diff --git a/v3.0.0a3/_modules/index.html b/v3.0.0a3/_modules/index.html new file mode 100644 index 0000000..03e300a --- /dev/null +++ b/v3.0.0a3/_modules/index.html @@ -0,0 +1,112 @@ + + + + + + + Overview: module code — Odes 3.0.0a3 documentation + + + + + + + + + + + + + + + + + + + + + +
+
+
+ + +
+ +

All modules for which code is available

+ + +
+ +
+
+ +
+
+
+ ©2016, B. Malengier. + + | + Powered by Sphinx 7.3.7 + & Alabaster 0.7.16 + +
+ + + + + + \ No newline at end of file diff --git a/v3.0.0a3/_modules/scikits_odes/dae.html b/v3.0.0a3/_modules/scikits_odes/dae.html new file mode 100644 index 0000000..f50e7ea --- /dev/null +++ b/v3.0.0a3/_modules/scikits_odes/dae.html @@ -0,0 +1,454 @@ + + + + + + + scikits_odes.dae — Odes 3.0.0a3 documentation + + + + + + + + + + + + + + + + + + + + + +
+
+
+ + +
+ +

Source code for scikits_odes.dae

+# -*- coding: utf-8 -*-
+# Authors: B. Malengier based on ode.py
+r"""
+First-order DAE solver
+======================
+
+User-friendly interface to various numerical integrators for solving an
+algebraic system of first order ODEs with prescribed initial conditions:
+
+.. math::
+    A \frac{dy(t)}{dt} = f(t,y(t)),
+
+    y(t=0)[i] = y0[i],
+
+    \frac{d y(t=0)}{dt}[i]  = yprime0[i],
+
+where :math:`i = 0, ..., len(y0) - 1`; :math:`A` is a (possibly singular) matrix
+of size :math:`i × i`; and :math:`f(t,y)` is a vector of size :math:`i` or more generally, equations of the form
+
+.. math::
+    G(t,y,y') = 0
+
+"""
+__all__ = ['dae']
+__docformat__ = "restructuredtext en"
+import re
+import sys
+
+from scikits_odes_core import DaeBase
+
+
+#------------------------------------------------------------------------------
+# User interface
+#------------------------------------------------------------------------------
+
+

+[docs]
+class dae(object):
+    """
+    A generic interface class to differential algebraic equations.
+
+    Define equation res = G(t,y,y') which can eg be G = f(y,t) - A y' when
+    solving A y' = f(y,t), and where (optional) jac is the jacobian matrix of
+    the nonlinear system see fortran source code), so d res/dy + scaling * d
+    res/dy' or d res/dy depending on the backend.
+
+    Parameters
+    ----------
+    integrator_name : ``'ida'``, ``'ddaspk'`` or ``'lsodi'``
+        The integrator solver to use.
+
+    eqsres : residual function
+        Residual of the DAE. The signature of this function depends on the
+        solver used, see the solver documentation for details.
+        Generally however, you can assume the following signature to work:
+
+            ``eqsres(x, y, yprime, return_residual)``
+
+        with
+        x       : independent variable, eg the time, float
+        y       : array of n unknowns in x
+        yprime  : dy/dx array of n unknowns in x, dimension = dim(y)
+        return_residual: array that must be updated with the value of the residuals, so G(t,y,y').  The dimension is equal to dim(y)
+        return value: integer, 0 for success. It is not guaranteed that a solver takes this status into account
+
+        Some solvers will allow userdata to be passed to eqsres, or optional
+        formats that are more performant.
+
+    options : mapping
+        Additional options for initialization, solver dependent
+        See set_options method of the `integrator_name` you selected for
+        details.
+
+
+    See Also
+    --------
+    odeint : an ODE integrator with a simpler interface based on lsoda from
+        ODEPACK
+    ode : class around vode ODE integrator
+
+
+    Notes
+    -----
+    Possible future solvers
+
+    ddaskr: Not included, starting hints:
+    http://osdir.com/ml/python.f2py.user/2005-07/msg00014.html
+    Modified Extended Backward Differentiation Formulae (MEBDF): Not included.
+    Fortran codes: http://www.ma.ic.ac.uk/~jcash/IVP_software/readme.html
+
+    Examples
+    --------
+    DAE arise in many applications of dynamical systems, as well as in
+    discritisations of PDE (eg moving mesh combined with method of
+    lines).
+    As an easy example, consider the simple oscillator, which we write as
+    G(y,y',t) = 0 instead of the normal ode, and solve as a DAE.
+
+    >>> from __future__ import print_function
+    >>> from numpy import cos, sin, sqrt
+    >>> k = 4.0
+    >>> m = 1.0
+    >>> initx = [1, 0.1]
+    >>> initxp = [initx[1], -k/m*initx[0]]
+    >>> def reseqn(t, x, xdot, result):
+        ... # we create residual equations for the problem
+        ... result[0] = m*xdot[1] + k*x[0]
+        ... result[1] = xdot[0] - x[1]
+    >>> from scikits.odes import dae
+    >>> solver = dae('ida', reseqn)
+    >>> result = solver.solve([0., 1., 2.], initx, initxp)
+    """
+
+    LOADED = False
+
+    def __init__(self, integrator_name, eqsres, **options):
+        integrator = find_dae_integrator(integrator_name)
+        if integrator is None:
+            raise ValueError('No integrator name match with %s or is not available.'\
+                  %(repr(integrator_name)))
+        else:
+            self._integrator = integrator(eqsres, **options)
+
+

+[docs]
+    def set_options(self, **options):
+        """
+        Set specific options for the solver.
+        See the solver documentation for details.
+
+        Calling set_options a second time, normally resets the solver.
+        """
+        return self._integrator.set_options(**options)

+
+
+

+[docs]
+    def solve(self, tspan, y0,  yp0):
+        """
+        Runs the solver.
+
+        Parameters
+        ----------
+        tspan : list/array
+            A list of times at which the computed value will be returned. Must
+            contain the start time as first entry.
+        y0 : list/array
+            list array of initial values
+        yp0 : list/array
+            list array of initial values of derivatives
+
+        Returns
+        -------
+        old_api is False : namedtuple
+            namedtuple with the following attributes
+
+            =========== ==========================================
+            Field       Meaning
+            =========== ==========================================
+            ``flag``    An integer flag (StatusEnumXXX)
+            ``values``  Named tuple with entries array t and array y and array ydot. y will correspond to y_retn value and ydot to yp_retn!
+            ``errors``  Named tuple with entries t and y and ydot of error
+            ``roots``   Named tuple with entries array t and array y and array ydot
+            ``tstop``   Named tuple with entries array t and array y and array ydot
+            ``message`` String with message in case of an error
+            =========== ==========================================
+
+        old_api is True : tuple
+            tuple with the following elements in order
+
+            ========== ==========================================
+            Field      Meaning
+            ========== ==========================================
+            ``flag``   indicating return status of the solver
+            ``t``      numpy array of times at which the computations were successful
+            ``y``      numpy array of values corresponding to times t (values of y[i, :] ~ t[i])
+            ``yp``     numpy array of derivatives corresponding to times t (values of yp[i, :] ~ t[i])
+            ``t_err``  float or None - if recoverable error occurred (for example reached maximum number of allowed iterations), this is the time at which it happened
+            ``y_err``  numpy array of values corresponding to time t_err
+            ``yp_err`` numpy array of derivatives corresponding to time t_err
+            ========== ==========================================
+
+        """
+        return self._integrator.solve(tspan, y0,  yp0)

+
+
+

+[docs]
+    def init_step(self, t0, y0, yp0, y_ic0_retn = None, yp_ic0_retn = None):
+        """
+        Initializes the solver and allocates memory. It is not needed to
+        call this method if solve is used to compute the solution. In the case
+        step is used, init_step must be called first.
+
+        Parameters
+        ----------
+        t0 : number
+            initial time
+        y0 : list/array
+            initial condition for y
+        yp0 :  list/array
+            initial condition for yp
+        y_ic0 : numpy array
+            (optional) returns the calculated consistent initial condition for y
+        yp_ic0 :  numpy array
+            (optional) returns the calculated consistent initial condition for y
+            derivated.
+
+        Returns
+        -------
+        old_api is False : namedtuple
+            namedtuple with the following attributes
+
+            =========== ==========================================
+            Field       Meaning
+            =========== ==========================================
+            ``flag``    An integer flag (StatusEnumXXX)
+            ``values``  Named tuple with entries t and y and ydot. y will correspond to y_retn value and ydot to yp_retn!
+            ``errors``  Named tuple with entries t and y and ydot
+            ``roots``   Named tuple with entries t and y and ydot
+            ``tstop``   Named tuple with entries t and y and ydot
+            ``message`` String with message in case of an error
+            =========== ==========================================
+
+        old_api is True : tuple
+            tuple with the following elements in order
+
+            =========== ==========================================
+            Field       Meaning
+            =========== ==========================================
+            ``flag``    status of the computation (successful or error occurred)
+            ``t_out``   time, where the solver stopped (when no error occurred, t_out == t)
+            =========== ==========================================
+
+        """
+        return self._integrator.init_step(t0, y0, yp0, y_ic0_retn, yp_ic0_retn)

+
+
+

+[docs]
+    def step(self, t, y_retn=None, yp_retn=None):
+        """
+        Method for calling successive next step of the IDA solver to allow
+        more precise control over the IDA solver. The 'init_step' method has to
+        be called before the 'step' method.
+
+        A step is done towards time t, and output at t returned. This time can
+        be higher or lower than the previous time. If option
+        'one_step_compute'==True, and the solver supports it, only one internal
+        solver step is done in the direction of t starting at the current step.
+
+        If old_api=True, the old behavior is used: if t>0.0 then integration is
+        performed until this time and results at this time are returned in
+        y_retn; else if if t<0.0 only one internal step is performed towards time
+        abs(t) and results after this one time step are returned.
+
+        Parameters
+        ----------
+        t : number
+        y_retn : numpy array (ndim = 1) or None.
+            (Needs to be preallocated) If not None, will be filled with y at
+            time t. If None y_retn is not used.
+        yp_retn : numpy array (ndim = 1) or None.
+            (Needs to be preallocated) If not None, will be filled with
+            derivatives of y at time t. If None yp_retn is not used.
+
+        Returns
+        -------
+        old_api is False : namedtuple
+            namedtuple with the following attributes
+
+            =========== ==========================================
+            Field       Meaning
+            =========== ==========================================
+            ``flag``    An integer flag (StatusEnumXXX)
+            ``values``  Named tuple with entries t and y and ydot. y will correspond to y_retn value and ydot to yp_retn!
+            ``errors``  Named tuple with entries t and y and ydot
+            ``roots``   Named tuple with entries t and y and ydot
+            ``tstop``   Named tuple with entries t and y and ydot
+            ``message`` String with message in case of an error
+            =========== ==========================================
+
+        old_api is True : tuple
+            tuple with the following elements in order
+
+            =========== ==========================================
+            Field       Meaning
+            =========== ==========================================
+            ``flag``    status of the computation (successful or error occurred)
+            ``t_out``   time, where the solver stopped (when no error occurred, t_out == t)
+            =========== ==========================================
+
+        """
+        return self._integrator.step(t, y_retn, yp_retn)

+
+
+    def __del__(self):
+        """
+        Clean up what is needed
+        """
+        if hasattr(self, '_integrator'):
+            del self._integrator

+
+
+#------------------------------------------------------------------------------
+# DAE integrators
+#------------------------------------------------------------------------------
+
+def find_dae_integrator(name):
+    if not dae.LOADED:
+        ## ida
+        try:
+            from scikits_odes_sundials import ida
+            DaeBase.integrator_classes.append(ida.IDA)
+        except ValueError as msg:
+            print('Could not load IDA solver', msg)
+        except ImportError:
+            print(sys.exc_info()[1])
+
+        ## idas
+        try:
+            from scikits_odes_sundials import idas
+            DaeBase.integrator_classes.append(idas.IDAS)
+        except ValueError as msg:
+            print('Could not load IDAS solver', msg)
+        except ImportError:
+            print(sys.exc_info()[1])
+
+        ## ddaspk
+        try:
+            from scikits_odes_daepack.ddaspkint import ddaspk
+        except ImportError:
+            print(sys.exc_info()[1])
+
+        ## lsodi
+        try:
+            from scikits_odes_daepack.lsodiint import lsodi
+        except ImportError:
+            print(sys.exc_info()[1])
+
+        dae.LOADED = True
+
+    for cl in DaeBase.integrator_classes:
+        if re.match(name, cl.__name__, re.I):
+            return cl
+        elif hasattr(cl, name) and re.match(name, cl.name, re.I):
+            return cl
+    raise ValueError('Integrator name %s does not exsist' % name)
+
+ +
+ +
+
+ +
+
+
+ ©2016, B. Malengier. + + | + Powered by Sphinx 7.3.7 + & Alabaster 0.7.16 + +
+ + + + + + \ No newline at end of file diff --git a/v3.0.0a3/_modules/scikits_odes/dopri5.html b/v3.0.0a3/_modules/scikits_odes/dopri5.html new file mode 100644 index 0000000..4dbafd1 --- /dev/null +++ b/v3.0.0a3/_modules/scikits_odes/dopri5.html @@ -0,0 +1,499 @@ + + + + + + + scikits_odes.dopri5 — Odes 3.0.0a3 documentation + + + + + + + + + + + + + + + + + + + + + +
+
+
+ + +
+ +

Source code for scikits_odes.dopri5

+# -*- coding: utf-8 -*-
+# Created on Thu Jan 28 14:59:25 2016
+# @author: benny
+"""
+Making scipy ode solvers available via the ode API
+==================================================
+
+dopri5
+------
+
+This is an explicit runge-kutta method of order (4)5 due to Dormand & Prince
+(with stepsize control and dense output).
+The API of this solver is as the other scikit.odes ODE solvers
+
+Authors:
+
+    E. Hairer and G. Wanner Universite de Geneve, Dept. de Mathematiques CH-1211 Geneve 24, Switzerland e-mail: ernst.hairer@math.unige.ch, gerhard.wanner@math.unige.ch
+
+This code is described in [HNW93].
+
+This integrator accepts the following options:
+
+    atol : float or sequence absolute tolerance for solution, default 1e-12
+    rtol : float or sequence relative tolerance for solution, default 1e-6
+    nsteps : int Maximum number of (internally defined) steps allowed during one call to the solver. Default=500
+    first_step : float
+    max_step : float
+    safety : float Safety factor on new step selection (default 0.9)
+    ifactor : float
+    dfactor : float Maximum factor to increase/decrease step size by in one step
+    beta : float Beta parameter for stabilised step size control.
+    verbosity : int Switch for printing messages (< 0 for no messages).
+
+References
+[HNW93]	(1, 2) E. Hairer, S.P. Norsett and G. Wanner, Solving Ordinary Differential Equations i. Nonstiff Problems. 2nd edition. Springer Series in Computational Mathematics, Springer-Verlag (1993)
+
+dop853
+------
+
+This is an explicit runge-kutta method of order 8(5,3) due to Dormand & Prince
+(with stepsize control and dense output).
+Options and references the same as “dopri5”.
+
+"""
+from collections import namedtuple
+from enum import IntEnum
+from warnings import warn
+import sys
+
+import numpy as np
+from scipy.integrate import ode as _runner
+
+from scikits_odes_core import OdeBase
+
+SolverReturn = namedtuple(
+    "SolverReturn", [
+        "flag", "values", "errors", "roots",
+        "tstop", "message"
+    ]
+)
+
+SolverVariables = namedtuple("SolverVariables", ["t", "y"])
+
+
+

+[docs]
+class StatusEnumDOP(IntEnum):
+    SUCCESS = 1
+    SOLOUT  = 2
+
+    INPUT_FAIL     = -1
+    NMAX_FAIL      = -2
+    STEPSIZE_FAIL  = -3
+    STIFFNESS_FAIL = -4
+
+    UNEXPECTED_IDID = -10

+
+
+STATUS_MESSAGE = {
+    StatusEnumDOP.SUCCESS: 'computation successful',
+    StatusEnumDOP.SOLOUT: 'comput. successful (interrupted by solout)',
+    StatusEnumDOP.INPUT_FAIL: 'input is not consistent',
+    StatusEnumDOP.NMAX_FAIL: 'larger nmax is needed',
+    StatusEnumDOP.STEPSIZE_FAIL: 'step size becomes too small',
+    StatusEnumDOP.STIFFNESS_FAIL: 'problem is probably stiff (interrupted)',
+    StatusEnumDOP.UNEXPECTED_IDID: 'Unexpected idid, check warnings for info',
+}
+
+

+[docs]
+class DOPSolveException(Exception):
+    """Base class for exceptions raised by `DOP.validate_flags`."""
+    def __init__(self, soln):
+        self.soln = soln
+        self.args = (self._message.format(soln),)

+
+
+

+[docs]
+class DOPSolveFailed(DOPSolveException):
+    """`DOP.solve` failed to reach endpoint"""
+    _message = (
+        "Solver failed with flag {0.flag} and finished at {0.errors.t}"
+        "with values {0.errors.y}."
+    )

+
+
+

+[docs]
+class dopri5(OdeBase):
+    name = 'dopri5'
+    _runner = _runner
+    default_values = {
+            'rtol': 1e-6,
+            'atol': 1e-12,
+            'nsteps': 500,
+            'max_step': 0.0,
+            'first_step': 0.0,  # determined by solver
+            'safety': 0.9,
+            'ifactor': 10.0,
+            'dfactor': 0.2,
+            'beta': 0.0,
+            'verbosity': -1, # no messages if negative
+            }
+
+    def __init__(self, Rfn, **options):
+        """
+        Initialize the ODE Solver and it's default values
+
+        Parameters
+        ----------
+            Rfn     - right-hand-side function
+            options - additional options for initialization
+        """
+        self.options = self.default_values
+        self.set_options(rfn=Rfn, **options)
+        self._validate_flags = None
+        self.solver = None
+        self.initialized = False
+
+

+[docs]
+    def set_options(self, **options):
+        """
+        Set specific options for the solver.
+
+        Calling set_options a second time, normally resets the solver.
+        """
+        for (key, value) in options.items():
+            self.options[key.lower()] = value
+        self.initialized = False

+
+
+    def _init_data(self):
+        self.rfn = self.options['rfn']
+        self.N = len(self.y0)
+
+    def _wrap_Rfn(self, t, y):
+        yout = np.empty(self.N, float)
+        self.rfn(t, y, yout)
+        return yout
+
+

+[docs]
+    def init_step(self, t0, y0):
+        """
+        Initializes the solver and allocates memory.
+
+        Parameters
+        ----------
+            t0     - initial time
+            y0     - initial condition for y (can be list or numpy array)
+
+        Returns
+        -------
+         if old_api:
+            not supported
+
+         if old_api False:
+            A named tuple, with entries:
+                flag   = An integer flag (StatusEnumDop)
+                values = Named tuple with entries t and y and ydot. y will correspond to y_retn value and ydot to yp_retn!
+                errors = Named tuple with entries t_err and y_err
+                roots  = Named tuple with entries t_roots and y_roots
+                tstop  = Named tuple with entries t_stop and y_tstop
+                message= String with message in case of an error
+
+        """
+        self.y0 = y0
+        self.t = t0
+        self._init_data()
+
+        self.solver = self._runner(self._wrap_Rfn)\
+                        .set_integrator(self.name,
+                            rtol = self.options['rtol'],
+                            atol = self.options['atol'],
+                            nsteps = self.options['nsteps'],
+                            max_step = self.options['max_step'],
+                            first_step = self.options['first_step'],  # determined by solver
+                            safety = self.options['safety'],
+                            ifactor = self.options['ifactor'],
+                            dfactor = self.options['dfactor'],
+                            beta = self.options['beta'],
+                            verbosity = self.options['verbosity'])\
+                        .set_initial_value(y0, t0)
+        self.initialized = True
+        y_retn  = np.empty(len(y0), float)
+        y_retn[:] = y0[:]
+        soln = SolverReturn(
+            flag=StatusEnumDOP.SUCCESS,
+            values=SolverVariables(t=t0, y=y_retn),
+            errors=SolverVariables(t=None, y=None),
+            roots=SolverVariables(t=None, y=None),
+            tstop=SolverVariables(t=None, y=None),
+            message=STATUS_MESSAGE[StatusEnumDOP.SUCCESS]
+        )
+        if self._validate_flags:
+            return self.validate_flags(soln)
+        return soln

