Add test for operations using symbolic and expressional tensors

diff --git a/tests/symengine/symengine_tensor_operations_02.cc b/tests/symengine/symengine_tensor_operations_02.cc
new file mode 100644 (file)
index 0000000..c9e075a
--- /dev/null
+++ b/tests/symengine/symengine_tensor_operations_02.cc
@@ -0,0 +1,219 @@
+// ---------------------------------------------------------------------
+//
+// Copyright (C) 2019 by the deal.II authors
+//
+// This file is part of the deal.II library.
+//
+// The deal.II library is free software; you can use it, redistribute
+// it, and/or modify it under the terms of the GNU Lesser General
+// Public License as published by the Free Software Foundation; either
+// version 2.1 of the License, or (at your option) any later version.
+// The full text of the license can be found in the file LICENSE at
+// the top level of the deal.II distribution.
+//
+// ---------------------------------------------------------------------
+
+
+// Check that some of the common tensor operations can be performed with
+// tensors of expressions
+
+#include <deal.II/base/numbers.h>
+
+#include <deal.II/differentiation/sd.h>
+
+#include "../tests.h"
+
+using namespace dealii;
+namespace SD = Differentiation::SD;
+
+template <int dim, typename NumberType>
+Tensor<2, dim, NumberType>
+make_tensor(const NumberType &val)
+{
+  Tensor<2, dim, NumberType> out;
+  for (unsigned int i = 0; i < out.n_independent_components; ++i)
+    out[out.unrolled_to_component_indices(i)] = NumberType(i) + val;
+  return out;
+}
+
+template <int dim, typename NumberType>
+SymmetricTensor<2, dim, NumberType>
+make_symm_tensor(const NumberType &val)
+{
+  SymmetricTensor<2, dim, NumberType> out;
+  for (unsigned int i = 0; i < out.n_independent_components; ++i)
+    out[out.unrolled_to_component_indices(i)] = NumberType(i) + val;
+  return out;
+}
+
+template <int dim, typename NumberType>
+void
+test_tensor()
+{
+  typedef SD::Expression                       SD_number_t;
+  typedef Tensor<2, dim, SD_number_t>          SD_tensor_t;
+  typedef SymmetricTensor<2, dim, SD_number_t> SD_symm_tensor_t;
+
+  // --- Values ---
+  deallog.push("Initialize");
+  SD_tensor_t      a(make_tensor<dim>(NumberType(10)));
+  SD_tensor_t      b(make_tensor<dim>(NumberType(10)));
+  SD_symm_tensor_t as(make_symm_tensor<dim>(NumberType(10)));
+  SD_symm_tensor_t bs(make_symm_tensor<dim>(NumberType(10)));
+  deallog << "a: " << a << std::endl;
+  deallog << "b: " << b << std::endl;
+  deallog << "as: " << as << std::endl;
+  deallog << "bs: " << bs << std::endl;
+  deallog.pop();
+
+  deallog.push("Relational operators 1");
+  deallog << "a == b: " << (a == b) << std::endl;
+  deallog << "a != b: " << (a != b) << std::endl;
+  if (numbers::NumberTraits<NumberType>::is_complex == false)
+    deallog << "a.norm() < b.norm(): " << (a.norm() < b.norm()) << std::endl;
+  deallog.pop();
+
+  deallog.push("Set new values");
+  a  = make_tensor<dim>(NumberType(5));
+  b  = make_tensor<dim>(NumberType(9));
+  as = make_symm_tensor<dim>(NumberType(5));
+  bs = make_symm_tensor<dim>(NumberType(7));
+  deallog << "a: " << a << std::endl;
+  deallog << "b: " << b << std::endl;
+  deallog << "as: " << as << std::endl;
+  deallog << "bs: " << bs << std::endl;
+  deallog.pop();
+  //
+  deallog.push("Relational operators 2");
+  deallog << "a == b: " << (a == b) << std::endl;
+  deallog << "a != b: " << (a != b) << std::endl;
+  if (numbers::NumberTraits<NumberType>::is_complex == false)
+    deallog << "a.norm() < b.norm(): " << (a.norm() < b.norm()) << std::endl;
+  deallog.pop();
+
+  deallog.push("Math operators");
+  deallog.push("Tensor");
+  deallog << "a+b: " << (a + b) << std::endl;
+  deallog << "a-b: " << (a - b) << std::endl;
+  deallog << "a*b: " << (a * b) << std::endl;
+  deallog.pop();
