#!/usr/bin/env python

"""

an example of using the multigrid class to solve Laplace's equation.  Here, we
solve

u_xx = cos(x) with u(0) = 0.0 and u(1) = 1.0

"""

from numarray import *
import multigrid

# the analytic solution
def true(x):
    return -cos(x) + x*cos(1.0) + 1.0


# the L2 error norm
def error(imin, imax, dx, r):

    # L2 norm of elements in r, multiplied by dx to
    # normalize
    return sqrt(dx*sum(r[imin:imax+1]**2))

                

# test the multigrid solver
nx = 128

# left and right boundary conditions
lbc = 0.0
rbc = 1.0

a = multigrid.MGfv(nx, lBC = lbc, rBC = rbc, verbose=1)

a.initSolution(zeros(nx, Float64))
a.initRHS(cos(a.x[a.imin:a.imax+1]))

# solve to a relative tolerance of 1.e-10
a.solve(rtol=1.e-10)

v = a.getSolution()


# compute the error compared to the true solution
e = v - true(a.grids[a.nlevels-1].x)
print "L2 error = %g, rel. error from previous cycle = %g, num. cycles = %d" % \
      (error(a.imin,a.imax, a.dx, e), a.error, a.numCycles)