Introduce new diag function for creating diagonal matrices and for returning the diagonal of a matrix

[marco.guazzone@…]

Introduce a new diag free function in the spirit of the MATLAB's diag function and Mathematica's DiagonalMatrix function.

Basically it allows both the creation of a generalized diagonal matrix and the creation of a diagonal view of an existing matrix.

A generalized k-th diagonal matrix is a special kind of matrix which has all elements set to zero but the ones on its k-th diagonal. The integer k is the offset from the main diagonal, that is:

• k = 0: the elements on the main diagonal can be different from zero.

• k > 0: only the elements on the k-th upper diagonal can be different from zero.

• k < 0: only the elements on the k-th lower diagonal can be different from zero.

A generalized diagonal matrix can be a rectangular matrix.

Here below is a list of the requested cases:

• Create a square diagonal matrix M with vector V

being the k-th diagonal

M = diag(v,k)

• Like the above, but M has layout l (e.g., column major) M = diag(v,k,l)

• Create a rectangular diagonal matrix M of size mXn with vector V being the k-th diagonal M = diag(v,m,n,k)

• Like the above, but M has layout l (e.g., column major) M = diag(v,m,n,k,l)

• Create a diagonal view of the k-th diagonal of matrix M v = diag(M,k)

[marco.guazzone@…]

I've included a possible implementation. In addition to the diag operation, two new types are provided: (1) generalized_diagonal_matrix: a new matrix container representing a generalized diagonal matrix. (2) matrix_diagonal: a new matrix proxy representing the k-th diagonal of a given matrix.