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rowanc1
404 lines
13 KiB
Python
404 lines
13 KiB
Python
import numpy as np
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import unittest
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from TestUtils import OrderTest
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from SimPEG import Utils
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class TestInnerProducts(OrderTest):
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"""Integrate an function over a unit cube domain using edgeInnerProducts and faceInnerProducts."""
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meshTypes = ['uniformTensorMesh', 'uniformLRM', 'rotateLRM']
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meshDimension = 3
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meshSizes = [16, 32]
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def getError(self):
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call = lambda fun, xyz: fun(xyz[:, 0], xyz[:, 1], xyz[:, 2])
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ex = lambda x, y, z: x**2+y*z
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ey = lambda x, y, z: (z**2)*x+y*z
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ez = lambda x, y, z: y**2+x*z
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sigma1 = lambda x, y, z: x*y+1
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sigma2 = lambda x, y, z: x*z+2
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sigma3 = lambda x, y, z: 3+z*y
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sigma4 = lambda x, y, z: 0.1*x*y*z
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sigma5 = lambda x, y, z: 0.2*x*y
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sigma6 = lambda x, y, z: 0.1*z
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Gc = self.M.gridCC
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if self.sigmaTest == 1:
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sigma = np.c_[call(sigma1, Gc)]
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analytic = 647./360 # Found using sympy.
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elif self.sigmaTest == 3:
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sigma = np.r_[call(sigma1, Gc), call(sigma2, Gc), call(sigma3, Gc)]
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analytic = 37./12 # Found using sympy.
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elif self.sigmaTest == 6:
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sigma = np.c_[call(sigma1, Gc), call(sigma2, Gc), call(sigma3, Gc),
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call(sigma4, Gc), call(sigma5, Gc), call(sigma6, Gc)]
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analytic = 69881./21600 # Found using sympy.
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if self.location == 'edges':
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cart = lambda g: np.c_[call(ex, g), call(ey, g), call(ez, g)]
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Ec = np.vstack((cart(self.M.gridEx),
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cart(self.M.gridEy),
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cart(self.M.gridEz)))
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E = self.M.projectEdgeVector(Ec)
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if self.invProp:
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A = self.M.getEdgeInnerProduct(Utils.invPropertyTensor(self.M, sigma), invProp=True)
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else:
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A = self.M.getEdgeInnerProduct(sigma)
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numeric = E.T.dot(A.dot(E))
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elif self.location == 'faces':
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cart = lambda g: np.c_[call(ex, g), call(ey, g), call(ez, g)]
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Fc = np.vstack((cart(self.M.gridFx),
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cart(self.M.gridFy),
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cart(self.M.gridFz)))
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F = self.M.projectFaceVector(Fc)
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if self.invProp:
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A = self.M.getFaceInnerProduct(Utils.invPropertyTensor(self.M, sigma), invProp=True)
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else:
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A = self.M.getFaceInnerProduct(sigma)
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numeric = F.T.dot(A.dot(F))
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err = np.abs(numeric - analytic)
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return err
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def test_order1_edges(self):
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self.name = "Edge Inner Product - Isotropic"
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self.location = 'edges'
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self.sigmaTest = 1
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self.invProp = False
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self.orderTest()
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def test_order1_edges_invProp(self):
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self.name = "Edge Inner Product - Isotropic - invProp"
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self.location = 'edges'
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self.sigmaTest = 1
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self.invProp = True
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self.orderTest()
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def test_order3_edges(self):
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self.name = "Edge Inner Product - Anisotropic"
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self.location = 'edges'
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self.sigmaTest = 3
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self.invProp = False
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self.orderTest()
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def test_order3_edges_invProp(self):
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self.name = "Edge Inner Product - Anisotropic - invProp"
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self.location = 'edges'
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self.sigmaTest = 3
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self.invProp = True
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self.orderTest()
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def test_order6_edges(self):
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self.name = "Edge Inner Product - Full Tensor"
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self.location = 'edges'
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self.sigmaTest = 6
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self.invProp = False
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self.orderTest()
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def test_order6_edges_invProp(self):
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self.name = "Edge Inner Product - Full Tensor - invProp"
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self.location = 'edges'
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self.sigmaTest = 6
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self.invProp = True
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self.orderTest()
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def test_order1_faces(self):
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self.name = "Face Inner Product - Isotropic"
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self.location = 'faces'
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self.sigmaTest = 1
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self.invProp = False
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self.orderTest()
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def test_order1_faces_invProp(self):
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self.name = "Face Inner Product - Isotropic - invProp"
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self.location = 'faces'
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self.sigmaTest = 1
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self.invProp = True
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self.orderTest()
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def test_order3_faces(self):
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self.name = "Face Inner Product - Anisotropic"
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self.location = 'faces'
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self.sigmaTest = 3
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self.invProp = False
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self.orderTest()
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def test_order3_faces_invProp(self):
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self.name = "Face Inner Product - Anisotropic - invProp"
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self.location = 'faces'
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self.sigmaTest = 3
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self.invProp = True
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self.orderTest()
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def test_order6_faces(self):
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self.name = "Face Inner Product - Full Tensor"
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self.location = 'faces'
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self.sigmaTest = 6
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self.invProp = False
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self.orderTest()
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def test_order6_faces_invProp(self):
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self.name = "Face Inner Product - Full Tensor - invProp"
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self.location = 'faces'
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self.sigmaTest = 6
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self.invProp = True
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self.orderTest()
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class TestInnerProducts2D(OrderTest):
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"""Integrate an function over a unit cube domain using edgeInnerProducts and faceInnerProducts."""
