optional pyfftw import for simulation.fractal.py (#1191)

* Fallback to `scipy.fft` if `pyfftw` is not available

* Multi-threading fft2 with scipy

src/mintpy/simulation/fractal.py

@@ -19,16 +19,27 @@
 import matplotlib.pyplot as plt
 import numpy as np
 
+NUM_THREADS = min(os.cpu_count(), 4)
+
 try:
     import pyfftw
+    from pyfftw.interfaces.numpy_fft import fft2, fftshift, ifft2
+
+    # speedup pyfftw
+    print(f'using {NUM_THREADS} threads for fft computation with pyfftw.')
+    pyfftw.config.NUM_THREADS = NUM_THREADS
 except ImportError:
-    raise ImportError('Cannot import pyfftw!')
+    import functools
+    import warnings
 
+    import scipy
+    from scipy.fft import fftshift
 
-# speedup pyfftw
-NUM_THREADS = min(os.cpu_count(), 4)
-print(f'using {NUM_THREADS} threads for pyfftw computation.')
-pyfftw.config.NUM_THREADS = NUM_THREADS
+    warnings.warn('Cannot import pyfftw, fallback to scipy.fft.')
+
+    fft2 = functools.partial(scipy.fft.fft2, workers=NUM_THREADS)
+    ifft2 = functools.partial(scipy.ifft2, workers=NUM_THREADS)
+    print(f'using {NUM_THREADS} threads for fft computation with scipy.')
 
 
 def fractal_surface_atmos(shape=(128, 128), resolution=60., p0=1., freq0=1e-3,
@@ -67,8 +78,8 @@ def fractal_surface_atmos(shape=(128, 128), resolution=60., p0=1., freq0=1e-3,
 
     # simulate a uniform random signal
     h = np.random.rand(length, width)
-    H = pyfftw.interfaces.numpy_fft.fft2(h)
-    H = pyfftw.interfaces.numpy_fft.fftshift(H)
+    H = fft2(h)
+    H = fftshift(H)
 
     # scale the spectrum with the power law
     yy, xx = np.mgrid[0:length-1:length*1j,
@@ -120,7 +131,7 @@ def fractal_surface_atmos(shape=(128, 128), resolution=60., p0=1., freq0=1e-3,
 
     # get the fractal spectrum and transform to spatial domain
     Hfrac = np.divide(H, fraction)
-    fsurf = pyfftw.interfaces.numpy_fft.ifft2(Hfrac)
+    fsurf = ifft2(Hfrac)
     fsurf = np.abs(fsurf).astype(np.float32)
     fsurf -= np.mean(fsurf)
 
@@ -129,7 +140,7 @@ def fractal_surface_atmos(shape=(128, 128), resolution=60., p0=1., freq0=1e-3,
 
     # scale the spectrum to match the input power spectral density.
     Hfrac *= np.sqrt(p0/p1)
-    fsurf = pyfftw.interfaces.numpy_fft.ifft2(Hfrac)
+    fsurf = ifft2(Hfrac)
     fsurf = np.abs(fsurf).astype(np.float32)
     fsurf -= np.mean(fsurf)
     return fsurf
@@ -162,8 +173,8 @@ def get_power_spectral_density(data, resolution=60., freq0=1e-3, display=False,
     N = data.shape[0]
 
     # calculate the normalized power spectrum (spectral density)
-    fdata2d = pyfftw.interfaces.numpy_fft.fft2(data)
-    fdata2d = pyfftw.interfaces.numpy_fft.fftshift(fdata2d)
+    fdata2d = fft2(data)
+    fdata2d = fftshift(fdata2d)
     psd2d = np.abs(np.multiply(fdata2d, np.conj(fdata2d))) / (N**2)
 
     # The frequency coordinate in cycle / m