Visualizing the sparsity pattern of the collocation matrix

demos/Laplace/30_laplace_super_scaled.py

@@ -11,7 +11,7 @@
 import jax.numpy as jnp
 
 # jax.config.update('jax_platform_name', 'cpu')
-# jax.config.update("jax_enable_x64", True)
+jax.config.update("jax_enable_x64", True)
 
 import matplotlib.pyplot as plt
 import seaborn as sns
@@ -21,12 +21,14 @@
 DATAFOLDER = "./data/TempFolder/"
 
 RBF = partial(polyharmonic, a=1)
+# RBF = partial(gaussian, eps=1e-1)
+# RBF = partial(thin_plate, a=3)
 MAX_DEGREE = 0
 
-Nx = Ny = 10
-SUPPORT_SIZE = "max"
-# SUPPORT_SIZE = 9*1
-facet_types={"South":"n", "West":"d", "North":"d", "East":"d"}
+Nx = Ny = 20
+# SUPPORT_SIZE = "max"
+SUPPORT_SIZE = 20*2
+facet_types={"South":"d", "West":"d", "North":"d", "East":"d"}
 
 start = time.time()
 cloud = SquareCloud(Nx=Nx, Ny=Ny, facet_types=facet_types, support_size=SUPPORT_SIZE)
@@ -65,9 +67,62 @@ def my_rhs_operator(x, centers=None, rbf=None, fields=None):
 rbf_sol = sol.vals
 
 
+
 fig = plt.figure(figsize=(6*1,5))
 ax= fig.add_subplot(1, 1, 1, projection='3d')
 cloud.visualize_field(rbf_sol, cmap="jet", projection="3d", title="Laplace with RBFs", ax=ax);
 plt.show()
 ## Savefig
 fig.savefig(DATAFOLDER+"super_scaled.png", dpi=300)
+
+
+# %%
+
+
+
+
+
+
+
+# ## Observing the sparsity patten of the matrices involved
+
+# RBF = partial(gaussian, eps=1)
+
+# Nx = Ny = 10
+# SUPPORT_SIZE = "max"
+# # SUPPORT_SIZE = 5
+# facet_types={"South":"n", "West":"d", "North":"d", "East":"d"}
+
+# cloud = SquareCloud(Nx=Nx, Ny=Ny, facet_types=facet_types, support_size=SUPPORT_SIZE)
+
+
+
+
+M = compute_nb_monomials(MAX_DEGREE, 2)
+A = assemble_A(cloud, RBF, M)
+mat1 = jnp.abs(A)
+
+inv_A = assemble_invert_A(cloud, RBF, M)
+mat2 = jnp.abs(inv_A)
+
+## Matrix B for the linear system
+mat3 = sol.mat
+
+## 3 figures
+fig, ax = plt.subplots(1, 3, figsize=(15,5))
+
+sns.heatmap(jnp.abs(mat1), ax=ax[0], cmap="grey", cbar=True, square=True, xticklabels=False, yticklabels=False)
+ax[0].set_title("Collocation Matrix")
+
+sns.heatmap(jnp.abs(mat2), ax=ax[1], cmap="grey", cbar=True, square=True, xticklabels=False, yticklabels=False)
+ax[1].set_title("Inverse of Collocation Matrix")
+
+sns.heatmap(jnp.abs(mat3), ax=ax[2], cmap="grey", cbar=True, square=True, xticklabels=False, yticklabels=False)
+ax[2].set_title("Linear System Matrix (B)")
+
+# plt.title("Sparsity Pattern of the Collocation Matrix")
+plt.show()
+
+
+#%%
+