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Liutex

+# import the necessary libraries
+import numpy as np
+import pyvista as pv
+from scipy.linalg import schur
+from pyvista import examples
+
+#Load a dataset
+mesh = examples.download_carotid()
+mesh
+
+#Compute the gradients of the vectors (assuming you have a vector field in the point data of the mesh)
+mesh_g = mesh.compute_derivative(scalars="vectors")
+
+
+
+#Compute the gradients of the vectors (assuming you have a scalar field in the point data of the mesh)
+mesh_g_s = mesh.compute_derivative(scalars="scalars")
+
+
+#Access the gradient values for a vector field
+gradients = mesh_g["gradient"]
+
+"""
+internal_mesh = gradients['internalMesh']
+boundary_mesh = gradients['boundary']['movingWall']
+"""
+#Access the gradient values for a scalar field
+gradients_s = mesh_g_s["gradient"]
+
+#Organize the gradients into a dictionary for easier access
+def gradients_to_dict(arr):
+    """A helper method to label the gradients into a dictionary."""
+    keys = np.array(
+        ["du/dx", "du/dy", "du/dz", "dv/dx", "dv/dy", "dv/dz", "dw/dx", "dw/dy", "dw/dz"],
+    )
+    keys = keys.reshape((3, 3))[:, : arr.shape[1]].ravel()
+    return dict(zip(keys, arr.T))
+
+#for a vector field
+gradients_dict = gradients_to_dict(gradients)
+
+#for a scalar field
+gradients_dict_s = gradients_to_dict(gradients_s)
+
+
+
+# And we can add all of those components as individual arrays back to the mesh for a vector
+# by:
+mesh_g.point_data.update(gradients_dict)
+
+
+
+
+
+# And we can add all of those components as individual arrays back to the mesh for a scalar
+# by:
+mesh_g_s.point_data.update(gradients_dict_s)
+
+# Visualize the gradients
+#keys for a vector
+keys = np.array(list(gradients_dict.keys())).reshape(3, 3)
+
+#keys for a scalar
+keys_s = np.array(list(gradients_dict_s.keys())).reshape(1, 3)
+
+# Transpose the matric keys
+#A = np.transpose(keys, axes=None)
+A = np.transpose(keys)
+
+
+#Visualize the gradients of a vector
+p = pv.Plotter(shape=keys.shape)
+for (i, j), name in np.ndenumerate(keys):
+    p.subplot(i, j)
+    p.add_mesh(mesh_g.contour(scalars=name), scalars=name, opacity=0.75)
+    p.add_mesh(mesh_g.outline(), color="k")
+p.link_views()
+p.view_isometric()
+p.show()
+
+points = pv.PointSet(mesh_g.points)
+points
+
+gradients_data = gradients.reshape(-1, 3)
+
+#Visualize the transpose of the gradients of a vector
+p = pv.Plotter(shape=A.shape)
+for (i, j), name in np.ndenumerate(A):
+    p.subplot(i, j)
+    p.add_mesh(mesh_g.contour(scalars=name), scalars=name, opacity=0.75)
+    p.add_mesh(mesh_g.outline(), color="k")
+p.link_views()
+p.view_isometric()
+p.show()
+
+#Print all the values of gradients_dict
+print(gradients_dict.values()) 
+
+#Print the items of gradients_dict
+items = gradients_dict.items()
+
+print(items) 
+print(len(gradients_dict)) 
+
+#get the value of each velocity  "du/dx", "du/dy", "du/dz" ....
+value_vect = gradients_dict.get("du/dx")     
+value_vect_1 = gradients_dict.get("du/dy")
+value_vect_2 = gradients_dict.get("du/dz")
+value_vect_3 = gradients_dict.get("dv/dx")
+value_vect_4 = gradients_dict.get("dv/dy")
+value_vect_5 = gradients_dict.get("dv/dz")
+value_vect_6 = gradients_dict.get("dw/dx")
+value_vect_7 = gradients_dict.get("dw/dy")
+value_vect_8 = gradients_dict.get("dw/dz")
+
+#print the value of "du/dx"
+print(value_vect)
+
+#change the gradient_dict to a matrix 
+def create_matrix_from_parameters(params):
+    if len(params)!=9:
+        raise ValueError("Sie müssen genau 9 Parameter eingeben.")
+        
+    matrix = []
+    for i in range(3):
+        row=params[i*3:(i+1)*3]
+        matrix.append(row)
+    return matrix
+
+
+  
+#params = [value_vect, value_vect_1, value_vect_2, value_vect_3, value_vect_4, value_vect_5, value_vect_6, value_vect_7, value_vect_8]
+
+params_trans = [value_vect, value_vect_3, value_vect_6, value_vect_1, value_vect_4, value_vect_7, value_vect_3, value_vect_5, value_vect_8]
+
+matrix = create_matrix_from_parameters(params_trans)
+
+print("Matrix 3x3", matrix )
+
+# Compute the real Schur decomposition
+Q_, S = schur(matrix, output='real')
+
+print ("Matrix Q*", Q_)
+
+print("Determinant of Q*", np.linalg.det(Q_))
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