+  deallog.push("SymmetricTensor");
+  deallog << "as+bs: " << (as + bs) << std::endl;
+  deallog << "as-bs: " << (as - bs) << std::endl;
+  deallog << "as*bs: " << (as * bs) << std::endl;
+  const SD_tensor_t as_ns = as;
+  deallog << "as: " << as << std::endl;
+  deallog << "as_ns: " << as_ns << std::endl;
+  const SD_tensor_t as_ns2(as);
+  deallog << "as+b: " << (as + b) << std::endl;
+  deallog << "as-b: " << (as - b) << std::endl;
+  deallog << "as*b: " << (static_cast<SD_tensor_t>(as) * b) << std::endl;
+  deallog.pop();
+  deallog.pop();
+
+  // --- Normal numbers ---
+  deallog.push("Copy constructor");
+  SD_tensor_t      c(a);   // Copy constructor
+  SD_symm_tensor_t cs(as); // Copy constructor
+  deallog << "c: " << c << std::endl;
+  deallog << "cs: " << cs << std::endl;
+  deallog.pop();
+
+  deallog.push("Math operators"); // including those with arithmetic numbers
+  const NumberType s(2);
+  deallog.push("Tensor");
+  c += b;
+  deallog << "c+=b: " << c << std::endl;
+  c *= s;
+  deallog << "c*=s: " << c << std::endl;
+  c -= b;
+  deallog << "c-=b: " << c << std::endl;
+  c /= s;
+  deallog << "c/=s: " << c << std::endl;
+  deallog.pop();
+  deallog.push("SymmetricTensor");
+  cs += bs;
+  deallog << "cs+=bs: " << cs << std::endl;
+  cs *= s;
+  deallog << "cs*=s: " << cs << std::endl;
+  cs -= bs;
+  deallog << "cs-=bs: " << cs << std::endl;
+  cs /= s;
+  deallog << "cs/=s: " << cs << std::endl;
+  deallog.pop();
+  deallog.pop();
+
+  // --- Symbols ---
+  deallog.push("Symbols");
+  const SD_number_t      y("y");
+  const SD_tensor_t      x(SD::make_tensor_of_symbols<2, dim>("x"));
+  const SD_symm_tensor_t z(SD::make_symmetric_tensor_of_symbols<2, dim>("z"));
+  deallog << "x: " << x << std::endl;
+  deallog << "y: " << y << std::endl;
+  deallog << "z: " << z << std::endl;
+  deallog.pop();
+
+  deallog.push("Math operators"); // including those with arithmetic numbers
+  deallog.push("Tensor");
+  c += x;
+  deallog << "c+=x: " << c << std::endl;
+  c *= y;
+  deallog << "c*=y: " << c << std::endl;
+  c *= s;
+  deallog << "c*=s: " << c << std::endl;
+  c -= x;
+  deallog << "c-=x: " << c << std::endl;
+  c /= y;
+  deallog << "c/=y: " << c << std::endl;
+  c /= s;
+  deallog << "c/=s: " << c << std::endl;
+  deallog.pop();
+  deallog.push("SymmetricTensor");
+  cs += z;
+  deallog << "cs+=z: " << cs << std::endl;
+  cs *= y;
+  deallog << "cs*=y: " << cs << std::endl;
+  cs *= s;
+  deallog << "cs*=s: " << cs << std::endl;
+  cs -= z;
+  deallog << "cs-=z: " << cs << std::endl;
+  cs /= y;
+  deallog << "cs/=y: " << cs << std::endl;
+  cs /= s;
+  deallog << "cs/=s: " << cs << std::endl;
+  deallog.pop();
+  deallog.pop();
+
+  deallog << "OK" << std::endl;
+}
+
+
+int
+main()
+{
+  initlog();
+
+  const int dim = 2;
+
+  deallog.push("Integer");
+  test_tensor<dim, int>();
+  deallog.pop();
+
+  deallog.push("Float");
+  test_tensor<dim, float>();
+  deallog.pop();
+
+  deallog.push("Double");
+  test_tensor<dim, double>();
+  deallog.pop();
+
+  deallog.push("Complex float");
+  test_tensor<dim, std::complex<float>>();
+  deallog.pop();
+
+  deallog.push("Complex double");
+  test_tensor<dim, std::complex<double>>();
+  deallog.pop();
+
+  deallog << "OK" << std::endl;
+}

diff --git a/tests/symengine/symengine_tensor_operations_02.output b/tests/symengine/symengine_tensor_operations_02.output
new file mode 100644 (file)
index 0000000..03cfc71
--- /dev/null
+++ b/tests/symengine/symengine_tensor_operations_02.output
@@ -0,0 +1,253 @@
+
+DEAL:Integer:Initialize::a: 10 11 12 13
+DEAL:Integer:Initialize::b: 10 11 12 13
+DEAL:Integer:Initialize::as: 10 12 12 11
+DEAL:Integer:Initialize::bs: 10 12 12 11
+DEAL:Integer:Relational operators 1::a == b: 1
+DEAL:Integer:Relational operators 1::a != b: 0
