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## Coding chains and arrays

With a collection of operators, we can build more elaborate operators. One method is chaining. For example, the operator product is represented in the subroutine chain2( op1, op2, ...). Likewise the operator product is represented in the in the subroutine chain3( op1, op2, op3,...).

Another amazing thing about matrices is that their elements may themselves be matrices. A very common example is a row matrix containing two elements, each element itself a matrix. This is done by subroutine row also in module chain.

api/c/chain.c
 ```void sf_chain( sf_operator oper1 /* outer operator */, sf_operator oper2 /* inner operator */, bool adj /* adjoint flag */, bool add /* addition flag */, int nm /* model size */, int nd /* data size */, int nt /* intermediate size */, /*@out@*/ float* mod /* [nm] model */, /*@out@*/ float* dat /* [nd] data */, float* tmp /* [nt] intermediate */) /*< Chains two operators, computing oper1{oper2{mod}} or its adjoint. The tmp array is used for temporary storage. >*/ { if (adj) { oper1 (true, false, nt, nd, tmp, dat); oper2 (true, add, nm, nt, mod, tmp); } else { oper2 (false, false, nm, nt, mod, tmp); oper1 (false, add, nt, nd, tmp, dat); } } ```
api/c/chain.c
 ```void sf_array( sf_operator oper1 /* top operator */, sf_operator oper2 /* bottom operator */, bool adj /* adjoint flag */, bool add /* addition flag */, int nm /* model size */, int nd1 /* top data size */, int nd2 /* bottom data size */, /*@out@*/ float* mod /* [nm] model */, /*@out@*/ float* dat1 /* [nd1] top data */, /*@out@*/ float* dat2 /* [nd2] bottom data */) /*< Constructs an array of two operators, computing {oper1{mod},oper2{mod}} or its adjoint. >*/ { if (adj) { oper1 (true, add, nm, nd1, mod, dat1); oper2 (true, true, nm, nd2, mod, dat2); } else { oper1 (false, add, nm, nd1, mod, dat1); oper2 (false, add, nm, nd2, mod, dat2); } } ```