+
+
+

+[docs]
+    def step(self, t, y_retn=None):
+        """
+        Method for calling successive next step of the ODE solver to allow
+        more precise control over the solver. The 'init_step' method has to
+        be called before the 'step' method.
+
+        Parameters
+        ----------
+            t - A step is done towards time t, and output at t returned.
+                This time can be higher or lower than the previous time.
+                If option 'one_step_compute'==True, and the solver supports
+                it, only one internal solver step is done in the direction
+                of t starting at the current step.
+
+                If old_api=True, the old behavior is used:
+                 if t>0.0 then integration is performed until this time and results at this time are returned in y_retn
+                 if t<0.0 only one internal step is perfomed towards time abs(t) and results after this one time step are returned
+            y_retn - numpy vector (ndim = 1) in which the computed
+                     value will be stored  (needs to be preallocated).  If
+                     None y_retn is not used.
+        Returns
+        -------
+         if old_api:
+             not supported
+
+         if old_api False:
+            A named tuple, with entries:
+                flag   = An integer flag (StatusEnumDOP)
+                values = Named tuple with entries t and y. y will correspond to y_retn value
+                errors = Named tuple with entries t_err and y_err
+                roots  = Named tuple with entries t_roots and y_roots
+                tstop  = Named tuple with entries t_stop and y_tstop
+                message= String with message in case of an error
+
+        """
+        if not self.initialized == False:
+            raise ValueError("DOPRI:step: init_step must be run before running the step method.")
+        if t <= self.t:
+            raise ValueError("Integration must be forward! t must be > previous timestep")
+        y = self.solver.integrate(t)
+        y_err = None
+        t_err = None
+        if not self.solver.successful():
+            flag = StatusEnumDOP.UNEXPECTED_IDID
+            y_err = y
+            t_err = t
+        else:
+            flag = StatusEnumDOP.SUCCESS
+            self.y = y
+            self.t = self.solver.t
+
+        return SolverReturn(
+            flag=flag,
+            values=SolverVariables(t=self.t, y=y),
+            errors=SolverVariables(t=t_err, y=y_err),
+            roots=SolverVariables(t=None, y=None),
+            tstop=SolverVariables(t=None, y=None),
+            message=STATUS_MESSAGE[flag]
+        )

+
+
+

+[docs]
+    def solve(self, tspan, y0):
+        """
+        Runs the solver.
+
+        Parameters
+        ----------
+            tspan - an list/array of times at which the computed value will be
+                    returned. Must contain the start time as first entry..
+            y0    - list/numpy array of initial values
+
+        Returns
+        -------
+         if old_api
+            Not supported
+         if old_api False:
+            A named tuple, with entries:
+                flag   = An integer flag
+                values = Named tuple with entries t and y
+                errors = Named tuple with entries t and y
+                roots  = Named tuple with entries t and y
+                tstop  = Named tuple with entries t and y
+                message= String with message in case of an error
+        """
+        self.initialized = False
+        soln = self.init_step(tspan[0], y0)
+        nrt = len(tspan)
+        t_retn  = np.empty(np.shape(tspan), float)
+        y_retn  = np.empty([len(tspan), len(y0)], float)
+
+        t_retn[0] = tspan[0]
+        y_retn[0, :] = y0
+
+        idx = 1
+        while self.solver.successful() and idx<nrt:
+            time = tspan[idx]
+            y = self.solver.integrate(time)
+            t_retn[idx] = time
+            y_retn[idx, :] = y
+            idx += 1
+
+        y_err = None
+        t_err = None
+        if not self.solver.successful():
+            flag = StatusEnumDOP.UNEXPECTED_IDID
+            y_err = y_retn[idx-1]
+            t_err = t_retn[idx-1]
+            # return values computed so far
+            t_retn  = t_retn[0:idx-1]
+            y_retn  = y_retn[0:idx-1, :]
+        else:
+            flag = StatusEnumDOP.SUCCESS
+
+        soln = SolverReturn(
+            flag=flag,
+            values=SolverVariables(t=t_retn, y=y_retn),
+            errors=SolverVariables(t=t_err, y=y_err),
+            roots=SolverVariables(t=None, y=None),
+            tstop=SolverVariables(t=None, y=None),
+            message=STATUS_MESSAGE[flag]
+        )
+        if self._validate_flags:
+            return self.validate_flags(soln)
+        return soln

+
+
+

+[docs]
+    def validate_flags(self, soln):
+        """
+        Validates the flag returned by `dopri.solve`.
+
+        Validation happens using the following scheme:
+         * failures (`flag` < 0) raise `DOPSolveFailed` or a subclass of it;
+         * otherwise, return an instance of `SolverReturn`.
+
+        """
+        if soln.flag == StatusEnumDOP.SUCCESS:
+            return soln
+        if soln.flag < 0:
+            raise DOPSolveFailed(soln)
+        warn(WARNING_STR.format(soln.flag, *soln.err_values))
+        return soln

+

+
+
+
+

+[docs]
+class dop853(dopri5):
+    name = 'dop853'
+    default_values = {
+            'rtol': 1e-6,
+            'atol': 1e-12,
+            'nsteps': 500,
+            'max_step': 0.0,
+            'first_step': 0.0,  # determined by solver
+            'safety': 0.9,
+            'ifactor': 6.0,
+            'dfactor': 0.3,
+            'beta': 0.0,
+            'verbosity': -1, # no messages if negative
+            }

+
+
+
+OdeBase.integrator_classes.append(dopri5)
+OdeBase.integrator_classes.append(dop853)
+
+ +
+ +
+
+ +
+
+
+ ©2016, B. Malengier. + + | + Powered by Sphinx 7.3.7 + & Alabaster 0.7.16 + +
+ + + + + + \ No newline at end of file diff --git a/v3.0.0a3/_modules/scikits_odes/ode.html b/v3.0.0a3/_modules/scikits_odes/ode.html new file mode 100644 index 0000000..4c3a2f2 --- /dev/null +++ b/v3.0.0a3/_modules/scikits_odes/ode.html @@ -0,0 +1,472 @@ + + + + + + + scikits_odes.ode — Odes 3.0.0a3 documentation + + + + + + + + + + + + + + + + + + + + + +
+
+
+ + +
+ +

Source code for scikits_odes.ode

+# -*- coding: utf-8 -*-
+# Authors: B. Malengier based on ode.py
+r"""
+First-order ODE solver
+======================
+
+User-friendly interface to various numerical integrators for solving a
+system of first order ODEs with prescribed initial conditions:
+
+.. math::
+
+    \frac{dy(t)}{dt} = f(t, y(t)), \quad y(t_0)=y_0
+
+    y(t_0)[i] = y_0[i], i = 0, ..., \mathrm{len}(y_0) - 1
+
+:math:`f(t,y)` is the right hand side function and returns a vector of size
+:math:`\mathrm{len}(y_0)`.
+
+"""
+__all__ = ['ode']
+__docformat__ = "restructuredtext en"
+
+import re
+import sys
+
+
+from scikits_odes_core import OdeBase
+
+#------------------------------------------------------------------------------
+# User interface
+#------------------------------------------------------------------------------
+
+

+[docs]
+class ode(object):
+    """
+    A generic interface class to differential equation solvers.
+
+
+    Parameters
+    ----------
+
+    integrator_name : ``'cvode'``, ``'dopri5'`` or ``'dop853'``
+        The solver to use.
+
+        ``'cvode'`` selects the CVODE solver from the SUNDIALS package.
+        See py:class:`scikits.odes.sundials.cvode.CVODE` for solver specific
+        options.
+
+        ``'dopri5'`` selects the Dormand & Prince Runge-Kutta order (4)5
+        solver from scipy.
+
+    eqsrhs : right-hand-side function
+        Right-hand-side of a first order ode.
+        Generally, you can assume the following signature to work:
+
+            eqsrhs(x, y, return_rhs)
+
+        with
+
+            x: independent variable, eg the time, float
+
+            y: array of n unknowns in x
+
+            return_rhs : array that must be updated with the value of the
+            right-hand-side, so f(t,y).  The dimension is equal to
+            dim(y)
+
+        return value: An integer, 0 for success, 1 for failure.
+            It is not guaranteed that a solver takes this status into account
+
+        Some solvers will allow userdata to be passed to eqsrhs, or optional
+        formats that are more performant.
+
+    options :  additional options of the solver
+        See set_options method of the `integrator_name` you selected for
+        details.
+        Set option `old_api=False` to use the new API. In the future, this
+        will become the default!
+
+    See Also
+    --------
+    scikits.odes.odeint.odeint : an ODE integrator with a simpler interface
+    scipy.integrate : Methods in scipy for ODE integration
+
+    Examples
+    --------
+    ODE arise in many applications of dynamical systems, as well as in
+    discritisations of PDE (eg moving mesh combined with method of
+    lines).
+    As an easy example, consider the simple oscillator,
+
+    >>> from __future__ import print_function
+    >>> from numpy import cos, sin, sqrt
+    >>> k = 4.0
+    >>> m = 1.0
+    >>> initx = [1, 0.1]
+    >>> def rhseqn(t, x, xdot):
+            # we create rhs equations for the problem
+            xdot[0] = x[1]
+            xdot[1] = - k/m * x[0]
+
+    >>> from scikits.odes import ode
+    >>> solver = ode('cvode', rhseqn, old_api=False)
+    >>> result = solver.solve([0., 1., 2.], initx)
+    >>> print('   t        Solution          Exact')
+    >>> print('------------------------------------')
+    >>> for t, u in zip(result.values.t, result.values.y):
+            print('%4.2f %15.6g %15.6g' % (t, u[0], initx[0]*cos(sqrt(k/m)*t)+initx[1]*sin(sqrt(k/m)*t)/sqrt(k/m)))
+
+    More examples in the Examples_ directory and IPython_ worksheets.
+
+    .. _Examples: https://github.com/bmcage/odes/tree/master/docs/src/examples
+    .. _IPython: https://github.com/bmcage/odes/tree/master/docs/ipython
+    """
+    LOADED = False
+
+    def __init__(self, integrator_name, eqsrhs, **options):
+        integrator = find_ode_integrator(integrator_name)
+        if integrator is None:
+            raise ValueError('No integrator name match with %s or is not available.'\
+                  %(repr(integrator_name)))
+        else:
+            self._integrator = integrator(eqsrhs, **options)
+
+

+[docs]
+    def set_options(self, **options):
+        """
+        Set specific options for the solver.
+        See the solver documentation for details.
+
+        Calling set_options a second time, is only possible for options that
+        can change during runtime.
+        """
+        return self._integrator.set_options(**options)

+
+
+

+[docs]
+    def solve(self, tspan, y0):
+        """
+        Runs the solver.
+
+        Parameters
+        ----------
+        tspan : array (or similar)
+            a list of times at which the computed value will be returned. Must
+            contain the start time as first entry.
+
+        y0 : array (or similar)
+            a list of initial values
+
+        Returns
+        -------
+        old_api is False : namedtuple
+            namedtuple with the following attributes
+
+            =========== ==========================================
+            Field       Meaning
+            =========== ==========================================
+            ``flag``    An integer flag (StatusEnum)
+            ``values``  Named tuple with entries t and y
+            ``errors``  Named tuple with entries t and y
+            ``roots``   Named tuple with entries t and y
+            ``tstop``   Named tuple with entries t and y
+            ``message`` String with message in case of an error
+            =========== ==========================================
+
+        old_api is True : tuple
+            tuple with the following elements in order
+
+            ========== ==========================================
+            Field      Meaning
+            ========== ==========================================
+            ``flag``   indicating return status of the solver
+            ``t``      numpy array of times at which the computations were successful
+            ``y``      numpy array of values corresponding to times t (values of y[i, :] ~ t[i])
+            ``t_err``  float or None - if recoverable error occured (for example reached maximum number of allowed iterations), this is the time at which it happened
+            ``y_err``  numpy array of values corresponding to time t_err
+            ========== ==========================================
+
+        """
+        return self._integrator.solve(tspan, y0)

+
+
+

+[docs]
+    def init_step(self, t0, y0):
+        """
+        Initializes the solver and allocates memory. It is not needed to
+        call this method if solve is used to compute the solution. In the case
+        step is used, init_step must be called first.
+
+        Parameters
+        ----------
+        t0 : number
+            initial time
+        y0 : array
+            initial condition for y (can be list or numpy array)
+
+        Returns
+        -------
+        old_api is False : namedtuple
+            namedtuple with the following attributes
+
+            =========== ==========================================
+            Field       Meaning
+            =========== ==========================================
+            ``flag``    An integer flag (StatusEnum)
+            ``values``  Named tuple with entries t and y
+            ``errors``  Named tuple with entries t and y
+            ``roots``   Named tuple with entries t and y
+            ``tstop``   Named tuple with entries t and y
+            ``message`` String with message in case of an error
+            =========== ==========================================
+
+        old_api is True : tuple
+            tuple with the following elements in order
+
+            ========== ==========================================
+            Field      Meaning
+            ========== ==========================================
+            ``flag``   boolean status of the computation (successful or error occured)
+            ``t_out``  inititial time
+            ========== ==========================================
+
+        """
+        return self._integrator.init_step(t0, y0)

+
+
+

+[docs]
+    def step(self, t, y_retn=None):
+        """
+        Method for calling successive next step of the ODE solver to allow
+        more precise control over the solver. The 'init_step' method has to
+        be called before the 'step' method.
+
+        A step is done towards time t, and output at t returned.  This time can
+        be higher or lower than the previous time.  If option
+        'one_step_compute'==True, and the solver supports it, only one internal
+        solver step is done in the direction of t starting at the current step.
+
+        If old_api=True, the old behavior is used: if t>0.0 then integration is
+        performed until this time and results at this time are returned in
+        y_retn if t<0.0 only one internal step is perfomed towards time abs(t)
+        and results after this one time step are returned
+
+        Parameters
+        ----------
+        t : number
+
+        y_retn : numpy vector (ndim = 1)
+            in which the computed value will be stored  (needs to be
+            preallocated).  If None y_retn is not used.
+
+        Returns
+        -------
+        old_api is False : namedtuple
+            namedtuple with the following attributes
+
+            =========== ==========================================
+            Field       Meaning
+            =========== ==========================================
+            ``flag``    An integer flag (StatusEnum)
+            ``values``  Named tuple with entries t and y
+            ``errors``  Named tuple with entries t and y
+            ``roots``   Named tuple with entries t and y
+            ``tstop``   Named tuple with entries t and y
+            ``message`` String with message in case of an error
+            =========== ==========================================
+
+        old_api is True : tuple
+            tuple with the following elements in order
+
+            ========== ==========================================
+            Field      Meaning
+            ========== ==========================================
+            ``flag``   status of the computation (successful or error occured)
+            ``t_out``  time, where the solver stopped (when no error occured, t_out == t)
+            ========== ==========================================
+
+        """
+        return self._integrator.step(t, y_retn)

+
+
+

+[docs]
+    def set_tstop(self, tstop):
+        """
+        Add a stop time to the integrator past which he is not allowed to
+        integrate.
+
+        Parameters
+        ----------
+        tstop : float time
+            Time point in the future where the integration must stop. You can
+            indicate like this that integration past this point is not allowed,
+            in order to avoid undefined behavior.
+            You can achieve the same result with a call to
+            `set_options(tstop=tstop)`
+        """
+        if hasattr(self._integrator, 'set_tstop'):
+            self._integrator.set_tstop(tcrit)
+        else:
+            self._integrator.set_options(tstop=tstop)

+
+
+

+[docs]
+    def get_info(self):
+        """
+        Return additional information about the state of the integrator.
+
+        Returns
+        -------
+
+        A dictionary filled with internal data as exposed by the integrator.
+        See the `get_info` method of your chosen integrator for details.
+
+        """
+        if hasattr(self._integrator, 'get_info'):
+            return self._integrator.get_info()
+        else:
+            return {}

+

+
+
+#------------------------------------------------------------------------------
+# ODE integrators
+#------------------------------------------------------------------------------
+
+def find_ode_integrator(name):
+    if not ode.LOADED:
+        ## cvode
+        try:
+            from scikits_odes_sundials import cvode
+            OdeBase.integrator_classes.append(cvode.CVODE)
+        except ValueError as msg:
+            print('Could not load CVODE solver', msg)
+        except ImportError:
+            print(sys.exc_info()[1])
+        ## cvodes
+        try:
+            from scikits_odes_sundials import cvodes
+            OdeBase.integrator_classes.append(cvodes.CVODES)
+        except ValueError as msg:
+            print('Could not load CVODES solver', msg)
+        except ImportError:
+            print(sys.exc_info()[1])
+
+        ## dopri5 and dop853
+        try:
+            from .dopri5 import dopri5, dop853
+        except ImportError:
+            print(sys.exc_info()[1])
+
+        ode.LOADED = True
+
+    for cl in OdeBase.integrator_classes:
+        if re.match(name, cl.__name__, re.I):
+            return cl
+        elif hasattr(cl, name) and re.match(name, cl.name, re.I):
+            return cl
+    raise ValueError('Integrator name %s does not exist' % name)
+
+ +
+ +
+
+ +
+
+
+ ©2016, B. Malengier. + + | + Powered by Sphinx 7.3.7 + & Alabaster 0.7.16 + +
+ + + + + + \ No newline at end of file diff --git a/v3.0.0a3/_modules/scikits_odes/odeint.html b/v3.0.0a3/_modules/scikits_odes/odeint.html new file mode 100644 index 0000000..7e25967 --- /dev/null +++ b/v3.0.0a3/_modules/scikits_odes/odeint.html @@ -0,0 +1,323 @@ + + + + + + + scikits_odes.odeint — Odes 3.0.0a3 documentation + + + + + + + + + + + + + + + + + + + + + +
+
+
+ + +
+ +

Source code for scikits_odes.odeint

+# -*- coding: utf-8 -*-
+"""
+Created on Mon Feb  1 13:38:24 2016
+
+@author: benny
+"""
+from copy import copy
+from .ode import ode
+
+
+

+[docs]
+def odeint(rhsfun, tout, y0,  method='bdf', **options):
+    """
+    Integrate a system of ordinary differential equations.
+    *odeint* is a wrapper around the ode class, as a convenience function to
+    quickly integrate a system of ode.
+    Solves the initial value problem for stiff or non-stiff systems
+    of first order ode's:
+
+        rhs = dy/dt = fun(t, y)
+
+    where y can be a vector, then rhsfun must be a function computing rhs with
+    signature:
+
+        rhsfun(t, y, rhs)
+
+    storing the computed dy/dt in the rhs array passed to the function
+
+    Parameters
+    ----------
+    rhsfun : callable(t, y, out)
+        Computes the derivative at dy/dt in terms of t and y, and stores in out
+    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.
+    method : string, solution method to use.
+        Available are all the ode class solvers as well as some convenience
+        shorthands:
+
+        =======  ==============================================================
+        Method   Meaning
+        =======  ==============================================================
+        bdf      This uses the 'cvode' solver in default from, which is a
+                 variable step, variable coefficient Backward Differentiation
+                 Formula solver, good for stiff ODE. Newton iterations are
+                 used to solve the nonlinear system.
+        admo     This uses the 'cvode' solver with option lmm_type='ADAMS',
+                 which is a variable step Adams-Moulton method (linear
+                 multistep method), good for non-stiff ODE. Functional
+                 iterations are used to solve the nonlinear system.
+        rk5      This uses the 'dopri5' solver, which is a variable step
+                 Runge-Kutta method of order (4)5 (use for non-stiff ODE)
+        rk8      This uses the 'dop853' solver, which is a variable step
+                 Runge-Kutta method of order 8(5,3)
+        =======  ==============================================================
+
+        For educational purposes, you can also access following methods:
+
+        =======  ==============================================================
+        Method   Meaning
+        =======  ==============================================================
+        beuler   This is the Implicit Euler (backward Euler) method (order 1),
+                 which is obtained via the 'bdf' method, setting the order
+                 option to 1, setting large tolerances,  and fixing the
+                 stepsize.
+                 Use option 'step' to change stepsize, default: step=0.05.
+                 Use option 'rtol' and 'atol' to use more strict tolerances
+                 Note: this is not completely the backward Euler method, as
+                 the cvode solver has added control options!
+        trapz    This is the Trapezoidal Rule method (order 2), which is
+                 obtained via the 'admo' method, setting option order to 2,
+                 setting large tolerances and fixing the stepsize.
+                 Use option 'step' to change stepsize, default: step=0.05.
+                 Use option 'rtol' and 'atol' to use more strict tolerances
+                 Note: The cvode solver might change the order to 1 internally
+                 in which case this becomes beuler method. Set atol, rtol
+                 options as strict as possible.
+        =======  ==============================================================
+
+        You can also access the solvers of ode via their names:
+
+        =======  ==============================================================
+        Method   Meaning
+        =======  ==============================================================
+        cvode    This uses the 'cvode' solver
+        dopri5   This uses the 'dopri5' solver
+        dop853   This uses the 'dop853' solver
+        =======  ==============================================================
+
+    options : extra solver options, optional
+        Every solver has it's own extra options, see the ode class and the
+        details of the solvers available there to know the options possible per
+        solver
+
+    Returns
+    -------
+    solution : named tuple
+        A single named tuple is returned containing the result of the
+        integration.
+
+        ========  ==========================================
+        Field     Meaning
+        ========  ==========================================
+        flag      An integer flag
+        values    Named tuple with fields t and y
+        errors    Named tuple with fields t and y
+        roots     Named tuple with fields t and y
+        tstop     Named tuple with fields t and y
+        message   String with message in case of an error
+        ========  ==========================================
+
+    See Also
+    --------
+    scikits.odes.ode.ode : a more object-oriented integrator
+    scikits.odes.dae.dae : a solver for differential-algebraic equations
+    scipy.integrate.quad : for finding the area under a curve
+
+    Examples
+    --------
+    The second order differential equation for the angle `theta` of a
+    pendulum acted on by gravity with friction can be written:
+
+    .. math:: \\theta''(t) + b \\theta'(t) + c \\sin(\\theta(t)) = 0
+
+    where `b` and `c` are positive constants, and a prime (') denotes a
+    derivative.  To solve this equation with `odeint`, we must first convert
+    it to a system of first order equations.  By defining the angular
+    velocity ``omega(t) = theta'(t)``, we obtain the system:
+
+    .. math:: \\theta'(t) = \\omega(t)
+     \\omega'(t) = -b \\omega(t) - c \\sin(\\theta(t))
+
+    We assume the constants are `b` = 0.25 and `c` = 5.0:
+
+    >>> b = 0.25
+    >>> c = 5.0
+
+    Let `y` be the vector [`theta`, `omega`].  We implement this system
+    in python as:
+
+    >>> def pend(t, y, out):
+     ...     theta, omega = y
+     ...     out[:] = [omega, -b*omega - c*np.sin(theta)]
+     ...
+
+    In case you want b and c easily changable, make pend a class method, and
+    consider attributes b and c accessible via `self.b` and `self.c`.
+    For initial conditions, we assume the pendulum is nearly vertical
+    with `theta(0)` = `pi` - 0.1, and it initially at rest, so
+    `omega(0)` = 0.  Then the vector of initial conditions is
+
+    >>> y0 = [np.pi - 0.1, 0.0]
+
+    We generate a solution 101 evenly spaced samples in the interval
+    0 <= `t` <= 10.  So our array of times is
+
+    >>> t = np.linspace(0, 10, 101)
+
+    Call `odeint` to generate the solution.
+
+    >>> from scikits.odes.odeint import odeint
+    >>> sol = odeint(pend, t, y0)
+
+    The solution is a named tuple `sol`. sol.values.y is an array with shape (101, 2).
+    The first column is `theta(t)`, and the second is `omega(t)`.
+    The following code plots both components.
+
+    >>> import matplotlib.pyplot as plt
+    >>> plt.plot(sol.values.t, sol.values.y[:, 0], 'b', label='theta(t)')
+    >>> plt.plot(sol.values.t, sol.values.y[:, 1], 'g', label='omega(t)')
+    >>> plt.legend(loc='best')
+    >>> plt.xlabel('t')
+    >>> plt.grid()
+    >>> plt.show()
+    """
+    t = copy(tout)
+    y0 = copy(y0)
+
+    int_name = 'cvode'
+    #always use old api
+    options['old_api'] = False
+    if (method == 'bdf'):
+        int_name = 'cvode'
+    elif (method == 'admo'):
+        options['lmm_type'] = 'ADAMS'
+        options['nonlinsolver'] = 'fixedpoint'
+        int_name = 'cvode'
+    elif (method == 'rk5'):
+        int_name = 'dopri5'
+    elif (method == 'rk8'):
+        int_name = 'dop853'
+    elif (method == 'beuler' or method == 'trapz'):
+        int_name = 'cvode'
+        options['order'] = 1
+        if not options.has_key('step'):
+            options['step'] = 0.05
+        options['min_step_size'] = options['step']
+        options['max_step_size'] = options['step']
+        #no error control possible, try to disable it:
+        if not options.has_key('atol'):
+            options['atol'] = 1e3
+        if not options.has_key('rtol'):
+            options['rtol'] = 1e3
+        del options['step']
+        if (method == 'trapz'):
+            options['lmm_type'] = 'ADAMS'
+            options['nonlinsolver'] = 'fixedpoint'
+            options['order'] = 2
+    else:
+        int_name = method
+
+    solver = ode(int_name, rhsfun, **options)
+    return solver.solve(t, y0)