+DEAL:Integer:Relational operators 1::a.norm() < b.norm(): False
+DEAL:Integer:Set new values::a: 5 6 7 8
+DEAL:Integer:Set new values::b: 9 10 11 12
+DEAL:Integer:Set new values::as: 5 7 7 6
+DEAL:Integer:Set new values::bs: 7 9 9 8
+DEAL:Integer:Relational operators 2::a == b: 0
+DEAL:Integer:Relational operators 2::a != b: 1
+DEAL:Integer:Relational operators 2::a.norm() < b.norm(): sqrt(174) < sqrt(446)
+DEAL:Integer:Math operators:Tensor::a+b: 14 16 18 20
+DEAL:Integer:Math operators:Tensor::a-b: -4 -4 -4 -4
+DEAL:Integer:Math operators:Tensor::a*b: 111 122 151 166
+DEAL:Integer:Math operators:SymmetricTensor::as+bs: 12 16 16 14
+DEAL:Integer:Math operators:SymmetricTensor::as-bs: -2 -2 -2 -2
+DEAL:Integer:Math operators:SymmetricTensor::as*bs: 209
+DEAL:Integer:Math operators:SymmetricTensor::as: 5 7 7 6
+DEAL:Integer:Math operators:SymmetricTensor::as_ns: 5 7 7 6
+DEAL:Integer:Math operators:SymmetricTensor::as+b: 14 17 18 18
+DEAL:Integer:Math operators:SymmetricTensor::as-b: -4 -3 -4 -6
+DEAL:Integer:Math operators:SymmetricTensor::as*b: 122 134 129 142
+DEAL:Integer:Copy constructor::c: 5 6 7 8
+DEAL:Integer:Copy constructor::cs: 5 7 7 6
+DEAL:Integer:Math operators:Tensor::c+=b: 14 16 18 20
+DEAL:Integer:Math operators:Tensor::c*=s: 28 32 36 40
+DEAL:Integer:Math operators:Tensor::c-=b: 19 22 25 28
+DEAL:Integer:Math operators:Tensor::c/=s: 19/2 11 25/2 14
+DEAL:Integer:Math operators:SymmetricTensor::cs+=bs: 12 16 16 14
+DEAL:Integer:Math operators:SymmetricTensor::cs*=s: 24 32 32 28
+DEAL:Integer:Math operators:SymmetricTensor::cs-=bs: 17 23 23 20
+DEAL:Integer:Math operators:SymmetricTensor::cs/=s: 17/2 23/2 23/2 10
+DEAL:Integer:Symbols::x: x_00 x_01 x_10 x_11
+DEAL:Integer:Symbols::y: y
+DEAL:Integer:Symbols::z: z_00 z_01 z_01 z_11
+DEAL:Integer:Math operators:Tensor::c+=x: 19/2 + x_00 11 + x_01 25/2 + x_10 14 + x_11
+DEAL:Integer:Math operators:Tensor::c*=y: y*(19/2 + x_00) y*(11 + x_01) y*(25/2 + x_10) y*(14 + x_11)
+DEAL:Integer:Math operators:Tensor::c*=s: 2*y*(19/2 + x_00) 2*y*(11 + x_01) 2*y*(25/2 + x_10) 2*y*(14 + x_11)
+DEAL:Integer:Math operators:Tensor::c-=x: -x_00 + 2*y*(19/2 + x_00) -x_01 + 2*y*(11 + x_01) -x_10 + 2*y*(25/2 + x_10) -x_11 + 2*y*(14 + x_11)
+DEAL:Integer:Math operators:Tensor::c/=y: (-x_00 + 2*y*(19/2 + x_00))/y (-x_01 + 2*y*(11 + x_01))/y (-x_10 + 2*y*(25/2 + x_10))/y (-x_11 + 2*y*(14 + x_11))/y
+DEAL:Integer:Math operators:Tensor::c/=s: (1/2)*(-x_00 + 2*y*(19/2 + x_00))/y (1/2)*(-x_01 + 2*y*(11 + x_01))/y (1/2)*(-x_10 + 2*y*(25/2 + x_10))/y (1/2)*(-x_11 + 2*y*(14 + x_11))/y
+DEAL:Integer:Math operators:SymmetricTensor::cs+=z: 17/2 + z_00 23/2 + z_01 23/2 + z_01 10 + z_11
+DEAL:Integer:Math operators:SymmetricTensor::cs*=y: y*(17/2 + z_00) y*(23/2 + z_01) y*(23/2 + z_01) y*(10 + z_11)
+DEAL:Integer:Math operators:SymmetricTensor::cs*=s: 2*y*(17/2 + z_00) 2*y*(23/2 + z_01) 2*y*(23/2 + z_01) 2*y*(10 + z_11)
+DEAL:Integer:Math operators:SymmetricTensor::cs-=z: -z_00 + 2*y*(17/2 + z_00) -z_01 + 2*y*(23/2 + z_01) -z_01 + 2*y*(23/2 + z_01) -z_11 + 2*y*(10 + z_11)
+DEAL:Integer:Math operators:SymmetricTensor::cs/=y: (-z_00 + 2*y*(17/2 + z_00))/y (-z_01 + 2*y*(23/2 + z_01))/y (-z_01 + 2*y*(23/2 + z_01))/y (-z_11 + 2*y*(10 + z_11))/y
+DEAL:Integer:Math operators:SymmetricTensor::cs/=s: (1/2)*(-z_00 + 2*y*(17/2 + z_00))/y (1/2)*(-z_01 + 2*y*(23/2 + z_01))/y (1/2)*(-z_01 + 2*y*(23/2 + z_01))/y (1/2)*(-z_11 + 2*y*(10 + z_11))/y
+DEAL:Integer::OK
+DEAL:Float:Initialize::a: 10.0 11.0 12.0 13.0
+DEAL:Float:Initialize::b: 10.0 11.0 12.0 13.0
+DEAL:Float:Initialize::as: 10.0 12.0 12.0 11.0
+DEAL:Float:Initialize::bs: 10.0 12.0 12.0 11.0
+DEAL:Float:Relational operators 1::a == b: 1
+DEAL:Float:Relational operators 1::a != b: 0
+DEAL:Float:Relational operators 1::a.norm() < b.norm(): False
+DEAL:Float:Set new values::a: 5.0 6.0 7.0 8.0
