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### D.17.1 `umf` input parameters

For a square matrix A and a column vector b, the `umf` functions find the solution x to the matrix equation M x = b, where M is either A, the transpose of A, or its conjugate transpose. As noted above, the choice is determined by whether the the function name is of the form *`_a_`*, *`_t_`*, or *`_c_`* respectively.

The argument to any of these functions is a pair `(A,b)`, where A represents the matrix mentioned above and b represents the column vector.

The parameter b is required to be a list of numbers whose length matches the number of rows in the matrix. The numbers are either real numbers for the `di_`* functions (`math`), or complex for the `zi_`* functions (`complex`).

There is a choice of representations for the parameter A, depending on whether the function being called is one of the *`_trp` functions or one of the *`_col` functions.

For the *`_trp` functions, A is represented as a non-empty list of triples `<((i,j),v)...>`, where each item of the list corresponds to a non-zero entry in the matrix.

- The parameters i and j are natural numbers as in Representation of Numeric and Textual Data.
- The value v is a real number for the `di_`*`_trp` functions or a complex number for the `zi_`*`_trp` functions.
- The presence of a triple ((i,j),v) in the list signifies that the i,j-th entry in the matrix A (numbered from zero) has a value of v.

For the *`_col` functions, the representation of A is more complicated but has a slight advantage in memory usage. It may also have an advantage in speed unless more time is wasted on the virtual side transforming a matrix to this representation than it saves.

In this case, A is represented by a triple of the form `((p,i),v)`. The parameters p and i are lists of natural numbers. The parameter v is a list of real numbers for the `di_`*`_col` functions and complex numbers for the `zi_`*`_col` functions. They have the following interpretations.

- v is the list of non-zero entries in the matrix in column major order.
- i has the same length as v, and each item of i is the row index of the corresponding item in v, numbered from zero.
- p has the length of the number of columns in the matrix, and each item identifies the starting position of a column in v and i, numbered from zero.

The first item of p is always zero. Further explanation of this format in terms of an array representation can be found in the file ‘`UMFPACK_UserGuide.pdf`’, available from the `umf` library home page at http://www.cise.ufl.edu/research/sparse/SuiteSparse/current/SuiteSparse/.

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