我们从Python开源项目中，提取了以下11个代码示例，用于说明如何使用numpy.fft.ifftn()。
def run_test_c2c_impl(self, shape, axes, inverse=False, fftshift=False): shape = list(shape) shape[-1] *= 2 # For complex known_data = np.random.normal(size=shape).astype(np.float32).view(np.complex64) idata = bf.ndarray(known_data, space='cuda') odata = bf.empty_like(idata) fft = Fft() fft.init(idata, odata, axes=axes, apply_fftshift=fftshift) fft.execute(idata, odata, inverse) if inverse: if fftshift: known_data = np.fft.ifftshift(known_data, axes=axes) # Note: Numpy applies normalization while CUFFT does not norm = reduce(lambda a, b: a * b, [known_data.shape[d] for d in axes]) known_result = gold_ifftn(known_data, axes=axes) * norm else: known_result = gold_fftn(known_data, axes=axes) if fftshift: known_result = np.fft.fftshift(known_result, axes=axes) x = (np.abs(odata.copy('system') - known_result) / known_result > RTOL).astype(np.int32) a = odata.copy('system') b = known_result compare(odata.copy('system'), known_result)
def correlate(x, y): from numpy import fft sx = numpy.array(x.shape) sy = numpy.array(y.shape) if (sx >= sy).sum(): slices = [slice(None, sx[i] - sy[i] + 1) for i in range(len(sx))] X = fft.fftn(x) Y = fft.fftn(zerofill(y, sx)) else: sf = sx + sy - 1 slices = [slice(None, sf[i]) for i in range(len(sf))] X = fft.fftn(x, sf) Y = fft.fftn(zerofill(y, sf), sf) return fft.ifftn(X.conjugate() * Y)[slices].real
def kfilter(ar, kf, lx=2*pi, ly=2*pi, lz=2*pi): """ Function to filter a 3D array by zeroing out larger k values """ while len(ar.shape) < 3: ar = ar.reshape(ar.shape + (1,)) # COMPUTE THE ARRAY SIZE kx, ky, kz, km = create_kgrid(*ar.shape, lx=lx, ly=ly, lz=lz) # FOURIER TRANSFORM THE ARRAY far = nf.fftshift(nf.fftn(ar)) # SET VALUES ABOVE kf AS 0+0i far = (np.sign(km - kf) - 1.)/(-2.)*far # BACK TRANSFORM TO REAL SPACE arf = np.real(nf.ifftn(nf.ifftshift(far))) return arf #==================================================
def kdiv(arx,ary,arz,kf=None,lx=2*pi,ly=2*pi,lz=2*pi): """ Function to compute divergence in Fourier space """ # COMPUTE THE ARRAY SIZE kx, ky, kz, km = create_kgrid(*np.shape(arx), lx=lx, ly=ly, lz=lz) # FOURIER TRANSFORM THE ARRAY far = [nf.fftshift(nf.fftn(a)) for a in (arx, ary, arz)] # COMPUTE div=i*(kx*ax+ky*ay+kz*az) mg = np.meshgrid(kx,ky,kz) divarf = 1.j*reduce(operator.add, [a*b for a,b in zip(mg, far)]) # SET VALUES ABOVE kf AS 0+0i if kf non zero if kf is not None: divarf = (np.sign(km - kf) - 1.)/(-2.)*divarf divar = np.real(nf.ifftn(nf.ifftshift(divarf))) return divar
def kurl(arx,ary,arz, kf, lx=2*np.pi, ly=2*np.pi, lz=2*np.pi): kx, ky, kz, km = create_kgrid(*arx.shape, lx=lx, ly=ly, lz=lz) # FOURIER TRANSFORM THE ARRAY farx = nf.fftshift(nf.fftn(arx)) fary = nf.fftshift(nf.fftn(ary)) farz = nf.fftshift(nf.fftn(arz)) # SET VALUES ABOVE kf AS 0+0i farx = (np.sign(km - kf) - 1.)/(-2.)*farx fary = (np.sign(km - kf) - 1.)/(-2.)*fary farz = (np.sign(km - kf) - 1.)/(-2.)*farz # COMPUTE VORTICITY axf = eye*(ky*farz-kz*fary) ayf = eye*(kz*farx-kx*farz) azf = eye*(kx*fary-ky*farx) # BACK TRANSFORM TO REAL SPACE wx = np.real(nf.ifftn(nf.ifftshift(axf))) wy = np.real(nf.ifftn(nf.ifftshift(ayf))) wz = np.real(nf.ifftn(nf.ifftshift(azf))) return wx,wy,wz
def convolve(x, f): from numpy import fft, all sx = numpy.array(x.shape) sf = numpy.array(f.shape) if not all(sx >= sf): return convolve(f, x) y = fft.ifftn(fft.fftn(x) * fft.fftn(f, sx)).real slices = [slice(sf[i] - 1, sx[i]) for i in range(len(sf))] return y[slices]
