add multiple examples

examples/10_simple_kriging.py

@@ -0,0 +1,14 @@
+import numpy as np
+from gstools import Gaussian, krige
+# condtions
+cond_pos = [0.3, 1.9, 1.1, 3.3, 4.7]
+cond_val = [0.47, 0.56, 0.74, 1.47, 1.74]
+# resulting grid
+gridx = np.linspace(0.0, 15.0, 151)
+# spatial random field class
+model = Gaussian(dim=1, var=0.5, len_scale=2)
+krig = krige.Simple(model, mean=1, cond_pos=[cond_pos], cond_val=cond_val)
+krig([gridx])
+ax = krig.plot()
+ax.scatter(cond_pos, cond_val, color="k", zorder=10, label="Conditions")
+ax.legend()

examples/11_ordinary_kriging.py

@@ -0,0 +1,14 @@
+import numpy as np
+from gstools import Gaussian, krige
+# condtions
+cond_pos = [0.3, 1.9, 1.1, 3.3, 4.7]
+cond_val = [0.47, 0.56, 0.74, 1.47, 1.74]
+# resulting grid
+gridx = np.linspace(0.0, 15.0, 151)
+# spatial random field class
+model = Gaussian(dim=1, var=0.5, len_scale=2)
+krig = krige.Ordinary(model, cond_pos=[cond_pos], cond_val=cond_val)
+krig([gridx])
+ax = krig.plot()
+ax.scatter(cond_pos, cond_val, color="k", zorder=10, label="Conditions")
+ax.legend()

examples/12_compare_kriging.py

@@ -0,0 +1,19 @@
+import numpy as np
+from gstools import Gaussian, krige
+import matplotlib.pyplot as plt
+# condtions
+cond_pos = [0.3, 1.9, 1.1, 3.3, 4.7]
+cond_val = [0.47, 0.56, 0.74, 1.47, 1.74]
+# resulting grid
+gridx = np.linspace(0.0, 15.0, 151)
+# spatial random field class
+model = Gaussian(dim=1, var=0.5, len_scale=2)
+kr1 = krige.Simple(model=model, mean=1, cond_pos=[cond_pos], cond_val=cond_val)
+kr2 = krige.Ordinary(model=model, cond_pos=[cond_pos], cond_val=cond_val)
+kr1([gridx])
+kr2([gridx])
+plt.plot(gridx, kr1.field, label="simple kriged field")
+plt.plot(gridx, kr2.field, label="ordinary kriged field")
+plt.scatter(cond_pos, cond_val, color="k", zorder=10, label="Conditions")
+plt.legend()
+plt.show()

examples/13_condition_ensemble.py

@@ -0,0 +1,23 @@
+import numpy as np
+from gstools import Gaussian, SRF
+import matplotlib.pyplot as plt
+# condtions
+cond_pos = [0.3, 1.9, 1.1, 3.3, 4.7]
+cond_val = [0.47, 0.56, 0.74, 1.47, 1.74]
+gridx = np.linspace(0.0, 15.0, 151)
+# spatial random field class
+model = Gaussian(dim=1, var=0.5, len_scale=2)
+srf = SRF(model)
+srf.set_condition([cond_pos], cond_val, "ordinary")
+fields = []
+for i in range(100):
+    if i % 10 == 0: print(i)
+    fields.append(srf([gridx], seed=i))
+    label = "Conditioned ensemble" if i == 0 else None
+    plt.plot(gridx, fields[i], color="k", alpha=0.1, label=label)
+plt.plot(gridx, np.full_like(gridx, srf.mean), label="estimated mean")
+plt.plot(gridx, np.mean(fields, axis=0), linestyle=':', label="Ensemble mean")
+plt.plot(gridx, srf.krige_field, linestyle='dashed', label="kriged field")
+plt.scatter(cond_pos, cond_val, color="k", zorder=10, label="Conditions")
+plt.legend()
+plt.show()

examples/14_transform_01.py

@@ -0,0 +1,9 @@
+from gstools import SRF, Gaussian
+from gstools import transform as tf
+# structured field with a size of 100x100 and a grid-size of 1x1
+x = y = range(100)
+model = Gaussian(dim=2, var=1, len_scale=10)
+srf = SRF(model, seed=20170519)
+srf.structured([x, y])
+tf.normal_to_lognormal(srf)
+srf.plot()

examples/15_transform_02.py

@@ -0,0 +1,9 @@
+from gstools import SRF, Gaussian
+from gstools import transform as tf
+# structured field with a size of 100x100 and a grid-size of 1x1
+x = y = range(100)
+model = Gaussian(dim=2, var=1, len_scale=10)
+srf = SRF(model, seed=20170519)
+srf.structured([x, y])
+tf.binary(srf)
+srf.plot()

