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## D.17 `umf`

Systems of equations described by sparse matrices (i.e., matrices containing mostly zeros) arise in certain practical problems. The usual array representation in which zeros are explicitly stored would be prohibitive for large matrices occurring in many problems of interest. A more sophisticated approach is used by the `umf` library to manage memory efficiently, which is documented at http://www.cise.ufl.edu/research/sparse/SuiteSparse/current/SuiteSparse/UMFPACK/Doc/.

A virtual code interface to functions for solving sparse systems of equations by these methods is afforded by library functions of the form

    library('umf',f)

where the library function name, `f` is a character string of the form `tt_m_rrr`.

- tt can be either `di` for real matrices, or `zi` for complex.
- m can be one of `a`, `t`, or `c` for solving a system given either by a matrix, its transpose, or its conjugate transpose, respectively, corresponding to mnemonics `A`, `Aat` and `At` used in the C language API.
- rrr is either `trp` or `col`, to indicate a sparse matrix expressed either as a list of triples, or in packed column form, as documented below.

The complete set of function names for this library interface is as follows.

    di_a_trp      di_a_col       zi_a_trp       zi_a_col
    di_t_trp      di_t_col       zi_t_trp       zi_t_col
                                 zi_c_trp       zi_c_col

Not all combinations are represented, because the conjugate transpose is relevant only to complex matrices.

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