+
+
+ +
+ +
+
+ +
+
+
+ ©2016, B. Malengier. + + | + Powered by Sphinx 7.3.7 + & Alabaster 0.7.16 + +
+ + + + + + \ No newline at end of file diff --git a/v3.0.0a3/_modules/scikits_odes_core.html b/v3.0.0a3/_modules/scikits_odes_core.html new file mode 100644 index 0000000..170a130 --- /dev/null +++ b/v3.0.0a3/_modules/scikits_odes_core.html @@ -0,0 +1,478 @@ + + + + + + + scikits_odes_core — Odes 3.0.0a3 documentation + + + + + + + + + + + + + + + + + + + + + +
+
+
+ + +
+ +

Source code for scikits_odes_core

+from . import _version
+__version__ = _version.get_versions()['version']
+
+
+

+[docs]
+class DaeBase:
+    """
+    The interface which DAE solvers must implement.
+
+    Parameters
+    ----------
+    Rfn : function
+        residual function
+    options : mapping
+        Additional options for initialization, solver dependent
+    """
+
+    integrator_classes = []
+
+    def __init__(self, Rfn, **options):
+        raise NotImplementedError('all DAE solvers must implement this')
+
+

+[docs]
+    def set_options(self, **options):
+        """
+        Set specific options for the solver.
+
+        Calling set_options a second time, normally resets the solver.
+        """
+        raise NotImplementedError('all DAE solvers must implement this')

+
+
+

+[docs]
+    def solve(self, tspan, y0,  yp0):
+        """
+        Runs the solver.
+
+        Parameters
+        ----------
+            tspan : list/array
+                A list of times at which the computed value will be returned.
+                Must contain the start time as first entry.
+            y0 : list/array
+                List of initial values
+            yp0 : list/array
+                List of initial values of derivatives
+
+        Returns
+        -------
+        old_api is False : namedtuple
+            namedtuple with the following attributes
+
+            =========== ==========================================
+            Field       Meaning
+            =========== ==========================================
+            ``flag``    An integer flag (StatusEnumXXX)
+            ``values``  Named tuple with entries array t and array y and array ydot. y will correspond to y_retn value and ydot to yp_retn!
+            ``errors``  Named tuple with entries t and y and ydot of error
+            ``roots``   Named tuple with entries array t and array y and array ydot
+            ``tstop``   Named tuple with entries array t and array y and array ydot
+            ``message`` String with message in case of an error
+            =========== ==========================================
+
+        old_api is True : tuple
+            tuple with the following elements in order
+
+            ========== ==========================================
+            Field      Meaning
+            ========== ==========================================
+            ``flag``   indicating return status of the solver
+            ``t``      numpy array of times at which the computations were successful
+            ``y``      numpy array of values corresponding to times t (values of y[i, :] ~ t[i])
+            ``yp``     numpy array of derivatives corresponding to times t (values of yp[i, :] ~ t[i])
+            ``t_err``  float or None - if recoverable error occurred (for example reached maximum number of allowed iterations), this is the time at which it happened
+            ``y_err``  numpy array of values corresponding to time t_err
+            ``yp_err`` numpy array of derivatives corresponding to time t_err
+            ========== ==========================================
+
+        """
+        raise NotImplementedError('all DAE solvers must implement this')

+
+
+

+[docs]
+    def init_step(self, t0, y0, yp0, y_ic0_retn = None, yp_ic0_retn = None):
+        """
+        Initializes the solver and allocates memory.
+
+        Parameters
+        ----------
+        t0 : number
+            initial time
+        y0 : list/array
+            initial condition for y
+        yp0 :  list/array
+            initial condition for yp
+        y_ic0 : numpy array
+            (optional) returns the calculated consistent initial condition for y
+        yp_ic0 :  numpy array
+            (optional) returns the calculated consistent initial condition for y
+            derivated.
+
+        Returns
+        -------
+        old_api is False : namedtuple
+            namedtuple with the following attributes
+
+            =========== ==========================================
+            Field       Meaning
+            =========== ==========================================
+            ``flag``    An integer flag (StatusEnumXXX)
+            ``values``  Named tuple with entries t and y and ydot. y will correspond to y_retn value and ydot to yp_retn!
+            ``errors``  Named tuple with entries t and y and ydot
+            ``roots``   Named tuple with entries t and y and ydot
+            ``tstop``   Named tuple with entries t and y and ydot
+            ``message`` String with message in case of an error
+            =========== ==========================================
+
+        old_api is True : tuple
+            tuple with the following elements in order
+
+            =========== ==========================================
+            Field       Meaning
+            =========== ==========================================
+            ``flag``    status of the computation (successful or error occurred)
+            ``t_out``   time, where the solver stopped (when no error occurred, t_out == t)
+            =========== ==========================================
+
+        """
+        raise NotImplementedError('all DAE solvers must implement this')

+
+
+

+[docs]
+    def step(self, t, y_retn=None, yp_retn=None):
+        """
+        Method for calling successive next step of the IDA solver to allow
+        more precise control over the IDA solver. The 'init_step' method has to
+        be called before the 'step' method.
+
+        A step is done towards time t, and output at t returned. This time can
+        be higher or lower than the previous time. If option
+        'one_step_compute'==True, and the solver supports it, only one internal
+        solver step is done in the direction of t starting at the current step.
+
+        If old_api=True, the old behavior is used: if t>0.0 then integration is
+        performed until this time and results at this time are returned in
+        y_retn; else if if t<0.0 only one internal step is performed towards
+        time abs(t) and results after this one time step are returned.
+
+        Parameters
+        ----------
+        t : number
+        y_retn : numpy array (ndim = 1) or None.
+            (Needs to be preallocated) If not None, will be filled with y at
+            time t. If None y_retn is not used.
+        yp_retn : numpy array (ndim = 1) or None.
+            (Needs to be preallocated) If not None, will be filled with
+            derivatives of y at time t. If None yp_retn is not used.
+
+        Returns
+        -------
+        old_api is False : namedtuple
+            namedtuple with the following attributes
+
+            =========== ==========================================
+            Field       Meaning
+            =========== ==========================================
+            ``flag``    An integer flag (StatusEnumXXX)
+            ``values``  Named tuple with entries t and y and ydot. y will correspond to y_retn value and ydot to yp_retn!
+            ``errors``  Named tuple with entries t and y and ydot
+            ``roots``   Named tuple with entries t and y and ydot
+            ``tstop``   Named tuple with entries t and y and ydot
+            ``message`` String with message in case of an error
+            =========== ==========================================
+
+        old_api is True : tuple
+            tuple with the following elements in order
+
+            =========== ==========================================
+            Field       Meaning
+            =========== ==========================================
+            ``flag``    status of the computation (successful or error occurred)
+            ``t_out``   time, where the solver stopped (when no error occurred, t_out == t)
+            =========== ==========================================
+
+        """
+        raise NotImplementedError('all DAE solvers must implement this')

+

+
+
+
+

+[docs]
+class OdeBase:
+    """
+    The interface which ODE solvers must implement.
+
+    Parameters
+    ----------
+    Rfn : function
+        A function which computes the required derivatives. The signature
+        should be ``func(t, y, y_dot, *args, **kwargs)``. Note that ``*args``
+        and ``**kwargs`` handling are solver dependent.
+
+    options : mapping
+        Additional options for initialization, solver dependent
+    """
+
+    integrator_classes = []
+
+    def __init__(self, Rfn, **options):
+        raise NotImplementedError('all ODE solvers must implement this')
+
+

+[docs]
+    def set_options(self, **options):
+        """
+        Set specific options for the solver.
+
+        Calling set_options a second time, normally resets the solver.
+        """
+        raise NotImplementedError('all ODE solvers must implement this')

+
+
+

+[docs]
+    def solve(self, tspan, y0):
+        """
+        Runs the solver.
+
+        Parameters
+        ----------
+        tspan : array (or similar)
+            a list of times at which the computed value will be returned. Must
+            contain the start time as first entry.
+
+        y0 : array (or similar)
+            a list of initial values
+
+        Returns
+        -------
+        old_api is False : namedtuple
+            namedtuple with the following attributes
+
+            =========== ==========================================
+            Field       Meaning
+            =========== ==========================================
+            ``flag``    An integer flag (StatusEnum)
+            ``values``  Named tuple with entries t and y
+            ``errors``  Named tuple with entries t and y
+            ``roots``   Named tuple with entries t and y
+            ``tstop``   Named tuple with entries t and y
+            ``message`` String with message in case of an error
+            =========== ==========================================
+
+        old_api is True : tuple
+            tuple with the following elements in order
+
+            ========== ==========================================
+            Field      Meaning
+            ========== ==========================================
+            ``flag``   indicating return status of the solver
+            ``t``      numpy array of times at which the computations were successful
+            ``y``      numpy array of values corresponding to times t (values of y[i, :] ~ t[i])
+            ``t_err``  float or None - if recoverable error occurred (for example reached maximum number of allowed iterations), this is the time at which it happened
+            ``y_err``  numpy array of values corresponding to time t_err
+            ========== ==========================================
+        """
+        raise NotImplementedError('all ODE solvers must implement this')

+
+
+

+[docs]
+    def init_step(self, t0, y0):
+        """
+        Initializes the solver and allocates memory.
+
+        Parameters
+        ----------
+        t0 : number
+            initial time
+        y0 : array
+            initial condition for y (can be list or numpy array)
+
+        Returns
+        -------
+        old_api is False : namedtuple
+            namedtuple with the following attributes
+
+            =========== ==========================================
+            Field       Meaning
+            =========== ==========================================
+            ``flag``    An integer flag (StatusEnum)
+            ``values``  Named tuple with entries t and y
+            ``errors``  Named tuple with entries t and y
+            ``roots``   Named tuple with entries t and y
+            ``tstop``   Named tuple with entries t and y
+            ``message`` String with message in case of an error
+            =========== ==========================================
+
+        old_api is True : tuple
+            tuple with the following elements in order
+
+            ========== ==========================================
+            Field      Meaning
+            ========== ==========================================
+            ``flag``   boolean status of the computation (successful or error occurred)
+            ``t_out``  initial time
+            ========== ==========================================
+        """
+        raise NotImplementedError('all ODE solvers must implement this')

+
+
+

+[docs]
+    def step(self, t, y_retn=None):
+        """
+        Method for calling successive next step of the ODE solver to allow
+        more precise control over the solver. The 'init_step' method has to
+        be called before the 'step' method.
+
+        A step is done towards time t, and output at t returned.  This time can
+        be higher or lower than the previous time.  If option
+        'one_step_compute'==True, and the solver supports it, only one internal
+        solver step is done in the direction of t starting at the current step.
+
+        If old_api=True, the old behavior is used: if t>0.0 then integration is
+        performed until this time and results at this time are returned in
+        y_retn if t<0.0 only one internal step is performed towards time abs(t)
+        and results after this one time step are returned
+
+        Parameters
+        ----------
+        t : number
+
+        y_retn : numpy vector (ndim = 1)
+            in which the computed value will be stored  (needs to be
+            preallocated).  If None y_retn is not used.
+
+        Returns
+        -------
+        old_api is False : namedtuple
+            namedtuple with the following attributes
+
+            =========== ==========================================
+            Field       Meaning
+            =========== ==========================================
+            ``flag``    An integer flag (StatusEnum)
+            ``values``  Named tuple with entries t and y
+            ``errors``  Named tuple with entries t and y
+            ``roots``   Named tuple with entries t and y
+            ``tstop``   Named tuple with entries t and y
+            ``message`` String with message in case of an error
+            =========== ==========================================
+
+        old_api is True : tuple
+            tuple with the following elements in order
+
+            ========== ==========================================
+            Field      Meaning
+            ========== ==========================================
+            ``flag``   status of the computation (successful or error occurred)
+            ``t_out``  time, where the solver stopped (when no error occurred, t_out == t)
+            ========== ==========================================
+        """
+        raise NotImplementedError('all ODE solvers must implement this')

+

+
+
+ +
+ +
+
+ +
+
+
+ ©2016, B. Malengier. + + | + Powered by Sphinx 7.3.7 + & Alabaster 0.7.16 + +
+ + + + + + \ No newline at end of file diff --git a/v3.0.0a3/_modules/scikits_odes_sundials.html b/v3.0.0a3/_modules/scikits_odes_sundials.html new file mode 100644 index 0000000..a0e6dea --- /dev/null +++ b/v3.0.0a3/_modules/scikits_odes_sundials.html @@ -0,0 +1,195 @@ + + + + + + + scikits_odes_sundials — Odes 3.0.0a3 documentation + + + + + + + + + + + + + + + + + + + + + +
+
+
+ + +
+ +

Source code for scikits_odes_sundials

+"""
+SUNDIALS wrapper
+"""
+
+import inspect
+from . import _version
+__version__ = _version.get_versions()['version']
+
+
+

+[docs]
+class CVODESolveException(Exception):
+    """Base class for exceptions raised by ``CVODE.validate_flags``."""
+    def __init__(self, soln):
+        self.soln = soln
+        self.args = (self._message.format(soln),)

+
+
+

+[docs]
+class CVODESolveFailed(CVODESolveException):
+    """``CVODE.solve`` failed to reach endpoint"""
+    _message = (
+        "Solver failed with flag {0.flag} and finished at {0.errors.t}"
+        "with values {0.errors.y}."
+    )

+
+
+

+[docs]
+class CVODESolveFoundRoot(CVODESolveException):
+    """``CVODE.solve`` found a root"""
+    _message = "Solver found a root at {0.roots.t[0]}."

+
+
+

+[docs]
+class CVODESolveReachedTSTOP(CVODESolveException):
+    """``CVODE.solve`` reached the endpoint specified by tstop."""
+    _message = "Solver reached tstop at {0.tstop.t[0]}."

+
+
+

+[docs]
+class IDASolveException(Exception):
+    """Base class for exceptions raised by ``IDA.validate_flags``."""
+    def __init__(self, soln):
+        self.soln = soln
+        self.args = (self._message.format(soln),)

+
+
+

+[docs]
+class IDASolveFailed(IDASolveException):
+    """``IDA.solve`` failed to reach endpoint"""
+    _message = (
+        "Solver failed with flag {0.flag} and finished at {0.errors.t}"
+        "with values {0.errors.y} and derivatives {0.errors.ydot}."
+    )

+
+
+

+[docs]
+class IDASolveFoundRoot(IDASolveException):
+    """``IDA.solve`` found a root"""
+    _message = "Solver found a root at {0.roots.t[0]}."

+
+
+

+[docs]
+class IDASolveReachedTSTOP(IDASolveException):
+    """``IDA.solve`` reached the endpoint specified by tstop."""
+    _message = "Solver reached tstop at {0.tstop.t[0]}."

