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numerical.py

RichterSlopeModel dataclass 

RichterSlopeModel(
    n: int | float | Rational | None = None,
    phi: float | None = None,
    xi_h0: float | None = None,
    sub: dict | None = None,
    px_lambda: Callable | None = None,
    pz_lambda: Callable | None = None,
    p_lambda: Callable | None = None,
    ξrt_lambda: Callable | None = None,
    ξup_lambda: Callable | None = None,
    ξx_lambda: Callable | None = None,
    ξz_lambda: Callable | None = None,
    vx_lambda: Callable | None = None,
    vz_lambda: Callable | None = None,
    v_lambda: Callable | None = None,
    H_detHessian: Mul | None = None,
    H_critical_t: Mul | None = None,
    H_critical_t_numer: Add | None = None,
    H_critical_t_poly: Poly | None = None,
    tanbeta_crits: list | None = None,
    beta_crits: list | None = None,
    idtx_fgtx_markers: list | None = None,
    gstar_eq: Eq | None = None,
)

Collection of numerical lambdas implementing Hamiltonian rock slope model.

Attributes

n: int | float | Rational | None = None phi: float | None = None xi_h0: float | None = None sub: dict | None = None px_lambda: Callable | None = None pz_lambda: Callable | None = None p_lambda: Callable | None = None ξrt_lambda: Callable | None = None ξup_lambda: Callable | None = None ξrt_lambda: Callable | None = None ξx_lambda: Callable | None = None ξz_lambda: Callable | None = None vx_lambda: Callable | None = None vz_lambda: Callable | None = None v_lambda: Callable | None = None H_detHessian: Mul | None = None H_critical_t: Mul | None = None H_critical_t_numer: Add | None = None H_critical_t_poly: Poly | None = None tanbeta_crits: list | None = None beta_crits: list | None = None idtx_fgtx_markers: list | None = None gstar_eq: Eq | None = None

Used by:

Methods:

  • build –

    Lambdify set of Hamiltonian rock slope erosion model equations.

  • get_gstar_signature –

    Generate metric signature from dual metric tensor as fn(beta).

build 

build(rst: RichterSlopeTheory, parameters: dict) -> None

Lambdify set of Hamiltonian rock slope erosion model equations.

Parameters

rst: RichterSlopeTheory Instance of Hamiltonian rock slope theory class. parameters: dict Choices of model parameters needed by theory equations.

Attributes

n: int | float | Rational | None = None phi: float | None = None xi_h0: float | None = None sub: dict | None = None px_lambda: Callable | None = None pz_lambda: Callable | None = None p_lambda: Callable | None = None ξrt_lambda: Callable | None = None ξup_lambda: Callable | None = None ξrt_lambda: Callable | None = None ξx_lambda: Callable | None = None ξz_lambda: Callable | None = None vx_lambda: Callable | None = None vz_lambda: Callable | None = None v_lambda: Callable | None = None H_detHessian: Mul | None = None H_critical_t: Mul | None = None H_critical_t_numer: Add | None = None H_critical_t_poly: Poly | None = None tanbeta_crits: list | None = None beta_crits: list | None = None idtx_fgtx_markers: list | None = None gstar_eq: Eq | None = None

Source code in erosionfront/theory/numerical.py 
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    def build(self, rst: RichterSlopeTheory, parameters: dict,) -> None:
        """
        Lambdify set of Hamiltonian rock slope erosion model equations.

        Parameters
        ----------
        rst: RichterSlopeTheory
            Instance of Hamiltonian rock slope theory class.
        parameters: dict
            Choices of model parameters needed by theory equations.

        Attributes
        ----------
        n: int | float | Rational | None = None
        phi: float | None = None
        xi_h0: float | None = None
        sub: dict | None = None
        px_lambda: Callable | None = None
        pz_lambda: Callable | None = None
        p_lambda: Callable | None = None
        ξrt_lambda: Callable | None = None
        ξup_lambda: Callable | None = None
        ξrt_lambda: Callable | None = None
        ξx_lambda: Callable | None = None
        ξz_lambda: Callable | None = None
        vx_lambda: Callable | None = None
        vz_lambda: Callable | None = None
        v_lambda: Callable | None = None
        H_detHessian: Mul | None = None
        H_critical_t: Mul | None = None
        H_critical_t_numer: Add | None = None
        H_critical_t_poly: Poly | None = None
        tanbeta_crits: list | None = None
        beta_crits: list | None = None
        idtx_fgtx_markers: list | None = None
        gstar_eq: Eq | None = None
        """
        self.n = parameters["n"]
        self.phi = parameters["phi"]
        self.xi_h0 = parameters["xi_h0"]
        self.sub = {
            xi_h0: self.xi_h0, 
            n: self.n, 
            phi: self.phi
        }

        self.px_lambda = lambdify([beta], rst.p_covec_fn[0].subs(self.sub))
        self.pz_lambda = lambdify([beta], rst.p_covec_fn[1].subs(self.sub))
        self.p_lambda = lambdify([beta], rst.p_fn.subs(self.sub))

