# sub-vectors and sub-matrices¶

It is possible to obtain any sub-vector or sub-matrix of a fully interfaced object. There are four types of sub indices:

gmm::sub_interval(first, length);


represents an interval whose first index is first and length is length ( for instance gmm::sub_interval(10, 3); represents the indices {10, 11, 12}).

gmm::sub_slice(first, length, step);


represents also an interval in which one index over step is taken. ( for instance gmm::sub_slice(10, 3, 2); represents the indices {10, 12, 14})

gmm::sub_index(CONT c);


represents the sub-index which is the collection of index contained in the container c. For instance:

std::vector<size_t> c(3);
c[0] = 1; c[1] = 3; c[2] = 16;
gmm::sub_index(c);


represents the indices {1, 3, 16}.

VERY IMPORTANT : the container c has to be sorted from the smaller index to the greater one (i.e. with increasing order) and no repetition is allowed.

For unsorted index such as permutation, a special type of sub index is defined:

gmm::unsorted_sub_index(CONT c);


Some algorithms are a little bit slower with unsorted sub indices.

Now gmm::sub_vector(V, subi) gives a reference to a sub-vector:

gmm::vsvector<double> V(10);
V[5] = 3.0;
std::cout << gmm::sub_vector(V, gmm::sub_interval(2, 3)) << std::endl;


prints to the standard output V[2], V[3] and V[4].

gmm::sub_matrix(V, subi1, subi2) gives a reference to a sub-matrix. For instance:

gmm::col_matrix< gmm::wsvector<double> > M(5, 20);
M(3, 2) = 5.0;
std::cout << gmm::sub_matrix(M, gmm::sub_interval(2, 3), gmm::sub_interval(2, 3))
<< std::endl;


prints to the output a sub-matrix. If the two sub-indices are equal, it is possible to omit the second. For instance:

gmm::col_matrix< gmm::wsvector<double> > M(5, 20);
M(3, 2) = 5.0;
std::cout << gmm::sub_matrix(V, gmm::sub_interval(2, 3)) << std::endl;


The reference on sub_matrix is writable if the corresponding matrix is writable (so you can copy on a sub_matrix, add sub-matrices …).

## row and column of a matrix¶

gmm::mat_row(M, i) gives a (possibly writable) reference to the row i of matrix M, and gmm::mat_col(M, i) gives a (possibly writable) reference to the column i. It is not possible to access to the rows if M is a column matrix and to the columns if it is a row matrix. It is possible to use gmm::mat_const_row(M, i) and gmm::mat_const_col(M, i) to have constant references.