Python sympy.lambdify方法代碼示例

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import lambdify [as 別名]
def testSymbolicDims(self):
    p = builder.Base.Params()
    b = p.Instantiate()

    f1 = tshape.Shape(['kh', 'kw', 'idims', 'odims'])
    kh, kw, idims, odims = f1
    f2 = tshape.Shape([kh, kw, odims, odims])
    p = b._Seq('test', b._Conv2D('conv', f1, (2, 2)),
               b._Conv2D('conv', f2, (2, 2)), b._Bias('bias', odims))

    inp = tshape.Shape(['b', 'h', 'w', idims])
    b, h, w, _ = inp
    meta = p.cls.FPropMeta(p, inp)
    print('flops = ', meta.flops)
    out = meta.out_shapes[0]
    print('outputs = ', out)

    # sympy.lambdify can help us to do faster numerical evaluation.
    # Might be useful to build a "cost" model given a builder layer.
    f = sympy.lambdify([b, h, w, kh, kw, idims, odims], meta.flops, 'numpy')
    print('f.source = ', inspect.getsource(f))
    self.assertEqual(f(8, 224, 224, 3, 3, 8, 32), 925646848)
    self.assertEqual(f(8, 224, 224, 5, 5, 8, 32), 2569814016) 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import lambdify [as 別名]
def EvalExpr(value_type, x):
  """Evaluates x with symbol_to_value_map within the current context.

  Args:
    value_type: the target value type (see VALUE_TYPE).
    x: a sympy.Expr, an object, or a list/tuple of Exprs and objects.

  Returns:
    Evaluation result of 'x'.
  """
  if isinstance(x, (list, tuple)):
    return type(x)(EvalExpr(value_type, y) for y in x)
  elif isinstance(x, sympy.Expr):
    symbol_to_value_map = SymbolToValueMap.Get(value_type)
    if not symbol_to_value_map:
      return x
    # In theory the below should be equivalent to:
    #   y = x.subs(symbol_to_value_map).
    # In practice subs() doesn't work for when values are Tensors.
    k, v = list(zip(*(list(symbol_to_value_map.items()))))
    y = sympy.lambdify(k, x)(*v)
    return y
  else:
    return x 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import lambdify [as 別名]
def get_equations(self):
        """
        :return: Functions to calculate A, B and f given state x and input u
        """
        f = sp.zeros(3, 1)

        x = sp.Matrix(sp.symbols('x y theta', real=True))
        u = sp.Matrix(sp.symbols('v w', real=True))

        f[0, 0] = u[0, 0] * sp.cos(x[2, 0])
        f[1, 0] = u[0, 0] * sp.sin(x[2, 0])
        f[2, 0] = u[1, 0]

        f = sp.simplify(f)
        A = sp.simplify(f.jacobian(x))
        B = sp.simplify(f.jacobian(u))

        f_func = sp.lambdify((x, u), f, 'numpy')
        A_func = sp.lambdify((x, u), A, 'numpy')
        B_func = sp.lambdify((x, u), B, 'numpy')

        return f_func, A_func, B_func 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import lambdify [as 別名]
def get_equations(self):
        """
        :return: Functions to calculate A, B and f given state x and input u
        """
        f = sp.zeros(6, 1)

        x = sp.Matrix(sp.symbols('rx ry vx vy t w', real=True))
        u = sp.Matrix(sp.symbols('gimbal T', real=True))

        f[0, 0] = x[2, 0]
        f[1, 0] = x[3, 0]
        f[2, 0] = 1 / self.m * sp.sin(x[4, 0] + u[0, 0]) * u[1, 0]
        f[3, 0] = 1 / self.m * (sp.cos(x[4, 0] + u[0, 0]) * u[1, 0] - self.m * self.g)
        f[4, 0] = x[5, 0]
        f[5, 0] = 1 / self.I * (-sp.sin(u[0, 0]) * u[1, 0] * self.r_T)

        f = sp.simplify(f)
        A = sp.simplify(f.jacobian(x))
        B = sp.simplify(f.jacobian(u))

        f_func = sp.lambdify((x, u), f, 'numpy')
        A_func = sp.lambdify((x, u), A, 'numpy')
        B_func = sp.lambdify((x, u), B, 'numpy')

        return f_func, A_func, B_func 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import lambdify [as 別名]
def _is_non_decreasing(fn, q, bounds):
  """Verifies whether the function is non-decreasing within a range.

