Efficient Transfer Of Contact-Point Local Deformations for Data-Driven Simulation
@line 251: r:
@line 252: [r0, r1, r2]
@line 256: omega([0,0,0]) = sqrt(2)/(4*pi**(3/2))

@line 262: H0 = 1

@line 266: H1 = [r0, r1, r2]

@line 270: H2 = [[sqrt(2)*r0**2/2 - sqrt(2)/2, sqrt(2)*r0*r1/2, sqrt(2)*r0*r2/2], [sqrt(2)*r0*r1/2, sqrt(2)*r1**2/2 - sqrt(2)/2, sqrt(2)*r1*r2/2], [sqrt(2)*r0*r2/2, sqrt(2)*r1*r2/2, sqrt(2)*r2**2/2 - sqrt(2)/2]]

@line 274: H3 = [[[sqrt(6)*r0**3/6 - sqrt(6)*r0/2, sqrt(6)*r0**2*r1/6 - sqrt(6)*r1/6, sqrt(6)*r0**2*r2/6 - sqrt(6)*r2/6], [sqrt(6)*r0**2*r1/6 - sqrt(6)*r1/6, sqrt(6)*r0*r1**2/6 - sqrt(6)*r0/6, sqrt(6)*r0*r1*r2/6], [sqrt(6)*r0**2*r2/6 - sqrt(6)*r2/6, sqrt(6)*r0*r1*r2/6, sqrt(6)*r0*r2**2/6 - sqrt(6)*r0/6]], [[sqrt(6)*r0**2*r1/6 - sqrt(6)*r1/6, sqrt(6)*r0*r1**2/6 - sqrt(6)*r0/6, sqrt(6)*r0*r1*r2/6], [sqrt(6)*r0*r1**2/6 - sqrt(6)*r0/6, sqrt(6)*r1**3/6 - sqrt(6)*r1/2, sqrt(6)*r1**2*r2/6 - sqrt(6)*r2/6], [sqrt(6)*r0*r1*r2/6, sqrt(6)*r1**2*r2/6 - sqrt(6)*r2/6, sqrt(6)*r1*r2**2/6 - sqrt(6)*r1/6]], [[sqrt(6)*r0**2*r2/6 - sqrt(6)*r2/6, sqrt(6)*r0*r1*r2/6, sqrt(6)*r0*r2**2/6 - sqrt(6)*r0/6], [sqrt(6)*r0*r1*r2/6, sqrt(6)*r1**2*r2/6 - sqrt(6)*r2/6, sqrt(6)*r1*r2**2/6 - sqrt(6)*r1/6], [sqrt(6)*r0*r2**2/6 - sqrt(6)*r0/6, sqrt(6)*r1*r2**2/6 - sqrt(6)*r1/6, sqrt(6)*r2**3/6 - sqrt(6)*r2/2]]]

@line 281: The same result can be obtained using the formula (3+n-1 over n),
 which, for n = 3, is (5 over 3) = 10

@line 294: We expect 1/3:  1/3
@line 295: We expect   1:  1

@line 321: Checking whether `iR` is the inverse of `R`. It works if we get I:
@line 322: [[1.0000153676595458, -1.4205979286807668e-06, 5.119800505770655e-08], [-1.420597928736278e-06, 0.9999790285205123, 6.342174253548549e-06], [5.1198005113217704e-08, 6.342174253493038e-06, 1.0000047450156853]]

@line 325: Checking whether rotation works for H4. It works if we get zero:
@line 327: 1.11196879703057e-9

@line 354: Sampling from H2_01: r0*r1

@line 372: [[0.0320606175393373, 0.683191650828152, -0.0262942028062137], [0.683191650828152, -0.0376414158094994, -0.0219565420667020], [-0.0262942028062137, -0.0219565420667020, 0.0341481412729852]]

@line 377: [[-0.129906466982846, -0.381473603507890, -0.188692315910441], [-0.381473603507890, -0.425543343821029, 0.138161613622368], [-0.188692315910441, 0.138161613622368, 0.584011065658344]]

@line 383: Squared error: 1.51048776133663e-10
@line 386: Reconstruction:
@line 390: sqrt(2)*(0.0320606175393373*r0**2 + 1.3663833016563*r0*r1 - 0.0525884056124275*r0*r2 - 0.0376414158094994*r1**2 - 0.043913084133404*r1*r2 + 0.0341481412729852*r2**2 - 0.0285673430028231)/2

@line 402: Self similarity with the generic dot product 0.939459468137621
@line 403: Self similarity with equation (11) 0.939459468137621
@line 404: Expected self-similarity using the original sampled function: 1

@line 407: the end.