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The Eigen library can map existing memory into Eigen matrices.

float array[3];
Map<Vector3f>(array, 3).fill(10);
int data[4] = 1, 2, 3, 4;
Matrix2i mat2x2(data);
MatrixXi mat2x2 = Map<Matrix2i>(data);
MatrixXi mat2x2 = Map<MatrixXi>(data, 2, 2);

My question is, how can we get c array (e.g. float[] a) from eigen matrix (e.g. Matrix3f m)? What it the real layout of eigen matrix? Is the real data stored as in normal c array?

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You can use the data() member function of the Eigen Matrix class. The layout by default is column-major, not row-major as a multidimensional C array (the layout can be chosen when creating a Matrix object). For sparse matrices the preceding sentence obviously doesn't apply.

Example:

ArrayXf v = ArrayXf::LinSpaced(11, 0.f, 10.f);
// vc is the corresponding C array. Here's how you can use it yourself:
float *vc = v.data();
cout << vc[3] << endl;  // 3.0
// Or you can give it to some C api call that takes a C array:
some_c_api_call(vc, v.size());
// Be careful not to use this pointer after v goes out of scope! If
// you still need the data after this point, you must copy vc. This can
// be done using in the usual C manner, or with Eigen's Map<> class.

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