pxpoly.py¶
Equation definitions and derivations using SymPy.
- class gme.core.pxpoly.PxpolyMixin¶
Polynomial \(p_x\) eqns supplement to equation definition class.
- define_px_poly_eqn(eta_choice: Optional[sympy.core.numbers.Rational] = None, do_ndim: bool = False) → None¶
Define \(p_x\) polynomial.
TODO: remove ref to xiv_0
Define polynomial form of function combining normal-slowness covector components \((p_x,p_z)\) (where the latter is given in terms of the vertical erosion rate \(\xi^{\downarrow} = -\dfrac{1}{p_z}\)) and the erosion model flow component \(\varphi(\mathbf{r})\)
- Parameters
eta_choice (
Rational) – value of \(\eta\) to use instead value given at instantiation; otherwise the latter value is used
- poly_px_xiv_varphi_eqn¶
\(\operatorname{Poly}{\left( \left(\xi^{\downarrow}\right)^{4} \varphi^{4}{\left(\mathbf{r} \right)} p_{x}^{6} - \left(\xi^{\downarrow}\right)^{4} p_{x}^{2} - \left(\xi^{\downarrow}\right)^{2}, p_{x}, domain=\mathbb{Z}\left[\varphi{\left(\mathbf{r} \right)}, \xi^{\downarrow}\right] \right)}\)
- Type
Code¶
"""
Equation definitions and derivations using :mod:`SymPy <sympy>`.
---------------------------------------------------------------------
Requires Python packages/modules:
- :mod:`SymPy <sympy>`
- `GMPLib`_
- `GME`_
.. _GMPLib: https://github.com/geomorphysics/GMPLib
.. _GME: https://github.com/geomorphysics/GME
.. _Matrix:
https://docs.sympy.org/latest/modules/matrices/immutablematrices.html
---------------------------------------------------------------------
"""
# Disable these pylint errors because it doesn't understand SymPy syntax
# - notably minus signs in equations flag an error
# pylint: disable=invalid-unary-operand-type, not-callable
# Library
import warnings
import logging
# from typing import Dict, Type, Optional # , Tuple, Eq, List
# SymPy
from sympy import (
Eq,
Rational,
simplify,
solve,
numer,
denom,
separatevars,
poly,
)
# GMPLib
from gmplib.utils import e2d
# GME
from gme.core.symbols import (
px,
eta,
varphi_0,
varphi_r,
rvec,
xiv,
xiv_0,
xih_0,
)
warnings.filterwarnings("ignore")
__all__ = ["PxpolyMixin"]
class PxpolyMixin:
r"""Polynomial :math:`p_x` eqns supplement to equation definition class."""
# Prerequisites
sinCi_xih0_eqn: Eq
px_xiv_varphi_eqn: Eq
varphi_rxhat_eqn: Eq
px_pxhat_eqn: Eq
xiv0_xih0_Ci_eqn: Eq
varphi_rx_eqn: Eq
# Definitions
poly_pxhat_xiv_eqn: Eq
poly_pxhat_xiv0_eqn: Eq
poly_px_xiv_varphi_eqn: Eq
poly_px_xiv_eqn: Eq
poly_px_xiv0_eqn: Eq # HACK
def define_px_poly_eqn(
self, eta_choice: Rational = None, do_ndim: bool = False
) -> None:
r"""
Define :math:`p_x` polynomial.
TODO: remove ref to xiv_0
Define polynomial form of function combining normal-slowness
covector components :math:`(p_x,p_z)`
(where the latter is given in terms of the vertical erosion rate
:math:`\xi^{\downarrow} = -\dfrac{1}{p_z}`)
and the erosion model flow component :math:`\varphi(\mathbf{r})`
Args:
eta_choice (:class:`~sympy.core.numbers.Rational`):
value of :math:`\eta` to use instead value given at
instantiation; otherwise the latter value is used
Attributes:
poly_px_xiv_varphi_eqn (:class:`~sympy.polys.polytools.Poly`):
:math:`\operatorname{Poly}{\left(
\left(\xi^{\downarrow}\right)^{4}
\varphi^{4}{\left(\mathbf{r} \right)} p_{x}^{6}
- \left(\xi^{\downarrow}\right)^{4} p_{x}^{2}
- \left(\xi^{\downarrow}\right)^{2}, p_{x},
domain=\mathbb{Z}\left[\varphi{\left(\mathbf{r} \right)},
\xi^{\downarrow}\right] \right)}`
poly_px_xiv_eqn (:class:`~sympy.core.relational.Equality`):
:math:`\varphi_0^{4}
\left(\xi^{\downarrow{0}}\right)^{4} p_{x}^{6}
\left(\varepsilon
+ \left(\frac{x_{1} - {r}^x}{x_{1}}\right)^{2 \mu}\right)^{4}
- \left(\xi^{\downarrow{0}}\right)^{4} p_{x}^{2}
- \left(\xi^{\downarrow{0}}\right)^{2} = 0`
"""
logging.info(f"gme.core.pxpoly.define_px_poly_eqn (ndim={do_ndim})")
if do_ndim:
# Non-dimensionalized version
varphi0_solns = solve(
self.sinCi_xih0_eqn.subs({eta: eta_choice}), varphi_0
)
varphi0_eqn = Eq(varphi_0, varphi0_solns[0])
if eta_choice is not None and eta_choice <= 1:
tmp_eqn = separatevars(
simplify(
self.px_xiv_varphi_eqn.subs({eta: eta_choice})
.subs({varphi_r(rvec): self.varphi_rxhat_eqn.rhs})
.subs(e2d(self.px_pxhat_eqn))
.subs(e2d(varphi0_eqn))
)
)
self.poly_pxhat_xiv_eqn = simplify(
Eq(
(
numer(tmp_eqn.lhs)
- denom(tmp_eqn.lhs) * (tmp_eqn.rhs)
)
/ xiv ** 2,
0,
)
)
self.poly_pxhat_xiv0_eqn = self.poly_pxhat_xiv_eqn.subs(
{xiv: xiv_0}
).subs(e2d(self.xiv0_xih0_Ci_eqn))
else:
tmp_eqn = separatevars(
simplify(
self.px_xiv_varphi_eqn.subs({eta: eta_choice})
.subs({varphi_r(rvec): self.varphi_rxhat_eqn.rhs})
.subs(e2d(self.px_pxhat_eqn))
.subs(e2d(varphi0_eqn))
)
)
self.poly_pxhat_xiv_eqn = simplify(
Eq(
(
numer(tmp_eqn.lhs)
- denom(tmp_eqn.lhs) * (tmp_eqn.rhs)
)
/ xiv ** 2,
0,
)
)
self.poly_pxhat_xiv0_eqn = simplify(
Eq(
self.poly_pxhat_xiv_eqn.lhs.subs({xiv: xiv_0}).subs(
e2d(self.xiv0_xih0_Ci_eqn)
)
/ xih_0 ** 2,
0,
)
)
else:
# Dimensioned version
tmp_eqn = simplify(self.px_xiv_varphi_eqn.subs({eta: eta_choice}))
if eta_choice is not None and eta_choice <= 1:
self.poly_px_xiv_varphi_eqn = poly(tmp_eqn.lhs, px)
else:
self.poly_px_xiv_varphi_eqn = poly(
numer(tmp_eqn.lhs) - denom(tmp_eqn.lhs) * (tmp_eqn.rhs), px
)
self.poly_px_xiv_eqn = Eq(
self.poly_px_xiv_varphi_eqn.subs(e2d(self.varphi_rx_eqn)), 0
)
#
