Stokhos_SacadoPCEUnitTest.hpp

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namespace SacadoPCEUnitTest {
 
  // Common setup for unit tests
  template <typename PCEType>
  struct UnitTestSetup {
    
    typedef PCEType pce_type;
    typedef Stokhos::OrthogPolyApprox<int,double> opa_type;
    double rtol, atol;
    double crtol, catol;
    int sz;
    Teuchos::RCP<const Stokhos::CompletePolynomialBasis<int,double> > basis;
    Teuchos::RCP<const Stokhos::Quadrature<int,double> > quad;
    Teuchos::RCP<Stokhos::Sparse3Tensor<int,double> > Cijk;
    Teuchos::RCP< Stokhos::QuadOrthogPolyExpansion<int,double> > exp;
    pce_type x, y, u, u2, cx, cu, cu2, sx, su, su2;
    double a;
    
    UnitTestSetup() {
      rtol = 1e-4;
      atol = 1e-5;
      crtol = 1e-12;
      catol = 1e-12;
      a = 3.1;
      const int d = 2;
      const int p = 7;
      
      // Create product basis
      Teuchos::Array< Teuchos::RCP<const Stokhos::OneDOrthogPolyBasis<int,double> > > bases(d);
      for (int i=0; i<d; i++)
  bases[i] = 
    Teuchos::rcp(new Stokhos::LegendreBasis<int,double>(p));
      basis =
  Teuchos::rcp(new Stokhos::CompletePolynomialBasis<int,double>(bases));
      
      // Tensor product quadrature
      quad = 
  Teuchos::rcp(new Stokhos::TensorProductQuadrature<int,double>(basis));
 
      // Triple product tensor
      Cijk = basis->computeTripleProductTensor();
      
      // Quadrature expansion
      exp = 
  Teuchos::rcp(new Stokhos::QuadOrthogPolyExpansion<int,double>(basis, Cijk, quad));
      
      // Create approximation
      sz = basis->size();
      x.reset(exp);
      y.reset(exp);
      u.reset(exp); 
      u2.reset(exp);
      cx.reset(exp, 1);
      x.term(0, 0) = 1.0;
      cx.term(0, 0) = a;
      cu.reset(exp);
      cu2.reset(exp, 1);
      sx.reset(exp, d+1);
      su.reset(exp, d+1);
      su2.reset(exp, d+1);
      for (int i=0; i<d; i++) {
  x.term(i, 1) = 0.1;
  sx.term(i, 1) = 0.0;
      }
      y.term(0, 0) = 2.0;
      for (int i=0; i<d; i++)
  y.term(i, 1) = 0.25;
    }
  };
 
  typedef UnitTestSetup<pce_type> UTS;
  UTS setup;
 
  TEUCHOS_UNIT_TEST( Stokhos_PCE, UMinus) {
    UTS::pce_type v = std::sin(setup.x);
    UTS::pce_type u = -v;
    UTS::opa_type u_opa(setup.basis);
    setup.exp->unaryMinus(u_opa, v.getOrthogPolyApprox());
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u", 
           u_opa, "u_opa", 
           setup.rtol, setup.atol, out);
  }
 
#define UNARY_UNIT_TEST(OP)           \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, OP) {         \
    UTS::pce_type u = OP(setup.x);          \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->OP(u_opa, setup.x.getOrthogPolyApprox());    \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
           u_opa, "u_opa",      \
           setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, OP##_const) {       \
    UTS::pce_type u = OP(setup.cx);         \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->OP(u_opa, setup.cx.getOrthogPolyApprox());   \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
           u_opa, "u_opa",      \
           setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, OP##_resize) {      \
    UTS::pce_type u;              \
    u = OP(setup.x);              \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->OP(u_opa, setup.x.getOrthogPolyApprox());    \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
           u_opa, "u_opa",      \
           setup.rtol, setup.atol, out);  \
  }
 
  UNARY_UNIT_TEST(exp)
  UNARY_UNIT_TEST(log)
  UNARY_UNIT_TEST(log10)
  UNARY_UNIT_TEST(sqrt)
  UNARY_UNIT_TEST(cbrt)
  UNARY_UNIT_TEST(sin)
  UNARY_UNIT_TEST(cos)
  UNARY_UNIT_TEST(tan)
  UNARY_UNIT_TEST(sinh)
  UNARY_UNIT_TEST(cosh)
  UNARY_UNIT_TEST(tanh)
  UNARY_UNIT_TEST(asin)
  UNARY_UNIT_TEST(acos)
  UNARY_UNIT_TEST(atan)
  UNARY_UNIT_TEST(asinh)
  UNARY_UNIT_TEST(acosh)
  UNARY_UNIT_TEST(atanh)
 
