def accuracy_speed_tests(num_nonuniform_points, num_uniform_points, eps): nj, nk = int(num_nonuniform_points), int(num_nonuniform_points) iflag = 1 num_samples = int(np.minimum(20, num_uniform_points * 0.5 + 1)) #for estimating accuracy print( 'Accuracy and speed tests for %d nonuniform points and eps=%g (error estimates use %d samples per run)' % (num_nonuniform_points, eps, num_samples)) # for doing the error estimates Xest = np.zeros(num_samples, dtype=np.complex128) Xtrue = np.zeros(num_samples, dtype=np.complex128) ###### 1-d ms = int(num_uniform_points) xj = np.random.rand(nj) * 2 * math.pi - math.pi cj = np.random.rand(nj) + 1j * np.random.rand(nj) fk = np.zeros([ms], dtype=np.complex128) timer = time.time() ret = finufftpy.nufft1d1(xj, cj, iflag, eps, ms, fk) elapsed = time.time() - timer k = np.arange(-np.floor(ms / 2), np.floor((ms - 1) / 2 + 1)) for ii in np.arange(0, num_samples): Xest[ii] = np.sum(cj * np.exp(1j * k[ii] * xj)) Xtrue[ii] = fk[ii] print_report('finufft1d1', elapsed, Xest, Xtrue, nj) xj = np.random.rand(nj) * 2 * math.pi - math.pi cj = np.zeros([nj], dtype=np.complex128) fk = np.random.rand(ms) + 1j * np.random.rand(ms) timer = time.time() ret = finufftpy.nufft1d2(xj, cj, iflag, eps, fk) elapsed = time.time() - timer k = np.arange(-np.floor(ms / 2), np.floor((ms - 1) / 2 + 1)) for ii in np.arange(0, num_samples): Xest[ii] = np.sum(fk * np.exp(1j * k * xj[ii])) Xtrue[ii] = cj[ii] print_report('finufft1d2', elapsed, Xest, Xtrue, nj) x = np.random.rand(nj) * 2 * math.pi - math.pi c = np.random.rand(nj) + 1j * np.random.rand(nj) s = np.random.rand(nk) * 2 * math.pi - math.pi f = np.zeros([nk], dtype=np.complex128) timer = time.time() ret = finufftpy.nufft1d3(x, c, iflag, eps, s, f) elapsed = time.time() - timer for ii in np.arange(0, num_samples): Xest[ii] = np.sum(c * np.exp(1j * s[ii] * x)) Xtrue[ii] = f[ii] print_report('finufft1d3', elapsed, Xest, Xtrue, nj + nk) ###### 2-d ms = int(np.ceil(np.sqrt(num_uniform_points))) mt = ms xj = np.random.rand(nj) * 2 * math.pi - math.pi yj = np.random.rand(nj) * 2 * math.pi - math.pi cj = np.random.rand(nj) + 1j * np.random.rand(nj) fk = np.zeros([ms, mt], dtype=np.complex128, order='F') timer = time.time() ret = finufftpy.nufft2d1(xj, yj, cj, iflag, eps, ms, mt, fk) elapsed = time.time() - timer Ks, Kt = np.mgrid[-np.floor(ms / 2):np.floor((ms - 1) / 2 + 1), -np.floor(mt / 2):np.floor((mt - 1) / 2 + 1)] for ii in np.arange(0, num_samples): Xest[ii] = np.sum( cj * np.exp(1j * (Ks.ravel()[ii] * xj + Kt.ravel()[ii] * yj))) Xtrue[ii] = fk.ravel()[ii] print_report('finufft2d1', elapsed, Xest, Xtrue, nj) xj = np.random.rand(nj) * 2 * math.pi - math.pi yj = np.random.rand(nj) * 2 * math.pi - math.pi cj = np.zeros([nj], dtype=np.complex128) fk = np.random.rand(ms, mt) + 1j * np.random.rand(ms, mt) timer = time.time() ret = finufftpy.nufft2d2(xj, yj, cj, iflag, eps, fk) elapsed = time.time() - timer Ks, Kt = np.mgrid[-np.floor(ms / 2):np.floor((ms - 1) / 2 + 1), -np.floor(mt / 2):np.floor((mt - 1) / 2 + 1)] for ii in np.arange(0, num_samples): Xest[ii] = np.sum(fk * np.exp(1j * (Ks * xj[ii] + Kt * yj[ii]))) Xtrue[ii] = cj[ii] print_report('finufft2d2', elapsed, Xest, Xtrue, nj) x = np.random.rand(nj) * 2 * math.pi - math.pi y = np.random.rand(nj) * 2 * math.pi - math.pi c = np.random.rand(nj) + 1j * np.random.rand(nj) s = np.random.rand(nk) * 2 * math.pi - math.pi t = np.random.rand(nk) * 2 * math.pi - math.pi f = np.zeros([nk], dtype=np.complex128) timer = time.time() ret = finufftpy.nufft2d3(x, y, c, iflag, eps, s, t, f) elapsed = time.time() - timer for ii in np.arange(0, num_samples): Xest[ii] = np.sum(c * np.exp(1j * (s[ii] * x + t[ii] * y))) Xtrue[ii] = f[ii] print_report('finufft2d3', elapsed, Xest, Xtrue, nj + nk) ###### 3-d ms = int(np.ceil(num_uniform_points**(1.0 / 3))) mt = ms mu = ms xj = np.random.rand(nj) * 2 * math.pi - math.pi yj = np.random.rand(nj) * 2 * math.pi - math.pi zj = np.random.rand(nj) * 2 * math.pi - math.pi cj = np.random.rand(nj) + 1j * np.random.rand(nj) fk = np.zeros([ms, mt, mu], dtype=np.complex128, order='F') timer = time.time() ret = finufftpy.nufft3d1(xj, yj, zj, cj, iflag, eps, ms, mt, mu, fk) elapsed = time.time() - timer Ks, Kt, Ku = np.mgrid[-np.floor(ms / 2):np.floor((ms - 1) / 2 + 1), -np.floor(mt / 2):np.floor((mt - 1) / 2 + 1), -np.floor(mu / 2):np.floor((mu - 1) / 2 + 1)] for ii in np.arange(0, num_samples): Xest[ii] = np.sum(cj * np.exp( 1j * (Ks.ravel()[ii] * xj + Kt.ravel()[ii] * yj + Ku.ravel()[ii] * zj))) Xtrue[ii] = fk.ravel()[ii] print_report('finufft3d1', elapsed, Xest, Xtrue, nj) xj = np.random.rand(nj) * 2 * math.pi - math.pi yj = np.random.rand(nj) * 2 * math.pi - math.pi zj = np.random.rand(nj) * 2 * math.pi - math.pi cj = np.zeros([nj], dtype=np.complex128) fk = np.random.rand(ms, mt, mu) + 1j * np.random.rand(ms, mt, mu) timer = time.time() ret = finufftpy.nufft3d2(xj, yj, zj, cj, iflag, eps, fk) elapsed = time.time() - timer Ks, Kt, Ku = np.mgrid[-np.floor(ms / 2):np.floor((ms - 1) / 2 + 1), -np.floor(mt / 2):np.floor((mt - 1) / 2 + 1), -np.floor(mu / 2):np.floor((mu - 1) / 2 + 1)] for ii in np.arange(0, num_samples): Xest[ii] = np.sum( fk * np.exp(1j * (Ks * xj[ii] + Kt * yj[ii] + Ku * zj[ii]))) Xtrue[ii] = cj[ii] print_report('finufft3d2', elapsed, Xest, Xtrue, nj) x = np.random.rand(nj) * 2 * math.pi - math.pi y = np.random.rand(nj) * 2 * math.pi - math.pi z = np.random.rand(nj) * 2 * math.pi - math.pi c = np.random.rand(nj) + 1j * np.random.rand(nj) s = np.random.rand(nk) * 2 * math.pi - math.pi t = np.random.rand(nk) * 2 * math.pi - math.pi u = np.random.rand(nk) * 2 * math.pi - math.pi f = np.zeros([nk], dtype=np.complex128) timer = time.time() ret = finufftpy.nufft3d3(x, y, z, c, iflag, eps, s, t, u, f) elapsed = time.time() - timer for ii in np.arange(0, num_samples): Xest[ii] = np.sum(c * np.exp(1j * (s[ii] * x + t[ii] * y + u[ii] * z))) Xtrue[ii] = f[ii] print_report('finufft3d3', elapsed, Xest, Xtrue, nj + nk)
