I would like to understand how sympy.inverse_laplace_transform is
evaluated, so I attempted to view the source code.
When execute the command:
print(inspect.getsource(sympy.inverse_laplace_transform))
I see the following source code which looks like is is almost all
explanation. ( I don't see the part that actually gets executed to
calculate the inverse Laplace transform. The part at the end where it
says "return InverseLaplaceTransform(F, s, t, plane)" is just to return the
symbolic expression of the integral if it fails to evaluate, the part just
before that doesn't make sense to me where it says: "return
F.applyfunc(lambda Fij: inverse_laplace_transform(Fij, s, t, plane,
**hints)) It doesn't make sense because it refers the the function itself
rather than defining how the function should be calculated. )
Here is the source code for sympy.inverse_laplace_transform:
def inverse_laplace_transform(F, s, t, plane=None, **hints): r""" Compute
the inverse Laplace transform of `F(s)`, defined as .. math :: f(t) =
\frac{1}{2\pi i} \int_{c-i\infty}^{c+i\infty} e^{st} F(s) \mathrm{d}s, for
`c` so large that `F(s)` has no singularites in the half-plane
`\operatorname{Re}(s) > c-\epsilon`. Explanation =========== The plane can
be specified by argument ``plane``, but will be inferred if passed as None.
Under certain regularity conditions, this recovers `f(t)` from its Laplace
Transform `F(s)`, for non-negative `t`, and vice versa. If the integral
cannot be computed in closed form, this function returns an unevaluated
:class:`InverseLaplaceTransform` object. Note that this function will
always assume `t` to be real, regardless of the SymPy assumption on `t`.
For a description of possible hints, refer to the docstring of
:func:`sympy.integrals.transforms.IntegralTransform.doit`. Examples
======== >>> from sympy import inverse_laplace_transform, exp, Symbol >>>
from sympy.abc import s, t >>> a = Symbol('a', positive=True) >>>
inverse_laplace_transform(exp(-a*s)/s, s, t) Heaviside(-a + t) See Also
======== laplace_transform, _fast_inverse_laplace hankel_transform,
inverse_hankel_transform """ if isinstance(F, MatrixBase) and hasattr(F,
'applyfunc'): return F.applyfunc(lambda Fij: inverse_laplace_transform(Fij,
s, t, plane, **hints)) return InverseLaplaceTransform(F, s, t,
plane).doit(**hints)
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