#define BINARY_UNIT_TEST(OP, EXPOP)         \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP) {        \
    UTS::pce_type v = std::sin(setup.x);        \
    UTS::pce_type w = std::cos(setup.x);        \
    UTS::pce_type u = OP(v,w);            \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->EXPOP(u_opa, v.getOrthogPolyApprox(),      \
         w.getOrthogPolyApprox());        \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
           u_opa, "u_opa",      \
           setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_left_const) {     \
    UTS::pce_type w = std::cos(setup.x);        \
    UTS::pce_type u = OP(setup.a, w);         \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->EXPOP(u_opa, setup.a,          \
           w.getOrthogPolyApprox());        \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
             u_opa, "u_opa",      \
             setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_right_const) {    \
    UTS::pce_type v = std::sin(setup.x);        \
    UTS::pce_type u = OP(v, setup.a);         \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->EXPOP(u_opa, v.getOrthogPolyApprox(),      \
           setup.a);            \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
             u_opa, "u_opa",      \
             setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_both_const) {     \
    UTS::pce_type u = OP(setup.cx, setup.cx);       \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->EXPOP(u_opa, setup.cx.getOrthogPolyApprox(),   \
           setup.cx.getOrthogPolyApprox());     \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
             u_opa, "u_opa",      \
             setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_left_const2) {    \
    UTS::pce_type w = std::cos(setup.x);        \
    UTS::pce_type u = OP(setup.cx, w);          \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->EXPOP(u_opa, setup.cx.getOrthogPolyApprox(),   \
           w.getOrthogPolyApprox());        \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
             u_opa, "u_opa",      \
             setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_right_const2) {   \
    UTS::pce_type v = std::sin(setup.x);        \
    UTS::pce_type u = OP(v, setup.cx);          \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->EXPOP(u_opa, v.getOrthogPolyApprox(),      \
           setup.cx.getOrthogPolyApprox());     \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
             u_opa, "u_opa",      \
             setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_resize) {     \
    UTS::pce_type v = std::sin(setup.x);        \
    UTS::pce_type w = std::cos(setup.x);        \
    UTS::pce_type u;              \
    u = OP(v, w);             \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->EXPOP(u_opa, v.getOrthogPolyApprox(),      \
           w.getOrthogPolyApprox());        \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
             u_opa, "u_opa",      \
             setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_left_const_resize) {    \
    UTS::pce_type w = std::cos(setup.x);        \
    UTS::pce_type u;              \
    u = OP(setup.a, w);             \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->EXPOP(u_opa, setup.a,          \
           w.getOrthogPolyApprox());        \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
             u_opa, "u_opa",      \
             setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_right_const_resize) {   \
    UTS::pce_type v = std::sin(setup.x);        \
    UTS::pce_type u;              \
    u = OP(v, setup.a);             \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->EXPOP(u_opa, v.getOrthogPolyApprox(),      \
           setup.a);            \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
             u_opa, "u_opa",      \
             setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_left_short) {     \
    UTS::pce_type w = std::cos(setup.x);        \
    UTS::pce_type u = OP(setup.sx, w);          \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->EXPOP(u_opa, setup.sx.getOrthogPolyApprox(),   \
           w.getOrthogPolyApprox());        \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
             u_opa, "u_opa",      \
             setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_right_short) {    \
    UTS::pce_type v = std::sin(setup.x);        \
    UTS::pce_type u = OP(v, setup.sx);          \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->EXPOP(u_opa, v.getOrthogPolyApprox(),      \
           setup.sx.getOrthogPolyApprox());     \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
             u_opa, "u_opa",      \
             setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_both_short) {     \
    UTS::pce_type u = OP(setup.sx, setup.sx);       \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->EXPOP(u_opa, setup.sx.getOrthogPolyApprox(),   \
           setup.sx.getOrthogPolyApprox());     \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
             u_opa, "u_opa",      \
             setup.rtol, setup.atol, out);  \
  }                 \
TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_left_short_resize) {    \
    UTS::pce_type w = std::cos(setup.x);        \
    UTS::pce_type u;              \
    u = OP(setup.sx, w);            \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->EXPOP(u_opa, setup.sx.getOrthogPolyApprox(),   \
           w.getOrthogPolyApprox());        \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
             u_opa, "u_opa",      \
             setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_right_short_resize) {   \
    UTS::pce_type v = std::sin(setup.x);        \
    UTS::pce_type u;              \
    u = OP(v, setup.sx);            \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->EXPOP(u_opa, v.getOrthogPolyApprox(),      \
           setup.sx.getOrthogPolyApprox());     \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
             u_opa, "u_opa",      \
             setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_left_short_right_const) { \
    UTS::pce_type u = OP(setup.sx, setup.a);        \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->EXPOP(u_opa, setup.sx.getOrthogPolyApprox(),   \
           setup.a);            \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
             u_opa, "u_opa",      \
             setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_right_short_left_const) { \
    UTS::pce_type u = OP(setup.a, setup.sx);        \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->EXPOP(u_opa, setup.a,          \
           setup.sx.getOrthogPolyApprox());     \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
             u_opa, "u_opa",      \
             setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_left_short_right_const2) {  \
    UTS::pce_type u = OP(setup.sx, setup.cx);       \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->EXPOP(u_opa, setup.sx.getOrthogPolyApprox(),   \
           setup.cx.getOrthogPolyApprox());     \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
             u_opa, "u_opa",      \
             setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_right_short_left_const2) {  \
    UTS::pce_type u = OP(setup.cx, setup.sx);       \
    UTS::opa_type u_opa(setup.basis);         \
    setup.exp->EXPOP(u_opa, setup.cx.getOrthogPolyApprox(),   \
           setup.sx.getOrthogPolyApprox());     \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
             u_opa, "u_opa",      \
             setup.rtol, setup.atol, out);  \
  }
 