def accuracy_speed_tests(num_nonuniform_points,num_uniform_points,eps): nj,nk = int(num_nonuniform_points),int(num_nonuniform_points) iflag=1 num_samples=int(np.minimum(5,num_uniform_points*0.5+1)) # number of outputs used for estimating accuracy; is small for speed print('Accuracy and speed tests for %d nonuniform points and eps=%g (error estimates use %d samples per run)' % (num_nonuniform_points,eps,num_samples)) # for doing the error estimates Xest=np.zeros(num_samples,dtype=np.complex128) Xtrue=np.zeros(num_samples,dtype=np.complex128) ###### 1-d cases ........................................................ ms=int(num_uniform_points) xj=np.random.rand(nj)*2*math.pi-math.pi cj=np.random.rand(nj)+1j*np.random.rand(nj); fk=np.zeros([ms],dtype=np.complex128) timer=time.time() ret=finufftpy.nufft1d1(xj,cj,iflag,eps,ms,fk) elapsed=time.time()-timer k=np.arange(-np.floor(ms/2),np.floor((ms-1)/2+1)) for ii in np.arange(0,num_samples): Xest[ii]=np.sum(cj * np.exp(1j*k[ii]*xj)) Xtrue[ii]=fk[ii] print_report('finufft1d1',elapsed,Xest,Xtrue,nj) xj=np.random.rand(nj)*2*math.pi-math.pi cj=np.zeros([nj],dtype=np.complex128); fk=np.random.rand(ms)+1j*np.random.rand(ms); timer=time.time() ret=finufftpy.nufft1d2(xj,cj,iflag,eps,fk) elapsed=time.time()-timer k=np.arange(-np.floor(ms/2),np.floor((ms-1)/2+1)) for ii in np.arange(0,num_samples): Xest[ii]=np.sum(fk * np.exp(1j*k*xj[ii])) Xtrue[ii]=cj[ii] print_report('finufft1d2',elapsed,Xest,Xtrue,nj) x=np.random.rand(nj)*2*math.pi-math.pi c=np.random.rand(nj)+1j*np.random.rand(nj); s=np.random.rand(nk)*2*math.pi-math.pi f=np.zeros([nk],dtype=np.complex128) timer=time.time() ret=finufftpy.nufft1d3(x,c,iflag,eps,s,f) elapsed=time.time()-timer for ii in np.arange(0,num_samples): Xest[ii]=np.sum(c * np.exp(1j*s[ii]*x)) Xtrue[ii]=f[ii] print_report('finufft1d3',elapsed,Xest,Xtrue,nj+nk) ###### 2-d cases .................................................... ms=int(np.ceil(np.sqrt(num_uniform_points))) mt=ms xj=np.random.rand(nj)*2*math.pi-math.pi yj=np.random.rand(nj)*2*math.pi-math.pi cj=np.random.rand(nj)+1j*np.random.rand(nj) fk=np.zeros([ms,mt],dtype=np.complex128,order='F') timer=time.time() ret=finufftpy.nufft2d1(xj,yj,cj,iflag,eps,ms,mt,fk) elapsed=time.time()-timer Ks,Kt=np.mgrid[-np.floor(ms/2):np.floor((ms-1)/2+1),-np.floor(mt/2):np.floor((mt-1)/2+1)] for ii in np.arange(0,num_samples): Xest[ii]=np.sum(cj * np.exp(1j*(Ks.ravel()[ii]*xj+Kt.ravel()[ii]*yj))) Xtrue[ii]=fk.ravel()[ii] print_report('finufft2d1',elapsed,Xest,Xtrue,nj) ## 2d1many: ndata = 5 # how many vectors to do cj=np.array(np.random.rand(nj,ndata)+1j*np.random.rand(nj,ndata),order='F') fk=np.zeros([ms,mt,ndata],dtype=np.complex128,order='F') timer=time.time() ret=finufftpy.nufft2d1many(xj,yj,cj,iflag,eps,ms,mt,fk) elapsed=time.time()-timer dtest = ndata-1 # which of the ndata to test (in 0,..,ndata-1) for ii in np.arange(0,num_samples): Xest[ii]=np.sum(cj[:,dtest] * np.exp(1j*(Ks.ravel(order='F')[ii]*xj+Kt.ravel(order='F')[ii]*yj))) # note