adjointness looks really good except for theta borders

interpol_ng/demo.py

@@ -4,7 +4,7 @@ import pysharp
 import time
 import matplotlib.pyplot as plt
 
-np.random.seed(20)
+np.random.seed(20909)
 
 def nalm(lmax, mmax):
     return ((mmax+1)*(mmax+2))//2 + (mmax+1)*(lmax-mmax)
@@ -27,35 +27,12 @@ def compress_alm(alm,lmax):
 
 def myalmdot(a1,a2,lmax,mmax,spin):
     return np.vdot(compress_alm(a1,lmax),compress_alm(a2,lmax))
-def theta_extend(arr, spin):
-    nth, nph = arr.shape
-    arr2 = np.zeros(((nth-1)*2,nph))
-    arr2[0:nth,:] = arr
-    arr2[nth:,:] = np.roll(arr[nth-2:0:-1,:],nph//2,axis=1)
-    if spin&1:
-        arr2 = -arr2
-    return arr2
-
 def mydot(a1,a2,spin):
     return np.vdot(theta_extend(a1,spin),theta_extend(a2,spin))
 
-def deltabeam(lmax,kmax):
-    beam=np.zeros(nalm(lmax, kmax))+0j
-    for l in range(lmax+1):
-        beam[l] = np.sqrt((2*l+1.)/(4*np.pi))
-    return beam
-
-def convolve(alm1, alm2, lmax):
-    job = pysharp.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=40
+lmax=512
 mmax=lmax
-kmax=10
+kmax=12
 
 
 # get random sky a_lm
@@ -64,41 +41,14 @@ slmT = random_alm(lmax, mmax)
 
 # build beam a_lm
 blmT = random_alm(lmax, kmax)
-
-t0=time.time()
-# build interpolator object for slmT and blmT
+ptg = np.array([[1.2,0.01,1.],[1.4,0.7,2.]])
 foo = interpol_ng.PyInterpolator(slmT,blmT,lmax, kmax, epsilon=1e-6, nthreads=1)
-print("setup time: ",time.time()-t0)
-nth = 2*lmax+1
-nph = 2*mmax+1
-#exit()
-ptg = np.zeros((nth,nph,3))
-ptg[:,:,0] = (np.pi*np.arange(nth)/(nth-1)).reshape((-1,1))
-ptg[:,:,1] = (2*np.pi*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))
-print("interpolation time: ", time.time()-t0)
-plt.subplot(2,2,1)
-plt.imshow(bar.reshape((nth,nph)))
-bar2 = np.zeros((nth,nph))
-blmTfull = np.zeros(slmT.size)+0j
-blmTfull[0:blmT.size] = blmT
-for ith in range(nth):
-    rbeamth=interpol_ng.rotate_alm(blmTfull, lmax, ptg[ith,0,2],ptg[ith,0,0],0)
-    for iph in range(nph):
-        rbeam=interpol_ng.rotate_alm(rbeamth, lmax, 0, 0, ptg[ith,iph,1])
-        bar2[ith,iph] = convolve(slmT, rbeam, lmax).real
-plt.subplot(2,2,2)
-plt.imshow(bar2)
-plt.subplot(2,2,3)
-plt.imshow((bar2-bar.reshape((nth,nph))))
-plt.show()
-
-fake = np.random.uniform(-1.,1., bar.size)
+bar=foo.interpol(ptg)
+print(foo.Nphi(),foo.Nphi0())
+fake = np.random.uniform(0.,1., ptg.shape[0])
 foo2 = interpol_ng.PyInterpolator(lmax, kmax, epsilon=1e-6, nthreads=2)
 foo2.deinterpol(ptg.reshape((-1,3)), fake)
 bla=foo2.getSlm(blmT)
-print(myalmdot(slmT, bla, lmax, lmax, 0))
+print(myalmdot(slmT, np.conj(bla), lmax, lmax, 0))
 print(np.vdot(fake,bar))
+print(myalmdot(slmT, np.conj(bla), lmax, lmax, 0)/np.vdot(fake,bar))

interpol_ng/interpol_ng.cc

@@ -142,6 +142,9 @@ arr.apply([](T &v){v=0.;});
       auto m1 = cube.template subarray<2>({supp,supp,0},{ntheta,nphi,0});
       sharp_alm2map(a1.Alms().data(), m1.vdata(), *ginfo, *ainfo, 0, nthreads);
       correct(m1,0);
+//  for (size_t i=1; i+1<ntheta; ++i)
+//    for (size_t j=0; j<nphi; ++j)
+//      m1.v(i,j)*=2;
       }
       for (size_t k=1; k<=kmax; ++k)
         {
@@ -357,6 +360,11 @@ arr.apply([](T &v){v=0.;});
       {
       auto m1 = cube.template subarray<2>({supp,supp,0},{ntheta,nphi,0});
       decorrect(m1,0);
+   for (size_t j=0; j<nphi0; ++j)
+     {
+     m1.v(0,j)*=0.5;;
+     m1.v(ntheta0-1,j)*=0.5;;
+     }
       sharp_alm2map_adjoint(a1.Alms().vdata(), m1.data(), *ginfo, *ainfo, 0, nthreads);
       for (size_t m=0; m<=lmax; ++m)
         for (size_t l=m; l<=lmax; ++l)
@@ -369,6 +377,16 @@ arr.apply([](T &v){v=0.;});
         auto m2 = cube.template subarray<2>({supp,supp,2*k  },{ntheta,nphi,0});
         decorrect(m1,k);
         decorrect(m2,k);
+   for (size_t j=0; j<nphi0; ++j)
+     {
+     m1.v(0,j)*=0.5;;
+     m1.v(ntheta0-1,j)*=0.5;;
+     }
+   for (size_t j=0; j<nphi0; ++j)
+     {
+     m2.v(0,j)*=0.5;;
+     m2.v(ntheta0-1,j)*=0.5;;
+     }
 
         sharp_alm2map_spin_adjoint(k, a1.Alms().vdata(), a2.Alms().vdata(), m1.data(),
           m2.data(), *ginfo, *ainfo, 0, nthreads);
@@ -379,7 +397,7 @@ arr.apply([](T &v){v=0.;});
               {
               auto tmp = -2.*conj(blmT(l,k))*T(lnorm[l]);
               slmT(l,m) += conj(a1(l,m))*tmp.real();
-              slmT(l,m) += conj(a2(l,m))*tmp.imag();
+              slmT(l,m) -= conj(a2(l,m))*tmp.imag();
               }
             }
         }