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#ifdef HAVE_STDLIB_H
#include <stdlib.h>
#endif
#include <stdio.h>
#include <memory.h>
#include <errno.h>
#include "yagi.h"
#define MAX_NON_ITERATIVE 100000
void solve_equations(double frequency, int driven, int parasitic, double **driven_data, double **parasitic_data, double *v, double **z, double *pin, struct FCOMPLEX *voltage, struct FCOMPLEX *current, struct FCOMPLEX *input_impedance, struct element_data *coordinates, double **A, double *b, int *indx)
{
int elements, element_number, i, j;
double d, **A_pre_LUdcmp, *b_copy, t1, t2;
elements=driven+parasitic;
fill_z_matrix(frequency,driven,parasitic,driven_data,parasitic_data, z);
/* Now we must fill the V vector, which gives the voltage at the centre of
each driven element. Since we know the magnitude of the voltage and phase,
we can calculate the real and imaginary components of voltage. NB */
fill_v_vector(driven, parasitic, driven_data, v);
/* We now have the voltage vector V, and the impedance matrix Z. All
we need to do now is solve a set of NxN equations, where N is the
number of elements, to get N values of current, which we can put in
the I matrix.
Unfortunately, this is not trivual, by any standards!!! It is
complicated by the fact the the N equations are all complex.
The method used us a brute-force approach mentioned by Press
in their 2nd Edition of the Numerical Recipes in C book. Here we
put the data in the form:
|Zr -Zi| |Ir| = |Vr| which we will call A.x=b
|Zi Zr| |Ii| |Vi|
so the Z data goes now in a 2Nx2N matrix. This is a bit wasteful of space
and time, but it will do here. */
/* Copy impedance data from 'z' to matrix A */
copy_complex_data_to_real_matrix(elements,z,A);
/* The following function prints to stantard output the z matrix of the
antenna. It is really only used during debugging, so it can be commented
out normally. */
/* print_z_matrix(frequency,elements,z); */
/* read voltage data from v into b */
for(i=1;i<=elements;++i)
{
b[i]= v[2*i-1]; /* real data */
b[i+elements]=v[2*i]; /* imaginary data */
voltage[i].r=v[2*i-1];
voltage[i].i=v[2*i];
}
/* If there are a lot of elements, its possible that rounding errors
will destroy the accuracy of the results. If there are more than
MAX_NON_ITERATIVE elements, we do the usual LU decompositioon and
back-substitution, then do an iterative improvement of the
solution */
if(elements > MAX_NON_ITERATIVE)
{
A_pre_LUdcmp=dmatrix(1L, 2L*(long)elements, 1L, 2L*(long) elements);
b_copy=dvector(1L, 2L*(long)elements);
/* I had troubled using memcpy to copy matrices - probably becuase
they are offset by 1 */
copy_matrix(2*elements, 2*elements, A_pre_LUdcmp, A);
/* copy vector b */
for(j=1;j<=2*elements;++j)
b_copy[j]=b[j];
}
/* Perform a LU decompositon of A */
ludcmp(A, elements*2, indx, &d);
/* We now have the voltages in b. After lubksb is run, we get the
currents in b . A contains an LU decomposed version of the original A*/
lubksb(A, 2*elements, indx, b); /* current's in b after lubksb has run*/
if(elements>MAX_NON_ITERATIVE)
{
t1=b[1];
mprove(A_pre_LUdcmp, A, 2*elements, indx, b_copy, v);
free_dmatrix(A_pre_LUdcmp,1L, 2L*(long)elements, 1L, 2L*(long) elements);
/* free_dvector(bcopy,1L,2L*elements); */
t2=b[1];
if(t1!=t2)
{
printf("b[1]'s differ before and after mprove: before = %.16f after =%.16f\n", t1, t2);
exit(1);
}
}
/* Put currents an FCOMPLEX matrix current[element]
currents are stored in b as r,r,r,r ..... i,i,i,i */
for(element_number=1;element_number<=elements;element_number++)
{
current[element_number].r=b[element_number];
current[element_number].i=b[element_number+elements];
}
z_input(voltage[1], current[1], input_impedance);
*pin=calculate_power_input(input_impedance->r,current[1]); /* in Watts */
/* Sometimes the input power goes < 0. I'm not sure why this occurs, but
the implication is that the antenna is a source of energy, which is silly.
The gain is negative then (not in dB), so taking the log to put in dB
would cause a numerical error. When this occurs, we print a message to
stderr, then write the data in a file "problem". The user may then
investigate what went wrong. */
if(*pin <= 0.0)
{
/* fprintf(stderr,"Input power less than 0! Undesirable, but non-fatal error.\n"); */
*pin=1e20; /* Force it to a large value */
/* do_since_better(0,"problem","problem",*input_impedance, \
rubbish,flag, "This causes Pin < 0.0 - findout why!",frequency, frequency, \
frequency,frequency/10.0, elements, driven, parasitic, \
180.0, driven_data, parasitic_data, 1.0, 0.0); */
}
for(i=1;i<=driven;++i)
{
coordinates[i].x=driven_data[i][X];
coordinates[i].y=driven_data[i][Y];
coordinates[i].length=driven_data[i][LENGTH];
}
for(i=driven+1;i<=elements;++i)
{
coordinates[i].x=parasitic_data[i-driven][X];
coordinates[i].y=parasitic_data[i-driven][Y];
coordinates[i].length=parasitic_data[i-driven][LENGTH];
}
#ifdef DEBUG
if(errno)
{
fprintf(stderr,"Errno =%d in solve.c\n", errno);
exit(1);
}
#endif
}
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