fortran-ravel-order needed throughout - mess. Xtrue[ii]=fk.ravel(order='F')[ii + dtest*ms*mt] # hack the offset in fk array - has to be better way print_report('finufft2d1many',elapsed,Xest,Xtrue,ndata*nj) # 2d2 xj=np.random.rand(nj)*2*math.pi-math.pi yj=np.random.rand(nj)*2*math.pi-math.pi cj=np.zeros([nj],dtype=np.complex128); fk=np.random.rand(ms,mt)+1j*np.random.rand(ms,mt); timer=time.time() ret=finufftpy.nufft2d2(xj,yj,cj,iflag,eps,fk) elapsed=time.time()-timer Ks,Kt=np.mgrid[-np.floor(ms/2):np.floor((ms-1)/2+1),-np.floor(mt/2):np.floor((mt-1)/2+1)] for ii in np.arange(0,num_samples): Xest[ii]=np.sum(fk * np.exp(1j*(Ks*xj[ii]+Kt*yj[ii]))) Xtrue[ii]=cj[ii] print_report('finufft2d2',elapsed,Xest,Xtrue,nj) # 2d2many (using same ndata and dtest as 2d1many; see above) cj=np.zeros([nj,ndata],order='F',dtype=np.complex128); fk=np.array(np.random.rand(ms,mt,ndata)+1j*np.random.rand(ms,mt,ndata),order='F') timer=time.time() ret=finufftpy.nufft2d2many(xj,yj,cj,iflag,eps,fk) elapsed=time.time()-timer for ii in np.arange(0,num_samples): Xest[ii]=np.sum(fk[:,:,dtest] * np.exp(1j*(Ks*xj[ii]+Kt*yj[ii]))) Xtrue[ii]=cj[ii,dtest] print_report('finufft2d2many',elapsed,Xest,Xtrue,ndata*nj) # 2d3 x=np.random.rand(nj)*2*math.pi-math.pi y=np.random.rand(nj)*2*math.pi-math.pi c=np.random.rand(nj)+1j*np.random.rand(nj); s=np.random.rand(nk)*2*math.pi-math.pi t=np.random.rand(nk)*2*math.pi-math.pi f=np.zeros([nk],dtype=np.complex128) timer=time.time() ret=finufftpy.nufft2d3(x,y,c,iflag,eps,s,t,f) elapsed=time.time()-timer for ii in np.arange(0,num_samples): Xest[ii]=np.sum(c * np.exp(1j*(s[ii]*x+t[ii]*y))) Xtrue[ii]=f[ii] print_report('finufft2d3',elapsed,Xest,Xtrue,nj+nk) ###### 3-d cases ............................................................ ms=int(np.ceil(num_uniform_points**(1.0/3))) mt=ms mu=ms xj=np.random.rand(nj)*2*math.pi-math.pi yj=np.random.rand(nj)*2*math.pi-math.pi zj=np.random.rand(nj)*2*math.pi-math.pi cj=np.random.rand(nj)+1j*np.random.rand(nj); fk=np.zeros([ms,mt,mu],dtype=np.complex128,order='F') timer=time.time() ret=finufftpy.nufft3d1(xj,yj,zj,cj,iflag,eps,ms,mt,mu,fk) elapsed=time.time()-timer Ks,Kt,Ku=np.mgrid[-np.floor(ms/2):np.floor((ms-1)/2+1),-np.floor(mt/2):np.floor((mt-1)/2+1),-np.floor(mu/2):np.floor((mu-1)/2+1)] for ii in np.arange(0,num_samples): Xest[ii]=np.sum(cj * np.exp(1j*(Ks.ravel()[ii]*xj+Kt.ravel()[ii]*yj+Ku.ravel()[ii]*zj))) Xtrue[ii]=fk.ravel()[ii] print_report('finufft3d1',elapsed,Xest,Xtrue,nj) xj=np.random.rand(nj)*2*math.pi-math.pi yj=np.random.rand(nj)*2*math.pi-math.pi zj=np.random.rand(nj)*2*math.pi-math.pi cj=np.zeros([nj],dtype=np.complex128); fk=np.random.rand(ms,mt,mu)+1j*np.random.rand(ms,mt,mu); timer=time.time() ret=finufftpy.nufft3d2(xj,yj,zj,cj,iflag,eps,fk) elapsed=time.time()-timer Ks,Kt,Ku=np.mgrid[-np.floor(ms/2):np.floor((ms-1)/2+1),-np.floor(mt/2):np.floor((mt-1)/2+1),-np.floor(mu/2):np.floor((mu-1)/2+1)] for ii in np.arange(0,num_samples): Xest[ii]=np.sum(fk * np.exp(1j*(Ks*xj[ii]+Kt*yj[ii]+Ku*zj[ii]))) Xtrue[ii]=cj[ii] print_report('finufft3d2',elapsed,Xest,Xtrue,nj) x=np.random.rand(nj)*2*math.pi-math.pi y=np.random.rand(nj)*2*math.pi-math.pi z=np.random.rand(nj)*2*math.pi-math.pi c=np.random.rand(nj)+1j*np.random.rand(nj); s=np.random.rand(nk)*2*math.pi-math.pi t=np.random.rand(nk)*2*math.pi-math.pi u=np.random.rand(nk)*2*math.pi-math.pi f=np.zeros([nk],dtype=np.complex128) timer=time.time() ret=finufftpy.nufft3d3(x,y,z,c,iflag,eps,s,t,u,f) elapsed=time.time()-timer for ii in np.arange(0,num_samples): Xest[ii]=np.sum(c * np.exp(1j*(s[ii]*x+t[ii]*y+u[ii]*z))) Xtrue[ii]=f[ii] print_report('finufft3d3',elapsed,Xest,Xtrue,nj+nk)
def EwaldFarVel(self, ptsxyz, forces, nThr): """ This function computes the far field Ewald velocity. Inputs: ptsxyz = the list of points in undeformed, Cartesian coordinates, forces = forces at those points. This function relies entirely on calls to FINUFFT. See the documentation there for more information. """ # Compute the coordinates in the transformed basis pts = self._currentDomain.primecoords(ptsxyz) # Rescale to [-pi,pi] (for FINUFFT) Lens = self._currentDomain.getPeriodicLens() pts = 2 * pi * np.mod(pts, Lens) / Lens - pi # Forcing on the grid (FINUFFT type 1) fi.nufft3d1(pts[:,0],pts[:,1],pts[:,2],forces[:,0],-1,fartol,\ self._nx,self._ny,self._nz,self._fxhat,modeord=1,nThreads=nThr) fi.nufft3d1(pts[:,0],pts[:,1],pts[:,2],forces[:,1],-1,fartol,\ self._nx,self._ny,self._nz,self._fyhat,modeord=1,nThreads=nThr) fi.nufft3d1(pts[:,0],pts[:,1],pts[:,2],forces[:,2],-1,fartol,\ self._nx,self._ny,self._nz,self._fzhat,modeord=1,nThreads=nThr) # Manipulation in Fourier space kxP, kyP, kzP = self._currentDomain.primeWaveNumbersFromUnprimed( self._kx, self._ky, self._kz) k = np.sqrt(kxP * kxP + kyP * kyP + kzP * kzP) # Multiplication factor for the RPY tensor factor = 1.0 / (self._mu * k * k) * np.sinc(k * self._a / pi)**2 factor *= (1 + k * k / (4 * self._xi * self._xi)) * np.exp( -k * k / (4 * self._xi * self._xi)) # splitting function factor[0, 0, 0] = 0 # zero out 0 mode uxhat = factor * self._fxhat uyhat = factor * self._fyhat uzhat = factor * self._fzhat # Project off so we get divergence free uprojx = uxhat - (kxP * uxhat + kyP * uyhat + kzP * uzhat) * kxP / (k * k) uprojx[0, 0, 0] = 0 uprojy = uyhat - (kxP * uxhat + kyP * uyhat + kzP * uzhat) * kyP / (k * k) uprojy[0, 0, 0] = 0 uprojz = uzhat - (kxP * uxhat + kyP * uyhat + kzP * uzhat) * kzP / (k * k) uprojz[0, 0, 0] = 0 # Velocities at the points (FINUFFT type 2) fi.nufft3d2(pts[:, 0], pts[:, 1], pts[:, 2], self._ufarx, 1, fartol, uprojx, modeord=1, nThreads=nThr) fi.nufft3d2(pts[:, 0], pts[:, 1], pts[:, 2], self._ufary, 1, fartol, uprojy, modeord=1, nThreads=nThr) fi.nufft3d2(pts[:, 0], pts[:, 1], pts[:, 2], self._ufarz, 1, fartol, uprojz, modeord=1, nThreads=nThr) vol = self._currentDomain.getVol() return np.concatenate( ([np.real(self._ufarx) / vol], [np.real(self._ufary) / vol], [np.real(self._ufarz) / vol])).T