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meshTypes = ['uniformTensorMesh', 'uniformLRM', 'rotateLRM']
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meshDimension = 2
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meshSizes = [4, 8, 16, 32, 64, 128]
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def getError(self):
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z = 5 # Because 5 is just such a great number.
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call = lambda fun, xy: fun(xy[:, 0], xy[:, 1])
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ex = lambda x, y: x**2+y*z
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ey = lambda x, y: (z**2)*x+y*z
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sigma1 = lambda x, y: x*y+1
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sigma2 = lambda x, y: x*z+2
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sigma3 = lambda x, y: 3+z*y
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Gc = self.M.gridCC
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if self.sigmaTest == 1:
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sigma = np.c_[call(sigma1, Gc)]
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analytic = 144877./360 # Found using sympy. z=5
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elif self.sigmaTest == 2:
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sigma = np.c_[call(sigma1, Gc), call(sigma2, Gc)]
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analytic = 189959./120 # Found using sympy. z=5
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elif self.sigmaTest == 3:
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sigma = np.r_[call(sigma1, Gc), call(sigma2, Gc), call(sigma3, Gc)]
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analytic = 781427./360 # Found using sympy. z=5
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if self.location == 'edges':
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cart = lambda g: np.c_[call(ex, g), call(ey, g)]
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Ec = np.vstack((cart(self.M.gridEx),
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cart(self.M.gridEy)))
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E = self.M.projectEdgeVector(Ec)
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if self.invProp:
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A = self.M.getEdgeInnerProduct(Utils.invPropertyTensor(self.M, sigma), invProp=True)
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else:
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A = self.M.getEdgeInnerProduct(sigma)
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numeric = E.T.dot(A.dot(E))
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elif self.location == 'faces':
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cart = lambda g: np.c_[call(ex, g), call(ey, g)]
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Fc = np.vstack((cart(self.M.gridFx),
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cart(self.M.gridFy)))
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F = self.M.projectFaceVector(Fc)
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if self.invProp:
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A = self.M.getFaceInnerProduct(Utils.invPropertyTensor(self.M, sigma), invProp=True)
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else:
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A = self.M.getFaceInnerProduct(sigma)
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numeric = F.T.dot(A.dot(F))
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err = np.abs(numeric - analytic)
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return err
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def test_order1_edges(self):
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self.name = "2D Edge Inner Product - Isotropic"
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self.location = 'edges'
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self.sigmaTest = 1
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self.invProp = False
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self.orderTest()
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def test_order1_edges_invProp(self):
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self.name = "2D Edge Inner Product - Isotropic - invProp"
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self.location = 'edges'
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self.sigmaTest = 1
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self.invProp = True
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self.orderTest()
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def test_order3_edges(self):
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self.name = "2D Edge Inner Product - Anisotropic"
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self.location = 'edges'
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self.sigmaTest = 2
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self.invProp = False
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self.orderTest()
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def test_order3_edges_invProp(self):
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self.name = "2D Edge Inner Product - Anisotropic - invProp"
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self.location = 'edges'
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self.sigmaTest = 2
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self.invProp = True
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self.orderTest()
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def test_order6_edges(self):
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self.name = "2D Edge Inner Product - Full Tensor"
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self.location = 'edges'
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self.sigmaTest = 3
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self.invProp = False
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self.orderTest()
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def test_order6_edges_invProp(self):
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self.name = "2D Edge Inner Product - Full Tensor - invProp"
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self.location = 'edges'
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self.sigmaTest = 3
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self.invProp = True
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self.orderTest()
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def test_order1_faces(self):
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self.name = "2D Face Inner Product - Isotropic"
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self.location = 'faces'
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self.sigmaTest = 1
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self.invProp = False
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self.orderTest()
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def test_order1_faces_invProp(self):
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self.name = "2D Face Inner Product - Isotropic - invProp"
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self.location = 'faces'
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self.sigmaTest = 1
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self.invProp = True
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self.orderTest()
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def test_order2_faces(self):
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self.name = "2D Face Inner Product - Anisotropic"
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self.location = 'faces'
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self.sigmaTest = 2
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self.invProp = False
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self.orderTest()
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def test_order2_faces_invProp(self):
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self.name = "2D Face Inner Product - Anisotropic - invProp"
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self.location = 'faces'
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self.sigmaTest = 2
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self.invProp = True
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self.orderTest()
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def test_order3_faces(self):
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self.name = "2D Face Inner Product - Full Tensor"
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self.location = 'faces'
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self.sigmaTest = 3
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self.invProp = False
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self.orderTest()
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def test_order3_faces_invProp(self):
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self.name = "2D Face Inner Product - Full Tensor - invProp"
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self.location = 'faces'
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self.sigmaTest = 3
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self.invProp = True
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self.orderTest()
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class TestInnerProducts1D(OrderTest):
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"""Integrate an function over a unit cube domain using edgeInnerProducts and faceInnerProducts."""