+DEAL:Float:Set new values::b: 9.0 10.0 11.0 12.0
+DEAL:Float:Set new values::as: 5.0 7.0 7.0 6.0
+DEAL:Float:Set new values::bs: 7.0 9.0 9.0 8.0
+DEAL:Float:Relational operators 2::a == b: 0
+DEAL:Float:Relational operators 2::a != b: 1
+DEAL:Float:Relational operators 2::a.norm() < b.norm(): True
+DEAL:Float:Math operators:Tensor::a+b: 14.0 16.0 18.0 20.0
+DEAL:Float:Math operators:Tensor::a-b: -4.0 -4.0 -4.0 -4.0
+DEAL:Float:Math operators:Tensor::a*b: 111.0 122.0 151.0 166.0
+DEAL:Float:Math operators:SymmetricTensor::as+bs: 12.0 16.0 16.0 14.0
+DEAL:Float:Math operators:SymmetricTensor::as-bs: -2.0 -2.0 -2.0 -2.0
+DEAL:Float:Math operators:SymmetricTensor::as*bs: 209.0
+DEAL:Float:Math operators:SymmetricTensor::as: 5.0 7.0 7.0 6.0
+DEAL:Float:Math operators:SymmetricTensor::as_ns: 5.0 7.0 7.0 6.0
+DEAL:Float:Math operators:SymmetricTensor::as+b: 14.0 17.0 18.0 18.0
+DEAL:Float:Math operators:SymmetricTensor::as-b: -4.0 -3.0 -4.0 -6.0
+DEAL:Float:Math operators:SymmetricTensor::as*b: 122.0 134.0 129.0 142.0
+DEAL:Float:Copy constructor::c: 5.0 6.0 7.0 8.0
+DEAL:Float:Copy constructor::cs: 5.0 7.0 7.0 6.0
+DEAL:Float:Math operators:Tensor::c+=b: 14.0 16.0 18.0 20.0
+DEAL:Float:Math operators:Tensor::c*=s: 28.0 32.0 36.0 40.0
+DEAL:Float:Math operators:Tensor::c-=b: 19.0 22.0 25.0 28.0
+DEAL:Float:Math operators:Tensor::c/=s: 9.5 11.0 12.5 14.0
+DEAL:Float:Math operators:SymmetricTensor::cs+=bs: 12.0 16.0 16.0 14.0
+DEAL:Float:Math operators:SymmetricTensor::cs*=s: 24.0 32.0 32.0 28.0
+DEAL:Float:Math operators:SymmetricTensor::cs-=bs: 17.0 23.0 23.0 20.0
+DEAL:Float:Math operators:SymmetricTensor::cs/=s: 8.5 11.5 11.5 10.0
+DEAL:Float:Symbols::x: x_00 x_01 x_10 x_11
+DEAL:Float:Symbols::y: y
+DEAL:Float:Symbols::z: z_00 z_01 z_01 z_11
+DEAL:Float:Math operators:Tensor::c+=x: 9.5 + x_00 11.0 + x_01 12.5 + x_10 14.0 + x_11
+DEAL:Float:Math operators:Tensor::c*=y: y*(9.5 + x_00) y*(11.0 + x_01) y*(12.5 + x_10) y*(14.0 + x_11)
+DEAL:Float:Math operators:Tensor::c*=s: 2.0*y*(9.5 + x_00) 2.0*y*(11.0 + x_01) 2.0*y*(12.5 + x_10) 2.0*y*(14.0 + x_11)
+DEAL:Float:Math operators:Tensor::c-=x: -x_00 + 2.0*y*(9.5 + x_00) -x_01 + 2.0*y*(11.0 + x_01) -x_10 + 2.0*y*(12.5 + x_10) -x_11 + 2.0*y*(14.0 + x_11)
+DEAL:Float:Math operators:Tensor::c/=y: (-x_00 + 2.0*y*(9.5 + x_00))/y (-x_01 + 2.0*y*(11.0 + x_01))/y (-x_10 + 2.0*y*(12.5 + x_10))/y (-x_11 + 2.0*y*(14.0 + x_11))/y
+DEAL:Float:Math operators:Tensor::c/=s: 0.5*(-x_00 + 2.0*y*(9.5 + x_00))/y 0.5*(-x_01 + 2.0*y*(11.0 + x_01))/y 0.5*(-x_10 + 2.0*y*(12.5 + x_10))/y 0.5*(-x_11 + 2.0*y*(14.0 + x_11))/y
+DEAL:Float:Math operators:SymmetricTensor::cs+=z: 8.5 + z_00 11.5 + z_01 11.5 + z_01 10.0 + z_11
+DEAL:Float:Math operators:SymmetricTensor::cs*=y: y*(8.5 + z_00) y*(11.5 + z_01) y*(11.5 + z_01) y*(10.0 + z_11)
+DEAL:Float:Math operators:SymmetricTensor::cs*=s: 2.0*y*(8.5 + z_00) 2.0*y*(11.5 + z_01) 2.0*y*(11.5 + z_01) 2.0*y*(10.0 + z_11)
+DEAL:Float:Math operators:SymmetricTensor::cs-=z: -z_00 + 2.0*y*(8.5 + z_00) -z_01 + 2.0*y*(11.5 + z_01) -z_01 + 2.0*y*(11.5 + z_01) -z_11 + 2.0*y*(10.0 + z_11)
+DEAL:Float:Math operators:SymmetricTensor::cs/=y: (-z_00 + 2.0*y*(8.5 + z_00))/y (-z_01 + 2.0*y*(11.5 + z_01))/y (-z_01 + 2.0*y*(11.5 + z_01))/y (-z_11 + 2.0*y*(10.0 + z_11))/y
+DEAL:Float:Math operators:SymmetricTensor::cs/=s: 0.5*(-z_00 + 2.0*y*(8.5 + z_00))/y 0.5*(-z_01 + 2.0*y*(11.5 + z_01))/y 0.5*(-z_01 + 2.0*y*(11.5 + z_01))/y 0.5*(-z_11 + 2.0*y*(10.0 + z_11))/y
+DEAL:Float::OK
+DEAL:Double:Initialize::a: 10.0 11.0 12.0 13.0
+DEAL:Double:Initialize::b: 10.0 11.0 12.0 13.0
+DEAL:Double:Initialize::as: 10.0 12.0 12.0 11.0
+DEAL:Double:Initialize::bs: 10.0 12.0 12.0 11.0
+DEAL:Double:Relational operators 1::a == b: 1
+DEAL:Double:Relational operators 1::a != b: 0
+DEAL:Double:Relational operators 1::a.norm() < b.norm(): False
