[Scipysvn] r4466  trunk/scipy/integrate
scipysvn@scip...
scipysvn@scip...
Mon Jun 23 15:53:30 CDT 2008
Author: ptvirtan
Date: 20080623 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 20080623 14:37:03 UTC (rev 4465)
+++ trunk/scipy/integrate/odepack.py 20080623 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 nonstiff systems
+ of first order odes::
+
+ dy/dt = func(y,t0,...)
 Solves the initial value problem for stiff or nonstiff systems
 of first order odes:
 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  nonzero implies that Dfun defines derivatives down
 columns (faster), otherwise Dfun should define derivatives
 across rows.
 full_output  nonzero 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 notNone or nonnegative, then the
+ Jacobian is assumed to be banded. These give the number of
+ lower and upper nonzero diagonals in this banded matrix.
+ For the banded case, Dfun should return a matrix whose
+ columns contain the nonzero 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::
+ maxnorm 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: solverdetermined)
+ The step size to be attempted on the first step.
+ hmax : float, (0: solverdetermined)
+ The maximum absolute step size allowed.
+ hmin : float, (0: solverdetermined)
+ The minimum absolute step size allowed.
+ ixpr : boolean
+ Whether to generate extra printing at method switches.
+ mxstep : integer, (0: solverdetermined)
+ Maximum number of (internally defined) steps allowed for each
+ integration point in t.
+ mxhnil : integer, (0: solverdetermined)
+ Maximum number of messages printed.
+ mxordn : integer, (0: solverdetermined)
+ Maximum order to be allowed for the nonstiff (Adams) method.
+ mxords : integer, (0: solverdetermined)
+ Maximum order to be allowed for the stiff (BDF) method.
 Outputs: (y, {infodict,})

 y  a rank2 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 notNone or nonnegative, then the
 Jacobian is assumed to be banded. These give the number of
 lower and upper nonzero diagonals in this banded matrix.
 For the banded case, Dfun should return a matrix whose
 columns contain the nonzero 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
 maxnorm 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  nonzero 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 objectoriented integrator based on VODE
 quad  for finding the area under a curve
+ See Also
+ 
+ ode : a more objectoriented integrator based on VODE
+ quad : for finding the area under a curve
+
"""
if ml is None:
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