+
+
+
+def _get_num_args(func):
+    """
+    Python 2/3 compatible method of getting number of args that `func` accepts
+    """
+    if hasattr(inspect, "getfullargspec"):
+        argspec = inspect.getfullargspec(func)
+    else:
+        argspec = inspect.getargspec(func)
+    arg_cnt = 0
+    for arg in argspec.args:
+        if arg not in ("self", "cls"):
+            arg_cnt += 1
+    return arg_cnt
+
+ +
+ +
+
+ +
+
+
+ ©2016, B. Malengier. + + | + Powered by Sphinx 7.3.7 + & Alabaster 0.7.16 + +
+ + + + + + \ No newline at end of file diff --git a/v3.0.0a3/_sources/api/compat.rst.txt b/v3.0.0a3/_sources/api/compat.rst.txt new file mode 100644 index 0000000..fdc5db1 --- /dev/null +++ b/v3.0.0a3/_sources/api/compat.rst.txt @@ -0,0 +1,47 @@ +scikits.odes +============ + +scikits.odes +------------ +.. automodule:: scikits.odes + :members: + +scikits.odes.ode +---------------- +.. automodule:: scikits.odes.ode + :members: + +scikits.odes.dae +---------------- +.. automodule:: scikits.odes.dae + :members: + +scikits.odes.dopri5 +-------------------- +.. automodule:: scikits.odes.dopri5 + :members: + +scikits.odes.ddaspkint +---------------------- +.. automodule:: scikits.odes.ddaspkint + :members: + +scikits.odes.lsodiint +--------------------- +.. automodule:: scikits.odes.lsodiint + :members: + +scikits.odes.sundials +--------------------- +.. automodule:: scikits.odes.sundials + :members: + +scikits.odes.sundials.cvode +--------------------------- +.. automodule:: scikits.odes.sundials.cvode + :members: + +scikits.odes.sundials.ida +------------------------- +.. automodule:: scikits.odes.sundials.ida + :members: diff --git a/v3.0.0a3/_sources/api/core.rst.txt b/v3.0.0a3/_sources/api/core.rst.txt new file mode 100644 index 0000000..294563d --- /dev/null +++ b/v3.0.0a3/_sources/api/core.rst.txt @@ -0,0 +1,5 @@ +scikits-odes-core +----------------- + +.. automodule:: scikits_odes_core + :members: diff --git a/v3.0.0a3/_sources/api/daepack.rst.txt b/v3.0.0a3/_sources/api/daepack.rst.txt new file mode 100644 index 0000000..24b3b14 --- /dev/null +++ b/v3.0.0a3/_sources/api/daepack.rst.txt @@ -0,0 +1,12 @@ +scikits-odes-daepack +==================== + +.. scikits_odes_daepack.ddaspkint +.. ------------------------------ +.. .. automodule:: scikits_odes_daepack.ddaspkint +.. :members: +.. +.. scikits_odes_daepack.lsodiint +.. ----------------------------- +.. .. automodule:: scikits_odes_daepack.lsodiint +.. :members: diff --git a/v3.0.0a3/_sources/api/index.rst.txt b/v3.0.0a3/_sources/api/index.rst.txt new file mode 100644 index 0000000..4ca2274 --- /dev/null +++ b/v3.0.0a3/_sources/api/index.rst.txt @@ -0,0 +1,11 @@ +Lower Level API +=============== + +.. toctree:: + :maxdepth: 2 + + core + daepack + sundials + main + compat diff --git a/v3.0.0a3/_sources/api/main.rst.txt b/v3.0.0a3/_sources/api/main.rst.txt new file mode 100644 index 0000000..f4f699e --- /dev/null +++ b/v3.0.0a3/_sources/api/main.rst.txt @@ -0,0 +1,23 @@ +scikits-odes +============ + +scikits_odes +------------ +.. automodule:: scikits_odes + :members: + +scikits_odes.ode +---------------- +.. automodule:: scikits_odes.ode + :members: + +scikits_odes.dae +---------------- +.. automodule:: scikits_odes.dae + :members: + +scikits_odes.dopri5 +-------------------- +.. automodule:: scikits_odes.dopri5 + :members: + diff --git a/v3.0.0a3/_sources/api/sundials.rst.txt b/v3.0.0a3/_sources/api/sundials.rst.txt new file mode 100644 index 0000000..d2a186d --- /dev/null +++ b/v3.0.0a3/_sources/api/sundials.rst.txt @@ -0,0 +1,17 @@ +scikits-odes-sundials +===================== + +scikits_odes_sundials +--------------------- +.. automodule:: scikits_odes_sundials + :members: + +scikits_odes_sundials.cvode +--------------------------- +.. automodule:: scikits_odes_sundials.cvode + :members: + +scikits_odes_sundials.ida +------------------------- +.. automodule:: scikits_odes_sundials.ida + :members: diff --git a/v3.0.0a3/_sources/dae.rst.txt b/v3.0.0a3/_sources/dae.rst.txt new file mode 100644 index 0000000..bf4609a --- /dev/null +++ b/v3.0.0a3/_sources/dae.rst.txt @@ -0,0 +1,5 @@ +DAE Solvers +----------------------------- + +.. autoclass:: scikits.odes.dae.dae + :members: diff --git a/v3.0.0a3/_sources/index.rst.txt b/v3.0.0a3/_sources/index.rst.txt new file mode 100644 index 0000000..8930452 --- /dev/null +++ b/v3.0.0a3/_sources/index.rst.txt @@ -0,0 +1,26 @@ +Welcome to the ODES scikit API Documentation +============================================ + +The ODES scikit provides access to Ordinary Differential Equation (ODE) solvers and Differential Algebraic Equation (DAE) solvers. + +This is the generated API documentation for version |version|, see https://scikits-odes.readthedocs.io/en/latest/ for the main documentation and user guide. + +For other versions of the API documentation, see https://bmcage.github.io/odes. + +Contents: + +.. toctree:: + :maxdepth: 4 + + ode + dae + sundials + api/index + +Indices and tables +================== + +* :ref:`genindex` +* :ref:`modindex` +* :ref:`search` + diff --git a/v3.0.0a3/_sources/ode.rst.txt b/v3.0.0a3/_sources/ode.rst.txt new file mode 100644 index 0000000..afa8e2d --- /dev/null +++ b/v3.0.0a3/_sources/ode.rst.txt @@ -0,0 +1,12 @@ +ODE Solvers +----------- +:py:mod:`scikits.odes` contains two main routines for solving ODEs: the simpler +:py:func:`scikits.odes.odeint.odeint`, and the more configurable +:py:class:`scikits.odes.ode.ode`. Both these routines allow selection of the +solver and solution method used. Additionally, it is also possible to directly +use the low level interface to individual solvers. + +.. autofunction:: scikits.odes.odeint.odeint + +.. autoclass:: scikits.odes.ode.ode + :members: diff --git a/v3.0.0a3/_sources/sundials.rst.txt b/v3.0.0a3/_sources/sundials.rst.txt new file mode 100644 index 0000000..acf899d --- /dev/null +++ b/v3.0.0a3/_sources/sundials.rst.txt @@ -0,0 +1,32 @@ +Sundials Solver Options +####################### + +Selecting Precision +------------------- +Sundials can be built with different precisions (currently `'single'` which maps +to C `'float'`; `'double'` (the default) which maps to C `'double'`; and +`'extended'` which maps to C `'long double'`), and scikits-odes-sundials +supports using whichever precision Sundials is built with. To take advantage of +this, you must first have sundials built and installed with the desired +precision setting. + +Once you have done this, build scikits-odes-sundials against this particular +version of sundials (see the main documentation for how to do this). +scikits-odes-sundials will automatically detect the precision, and store this in +a variable called +:py:const:`DTYPE`. :py:const:`DTYPE` should be accessed from +:py:mod:`scikits_odes_sundials` (other modules may have :py:const:`DTYPE` +defined, but :py:mod:`scikits_odes_sundials` should be preferred). Additionally +:py:const:`scikits_odes_sundials.precision` contains the precision setting found +by scikits.odes. + +To use :py:const:`DTYPE`, treat it as a numpy dtype; use it whenever you need to +create an array:: + + np.array([1,2,3], dtype=DTYPE) + +or when using scalars:: + + DTYPE(0.1) * DTYPE(0.1) + + diff --git a/v3.0.0a3/_static/_sphinx_javascript_frameworks_compat.js b/v3.0.0a3/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 0000000..8141580 --- /dev/null +++ b/v3.0.0a3/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,123 @@ +/* Compatability shim for jQuery and underscores.js. + * + * Copyright Sphinx contributors + * Released under the two clause BSD licence + */ + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. Multiple values per key are supported, + * it will always return arrays of strings for the value parts. + */ +jQuery.getQueryParameters = function(s) { + if (typeof s === 'undefined') + s = document.location.search; + var parts = s.substr(s.indexOf('?') + 1).split('&'); + var result = {}; + for (var i = 0; i < parts.length; i++) { + var tmp = parts[i].split('=', 2); + var key = jQuery.urldecode(tmp[0]); + var value = jQuery.urldecode(tmp[1]); + if (key in result) + result[key].push(value); + else + result[key] = [value]; + } + return result; +}; + +/** + * highlight a given string on a jquery object by wrapping it in + * span elements with the given class name. + */ +jQuery.fn.highlightText = function(text, className) { + function highlight(node, addItems) { + if (node.nodeType === 3) { + var val = node.nodeValue; + var pos = val.toLowerCase().indexOf(text); + if (pos >= 0 && + !jQuery(node.parentNode).hasClass(className) && + !jQuery(node.parentNode).hasClass("nohighlight")) { + var span; + var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.className = className; + } + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + node.parentNode.insertBefore(span, node.parentNode.insertBefore( + document.createTextNode(val.substr(pos + text.length)), + node.nextSibling)); + node.nodeValue = val.substr(0, pos); + if (isInSVG) { + var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect"); + var bbox = node.parentElement.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute('class', className); + addItems.push({ + "parent": node.parentNode, + "target": rect}); + } + } + } + else if (!jQuery(node).is("button, select, textarea")) { + jQuery.each(node.childNodes, function() { + highlight(this, addItems); + }); + } + } + var addItems = []; + var result = this.each(function() { + highlight(this, addItems); + }); + for (var i = 0; i < addItems.length; ++i) { + jQuery(addItems[i].parent).before(addItems[i].target); + } + return result; +}; + +/* + * backward compatibility for jQuery.browser + * This will be supported until firefox bug is fixed. + */ +if (!jQuery.browser) { + jQuery.uaMatch = function(ua) { + ua = ua.toLowerCase(); + + var match = /(chrome)[ \/]([\w.]+)/.exec(ua) || + /(webkit)[ \/]([\w.]+)/.exec(ua) || + /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) || + /(msie) ([\w.]+)/.exec(ua) || + ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) || + []; + + return { + browser: match[ 1 ] || "", + version: match[ 2 ] || "0" + }; + }; + jQuery.browser = {}; + jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true; +} diff --git a/v3.0.0a3/_static/alabaster.css b/v3.0.0a3/_static/alabaster.css new file mode 100644 index 0000000..e3174bf --- /dev/null +++ b/v3.0.0a3/_static/alabaster.css @@ -0,0 +1,708 @@ +@import url("basic.css"); + +/* -- page layout ----------------------------------------------------------- */ + +body { + font-family: Georgia, serif; + font-size: 17px; + background-color: #fff; + color: #000; + margin: 0; + padding: 0; +} + + +div.document { + width: 940px; + margin: 30px auto 0 auto; +} + +div.documentwrapper { + float: left; + width: 100%; +} + +div.bodywrapper { + margin: 0 0 0 220px; +} + +div.sphinxsidebar { + width: 220px; + font-size: 14px; + line-height: 1.5; +} + +hr { + border: 1px solid #B1B4B6; +} + +div.body { + background-color: #fff; + color: #3E4349; + padding: 0 30px 0 30px; +} + +div.body > .section { + text-align: left; +} + +div.footer { + width: 940px; + margin: 20px auto 30px auto; + font-size: 14px; + color: #888; + text-align: right; +} + +div.footer a { + color: #888; +} + +p.caption { + font-family: inherit; + font-size: inherit; +} + + +div.relations { + display: none; +} + + +div.sphinxsidebar { + max-height: 100%; + overflow-y: auto; +} + +div.sphinxsidebar a { + color: #444; + text-decoration: none; + border-bottom: 1px dotted #999; +} + +div.sphinxsidebar a:hover { + border-bottom: 1px solid #999; +} + +div.sphinxsidebarwrapper { + padding: 18px 10px; +} + +div.sphinxsidebarwrapper p.logo { + padding: 0; + margin: -10px 0 0 0px; + text-align: center; +} + +div.sphinxsidebarwrapper h1.logo { + margin-top: -10px; + text-align: center; + margin-bottom: 5px; + text-align: left; +} + +div.sphinxsidebarwrapper h1.logo-name { + margin-top: 0px; +} + +div.sphinxsidebarwrapper p.blurb { + margin-top: 0; + font-style: normal; +} + +div.sphinxsidebar h3, +div.sphinxsidebar h4 { + font-family: Georgia, serif; + color: #444; + font-size: 24px; + font-weight: normal; + margin: 0 0 5px 0; + padding: 0; +} + +div.sphinxsidebar h4 { + font-size: 20px; +} + +div.sphinxsidebar h3 a { + color: #444; +} + +div.sphinxsidebar p.logo a, +div.sphinxsidebar h3 a, +div.sphinxsidebar p.logo a:hover, +div.sphinxsidebar h3 a:hover { + border: none; +} + +div.sphinxsidebar p { + color: #555; + margin: 10px 0; +} + +div.sphinxsidebar ul { + margin: 10px 0; + padding: 0; + color: #000; +} + +div.sphinxsidebar ul li.toctree-l1 > a { + font-size: 120%; +} + +div.sphinxsidebar ul li.toctree-l2 > a { + font-size: 110%; +} + +div.sphinxsidebar input { + border: 1px solid #CCC; + font-family: Georgia, serif; + font-size: 1em; +} + +div.sphinxsidebar #searchbox input[type="text"] { + width: 160px; +} + +div.sphinxsidebar .search > div { + display: table-cell; +} + +div.sphinxsidebar hr { + border: none; + height: 1px; + color: #AAA; + background: #AAA; + + text-align: left; + margin-left: 0; + width: 50%; +} + +div.sphinxsidebar .badge { + border-bottom: none; +} + +div.sphinxsidebar .badge:hover { + border-bottom: none; +} + +/* To address an issue with donation coming after search */ +div.sphinxsidebar h3.donation { + margin-top: 10px; +} + +/* -- body styles ----------------------------------------------------------- */ + +a { + color: #004B6B; + text-decoration: underline; +} + +a:hover { + color: #6D4100; + text-decoration: underline; +} + +div.body h1, +div.body h2, +div.body h3, +div.body h4, +div.body h5, +div.body h6 { + font-family: Georgia, serif; + font-weight: normal; + margin: 30px 0px 10px 0px; + padding: 0; +} + +div.body h1 { margin-top: 0; padding-top: 0; font-size: 240%; } +div.body h2 { font-size: 180%; } +div.body h3 { font-size: 150%; } +div.body h4 { font-size: 130%; } +div.body h5 { font-size: 100%; } +div.body h6 { font-size: 100%; } + +a.headerlink { + color: #DDD; + padding: 0 4px; + text-decoration: none; +} + +a.headerlink:hover { + color: #444; + background: #EAEAEA; +} + +div.body p, div.body dd, div.body li { + line-height: 1.4em; +} + +div.admonition { + margin: 20px 0px; + padding: 10px 30px; + background-color: #EEE; + border: 1px solid #CCC; +} + +div.admonition tt.xref, div.admonition code.xref, div.admonition a tt { + background-color: #FBFBFB; + border-bottom: 1px solid #fafafa; +} + +div.admonition p.admonition-title { + font-family: Georgia, serif; + font-weight: normal; + font-size: 24px; + margin: 0 0 10px 0; + padding: 0; + line-height: 1; +} + +div.admonition p.last { + margin-bottom: 0; +} + +div.highlight { + background-color: #fff; +} + +dt:target, .highlight { + background: #FAF3E8; +} + +div.warning { + background-color: #FCC; + border: 1px solid #FAA; +} + +div.danger { + background-color: #FCC; + border: 1px solid #FAA; + -moz-box-shadow: 2px 2px 4px #D52C2C; + -webkit-box-shadow: 2px 2px 4px #D52C2C; + box-shadow: 2px 2px 4px #D52C2C; +} + +div.error { + background-color: #FCC; + border: 1px solid #FAA; + -moz-box-shadow: 2px 2px 4px #D52C2C; + -webkit-box-shadow: 2px 2px 4px #D52C2C; + box-shadow: 2px 2px 4px #D52C2C; +} + +div.caution { + background-color: #FCC; + border: 1px solid #FAA; +} + +div.attention { + background-color: #FCC; + border: 1px solid #FAA; +} + +div.important { + background-color: #EEE; + border: 1px solid #CCC; +} + +div.note { + background-color: #EEE; + border: 1px solid #CCC; +} + +div.tip { + background-color: #EEE; + border: 1px solid #CCC; +} + +div.hint { + background-color: #EEE; + border: 1px solid #CCC; +} + +div.seealso { + background-color: #EEE; + border: 1px solid #CCC; +} + +div.topic { + background-color: #EEE; +} + +p.admonition-title { + display: inline; +} + +p.admonition-title:after { + content: ":"; +} + +pre, tt, code { + font-family: 'Consolas', 'Menlo', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', monospace; + font-size: 0.9em; +} + +.hll { + background-color: #FFC; + margin: 0 -12px; + padding: 0 12px; + display: block; +} + +img.screenshot { +} + +tt.descname, tt.descclassname, code.descname, code.descclassname { + font-size: 0.95em; +} + +tt.descname, code.descname { + padding-right: 0.08em; +} + +img.screenshot { + -moz-box-shadow: 2px 2px 4px #EEE; + -webkit-box-shadow: 2px 2px 4px #EEE; + box-shadow: 2px 2px 4px #EEE; +} + +table.docutils { + border: 1px solid #888; + -moz-box-shadow: 2px 2px 4px #EEE; + -webkit-box-shadow: 2px 2px 4px #EEE; + box-shadow: 2px 2px 4px #EEE; +} + +table.docutils td, table.docutils th { + border: 1px solid #888; + padding: 0.25em 0.7em; +} + +table.field-list, table.footnote { + border: none; + -moz-box-shadow: none; + -webkit-box-shadow: none; + box-shadow: none; +} + +table.footnote { + margin: 15px 0; + width: 100%; + border: 1px solid #EEE; + background: #FDFDFD; + font-size: 0.9em; +} + +table.footnote + table.footnote { + margin-top: -15px; + border-top: none; +} + +table.field-list th { + padding: 0 0.8em 0 0; +} + +table.field-list td { + padding: 0; +} + +table.field-list p { + margin-bottom: 0.8em; +} + +/* Cloned from + * https://github.com/sphinx-doc/sphinx/commit/ef60dbfce09286b20b7385333d63a60321784e68 + */ +.field-name { + -moz-hyphens: manual; + -ms-hyphens: manual; + -webkit-hyphens: manual; + hyphens: manual; +} + +table.footnote td.label { + width: .1px; + padding: 0.3em 0 0.3em 0.5em; +} + +table.footnote td { + padding: 0.3em 0.5em; +} + +dl { + margin-left: 0; + margin-right: 0; + margin-top: 0; + padding: 0; +} + +dl dd { + margin-left: 30px; +} + +blockquote { + margin: 0 0 0 30px; + padding: 0; +} + +ul, ol { + /* Matches the 30px from the narrow-screen "li > ul" selector below */ + margin: 10px 0 10px 30px; + padding: 0; +} + +pre { + background: #EEE; + padding: 7px 30px; + margin: 15px 0px; + line-height: 1.3em; +} + +div.viewcode-block:target { + background: #ffd; +} + +dl pre, blockquote pre, li pre { + margin-left: 0; + padding-left: 30px; +} + +tt, code { + background-color: #ecf0f3; + color: #222; + /* padding: 1px 2px; */ +} + +tt.xref, code.xref, a tt { + background-color: #FBFBFB; + border-bottom: 1px solid #fff; +} + +a.reference { + text-decoration: none; + border-bottom: 1px dotted #004B6B; +} + +/* Don't put an underline on images */ +a.image-reference, a.image-reference:hover { + border-bottom: none; +} + +a.reference:hover { + border-bottom: 1px solid #6D4100; +} + +a.footnote-reference { + text-decoration: none; + font-size: 0.7em; + vertical-align: top; + border-bottom: 1px dotted #004B6B; +} + +a.footnote-reference:hover { + border-bottom: 1px solid #6D4100; +} + +a:hover tt, a:hover code { + background: #EEE; +} + + +@media screen and (max-width: 870px) { + + div.sphinxsidebar { + display: none; + } + + div.document { + width: 100%; + + } + + div.documentwrapper { + margin-left: 0; + margin-top: 0; + margin-right: 0; + margin-bottom: 0; + } + + div.bodywrapper { + margin-top: 0; + margin-right: 0; + margin-bottom: 0; + margin-left: 0; + } + + ul { + margin-left: 0; + } + + li > ul { + /* Matches the 30px from the "ul, ol" selector above */ + margin-left: 30px; + } + + .document { + width: auto; + } + + .footer { + width: auto; + } + + .bodywrapper { + margin: 0; + } + + .footer { + width: auto; + } + + .github { + display: none; + } + + + +} + + + +@media screen and (max-width: 875px) { + + body { + margin: 0; + padding: 20px 30px; + } + + div.documentwrapper { + float: none; + background: #fff; + } + + div.sphinxsidebar { + display: block; + float: none; + width: 102.5%; + margin: 50px -30px -20px -30px; + padding: 10px 20px; + background: #333; + color: #FFF; + } + + div.sphinxsidebar h3, div.sphinxsidebar h4, div.sphinxsidebar p, + div.sphinxsidebar h3 a { + color: #fff; + } + + div.sphinxsidebar a { + color: #AAA; + } + + div.sphinxsidebar p.logo { + display: none; + } + + div.document { + width: 100%; + margin: 0; + } + + div.footer { + display: none; + } + + div.bodywrapper { + margin: 0; + } + + div.body { + min-height: 0; + padding: 0; + } + + .rtd_doc_footer { + display: none; + } + + .document { + width: auto; + } + + .footer { + width: auto; + } + + .footer { + width: auto; + } + + .github { + display: none; + } +} + + +/* misc. */ + +.revsys-inline { + display: none!important; +} + +/* Hide ugly table cell borders in ..bibliography:: directive output */ +table.docutils.citation, table.docutils.citation td, table.docutils.citation th { + border: none; + /* Below needed in some edge cases; if not applied, bottom shadows appear */ + -moz-box-shadow: none; + -webkit-box-shadow: none; + box-shadow: none; +} + + +/* relbar */ + +.related { + line-height: 30px; + width: 100%; + font-size: 0.9rem; +} + +.related.top { + border-bottom: 1px solid #EEE; + margin-bottom: 20px; +} + +.related.bottom { + border-top: 1px solid #EEE; +} + +.related ul { + padding: 0; + margin: 0; + list-style: none; +} + +.related li { + display: inline; +} + +nav#rellinks { + float: right; +} + +nav#rellinks li+li:before { + content: "|"; +} + +nav#breadcrumbs li+li:before { + content: "\00BB"; +} + +/* Hide certain items when printing */ +@media print { + div.related { + display: none; + } +} \ No newline at end of file diff --git a/v3.0.0a3/_static/badge_only.css b/v3.0.0a3/_static/badge_only.css new file mode 100644 index 0000000..a10bb0d --- /dev/null +++ b/v3.0.0a3/_static/badge_only.css @@ -0,0 +1,269 @@ +.rst-content .line-block { + margin-bottom: 24px +} + +nav.wy-nav-side { + padding-bottom: 3em; +} + +.fa:before { + -webkit-font-smoothing: antialiased +} + +.clearfix { + * zoom: 1 +} + +.clearfix:before, .clearfix:after { + display: table; + content: "" +} + +.clearfix:after { + clear: both +} + +@font-face { + font-family: FontAwesome; + font-weight: normal; + font-style: normal; + src: url("./fontawesome-webfont.eot"); + src: url("./fontawesome-webfont.eot?