+DEAL:Double:Set new values::a: 5.0 6.0 7.0 8.0
+DEAL:Double:Set new values::b: 9.0 10.0 11.0 12.0
+DEAL:Double:Set new values::as: 5.0 7.0 7.0 6.0
+DEAL:Double:Set new values::bs: 7.0 9.0 9.0 8.0
+DEAL:Double:Relational operators 2::a == b: 0
+DEAL:Double:Relational operators 2::a != b: 1
+DEAL:Double:Relational operators 2::a.norm() < b.norm(): True
+DEAL:Double:Math operators:Tensor::a+b: 14.0 16.0 18.0 20.0
+DEAL:Double:Math operators:Tensor::a-b: -4.0 -4.0 -4.0 -4.0
+DEAL:Double:Math operators:Tensor::a*b: 111.0 122.0 151.0 166.0
+DEAL:Double:Math operators:SymmetricTensor::as+bs: 12.0 16.0 16.0 14.0
+DEAL:Double:Math operators:SymmetricTensor::as-bs: -2.0 -2.0 -2.0 -2.0
+DEAL:Double:Math operators:SymmetricTensor::as*bs: 209.0
+DEAL:Double:Math operators:SymmetricTensor::as: 5.0 7.0 7.0 6.0
+DEAL:Double:Math operators:SymmetricTensor::as_ns: 5.0 7.0 7.0 6.0
+DEAL:Double:Math operators:SymmetricTensor::as+b: 14.0 17.0 18.0 18.0
+DEAL:Double:Math operators:SymmetricTensor::as-b: -4.0 -3.0 -4.0 -6.0
+DEAL:Double:Math operators:SymmetricTensor::as*b: 122.0 134.0 129.0 142.0
+DEAL:Double:Copy constructor::c: 5.0 6.0 7.0 8.0
+DEAL:Double:Copy constructor::cs: 5.0 7.0 7.0 6.0
+DEAL:Double:Math operators:Tensor::c+=b: 14.0 16.0 18.0 20.0
+DEAL:Double:Math operators:Tensor::c*=s: 28.0 32.0 36.0 40.0
+DEAL:Double:Math operators:Tensor::c-=b: 19.0 22.0 25.0 28.0
+DEAL:Double:Math operators:Tensor::c/=s: 9.5 11.0 12.5 14.0
+DEAL:Double:Math operators:SymmetricTensor::cs+=bs: 12.0 16.0 16.0 14.0
+DEAL:Double:Math operators:SymmetricTensor::cs*=s: 24.0 32.0 32.0 28.0
+DEAL:Double:Math operators:SymmetricTensor::cs-=bs: 17.0 23.0 23.0 20.0
+DEAL:Double:Math operators:SymmetricTensor::cs/=s: 8.5 11.5 11.5 10.0
+DEAL:Double:Symbols::x: x_00 x_01 x_10 x_11
+DEAL:Double:Symbols::y: y
+DEAL:Double:Symbols::z: z_00 z_01 z_01 z_11
+DEAL:Double:Math operators:Tensor::c+=x: 9.5 + x_00 11.0 + x_01 12.5 + x_10 14.0 + x_11
+DEAL:Double:Math operators:Tensor::c*=y: y*(9.5 + x_00) y*(11.0 + x_01) y*(12.5 + x_10) y*(14.0 + x_11)
+DEAL:Double:Math operators:Tensor::c*=s: 2.0*y*(9.5 + x_00) 2.0*y*(11.0 + x_01) 2.0*y*(12.5 + x_10) 2.0*y*(14.0 + x_11)
+DEAL:Double:Math operators:Tensor::c-=x: -x_00 + 2.0*y*(9.5 + x_00) -x_01 + 2.0*y*(11.0 + x_01) -x_10 + 2.0*y*(12.5 + x_10) -x_11 + 2.0*y*(14.0 + x_11)
+DEAL:Double:Math operators:Tensor::c/=y: (-x_00 + 2.0*y*(9.5 + x_00))/y (-x_01 + 2.0*y*(11.0 + x_01))/y (-x_10 + 2.0*y*(12.5 + x_10))/y (-x_11 + 2.0*y*(14.0 + x_11))/y
+DEAL:Double:Math operators:Tensor::c/=s: 0.5*(-x_00 + 2.0*y*(9.5 + x_00))/y 0.5*(-x_01 + 2.0*y*(11.0 + x_01))/y 0.5*(-x_10 + 2.0*y*(12.5 + x_10))/y 0.5*(-x_11 + 2.0*y*(14.0 + x_11))/y
+DEAL:Double:Math operators:SymmetricTensor::cs+=z: 8.5 + z_00 11.5 + z_01 11.5 + z_01 10.0 + z_11
+DEAL:Double:Math operators:SymmetricTensor::cs*=y: y*(8.5 + z_00) y*(11.5 + z_01) y*(11.5 + z_01) y*(10.0 + z_11)
+DEAL:Double:Math operators:SymmetricTensor::cs*=s: 2.0*y*(8.5 + z_00) 2.0*y*(11.5 + z_01) 2.0*y*(11.5 + z_01) 2.0*y*(10.0 + z_11)
+DEAL:Double:Math operators:SymmetricTensor::cs-=z: -z_00 + 2.0*y*(8.5 + z_00) -z_01 + 2.0*y*(11.5 + z_01) -z_01 + 2.0*y*(11.5 + z_01) -z_11 + 2.0*y*(10.0 + z_11)
+DEAL:Double:Math operators:SymmetricTensor::cs/=y: (-z_00 + 2.0*y*(8.5 + z_00))/y (-z_01 + 2.0*y*(11.5 + z_01))/y (-z_01 + 2.0*y*(11.5 + z_01))/y (-z_11 + 2.0*y*(10.0 + z_11))/y
+DEAL:Double:Math operators:SymmetricTensor::cs/=s: 0.5*(-z_00 + 2.0*y*(8.5 + z_00))/y 0.5*(-z_01 + 2.0*y*(11.5 + z_01))/y 0.5*(-z_01 + 2.0*y*(11.5 + z_01))/y 0.5*(-z_11 + 2.0*y*(10.0 + z_11))/y
+DEAL:Double::OK
+DEAL:Complex float:Initialize::a: 10.0 + 0.0*I 11.0 + 0.0*I 12.0 + 0.0*I 13.0 + 0.0*I
+DEAL:Complex float:Initialize::b: 10.0 + 0.0*I 11.0 + 0.0*I 12.0 + 0.0*I 13.0 + 0.0*I
+DEAL:Complex float:Initialize::as: 10.0 + 0.0*I 12.0 + 0.0*I 12.0 + 0.0*I 11.0 + 0.0*I
