![\[ (A_r + i*A_i)*(x_r + i*x_i) = (b_r + i*b_i) \]](form_0.png)
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "az_aztec.h"
#include "azk_komplex.h"
Include dependency graph for azk_create_vector.c:
Functions | |
| void | AZK_create_vector_c2k (int *options, double *params, int *proc_config, AZ_MATRIX *Amat_komplex, double *vc, double **vk) |
| Create Komplex vector from Complex vector. | |
| void | AZK_create_vector_g2k (int *options, double *params, int *proc_config, AZ_MATRIX *Amat_komplex, double *vr, double *vi, double **vk) |
| Create Komplex vector from Real and Imaginary Parts. | |
| void | AZK_create_vector_ri2k (int *options, double *params, int *proc_config, AZ_MATRIX *Amat_komplex, double *vr, double *vi, double **vk) |
| Create Komplex vector from Real and Imaginary Parts. | |
KOMPLEX is an add-on module to AZTEC that allows users to solve complex-valued linear systems.
KOMPLEX solves a complex-valued linear system Ax = b by solving an equivalent real-valued system of twice the dimension. Specifically, writing in terms of real and imaginary parts, we have
or by separating into real and imaginary equations we have
![\[ \left( \begin{array}{rr} A_r & -A_i\\ A_i & A_r \end{array} \right) \left( \begin{array}{r} x_r\\ x_i \end{array} \right) = \left( \begin{array}{r} b_r\\ b_i \end{array} \right) \]](form_1.png)
which is a real-valued system of twice the size. If we find xr and xi, we can form the solution to the original system as x = xr +i*xi.
KOMPLEX 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).
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Create Komplex vector from Complex vector. Transforms a complex-valued vector vc to a real vector where vc in Fortran complex format, i.e., if dimension of complex system is N then vc is of length 2*N and the first complex value is stored with the real part in vc[0] and the imaginary part in vc[1] and so on.
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Create Komplex vector from Real and Imaginary Parts. Transforms a complex vector where double precision arrays hold the real and imaginary parts separately.
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Create Komplex vector from Real and Imaginary Parts. Transforms a complex vector where double precision arrays hold the real and imaginary parts separately.
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1.3.9.1