  BINARY_UNIT_TEST(operator+, plus)
  BINARY_UNIT_TEST(operator-, minus)
  BINARY_UNIT_TEST(operator*, times)
  BINARY_UNIT_TEST(operator/, divide)
 
#define OPASSIGN_UNIT_TEST(OP, EXPOP)         \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP) {        \
    UTS::pce_type v = std::sin(setup.x);        \
    UTS::pce_type u = std::cos(setup.x);        \
    UTS::opa_type u_opa = u.getOrthogPolyApprox();      \
    u OP v;               \
    setup.exp->EXPOP(u_opa, v.getOrthogPolyApprox());     \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
           u_opa, "u_opa",      \
           setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_const) {      \
    UTS::pce_type u = std::cos(setup.x);        \
    UTS::opa_type u_opa = u.getOrthogPolyApprox();      \
    u OP setup.a;             \
    setup.exp->EXPOP(u_opa, setup.a);         \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
           u_opa, "u_opa",      \
           setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_const2) {     \
    UTS::pce_type u = std::cos(setup.x);        \
    UTS::opa_type u_opa = u.getOrthogPolyApprox();      \
    u OP setup.cx;              \
    setup.exp->EXPOP(u_opa, setup.cx.getOrthogPolyApprox());    \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
           u_opa, "u_opa",      \
           setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_resize) {     \
    UTS::pce_type v = std::sin(setup.x);        \
    UTS::pce_type u = setup.a;            \
    UTS::opa_type u_opa = u.getOrthogPolyApprox();      \
    u OP v;               \
    setup.exp->EXPOP(u_opa, v.getOrthogPolyApprox());     \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
           u_opa, "u_opa",      \
           setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_short) {      \
    UTS::pce_type u = std::cos(setup.x);        \
    UTS::opa_type u_opa = u.getOrthogPolyApprox();      \
    u OP setup.sx;              \
    setup.exp->EXPOP(u_opa, setup.sx.getOrthogPolyApprox());    \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
           u_opa, "u_opa",      \
           setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_short_resize) {   \
    UTS::pce_type u = setup.sx;           \
    UTS::pce_type v = std::cos(setup.x);        \
    UTS::opa_type u_opa = u.getOrthogPolyApprox();      \
    u OP v;               \
    setup.exp->EXPOP(u_opa, v.getOrthogPolyApprox());     \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
           u_opa, "u_opa",      \
           setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_short_const) {    \
    UTS::pce_type u = setup.sx;           \
    UTS::opa_type u_opa = u.getOrthogPolyApprox();      \
    u OP setup.a;             \
    setup.exp->EXPOP(u_opa, setup.a);         \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
           u_opa, "u_opa",      \
           setup.rtol, setup.atol, out);  \
  }                 \
  TEUCHOS_UNIT_TEST( Stokhos_PCE, EXPOP##_short_const2) {   \
    UTS::pce_type u = setup.sx;           \
    UTS::opa_type u_opa = u.getOrthogPolyApprox();      \
    u OP setup.cx;              \
    setup.exp->EXPOP(u_opa, setup.cx.getOrthogPolyApprox());    \
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",  \
           u_opa, "u_opa",      \
           setup.rtol, setup.atol, out);  \
  }
 
