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File: /home/ethan/software/sage-4.6.2-linux-32bit-ubuntu_10.04_lts-i686-Linux-i686-Linux/local/lib/python2.6/site-packages/scipy/integrate/odepack.py

Type: <type ‘function’>

Definition: slv.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)

Docstring:

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Integrate a system of ordinary differential equations.
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Solve a system of ordinary differential equations using lsoda from the\nFORTRAN library odepack.
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Solves the initial value problem for stiff or non-stiff systems\nof first order ode-s:
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dy/dt = func(y,t0,...)\n
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where y can be a vector.
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func : callable(y, t0, ...)
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Computes the derivative of y at t0.
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y0 : array
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Initial condition on y (can be a vector).
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t : array
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A sequence of time points for which to solve for y. The initial\nvalue point should be the first element of this sequence.
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args : tuple
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Extra arguments to pass to function.
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Dfun : callable(y, t0, ...)
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Gradient (Jacobian) of func.
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col_deriv : boolean
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True if Dfun defines derivatives down columns (faster),\notherwise Dfun should define derivatives across rows.
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full_output : boolean
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True if to return a dictionary of optional outputs as the second output
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printmessg : boolean
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Whether to print the convergence message
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y : array, shape (len(y0), len(t))
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Array containing the value of y for each desired time in t,\nwith the initial value y0 in the first row.
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infodict : dict, only returned if full_output == True
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Dictionary containing additional output information
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key meaning
‘hu’ vector of step sizes successfully used for each time step.
‘tcur’ vector with the value of t reached for each time step.\n(will always be at least as large as the input times).
‘tolsf’ vector of tolerance scale factors, greater than 1.0,\ncomputed when a request for too much accuracy was detected.
‘tsw’ value of t at the time of the last method switch\n(given for each time step)
‘nst’ cumulative number of time steps
‘nfe’ cumulative number of function evaluations for each time step
‘nje’ 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\nweighted local error vector (e / ewt) on an error return, -1\notherwise.
‘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:\n1: adams (nonstiff), 2: bdf (stiff)
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ml, mu : integer
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If either of these are not-None or non-negative, then the\nJacobian is assumed to be banded. These give the number of\nlower and upper non-zero diagonals in this banded matrix.\nFor the banded case, Dfun should return a matrix whose\ncolumns contain the non-zero bands (starting with the\nlowest diagonal). Thus, the return matrix from Dfun should\nhave shape len(y0) * (ml + mu + 1) when ml >=0 or mu >=0
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rtol, atol : float
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The input parameters rtol and atol determine the error\ncontrol performed by the solver. The solver will control the\nvector, e, of estimated local errors in y, according to an\ninequality of the form max-norm of (e / ewt) <= 1,\nwhere ewt is a vector of positive error weights computed as:\newt = rtol * abs(y) + atol\nrtol and atol can be either vectors the same length as y or scalars.\nDefaults to 1.49012e-8.
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tcrit : array
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Vector of critical points (e.g. singularities) where integration\ncare should be taken.
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h0 : float, (0: solver-determined)
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The step size to be attempted on the first step.
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hmax : float, (0: solver-determined)
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The maximum absolute step size allowed.
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hmin : float, (0: solver-determined)
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The minimum absolute step size allowed.
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ixpr : boolean
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Whether to generate extra printing at method switches.
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mxstep : integer, (0: solver-determined)
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Maximum number of (internally defined) steps allowed for each\nintegration point in t.
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mxhnil : integer, (0: solver-determined)
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Maximum number of messages printed.
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mxordn : integer, (0: solver-determined)
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Maximum order to be allowed for the nonstiff (Adams) method.
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mxords : integer, (0: solver-determined)
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Maximum order to be allowed for the stiff (BDF) method.
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ode : a more object-oriented integrator based on VODE\nquad : for finding the area under a curve
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key	meaning
‘hu’	vector of step sizes successfully used for each time step.
‘tcur’	vector with the value of t reached for each time step.\n(will always be at least as large as the input times).
‘tolsf’	vector of tolerance scale factors, greater than 1.0,\ncomputed when a request for too much accuracy was detected.
‘tsw’	value of t at the time of the last method switch\n(given for each time step)
‘nst’	cumulative number of time steps
‘nfe’	cumulative number of function evaluations for each time step
‘nje’	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\nweighted local error vector (e / ewt) on an error return, -1\notherwise.
‘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:\n1: adams (nonstiff), 2: bdf (stiff)