Re: [eigen] Using Matrix in conjunction with Matrix?

Have you considering using the Complex Step method for first order forward automatic differentiation ? Often this is a simple solution and avoids having to program ones own automatic differentiation class. See
```http://blogs.mathworks.com/cleve/2013/10/14/complex-step-differentiation/

On 3/31/2016 8:21 AM, Daniel.Vollmer@xxxxxx wrote:
```
```Hi,

I'm working with the (unsupported) AutoDiff module and I was wondering whether it might be worthwhile to support mixing expressions containing Matrix<AutoDiff<T> > with Matrix<T>, e.g.

typedef Eigen::Matrix<double, 3, 1> Vec;
```
```   Vec bar(Vec::Ones());
foo += bar; // fail: need to use cast, `bar.cast<AD>()` works
foo = bar * AD(0.5); // fail: error: invalid operands to binary expression ('Vec' (aka 'Matrix<double, 3, 1>') and'AD' (aka 'AutoDiffScalar<Matrix<double, 3, 1> >'))
AD v = foo.dot(bar); // fail: error: implicit instantiation of undefined template Eigen::internal::conj_helper<Eigen::AutoDiffScalar<Eigen::Matrix<double, 3, 1, 0, 3, 1> >, double, false, false>'

I can work around this by using `cast<AD>()`, but that is sub-optimal because the derivatives are then known to be zero (and could thus be implemented more efficiently).

Can I just extend the supported expressions to do this without too much trouble? How would I go about this?

As an additional note, in order to stream Matrices containing AD, I had to do the following:

namespace Eigen {
namespace internal {

// so we can print matrices of AutoDiffScalar
template<typename DerType>
struct significant_decimals_impl<AutoDiffScalar<DerType> > : significant_decimals_impl<typename DerType::Scalar> { };

} // end namespace internal
} // end namespace Eigen

Best regards

Daniel Vollmer

--------------------------
Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR)
German Aerospace Center
Institute of Aerodynamics and Flow Technology | Lilienthalplatz 7 | 38108 Braunschweig | Germany

Daniel Vollmer | AS C²A²S²E
www.DLR.de
```
```

```

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