## Automatically adapted for scipy Oct 21, 2005 by
# Author: Travis Oliphant
# Modified: Michael Forbes
__all__ = ['odeint']
import scipy.integrate._odepack as _odepack
from copy import copy
_msgs = {2: "Integration successful.",
-1: "Excess work done on this call (perhaps wrong Dfun type).",
-2: "Excess accuracy requested (tolerances too small).",
-3: "Illegal input detected (internal error).",
-4: "Repeated error test failures (internal error).",
-5: "Repeated convergence failures (perhaps bad Jacobian or tolerances).",
-6: "Error weight became zero during problem.",
-7: "Internal workspace insufficient to finish (internal error)."
}
[docs]def odeint(func, y0, t, args=(), Dfun=None, col_deriv=0, full_output=0,
ml=None, mu=None, rtol=None, atol=None, tcrit=None, h0=0.0,
hmax=0.0, hmin=0.0, ixpr=0, mxstep=0, mxhnil=0, mxordn=12,
mxords=5, printmessg=0):
"""Integrate a system of ordinary differential equations.
Description:
Solve a system of ordinary differential equations Using lsoda from the
FORTRAN library odepack.
Solves the initial value problem for stiff or non-stiff systems
of first order ode-s:
dy/dt = func(y,t0,...) where y can be a vector.
Inputs:
func -- func(y,t0,...) computes the derivative of y at t0.
y0 -- initial condition on y (can be a vector).
t -- a sequence of time points for which to solve for y. The intial
value point should be the first element of this sequence.
args -- extra arguments to pass to function.
Dfun -- the gradient (Jacobian) of func (same input signature as func).
col_deriv -- non-zero implies that Dfun defines derivatives down
columns (faster), otherwise Dfun should define derivatives
across rows.
full_output -- non-zero to return a dictionary of optional outputs as
the second output.
printmessg -- print the convergence message.
Outputs: (y, {infodict,})
y -- a rank-2 array containing the value of y in each row for each
desired time in t (with the initial value y0 in the first row).
infodict -- a dictionary of optional outputs:
'hu' : a vector of step sizes successfully used for each time step.
'tcur' : a vector with the value of t reached for each time step.
(will always be at least as large as the input times).
'tolsf' : a vector of tolerance scale factors, greater than 1.0,
computed when a request for too much accuracy was detected.
'tsw' : the value of t at the time of the last method switch
(given for each time step).
'nst' : the cumulative number of time steps.
'nfe' : the cumulative number of function evaluations for eadh
time step.
'nje' : the cumulative number of jacobian evaluations for each
time step.
'nqu' : a vector of method orders for each successful step.
'imxer' : index of the component of largest magnitude in the
weighted local error vector (e / ewt) on an error return.
'lenrw' : the length of the double work array required.
'leniw' : the length of integer work array required.
'mused' : a vector of method indicators for each successful time step:
1 -- adams (nonstiff)
2 -- bdf (stiff)
'istate': Exit status:
1 -- nothing was done, as tout was equal to t with
istate = 1 on input. (however, an internal counter was
set to detect and prevent repeated calls of this type.)
2 -- the integration was performed successfully.
-1 -- an excessive amount of work (more than mxstep
steps) was done on this call, before completing the
requested task, but the integration was otherwise
successful as far as t. (mxstep is an optional input
and is normally 500.) to continue, the user may
simply reset istate to a value .gt. 1 and call again
(the excess work step counter will be reset to 0).
in addition, the user may increase mxstep to avoid
this error return (see below on optional inputs).
-2 -- too much accuracy was requested for the precision
of the machine being used. this was detected before
completing the requested task, but the integration
was successful as far as t. to continue, the tolerance
parameters must be reset, and istate must be set
to 3. the optional output tolsf may be used for this
purpose. (note.. if this condition is detected before
taking any steps, then an illegal input return
(istate = -3) occurs instead.)
-3 -- illegal input was detected, before taking any
integration steps. see written message for details.
note.. if the solver detects an infinite loop of calls
to the solver with illegal input, it will cause
the run to stop.
-4 -- there were repeated error test failures on
one attempted step, before completing the requested
task, but the integration was successful as far as t.
the problem may have a singularity, or the input
may be inappropriate.
-5 -- there were repeated convergence test failures on
one attempted step, before completing the requested
task, but the integration was successful as far as t.
this may be caused by an inaccurate jacobian matrix,
if one is being used.
-6 -- ewt(i) became zero for some i during the
integration. pure relative error control (atol(i)=0.0)
was requested on a variable which has now vanished.
the integration was successful as far as t.
-7 -- the length of rwork and/or iwork was too small to
proceed, but the integration was successful as far as t.
this happens when lsoda chooses to switch methods
but lrw and/or liw is too small for the new method.
Additional Inputs:
ml, mu -- If either of these are not-None or non-negative, then the
Jacobian is assumed to be banded. These give the number of
lower and upper non-zero diagonals in this banded matrix.
For the banded case, Dfun should return a matrix whose
columns contain the non-zero bands (starting with the
lowest diagonal). Thus, the return matrix from Dfun should
have shape len(y0) x (ml + mu + 1) when ml >=0 or mu >=0
rtol -- The input parameters rtol and atol determine the error
atol control performed by the solver. The solver will control the
vector, e, of estimated local errors in y, according to an
inequality of the form
max-norm of (e / ewt) <= 1
where ewt is a vector of positive error weights computed as
ewt = rtol * abs(y) + atol
rtol and atol can be either vectors the same length as y or
scalars.
tcrit -- a vector of critical points (e.g. singularities) where
integration care should be taken.
(For the next inputs a zero default means the solver determines it).
h0 -- the step size to be attempted on the first step.
hmax -- the maximum absolute step size allowed.
hmin -- the minimum absolute step size allowed.
ixpr -- non-zero to generate extra printing at method switches.
mxstep -- maximum number of (internally defined) steps allowed
for each integration point in t.
mxhnil -- maximum number of messages printed.
mxordn -- maximum order to be allowed for the nonstiff (Adams) method.
mxords -- maximum order to be allowed for the stiff (BDF) method.
See also:
ode - a more object-oriented integrator based on VODE
quad - for finding the area under a curve
"""
if ml is None:
ml = -1 # changed to zero inside function call
if mu is None:
mu = -1 # changed to zero inside function call
t = copy(t)
y0 = copy(y0)
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)
if printmessg:
if output[-1] < 0:
print _msgs[output[-1]]
print "Run with full_output = 1 to get quantitative information."
else:
print _msgs[output[-1]]
if full_output:
output[1]['message'] = _msgs[output[-1]]
output[1]['istate'] = output[-1]
output = output[:-1]
if len(output) == 1:
return output[0]
else:
return output