Status: Accepted
Owner: ----
Labels: Type-Defect Priority-Medium
New issue 1400 by ondrej.certik: make cse optionally not to generate
subexpressions that are only used once
http://code.google.com/p/sympy/issues/detail?id=1400
Example:
In [1]: a1, a2, a3, a4, a5, a6 =
symbols(["a1", "a2", "a3", "a4", "a5", "a6"])
In [2]: result = sqrt((a1-a4)**2 + (a2-a5)**2 + (a3-a6)**2)
In [3]: grad = [diff(result, s) for s in (a1, a2, a3, a4, a5, a6)]
In [5]: output = [result] + grad
In [7]: cse(output)
Out[7]:
⎛⎡ ⎛ 2⎞ ⎛ 2⎞ ⎛
2⎞
⎜⎢(x₀, a₁ - a₄), (x₁, a₃ - a₆), ⎝x₂, x₁ ⎠, ⎝x₃, x₀ ⎠, (x₄, a₂ - a₅), ⎝x₅,
x₄ ⎠
⎜⎢
⎝⎣
⎛ 1 ⎞⎤ ⎡1
, (x₆, x₂ + x₃ + x₅), ⎜x₇, ──────⎟⎥, ⎢──, x₀⋅x₇, x₄⋅x₇, x₁⋅x₇, x₇⋅(a₄ -
a₁), x
⎜ ⎽⎽⎽⎽⎟⎥ ⎣x₇
⎝ ╲╱ x₆ ⎠⎦
⎤⎞
₇⋅(a₅ - a₂), x₇⋅(a₆ - a₃)⎥⎟
⎦⎟
⎠
The x2, x3 and x5 are only used once. So there should be a parameter to
cse() that would optionally make cse return something like:
(
[
(x0, a1 - a4),
(x1, a3 - a6),
(x3, a2 - a5),
(x7, (x1**2 + x3**2 + x0***2)**(-1/2))
], [
1/x7,
x0*x7,
x3*x7,
x1*x7,
x7*(a4 - a1),
x7*(a5 - a2),
x7*(a6 - a3)
]
)
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