+DEAL:Complex float:Initialize::bs: 10.0 + 0.0*I 12.0 + 0.0*I 12.0 + 0.0*I 11.0 + 0.0*I
+DEAL:Complex float:Relational operators 1::a == b: 1
+DEAL:Complex float:Relational operators 1::a != b: 0
+DEAL:Complex float:Set new values::a: 5.0 + 0.0*I 6.0 + 0.0*I 7.0 + 0.0*I 8.0 + 0.0*I
+DEAL:Complex float:Set new values::b: 9.0 + 0.0*I 10.0 + 0.0*I 11.0 + 0.0*I 12.0 + 0.0*I
+DEAL:Complex float:Set new values::as: 5.0 + 0.0*I 7.0 + 0.0*I 7.0 + 0.0*I 6.0 + 0.0*I
+DEAL:Complex float:Set new values::bs: 7.0 + 0.0*I 9.0 + 0.0*I 9.0 + 0.0*I 8.0 + 0.0*I
+DEAL:Complex float:Relational operators 2::a == b: 0
+DEAL:Complex float:Relational operators 2::a != b: 1
+DEAL:Complex float:Math operators:Tensor::a+b: 14.0 + 0.0*I 16.0 + 0.0*I 18.0 + 0.0*I 20.0 + 0.0*I
+DEAL:Complex float:Math operators:Tensor::a-b: -4.0 + 0.0*I -4.0 + 0.0*I -4.0 + 0.0*I -4.0 + 0.0*I
+DEAL:Complex float:Math operators:Tensor::a*b: 111.0 + 0.0*I 122.0 + 0.0*I 151.0 + 0.0*I 166.0 + 0.0*I
+DEAL:Complex float:Math operators:SymmetricTensor::as+bs: 12.0 + 0.0*I 16.0 + 0.0*I 16.0 + 0.0*I 14.0 + 0.0*I
+DEAL:Complex float:Math operators:SymmetricTensor::as-bs: -2.0 + 0.0*I -2.0 + 0.0*I -2.0 + 0.0*I -2.0 + 0.0*I
+DEAL:Complex float:Math operators:SymmetricTensor::as*bs: 209.0 + 0.0*I
+DEAL:Complex float:Math operators:SymmetricTensor::as: 5.0 + 0.0*I 7.0 + 0.0*I 7.0 + 0.0*I 6.0 + 0.0*I
+DEAL:Complex float:Math operators:SymmetricTensor::as_ns: 5.0 + 0.0*I 7.0 + 0.0*I 7.0 + 0.0*I 6.0 + 0.0*I
+DEAL:Complex float:Math operators:SymmetricTensor::as+b: 14.0 + 0.0*I 17.0 + 0.0*I 18.0 + 0.0*I 18.0 + 0.0*I
+DEAL:Complex float:Math operators:SymmetricTensor::as-b: -4.0 + 0.0*I -3.0 + 0.0*I -4.0 + 0.0*I -6.0 + 0.0*I
+DEAL:Complex float:Math operators:SymmetricTensor::as*b: 122.0 + 0.0*I 134.0 + 0.0*I 129.0 + 0.0*I 142.0 + 0.0*I
+DEAL:Complex float:Copy constructor::c: 5.0 + 0.0*I 6.0 + 0.0*I 7.0 + 0.0*I 8.0 + 0.0*I
+DEAL:Complex float:Copy constructor::cs: 5.0 + 0.0*I 7.0 + 0.0*I 7.0 + 0.0*I 6.0 + 0.0*I
+DEAL:Complex float:Math operators:Tensor::c+=b: 14.0 + 0.0*I 16.0 + 0.0*I 18.0 + 0.0*I 20.0 + 0.0*I
+DEAL:Complex float:Math operators:Tensor::c*=s: 28.0 + 0.0*I 32.0 + 0.0*I 36.0 + 0.0*I 40.0 + 0.0*I
+DEAL:Complex float:Math operators:Tensor::c-=b: 19.0 + 0.0*I 22.0 + 0.0*I 25.0 + 0.0*I 28.0 + 0.0*I
+DEAL:Complex float:Math operators:Tensor::c/=s: 9.5 + 0.0*I 11.0 + 0.0*I 12.5 + 0.0*I 14.0 + 0.0*I
+DEAL:Complex float:Math operators:SymmetricTensor::cs+=bs: 12.0 + 0.0*I 16.0 + 0.0*I 16.0 + 0.0*I 14.0 + 0.0*I
+DEAL:Complex float:Math operators:SymmetricTensor::cs*=s: 24.0 + 0.0*I 32.0 + 0.0*I 32.0 + 0.0*I 28.0 + 0.0*I
+DEAL:Complex float:Math operators:SymmetricTensor::cs-=bs: 17.0 + 0.0*I 23.0 + 0.0*I 23.0 + 0.0*I 20.0 + 0.0*I
+DEAL:Complex float:Math operators:SymmetricTensor::cs/=s: 8.5 + 0.0*I 11.5 + 0.0*I 11.5 + 0.0*I 10.0 + 0.0*I
+DEAL:Complex float:Symbols::x: x_00 x_01 x_10 x_11
+DEAL:Complex float:Symbols::y: y
+DEAL:Complex float:Symbols::z: z_00 z_01 z_01 z_11
+DEAL:Complex float:Math operators:Tensor::c+=x: 9.5 + 0.0*I + x_00 11.0 + 0.0*I + x_01 12.5 + 0.0*I + x_10 14.0 + 0.0*I + x_11
+DEAL:Complex float:Math operators:Tensor::c*=y: y*(9.5 + 0.0*I + x_00) y*(11.0 + 0.0*I + x_01) y*(12.5 + 0.0*I + x_10) y*(14.0 + 0.0*I + x_11)
+DEAL:Complex float:Math operators:Tensor::c*=s: (2.0 + 0.0*I)*y*(9.5 + 0.0*I + x_00) (2.0 + 0.0*I)*y*(11.0 + 0.0*I + x_01) (2.0 + 0.0*I)*y*(12.5 + 0.0*I + x_10) (2.0 + 0.0*I)*y*(14.0 + 0.0*I + x_11)
+DEAL:Complex float:Math operators:Tensor::c-=x: -x_00 + (2.0 + 0.0*I)*y*(9.5 + 0.0*I + x_00) -x_01 + (2.0 + 0.0*I)*y*(11.0 + 0.0*I + x_01) -x_10 + (2.0 + 0.0*I)*y*(12.5 + 0.0*I + x_10) -x_11 + (2.0 + 0.0*I)*y*(14.0 + 0.0*I + x_11)
+DEAL:Complex float:Math operators:Tensor::c/=y: (-x_00 + (2.0 + 0.0*I)*y*(9.5 + 0.0*I + x_00))/y (-x_01 + (2.0 + 0.0*I)*y*(11.0 + 0.0*I + x_01))/y (-x_10 + (2.0 + 0.0*I)*y*(12.5 + 0.0*I + x_10))/y (-x_11 + (2.0 + 0.0*I)*y*(14.0 + 0.0*I + x_11))/y