  Args:
    fn: Symbolic function of a single variable.
    q: The name of f's variable.
    bounds: Pair of (lower_bound, upper_bound) reals.

  Returns:
    True iff the function is non-decreasing in the range.
  """
  diff_fn = sp.diff(fn, q)  # Symbolically compute the derivative.
  diff_fn_lambdified = sp.lambdify(
      q,
      diff_fn,
      modules=[
          "numpy", {
              "erfc": scipy.special.erfc,
              "erfcinv": scipy.special.erfcinv
          }
      ])
  r = scipy.optimize.minimize_scalar(
      diff_fn_lambdified, bounds=bounds, method="bounded")
  assert r.success, "Minimizer failed to converge."
  return r.fun >= 0  # Check whether the derivative is non-negative. 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import lambdify [as 別名]
def test_more_than_255_args():
    # SymPy's lambdify can handle at most 255 arguments
    # this is a proof of concept that this limitation does
    # not affect SymEngine's Lambdify class
    n = 257
    x = se.symarray('x', n)
    p, q, r = 17, 42, 13
    terms = [i*s for i, s in enumerate(x, p)]
    exprs = [se.add(*terms), r + x[0], -99]
    callback = se.Lambdify(x, exprs)
    input_arr = np.arange(q, q + n*n).reshape((n, n))
    out = callback(input_arr)
    ref = np.empty((n, 3))
    coeffs = np.arange(p, p + n, dtype=np.int64)
    for i in range(n):
        ref[i, 0] = coeffs.dot(np.arange(q + n*i, q + n*(i+1), dtype=np.int64))
        ref[i, 1] = q + n*i + r
    ref[:, 2] = -99
    assert np.allclose(out, ref) 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import lambdify [as 別名]
def test_call_sim_with_args():
    a, a_unc, b, b_unc = 3.0, 0.1, 4.0, 0.1
    c = f_hypotenuse(a, b)
    m1 = PythagorasModel()
    data = {'PythagorasData': {'a': a, 'b': b, 'a_unc': a_unc, 'b_unc': b_unc}}
    m1.command('run', data=data)
    assert m1.registries['outputs']['c'].m == c
    assert m1.registries['outputs']['c'].u == UREG.cm
    x, y = sympy.symbols('x, y')
    z = sympy.sqrt(x * x + y * y)
    fx = sympy.lambdify((x, y), z.diff(x))
    fy = sympy.lambdify((x, y), z.diff(y))
    dz = np.sqrt(fx(a, b) ** 2 * a_unc ** 2 + fy(a, b) ** 2 * b_unc ** 2)
    c_unc = c * np.sqrt(m1.registries['outputs'].variance['c']['c'])
    LOGGER.debug('uncertainty in c is %g', c_unc)
    assert np.isclose(dz, c_unc.item())
    c_unc = c * m1.registries['outputs'].uncertainty['c']['c'].to('fraction')
    assert np.isclose(dz, c_unc.m.item())
    return m1 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import lambdify [as 別名]
def vectors(self, mesh):
        j, Sig = self.fcts()

        f_jr = sympy.lambdify((r, t, z), j[0], 'numpy')
        f_jt = sympy.lambdify((r, t, z), j[1], 'numpy')
        f_jz = sympy.lambdify((r, t, z), j[2], 'numpy')

        f_sig = sympy.lambdify((r, t, z), Sig[0], 'numpy')

        jr = f_jr(mesh.gridFx[:, 0], mesh.gridFx[:, 1], mesh.gridFx[:, 2])
        jt = f_jt(mesh.gridFy[:, 0], mesh.gridFy[:, 1], mesh.gridFy[:, 2])
        jz = f_jz(mesh.gridFz[:, 0], mesh.gridFz[:, 1], mesh.gridFz[:, 2])

        sig = f_sig(mesh.gridCC[:, 0], mesh.gridCC[:, 1], mesh.gridCC[:, 2])

        return sig, np.r_[jr, jt, jz] 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import lambdify [as 別名]
def set_symbolic_to_numeric_method(method): 
  ''' 
  Sets the method that all RBF instances will use for converting sympy
  expressions to numeric functions. This can be either "ufuncify" or
  "lambdify". "ufuncify" will write and compile C code for a numpy universal
  function, and "lambdify" will evaluate the sympy expression using
  python-level numpy functions. Calling this function will cause all caches of
  numeric functions to be cleared.
  '''
  global _SYMBOLIC_TO_NUMERIC_METHOD
  if method not in {'lambdify', 'ufuncify'}:
    raise ValueError(
      '`method` must be either "lambdify" or "ufuncify"')
            
