[Scipy-svn] r4466 - trunk/scipy/integrate
scipy-svn at scipy.org
scipy-svn at scipy.org
Mon Jun 23 16:53:30 EDT 2008
Author: ptvirtan
Date: 2008-06-23 15:53:22 -0500 (Mon, 23 Jun 2008)
New Revision: 4466
Modified:
trunk/scipy/integrate/odepack.py
Log:
Reformat integrate.odeint docstring
Modified: trunk/scipy/integrate/odepack.py
===================================================================
--- trunk/scipy/integrate/odepack.py 2008-06-23 14:37:03 UTC (rev 4465)
+++ trunk/scipy/integrate/odepack.py 2008-06-23 20:53:22 UTC (rev 4466)
@@ -21,96 +21,115 @@
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.
- 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,...)
- 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.
+ where y can be a vector.
- Inputs:
+ Parameters
+ ----------
+ func : callable(y, t0, ...)
+ Computes the derivative of y at t0.
+ y0 : array
+ Initial condition on y (can be a vector).
+ t : array
+ A sequence of time points for which to solve for y. The initial
+ value point should be the first element of this sequence.
+ args : tuple
+ Extra arguments to pass to function.
+ Dfun : callable(y, t0, ...)
+ Gradient (Jacobian) of func.
+ col_deriv : boolean
+ True if Dfun defines derivatives down columns (faster),
+ otherwise Dfun should define derivatives across rows.
+ full_output : boolean
+ True if to return a dictionary of optional outputs as the second output
+ printmessg : boolean
+ Whether to print the convergence message
- 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.
+ Returns
+ -------
+ y : array, shape (len(y0), len(t))
+ Array containing the value of y for each desired time in t,
+ with the initial value y0 in the first row.
+
+ infodict : dict, only returned if full_output == True
+ Dictionary containing additional output information
+
+ ======= ============================================================
+ 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.
+ (will always be at least as large as the input times).
+ 'tolsf' vector of tolerance scale factors, greater than 1.0,
+ computed when a request for too much accuracy was detected.
+ 'tsw' value of t at the time of the last method switch
+ (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
+ 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)
+ ======= ============================================================
+
+ Other Parameters
+ ----------------
+ ml, mu : integer
+ 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) * (ml + mu + 1) when ml >=0 or mu >=0
+ rtol, atol : float
+ The input parameters rtol and atol determine the error
+ 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 : array
+ Vector of critical points (e.g. singularities) where integration
+ care should be taken.
+ h0 : float, (0: solver-determined)
+ The step size to be attempted on the first step.
+ hmax : float, (0: solver-determined)
+ The maximum absolute step size allowed.
+ hmin : float, (0: solver-determined)
+ The minimum absolute step size allowed.
+ ixpr : boolean
+ Whether to generate extra printing at method switches.
+ mxstep : integer, (0: solver-determined)
+ Maximum number of (internally defined) steps allowed for each
+ integration point in t.
+ mxhnil : integer, (0: solver-determined)
+ Maximum number of messages printed.
+ mxordn : integer, (0: solver-determined)
+ Maximum order to be allowed for the nonstiff (Adams) method.
+ mxords : integer, (0: solver-determined)
+ Maximum order to be allowed for the stiff (BDF) method.
- 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)
-
- 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
+ See Also
+ --------
+ ode : a more object-oriented integrator based on VODE
+ quad : for finding the area under a curve
+
"""
if ml is None:
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