mirror of
https://github.com/wassname/simpeg.git
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Rowan Cockett
119 lines
3.5 KiB
Python
119 lines
3.5 KiB
Python
import numpy as np
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import unittest
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from OrderTest import OrderTest
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# MATLAB code:
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# syms 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 = [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 = [sigma1,0,0;0,sigma1,0;0,0,sigma1];
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# S2 = [sigma1,0,0;0,sigma2,0;0,0,sigma3];
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# S3 = [sigma1,sigma4,sigma5;sigma4,sigma2,sigma6;sigma5,sigma6,sigma3];
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# i1 = int(int(int(e.'*S1*e,x,0,1),y,0,1),z,0,1);
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# i2 = int(int(int(e.'*S2*e,x,0,1),y,0,1),z,0,1);
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# i3 = int(int(int(e.'*S3*e,x,0,1),y,0,1),z,0,1);
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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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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 matlab symbolic toolbox.
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elif self.sigmaTest == 3:
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sigma = np.c_[call(sigma1, Gc), call(sigma2, Gc), call(sigma3, Gc)]
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analytic = 37./12 # Found using matlab symbolic toolbox.
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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 matlab symbolic toolbox.
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if self.location == 'edges':
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Ex = call(ex, self.M.gridEx)
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Ey = call(ey, self.M.gridEy)
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Ez = call(ez, self.M.gridEz)
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E = np.matrix(np.r_[Ex, Ey, Ez]).T
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A = self.M.getEdgeInnerProduct(sigma)
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numeric = E.T*A*E
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elif self.location == 'faces':
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Fx = call(ex, self.M.gridFx)
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Fy = call(ey, self.M.gridFy)
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Fz = call(ez, self.M.gridFz)
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F = np.matrix(np.r_[Fx, Fy, Fz]).T
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A = self.M.getFaceInnerProduct(sigma)
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numeric = F.T*A*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.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.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.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.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.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.orderTest()
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if __name__ == '__main__':
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unittest.main()
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