Python sympy.Derivative方法代碼示例

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Derivative [as 別名]
def test_oprint():
    s = io.StringIO()
    with contextlib.redirect_stdout(s):
        oprint(
            'int', 1,
            'dictionary', dict(a=1, b=2),
            'set', {1},
            'tuple', (1, 2),
            'list', [1, 2, 3],
            'str', 'a quote: "',
            'deriv', Derivative(Symbol('x'), Symbol('x'), evaluate=False),
        )

    if has_ordered_dictionaries:
        assert s.getvalue() == textwrap.dedent("""\
            int        = 1
            dictionary = {a: 1, b: 2}
            set        = {1}
            tuple      = (1, 2)
            list       = [1, 2, 3]
            str        = a quote: "
            deriv      = D{x}x
            """) 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Derivative [as 別名]
def variables(self):
        """
        Returns the variables with which the function in the specified
        arbitrary expression is evaluated

        Examples
        ========

        >>> from sympsi.operator import DifferentialOperator
        >>> from sympy import Symbol, Function, Derivative
        >>> x = Symbol('x')
        >>> f = Function('f')
        >>> d = DifferentialOperator(1/x*Derivative(f(x), x), f(x))
        >>> d.variables
        (x,)
        >>> y = Symbol('y')
        >>> d = DifferentialOperator(Derivative(f(x, y), x) +
        ...                          Derivative(f(x, y), y), f(x, y))
        >>> d.variables
        (x, y)
        """

        return self.args[-1].args 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Derivative [as 別名]
def function(self):
        """
        Returns the function which is to be replaced with the Wavefunction

        Examples
        ========

        >>> from sympsi.operator import DifferentialOperator
        >>> from sympy import Function, Symbol, Derivative
        >>> x = Symbol('x')
        >>> f = Function('f')
        >>> d = DifferentialOperator(Derivative(f(x), x), f(x))
        >>> d.function
        f(x)
        >>> y = Symbol('y')
        >>> d = DifferentialOperator(Derivative(f(x, y), x) +
        ...                          Derivative(f(x, y), y), f(x, y))
        >>> d.function
        f(x, y)
        """

        return self.args[-1] 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Derivative [as 別名]
def expr(self):
        """
        Returns the arbitary expression which is to have the Wavefunction
        substituted into it

        Examples
        ========

        >>> from sympsi.operator import DifferentialOperator
        >>> from sympy import Function, Symbol, Derivative
        >>> x = Symbol('x')
        >>> f = Function('f')
        >>> d = DifferentialOperator(Derivative(f(x), x), f(x))
        >>> d.expr
        Derivative(f(x), x)
        >>> y = Symbol('y')
        >>> d = DifferentialOperator(Derivative(f(x, y), x) +
        ...                          Derivative(f(x, y), y), f(x, y))
        >>> d.expr
        Derivative(f(x, y), x) + Derivative(f(x, y), y)
        """

        return self.args[0] 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Derivative [as 別名]
def __new__(cls, expr, *dims, **kwargs):
        if type(expr) == sympy.Derivative:
            raise ValueError("Cannot nest sympy.Derivative with devito.Derivative")
        if not isinstance(expr, Differentiable):
            raise ValueError("`expr` must be a Differentiable object")

        new_dims, orders, fd_o, var_count = cls._process_kwargs(expr, *dims, **kwargs)

        # Construct the actual Derivative object
        obj = Differentiable.__new__(cls, expr, *var_count)
        obj._dims = tuple(OrderedDict.fromkeys(new_dims))

        skip = kwargs.get('preprocessed', False) or obj.ndims == 1

        obj._fd_order = fd_o if skip else DimensionTuple(*fd_o, getters=obj._dims)
        obj._deriv_order = orders if skip else DimensionTuple(*orders, getters=obj._dims)
        obj._side = kwargs.get("side")
        obj._transpose = kwargs.get("transpose", direct)
        obj._subs = as_tuple(kwargs.get("subs"))
        obj._x0 = kwargs.get('x0', None)
        return obj 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Derivative [as 別名]
def __call__(self, x0=None, fd_order=None, side=None):
        if self.ndims == 1:
            _fd_order = fd_order or self._fd_order
            _side = side or self._side
            new_x0 = {self.dims[0]: x0} if x0 is not None else self.x0
            return self._new_from_self(fd_order=_fd_order, side=_side, x0=new_x0)

        if side is not None:
            raise TypeError("Side only supported for first order single"
                            "Dimension derivative such as `.dxl` or .dx(side=left)")
        # Cross derivative
        _x0 = self._x0 or {}
        _fd_order = dict(self.fd_order._getters)
        try:
            _fd_order.update(**(fd_order or {}))
            _fd_order = tuple(_fd_order.values())
            _fd_order = DimensionTuple(*_fd_order, getters=self.dims)
            _x0.update(x0)
        except AttributeError:
            raise TypeError("Multi-dimensional Derivative, input expected as a dict")

        return self._new_from_self(fd_order=_fd_order, x0=_x0) 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Derivative [as 別名]
def find_functions(expr):
    f_lst = []
    for f in list(expr.atoms(Function)):
        if str(f) not in GaPrinter.function_names:
            f_lst.append(f)
    f_lst += list(expr.atoms(Derivative))
    return f_lst 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Derivative [as 別名]
def __init__(self, base=None, fct=None, deriv=None, on=True, debug=False):
        if on:
            OS = 'unix'
            if 'win' in sys.platform and 'darwin' not in sys.platform:
                OS = 'win'