#iefix") format("embedded-opentype"), url("./fontawesome-webfont.woff") format("woff"), url("./fontawesome-webfont.ttf") format("truetype"), url("./fontawesome-webfont.svg#FontAwesome") format("svg") +} + +.fa:before { + display: inline-block; + font-family: FontAwesome; + font-style: normal; + font-weight: normal; + line-height: 1; + text-decoration: inherit +} + +a .fa { + display: inline-block; + text-decoration: inherit +} + +li .fa { + display: inline-block +} + +li .fa-large:before, li .fa-large:before { + width: 1.875em +} + +ul.fas { + list-style-type: none; + margin-left: 2em; + text-indent: -0.8em +} + +ul.fas li .fa { + width: .8em +} + +ul.fas li .fa-large:before, ul.fas li .fa-large:before { + vertical-align: baseline +} + +.fa-book:before { + content: "" +} + +.icon-book:before { + content: "" +} + +.fa-caret-down:before { + content: "" +} + +.icon-caret-down:before { + content: "" +} + +.fa-caret-up:before { + content: "" +} + +.icon-caret-up:before { + content: "" +} + +.fa-caret-left:before { + content: "" +} + +.icon-caret-left:before { + content: "" +} + +.fa-caret-right:before { + content: "" +} + +.icon-caret-right:before { + content: "" +} + +.rst-versions { + position: fixed; + bottom: 0; + left: 0; + width: 300px; + max-width: 300px; + color: #fcfcfc; + background: #1f1d1d; + font-family: "Lato", "proxima-nova", "Helvetica Neue", Arial, sans-serif; + z-index: 400 +} + +.rst-versions a { + color: #2980B9; + text-decoration: none +} + +.rst-versions .rst-badge-small { + display: none +} + +.rst-versions .rst-current-version { + padding: 12px; + background-color: #272525; + display: block; + text-align: right; + font-size: 90%; + cursor: pointer; + color: #27AE60; + * zoom: 1 +} + +.rst-versions .rst-current-version:before, .rst-versions .rst-current-version:after { + display: table; + content: "" +} + +.rst-versions .rst-current-version:after { + clear: both +} + +.rst-versions .rst-current-version .fa { + color: #fcfcfc +} + +.rst-versions .rst-current-version .fa-book.shift-up { + float: left +} + +.rst-versions .rst-current-version .icon-book { + float: left +} + +.rst-versions .rst-current-version.rst-out-of-date { + background-color: #E74C3C; + color: #fff +} + +.rst-versions .rst-current-version.rst-active-old-version { + background-color: #F1C40F; + color: #000 +} + +.rst-versions.shift-up { + height: auto; + max-height: 100% +} + +.rst-other-versions { + text-align: left; +} +.rst-other-versions a { + border: 0; +} +.rst-other-versions dl { + margin: 0; +} + +.rst-versions.shift-up .rst-other-versions { + display: block +} + +.rst-versions .rst-other-versions { + font-size: 90%; + padding: 12px; + color: gray; + display: none +} + +.rst-versions .rst-other-versions hr { + display: block; + height: 1px; + border: 0; + margin: 20px 0; + padding: 0; + border-top: solid 1px #413d3d +} + +.rst-versions .rst-other-versions dd { + display: inline-block; + margin: 0 +} + +.rst-versions .rst-other-versions dd a { + display: inline-block; + padding: 6px; + color: #fcfcfc +} + +.rst-versions.rst-badge { + display: block; + width: auto; + bottom: 20px; + right: 20px; + left: auto; + border: none; + max-width: 300px + height: auto; +} + +.rst-versions.rst-badge .icon-book { + float: none +} + +.rst-versions.rst-badge .fa-book { + float: none +} + +.rst-versions.rst-badge.shift-up .rst-current-version { + text-align: right +} + +.rst-versions.rst-badge.shift-up .rst-current-version .fa-book { + float: left +} + +.rst-versions.rst-badge.shift-up .rst-current-version .icon-book { + float: left +} + +.rst-versions.rst-badge .rst-current-version { + height: 30px; + line-height: 30px; + padding: 0 6px; + display: block; +} + +@media screen and (max-width: 768px) { + .rst-versions { + width: 85%; + display: none + } + + .rst-versions.shift { + display: block + } +} + + + diff --git a/v3.0.0a3/_static/basic.css b/v3.0.0a3/_static/basic.css new file mode 100644 index 0000000..e5179b7 --- /dev/null +++ b/v3.0.0a3/_static/basic.css @@ -0,0 +1,925 @@ +/* + * basic.css + * ~~~~~~~~~ + * + * Sphinx stylesheet -- basic theme. + * + * :copyright: Copyright 2007-2024 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ + +/* -- main layout ----------------------------------------------------------- */ + +div.clearer { + clear: both; +} + +div.section::after { + display: block; + content: ''; + clear: left; +} + +/* -- relbar ---------------------------------------------------------------- */ + +div.related { + width: 100%; + font-size: 90%; +} + +div.related h3 { + display: none; +} + +div.related ul { + margin: 0; + padding: 0 0 0 10px; + list-style: none; +} + +div.related li { + display: inline; +} + +div.related li.right { + float: right; + margin-right: 5px; +} + +/* -- sidebar --------------------------------------------------------------- */ + +div.sphinxsidebarwrapper { + padding: 10px 5px 0 10px; +} + +div.sphinxsidebar { + float: left; + width: 230px; + margin-left: -100%; + font-size: 90%; + word-wrap: break-word; + overflow-wrap : break-word; +} + +div.sphinxsidebar ul { + list-style: none; +} + +div.sphinxsidebar ul ul, +div.sphinxsidebar ul.want-points { + margin-left: 20px; + list-style: square; +} + +div.sphinxsidebar ul ul { + margin-top: 0; + margin-bottom: 0; +} + +div.sphinxsidebar form { + margin-top: 10px; +} + +div.sphinxsidebar input { + border: 1px solid #98dbcc; + font-family: sans-serif; + font-size: 1em; +} + +div.sphinxsidebar #searchbox form.search { + overflow: hidden; +} + +div.sphinxsidebar #searchbox input[type="text"] { + float: left; + width: 80%; + padding: 0.25em; + box-sizing: border-box; +} + +div.sphinxsidebar #searchbox input[type="submit"] { + float: left; + width: 20%; + border-left: none; + padding: 0.25em; + box-sizing: border-box; +} + + +img { + border: 0; + max-width: 100%; +} + +/* -- search page ----------------------------------------------------------- */ + +ul.search { + margin: 10px 0 0 20px; + padding: 0; +} + +ul.search li { + padding: 5px 0 5px 20px; + background-image: url(file.png); + background-repeat: no-repeat; + background-position: 0 7px; +} + +ul.search li a { + font-weight: bold; +} + +ul.search li p.context { + color: #888; + margin: 2px 0 0 30px; + text-align: left; +} + +ul.keywordmatches li.goodmatch a { + font-weight: bold; +} + +/* -- index page ------------------------------------------------------------ */ + +table.contentstable { + width: 90%; + margin-left: auto; + margin-right: auto; +} + +table.contentstable p.biglink { + line-height: 150%; +} + +a.biglink { + font-size: 1.3em; +} + +span.linkdescr { + font-style: italic; + padding-top: 5px; + font-size: 90%; +} + +/* -- general index --------------------------------------------------------- */ + +table.indextable { + width: 100%; +} + +table.indextable td { + text-align: left; + vertical-align: top; +} + +table.indextable ul { + margin-top: 0; + margin-bottom: 0; + list-style-type: none; +} + +table.indextable > tbody > tr > td > ul { + padding-left: 0em; +} + +table.indextable tr.pcap { + height: 10px; +} + +table.indextable tr.cap { + margin-top: 10px; + background-color: #f2f2f2; +} + +img.toggler { + margin-right: 3px; + margin-top: 3px; + cursor: pointer; +} + +div.modindex-jumpbox { + border-top: 1px solid #ddd; + border-bottom: 1px solid #ddd; + margin: 1em 0 1em 0; + padding: 0.4em; +} + +div.genindex-jumpbox { + border-top: 1px solid #ddd; + border-bottom: 1px solid #ddd; + margin: 1em 0 1em 0; + padding: 0.4em; +} + +/* -- domain module index --------------------------------------------------- */ + +table.modindextable td { + padding: 2px; + border-collapse: collapse; +} + +/* -- general body styles --------------------------------------------------- */ + +div.body { + min-width: inherit; + max-width: 800px; +} + +div.body p, div.body dd, div.body li, div.body blockquote { + -moz-hyphens: auto; + -ms-hyphens: auto; + -webkit-hyphens: auto; + hyphens: auto; +} + +a.headerlink { + visibility: hidden; +} + +a:visited { + color: #551A8B; +} + +h1:hover > a.headerlink, +h2:hover > a.headerlink, +h3:hover > a.headerlink, +h4:hover > a.headerlink, +h5:hover > a.headerlink, +h6:hover > a.headerlink, +dt:hover > a.headerlink, +caption:hover > a.headerlink, +p.caption:hover > a.headerlink, +div.code-block-caption:hover > a.headerlink { + visibility: visible; +} + +div.body p.caption { + text-align: inherit; +} + +div.body td { + text-align: left; +} + +.first { + margin-top: 0 !important; +} + +p.rubric { + margin-top: 30px; + font-weight: bold; +} + +img.align-left, figure.align-left, .figure.align-left, object.align-left { + clear: left; + float: left; + margin-right: 1em; +} + +img.align-right, figure.align-right, .figure.align-right, object.align-right { + clear: right; + float: right; + margin-left: 1em; +} + +img.align-center, figure.align-center, .figure.align-center, object.align-center { + display: block; + margin-left: auto; + margin-right: auto; +} + +img.align-default, figure.align-default, .figure.align-default { + display: block; + margin-left: auto; + margin-right: auto; +} + +.align-left { + text-align: left; +} + +.align-center { + text-align: center; +} + +.align-default { + text-align: center; +} + +.align-right { + text-align: right; +} + +/* -- sidebars -------------------------------------------------------------- */ + +div.sidebar, +aside.sidebar { + margin: 0 0 0.5em 1em; + border: 1px solid #ddb; + padding: 7px; + background-color: #ffe; + width: 40%; + float: right; + clear: right; + overflow-x: auto; +} + +p.sidebar-title { + font-weight: bold; +} + +nav.contents, +aside.topic, +div.admonition, div.topic, blockquote { + clear: left; +} + +/* -- topics ---------------------------------------------------------------- */ + +nav.contents, +aside.topic, +div.topic { + border: 1px solid #ccc; + padding: 7px; + margin: 10px 0 10px 0; +} + +p.topic-title { + font-size: 1.1em; + font-weight: bold; + margin-top: 10px; +} + +/* -- admonitions ----------------------------------------------------------- */ + +div.admonition { + margin-top: 10px; + margin-bottom: 10px; + padding: 7px; +} + +div.admonition dt { + font-weight: bold; +} + +p.admonition-title { + margin: 0px 10px 5px 0px; + font-weight: bold; +} + +div.body p.centered { + text-align: center; + margin-top: 25px; +} + +/* -- content of sidebars/topics/admonitions -------------------------------- */ + +div.sidebar > :last-child, +aside.sidebar > :last-child, +nav.contents > :last-child, +aside.topic > :last-child, +div.topic > :last-child, +div.admonition > :last-child { + margin-bottom: 0; +} + +div.sidebar::after, +aside.sidebar::after, +nav.contents::after, +aside.topic::after, +div.topic::after, +div.admonition::after, +blockquote::after { + display: block; + content: ''; + clear: both; +} + +/* -- tables ---------------------------------------------------------------- */ + +table.docutils { + margin-top: 10px; + margin-bottom: 10px; + border: 0; + border-collapse: collapse; +} + +table.align-center { + margin-left: auto; + margin-right: auto; +} + +table.align-default { + margin-left: auto; + margin-right: auto; +} + +table caption span.caption-number { + font-style: italic; +} + +table caption span.caption-text { +} + +table.docutils td, table.docutils th { + padding: 1px 8px 1px 5px; + border-top: 0; + border-left: 0; + border-right: 0; + border-bottom: 1px solid #aaa; +} + +th { + text-align: left; + padding-right: 5px; +} + +table.citation { + border-left: solid 1px gray; + margin-left: 1px; +} + +table.citation td { + border-bottom: none; +} + +th > :first-child, +td > :first-child { + margin-top: 0px; +} + +th > :last-child, +td > :last-child { + margin-bottom: 0px; +} + +/* -- figures --------------------------------------------------------------- */ + +div.figure, figure { + margin: 0.5em; + padding: 0.5em; +} + +div.figure p.caption, figcaption { + padding: 0.3em; +} + +div.figure p.caption span.caption-number, +figcaption span.caption-number { + font-style: italic; +} + +div.figure p.caption span.caption-text, +figcaption span.caption-text { +} + +/* -- field list styles ----------------------------------------------------- */ + +table.field-list td, table.field-list th { + border: 0 !important; +} + +.field-list ul { + margin: 0; + padding-left: 1em; +} + +.field-list p { + margin: 0; +} + +.field-name { + -moz-hyphens: manual; + -ms-hyphens: manual; + -webkit-hyphens: manual; + hyphens: manual; +} + +/* -- hlist styles ---------------------------------------------------------- */ + +table.hlist { + margin: 1em 0; +} + +table.hlist td { + vertical-align: top; +} + +/* -- object description styles --------------------------------------------- */ + +.sig { + font-family: 'Consolas', 'Menlo', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', monospace; +} + +.sig-name, code.descname { + background-color: transparent; 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+ padding-right: 5px; +} + +dl.field-list > dd { + padding-left: 0.5em; + margin-top: 0em; + margin-left: 0em; + margin-bottom: 0em; +} + +dl { + margin-bottom: 15px; +} + +dd > :first-child { + margin-top: 0px; +} + +dd ul, dd table { + margin-bottom: 10px; +} + +dd { + margin-top: 3px; + margin-bottom: 10px; + margin-left: 30px; +} + +.sig dd { + margin-top: 0px; + margin-bottom: 0px; +} + +.sig dl { + margin-top: 0px; + margin-bottom: 0px; +} + +dl > dd:last-child, +dl > dd:last-child > :last-child { + margin-bottom: 0; +} + +dt:target, span.highlighted { + background-color: #fbe54e; +} + +rect.highlighted { + fill: #fbe54e; +} + +dl.glossary dt { + font-weight: bold; + font-size: 1.1em; +} + +.versionmodified { + font-style: italic; +} + +.system-message { + background-color: #fda; + padding: 5px; + border: 3px solid red; +} + +.footnote:target { + background-color: #ffa; +} + +.line-block { + display: block; + margin-top: 1em; + margin-bottom: 1em; +} + +.line-block .line-block { + margin-top: 0; + margin-bottom: 0; + margin-left: 1.5em; +} + +.guilabel, .menuselection { + font-family: sans-serif; +} + +.accelerator { + text-decoration: underline; +} + +.classifier { + font-style: oblique; +} + +.classifier:before { + font-style: normal; + margin: 0 0.5em; + content: ":"; + display: inline-block; +} + +abbr, acronym { + border-bottom: dotted 1px; + cursor: help; +} + +.translated { + background-color: rgba(207, 255, 207, 0.2) +} + +.untranslated { + background-color: rgba(255, 207, 207, 0.2) +} + +/* -- code displays --------------------------------------------------------- */ + +pre { + overflow: auto; + overflow-y: hidden; /* fixes display issues on Chrome browsers */ +} + +pre, div[class*="highlight-"] { + clear: both; +} + +span.pre { + -moz-hyphens: none; + -ms-hyphens: none; + -webkit-hyphens: none; + hyphens: none; + white-space: nowrap; +} + +div[class*="highlight-"] { + margin: 1em 0; +} + +td.linenos pre { + border: 0; + background-color: transparent; + color: #aaa; +} + +table.highlighttable { + display: block; +} + +table.highlighttable tbody { + display: block; +} + +table.highlighttable tr { + display: flex; +} + +table.highlighttable td { + margin: 0; + padding: 0; +} + +table.highlighttable td.linenos { + padding-right: 0.5em; +} + +table.highlighttable td.code { + flex: 1; + overflow: hidden; +} + +.highlight .hll { + display: block; +} + +div.highlight pre, +table.highlighttable pre { + margin: 0; +} + +div.code-block-caption + div { + margin-top: 0; +} + +div.code-block-caption { + margin-top: 1em; + padding: 2px 5px; + font-size: small; +} + +div.code-block-caption code { + background-color: transparent; +} + +table.highlighttable td.linenos, +span.linenos, +div.highlight span.gp { /* gp: Generic.Prompt */ + user-select: none; + -webkit-user-select: text; /* Safari fallback only */ + -webkit-user-select: none; /* Chrome/Safari */ + -moz-user-select: none; /* Firefox */ + -ms-user-select: none; /* IE10+ */ +} + +div.code-block-caption span.caption-number { + padding: 0.1em 0.3em; + font-style: italic; +} + +div.code-block-caption span.caption-text { +} + +div.literal-block-wrapper { + margin: 1em 0; +} + +code.xref, a code { + background-color: transparent; + font-weight: bold; +} + +h1 code, h2 code, h3 code, h4 code, h5 code, h6 code { + background-color: transparent; +} + +.viewcode-link { + float: right; +} + +.viewcode-back { + float: right; + font-family: sans-serif; +} + +div.viewcode-block:target { + margin: -1px -10px; + padding: 0 10px; +} + +/* -- math display ---------------------------------------------------------- */ + +img.math { + vertical-align: middle; +} + +div.body div.math p { + text-align: center; +} + +span.eqno { + float: right; +} + +span.eqno a.headerlink { + position: absolute; + z-index: 1; +} + +div.math:hover a.headerlink { + visibility: visible; +} + +/* -- printout stylesheet --------------------------------------------------- */ + +@media print { + div.document, + div.documentwrapper, + div.bodywrapper { + margin: 0 !important; + width: 100%; + } + + div.sphinxsidebar, + div.related, + div.footer, + #top-link { + display: none; + } +} \ No newline at end of file diff --git a/v3.0.0a3/_static/custom.css b/v3.0.0a3/_static/custom.css new file mode 100644 index 0000000..2a924f1 --- /dev/null +++ b/v3.0.0a3/_static/custom.css @@ -0,0 +1 @@ +/* This file intentionally left blank. */ diff --git a/v3.0.0a3/_static/docs-versions-menu.js b/v3.0.0a3/_static/docs-versions-menu.js new file mode 100644 index 0000000..8d1b253 --- /dev/null +++ b/v3.0.0a3/_static/docs-versions-menu.js @@ -0,0 +1,153 @@ +"use strict"; + +function getGhPagesCurrentFolder() { + // Extract version folder under the assumpgion that the URL is of the form + // https://.github.io///... + if (window.location.hostname.includes("github.io")){ + return window.location.pathname.split('/')[2]; + } +} + +function getRootUrl() { + // Return the "root" URL, i.e. everything before the current folder + // (getGhPagesCurrentFolder). On gh-pages, this includes the project name. + var root_url = window.location.origin; + if (window.location.hostname.includes("github.io")){ + root_url = root_url + '/' + window.location.pathname.split('/')[1]; + } + return root_url; +} + +function getGithubProjectUrl(){ + // Return the project url on Github, under the assumption that the current + // page is hosted on github-pages (https://.github.io//) + var root_url = getRootUrl(); + var match = root_url.match(/([\w\d-]+)\.github\.io\/([\w\d-]+)/) + if (match !== null){ + var username = match[1]; + var projectname = match[2]; + return "https://github.com/" + username + "/" + projectname; + } else { + return null + } +} + +function _addVersionsMenu(version_data) { + // The menu was reverse-engineered from the RTD websites, so it's very + // specific to the sphinx_rtd_theme + var folders = version_data["versions"]; + var root_url = getRootUrl(); + var current_url = document.URL; + var current_folder = getGhPagesCurrentFolder(); + if (current_folder === undefined) return; + var current_version = version_data["labels"][current_folder]; + var menu = document.createElement('div'); + menu.setAttribute('class', 'rst-versions rst-badge'); + menu.setAttribute('data-toggle', 'rst-versions'); + menu.setAttribute('role', 'note'); + menu.setAttribute('aria-label', 'versions'); + var inner_html = + "" + + " " + + "" + current_version + " " + + "" + + "" + + "
" + + "
" + + "
" + + "
Versions
"; + var i; + for (i in folders) { + var folder = folders[i]; + if (folder == current_folder){ + var inner_html = inner_html + "
" + current_version + "
"; + } else { + var inner_html = inner_html + "
" + version_data["labels"][folder] + "
"; + } + } + var downloads = version_data["downloads"][current_folder]; + if (downloads.length > 0){ + var inner_html = inner_html + + "
Downloads
"; + for (i in downloads) { + var download_label = downloads[i][0]; + var download_url = downloads[i][1]; + if (!(/^(https?|ftp):/.test(download_url))){ + if (!download_url.startsWith('/')){ + var download_url = '/' + download_url; + } + var download_url = root_url + download_url; + } + var inner_html = inner_html + "
" + + download_label + "
"; + } + } + var github_project_url = getGithubProjectUrl(); + if (github_project_url !== null && github_project_url.length > 0){ + var inner_html = inner_html + + "
On Github
" + + "
Project Home
" + + "
Issues
"; + } + var inner_html = inner_html + + "
" + + "
" + + "Generated by Docs Versions Menu" + + "" + + "
" + + "
"; + menu.innerHTML = inner_html; + var parent = document.body; + parent.insertBefore(menu, parent.lastChild); + + // Add a warning banner for dev/outdated versions + var warning; + var msg; + if (version_data["warnings"][current_folder].indexOf("outdated") >=0){ + warning = document.createElement('div'); + warning.setAttribute('class', 'admonition danger'); + msg = "This document is for an outdated version."; + } else if (version_data["warnings"][current_folder].indexOf("unreleased") >=0){ + warning = document.createElement('div'); + warning.setAttribute('class', 'admonition danger'); + msg = "This document is for an unreleased development version."; + } else if (version_data["warnings"][current_folder].indexOf("prereleased") >=0){ + warning = document.createElement('div'); + warning.setAttribute('class', 'admonition danger'); + msg = "This document is for a pre-release development version."; + } + if (warning !== undefined){ + if (version_data["latest"] !== null){ + msg = msg + " Documentation is available for the " + "latest public release." + } + warning.innerHTML = "

