azk_create_linsys.c File Reference

Creation routines for building Komplex systems. More...

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "az_aztec.h"
#include "azk_komplex.h"

Include dependency graph for azk_create_linsys.c:


Functions

void AZK_create_linsys_c2k (double *xc, double *bc, int *options, double *params, int *proc_config, AZ_MATRIX *Amat_complex, double **x, double **b, AZ_MATRIX **Amat_komplex)
 Create Komplex System from Complex System.
void AZK_create_linsys_g2k (double *xr, double *xi, double *br, double *bi, int *options, double *params, int *proc_config, double c0r, double c0i, AZ_MATRIX *Amat_mat0, double c1r, double c1i, AZ_MATRIX *Amat_mat1, double **x, double **b, AZ_MATRIX **Amat_komplex)
 Create Komplex System from General System.
void AZK_create_linsys_ri2k (double *xr, double *xi, double *br, double *bi, int *options, double *params, int *proc_config, AZ_MATRIX *Amat_real, double *val_imag, double **x, double **b, AZ_MATRIX **Amat_komplex)
 Create Komplex System from Real and Imaginary Parts.

Detailed Description

Creation routines for building Komplex systems.

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

\[ (A_r + i*A_i)*(x_r + i*x_i) = (b_r + i*b_i) \]

or by separating into real and imaginary equations we have

\[ \left( \begin{array}{rr} A_r & -A_i\\ A_i & A_r \end{array} \right) \left( \begin{array}{r} x_r\\ x_i \end{array} \right) = \left( \begin{array}{r} b_r\\ b_i \end{array} \right) \]

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).


Function Documentation

void AZK_create_linsys_c2k ( double *  xc,
double *  bc,
int *  options,
double *  params,
int *  proc_config,
AZ_MATRIX *  Amat_complex,
double **  x,
double **  b,
AZ_MATRIX **  Amat_komplex 
)

Create Komplex System from Complex System.

Transforms a complex-valued system

Amat_complex * xc = bc

where double precision arrays hold the complex values of Amat_complex, xc and bc in Fortran complex format, i.e., if dimension of complex system is N then xc is of length 2*N and the first complex value is stored with the real part in xc[0] and the imaginary part in xc[1] and so on.

Parameters:
xc (In) Contains the complex initial guess/solution vector with the real/imag parts interleaved as in Fortran complex format.
bc (In) RHS in Fortran complex format.
options (In) Determines specific solution method and other parameters.
params (In) Drop tolerance and convergence tolerance info.
proc_config (In) Machine configuration. proc_config[AZ_node] is the node number. proc_config[AZ_N_procs] is the number of processors.
Amat_complex (In) An AZ_MATRIX structure where Amat_complex->val contain the values of the complex matrix in Fortran complex format.
x (Out) Komplex version of initial guess and solution.
b (Out) Komplex version of RHS.
Amat_komplex (Out) Komplex version of matrix stored as an AZ_MATRIX structure.

void AZK_create_linsys_g2k ( double *  xr,
double *  xi,
double *  br,
double *  bi,
int *  options,
double *  params,
int *  proc_config,
double  c0r,
double  c0i,
AZ_MATRIX *  Amat_mat0,
double  c1r,
double  c1i,
AZ_MATRIX *  Amat_mat1,
double **  x,
double **  b,
AZ_MATRIX **  Amat_komplex 
)

Create Komplex System from General System.

Transforms a complex-valued system

(c0r+i*c0i)*A0 +(c1r+i*c1i)*A1) * (xr+i*xi) = (br+i*bi)

to a Komplex system.

Parameters:
xr (In) Real part of initial guess.
xi (In) Imaginary part of initial guess.
br (In) Real part of right hand side of linear system.
bi (In) Imaginary part of right hand side of linear system.
options (In) Determines specific solution method and other parameters.
params (In) Drop tolerance and convergence tolerance info.
proc_config (In) Machine configuration. proc_config[AZ_node] is the node number. proc_config[AZ_N_procs] is the number of processors.
c0r (In) Real part of constant to be multiplied with first matrix.
c0i (In) Imaginary part of constant to be multiplied with first matrix.
c1r (In) Real part of constant to be multiplied with second matrix.
c1i (In) Imaginary part of constant to be multiplied with second matrix.
Amat_mat0 (In) AZ_MATRIX object containing first real-valued matrix.
Amat_mat1 (In) AZ_MATRIX object containing second real-valued matrix.
x (Out) Komplex version of initial guess and solution.
b (Out) Komplex version of RHS.
Amat_komplex (Out) Komplex version of matrix stored as an AZ_MATRIX structure.

void AZK_create_linsys_ri2k ( double *  xr,
double *  xi,
double *  br,
double *  bi,
int *  options,
double *  params,
int *  proc_config,
AZ_MATRIX *  Amat_real,
double *  val_imag,
double **  x,
double **  b,
AZ_MATRIX **  Amat_komplex 
)

Create Komplex System from Real and Imaginary Parts.

Transforms a complex-valued system

(Ar +i*Ai) * (xr + i*xi) = (br + i*bi)

where double precision arrays hold the real and imaginary parts separately. The pattern of the imaginary part matches the real part. Thus no structure for the imaginary part is passed in.

Parameters:
xr (In) Real part of initial guess.
xi (In) Imaginary part of initial guess.
br (In) Real part of right hand side of linear system.
bi (In) Imaginary part of right hand side of linear system.
options (In) Determines specific solution method and other parameters.
params (In) Drop tolerance and convergence tolerance info.
proc_config (In) Machine configuration. proc_config[AZ_node] is the node number. proc_config[AZ_N_procs] is the number of processors.
Amat_real (In) AZ_MATRIX object containing real matrix.
val_imag (In) Double arrya containing the values ONLY for imaginary matrix.
x (Out) Komplex version of initial guess and solution.
b (Out) Komplex version of RHS.
Amat_komplex (Out) Komplex version of matrix stored as an AZ_MATRIX structure.


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