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/.