def bfio_eval(N, input_sources, input_phase, n_cheby, tree_length):
# some pre-processing
phase = lambda x,p: CONST_PI_SQRT2_J*N*p[0]*input_phase(x,(numpy.cos(CONST_2PI*p[1]),numpy.sin(CONST_2PI*p[1])))
sources = [ (polar(N, (float(j1)-N/2, float(j2)-N/2)), input_sources[j1,j2]) for j1,j2 in range2(N) ]
boxed_sources = {}
for j1,j2 in range2(2**tree_length):
a1,a2,b1,b2 = k_spacing*j1, k_spacing*j2, k_spacing*(j1+1), k_spacing*(j2+1)
leaf=[]
for (source_point, source) in sources:
if a1 <= source_point[0] and source_point[0] < b1 and a2 <= source_point[1] and source_point[1] < b2:
leaf.append( (source_point, source) )
boxed_sources[j1,j2] = leaf
sources = boxed_sources
# preliminaries
unit_cheby_grid_1d = interpolation.chebyshev_grid(n_cheby )*0.5+0.5
unit_cheby_grid_2d = numpy.zeros((n_cheby,n_cheby))
for i,j in range2(n_cheby):
unit_cheby_grid_2d[i,j] = unit_cheby_grid1[i]*unit_cheby_grid2[j]
lagrange_tensor
# initialization
print "initialization"
k_level = tree_length
x_level = log2(N)-tree_length
next_coefficients = {}
for i1,i2 in range2(2**x_level):
next_coefficients[i1,i2] = {}
for j1,j2 in range2(2**k_level):
for i1,i2 in range2(2**x_level):
next_coefficients[i1,i2][j1,j2] = numpy.zeros((n_cheby,n_cheby))
interp_grid1 = (unit_cheby_grid_1d+j1)*2**-k_level
interp_grid2 = (unit_cheby_grid_1d+j2)*2**-k_level
if len(sources[j1,j2])>0:
for i1,i2 in range2(2**x_level):
x_center = ((i1+0.5)*x_spacing, (i2+0.5)*2**-x_level)
for t1,t2 in range2(n_cheby):
interp_point = (interp_grid1[t1], interp_grid2[t2])
value = 0.0j
for (source_point, source) in sources:
prod = interpolation.lagrange_prod(source_point[0], interp_grid1, t1)
prod *= interpolation.lagrange_prod(source_point[1], interp_grid2, t2)
prod *= numpy.exp( phase(x_center, interp_point)-phase_p(x_center, source_point) )
value += prod*source
next_coefficients[i1,i2][j1,j2][t1,t2] = value
coefficients = next_coefficients
k_level -= 1
x_level += 1
#recurrence, first half
print "recurrence first half"
while k_level >= log2(N)/2:
print k_level
next_coefficients = {}
for i1,i2 in range2(2**x_level):
next_coefficients[i1,i2] = {}
for j1,j2 in range2(2**k_level): # looping over index of frequency-boxes
print '\t', j1,j2
cheby_grid1 = (unit_cheby_grid+j1)*k_spacing
cheby_grid2 = (unit_cheby_grid+j2)*k_spacing
for i1,i2 in range2(2**x_level): # looping over index of space-boxes
x_center = ( (0.5+i1)*x_spacing, (0.5+i2)*x_spacing)
points = []
values = []
for c1, c2 in [ (j1*2,j2*2), (j1*2+1,j2*2), (j1*2,j2*2+1), (j1*2+1,j2*2+1) ]: # looping over index of child frequency-boxes
temp = expansion_coefficients_firsthalf(N, phase, x_center, tree[k_level+1][i1/2,i2/2][c1,c2], cheby_grid1, cheby_grid2)
for point, value in temp:
if point in points:
values[points.index(point)] += value
else:
points.append(point)
values.append(value)
tree[k_level][i1,i2][j1,j2] = [ (points[k], values[k]) for k in range(len(points)) ]
k_level -= 1
x_level += 1
print "at middle; switching representation"
switch_representation(N, phase, tree, k_level, n_cheby )
print "recursion second half"
while k_level >= 0:
print k_level
x_level = log2(N)-k_level
x_spacing = 2**-x_level
k_spacing = 2**-k_level
for i1,i2 in range2(2**x_level):
tree[k_level][i1,i2] = {}
for i1,i2 in range2(2**x_level): # looping over index of space-boxes
print '\t', i1,i2
cheby_grid1 = (unit_cheby_grid+i1)*x_spacing
cheby_grid2 = (unit_cheby_grid+i2)*x_spacing
for j1,j2 in range2(2**k_level): # looping over index of frequency-boxes
points = []
values = []
for c1, c2 in [ (j1*2,j2*2), (j1*2+1,j2*2), (j1*2,j2*2+1), (j1*2+1,j2*2+1) ]: # looping over index of child frequency-boxes
k_center = ( (0.5+j1)*k_spacing, (0.5+j2)*k_spacing)
temp = expansion_coefficients_secondhalf(N, phase, k_center, tree[k_level+1][i1/2,i2/2][c1,c2], cheby_grid1, cheby_grid2)
for point, value in temp:
if point in points:
values[points.index(point)] += value
else:
points.append(point)
values.append(value)
tree[k_level][i1,i2][j1,j2] = [ (points[k], values[k]) for k in range(len(points)) ]
k_level -= 1
print "termination"
for i1,i2 in range2(N):
x_level = log2(N)-tree_length
next_coefficients = expansion_coefficients(k_level)
for j1,j2 in range2(2**k_level):
for i1,i2 in range2(2**x_level):
interp_grid1 = (unit_cheby_grid+j1)*2**-k_level
interp_grid2 = (unit_cheby_grid+j2)*2**-k_level
if len(sources[j1,j2]) > 0:
for i1,i2 in range2(2**x_level):
x_center = ((i1+0.5)*2**-x_level, (i2+0.5)*2**-x_level)
for t1,t2 in range2(n_cheby):
interp_point = (interp_grid1[t1], interp_grid2[t2])
value = 0
for (source_point, source) in sources[j1,j2]:
prod = interpolation.lagrange_prod(source_point[0], interp_grid1, t1)
prod *= interpolation.lagrange_prod(source_point[1], interp_grid2, t2)
prod *= numpy.exp( +phase(x_center, source_point))
value += prod*source
next_coefficients[i1,i2][j1,j2][t1,t2] = value*numpy.exp( -phase(x_center, interp_point))
coefficients = next_coefficients
k_level -= 1
x_level += 1
#recurrence, first half
print "recurrence first half"
while k_level >= log2(N)/2:
print k_level
next_coefficients = expansion_coefficients(k_level)
