def test_legendre_transforms():
nmaps = 2
plan = make_plan(nmaps, nthreads=3)
k = np.arange(1, 3)
for l in range(lmax + 1):
for m in range(l, lmax + 1):
plan.input[lm_to_idx_mmajor(l, m), :] = 10 * k * np.cos(l * 0.1) * np.sqrt(m)
plan.input[1, :] = (5 + 5j) * k
plan.input[2, :] = 34 + 3j
plan.perform_legendre_transform()
work = plan.get_work()
nodes = get_ring_thetas(Nside, positive_only=True)
work0 = np.zeros((lmax + 1, 2, 2 * Nside, nmaps), dtype=np.complex128)
idx = 0
for m in range(lmax + 1):
Lambda = compute_normalized_associated_legendre(m, nodes, lmax,
epsilon=1e-30).T
ncoef = lmax - m + 1
a_l = plan.input[idx:idx + ncoef, :]
idx += ncoef
for odd in range(2):
work0[m, odd, :, :] = np.dot(a_l[odd::2, :].T, Lambda[odd::2, :]).T
assert_almost_equal(work0, work)
if 0:
as_matrix(work[:, 0, :, 0]).plot()
as_matrix(work0[:, 0, :, 0]).plot()
plt.show()
def test_legendre_transforms():
nmaps = 2
plan = make_plan(nmaps, nthreads=3)
k = np.arange(1, 3)
for l in range(lmax + 1):
for m in range(l, lmax + 1):
plan.input[lm_to_idx_mmajor(l, m), :] = 10 * k * np.cos(
l * 0.1) * np.sqrt(m)
plan.input[1, :] = (5 + 5j) * k
plan.input[2, :] = 34 + 3j
plan.perform_legendre_transform()
work = plan.get_work()
nodes = get_ring_thetas(Nside, positive_only=True)
work0 = np.zeros((lmax + 1, 2, 2 * Nside, nmaps), dtype=np.complex128)
idx = 0
for m in range(lmax + 1):
Lambda = compute_normalized_associated_legendre(m,
nodes,
lmax,
epsilon=1e-30).T
ncoef = lmax - m + 1
a_l = plan.input[idx:idx + ncoef, :]
idx += ncoef
for odd in range(2):
work0[m, odd, :, :] = np.dot(a_l[odd::2, :].T, Lambda[odd::2, :]).T
assert_almost_equal(work0, work)
if 0:
as_matrix(work[:, 0, :, 0]).plot()
as_matrix(work0[:, 0, :, 0]).plot()
plt.show()
from wavemoth import *
from wavemoth.healpix import *
from wavemoth.fastsht import *
from cmb import as_matrix
from wavemoth.butterfly import *
from matplotlib import pyplot as plt
from wavemoth.lib import stripify
from concurrent.futures import ProcessPoolExecutor#, ThreadPoolExecutor
from wavemoth.utils import FakeExecutor
from numpy.linalg import norm
def logabs(x): return np.log(np.abs(x))
Nside = 64
lmax = 3 * Nside
nodes = get_ring_thetas(Nside, positive_only=True)
m = 2 * Nside
Lambda = compute_normalized_associated_legendre(m, nodes, lmax).T
stripes = stripify(Lambda)
X = Lambda * 0
for ra, rb, ca, cb in stripes:
X[ra:rb, ca:cb] = 1
as_matrix(X).plot()
print stripes
#as_matrix(np.log10(np.abs(Lambda) + 1e-150)).plot()
B_odd = B[1::2, :] #as_matrix(P[::2, :]).plot() #as_matrix(P[1::2, :]).plot() iden_list1, ipol_list1, A_ip1 = sparse_interpolative_decomposition(B_even, 1e-13) #iden_list2, ipol_list2, A_ip2 = sparse_interpolative_decomposition(B[1::2, :], 1e-13) filter1 = permutations_to_filter(iden_list1, ipol_list1).astype(np.bool) print filter1 #filter1[...] = False S = lssolve(B_even, iden_list1) as_matrix(A_ip1).plot() as_matrix(S).plot() B_k = B_even[:, ~filter1] B_recon = np.dot(B_k, A_ip1) B_other = B[:, filter1] as_matrix(B_other).plot() print np.linalg.norm(B_even[:, filter1] - B_recon) #as_matrix(np.log(np.abs(A_ip1))).plot() #as_matrix(np.log(np.abs(C))).plot() #as_matrix(np.dot(B_odd[:, filter1], S) - B_odd[:, ~filter1]).plot()
from __future__ import division # Stick .. in PYTHONPATH import sys import os sys.path.insert(0, os.path.join(os.path.dirname(__file__), '..')) from wavemoth import * from wavemoth.healpix import * from cmb import as_matrix lmax = 400 Nside = 256 m = 100 nodes = get_ring_thetas(Nside) P = compute_normalized_associated_legendre(m, nodes, lmax) as_matrix(P[:300, :]).plot()
from cmb import as_matrix
from wavemoth.butterfly import *
from matplotlib import pyplot as plt
from wavemoth.lib import stripify
from concurrent.futures import ProcessPoolExecutor #, ThreadPoolExecutor
from wavemoth.utils import FakeExecutor
from numpy.linalg import norm
def logabs(x):
return np.log(np.abs(x))
Nside = 64
lmax = 3 * Nside
nodes = get_ring_thetas(Nside, positive_only=True)
m = 2 * Nside
Lambda = compute_normalized_associated_legendre(m, nodes, lmax).T
stripes = stripify(Lambda)
X = Lambda * 0
for ra, rb, ca, cb in stripes:
X[ra:rb, ca:cb] = 1
as_matrix(X).plot()
print stripes
#as_matrix(np.log10(np.abs(Lambda) + 1e-150)).plot()
from __future__ import division # Stick .. in PYTHONPATH import sys import os sys.path.insert(0, os.path.join(os.path.dirname(__file__), '..')) from wavemoth import * from wavemoth.healpix import * from cmb import as_matrix lmax = 400 Nside = 256 m = 100 nodes = get_ring_thetas(Nside) P = compute_normalized_associated_legendre(m, nodes, lmax) as_matrix(P[:300, :]).plot()
B_odd = B[1::2, :] # as_matrix(P[::2, :]).plot() # as_matrix(P[1::2, :]).plot() iden_list1, ipol_list1, A_ip1 = sparse_interpolative_decomposition(B_even, 1e-13) # iden_list2, ipol_list2, A_ip2 = sparse_interpolative_decomposition(B[1::2, :], 1e-13) filter1 = permutations_to_filter(iden_list1, ipol_list1).astype(np.bool) print filter1 # filter1[...] = False S = lssolve(B_even, iden_list1) as_matrix(A_ip1).plot() as_matrix(S).plot() B_k = B_even[:, ~filter1] B_recon = np.dot(B_k, A_ip1) B_other = B[:, filter1] as_matrix(B_other).plot() print np.linalg.norm(B_even[:, filter1] - B_recon) # as_matrix(np.log(np.abs(A_ip1))).plot() # as_matrix(np.log(np.abs(C))).plot() # as_matrix(np.dot(B_odd[:, filter1], S) - B_odd[:, ~filter1]).plot()