python_graphics_demos/30_laplace2_eigen.py at master · chatyan/python_graphics_demos · GitHub

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import numpy
import scipy
import moderngl
from PyQt5 import QtWidgets
from util_moderngl_qt import DrawerMeshColormap, QGLWidgetViewer3, Colormap
from del_msh import TriMesh, PolyLoop
from del_fem import LaplacianMatrix, MassMatrix

if __name__ == "__main__":
    vtxi2xyi = numpy.array([
        [0, 0],
        [1, 0],
        [1, 0.6],
        [0.6, 0.6],
        [0.6, 1.0],
        [0, 1]], dtype=numpy.float32)
    ##
    tri2vtx, vtx2xy = PolyLoop.tesselation2d(
        vtxi2xyi, resolution_edge=0.04, resolution_face=0.04)
    print("# vtx: ", vtx2xy.shape[0])
    smat = LaplacianMatrix.from_uniform_mesh(tri2vtx, vtx2xy)
    assert scipy.sparse.linalg.norm(smat - smat.transpose()) < 1.0e-10
    assert scipy.linalg.norm(smat * numpy.ones((vtx2xy.shape[0]))) < 1.0e-4
    mmat = MassMatrix.from_uniform_mesh(tri2vtx, vtx2xy)
    eig = scipy.sparse.linalg.eigsh(smat, M=mmat, sigma=0.0)
    i_eig = 4
    evec0 = eig[1].transpose()[i_eig].copy()
    eval0 = eig[0][i_eig]
    print(eval0)
    evec0 /= scipy.linalg.norm(evec0)
    assert abs(eval0*(mmat * evec0).dot(evec0)-(smat * evec0).dot(evec0)) < 1.0e-4
    vtx2val = evec0.copy() * 10 + 0.5
    edge2vtx = TriMesh.edge2vtx(tri2vtx, vtx2xy.shape[0])
    drawer_edge = DrawerMeshColormap.Drawer(
        vtx2xyz=vtx2xy,
        list_elem2vtx=[
            DrawerMeshColormap.ElementInfo(index=edge2vtx, color=(0, 0, 0), mode=moderngl.LINES),
            DrawerMeshColormap.ElementInfo(index=tri2vtx, color=(1, 1, 1), mode=moderngl.TRIANGLES)
        ],
        vtx2val=vtx2val,
        color_map=Colormap.jet())
    '''
    numpy.array([
            [0.0, 0.0, 0.5],
            [0.0, 0.0, 1.0],
            [0.0, 0.5, 1.0],
            [0.0, 1.0, 1.0],
            [0.5, 1.0, 0.5],
            [1.0, 1.0, 0.0],
            [1.0, 0.5, 0.0],
            [1.0, 0.0, 0.0],
            [0.5, 0.0, 0.0]])
    '''

    with QtWidgets.QApplication([]) as app:
        win = QGLWidgetViewer3.QtGLWidget_Viewer3(
            [drawer_edge])
        win.show()
        app.exec()