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BUG: integrate: Handle y0=[] in odeint. #13278

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BUG: integrate: Handle y0=[] in odeint. #13278

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41 changes: 41 additions & 0 deletions scipy/integrate/odepack.py
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Original file line number Diff line number Diff line change
Expand Up @@ -238,6 +238,19 @@ def odeint(func, y0, t, args=(), Dfun=None, col_deriv=0, full_output=0,

t = copy(t)
y0 = copy(y0)

if np.shape(y0) == (0,):
# y0 is a 1-d sequence with length 0. Handle this edge case here
# instead of passing it to the C code. (The C code can handle a
# scalar, and it will correctly raise an exception if y0.ndim > 1,
# so it is OK to let those cases get passed in.)
n = len(t)
y = np.empty((n, 0))
if full_output:
return y, _make_empty_info(n)
else:
return y

output = _odepack.odeint(func, y0, t, args, Dfun, col_deriv, ml, mu,
full_output, rtol, atol, tcrit, h0, hmax, hmin,
ixpr, mxstep, mxhnil, mxordn, mxords,
Expand All @@ -257,3 +270,31 @@ def odeint(func, y0, t, args=(), Dfun=None, col_deriv=0, full_output=0,
return output[0]
else:
return output


def _make_empty_info(n):
"""
Create an `info` dictionary for the return value of odeint in the
case where y0 has length 0 and full_output is True.
"""
nm1 = n - 1
info = {
'hu': np.zeros(nm1, dtype=np.float64),
'tcur': np.zeros(nm1, dtype=np.float64),
'tolsf': np.zeros(nm1, dtype=np.float64),
'tsw': np.zeros(nm1, dtype=np.float64),
'nst': np.zeros(nm1, dtype=np.int32),
'nfe': np.zeros(nm1, dtype=np.int32),
'nje': np.zeros(nm1, dtype=np.int32),
'nqu': np.zeros(nm1, dtype=np.int32),
'imxer': -1,
'lenrw': 0,
'leniw': 0,
'mused': np.zeros(nm1, dtype=np.int32),
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Is a mused value of zero documented? (I see only 1 is adams, 2 is bdf.)

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I wanted to return an array with the expected shape and dtype for the given length of t, but I didn't think it was meaningful to use the values 1 or 2, since neither method was actually used.

All these arrays of zeros are just placeholders put there for consistency. An alternative approach that is probably justifiable is to put the value None instead of an array. The arrays provide information about the behavior of the solver, and since a solver never ran in this edge case, maybe we shouldn't provide these arrays at all.

}
if nm1 == 0:
info['message'] = 'Nothing was done; the integration time was 0.'
else:
info['message'] = 'Integration successful.'
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@mdhaber mdhaber Dec 21, 2020 •
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Isn't nothing done even in this case? "Integration successful." doesn't sound appropriate to me when there is nothing to integrate.

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@WarrenWeckesser WarrenWeckesser Dec 21, 2020 •
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I'm preserving the invariants where len(t) == 1 gives the message 'Nothing was done...' and len(t) > 1 gives the message 'Integration successful.'. I don't think even this distinction is useful, and I'd be happy to always give a simple "success" message in any case that is not an error, but I'm copying the current behavior for the sake of consistency.


return info
16 changes: 16 additions & 0 deletions scipy/integrate/tests/test_integrate.py
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Original file line number Diff line number Diff line change
Expand Up @@ -669,6 +669,22 @@ def test_odeint_trivial_time():
assert_array_equal(y, np.array([[y0]]))


def test_odeint_empty_y0():
y0 = []
t = [0, 1, 2, 3]

y = odeint(lambda x, t: -x, y0, t)
assert y.shape == (len(t), 0)

y, info = odeint(lambda x, t: -x, y0, t, full_output=True)
assert y.shape == (len(t), 0)
assert info['message'] == 'Integration successful.'

y, info = odeint(lambda x, t: -x, y0, [0], full_output=True)
assert y.shape == (1, 0)
assert info['message'] == 'Nothing was done; the integration time was 0.'


def test_odeint_banded_jacobian():
# Test the use of the `Dfun`, `ml` and `mu` options of odeint.

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