL_SUBTEST_, NB)((trmm<SCALAR, MODE, RowMajor, ColMajor, ColMajor>())); \
  EIGEN_CAT(CALL_SUBTEST_, NB)((trmm<SCALAR, MODE, RowMajor, ColMajor, RowMajor>())); \
  EIGEN_CAT(CALL_SUBTEST_, NB)((trmm<SCALAR, MODE, RowMajor, RowMajor, ColMajor>())); \
  EIGEN_CAT(CALL_SUBTEST_, NB)((trmm<SCALAR, MODE, RowMajor, RowMajor, RowMajor>())); \
                                                                                      \
  EIGEN_CAT(CALL_SUBTEST_1, NB)((trmv<SCALAR, MODE, ColMajor>()));                    \
  EIGEN_CAT(CALL_SUBTEST_1, NB)((trmv<SCALAR, MODE, RowMajor>()));

#define CALL_ALL(NB, SCALAR)                               \
  CALL_ALL_ORDERS(EIGEN_CAT(1, NB), SCALAR, Upper)         \
  CALL_ALL_ORDERS(EIGEN_CAT(2, NB), SCALAR, UnitUpper)     \
  CALL_ALL_ORDERS(EIGEN_CAT(3, NB), SCALAR, StrictlyUpper) \
  CALL_ALL_ORDERS(EIGEN_CAT(1, NB), SCALAR, Lower)         \
  CALL_ALL_ORDERS(EIGEN_CAT(2, NB), SCALAR, UnitLower)     \
  CALL_ALL_ORDERS(EIGEN_CAT(3, NB), SCALAR, StrictlyLower)

EIGEN_DECLARE_TEST(product_trmm) {
  for (int i = 0; i < g_repeat; i++) {
    CALL_ALL(1, float);                 //  EIGEN_SUFFIXES;11;111;21;121;31;131
    CALL_ALL(2, double);                //  EIGEN_SUFFIXES;12;112;22;122;32;132
    CALL_ALL(3, std::complex<float>);   //  EIGEN_SUFFIXES;13;113;23;123;33;133
    CALL_ALL(4, std::complex<double>);  //  EIGEN_SUFFIXES;14;114;24;124;34;134
  }
}