  OPASSIGN_UNIT_TEST(+=, plusEqual)
  OPASSIGN_UNIT_TEST(-=, minusEqual)
  OPASSIGN_UNIT_TEST(*=, timesEqual)
  OPASSIGN_UNIT_TEST(/=, divideEqual)
 
  TEUCHOS_UNIT_TEST( Stokhos_PCE, saxpy) {
    UTS::pce_type u = std::sin(setup.x);
    UTS::pce_type v = std::cos(setup.x);
    UTS::pce_type w = std::exp(setup.x);
    UTS::opa_type u_opa = u.getOrthogPolyApprox();
    UTS::opa_type t_opa(setup.basis);
    u += v*w;
    setup.exp->times(t_opa, v.getOrthogPolyApprox(), w.getOrthogPolyApprox());
    setup.exp->plusEqual(u_opa, t_opa);
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",
           u_opa, "u_opa",
           setup.rtol, setup.atol, out);
  }
  TEUCHOS_UNIT_TEST( Stokhos_PCE, saxpy_resize) {
    UTS::pce_type u = setup.cx;
    UTS::pce_type v = std::cos(setup.x);
    UTS::pce_type w = std::exp(setup.x);
    UTS::opa_type u_opa = u.getOrthogPolyApprox();
    UTS::opa_type t_opa(setup.basis);
    u += v*w;
    setup.exp->times(t_opa, v.getOrthogPolyApprox(), w.getOrthogPolyApprox());
    setup.exp->plusEqual(u_opa, t_opa);
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",
           u_opa, "u_opa",
           setup.rtol, setup.atol, out);
  }
  TEUCHOS_UNIT_TEST( Stokhos_PCE, saxpy_resize2) {
    UTS::pce_type u = setup.sx;
    UTS::pce_type v = std::cos(setup.x);
    UTS::pce_type w = std::exp(setup.x);
    UTS::opa_type u_opa = u.getOrthogPolyApprox();
    UTS::opa_type t_opa(setup.basis);
    u += v*w;
    setup.exp->times(t_opa, v.getOrthogPolyApprox(), w.getOrthogPolyApprox());
    setup.exp->plusEqual(u_opa, t_opa);
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",
           u_opa, "u_opa",
           setup.rtol, setup.atol, out);
  }
  TEUCHOS_UNIT_TEST( Stokhos_PCE, saxpy_const) {
    UTS::pce_type u = std::sin(setup.x);
    UTS::pce_type w = std::exp(setup.x);
    UTS::opa_type u_opa = u.getOrthogPolyApprox();
    UTS::opa_type t_opa(setup.basis);
    u += setup.a*w;
    setup.exp->times(t_opa, setup.a, w.getOrthogPolyApprox());
    setup.exp->plusEqual(u_opa, t_opa);
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",
           u_opa, "u_opa",
           setup.rtol, setup.atol, out);
  }
  TEUCHOS_UNIT_TEST( Stokhos_PCE, saxpy_const2) {
    UTS::pce_type u = std::sin(setup.x);
    UTS::pce_type w = std::exp(setup.x);
    UTS::opa_type u_opa = u.getOrthogPolyApprox();
    UTS::opa_type t_opa(setup.basis);
    u += setup.cx*w;
    setup.exp->times(t_opa, setup.cx.getOrthogPolyApprox(), 
         w.getOrthogPolyApprox());
    setup.exp->plusEqual(u_opa, t_opa);
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",
           u_opa, "u_opa",
           setup.rtol, setup.atol, out);
  }
  TEUCHOS_UNIT_TEST( Stokhos_PCE, saxpy_short) {
    UTS::pce_type u = std::sin(setup.x);
    UTS::pce_type w = std::exp(setup.x);
    UTS::opa_type u_opa = u.getOrthogPolyApprox();
    UTS::opa_type t_opa(setup.basis);
    u += setup.sx*w;
    setup.exp->times(t_opa, setup.sx.getOrthogPolyApprox(), 
         w.getOrthogPolyApprox());
    setup.exp->plusEqual(u_opa, t_opa);
