/**
# Poisson solution with a circular refined patch

~~~gnuplot Error as a function of resolution
minlevel = 7
maxlevel = 10

ftitle(a,b) = sprintf("%.0f/x^{%4.2f}", exp(a), -b)
f(x)=a+b*x
fit f(x) '< grep "max error" log' u (log(2**$3)):(log($4)) via a,b
set xlabel 'Maximum resolution'
set ylabel 'Maximum error'
set logscale
set cbrange [1:2]
set xrange [2**(minlevel-1):2**(maxlevel+1)]
set xtics 2**(minlevel-1),2,2**(maxlevel+1)
set grid ytics
plot '< grep "max error" log' u (2**$3):4 t '', exp(f(log(x))) t ftitle(a,b)
~~~~

~~~gnuplot Residual as a function of iterations
reset
set xlabel 'Multigrid iteration'
set ylabel 'Residual'
set logscale y
set grid ytics
plot for [i = minlevel:maxlevel] \
     '< grep "residual '.i.'" log' u 3:4 w lp t 'level '.i
~~~

~~~gnuplot Residual as a function of CPU time
reset
set xlabel 'CPU Time'
set ylabel 'Residual'
set logscale
plot for [i = minlevel:maxlevel] \
     '< grep "speed '.i.'" out' u 4:5 w lp t 'level '.i
~~~

## See also

* [Similar test with Gerris](http://gerris.dalembert.upmc.fr/gerris/tests/tests/poisson.html#circle)
*/

#include "utils.h"
#include "poisson.h"

scalar a[], b[], res[], dp[];

double solution (double x, double y, double z)
{
  return cos(3.*pi*x)*cos(3.*pi*y)*cos(3.*pi*z);
}

void solve (int depth)
{
  /* Dirichlet condition on all boundaries */
  foreach_dimension() {
    a[right] = dirichlet (solution(x, y, z));
    a[left]  = dirichlet (solution(x, y, z));
  }
  /* homogeneous conditions for dp */
  foreach_dimension() {
    dp[right] = dirichlet(0);
    dp[left]  = dirichlet(0);
  }

  size (1. [0]); // space is dimensionless
  origin (-0.5, -0.5, -0.5);
  int nrelax = 4;
  init_grid(1);

  refine (level < depth - 2 || level <= depth*(1. - sqrt(x*x + y*y + z*z)));
  
  foreach() {
    b[] = - 9.*dimension*pi*pi*cos(3.*pi*x)*cos(3.*pi*y)*cos(3.*pi*z);
    a[] = 0.;
  }

  #define NITER 15
  clock_t start = clock(), iter[NITER];
  double maxres[NITER];
  const scalar lambda[] = 0.;
  struct Poisson p;
  p.a = a; p.b = b; p.alpha = unityf; p.lambda = lambda;
  scalar * lres = {res};
  residual ({a}, {b}, lres, &p);
  for (int i = 0; i < NITER; i++) {
    mg_cycle ({a}, lres, {dp}, relax, &p, nrelax, 0, depth());
    residual ({a}, {b}, lres, &p);
    double max = 0.;
    foreach(reduction(max:max))
      if (fabs(res[]) > max)
	max = fabs(res[]);
    iter[i] = clock();
    maxres[i] = max;
  }
  for (int i = 0; i < NITER; i++) {
    fprintf (stderr, "residual %d %d %.1g\n", depth, i, maxres[i]);
    printf ("speed %d %d %g %g\n", depth, i, 
	    (iter[i] - start)/(double)CLOCKS_PER_SEC, maxres[i]);
  }

  double max = 0;
  foreach(reduction(max:max)) {
    double e = a[] - solution(x, y, z);
    if (fabs(e) > max) max = fabs(e);
    //    printf ("%g %g %g %g %g %g\n", x, y, a[], b[], res[], e);
  }
  fprintf (stderr, "max error %d %g\n", depth, max);
}

int main (int argc, char ** argv)
{
#if dimension <= 2
  for (int depth = 7; depth <= 10; depth++)
#else
  for (int depth = 5; depth <= 7; depth++)
#endif
    solve (depth);
}