Source code for sympy.vector.dyadic

from sympy.vector.basisdependent import (BasisDependent, BasisDependentAdd,
                                         BasisDependentMul, BasisDependentZero)
from sympy.core import S, Pow
from sympy.core.expr import AtomicExpr
from sympy import ImmutableMatrix as Matrix
import sympy.vector


[docs]class Dyadic(BasisDependent): """ Super class for all Dyadic-classes. References ========== .. [1] http://en.wikipedia.org/wiki/Dyadic_tensor .. [2] Kane, T., Levinson, D. Dynamics Theory and Applications. 1985 McGraw-Hill """ _op_priority = 13.0 @property def components(self): """ Returns the components of this dyadic in the form of a Python dictionary mapping BaseDyadic instances to the corresponding measure numbers. """ # The '_components' attribute is defined according to the # subclass of Dyadic the instance belongs to. return self._components
[docs] def dot(self, other): """ Returns the dot product(also called inner product) of this Dyadic, with another Dyadic or Vector. If 'other' is a Dyadic, this returns a Dyadic. Else, it returns a Vector (unless an error is encountered). Parameters ========== other : Dyadic/Vector The other Dyadic or Vector to take the inner product with Examples ======== >>> from sympy.vector import CoordSys3D >>> N = CoordSys3D('N') >>> D1 = N.i.outer(N.j) >>> D2 = N.j.outer(N.j) >>> D1.dot(D2) (N.i|N.j) >>> D1.dot(N.j) N.i """ Vector = sympy.vector.Vector if isinstance(other, BasisDependentZero): return Vector.zero elif isinstance(other, Vector): outvec = Vector.zero for k, v in self.components.items(): vect_dot = k.args[1].dot(other) outvec += vect_dot * v * k.args[0] return outvec elif isinstance(other, Dyadic): outdyad = Dyadic.zero for k1, v1 in self.components.items(): for k2, v2 in other.components.items(): vect_dot = k1.args[1].dot(k2.args[0]) outer_product = k1.args[0].outer(k2.args[1]) outdyad += vect_dot * v1 * v2 * outer_product return outdyad else: raise TypeError("Inner product is not defined for " + str(type(other)) + " and Dyadics.")
def __and__(self, other): return self.dot(other) __and__.__doc__ = dot.__doc__
[docs] def cross(self, other): """ Returns the cross product between this Dyadic, and a Vector, as a Vector instance. Parameters ========== other : Vector The Vector that we are crossing this Dyadic with Examples ======== >>> from sympy.vector import CoordSys3D >>> N = CoordSys3D('N') >>> d = N.i.outer(N.i) >>> d.cross(N.j) (N.i|N.k) """ Vector = sympy.vector.Vector if other == Vector.zero: return Dyadic.zero elif isinstance(other, Vector): outdyad = Dyadic.zero for k, v in self.components.items(): cross_product = k.args[1].cross(other) outer = k.args[0].outer(cross_product) outdyad += v * outer return outdyad else: raise TypeError(str(type(other)) + " not supported for " + "cross with dyadics")
def __xor__(self, other): return self.cross(other) __xor__.__doc__ = cross.__doc__
[docs] def to_matrix(self, system, second_system=None): """ Returns the matrix form of the dyadic with respect to one or two coordinate systems. Parameters ========== system : CoordSys3D The coordinate system that the rows and columns of the matrix correspond to. If a second system is provided, this only corresponds to the rows of the matrix. second_system : CoordSys3D, optional, default=None The coordinate system that the columns of the matrix correspond to. Examples ======== >>> from sympy.vector import CoordSys3D >>> N = CoordSys3D('N') >>> v = N.i + 2*N.j >>> d = v.outer(N.i) >>> d.to_matrix(N) Matrix([ [1, 0, 0], [2, 0, 0], [0, 0, 0]]) >>> from sympy import Symbol >>> q = Symbol('q') >>> P = N.orient_new_axis('P', q, N.k) >>> d.to_matrix(N, P) Matrix([ [ cos(q), -sin(q), 0], [2*cos(q), -2*sin(q), 0], [ 0, 0, 0]]) """ if second_system is None: second_system = system return Matrix([i.dot(self).dot(j) for i in system for j in second_system]).reshape(3, 3)
class BaseDyadic(Dyadic, AtomicExpr): """ Class to denote a base dyadic tensor component. """ def __new__(cls, vector1, vector2): Vector = sympy.vector.Vector BaseVector = sympy.vector.BaseVector VectorZero = sympy.vector.VectorZero # Verify arguments if not isinstance(vector1, (BaseVector, VectorZero)) or \ not isinstance(vector2, (BaseVector, VectorZero)): raise TypeError("BaseDyadic cannot be composed of non-base " + "vectors") # Handle special case of zero vector elif vector1 == Vector.zero or vector2 == Vector.zero: return Dyadic.zero # Initialize instance obj = super(BaseDyadic, cls).__new__(cls, vector1, vector2) obj._base_instance = obj obj._measure_number = 1 obj._components = {obj: S(1)} obj._sys = vector1._sys obj._pretty_form = (u'(' + vector1._pretty_form + '|' + vector2._pretty_form + ')') obj._latex_form = ('(' + vector1._latex_form + "{|}" + vector2._latex_form + ')') return obj def __str__(self, printer=None): return "(" + str(self.args[0]) + "|" + str(self.args[1]) + ")" _sympystr = __str__ _sympyrepr = _sympystr class DyadicMul(BasisDependentMul, Dyadic): """ Products of scalars and BaseDyadics """ def __new__(cls, *args, **options): obj = BasisDependentMul.__new__(cls, *args, **options) return obj @property def base_dyadic(self): """ The BaseDyadic involved in the product. """ return self._base_instance @property def measure_number(self): """ The scalar expression involved in the definition of this DyadicMul. """ return self._measure_number class DyadicAdd(BasisDependentAdd, Dyadic): """ Class to hold dyadic sums """ def __new__(cls, *args, **options): obj = BasisDependentAdd.__new__(cls, *args, **options) return obj def __str__(self, printer=None): ret_str = '' items = list(self.components.items()) items.sort(key=lambda x: x[0].__str__()) for k, v in items: temp_dyad = k * v ret_str += temp_dyad.__str__(printer) + " + " return ret_str[:-3] __repr__ = __str__ _sympystr = __str__ class DyadicZero(BasisDependentZero, Dyadic): """ Class to denote a zero dyadic """ _op_priority = 13.1 _pretty_form = u'(0|0)' _latex_form = r'(\mathbf{\hat{0}}|\mathbf{\hat{0}})' def __new__(cls): obj = BasisDependentZero.__new__(cls) return obj def _dyad_div(one, other): """ Helper for division involving dyadics """ if isinstance(one, Dyadic) and isinstance(other, Dyadic): raise TypeError("Cannot divide two dyadics") elif isinstance(one, Dyadic): return DyadicMul(one, Pow(other, S.NegativeOne)) else: raise TypeError("Cannot divide by a dyadic") Dyadic._expr_type = Dyadic Dyadic._mul_func = DyadicMul Dyadic._add_func = DyadicAdd Dyadic._zero_func = DyadicZero Dyadic._base_func = BaseDyadic Dyadic._div_helper = _dyad_div Dyadic.zero = DyadicZero()