        self.ξrt_lambda = lambda beta_: 1/self.px_lambda(beta_)
        self.ξup_lambda = lambda beta_: 1/self.pz_lambda(beta_)

        self.ξx_lambda \
            = lambda beta_: self.px_lambda(beta_)/self.p_lambda(beta_)**2
        self.ξz_lambda \
            = lambda beta_: self.pz_lambda(beta_)/self.p_lambda(beta_)**2

        self.vx_lambda = lambdify(
            [beta],
            exp(expand_log(
                log(rst.v_vec_fn[0].subs({p:rst.p_fn}).subs(self.sub)),
            force=True)),
        )
        self.vz_lambda = lambdify(
            [beta],
            exp(expand_log(
                log(rst.v_vec_fn[1].subs({p:rst.p_fn}).subs(self.sub)),
            force=True)),
        )
        self.v_lambda = lambdify(
            [beta],
            sqrt(
                exp(2*expand_log(
                    log(rst.v_vec_fn[0].subs({p:rst.p_fn}).subs(self.sub)),
                force=True))
                +exp(2*expand_log(
                    log(rst.v_vec_fn[1].subs({p:rst.p_fn}).subs(self.sub)),
                force=True)),
            ),
        )

        self.H_detHessian = collect(
                (factor( 
                    (rst.d2Hdpx2*rst.d2Hdpz2 
                     - rst.d2Hdpxpz*rst.d2Hdpxpz).subs({pz:pzp}) )
                .subs({pzp:pz})
                .subs({n:parameters["n"]})
                .subs({px: -pz*tan(beta)})
                ), 
            pz
        )

        self.H_critical_t = (
            factor(
                self.H_detHessian
                .subs({
                    phi:parameters["phi"], 
                    xi_h0:1, 
                    px: -pz*tan(beta)
                })
            )
            # .subs({sqrt(1+tan(beta)**2):sec(beta)})
            # .subs({tan(beta):sqrt(sec(beta)**2-1)})
            # .subs({sec(beta):1/cos(beta)})
)
        self.H_critical_t_numer = numer(factor(
            self.H_critical_t
        ).subs({tan(beta):t_h}))#.args[1]

        self.gstar_eq = simplify(
            rst.gstar_eq.subs({px:-pz*tan(beta)}).subs(self.sub))

        try:
            self.H_critical_t_poly = poly(self.H_critical_t_numer,t_h)
        except:
            print("Failed to solve critical beta polynomial")
            return

        self.tanbeta_crits = sorted([
            float(root_)
            for root_ in self.H_critical_t_poly.nroots()
            if Abs(im(root_)) < 1e-10 and re(root_) > 0
        ])
        self.β_crits = [
            np.arctan(tanbeta_crit_) for tanbeta_crit_ in self.tanbeta_crits
        ]

get_gstar_signature 

get_gstar_signature() -> Generator[tuple[list, list]]

Generate metric signature from dual metric tensor as fn(beta).

Attributes

Uses px_lambda, pz_lambda, and gstar_eq methods.

Yields

tuple[list,list] Lists of critical betas and corresponding metric signatures.

Source code in erosionfront/theory/numerical.py 
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def get_gstar_signature(self,) -> Generator[tuple[list, list]]:
    """
    Generate metric signature from dual metric tensor as fn(beta).

    Attributes
    ----------
    Uses px_lambda, pz_lambda, and gstar_eq methods.

    Yields
    -------
    tuple[list,list]
        Lists of critical betas and corresponding metric signatures.
    """
    betas_: list
    for betas_ in list(zip([0]+self.β_crits, self.β_crits+[np.pi/2])):
        bias: float = 0.9
        beta_: float  = betas_[0]*(1-bias) + betas_[1]*bias
        px_: float = self.px_lambda(beta_)
        pz_: float = self.pz_lambda(beta_)
        gstar_: Matrix \
            = self.gstar_eq.rhs.subs({px:px_, pz:pz_}).subs({beta:beta_})
        gstar_eigenvals_: list = gstar_.eigenvals(multiple=True)
        gstar_signature_: list = [np.sign(ev_) for ev_ in gstar_eigenvals_]
        yield(betas_, gstar_signature_,)

make_rays 

make_rays(rsm: RichterSlopeModel, beta: NDArray) -> tuple[NDArray, NDArray]

XXXX

Parameters

XXX

Attributes

TBD

Returns

XXX

Source code in erosionfront/theory/numerical.py 
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def make_rays(
        rsm: RichterSlopeModel, 
        beta: NDArray,
    ) -> tuple[NDArray,NDArray]:
    """
    XXXX

    Parameters
    ----------
    XXX

    Attributes
    ----------
    TBD

    Returns
    -------
    XXX
    """
    # Just for the record, these are not simply 1/px, 1/pz
    vx: NDArray = rsm.vx_lambda(beta) 
    vz: NDArray = rsm.vz_lambda(beta)
    return (vx,vz,)