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meshTypes = ['uniformTensorMesh']
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meshDimension = 1
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meshSizes = [4, 8, 16, 32, 64, 128]
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def getError(self):
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y = 12 # Because 12 is just such a great number.
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z = 5 # Because 5 is just such a great number as well!
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call = lambda fun, x: fun(x)
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ex = lambda x: x**2+y*z
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sigma1 = lambda x: x*y+1
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Gc = self.M.gridCC
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sigma = call(sigma1, Gc)
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analytic = 128011./5 # Found using sympy. y=12, z=5
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if self.location == 'faces':
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F = call(ex, self.M.gridFx)
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if self.invProp:
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A = self.M.getFaceInnerProduct(1/sigma, invProp=True)
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else:
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A = self.M.getFaceInnerProduct(sigma)
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numeric = F.T.dot(A.dot(F))
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err = np.abs(numeric - analytic)
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return err
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def test_order1_faces(self):
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self.name = "1D Face Inner Product"
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self.location = 'faces'
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self.sigmaTest = 1
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self.invProp = False
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self.orderTest()
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def test_order1_faces_invProp(self):
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self.name = "1D Face Inner Product - invProp"
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self.location = 'faces'
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self.sigmaTest = 1
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self.invProp = True
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self.orderTest()
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if __name__ == '__main__':
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unittest.main()
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###################################################
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#### Uncomment to Reevaluate the InnerProducts ####
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###################################################
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# if __name__ == '__main__':
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# import sympy
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# x,y,z = sympy.symbols(['x','y','z'])
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# ex = x**2+y*z
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# ey = (z**2)*x+y*z
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# ez = y**2+x*z
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# e = sympy.Matrix([ex,ey,ez])
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# sigma1 = x*y+1
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# sigma2 = x*z+2
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# sigma3 = 3+z*y
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# sigma4 = 0.1*x*y*z
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# sigma5 = 0.2*x*y
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# sigma6 = 0.1*z
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# S1 = sympy.Matrix([[sigma1,0,0],[0,sigma1,0],[0,0,sigma1]])
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# S2 = sympy.Matrix([[sigma1,0,0],[0,sigma2,0],[0,0,sigma3]])
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# S3 = sympy.Matrix([[sigma1,sigma4,sigma5],[sigma4,sigma2,sigma6],[sigma5,sigma6,sigma3]])
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# print '3D'
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# print sympy.integrate(sympy.integrate(sympy.integrate(e.T*S1*e, (x,0,1)), (y,0,1)), (z,0,1))
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# print sympy.integrate(sympy.integrate(sympy.integrate(e.T*S2*e, (x,0,1)), (y,0,1)), (z,0,1))
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# print sympy.integrate(sympy.integrate(sympy.integrate(e.T*S3*e, (x,0,1)), (y,0,1)), (z,0,1))
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# z = 5
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# ex = x**2+y*z
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# ey = (z**2)*x+y*z
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# e = sympy.Matrix([ex,ey])
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# sigma1 = x*y+1
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# sigma2 = x*z+2
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# sigma3 = 3+z*y
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# S1 = sympy.Matrix([[sigma1,0],[0,sigma1]])
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# S2 = sympy.Matrix([[sigma1,0],[0,sigma2]])
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# S3 = sympy.Matrix([[sigma1,sigma3],[sigma3,sigma2]])
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# print '2D'
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# print sympy.integrate(sympy.integrate(e.T*S1*e, (x,0,1)), (y,0,1))
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# print sympy.integrate(sympy.integrate(e.T*S2*e, (x,0,1)), (y,0,1))
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# print sympy.integrate(sympy.integrate(e.T*S3*e, (x,0,1)), (y,0,1))
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# y = 12
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# z = 5
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# ex = x**2+y*z
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# e = ex
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# sigma1 = x*y+1
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# print '1D'
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# print sympy.integrate(e*sigma1*e, (x,0,1))
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