+DEAL:Complex float:Math operators:Tensor::c/=s: (0.5 + 0.0*I)*(-x_00 + (2.0 + 0.0*I)*y*(9.5 + 0.0*I + x_00))/y (0.5 + 0.0*I)*(-x_01 + (2.0 + 0.0*I)*y*(11.0 + 0.0*I + x_01))/y (0.5 + 0.0*I)*(-x_10 + (2.0 + 0.0*I)*y*(12.5 + 0.0*I + x_10))/y (0.5 + 0.0*I)*(-x_11 + (2.0 + 0.0*I)*y*(14.0 + 0.0*I + x_11))/y
+DEAL:Complex float:Math operators:SymmetricTensor::cs+=z: 8.5 + 0.0*I + z_00 11.5 + 0.0*I + z_01 11.5 + 0.0*I + z_01 10.0 + 0.0*I + z_11
+DEAL:Complex float:Math operators:SymmetricTensor::cs*=y: y*(8.5 + 0.0*I + z_00) y*(11.5 + 0.0*I + z_01) y*(11.5 + 0.0*I + z_01) y*(10.0 + 0.0*I + z_11)
+DEAL:Complex float:Math operators:SymmetricTensor::cs*=s: (2.0 + 0.0*I)*y*(8.5 + 0.0*I + z_00) (2.0 + 0.0*I)*y*(11.5 + 0.0*I + z_01) (2.0 + 0.0*I)*y*(11.5 + 0.0*I + z_01) (2.0 + 0.0*I)*y*(10.0 + 0.0*I + z_11)
+DEAL:Complex float:Math operators:SymmetricTensor::cs-=z: -z_00 + (2.0 + 0.0*I)*y*(8.5 + 0.0*I + z_00) -z_01 + (2.0 + 0.0*I)*y*(11.5 + 0.0*I + z_01) -z_01 + (2.0 + 0.0*I)*y*(11.5 + 0.0*I + z_01) -z_11 + (2.0 + 0.0*I)*y*(10.0 + 0.0*I + z_11)
+DEAL:Complex float:Math operators:SymmetricTensor::cs/=y: (-z_00 + (2.0 + 0.0*I)*y*(8.5 + 0.0*I + z_00))/y (-z_01 + (2.0 + 0.0*I)*y*(11.5 + 0.0*I + z_01))/y (-z_01 + (2.0 + 0.0*I)*y*(11.5 + 0.0*I + z_01))/y (-z_11 + (2.0 + 0.0*I)*y*(10.0 + 0.0*I + z_11))/y
+DEAL:Complex float:Math operators:SymmetricTensor::cs/=s: (0.5 + 0.0*I)*(-z_00 + (2.0 + 0.0*I)*y*(8.5 + 0.0*I + z_00))/y (0.5 + 0.0*I)*(-z_01 + (2.0 + 0.0*I)*y*(11.5 + 0.0*I + z_01))/y (0.5 + 0.0*I)*(-z_01 + (2.0 + 0.0*I)*y*(11.5 + 0.0*I + z_01))/y (0.5 + 0.0*I)*(-z_11 + (2.0 + 0.0*I)*y*(10.0 + 0.0*I + z_11))/y
+DEAL:Complex float::OK
+DEAL:Complex double:Initialize::a: 10.0 + 0.0*I 11.0 + 0.0*I 12.0 + 0.0*I 13.0 + 0.0*I
+DEAL:Complex double:Initialize::b: 10.0 + 0.0*I 11.0 + 0.0*I 12.0 + 0.0*I 13.0 + 0.0*I
+DEAL:Complex double:Initialize::as: 10.0 + 0.0*I 12.0 + 0.0*I 12.0 + 0.0*I 11.0 + 0.0*I
+DEAL:Complex double:Initialize::bs: 10.0 + 0.0*I 12.0 + 0.0*I 12.0 + 0.0*I 11.0 + 0.0*I
+DEAL:Complex double:Relational operators 1::a == b: 1
+DEAL:Complex double:Relational operators 1::a != b: 0
+DEAL:Complex double:Set new values::a: 5.0 + 0.0*I 6.0 + 0.0*I 7.0 + 0.0*I 8.0 + 0.0*I
+DEAL:Complex double:Set new values::b: 9.0 + 0.0*I 10.0 + 0.0*I 11.0 + 0.0*I 12.0 + 0.0*I
+DEAL:Complex double:Set new values::as: 5.0 + 0.0*I 7.0 + 0.0*I 7.0 + 0.0*I 6.0 + 0.0*I
+DEAL:Complex double:Set new values::bs: 7.0 + 0.0*I 9.0 + 0.0*I 9.0 + 0.0*I 8.0 + 0.0*I
+DEAL:Complex double:Relational operators 2::a == b: 0
+DEAL:Complex double:Relational operators 2::a != b: 1
+DEAL:Complex double:Math operators:Tensor::a+b: 14.0 + 0.0*I 16.0 + 0.0*I 18.0 + 0.0*I 20.0 + 0.0*I
+DEAL:Complex double:Math operators:Tensor::a-b: -4.0 + 0.0*I -4.0 + 0.0*I -4.0 + 0.0*I -4.0 + 0.0*I
+DEAL:Complex double:Math operators:Tensor::a*b: 111.0 + 0.0*I 122.0 + 0.0*I 151.0 + 0.0*I 166.0 + 0.0*I
+DEAL:Complex double:Math operators:SymmetricTensor::as+bs: 12.0 + 0.0*I 16.0 + 0.0*I 16.0 + 0.0*I 14.0 + 0.0*I
+DEAL:Complex double:Math operators:SymmetricTensor::as-bs: -2.0 + 0.0*I -2.0 + 0.0*I -2.0 + 0.0*I -2.0 + 0.0*I
+DEAL:Complex double:Math operators:SymmetricTensor::as*bs: 209.0 + 0.0*I
+DEAL:Complex double:Math operators:SymmetricTensor::as: 5.0 + 0.0*I 7.0 + 0.0*I 7.0 + 0.0*I 6.0 + 0.0*I
+DEAL:Complex double:Math operators:SymmetricTensor::as_ns: 5.0 + 0.0*I 7.0 + 0.0*I 7.0 + 0.0*I 6.0 + 0.0*I
+DEAL:Complex double:Math operators:SymmetricTensor::as+b: 14.0 + 0.0*I 17.0 + 0.0*I 18.0 + 0.0*I 18.0 + 0.0*I
+DEAL:Complex double:Math operators:SymmetricTensor::as-b: -4.0 + 0.0*I -3.0 + 0.0*I -4.0 + 0.0*I -6.0 + 0.0*I
+DEAL:Complex double:Math operators:SymmetricTensor::as*b: 122.0 + 0.0*I 134.0 + 0.0*I 129.0 + 0.0*I 142.0 + 0.0*I