Note

" + + "

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"; + var parent = document.querySelector('div.body') + || document.querySelector('div.document') + || document.body; + parent.insertBefore(warning, parent.firstChild); + } + + +} + +function addVersionsMenu() { + // We assume that we can load versions.json from + // https://.github.io//versions.json + // That is, there's a path between the hostname and versions.json + var json_file = "/" + window.location.pathname.split("/")[1] + "/versions.json"; + $.getJSON(json_file, _addVersionsMenu); + + $( "body" ).on('click', "div.rst-versions.rst-badge", function() { + $('.rst-other-versions').toggle(); + $('.rst-versions .rst-current-version .fa-book').toggleClass('shift-up'); + }); +} + +document.addEventListener('DOMContentLoaded', addVersionsMenu); \ No newline at end of file diff --git a/v3.0.0a3/_static/doctools.js b/v3.0.0a3/_static/doctools.js new file mode 100644 index 0000000..4d67807 --- /dev/null +++ b/v3.0.0a3/_static/doctools.js @@ -0,0 +1,156 @@ +/* + * doctools.js + * ~~~~~~~~~~~ + * + * Base JavaScript utilities for all Sphinx HTML documentation. + * + * :copyright: Copyright 2007-2024 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ +"use strict"; + +const BLACKLISTED_KEY_CONTROL_ELEMENTS = new Set([ + "TEXTAREA", + "INPUT", + "SELECT", + "BUTTON", +]); + +const _ready = (callback) => { + if (document.readyState !== "loading") { + callback(); + } else { + document.addEventListener("DOMContentLoaded", callback); + } +}; + +/** + * Small JavaScript module for the documentation. + */ +const Documentation = { + init: () => { + Documentation.initDomainIndexTable(); + Documentation.initOnKeyListeners(); + }, + + /** + * i18n support + */ + TRANSLATIONS: {}, + PLURAL_EXPR: (n) => (n === 1 ? 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font-weight: bold } /* Literal.String.Escape */ +.highlight .sh { color: #4070a0 } /* Literal.String.Heredoc */ +.highlight .si { color: #70a0d0; font-style: italic } /* Literal.String.Interpol */ +.highlight .sx { color: #c65d09 } /* Literal.String.Other */ +.highlight .sr { color: #235388 } /* Literal.String.Regex */ +.highlight .s1 { color: #4070a0 } /* Literal.String.Single */ +.highlight .ss { color: #517918 } /* Literal.String.Symbol */ +.highlight .bp { color: #007020 } /* Name.Builtin.Pseudo */ +.highlight .fm { color: #06287e } /* Name.Function.Magic */ +.highlight .vc { color: #bb60d5 } /* Name.Variable.Class */ +.highlight .vg { color: #bb60d5 } /* Name.Variable.Global */ +.highlight .vi { color: #bb60d5 } /* Name.Variable.Instance */ +.highlight .vm { color: #bb60d5 } /* Name.Variable.Magic */ +.highlight .il { color: #208050 } /* Literal.Number.Integer.Long */ \ No newline at end of file diff --git a/v3.0.0a3/_static/searchtools.js b/v3.0.0a3/_static/searchtools.js new file mode 100644 index 0000000..92da3f8 --- /dev/null +++ b/v3.0.0a3/_static/searchtools.js @@ -0,0 +1,619 @@ +/* + * searchtools.js + * ~~~~~~~~~~~~~~~~ + * + * Sphinx JavaScript utilities for the full-text search. + * + * :copyright: Copyright 2007-2024 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ +"use strict"; + +/** + * Simple result scoring code. + */ +if (typeof Scorer === "undefined") { + var Scorer = { + // Implement the following function to further tweak the score for each result + // The function takes a result array [docname, title, anchor, descr, score, filename] + // and returns the new score. + /* + score: result => { + const [docname, title, anchor, descr, score, filename] = result + return score + }, + */ + + // query matches the full name of an object + objNameMatch: 11, + // or matches in the last dotted part of the object name + objPartialMatch: 6, + // Additive scores depending on the priority of the object + objPrio: { + 0: 15, // used to be importantResults + 1: 5, // used to be objectResults + 2: -5, // used to be unimportantResults + }, + // Used when the priority is not in the mapping. + objPrioDefault: 0, + + // query found in title + title: 15, + partialTitle: 7, + // query found in terms + term: 5, + partialTerm: 2, + }; +} + +const _removeChildren = (element) => { + while (element && element.lastChild) element.removeChild(element.lastChild); +}; + +/** + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions#escaping + */ +const _escapeRegExp = (string) => + string.replace(/[.*+\-?^${}()|[\]\\]/g, "\\$&"); // $& means the whole matched string + +const _displayItem = (item, searchTerms, highlightTerms) => { + const docBuilder = DOCUMENTATION_OPTIONS.BUILDER; + const docFileSuffix = DOCUMENTATION_OPTIONS.FILE_SUFFIX; + const docLinkSuffix = DOCUMENTATION_OPTIONS.LINK_SUFFIX; + const showSearchSummary = DOCUMENTATION_OPTIONS.SHOW_SEARCH_SUMMARY; + const contentRoot = document.documentElement.dataset.content_root; + + const [docName, title, anchor, descr, score, _filename] = item; + + let listItem = document.createElement("li"); + let requestUrl; + let linkUrl; + if (docBuilder === "dirhtml") { + // dirhtml builder + let dirname = docName + "/"; + if (dirname.match(/\/index\/$/)) + dirname = dirname.substring(0, dirname.length - 6); + else if (dirname === "index/") dirname = ""; + requestUrl = contentRoot + dirname; + linkUrl = requestUrl; + } else { + // normal html builders + requestUrl = contentRoot + docName + docFileSuffix; + linkUrl = docName + docLinkSuffix; + } + let linkEl = listItem.appendChild(document.createElement("a")); + linkEl.href = linkUrl + anchor; + linkEl.dataset.score = score; + linkEl.innerHTML = title; + if (descr) { + listItem.appendChild(document.createElement("span")).innerHTML = + " (" + descr + ")"; + // highlight search terms in the description + if (SPHINX_HIGHLIGHT_ENABLED) // set in sphinx_highlight.js + highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted")); + } + else if (showSearchSummary) + fetch(requestUrl) + .then((responseData) => responseData.text()) + .then((data) => { + if (data) + listItem.appendChild( + Search.makeSearchSummary(data, searchTerms, anchor) + ); + // highlight search terms in the summary + if (SPHINX_HIGHLIGHT_ENABLED) // set in sphinx_highlight.js + highlightTerms.forEach((term) => _highlightText(listItem, term, "highlighted")); + }); + Search.output.appendChild(listItem); +}; +const _finishSearch = (resultCount) => { + Search.stopPulse(); + Search.title.innerText = _("Search Results"); + if (!resultCount) + Search.status.innerText = Documentation.gettext( + "Your search did not match any documents. Please make sure that all words are spelled correctly and that you've selected enough categories." + ); + else + Search.status.innerText = _( + "Search finished, found ${resultCount} page(s) matching the search query." + ).replace('${resultCount}', resultCount); +}; +const _displayNextItem = ( + results, + resultCount, + searchTerms, + highlightTerms, +) => { + // results left, load the summary and display it + // this is intended to be dynamic (don't sub resultsCount) + if (results.length) { + _displayItem(results.pop(), searchTerms, highlightTerms); + setTimeout( + () => _displayNextItem(results, resultCount, searchTerms, highlightTerms), + 5 + ); + } + // search finished, update title and status message + else _finishSearch(resultCount); +}; +// Helper function used by query() to order search results. +// Each input is an array of [docname, title, anchor, descr, score, filename]. +// Order the results by score (in opposite order of appearance, since the +// `_displayNextItem` function uses pop() to retrieve items) and then alphabetically. +const _orderResultsByScoreThenName = (a, b) => { + const leftScore = a[4]; + const rightScore = b[4]; + if (leftScore === rightScore) { + // same score: sort alphabetically + const leftTitle = a[1].toLowerCase(); + const rightTitle = b[1].toLowerCase(); + if (leftTitle === rightTitle) return 0; + return leftTitle > rightTitle ? -1 : 1; // inverted is intentional + } + return leftScore > rightScore ? 1 : -1; +}; + +/** + * Default splitQuery function. Can be overridden in ``sphinx.search`` with a + * custom function per language. + * + * The regular expression works by splitting the string on consecutive characters + * that are not Unicode letters, numbers, underscores, or emoji characters. + * This is the same as ``\W+`` in Python, preserving the surrogate pair area. + */ +if (typeof splitQuery === "undefined") { + var splitQuery = (query) => query + .split(/[^\p{Letter}\p{Number}_\p{Emoji_Presentation}]+/gu) + .filter(term => term) // remove remaining empty strings +} + +/** + * Search Module + */ +const Search = { + _index: null, + _queued_query: null, + _pulse_status: -1, + + htmlToText: (htmlString, anchor) => { + const htmlElement = new DOMParser().parseFromString(htmlString, 'text/html'); + for (const removalQuery of [".headerlinks", "script", "style"]) { + htmlElement.querySelectorAll(removalQuery).forEach((el) => { el.remove() }); + } + if (anchor) { + const anchorContent = htmlElement.querySelector(`[role="main"] ${anchor}`); + if (anchorContent) return anchorContent.textContent; + + console.warn( + `Anchored content block not found. Sphinx search tries to obtain it via DOM query '[role=main] ${anchor}'. Check your theme or template.` + ); + } + + // if anchor not specified or not found, fall back to main content + const docContent = htmlElement.querySelector('[role="main"]'); + if (docContent) return docContent.textContent; + + console.warn( + "Content block not found. Sphinx search tries to obtain it via DOM query '[role=main]'. Check your theme or template." + ); + return ""; + }, + + init: () => { + const query = new URLSearchParams(window.location.search).get("q"); + document + .querySelectorAll('input[name="q"]') + .forEach((el) => (el.value = query)); + if (query) Search.performSearch(query); + }, + + loadIndex: (url) => + (document.body.appendChild(document.createElement("script")).src = url), + + setIndex: (index) => { + Search._index = index; + if (Search._queued_query !== null) { + const query = Search._queued_query; + Search._queued_query = null; + Search.query(query); + } + }, + + hasIndex: () => Search._index !== null, + + deferQuery: (query) => (Search._queued_query = query), + + stopPulse: () => (Search._pulse_status = -1), + + startPulse: () => { + if (Search._pulse_status >= 0) return; + + const pulse = () => { + Search._pulse_status = (Search._pulse_status + 1) % 4; + Search.dots.innerText = ".".repeat(Search._pulse_status); + if (Search._pulse_status >= 0) window.setTimeout(pulse, 500); + }; + pulse(); + }, + + /** + * perform a search for something (or wait until index is loaded) + */ + performSearch: (query) => { + // create the required interface elements + const searchText = document.createElement("h2"); + searchText.textContent = _("Searching"); + const searchSummary = document.createElement("p"); + searchSummary.classList.add("search-summary"); + searchSummary.innerText = ""; + const searchList = document.createElement("ul"); + searchList.classList.add("search"); + + const out = document.getElementById("search-results"); + Search.title = out.appendChild(searchText); + Search.dots = Search.title.appendChild(document.createElement("span")); + Search.status = out.appendChild(searchSummary); + Search.output = out.appendChild(searchList); + + const searchProgress = document.getElementById("search-progress"); + // Some themes don't use the search progress node + if (searchProgress) { + searchProgress.innerText = _("Preparing search..."); + } + Search.startPulse(); + + // index already loaded, the browser was quick! + if (Search.hasIndex()) Search.query(query); + else Search.deferQuery(query); + }, + + _parseQuery: (query) => { + // stem the search terms and add them to the correct list + const stemmer = new Stemmer(); + const searchTerms = new Set(); + const excludedTerms = new Set(); + const highlightTerms = new Set(); + const objectTerms = new Set(splitQuery(query.toLowerCase().trim())); + splitQuery(query.trim()).forEach((queryTerm) => { + const queryTermLower = queryTerm.toLowerCase(); + + // maybe skip this "word" + // stopwords array is from language_data.js + if ( + stopwords.indexOf(queryTermLower) !== -1 || + queryTerm.match(/^\d+$/) + ) + return; + + // stem the word + let word = stemmer.stemWord(queryTermLower); + // select the correct list + if (word[0] === "-") excludedTerms.add(word.substr(1)); + else { + searchTerms.add(word); + highlightTerms.add(queryTermLower); + } + }); + + if (SPHINX_HIGHLIGHT_ENABLED) { // set in sphinx_highlight.js + localStorage.setItem("sphinx_highlight_terms", [...highlightTerms].join(" ")) + } + + // console.debug("SEARCH: searching for:"); + // console.info("required: ", [...searchTerms]); + // console.info("excluded: ", [...excludedTerms]); + + return [query, searchTerms, excludedTerms, highlightTerms, objectTerms]; + }, + + /** + * execute search (requires search index to be loaded) + */ + _performSearch: (query, searchTerms, excludedTerms, highlightTerms, objectTerms) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + const allTitles = Search._index.alltitles; + const indexEntries = Search._index.indexentries; + + // Collect multiple result groups to be sorted separately and then ordered. + // Each is an array of [docname, title, anchor, descr, score, filename]. + const normalResults = []; + const nonMainIndexResults = []; + + _removeChildren(document.getElementById("search-progress")); + + const queryLower = query.toLowerCase().trim(); + for (const [title, foundTitles] of Object.entries(allTitles)) { + if (title.toLowerCase().trim().includes(queryLower) && (queryLower.length >= title.length/2)) { + for (const [file, id] of foundTitles) { + let score = Math.round(100 * queryLower.length / title.length) + normalResults.push([ + docNames[file], + titles[file] !== title ? `${titles[file]} > ${title}` : title, + id !== null ? "#" + id : "", + null, + score, + filenames[file], + ]); + } + } + } + + // search for explicit entries in index directives + for (const [entry, foundEntries] of Object.entries(indexEntries)) { + if (entry.includes(queryLower) && (queryLower.length >= entry.length/2)) { + for (const [file, id, isMain] of foundEntries) { + const score = Math.round(100 * queryLower.length / entry.length); + const result = [ + docNames[file], + titles[file], + id ? "#" + id : "", + null, + score, + filenames[file], + ]; + if (isMain) { + normalResults.push(result); + } else { + nonMainIndexResults.push(result); + } + } + } + } + + // lookup as object + objectTerms.forEach((term) => + normalResults.push(...Search.performObjectSearch(term, objectTerms)) + ); + + // lookup as search terms in fulltext + normalResults.push(...Search.performTermsSearch(searchTerms, excludedTerms)); + + // let the scorer override scores with a custom scoring function + if (Scorer.score) { + normalResults.forEach((item) => (item[4] = Scorer.score(item))); + nonMainIndexResults.forEach((item) => (item[4] = Scorer.score(item))); + } + + // Sort each group of results by score and then alphabetically by name. + normalResults.sort(_orderResultsByScoreThenName); + nonMainIndexResults.sort(_orderResultsByScoreThenName); + + // Combine the result groups in (reverse) order. + // Non-main index entries are typically arbitrary cross-references, + // so display them after other results. + let results = [...nonMainIndexResults, ...normalResults]; + + // remove duplicate search results + // note the reversing of results, so that in the case of duplicates, the highest-scoring entry is kept + let seen = new Set(); + results = results.reverse().reduce((acc, result) => { + let resultStr = result.slice(0, 4).concat([result[5]]).map(v => String(v)).join(','); + if (!seen.has(resultStr)) { + acc.push(result); + seen.add(resultStr); + } + return acc; + }, []); + + return results.reverse(); + }, + + query: (query) => { + const [searchQuery, searchTerms, excludedTerms, highlightTerms, objectTerms] = Search._parseQuery(query); + const results = Search._performSearch(searchQuery, searchTerms, excludedTerms, highlightTerms, objectTerms); + + // for debugging + //Search.lastresults = results.slice(); // a copy + // console.info("search results:", Search.lastresults); + + // print the results + _displayNextItem(results, results.length, searchTerms, highlightTerms); + }, + + /** + * search for object names + */ + performObjectSearch: (object, objectTerms) => { + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const objects = Search._index.objects; + const objNames = Search._index.objnames; + const titles = Search._index.titles; + + const results = []; + + const objectSearchCallback = (prefix, match) => { + const name = match[4] + const fullname = (prefix ? prefix + "." : "") + name; + const fullnameLower = fullname.toLowerCase(); + if (fullnameLower.indexOf(object) < 0) return; + + let score = 0; + const parts = fullnameLower.split("."); + + // check for different match types: exact matches of full name or + // "last name" (i.e. last dotted part) + if (fullnameLower === object || parts.slice(-1)[0] === object) + score += Scorer.objNameMatch; + else if (parts.slice(-1)[0].indexOf(object) > -1) + score += Scorer.objPartialMatch; // matches in last name + + const objName = objNames[match[1]][2]; + const title = titles[match[0]]; + + // If more than one term searched for, we require other words to be + // found in the name/title/description + const otherTerms = new Set(objectTerms); + otherTerms.delete(object); + if (otherTerms.size > 0) { + const haystack = `${prefix} ${name} ${objName} ${title}`.toLowerCase(); + if ( + [...otherTerms].some((otherTerm) => haystack.indexOf(otherTerm) < 0) + ) + return; + } + + let anchor = match[3]; + if (anchor === "") anchor = fullname; + else if (anchor === "-") anchor = objNames[match[1]][1] + "-" + fullname; + + const descr = objName + _(", in ") + title; + + // add custom score for some objects according to scorer + if (Scorer.objPrio.hasOwnProperty(match[2])) + score += Scorer.objPrio[match[2]]; + else score += Scorer.objPrioDefault; + + results.push([ + docNames[match[0]], + fullname, + "#" + anchor, + descr, + score, + filenames[match[0]], + ]); + }; + Object.keys(objects).forEach((prefix) => + objects[prefix].forEach((array) => + objectSearchCallback(prefix, array) + ) + ); + return results; + }, + + /** + * search for full-text terms in the index + */ + performTermsSearch: (searchTerms, excludedTerms) => { + // prepare search + const terms = Search._index.terms; + const titleTerms = Search._index.titleterms; + const filenames = Search._index.filenames; + const docNames = Search._index.docnames; + const titles = Search._index.titles; + + const scoreMap = new Map(); + const fileMap = new Map(); + + // perform the search on the required terms + searchTerms.forEach((word) => { + const files = []; + const arr = [ + { files: terms[word], score: Scorer.term }, + { files: titleTerms[word], score: Scorer.title }, + ]; + // add support for partial matches + if (word.length > 2) { + const escapedWord = _escapeRegExp(word); + if (!terms.hasOwnProperty(word)) { + Object.keys(terms).forEach((term) => { + if (term.match(escapedWord)) + arr.push({ files: terms[term], score: Scorer.partialTerm }); + }); + } + if (!titleTerms.hasOwnProperty(word)) { + Object.keys(titleTerms).forEach((term) => { + if (term.match(escapedWord)) + arr.push({ files: titleTerms[term], score: Scorer.partialTitle }); + }); + } + } + + // no match but word was a required one + if (arr.every((record) => record.files === undefined)) return; + + // found search word in contents + arr.forEach((record) => { + if (record.files === undefined) return; + + let recordFiles = record.files; + if (recordFiles.length === undefined) recordFiles = [recordFiles]; + files.push(...recordFiles); + + // set score for the word in each file + recordFiles.forEach((file) => { + if (!scoreMap.has(file)) scoreMap.set(file, {}); + scoreMap.get(file)[word] = record.score; + }); + }); + + // create the mapping + files.forEach((file) => { + if (!fileMap.has(file)) fileMap.set(file, [word]); + else if (fileMap.get(file).indexOf(word) === -1) fileMap.get(file).push(word); + }); + }); + + // now check if the files don't contain excluded terms + const results = []; + for (const [file, wordList] of fileMap) { + // check if all requirements are matched + + // as search terms with length < 3 are discarded + const filteredTermCount = [...searchTerms].filter( + (term) => term.length > 2 + ).length; + if ( + wordList.length !== searchTerms.size && + wordList.length !== filteredTermCount + ) + continue; + + // ensure that none of the excluded terms is in the search result + if ( + [...excludedTerms].some( + (term) => + terms[term] === file || + titleTerms[term] === file || + (terms[term] || []).includes(file) || + (titleTerms[term] || []).includes(file) + ) + ) + break; + + // select one (max) score for the file. + const score = Math.max(...wordList.map((w) => scoreMap.get(file)[w])); + // add result to the result list + results.push([ + docNames[file], + titles[file], + "", + null, + score, + filenames[file], + ]); + } + return results; + }, + + /** + * helper function to return a node containing the + * search summary for a given text. keywords is a list + * of stemmed words. + */ + makeSearchSummary: (htmlText, keywords, anchor) => { + const text = Search.htmlToText(htmlText, anchor); + if (text === "") return null; + + const textLower = text.toLowerCase(); + const actualStartPosition = [...keywords] + .map((k) => textLower.indexOf(k.toLowerCase())) + .filter((i) => i > -1) + .slice(-1)[0]; + const startWithContext = Math.max(actualStartPosition - 120, 0); + + const top = startWithContext === 0 ? "" : "..."; + const tail = startWithContext + 240 < text.length ? "..." : ""; + + let summary = document.createElement("p"); + summary.classList.add("context"); + summary.textContent = top + text.substr(startWithContext, 240).trim() + tail; + + return summary; + }, +}; + +_ready(Search.init); diff --git a/v3.0.0a3/_static/sphinx_highlight.js b/v3.0.0a3/_static/sphinx_highlight.js new file mode 100644 index 0000000..8a96c69 --- /dev/null +++ b/v3.0.0a3/_static/sphinx_highlight.js @@ -0,0 +1,154 @@ +/* Highlighting utilities for Sphinx HTML documentation. */ +"use strict"; + +const SPHINX_HIGHLIGHT_ENABLED = true + +/** + * highlight a given string on a node by wrapping it in + * span elements with the given class name. + */ +const _highlight = (node, addItems, text, className) => { + if (node.nodeType === Node.TEXT_NODE) { + const val = node.nodeValue; + const parent = node.parentNode; + const pos = val.toLowerCase().indexOf(text); + if ( + pos >= 0 && + !parent.classList.contains(className) && + !parent.classList.contains("nohighlight") + ) { + let span; + + const closestNode = parent.closest("body, svg, foreignObject"); + const isInSVG = closestNode && closestNode.matches("svg"); + if (isInSVG) { + span = document.createElementNS("http://www.w3.org/2000/svg", "tspan"); + } else { + span = document.createElement("span"); + span.classList.add(className); + } + + span.appendChild(document.createTextNode(val.substr(pos, text.length))); + const rest = document.createTextNode(val.substr(pos + text.length)); + parent.insertBefore( + span, + parent.insertBefore( + rest, + node.nextSibling + ) + ); + node.nodeValue = val.substr(0, pos); + /* There may be more occurrences of search term in this node. So call this + * function recursively on the remaining fragment. + */ + _highlight(rest, addItems, text, className); + + if (isInSVG) { + const rect = document.createElementNS( + "http://www.w3.org/2000/svg", + "rect" + ); + const bbox = parent.getBBox(); + rect.x.baseVal.value = bbox.x; + rect.y.baseVal.value = bbox.y; + rect.width.baseVal.value = bbox.width; + rect.height.baseVal.value = bbox.height; + rect.setAttribute("class", className); + addItems.push({ parent: parent, target: rect }); + } + } + } else if (node.matches && !node.matches("button, select, textarea")) { + node.childNodes.forEach((el) => _highlight(el, addItems, text, className)); + } +}; +const _highlightText = (thisNode, text, className) => { + let addItems = []; + _highlight(thisNode, addItems, text, className); + addItems.forEach((obj) => + obj.parent.insertAdjacentElement("beforebegin", obj.target) + ); +}; + +/** + * Small JavaScript module for the documentation. + */ +const SphinxHighlight = { + + /** + * highlight the search words provided in localstorage in the text + */ + highlightSearchWords: () => { + if (!SPHINX_HIGHLIGHT_ENABLED) return; // bail if no highlight + + // get and clear terms from localstorage + const url = new URL(window.location); + const highlight = + localStorage.getItem("sphinx_highlight_terms") + || url.searchParams.get("highlight") + || ""; + localStorage.removeItem("sphinx_highlight_terms") + url.searchParams.delete("highlight"); + window.history.replaceState({}, "", url); + + // get individual terms from highlight string + const terms = highlight.toLowerCase().split(/\s+/).filter(x => x); + if (terms.length === 0) return; // nothing to do + + // There should never be more than one element matching "div.body" + const divBody = document.querySelectorAll("div.body"); + const body = divBody.length ? divBody[0] : document.querySelector("body"); + window.setTimeout(() => { + terms.forEach((term) => _highlightText(body, term, "highlighted")); + }, 10); + + const searchBox = document.getElementById("searchbox"); + if (searchBox === null) return; + searchBox.appendChild( + document + .createRange() + .createContextualFragment( + '

