Add generation for fixed coeffs that are no model.

examples/example_2.ipynb

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 # Generate synthetic data
 
 %% Cell type:markdown id:7c938d6b tags:
 
 Here we briefly show how `pymagglobal` can be used to generate synthetic data. We first set up the model we want to use to generate the synthetic data:
 
-%% Cell type:code id:5380320c tags:
+%% Cell type:code id:f52a366b tags:
 
 ``` python
 from pymagglobal import Model
 
 myModel = Model('CALS10k.2')
 ```
 
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+%% Cell type:markdown id:13988168 tags:
 
 Next we have to generate a data distribution. We use `pymagglobal`s `get_z_at` routine, to generate `n_at` random locations, that are uniformly distributed on the sphere. Times are drawn uniformly as well.
 
-%% Cell type:code id:68d9a6d8 tags:
+%% Cell type:code id:6f57b72a tags:
 
 ``` python
 from pymagglobal.utils import get_z_at
 
 import numpy as np
 from matplotlib import pyplot as plt
 from cartopy import crs as ccrs
 
 # the number of artificial records
 n_at = 400
 z_at = get_z_at(n_at, random=True)
 # set the times to something arbitrary
 z_at[3] = np.random.uniform(-1000, 1900, size=n_at)
 
 # plot the records, convert co-lat to lat
 fig, ax = plt.subplots(1, 1, subplot_kw={'projection': ccrs.Mollweide()})
 ax.scatter(z_at[1], 90-z_at[0], transform=ccrs.PlateCarree())
 ax.set_global()
 ax.coastlines();
 ```
 
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+%% Cell type:markdown id:806081dc tags:
 
 Finally we can evaluate the model at the inputs, to get synthetic ''observations'' of the field
 
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+%% Cell type:code id:5842b198 tags:
 
 ``` python
 from pymagglobal.core import field
 obs = field(z_at, myModel)
 ```
 
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 Let's have a look at the records:
 
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 ``` python
 fig, axs = plt.subplots(1, 3, subplot_kw={'projection': ccrs.Mollweide()},
                         figsize=(15, 4))
 titles = [r'$B_N$', r'$B_E$', r'$B_Z$']
 for it in range(3):
     axs[it].set_title(titles[it])
     axs[it].scatter(z_at[1], 90-z_at[0], c=obs[it], transform=ccrs.PlateCarree())
     axs[it].set_global()
     axs[it].coastlines();
 ```
 
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+%% Cell type:markdown id:e96b4ec7 tags:
 
 Declination, inclination and intensity records are also easily generated, by using the `field` kwargs:
 
-%% Cell type:code id:8bda1baf tags:
+%% Cell type:code id:57b38352 tags:
 
 ``` python
 obs_dif = field(z_at, myModel, field_type='dif')
 fig, axs = plt.subplots(1, 3, subplot_kw={'projection': ccrs.Mollweide()},
                         figsize=(15, 4))
 titles = [r'$D$', r'$I$', r'$F$']
 for it in range(3):
     axs[it].set_title(titles[it])
     axs[it].scatter(z_at[1], 90-z_at[0], c=obs_dif[it], transform=ccrs.PlateCarree())
     axs[it].set_global()
     axs[it].coastlines();
 ```
+
+%% Cell type:markdown id:a16058b9 tags:
+
+##  Data from an arbitray set of coefficients
+
+%% Cell type:markdown id:003f37e3 tags:
+
+Sometimes it is helpful to generate data not from a model that's included in pymagglobal, but from an arbitrary set of coefficients. Provided they are in the ''standard order'', i.e. $g_1^0, g_1^1, g_1^{-1}, g_2^0, g_2^1, g_2^{-1}, ...$, this is also straight-forward using utility routines from pymagglobal:
+
+%% Cell type:code id:fdbdfd1c tags:
+
+``` python
+from pymagglobal.core import coefficients
+
+epoch = -3000
+# First generate coefficients at epoch
+_, _, coeffs = coefficients(epoch, myModel)
+
+# Generate new input locations at the given epoch
+z_at = get_z_at(n_at, random=True, t=epoch)
+```
+
+%% Cell type:markdown id:e81a742d tags:
+
+We use the pymagglobal routine `dsh_basis`, which evaluates the derivatives of the spherical harmonics up to a given degree at given inputs:
+
+%% Cell type:code id:5924dde3 tags:
+
+``` python
+from pymagglobal.utils import dsh_basis
+
+# dsh_basis was designed to work with a C backend,
+# so the return array has to be allocated beforehand
+# and is filled during the function call
+base = np.empty((len(coeffs), 3*z_at.shape[1]))
+dsh_basis(myModel.l_max, z_at, base)
+```
+
+%% Cell type:markdown id:0d875959 tags:
+
+Field values are then generated via a dot product:
+
+%% Cell type:code id:a0a43e60 tags:
+
+``` python
+obs = coeffs @ base
+```
+
+%% Cell type:markdown id:1c804ae2 tags:
+
+The outputs are now given by obs, every third value is N, E, Z. To have a more convenient form, we reshape the output:
+
+%% Cell type:code id:a6eb5bc3 tags:
+
+``` python
+obs = obs.reshape(n_at, 3).T
+```
+
+%% Cell type:code id:d3ffc91a tags:
+
+``` python
+fig, axs = plt.subplots(1, 3, subplot_kw={'projection': ccrs.Mollweide()},
+                        figsize=(15, 4))
+titles = [r'$B_N$', r'$B_E$', r'$B_Z$']
+for it in range(3):
+    axs[it].set_title(titles[it])
+    axs[it].scatter(z_at[1], 90-z_at[0], c=obs[it], transform=ccrs.PlateCarree())
+    axs[it].set_global()
+    axs[it].coastlines();
+```