103 lines
2.5 KiB
Python
Executable File
103 lines
2.5 KiB
Python
Executable File
#! /usr/bin/env python3
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import sympy as sp
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from sympy.utilities.codegen import codegen
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x, y, t = sp.symbols("x,y,t")
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rho, g = sp.symbols("rho,g", positive=True, real=True)
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# Ignoring rho, assumed to be constant
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eta = sp.Symbol("eta", positive=True, real=True)
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etau, etav = sp.symbols("etau,etav", real=True)
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u = etau / eta
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v = etav / eta
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q = sp.Matrix([eta, etau, etav])
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E = sp.Matrix([eta * u, eta * u ** 2 + g * eta ** 2 / 2, eta * u * v])
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F = sp.Matrix([eta * v, eta * u * v, eta * v ** 2 + g * eta ** 2 / 2])
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q = sp.Matrix([eta, etau, etav])
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A = E.jacobian(q)
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sp.pprint(A)
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B = F.jacobian(q)
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sp.pprint(B)
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f = sp.symbols("f")
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coriolis = sp.Matrix([0, -f * v * eta, +f * u * eta])
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sp.pprint(coriolis)
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b = sp.symbols("b")
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frictional = sp.Matrix([0, b * u * eta, b * v * eta])
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sp.pprint(frictional)
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print("A:")
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# We can also diagonalise the transpose,
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# which still gives the same (linearised) system.
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# This results in a much nicer formulation for A+ and A-
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A = A.T
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S, D = A.diagonalize()
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print("Diagonals:")
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sp.pprint(D[0, 0])
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sp.pprint(D[1, 1])
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sp.pprint(D[2, 2])
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print("S:")
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sp.pprint(S)
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print("SI:")
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sp.pprint(sp.simplify(S.inv()))
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m = abs(etau / eta) + abs(sp.sqrt(eta ** (3)) * sp.sqrt(g) / eta)
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L = D + sp.Matrix([[m, 0, 0], [0, m, 0], [0, 0, m]])
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Aplus = sp.simplify(S * L * S.inv()) / 2
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Aplus = Aplus.T
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L = D - sp.Matrix([[m, 0, 0], [0, m, 0], [0, 0, m]])
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Aminus = sp.simplify(S * L * S.inv()) / 2
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Aminus = Aminus.T
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print("A plus:")
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sp.pprint(Aplus)
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print("A minus:")
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sp.pprint(Aminus)
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print("A S:")
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sp.pprint(sp.simplify(Aminus - Aplus))
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assert sp.simplify(S * D * S.inv() - A) == sp.Matrix([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
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print("B:")
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S, D = B.diagonalize()
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print("Diagonals:")
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sp.pprint(D[0, 0])
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sp.pprint(D[1, 1])
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sp.pprint(D[2, 2])
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print("S:")
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sp.pprint(S)
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print("SI:")
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sp.pprint(sp.simplify(S.inv()))
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assert sp.simplify(S * D * S.inv() - B) == sp.Matrix([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
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m = abs(etav / eta) + abs(sp.sqrt(eta ** (3)) * sp.sqrt(g) / eta)
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L = D + sp.Matrix([[m, 0, 0], [0, m, 0], [0, 0, m]])
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Bplus = sp.simplify(S * L * S.inv()) / 2
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L = D - sp.Matrix([[m, 0, 0], [0, m, 0], [0, 0, m]])
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Bminus = sp.simplify(S * L * S.inv()) / 2
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print("B plus:")
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sp.pprint(Bplus)
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print("B minus:")
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sp.pprint(Bminus)
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print("B S:")
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sp.pprint(sp.simplify(Bminus - Bplus))
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assert sp.simplify((Bplus + Bminus) - B) == sp.Matrix([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
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breakpoint()
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code = codegen(
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[("Aplus", Aplus), ("Aminus", Aminus), ("Bplus", Bplus), ("Bminus", Bminus)], "rust"
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)
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with open("autogen.rs", "w") as f:
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f.write(code[0][1])
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