' + + '' + + _("Hide Search Matches") + + "

" + ) + ); + }, + + /** + * helper function to hide the search marks again + */ + hideSearchWords: () => { + document + .querySelectorAll("#searchbox .highlight-link") + .forEach((el) => el.remove()); + document + .querySelectorAll("span.highlighted") + .forEach((el) => el.classList.remove("highlighted")); + localStorage.removeItem("sphinx_highlight_terms") + }, + + initEscapeListener: () => { + // only install a listener if it is really needed + if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) return; + + document.addEventListener("keydown", (event) => { + // bail for input elements + if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return; + // bail with special keys + if (event.shiftKey || event.altKey || event.ctrlKey || event.metaKey) return; + if (DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS && (event.key === "Escape")) { + SphinxHighlight.hideSearchWords(); + event.preventDefault(); + } + }); + }, +}; + +_ready(() => { + /* Do not call highlightSearchWords() when we are on the search page. + * It will highlight words from the *previous* search query. + */ + if (typeof Search === "undefined") SphinxHighlight.highlightSearchWords(); + SphinxHighlight.initEscapeListener(); +}); diff --git a/v3.0.0a3/_static/theme_overrides.css b/v3.0.0a3/_static/theme_overrides.css new file mode 100644 index 0000000..eb66180 --- /dev/null +++ b/v3.0.0a3/_static/theme_overrides.css @@ -0,0 +1,14 @@ +/* from https://rackerlabs.github.io/docs-rackspace/tools/rtd-tables.html */ +/* override table width restrictions */ +@media screen and (min-width: 767px) { + + .wy-table-responsive table td { + /* !important prevents the common CSS stylesheets from overriding + this as on RTD they are loaded after this stylesheet */ + white-space: normal !important; + } + + .wy-table-responsive { + overflow: visible !important; + } +} diff --git a/v3.0.0a3/api/compat.html b/v3.0.0a3/api/compat.html new file mode 100644 index 0000000..5c45a6b --- /dev/null +++ b/v3.0.0a3/api/compat.html @@ -0,0 +1,173 @@ + + + + + + + + scikits.odes — Odes 3.0.0a3 documentation + + + + + + + + + + + + + + + + + + + + + + +
+
+
+ + +
+ +
+

scikits.odes

+
+

scikits.odes

+

scikits.odes is a scikit offering a cython wrapper around some extra ode/dae +solvers, so they can mature outside of scipy.

+
+
It offers wrappers around the following solvers from SUNDIALS
    +

  • CVODE

    • +

  • IDA

    • +
+
+
It additionally offers wrappers around
    +

  • ddaspk <http://www.netlib.org/ode/ddaspk.f> (included)

    • +

  • lsodi <http://www.netlib.org/ode/lsodi.f> (included)

    • +
+
+
+
+
+

scikits.odes.ode

+
+
+

scikits.odes.dae

+
+
+

scikits.odes.dopri5

+
+
+

scikits.odes.ddaspkint

+
+
+

scikits.odes.lsodiint

+
+
+

scikits.odes.sundials

+
+
+

scikits.odes.sundials.cvode

+
+
+

scikits.odes.sundials.ida

+
+
+ + +
+ +
+
+ +
+
+
+ ©2016, B. Malengier. + + | + Powered by Sphinx 7.3.7 + & Alabaster 0.7.16 + + | + Page source +
+ + + + + + \ No newline at end of file diff --git a/v3.0.0a3/api/core.html b/v3.0.0a3/api/core.html new file mode 100644 index 0000000..ba95a45 --- /dev/null +++ b/v3.0.0a3/api/core.html @@ -0,0 +1,628 @@ + + + + + + + + scikits-odes-core — Odes 3.0.0a3 documentation + + + + + + + + + + + + + + + + + + + + + + + +
+
+
+ + +
+ +
+

scikits-odes-core

+
+
+class scikits_odes_core.DaeBase(Rfn, **options)[source]
+

The interface which DAE solvers must implement.

+
+
Parameters:
+
    +

  • Rfn (function) – residual function

    • +

  • options (mapping) – Additional options for initialization, solver dependent

    • +
+
+
+
+
+init_step(t0, y0, yp0, y_ic0_retn=None, yp_ic0_retn=None)[source]
+

Initializes the solver and allocates memory.

+
+
Parameters:
+
    +

  • t0 (number) – initial time

    • +

  • y0 (list/array) – initial condition for y

    • +

  • yp0 (list/array) – initial condition for yp

    • +

  • y_ic0 (numpy array) – (optional) returns the calculated consistent initial condition for y

    • +

  • yp_ic0 (numpy array) – (optional) returns the calculated consistent initial condition for y +derivated.

    • +
+
+
Returns:
+

    +

  • old_api is False (namedtuple) – namedtuple with the following attributes

    + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    An integer flag (StatusEnumXXX)

    values

    Named tuple with entries t and y and ydot. y will correspond to y_retn value and ydot to yp_retn!

    errors

    Named tuple with entries t and y and ydot

    roots

    Named tuple with entries t and y and ydot

    tstop

    Named tuple with entries t and y and ydot

    message

    String with message in case of an error

    +
    • +

  • old_api is True (tuple) – tuple with the following elements in order

    + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    status of the computation (successful or error occurred)

    t_out

    time, where the solver stopped (when no error occurred, t_out == t)

    +
    • +
+

+
+
+
+ +
+
+set_options(**options)[source]
+

Set specific options for the solver.

+

Calling set_options a second time, normally resets the solver.

+
+ +
+
+solve(tspan, y0, yp0)[source]
+

Runs the solver.

+
+
Parameters:
+
    +

  • tspan (list/array) – A list of times at which the computed value will be returned. +Must contain the start time as first entry.

    • +

  • y0 (list/array) – List of initial values

    • +

  • yp0 (list/array) – List of initial values of derivatives

    • +
+
+
Returns:
+

    +

  • old_api is False (namedtuple) – namedtuple with the following attributes

    + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    An integer flag (StatusEnumXXX)

    values

    Named tuple with entries array t and array y and array ydot. y will correspond to y_retn value and ydot to yp_retn!

    errors

    Named tuple with entries t and y and ydot of error

    roots

    Named tuple with entries array t and array y and array ydot

    tstop

    Named tuple with entries array t and array y and array ydot

    message

    String with message in case of an error

    +
    • +

  • old_api is True (tuple) – tuple with the following elements in order

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    indicating return status of the solver

    t

    numpy array of times at which the computations were successful

    y

    numpy array of values corresponding to times t (values of y[i, :] ~ t[i])

    yp

    numpy array of derivatives corresponding to times t (values of yp[i, :] ~ t[i])

    t_err

    float or None - if recoverable error occurred (for example reached maximum number of allowed iterations), this is the time at which it happened

    y_err

    numpy array of values corresponding to time t_err

    yp_err

    numpy array of derivatives corresponding to time t_err

    +
    • +
+

+
+
+
+ +
+
+step(t, y_retn=None, yp_retn=None)[source]
+

Method for calling successive next step of the IDA solver to allow +more precise control over the IDA solver. The ‘init_step’ method has to +be called before the ‘step’ method.

+

A step is done towards time t, and output at t returned. This time can +be higher or lower than the previous time. If option +‘one_step_compute’==True, and the solver supports it, only one internal +solver step is done in the direction of t starting at the current step.

+

If old_api=True, the old behavior is used: if t>0.0 then integration is +performed until this time and results at this time are returned in +y_retn; else if if t<0.0 only one internal step is performed towards +time abs(t) and results after this one time step are returned.

+
+
Parameters:
+
    +

  • t (number)

    • +

  • y_retn (numpy array (ndim = 1) or None.) – (Needs to be preallocated) If not None, will be filled with y at +time t. If None y_retn is not used.

    • +

  • yp_retn (numpy array (ndim = 1) or None.) – (Needs to be preallocated) If not None, will be filled with +derivatives of y at time t. If None yp_retn is not used.

    • +
+
+
Returns:
+

    +

  • old_api is False (namedtuple) – namedtuple with the following attributes

    + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    An integer flag (StatusEnumXXX)

    values

    Named tuple with entries t and y and ydot. y will correspond to y_retn value and ydot to yp_retn!

    errors

    Named tuple with entries t and y and ydot

    roots

    Named tuple with entries t and y and ydot

    tstop

    Named tuple with entries t and y and ydot

    message

    String with message in case of an error

    +
    • +

  • old_api is True (tuple) – tuple with the following elements in order

    + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    status of the computation (successful or error occurred)

    t_out

    time, where the solver stopped (when no error occurred, t_out == t)

    +
    • +
+

+
+
+
+ +
+ +
+
+class scikits_odes_core.OdeBase(Rfn, **options)[source]
+

The interface which ODE solvers must implement.

+
+
Parameters:
+
    +

  • Rfn (function) – A function which computes the required derivatives. The signature +should be func(t, y, y_dot, *args, **kwargs). Note that *args +and **kwargs handling are solver dependent.

    • +

  • options (mapping) – Additional options for initialization, solver dependent

    • +
+
+
+
+
+init_step(t0, y0)[source]
+

Initializes the solver and allocates memory.

+
+
Parameters:
+
    +

  • t0 (number) – initial time

    • +

  • y0 (array) – initial condition for y (can be list or numpy array)

    • +
+
+
Returns:
+

    +

  • old_api is False (namedtuple) – namedtuple with the following attributes

    + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    An integer flag (StatusEnum)

    values

    Named tuple with entries t and y

    errors

    Named tuple with entries t and y

    roots

    Named tuple with entries t and y

    tstop

    Named tuple with entries t and y

    message

    String with message in case of an error

    +
    • +

  • old_api is True (tuple) – tuple with the following elements in order

    + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    boolean status of the computation (successful or error occurred)

    t_out

    initial time

    +
    • +
+

+
+
+
+ +
+
+set_options(**options)[source]
+

Set specific options for the solver.

+

Calling set_options a second time, normally resets the solver.

+
+ +
+
+solve(tspan, y0)[source]
+

Runs the solver.

+
+
Parameters:
+
    +

  • tspan (array (or similar)) – a list of times at which the computed value will be returned. Must +contain the start time as first entry.

    • +

  • y0 (array (or similar)) – a list of initial values

    • +
+
+
Returns:
+

    +

  • old_api is False (namedtuple) – namedtuple with the following attributes

    + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    An integer flag (StatusEnum)

    values

    Named tuple with entries t and y

    errors

    Named tuple with entries t and y

    roots

    Named tuple with entries t and y

    tstop

    Named tuple with entries t and y

    message

    String with message in case of an error

    +
    • +

  • old_api is True (tuple) – tuple with the following elements in order

    + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    indicating return status of the solver

    t

    numpy array of times at which the computations were successful

    y

    numpy array of values corresponding to times t (values of y[i, :] ~ t[i])

    t_err

    float or None - if recoverable error occurred (for example reached maximum number of allowed iterations), this is the time at which it happened

    y_err

    numpy array of values corresponding to time t_err

    +
    • +
+

+
+
+
+ +
+
+step(t, y_retn=None)[source]
+

Method for calling successive next step of the ODE solver to allow +more precise control over the solver. The ‘init_step’ method has to +be called before the ‘step’ method.

+

A step is done towards time t, and output at t returned. This time can +be higher or lower than the previous time. If option +‘one_step_compute’==True, and the solver supports it, only one internal +solver step is done in the direction of t starting at the current step.

+

If old_api=True, the old behavior is used: if t>0.0 then integration is +performed until this time and results at this time are returned in +y_retn if t<0.0 only one internal step is performed towards time abs(t) +and results after this one time step are returned

+
+
Parameters:
+
    +

  • t (number)

    • +

  • y_retn (numpy vector (ndim = 1)) – in which the computed value will be stored (needs to be +preallocated). If None y_retn is not used.

    • +
+
+
Returns:
+

    +

  • old_api is False (namedtuple) – namedtuple with the following attributes

    + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    An integer flag (StatusEnum)

    values

    Named tuple with entries t and y

    errors

    Named tuple with entries t and y

    roots

    Named tuple with entries t and y

    tstop

    Named tuple with entries t and y

    message

    String with message in case of an error

    +
    • +

  • old_api is True (tuple) – tuple with the following elements in order

    + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    status of the computation (successful or error occurred)

    t_out

    time, where the solver stopped (when no error occurred, t_out == t)

    +
    • +
+

+
+
+
+ +
+ +
+ + +
+ +
+
+ +
+
+
+ ©2016, B. Malengier. + + | + Powered by Sphinx 7.3.7 + & Alabaster 0.7.16 + + | + Page source +
+ + + + + + \ No newline at end of file diff --git a/v3.0.0a3/api/daepack.html b/v3.0.0a3/api/daepack.html new file mode 100644 index 0000000..d11c27d --- /dev/null +++ b/v3.0.0a3/api/daepack.html @@ -0,0 +1,123 @@ + + + + + + + + scikits-odes-daepack — Odes 3.0.0a3 documentation + + + + + + + + + + + + + + + + + + + + + + + +
+
+
+ + +
+ +
+

scikits-odes-daepack

+
+ + +
+ +
+
+ +
+
+
+ ©2016, B. Malengier. + + | + Powered by Sphinx 7.3.7 + & Alabaster 0.7.16 + + | + Page source +
+ + + + + + \ No newline at end of file diff --git a/v3.0.0a3/api/index.html b/v3.0.0a3/api/index.html new file mode 100644 index 0000000..08fa7cd --- /dev/null +++ b/v3.0.0a3/api/index.html @@ -0,0 +1,157 @@ + + + + + + + + Lower Level API — Odes 3.0.0a3 documentation + + + + + + + + + + + + + + + + + + + + + + + + +
+
+
+ + +
+ +
+

Lower Level API

+
+ +
+
+ + +
+ +
+
+ +
+
+
+ ©2016, B. Malengier. + + | + Powered by Sphinx 7.3.7 + & Alabaster 0.7.16 + + | + Page source +
+ + + + + + \ No newline at end of file diff --git a/v3.0.0a3/api/main.html b/v3.0.0a3/api/main.html new file mode 100644 index 0000000..c347d6a --- /dev/null +++ b/v3.0.0a3/api/main.html @@ -0,0 +1,1097 @@ + + + + + + + + scikits-odes — Odes 3.0.0a3 documentation + + + + + + + + + + + + + + + + + + + + + + + + +
+
+
+ + +
+ +
+

scikits-odes

+
+

scikits_odes

+

scikits-odes is a scikit offering a cython wrapper around some extra ode/dae +solvers, so they can mature outside of scipy.

+
+
It offers wrappers around the following solvers from SUNDIALS
    +

  • CVODE

    • +

  • IDA

    • +
+
+
It additionally offers wrappers around
    +

  • ddaspk <http://www.netlib.org/ode/ddaspk.f> (included)

    • +

  • lsodi <http://www.netlib.org/ode/lsodi.f> (included)

    • +
+
+
+
+
+

scikits_odes.ode

+
+

First-order ODE solver

+

User-friendly interface to various numerical integrators for solving a +system of first order ODEs with prescribed initial conditions:

+
+\[ \begin{align}\begin{aligned}\frac{dy(t)}{dt} = f(t, y(t)), \quad y(t_0)=y_0\\y(t_0)[i] = y_0[i], i = 0, ..., \mathrm{len}(y_0) - 1\end{aligned}\end{align} \]
+

\(f(t,y)\) is the right hand side function and returns a vector of size +\(\mathrm{len}(y_0)\).

+
+
+
+class scikits_odes.ode.ode(integrator_name, eqsrhs, **options)[source]
+

A generic interface class to differential equation solvers.

+
+
Parameters:
+
    +

  • integrator_name ('cvode', 'dopri5' or 'dop853') –

    The solver to use.

    +

    'cvode' selects the CVODE solver from the SUNDIALS package. +See py:class:scikits.odes.sundials.cvode.CVODE for solver specific +options.

    +

    'dopri5' selects the Dormand & Prince Runge-Kutta order (4)5 +solver from scipy.

    +

    • +

  • eqsrhs (right-hand-side function) –

    Right-hand-side of a first order ode. +Generally, you can assume the following signature to work:

    +
    +

    eqsrhs(x, y, return_rhs)

    +
    +

    with

    +
    +

    x: independent variable, eg the time, float

    +

    y: array of n unknowns in x

    +

    return_rhs : array that must be updated with the value of the +right-hand-side, so f(t,y). The dimension is equal to +dim(y)

    +
    +
    +
    return value: An integer, 0 for success, 1 for failure.