def test_UnscaledFFT_3d(backend, M, N, K, B ): b = backend() # forward x = b.rand_array( (M*N*K, B) ) y = b.rand_array( (M*N*K, B) ) x_h = x.to_host().reshape( (M,N,K,B), order='F' ) A = b.UnscaledFFT( (M,N,K), dtype=x.dtype ) A.eval(y, x) y_exp = np.fft.fftn( x_h, axes=(0,1,2) ) y_act = y.to_host().reshape( (M,N,K,B), order='F' ) npt.assert_allclose(y_act, y_exp, rtol=1e-2) # adjoint x = b.rand_array( (M*N*K, B) ) y = b.rand_array( (M*N*K, B) ) x_h = x.to_host().reshape( (M,N,K,B), order='F' ) A.H.eval(y, x) y_exp = np.fft.ifftn( x_h, axes=(0,1,2) ) * (M*N*K) y_act = y.to_host().reshape( (M,N,K,B), order='F' ) npt.assert_allclose(y_act, y_exp, rtol=1e-2)
def test_UnscaledFFT_2d(backend, M, N, B ): b = backend() # forward x = b.rand_array( (M*N, B) ) y = b.rand_array( (M*N, B) ) x_h = x.to_host().reshape( (M,N,B), order='F' ) A = b.UnscaledFFT( (M,N), dtype=x.dtype ) A.eval(y, x) y_exp = np.fft.fftn( x_h, axes=(0,1) ) y_act = y.to_host().reshape( (M,N,B), order='F' ) npt.assert_allclose(y_act, y_exp, rtol=1e-2) # adjoint x = b.rand_array( (M*N, B) ) y = b.rand_array( (M*N, B) ) x_h = x.to_host().reshape( (M,N,B), order='F' ) A.H.eval(y, x) y_exp = np.fft.ifftn( x_h, axes=(0,1) ) * (M*N) y_act = y.to_host().reshape( (M,N,B), order='F' ) npt.assert_allclose(y_act, y_exp, rtol=1e-2)
def test_UnscaledFFT_1d(backend, M, B ): b = backend() # forward x = b.rand_array( (M, B) ) y = b.rand_array( (M, B) ) x_h = x.to_host().reshape( (M,B), order='F' ) A = b.UnscaledFFT( (M,), dtype=x.dtype ) A.eval(y, x) y_exp = np.fft.fftn( x_h, axes=(0,) ) y_act = y.to_host().reshape( (M,B), order='F' ) npt.assert_allclose(y_act, y_exp, rtol=1e-2) # adjoint x = b.rand_array( (M, B) ) y = b.rand_array( (M, B) ) x_h = x.to_host().reshape( (M,B), order='F' ) A.H.eval(y, x) y_exp = np.fft.ifftn( x_h, axes=(0,) ) * M y_act = y.to_host().reshape( (M,B), order='F' ) npt.assert_allclose(y_act, y_exp, rtol=1e-2)
def test_CenteredFFT(backend, M, N, K, B ): from numpy.fft import fftshift, ifftshift, fftn, ifftn b = backend() A = b.FFTc( (M,N,K), dtype=np.dtype('complex64') ) # forward ax = (0,1,2) x = b.rand_array( (M*N*K,B) ) y = b.rand_array( (M*N*K,B) ) x_h = x.to_host().reshape( (M,N,K,B), order='F' ) A.eval(y, x) y_act = y.to_host().reshape( (M,N,K,B), order='F' ) y_exp = fftshift( fftn( ifftshift(x_h, axes=ax), axes=ax, norm='ortho'), axes=ax) npt.assert_allclose(y_act, y_exp, rtol=1e-2) # adjoint x = b.rand_array( (M*N*K,B) ) y = b.rand_array( (M*N*K,B) ) x_h = x.to_host().reshape( (M,N,K,B), order='F' ) A.H.eval(y, x) y_act = y.to_host().reshape( (M,N,K,B), order='F' ) y_exp = fftshift( ifftn( ifftshift(x_h, axes=ax), axes=ax, norm='ortho'), axes=ax) npt.assert_allclose(y_act, y_exp, rtol=1e-2)
def vecpot(arx,ary,arz, kf, lx=2*np.pi, ly=2*np.pi, lz=2*np.pi): """ Function to compute vector potential of a 3D array """ nx,ny,nz=arx.shape # COMPUTE THE ARRAY SIZE kx, ky, kz, km = create_kgrid(*arx.shape, lx=lx, ly=ly, lz=lz) #kx, ky, kz, k2 = kx[:,nna,nna],ky[nna,:,nna],kz[nna,nna,:], km**2 k2=km**2 k2[nx/2,ny/2,nz/2]=1. # FOURIER TRANSFORM THE ARRAY farx = nf.fftshift(nf.fftn(arx)) fary = nf.fftshift(nf.fftn(ary)) farz = nf.fftshift(nf.fftn(arz)) # SET VALUES ABOVE kf AS 0+0i farx = (np.sign(km - kf) - 1.)/(-2.)*farx fary = (np.sign(km - kf) - 1.)/(-2.)*fary farz = (np.sign(km - kf) - 1.)/(-2.)*farz # FIND THE CORRESPONDING VECTOR POTENTIAL A = -ik x B /k^2 axf = -eye*(ky*farz-kz*fary)/k2 ayf = -eye*(kz*farx-kx*farz)/k2 azf = -eye*(kx*fary-ky*farx)/k2 # BACK TRANSFORM TO REAL SPACE ax = np.real(nf.ifftn(nf.ifftshift(axf))) ay = np.real(nf.ifftn(nf.ifftshift(ayf))) az = np.real(nf.ifftn(nf.ifftshift(azf))) return ax,ay,az
