# Copyright (c) 2023, NVIDIA CORPORATION & AFFILIATES. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

"""
Helper functions for converting sympy equations to pytorch
"""

from sympy import lambdify, Symbol, Derivative, Function, Basic, Add, Max, Min
from sympy.printing.str import StrPrinter
import torch
import numpy as np
import functools
from typing import List, Dict

from modulus.sym.constants import diff_str, tf_dt


[docs]def torch_lambdify(f, r, separable=False):
    """
    generates a PyTorch function from a sympy equation

    Parameters
    ----------
    f : Sympy Exp, float, int, bool
      the equation to convert to torch.
      If float, int, or bool this gets converted
      to a constant function of value `f`.
    r : list, dict
      A list of the arguments for `f`. If dict then
      the keys of the dict are used.

    Returns
    -------
    torch_f : PyTorch function
    """

    try:
        f = float(f)
    except:
        pass
    if isinstance(f, (float, int, bool)):  # constant function

        def loop_lambda(constant):
            return lambda **x: torch.zeros_like(next(iter(x.items()))[1]) + constant

        lambdify_f = loop_lambda(f)
    else:
        vars = [k for k in r] if separable else [[k for k in r]]
        try:  # NOTE this fixes a very odd bug in SymPy TODO add issue to SymPy
            lambdify_f = lambdify(vars, f, [TORCH_SYMPY_PRINTER])
        except:
            lambdify_f = lambdify(vars, f, [TORCH_SYMPY_PRINTER])
    return lambdify_f
def _where_torch(conditions, x, y):
    if isinstance(x, (int, float)):
        x = float(x) * torch.ones(*conditions.get_shape())
    if isinstance(y, (int, float)):
        y = float(y) * torch.ones(*conditions.get_shape())
    return torch.where(conditions, x, y)


def _heaviside_torch(x):
    return torch.maximum(torch.sign(x), torch.zeros(1, device=x.device))


def _sqrt_torch(x):
    return torch.sqrt((x - 1e-6) * _heaviside_torch(x - 1e-6) + 1e-6)


# TODO: Add jit version here
def _or_torch(*x):
    return_value = x[0]
    for value in x:
        return_value = torch.logical_or(return_value, value)
    return return_value


# TODO: Add jit version here
def _and_torch(*x):
    return_value = x[0]
    for value in x:
        return_value = torch.logical_and(return_value, value)
    return return_value


@torch.jit.script
def _min_jit(x: List[torch.Tensor]):
    assert len(x) > 0
    min_tensor = x[0]
    for i in range(1, len(x)):
        min_tensor = torch.minimum(min_tensor, x[i])
    return min_tensor


def _min_torch(*x):
    # get tensor shape
    for value in x:
        if not isinstance(value, (int, float)):
            tensor_shape = list(map(int, value.shape))
            device = value.device

    # convert all floats and ints to tensor
    x_only_tensors = []
    for value in x:
        if isinstance(value, (int, float)):
            value = torch.zeros(tensor_shape, device=device) + value
        x_only_tensors.append(value)

    # reduce min
    min_tensor, _ = torch.min(torch.stack(x_only_tensors, -1), -1)
    return min_tensor

    # jit option
    # return _min_jit(x_only_tensors)

    # TODO: benchmark this other option that avoids stacking and extra memory movement
    # Update: cannot jit this because TorchScript doesn't support functools.reduce
    # return functools.reduce(torch.minimum, x)


@torch.jit.script
def _max_jit(x: List[torch.Tensor]):
    assert len(x) > 0
    max_tensor = x[0]
    for i in range(1, len(x)):
        max_tensor = torch.maximum(max_tensor, x[i])
    return max_tensor


def _max_torch(*x):
    # get tensor shape
    for value in x:
        if not isinstance(value, (int, float)):
            tensor_shape = list(map(int, value.shape))
            device = value.device

    # convert all floats and ints to tensor
    x_only_tensors = []
    for value in x:
        if isinstance(value, (int, float)):
            value = (torch.zeros(tensor_shape) + value).to(device)
        x_only_tensors.append(value)

    # reduce max
    max_tensor, _ = torch.max(torch.stack(x_only_tensors, -1), -1)
    return max_tensor

    # jit option
    # return _max_jit(x_only_tensors)


def _dirac_delta_torch(x):
    return torch.eq(x, 0.0).to(tf_dt)