  _SYMBOLIC_TO_NUMERIC_METHOD = method
  clear_rbf_caches()


## Instantiate some common RBFs
##################################################################### 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import lambdify [as 別名]
def expression_lambda(self) -> Callable:
        if self._expression_lambda is None:
            expression_lambda = sympy.lambdify(self.variables, self.underlying_expression,
                                                     [{'ceiling': ceiling}, 'numpy'])

            @functools.wraps(expression_lambda)
            def expression_wrapper(*args, **kwargs):
                result = expression_lambda(*args, **kwargs)
                if isinstance(result, sympy.NDimArray):
                    return numpy.array(result.tolist())
                elif isinstance(result, list):
                    return numpy.array(result).reshape(self.underlying_expression.shape)
                else:
                    return result.reshape(self.underlying_expression.shape)
            self._expression_lambda = expression_wrapper
        return self._expression_lambda 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import lambdify [as 別名]
def convert_to_function(string: str, scale_by_k=False):
    """Using the sympy module, parse string input
    into a mathematical expression.
    Returns the original string, the latexified string,
    the mathematical expression in terms of sympy symbols,
    and a lambdified function
    """
    string = string.replace("^", "**")
    symbolic_function = parse_expr(string)
    if scale_by_k:
        latexstring = latex(symbolic_function*abc.k)
    else:
        latexstring = latex(symbolic_function)
    lambda_function = lambdify(abc.x, symbolic_function,
                               modules=module_list)
    string = string.replace('*', '')
    latexstring = "$" + latexstring + "$"
    return string, latexstring, \
           symbolic_function, lambda_function 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import lambdify [as 別名]
def __init__(self, num_spherical, num_radial, cutoff=5.0,
                 envelope_exponent=5):
        super(SphericalBasisLayer, self).__init__()
        assert num_radial <= 64
        self.num_spherical = num_spherical
        self.num_radial = num_radial
        self.cutoff = cutoff
        self.envelope = Envelope(envelope_exponent)

        bessel_forms = bessel_basis(num_spherical, num_radial)
        sph_harm_forms = real_sph_harm(num_spherical)
        self.sph_funcs = []
        self.bessel_funcs = []

        x, theta = sym.symbols('x theta')
        modules = {'sin': torch.sin, 'cos': torch.cos}
        for i in range(num_spherical):
            if i == 0:
                sph1 = sym.lambdify([theta], sph_harm_forms[i][0], modules)(0)
                self.sph_funcs.append(lambda x: torch.zeros_like(x) + sph1)
            else:
                sph = sym.lambdify([theta], sph_harm_forms[i][0], modules)
                self.sph_funcs.append(sph)
            for j in range(num_radial):
                bessel = sym.lambdify([x], bessel_forms[i][j], modules)
                self.bessel_funcs.append(bessel) 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import lambdify [as 別名]
def _intensive_output(self):
        """
        :getter: Return vectorized symbolic intensive aggregate production.
        :type: function

        """
        if self.__intensive_output is None:
            args = [k] + sym.symbols(list(self.params.keys()))
            self.__intensive_output = sym.lambdify(args, self.intensive_output,
                                                   self._modules)
        return self.__intensive_output 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import lambdify [as 別名]
def _mpk(self):
        """
        :getter: Return vectorized symbolic marginal product capital.
        :type: function

        """
        if self.__mpk is None:
            args = [k] + sym.symbols(list(self.params.keys()))
            self.__mpk = sym.lambdify(args, self.marginal_product_capital,
                                      self._modules)
        return self.__mpk 

# 需要導入模塊: import sympy [as 別名]
# 或者: from sympy import lambdify [as 別名]
def _numeric_jacobian(self):
        """
        Vectorized, numpy-aware function defining the Jacobian matrix of
        partial derivatives.

        :getter: Return vectorized Jacobian matrix of partial derivatives.
        :type: function

        """
        if self.__numeric_jacobian is None:
            self.__numeric_jacobian = sym.lambdify(self._symbolic_args,
                                                   self._symbolic_jacobian,
                                                   self._modules)
        return self.__numeric_jacobian