Class template Dune::XT::Functions::DerivativeRangeTypeSelector¶
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template<size_t d, class R, size_t r, size_t rC>
class Dune::XT::Functions::DerivativeRangeTypeSelector¶ Since one is often interested in the derivatives of the individual functions u_s (see RangeTypeSelector), it makes sense to consider the jacobian u: R^d -> R^{r x {rC x d}} as a vector of the jacobians of the u_s (for s = 1, …, r) in the sense of
u.jacobian(x)[s];
jacobian u = (jacobian u_1, …, jacobian u_r)
where
| (d u_s_1 / d x_1)(x), (d u_s_1 / d x_2)(x), …, (d u_s_1 / d x_d)(x) | | (d u_s_2 / d x_1)(x), . … . | jacobian u_s(x) = | . . … . | | . . … . | | (d u_s_rC / d x_1)(x), (d u_s_rC / d x_2)(x), …, (d u_s_rC / d x_d)(x) |
for s = 1, …, r. Again, (d u_s_i / d x_j)(x) can be interpreted as the evaluation of a scalar function (jacobian u)_s_i_j: R^d -> R, and we can thus identify
(jacobian u)s = ( d u_s_i / d x_j ){i = 1, …, rC | j = 1, …, d}
This interpretation of the jacobian of u is modeled by DerivativeRangeTypeSelector, with a special case if rC = 1, to simplify manners. To access the jacobian of u_s, simply use
In addition, one is sometimes interested in evaluating the jacobian of the scalar function u_s_i (see RangeTypeSelector), jacobian u_s_i: R^d -> R^d. This is modeled by the single_type.
See also:
RangeTypeSelector
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static void Dune::XT::Functions::DerivativeRangeTypeSelector::ensure_size(int &arg)¶
No documentation provided.
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static void Dune::XT::Functions::DerivativeRangeTypeSelector::convert(const type &in, int &out)¶
No documentation provided.
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type Dune::XT::Functions::DerivativeRangeTypeSelector::single_type¶
No documentation provided.
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type Dune::XT::Functions::DerivativeRangeTypeSelector::return_single_type¶
No documentation provided.
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type Dune::XT::Functions::DerivativeRangeTypeSelector::row_derivative_type¶
No documentation provided.
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type Dune::XT::Functions::DerivativeRangeTypeSelector::row_derivative_return_type¶
No documentation provided.
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type Dune::XT::Functions::DerivativeRangeTypeSelector::type¶
No documentation provided.
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type Dune::XT::Functions::DerivativeRangeTypeSelector::return_type¶
No documentation provided.