P1673: `symmetric_matrix_vector_product`: bug in implementation

[fnrizzi]

In here the lines starting at 442 :

  if constexpr (std::is_same_v<Triangle, lower_triangle_t>) {
    for (size_type j = 0; j < A.extent(1); ++j) {
      for (size_type i = j; i < A.extent(0); ++i) {
        const auto A_ij = A(i,j);
        y(i) += A_ij * x(j);
        y(j) += A_ij * x(i);
      }
    }
  }
  else {
    for (size_type j = 0; j < A.extent(1); ++j) {
      for (size_type i = 0; i <= j; ++i) {
        const auto A_ij = A(i,j);
        y(i) += A_ij * x(j);
        y(j) += A_ij * x(i);
      }
    }
  }

should be:

  if constexpr (std::is_same_v<Triangle, lower_triangle_t>) {
    for (size_type j = 0; j < A.extent(1); ++j) {
      for (size_type i = j; i < A.extent(0); ++i) {
        const auto A_ij = A(i,j);
        y(i) += A_ij * x(j);
        if(i != j){
          y(j) += A_ij * x(i);
        }
      }
    }
  }
  else {
    for (size_type j = 0; j < A.extent(1); ++j) {
      for (size_type i = 0; i <= j; ++i) {
        const auto A_ij = A(i,j);
        y(i) += A_ij * x(j);
        if(i != j){
          y(j) += A_ij * x(i);
        }
      }
    }
  }

Otherwise we count twice for that element. Note the spec says: For i in the domain of y, the mathematical expression for the algorithm is y[i] = the sum of A[i,j] * x[j] for all j in the triangle of A specified by t, plus the sum of A[j,i] * x[j] for all j not equal to i such that j,i is in the domain of A but not in the triangle of A specified by t.

Most likely also the updating overload has same issue, have not checked that yet.

[iburyl]

@mhoemmen That one should be fixed by my PR