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",
           u_opa, "u_opa",
           setup.rtol, setup.atol, out);
  }
  TEUCHOS_UNIT_TEST( Stokhos_PCE, saxpy_short_const) {
    UTS::pce_type u = std::sin(setup.x);
    UTS::opa_type u_opa = u.getOrthogPolyApprox();
    UTS::opa_type t_opa(setup.basis);
    u += setup.sx*setup.a;
    setup.exp->times(t_opa, setup.sx.getOrthogPolyApprox(), 
         setup.a);
    setup.exp->plusEqual(u_opa, t_opa);
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",
           u_opa, "u_opa",
           setup.rtol, setup.atol, out);
  }
  TEUCHOS_UNIT_TEST( Stokhos_PCE, saxpy_short_const2) {
    UTS::pce_type u = std::sin(setup.x);
    UTS::opa_type u_opa = u.getOrthogPolyApprox();
    UTS::opa_type t_opa(setup.basis);
    u += setup.sx*setup.cx;
    setup.exp->times(t_opa, setup.sx.getOrthogPolyApprox(), 
         setup.cx.getOrthogPolyApprox());
    setup.exp->plusEqual(u_opa, t_opa);
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",
           u_opa, "u_opa",
           setup.rtol, setup.atol, out);
  }
  TEUCHOS_UNIT_TEST( Stokhos_PCE, saxpy_resize_const) {
    UTS::pce_type u = setup.cx;
    UTS::pce_type w = std::exp(setup.x);
    UTS::opa_type u_opa = u.getOrthogPolyApprox();
    UTS::opa_type t_opa(setup.basis);
    u += setup.a*w;
    setup.exp->times(t_opa, setup.a, w.getOrthogPolyApprox());
    setup.exp->plusEqual(u_opa, t_opa);
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",
           u_opa, "u_opa",
           setup.rtol, setup.atol, out);
  }
  TEUCHOS_UNIT_TEST( Stokhos_PCE, saxpy_resize_const2) {
    UTS::pce_type u = setup.cx;
    UTS::pce_type w = std::exp(setup.x);
    UTS::opa_type u_opa = u.getOrthogPolyApprox();
    UTS::opa_type t_opa(setup.basis);
    u += setup.cx*w;
    setup.exp->times(t_opa, setup.cx.getOrthogPolyApprox(), 
         w.getOrthogPolyApprox());
    setup.exp->plusEqual(u_opa, t_opa);
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",
           u_opa, "u_opa",
           setup.rtol, setup.atol, out);
  }
  TEUCHOS_UNIT_TEST( Stokhos_PCE, saxpy_short_resize_const) {
    UTS::pce_type u = setup.sx;
    UTS::pce_type w = std::exp(setup.x);
    UTS::opa_type u_opa = u.getOrthogPolyApprox();
    UTS::opa_type t_opa(setup.basis);
    u += setup.a*w;
    setup.exp->times(t_opa, setup.a, w.getOrthogPolyApprox());
    setup.exp->plusEqual(u_opa, t_opa);
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",
           u_opa, "u_opa",
           setup.rtol, setup.atol, out);
  }
  TEUCHOS_UNIT_TEST( Stokhos_PCE, saxpy_short_resize_const2) {
    UTS::pce_type u = setup.sx;
    UTS::pce_type w = std::exp(setup.x);
    UTS::opa_type u_opa = u.getOrthogPolyApprox();
    UTS::opa_type t_opa(setup.basis);
    u += setup.cx*w;
    setup.exp->times(t_opa, setup.cx.getOrthogPolyApprox(), 
         w.getOrthogPolyApprox());
    setup.exp->plusEqual(u_opa, t_opa);
    success = Stokhos::comparePCEs(u.getOrthogPolyApprox(), "u",
           u_opa, "u_opa",
           setup.rtol, setup.atol, out);
  }
}