Update examples

examples/00_misc/06_fourier.py

@@ -11,28 +11,52 @@
 import gstools as gs
 
 # We start off by defining the spatial grid.
-x = np.linspace(0, 500, 256)
-y = np.linspace(0, 500, 128)
+L = np.array((500, 500))
+x = np.linspace(0, L[0], 256)
+y = np.linspace(0, L[1], 128)
 
 # And by setting up a Gaussian covariance model with a correlation length
 # scale which is roughly half the size of the grid.
 model = gs.Gaussian(dim=2, var=1, len_scale=200)
 
 # Next, we hand the cov. model to the spatial random field class
-# and set the generator to `Fourier`. The higher the modes_no, the better
-# the quality of the generated field, but also the computing time increases.
-# The modes_truncation are the cut-off values of the Fourier modes and finally,
-# the seed ensures that we generate the same random field each time.
+# and set the generator to `Fourier`. We will let the class figure out the
+# modes internally, by handing over `period` and `mode_rel_cutoff` which is the cutoff
+# value of the spectral density, relative to the maximum spectral density at
+# the origin. Simply put, we will use `mode_rel_cutoff`% of the spectral
+# density for the calculations. The argument `period` is set to the domain
+# size.
 srf = gs.SRF(
     model,
     generator="Fourier",
-    modes_no=[16, 8],
-    modes_truncation=[16, 8],
+    mode_rel_cutoff=0.99,
+    period=L,
     seed=1681903,
 )
 
-# Now, we can finally calculate the field with the given parameters.
+# Now, we can calculate the field with the given parameters.
 srf((x, y), mesh_type='structured')
 
 # GSTools has a few simple visualization methods built in.
 srf.plot()
+
+# Alternatively, we could calculate the modes ourselves and hand them over to
+# GSTools. Therefore, we set the cutoff values to absolut values in Fourier
+# space. But always check, if you cover enough of the spectral density to not
+# run into numerical problems.
+modes_cutoff = [1., 1.]
+
+# Next, we have to compute the numerical step size in Fourier space. This choice
+# influences the periodicity, which we want to set to the domain size by
+modes_delta = 2 * np.pi / L
+
+# Now, we calculate the modes with
+modes = [np.arange(0, modes_cutoff[d], modes_delta[d]) for d in 2]
+
+# And we can create a new instance of the SRF class with our own modes.
+srf_modes = gs.SRF(
+    model,
+    generator="Fourier",
+    modes=modes,
+    seed=494754,
+)

examples/00_misc/07_fourier_trans.py

@@ -10,23 +10,24 @@
 import gstools as gs
 
 # We start off by defining the spatial grid.
-x = np.linspace(0, 500, 300)
-y = np.linspace(0, 500, 200)
+L = np.array((500, 500))
+x = np.linspace(0, L[0], 300)
+y = np.linspace(0, L[1], 200)
 
 # Instead of using a Gaussian covariance model, we will use the much rougher
 # exponential model and we will introduce an anisotropy by using two different
 # length scales in the x- and y-axes
 model = gs.Exponential(dim=2, var=2, len_scale=[30, 20])
 
-# Very similar as before, setting up the spatial random field
+# Same as before, we set up the spatial random field
 srf = gs.SRF(
     model,
     generator="Fourier",
-    modes_no=[30, 20],
-    modes_truncation=[30, 20],
+    mode_rel_cutoff=0.999,
+    period=L,
     seed=1681903,
 )
-# and computing it
+# and compute it on our spatial domain
 srf((x, y), mesh_type='structured')
 
 # With the field generated, we can now apply transformations