+DEAL:Complex double:Copy constructor::c: 5.0 + 0.0*I 6.0 + 0.0*I 7.0 + 0.0*I 8.0 + 0.0*I
+DEAL:Complex double:Copy constructor::cs: 5.0 + 0.0*I 7.0 + 0.0*I 7.0 + 0.0*I 6.0 + 0.0*I
+DEAL:Complex double:Math operators:Tensor::c+=b: 14.0 + 0.0*I 16.0 + 0.0*I 18.0 + 0.0*I 20.0 + 0.0*I
+DEAL:Complex double:Math operators:Tensor::c*=s: 28.0 + 0.0*I 32.0 + 0.0*I 36.0 + 0.0*I 40.0 + 0.0*I
+DEAL:Complex double:Math operators:Tensor::c-=b: 19.0 + 0.0*I 22.0 + 0.0*I 25.0 + 0.0*I 28.0 + 0.0*I
+DEAL:Complex double:Math operators:Tensor::c/=s: 9.5 + 0.0*I 11.0 + 0.0*I 12.5 + 0.0*I 14.0 + 0.0*I
+DEAL:Complex double:Math operators:SymmetricTensor::cs+=bs: 12.0 + 0.0*I 16.0 + 0.0*I 16.0 + 0.0*I 14.0 + 0.0*I
+DEAL:Complex double:Math operators:SymmetricTensor::cs*=s: 24.0 + 0.0*I 32.0 + 0.0*I 32.0 + 0.0*I 28.0 + 0.0*I
+DEAL:Complex double:Math operators:SymmetricTensor::cs-=bs: 17.0 + 0.0*I 23.0 + 0.0*I 23.0 + 0.0*I 20.0 + 0.0*I
+DEAL:Complex double:Math operators:SymmetricTensor::cs/=s: 8.5 + 0.0*I 11.5 + 0.0*I 11.5 + 0.0*I 10.0 + 0.0*I
+DEAL:Complex double:Symbols::x: x_00 x_01 x_10 x_11
+DEAL:Complex double:Symbols::y: y
+DEAL:Complex double:Symbols::z: z_00 z_01 z_01 z_11
+DEAL:Complex double:Math operators:Tensor::c+=x: 9.5 + 0.0*I + x_00 11.0 + 0.0*I + x_01 12.5 + 0.0*I + x_10 14.0 + 0.0*I + x_11
+DEAL:Complex double:Math operators:Tensor::c*=y: y*(9.5 + 0.0*I + x_00) y*(11.0 + 0.0*I + x_01) y*(12.5 + 0.0*I + x_10) y*(14.0 + 0.0*I + x_11)
+DEAL:Complex double:Math operators:Tensor::c*=s: (2.0 + 0.0*I)*y*(9.5 + 0.0*I + x_00) (2.0 + 0.0*I)*y*(11.0 + 0.0*I + x_01) (2.0 + 0.0*I)*y*(12.5 + 0.0*I + x_10) (2.0 + 0.0*I)*y*(14.0 + 0.0*I + x_11)
+DEAL:Complex double:Math operators:Tensor::c-=x: -x_00 + (2.0 + 0.0*I)*y*(9.5 + 0.0*I + x_00) -x_01 + (2.0 + 0.0*I)*y*(11.0 + 0.0*I + x_01) -x_10 + (2.0 + 0.0*I)*y*(12.5 + 0.0*I + x_10) -x_11 + (2.0 + 0.0*I)*y*(14.0 + 0.0*I + x_11)
+DEAL:Complex double:Math operators:Tensor::c/=y: (-x_00 + (2.0 + 0.0*I)*y*(9.5 + 0.0*I + x_00))/y (-x_01 + (2.0 + 0.0*I)*y*(11.0 + 0.0*I + x_01))/y (-x_10 + (2.0 + 0.0*I)*y*(12.5 + 0.0*I + x_10))/y (-x_11 + (2.0 + 0.0*I)*y*(14.0 + 0.0*I + x_11))/y
+DEAL:Complex double:Math operators:Tensor::c/=s: (0.5 + 0.0*I)*(-x_00 + (2.0 + 0.0*I)*y*(9.5 + 0.0*I + x_00))/y (0.5 + 0.0*I)*(-x_01 + (2.0 + 0.0*I)*y*(11.0 + 0.0*I + x_01))/y (0.5 + 0.0*I)*(-x_10 + (2.0 + 0.0*I)*y*(12.5 + 0.0*I + x_10))/y (0.5 + 0.0*I)*(-x_11 + (2.0 + 0.0*I)*y*(14.0 + 0.0*I + x_11))/y
+DEAL:Complex double:Math operators:SymmetricTensor::cs+=z: 8.5 + 0.0*I + z_00 11.5 + 0.0*I + z_01 11.5 + 0.0*I + z_01 10.0 + 0.0*I + z_11
+DEAL:Complex double:Math operators:SymmetricTensor::cs*=y: y*(8.5 + 0.0*I + z_00) y*(11.5 + 0.0*I + z_01) y*(11.5 + 0.0*I + z_01) y*(10.0 + 0.0*I + z_11)
+DEAL:Complex double:Math operators:SymmetricTensor::cs*=s: (2.0 + 0.0*I)*y*(8.5 + 0.0*I + z_00) (2.0 + 0.0*I)*y*(11.5 + 0.0*I + z_01) (2.0 + 0.0*I)*y*(11.5 + 0.0*I + z_01) (2.0 + 0.0*I)*y*(10.0 + 0.0*I + z_11)
+DEAL:Complex double:Math operators:SymmetricTensor::cs-=z: -z_00 + (2.0 + 0.0*I)*y*(8.5 + 0.0*I + z_00) -z_01 + (2.0 + 0.0*I)*y*(11.5 + 0.0*I + z_01) -z_01 + (2.0 + 0.0*I)*y*(11.5 + 0.0*I + z_01) -z_11 + (2.0 + 0.0*I)*y*(10.0 + 0.0*I + z_11)
+DEAL:Complex double:Math operators:SymmetricTensor::cs/=y: (-z_00 + (2.0 + 0.0*I)*y*(8.5 + 0.0*I + z_00))/y (-z_01 + (2.0 + 0.0*I)*y*(11.5 + 0.0*I + z_01))/y (-z_01 + (2.0 + 0.0*I)*y*(11.5 + 0.0*I + z_01))/y (-z_11 + (2.0 + 0.0*I)*y*(10.0 + 0.0*I + z_11))/y
+DEAL:Complex double:Math operators:SymmetricTensor::cs/=s: (0.5 + 0.0*I)*(-z_00 + (2.0 + 0.0*I)*y*(8.5 + 0.0*I + z_00))/y (0.5 + 0.0*I)*(-z_01 + (2.0 + 0.0*I)*y*(11.5 + 0.0*I + z_01))/y (0.5 + 0.0*I)*(-z_01 + (2.0 + 0.0*I)*y*(11.5 + 0.0*I + z_01))/y (0.5 + 0.0*I)*(-z_11 + (2.0 + 0.0*I)*y*(10.0 + 0.0*I + z_11))/y
+DEAL:Complex double::OK
+DEAL::OK