#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "az_aztec.h"
#include "azk_komplex.h"
Include dependency graph for azk_permute_ri.c:
KOMPLEX is an add-on module to AZTEC that allows users to solve complex-valued linear systems. accept user linear systems in three forms with either global or local index values.
1) The first form is true complex. The user passes in an MSR or VBR format matrix where the values are stored like Fortran complex numbers. Thus, the values array is of type double that is twice as long as the number of complex values. Each complex entry is stored with real part followed by imaginary part (as in Fortran).
2) The second form stores real and imaginary parts separately, but the pattern for each is identical. Thus only the values of the imaginary part are passed to the creation routines.
3) The third form accepts two real-valued matrices with no assumption about the structure of the matrices. Each matrix is multiplied by a user-supplied complex constant. This is the most general form.
Each of the above forms supports a global or local index set. By this we mean that the index values (stored in bindx) refer to the global problem indices, or the local indices (for example after calling AZ_transform).
Permute a Komplex system for better numerical stability.
An alternative to the standard Komplex formulation is to permute the block rows so that the imaginary part is on the main diagonal. For example:
This action may be desirable, or necessary in situations where the real part has small or zero diagonal entries. This routine looks at each real/imaginary pair and, based on a heuristic may swap the real and imaginary parts. This action does not affect the sparsity pattern, but only the mapping from the complex (or real/imaginary) mapping to the komplex mapping, and back.