cleanup

python/demos/totalconvolve_accuracy.py

+import ducc_0_1.totalconvolve as totalconvolve
+import numpy as np
+import ducc_0_1.sht as sht
+import ducc_0_1.misc as misc
+import time
+import matplotlib.pyplot as plt
+
+np.random.seed(48)
+
+def nalm(lmax, mmax):
+    return ((mmax+1)*(mmax+2))//2 + (mmax+1)*(lmax-mmax)
+
+
+def random_alm(lmax, mmax, ncomp):
+    res = np.random.uniform(-1., 1., (nalm(lmax, mmax), ncomp)) \
+     + 1j*np.random.uniform(-1., 1., (nalm(lmax, mmax), ncomp))
+    # make a_lm with m==0 real-valued
+    res[0:lmax+1,:].imag = 0.
+    return res
+
+
+def compress_alm(alm,lmax):
+    res = np.empty(2*len(alm)-lmax-1, dtype=np.float64)
+    res[0:lmax+1] = alm[0:lmax+1].real
+    res[lmax+1::2] = np.sqrt(2)*alm[lmax+1:].real
+    res[lmax+2::2] = np.sqrt(2)*alm[lmax+1:].imag
+    return res
+
+
+def myalmdot(a1,a2,lmax,mmax,spin):
+    return np.vdot(compress_alm(a1,lmax),compress_alm(np.conj(a2),lmax))
+
+
+def convolve(alm1, alm2, lmax):
+    job = sht.sharpjob_d()
+    job.set_triangular_alm_info(lmax, lmax)
+    job.set_gauss_geometry(lmax+1, 2*lmax+1)
+    map = job.alm2map(alm1)*job.alm2map(alm2)
+    job.set_triangular_alm_info(0,0)
+    return job.map2alm(map)[0]*np.sqrt(4*np.pi)
+
+
+lmax=60
+kmax=13
+ncomp=1
+separate=True
+ncomp2 = ncomp if separate else 1
+
+# get random sky a_lm
+# the a_lm arrays follow the same conventions as those in healpy
+slm = random_alm(lmax, lmax, ncomp)
+
+# build beam a_lm
+blm = random_alm(lmax, kmax, ncomp)
+
+
+t0=time.time()
+# build interpolator object for slm and blm
+foo = totalconvolve.PyInterpolator(slm,blm,separate,lmax, kmax, epsilon=1e-4, nthreads=2)
+print("setup time: ",time.time()-t0)
+nth = lmax+1
+nph = 2*lmax+1
+
+
+# compute a convolved map at a fixed psi and compare it to a map convolved
+# "by hand"
+
+ptg = np.zeros((nth,nph,3))
+ptg[:,:,0] = (np.pi*(0.5+np.arange(nth))/nth).reshape((-1,1))
+ptg[:,:,1] = (2*np.pi*(0.5+np.arange(nph))/nph).reshape((1,-1))
+ptg[:,:,2] = np.pi*0.2
+t0=time.time()
+# do the actual interpolation
+bar=foo.interpol(ptg.reshape((-1,3))).reshape((nth,nph,ncomp2))
+print("interpolation time: ", time.time()-t0)
+plt.subplot(2,2,1)
+plt.imshow(bar[:,:,0])
+bar2 = np.zeros((nth,nph))
+blmfull = np.zeros(slm.shape)+0j
+blmfull[0:blm.shape[0],:] = blm
+for ith in range(nth):
+    rbeamth=misc.rotate_alm(blmfull[:,0], lmax, ptg[ith,0,2],ptg[ith,0,0],0)
+    for iph in range(nph):
+        rbeam=misc.rotate_alm(rbeamth, lmax, 0, 0, ptg[ith,iph,1])
+        bar2[ith,iph] = convolve(slm[:,0], rbeam, lmax).real
+plt.subplot(2,2,2)
+plt.imshow(bar2)
+plt.subplot(2,2,3)
+plt.imshow(bar2-bar[:,:,0])
+plt.show()