            if base is None:
                Eprint.base = Eprint.ColorCode[Eprint.defaults[(OS, 'base')]]
            else:
                Eprint.base = Eprint.ColorCode[base]
            if fct is None:
                Eprint.fct = Eprint.ColorCode[Eprint.defaults[(OS, 'fct')]]
            else:
                Eprint.fct = Eprint.ColorCode[fct]
            if deriv is None:
                Eprint.deriv = Eprint.ColorCode[Eprint.defaults[(OS, 'deriv')]]
            else:
                Eprint.deriv = Eprint.ColorCode[deriv]
            Eprint.normal = '\033[0m'

            if debug:
                print('Enhanced Printing is on:')
                print('Base/Blade color is ' + Eprint.InvColorCode[Eprint.base])
                print('Function color is ' + Eprint.InvColorCode[Eprint.fct])
                print('Derivative color is ' + Eprint.InvColorCode[Eprint.deriv] + '\n')

            Eprint.base = '\033[' + Eprint.base + 'm'
            Eprint.fct = '\033[' + Eprint.fct + 'm'
            Eprint.deriv = '\033[' + Eprint.deriv + 'm' 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Derivative [as 別名]
def _eval_derivative(self, symbol):
        new_expr = Derivative(self.expr, symbol)
        return DifferentialOperator(new_expr, self.args[-1])

    #-------------------------------------------------------------------------
    # Printing
    #------------------------------------------------------------------------- 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Derivative [as 別名]
def diff(self, *symbols, **assumptions):
        """
        Like ``sympy.diff``, but return a ``devito.Derivative`` instead of a
        ``sympy.Derivative``.
        """
        from devito.finite_differences.derivative import Derivative
        return Derivative(self, *symbols, **assumptions) 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Derivative [as 別名]
def _new_from_self(self, **kwargs):
        _kwargs = {'deriv_order': self.deriv_order, 'fd_order': self.fd_order,
                   'side': self.side, 'transpose': self.transpose, 'subs': self._subs,
                   'x0': self.x0, 'preprocessed': True}
        expr = kwargs.pop('expr', self.expr)
        _kwargs.update(**kwargs)
        return Derivative(expr, *self.dims, **_kwargs) 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Derivative [as 別名]
def _eval_fd(self, expr):
        """
        Evaluate finite difference approximation of the Derivative.
        Evaluation is carried out via the following four steps:
        - 1: Evaluate derivatives within the expression. For example given
        `f.dx * g`, `f.dx` will be evaluated first.
        - 2: Evaluate the finite difference for the (new) expression.
        - 3: Evaluate remaining terms (as `g` may need to be evaluated
        at a different point).
        - 4: Apply substitutions.

        """
        # Step 1: Evaluate derivatives within expression
        expr = getattr(expr, '_eval_deriv', expr)

        # Step 2: Evaluate FD of the new expression
        if self.side is not None and self.deriv_order == 1:
            res = first_derivative(expr, self.dims[0], self.fd_order,
                                   side=self.side, matvec=self.transpose,
                                   x0=self.x0)
        elif len(self.dims) > 1:
            res = cross_derivative(expr, self.dims, self.fd_order, self.deriv_order,
                                   matvec=self.transpose, x0=self.x0)
        else:
            res = generic_derivative(expr, *self.dims, self.fd_order, self.deriv_order,
                                     matvec=self.transpose, x0=self.x0)

        # Step 3: Evaluate remaining part of expression
        res = res.evaluate

        # Step 4: Apply substitution
        for e in self._subs:
            res = res.xreplace(e)
        return res 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Derivative [as 別名]
def ordered_symbols(self):
        """
        :return: list of all symbols in this model, topologically sorted so they
            can be evaluated in the correct order.

            Within each group of equal priority symbols, we sort by the order of
            the derivative.
        """
        key_func = lambda s: [isinstance(s, sympy.Derivative),
                           isinstance(s, sympy.Derivative) and s.derivative_count]
        symbols = []
        for symbol in toposort(self.connectivity_mapping):
            symbols.extend(sorted(symbol, key=key_func))

        return symbols 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Derivative [as 別名]
def _partial_diff(var, *params):
    """
    Sympy does not handle repeated partial derivation correctly, e.g.
    D(D(y, a), a) = D(y, a, a) but D(D(y, a), b) = 0.
    Use this function instead to prevent evaluation to zero.
    """
    if isinstance(var, sympy.Derivative):
        return sympy.Derivative(var.expr, *(var.variables + params))
    else:
        return D(var, *params) 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import Derivative [as 別名]
def _partial_subs(func, func2vars):
    """
    Partial-bug proof substitution. Works by making the substitutions on
    the expression inside the derivative first, and then rebuilding the
    derivative safely without evaluating it using `_partial_diff`.
    """
    if isinstance(func, sympy.Derivative):
        new_func = func.expr.xreplace(func2vars)
        new_variables = tuple(var.xreplace(func2vars)
                              for var in func.variables)
        return _partial_diff(new_func, *new_variables)
    else:
        return func.xreplace(func2vars)