examples/16_transform_03.py

@@ -0,0 +1,9 @@
+from gstools import SRF, Gaussian
+from gstools import transform as tf
+# structured field with a size of 100x100 and a grid-size of 1x1
+x = y = range(100)
+model = Gaussian(dim=2, var=1, len_scale=10)
+srf = SRF(model, seed=20170519)
+srf.structured([x, y])
+tf.zinnharvey(srf, conn="high")
+srf.plot()

examples/17_transform_04.py

@@ -0,0 +1,9 @@
+from gstools import SRF, Gaussian
+from gstools import transform as tf
+# structured field with a size of 100x100 and a grid-size of 1x1
+x = y = range(100)
+model = Gaussian(dim=2, var=1, len_scale=10)
+srf = SRF(model, seed=20170519)
+field = srf.structured([x, y])
+tf.normal_to_arcsin(srf)
+srf.plot()

examples/18_transform_05.py

@@ -0,0 +1,12 @@
+from gstools import SRF, Gaussian
+from gstools import transform as tf
+# structured field with a size of 100x100 and a grid-size of 1x1
+x = y = range(100)
+model = Gaussian(dim=2, var=1, len_scale=10)
+srf = SRF(model, mean=-9, seed=20170519)
+srf.structured([x, y])
+tf.normal_force_moments(srf)
+tf.zinnharvey(srf, conn="low")
+tf.binary(srf)
+tf.normal_to_lognormal(srf)
+srf.plot()

examples/19_check_rand_meth_sampling.py

@@ -0,0 +1,64 @@
+import numpy as np
+from matplotlib import pyplot as plt
+from mpl_toolkits.mplot3d import Axes3D
+
+from gstools import SRF, Stable
+
+
+def norm_rad(vec):
+    """Direction on the unit sphere."""
+    vec = np.array(vec, ndmin=2)
+    norm = np.zeros(vec.shape[1])
+    for i in range(vec.shape[0]):
+        norm += vec[i]**2
+    norm = np.sqrt(norm)
+    return np.einsum("j,ij->ij", 1 / norm, vec), norm
+
+
+def plot_rand_meth_samples(generator):
+    """Plot the samples of the rand meth class."""
+    norm, rad = norm_rad(generator._cov_sample)
+
+    fig = plt.figure(figsize=(10, 4))
+
+    if generator.model.dim == 3:
+        ax = fig.add_subplot(121, projection=Axes3D.name)
+        u = np.linspace(0, 2 * np.pi, 100)
+        v = np.linspace(0, np.pi, 100)
+        x = np.outer(np.cos(u), np.sin(v))
+        y = np.outer(np.sin(u), np.sin(v))
+        z = np.outer(np.ones(np.size(u)), np.cos(v))
+        ax.plot_surface(x, y, z, rstride=4, cstride=4, color='b', alpha=0.1)
+        ax.scatter(norm[0], norm[1], norm[2])
+        ax.set_aspect('equal')
+    elif generator.model.dim == 2:
+        ax = fig.add_subplot(121)
+        u = np.linspace(0, 2 * np.pi, 100)
+        x = np.cos(u)
+        y = np.sin(u)
+        ax.plot(x, y, color='b', alpha=0.1)
+        ax.scatter(norm[0], norm[1])
+        ax.set_aspect('equal')
+    else:
+        ax = fig.add_subplot(121)
+        ax.bar(-1, np.sum(np.isclose(norm, -1)), color="C0")
+        ax.bar(1, np.sum(np.isclose(norm, 1)), color="C0")
+        ax.set_xticks([-1, 1])
+        ax.set_xticklabels(('-1', '1'))
+    ax.set_title("Direction sampling")
+
+    ax = fig.add_subplot(122)
+#    x = np.linspace(0, np.max(rad))
+    x = np.linspace(0, 10 / generator.model.integral_scale)
+    y = generator.model.spectral_rad_pdf(x)
+    ax.plot(x, y)
+    sample_in = np.sum(rad <= np.max(x))
+    ax.hist(rad[rad <= np.max(x)], bins=sample_in // 50, density=True)
+    ax.set_xlim([0, np.max(x)])
+    ax.set_title("Radius samples shown {}/{}".format(sample_in, len(rad)))
+    fig.show()
+
+
+model = Stable(dim=3, alpha=1)
+srf = SRF(model)
+plot_rand_meth_samples(srf.generator)