TORCH_SYMPY_PRINTER = {
    "abs": torch.abs,
    "Abs": torch.abs,
    "sign": torch.sign,
    "ceiling": torch.ceil,
    "floor": torch.floor,
    "log": torch.log,
    "exp": torch.exp,
    "sqrt": _sqrt_torch,
    "cos": torch.cos,
    "acos": torch.acos,
    "sin": torch.sin,
    "asin": torch.asin,
    "tan": torch.tan,
    "atan": torch.atan,
    "atan2": torch.atan2,
    "cosh": torch.cosh,
    "acosh": torch.acosh,
    "sinh": torch.sinh,
    "asinh": torch.asinh,
    "tanh": torch.tanh,
    "atanh": torch.atanh,
    "erf": torch.erf,
    "loggamma": torch.lgamma,
    "Min": _min_torch,
    "Max": _max_torch,
    "Heaviside": _heaviside_torch,
    "DiracDelta": _dirac_delta_torch,
    "logical_or": _or_torch,
    "logical_and": _and_torch,
    "where": _where_torch,
    "pi": np.pi,
    "conjugate": torch.conj,
}





[docs]class CustomDerivativePrinter(StrPrinter):
    def _print_Function(self, expr):
        """
        Custom printing of the SymPy Derivative class.
        Instead of:
        D(x(t), t)
        We will print:
        x__t
        """
        return expr.func.__name__

    def _print_Derivative(self, expr):
        """
        Custom printing of the SymPy Derivative class.
        Instead of:
        D(x(t), t)
        We will print:
        x__t
        """
        prefix = str(expr.args[0].func)
        for expr in expr.args[1:]:
            prefix += expr[1] * (diff_str + str(expr[0]))
        return prefix
def _subs_derivatives(expr):
    while True:
        try:
            deriv = expr.atoms(Derivative).pop()
            new_fn_name = str(deriv)
            expr = expr.subs(deriv, Function(new_fn_name)(*deriv.free_symbols))
        except:
            break
    while True:
        try:
            fn = {
                fn for fn in expr.atoms(Function) if fn.class_key()[1] == 0
            }.pop()  # check if standard Sympy Eq (TODO better check)
            new_symbol_name = str(fn)
            expr = expr.subs(fn, Symbol(new_symbol_name))
        except:
            break
    return expr


# Override the __str__ method of to use CustromStrPrinter
Basic.__str__ = lambda self: CustomDerivativePrinter().doprint(self)


# Class to compile and evaluate a sympy expression in PyTorch
# Cannot currently script this module because self.torch_expr is unknown



[docs]class SympyToTorch(torch.nn.Module):
    def __init__(
        self,
        sympy_expr,
        name: str,
        freeze_terms: List[int] = [],
        detach_names: List[str] = [],
    ):
        super().__init__()
        # Sort keys to guarantee ordering
        self.keys = sorted([k.name for k in sympy_expr.free_symbols])
        self.freeze_terms = freeze_terms
        if not self.freeze_terms:
            self.torch_expr = torch_lambdify(sympy_expr, self.keys)
        else:
            assert all(
                x < len(Add.make_args(sympy_expr)) for x in freeze_terms
            ), "The freeze term index cannot be larger than the total terms in the expression"
            self.torch_expr = []
            for i in range(len(Add.make_args(sympy_expr))):
                self.torch_expr.append(
                    torch_lambdify(Add.make_args(sympy_expr)[i], self.keys)
                )
            self.freeze_list = list(self.torch_expr[i] for i in freeze_terms)
        self.name = name
        self.detach_names = detach_names

[docs]    def forward(self, var: Dict[str, torch.Tensor]) -> Dict[str, torch.Tensor]:
        args = [
            var[k].detach() if k in self.detach_names else var[k] for k in self.keys
        ]
        if not self.freeze_terms:
            output = self.torch_expr(args)
        else:
            output = torch.zeros_like(var[self.keys[0]])
            for i, expr in enumerate(self.torch_expr):
                if expr in self.freeze_list:
                    output += expr(args).detach()
                else:
                    output += expr(args)

        return {self.name: output}