    It is not guaranteed that a solver takes this status into account

    +
    +
    +

    Some solvers will allow userdata to be passed to eqsrhs, or optional +formats that are more performant.

    +

    • +

  • options (additional options of the solver) – See set_options method of the integrator_name you selected for +details. +Set option old_api=False to use the new API. In the future, this +will become the default!

    • +
+
+
+
+

See also

+
+
scikits.odes.odeint.odeint

an ODE integrator with a simpler interface

+
+
scipy.integrate

Methods in scipy for ODE integration

+
+
+
+

Examples

+

ODE arise in many applications of dynamical systems, as well as in +discritisations of PDE (eg moving mesh combined with method of +lines). +As an easy example, consider the simple oscillator,

+
>>> from __future__ import print_function
+>>> from numpy import cos, sin, sqrt
+>>> k = 4.0
+>>> m = 1.0
+>>> initx = [1, 0.1]
+>>> def rhseqn(t, x, xdot):
+        # we create rhs equations for the problem
+        xdot[0] = x[1]
+        xdot[1] = - k/m * x[0]
+
+
+
>>> from scikits.odes import ode
+>>> solver = ode('cvode', rhseqn, old_api=False)
+>>> result = solver.solve([0., 1., 2.], initx)
+>>> print('   t        Solution          Exact')
+>>> print('------------------------------------')
+>>> for t, u in zip(result.values.t, result.values.y):
+        print('%4.2f %15.6g %15.6g' % (t, u[0], initx[0]*cos(sqrt(k/m)*t)+initx[1]*sin(sqrt(k/m)*t)/sqrt(k/m)))
+
+
+

More examples in the Examples directory and IPython worksheets.

+
+
+get_info()[source]
+

Return additional information about the state of the integrator.

+
+
Returns:
+

    +

  • A dictionary filled with internal data as exposed by the integrator.

    • +

  • See the get_info method of your chosen integrator for details.

    • +
+

+
+
+
+ +
+
+init_step(t0, y0)[source]
+

Initializes the solver and allocates memory. It is not needed to +call this method if solve is used to compute the solution. In the case +step is used, init_step must be called first.

+
+
Parameters:
+
    +

  • t0 (number) – initial time

    • +

  • y0 (array) – initial condition for y (can be list or numpy array)

    • +
+
+
Returns:
+

    +

  • old_api is False (namedtuple) – namedtuple with the following attributes

    + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    An integer flag (StatusEnum)

    values

    Named tuple with entries t and y

    errors

    Named tuple with entries t and y

    roots

    Named tuple with entries t and y

    tstop

    Named tuple with entries t and y

    message

    String with message in case of an error

    +
    • +

  • old_api is True (tuple) – tuple with the following elements in order

    + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    boolean status of the computation (successful or error occured)

    t_out

    inititial time

    +
    • +
+

+
+
+
+ +
+
+set_options(**options)[source]
+

Set specific options for the solver. +See the solver documentation for details.

+

Calling set_options a second time, is only possible for options that +can change during runtime.

+
+ +
+
+set_tstop(tstop)[source]
+

Add a stop time to the integrator past which he is not allowed to +integrate.

+
+
Parameters:
+

tstop (float time) – Time point in the future where the integration must stop. You can +indicate like this that integration past this point is not allowed, +in order to avoid undefined behavior. +You can achieve the same result with a call to +set_options(tstop=tstop)

+
+
+
+ +
+
+solve(tspan, y0)[source]
+

Runs the solver.

+
+
Parameters:
+
    +

  • tspan (array (or similar)) – a list of times at which the computed value will be returned. Must +contain the start time as first entry.

    • +

  • y0 (array (or similar)) – a list of initial values

    • +
+
+
Returns:
+

    +

  • old_api is False (namedtuple) – namedtuple with the following attributes

    + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    An integer flag (StatusEnum)

    values

    Named tuple with entries t and y

    errors

    Named tuple with entries t and y

    roots

    Named tuple with entries t and y

    tstop

    Named tuple with entries t and y

    message

    String with message in case of an error

    +
    • +

  • old_api is True (tuple) – tuple with the following elements in order

    + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    indicating return status of the solver

    t

    numpy array of times at which the computations were successful

    y

    numpy array of values corresponding to times t (values of y[i, :] ~ t[i])

    t_err

    float or None - if recoverable error occured (for example reached maximum number of allowed iterations), this is the time at which it happened

    y_err

    numpy array of values corresponding to time t_err

    +
    • +
+

+
+
+
+ +
+
+step(t, y_retn=None)[source]
+

Method for calling successive next step of the ODE solver to allow +more precise control over the solver. The ‘init_step’ method has to +be called before the ‘step’ method.

+

A step is done towards time t, and output at t returned. This time can +be higher or lower than the previous time. If option +‘one_step_compute’==True, and the solver supports it, only one internal +solver step is done in the direction of t starting at the current step.

+

If old_api=True, the old behavior is used: if t>0.0 then integration is +performed until this time and results at this time are returned in +y_retn if t<0.0 only one internal step is perfomed towards time abs(t) +and results after this one time step are returned

+
+
Parameters:
+
    +

  • t (number)

    • +

  • y_retn (numpy vector (ndim = 1)) – in which the computed value will be stored (needs to be +preallocated). If None y_retn is not used.

    • +
+
+
Returns:
+

    +

  • old_api is False (namedtuple) – namedtuple with the following attributes

    + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    An integer flag (StatusEnum)

    values

    Named tuple with entries t and y

    errors

    Named tuple with entries t and y

    roots

    Named tuple with entries t and y

    tstop

    Named tuple with entries t and y

    message

    String with message in case of an error

    +
    • +

  • old_api is True (tuple) – tuple with the following elements in order

    + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    status of the computation (successful or error occured)

    t_out

    time, where the solver stopped (when no error occured, t_out == t)

    +
    • +
+

+
+
+
+ +
+ +
+
+

scikits_odes.dae

+
+

First-order DAE solver

+

User-friendly interface to various numerical integrators for solving an +algebraic system of first order ODEs with prescribed initial conditions:

+
+\[ \begin{align}\begin{aligned}A \frac{dy(t)}{dt} = f(t,y(t)),\\y(t=0)[i] = y0[i],\\\frac{d y(t=0)}{dt}[i] = yprime0[i],\end{aligned}\end{align} \]
+

where \(i = 0, ..., len(y0) - 1\); \(A\) is a (possibly singular) matrix +of size \(i × i\); and \(f(t,y)\) is a vector of size \(i\) or more generally, equations of the form

+
+\[G(t,y,y') = 0\]
+
+
+
+class scikits_odes.dae.dae(integrator_name, eqsres, **options)[source]
+

A generic interface class to differential algebraic equations.

+

Define equation res = G(t,y,y’) which can eg be G = f(y,t) - A y’ when +solving A y’ = f(y,t), and where (optional) jac is the jacobian matrix of +the nonlinear system see fortran source code), so d res/dy + scaling * d +res/dy’ or d res/dy depending on the backend.

+
+
Parameters:
+
    +

  • integrator_name ('ida', 'ddaspk' or 'lsodi') – The integrator solver to use.

    • +

  • eqsres (residual function) –

    Residual of the DAE. The signature of this function depends on the +solver used, see the solver documentation for details. +Generally however, you can assume the following signature to work:

    +
    +

    eqsres(x, y, yprime, return_residual)

    +
    +

    with +x : independent variable, eg the time, float +y : array of n unknowns in x +yprime : dy/dx array of n unknowns in x, dimension = dim(y) +return_residual: array that must be updated with the value of the residuals, so G(t,y,y’). The dimension is equal to dim(y) +return value: integer, 0 for success. It is not guaranteed that a solver takes this status into account

    +

    Some solvers will allow userdata to be passed to eqsres, or optional +formats that are more performant.

    +

    • +

  • options (mapping) – Additional options for initialization, solver dependent +See set_options method of the integrator_name you selected for +details.

    • +
+
+
+
+

See also

+
+
odeint

an ODE integrator with a simpler interface based on lsoda from ODEPACK

+
+
ode

class around vode ODE integrator

+
+
+
+

Notes

+

Possible future solvers

+

ddaskr: Not included, starting hints: +http://osdir.com/ml/python.f2py.user/2005-07/msg00014.html +Modified Extended Backward Differentiation Formulae (MEBDF): Not included. +Fortran codes: http://www.ma.ic.ac.uk/~jcash/IVP_software/readme.html

+

Examples

+

DAE arise in many applications of dynamical systems, as well as in +discritisations of PDE (eg moving mesh combined with method of +lines). +As an easy example, consider the simple oscillator, which we write as +G(y,y’,t) = 0 instead of the normal ode, and solve as a DAE.

+
>>> from __future__ import print_function
+>>> from numpy import cos, sin, sqrt
+>>> k = 4.0
+>>> m = 1.0
+>>> initx = [1, 0.1]
+>>> initxp = [initx[1], -k/m*initx[0]]
+>>> def reseqn(t, x, xdot, result):
+    ... # we create residual equations for the problem
+    ... result[0] = m*xdot[1] + k*x[0]
+    ... result[1] = xdot[0] - x[1]
+>>> from scikits.odes import dae
+>>> solver = dae('ida', reseqn)
+>>> result = solver.solve([0., 1., 2.], initx, initxp)
+
+
+
+
+init_step(t0, y0, yp0, y_ic0_retn=None, yp_ic0_retn=None)[source]
+

Initializes the solver and allocates memory. It is not needed to +call this method if solve is used to compute the solution. In the case +step is used, init_step must be called first.

+
+
Parameters:
+
    +

  • t0 (number) – initial time

    • +

  • y0 (list/array) – initial condition for y

    • +

  • yp0 (list/array) – initial condition for yp

    • +

  • y_ic0 (numpy array) – (optional) returns the calculated consistent initial condition for y

    • +

  • yp_ic0 (numpy array) – (optional) returns the calculated consistent initial condition for y +derivated.

    • +
+
+
Returns:
+

    +

  • old_api is False (namedtuple) – namedtuple with the following attributes

    + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    An integer flag (StatusEnumXXX)

    values

    Named tuple with entries t and y and ydot. y will correspond to y_retn value and ydot to yp_retn!

    errors

    Named tuple with entries t and y and ydot

    roots

    Named tuple with entries t and y and ydot

    tstop

    Named tuple with entries t and y and ydot

    message

    String with message in case of an error

    +
    • +

  • old_api is True (tuple) – tuple with the following elements in order

    + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    status of the computation (successful or error occurred)

    t_out

    time, where the solver stopped (when no error occurred, t_out == t)

    +
    • +
+

+
+
+
+ +
+
+set_options(**options)[source]
+

Set specific options for the solver. +See the solver documentation for details.

+

Calling set_options a second time, normally resets the solver.

+
+ +
+
+solve(tspan, y0, yp0)[source]
+

Runs the solver.

+
+
Parameters:
+
    +

  • tspan (list/array) – A list of times at which the computed value will be returned. Must +contain the start time as first entry.

    • +

  • y0 (list/array) – list array of initial values

    • +

  • yp0 (list/array) – list array of initial values of derivatives

    • +
+
+
Returns:
+

    +

  • old_api is False (namedtuple) – namedtuple with the following attributes

    + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    An integer flag (StatusEnumXXX)

    values

    Named tuple with entries array t and array y and array ydot. y will correspond to y_retn value and ydot to yp_retn!

    errors

    Named tuple with entries t and y and ydot of error

    roots

    Named tuple with entries array t and array y and array ydot

    tstop

    Named tuple with entries array t and array y and array ydot

    message

    String with message in case of an error

    +
    • +

  • old_api is True (tuple) – tuple with the following elements in order

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    indicating return status of the solver

    t

    numpy array of times at which the computations were successful

    y

    numpy array of values corresponding to times t (values of y[i, :] ~ t[i])

    yp

    numpy array of derivatives corresponding to times t (values of yp[i, :] ~ t[i])

    t_err

    float or None - if recoverable error occurred (for example reached maximum number of allowed iterations), this is the time at which it happened

    y_err

    numpy array of values corresponding to time t_err

    yp_err

    numpy array of derivatives corresponding to time t_err

    +
    • +
+

+
+
+
+ +
+
+step(t, y_retn=None, yp_retn=None)[source]
+

Method for calling successive next step of the IDA solver to allow +more precise control over the IDA solver. The ‘init_step’ method has to +be called before the ‘step’ method.

+

A step is done towards time t, and output at t returned. This time can +be higher or lower than the previous time. If option +‘one_step_compute’==True, and the solver supports it, only one internal +solver step is done in the direction of t starting at the current step.

+

If old_api=True, the old behavior is used: if t>0.0 then integration is +performed until this time and results at this time are returned in +y_retn; else if if t<0.0 only one internal step is performed towards time +abs(t) and results after this one time step are returned.

+
+
Parameters:
+
    +

  • t (number)

    • +

  • y_retn (numpy array (ndim = 1) or None.) – (Needs to be preallocated) If not None, will be filled with y at +time t. If None y_retn is not used.

    • +

  • yp_retn (numpy array (ndim = 1) or None.) – (Needs to be preallocated) If not None, will be filled with +derivatives of y at time t. If None yp_retn is not used.

    • +
+
+
Returns:
+

    +

  • old_api is False (namedtuple) – namedtuple with the following attributes

    + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    An integer flag (StatusEnumXXX)

    values

    Named tuple with entries t and y and ydot. y will correspond to y_retn value and ydot to yp_retn!

    errors

    Named tuple with entries t and y and ydot

    roots

    Named tuple with entries t and y and ydot

    tstop

    Named tuple with entries t and y and ydot

    message

    String with message in case of an error

    +
    • +

  • old_api is True (tuple) – tuple with the following elements in order

    + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    status of the computation (successful or error occurred)

    t_out

    time, where the solver stopped (when no error occurred, t_out == t)

    +
    • +
+

+
+
+
+ +
+ +
+
+

scikits_odes.dopri5

+
+

Making scipy ode solvers available via the ode API

+
+

dopri5

+

This is an explicit runge-kutta method of order (4)5 due to Dormand & Prince +(with stepsize control and dense output). +The API of this solver is as the other scikit.odes ODE solvers

+

Authors:

+
+
    +

  1. Hairer and G. Wanner Universite de Geneve, Dept. de Mathematiques CH-1211 Geneve 24, Switzerland e-mail: ernst.hairer@math.unige.ch, gerhard.wanner@math.unige.ch

    2. +
+
+

This code is described in [HNW93].

+

This integrator accepts the following options:

+
+

atol : float or sequence absolute tolerance for solution, default 1e-12 +rtol : float or sequence relative tolerance for solution, default 1e-6 +nsteps : int Maximum number of (internally defined) steps allowed during one call to the solver. Default=500 +first_step : float +max_step : float +safety : float Safety factor on new step selection (default 0.9) +ifactor : float +dfactor : float Maximum factor to increase/decrease step size by in one step +beta : float Beta parameter for stabilised step size control. +verbosity : int Switch for printing messages (< 0 for no messages).

+
+

References +[HNW93] (1, 2) E. Hairer, S.P. Norsett and G. Wanner, Solving Ordinary Differential Equations i. Nonstiff Problems. 2nd edition. Springer Series in Computational Mathematics, Springer-Verlag (1993)

+
+
+

dop853

+

This is an explicit runge-kutta method of order 8(5,3) due to Dormand & Prince +(with stepsize control and dense output). +Options and references the same as “dopri5”.

+
+
+
+
+exception scikits_odes.dopri5.DOPSolveException(soln)[source]
+

Base class for exceptions raised by DOP.validate_flags.

+
+ +
+
+exception scikits_odes.dopri5.DOPSolveFailed(soln)[source]
+

DOP.solve failed to reach endpoint

+
+ +
+
+class scikits_odes.dopri5.SolverReturn(flag, values, errors, roots, tstop, message)
+
+
+errors
+

Alias for field number 2

+
+ +
+
+flag
+

Alias for field number 0

+
+ +
+
+message
+

Alias for field number 5

+
+ +
+
+roots
+

Alias for field number 3

+
+ +
+
+tstop
+

Alias for field number 4

+
+ +
+
+values
+

Alias for field number 1

+
+ +
+ +
+
+class scikits_odes.dopri5.SolverVariables(t, y)
+
+
+t
+

Alias for field number 0

+
+ +
+
+y
+

Alias for field number 1

+
+ +
+ +
+
+class scikits_odes.dopri5.StatusEnumDOP(value, names=None, *, module=None, qualname=None, type=None, start=1, boundary=None)[source]
+
+ +
+
+class scikits_odes.dopri5.dop853(Rfn, **options)[source]
+
+ +
+
+class scikits_odes.dopri5.dopri5(Rfn, **options)[source]
+
+
+init_step(t0, y0)[source]
+

Initializes the solver and allocates memory.

+
+
Parameters:
+
    +

  • time (t0 - initial)

    • +

  • array) (y0 - initial condition for y (can be list or numpy)

    • +
+
+
Returns:
+

    +

  • if old_api – not supported

    • +

  • if old_api False –

    +
    +
    A named tuple, with entries:

    flag = An integer flag (StatusEnumDop) +values = Named tuple with entries t and y and ydot. y will correspond to y_retn value and ydot to yp_retn! +errors = Named tuple with entries t_err and y_err +roots = Named tuple with entries t_roots and y_roots +tstop = Named tuple with entries t_stop and y_tstop +message= String with message in case of an error

    +
    +
    +
    • +
+

+
+
+
+ +
+
+set_options(**options)[source]
+

Set specific options for the solver.

+

Calling set_options a second time, normally resets the solver.

+
+ +
+
+solve(tspan, y0)[source]
+

Runs the solver.

+
+
Parameters:
+
    +

  • be (tspan - an list/array of times at which the computed value will) – returned. Must contain the start time as first entry..

    • +

  • values (y0 - list/numpy array of initial)

    • +
+
+
Returns:
+

    +

  • if old_api – Not supported

    • +

  • if old_api False –

    +
    +
    A named tuple, with entries:

    flag = An integer flag +values = Named tuple with entries t and y +errors = Named tuple with entries t and y +roots = Named tuple with entries t and y +tstop = Named tuple with entries t and y +message= String with message in case of an error

    +
    +
    +
    • +
+

+
+
+
+ +
+
+step(t, y_retn=None)[source]
+

Method for calling successive next step of the ODE solver to allow +more precise control over the solver. The ‘init_step’ method has to +be called before the ‘step’ method.

+
+
Parameters:
+
    +

  • t (t - A step is done towards time) –

    This time can be higher or lower than the previous time. +If option ‘one_step_compute’==True, and the solver supports +it, only one internal solver step is done in the direction +of t starting at the current step.

    +
    +
    If old_api=True, the old behavior is used:

    if t>0.0 then integration is performed until this time and results at this time are returned in y_retn +if t<0.0 only one internal step is perfomed towards time abs(t) and results after this one time step are returned

    +
    +
    +

    • +

  • returned. (and output at t) –

    This time can be higher or lower than the previous time. +If option ‘one_step_compute’==True, and the solver supports +it, only one internal solver step is done in the direction +of t starting at the current step.

    +
    +
    If old_api=True, the old behavior is used:

    if t>0.0 then integration is performed until this time and results at this time are returned in y_retn +if t<0.0 only one internal step is perfomed towards time abs(t) and results after this one time step are returned

    +
    +
    +

    • +

  • computed (y_retn - numpy vector (ndim = 1) in which the) – value will be stored (needs to be preallocated). If +None y_retn is not used.

    • +
+
+
Returns:
+

    +

  • if old_api – not supported

    • +

  • if old_api False –

    +
    +
    A named tuple, with entries:

    flag = An integer flag (StatusEnumDOP) +values = Named tuple with entries t and y. y will correspond to y_retn value +errors = Named tuple with entries t_err and y_err +roots = Named tuple with entries t_roots and y_roots +tstop = Named tuple with entries t_stop and y_tstop +message= String with message in case of an error

    +
    +
    +
    • +
+

+
+
+
+ +
+
+validate_flags(soln)[source]
+

Validates the flag returned by dopri.solve.

+
+
Validation happens using the following scheme:
    +

  • failures (flag < 0) raise DOPSolveFailed or a subclass of it;

    • +

  • otherwise, return an instance of SolverReturn.

    • +
+
+
+
+ +
+ +
+
+ + +
+ +
+
+ +
+
+
+ ©2016, B. Malengier. + + | + Powered by Sphinx 7.3.7 + & Alabaster 0.7.16 + + | + Page source +
+ + + + + + \ No newline at end of file diff --git a/v3.0.0a3/api/sundials.html b/v3.0.0a3/api/sundials.html new file mode 100644 index 0000000..4998286 --- /dev/null +++ b/v3.0.0a3/api/sundials.html @@ -0,0 +1,769 @@ + + + + + + + + scikits-odes-sundials — Odes 3.0.0a3 documentation + + + + + + + + + + + + + + + + + + + + + + + +
+
+
+ + +
+ +
+

scikits-odes-sundials

+
+

scikits_odes_sundials

+

SUNDIALS wrapper

+
+
+exception scikits_odes_sundials.CVODESolveException(soln)[source]
+

Base class for exceptions raised by CVODE.validate_flags.

+
+ +
+
+exception scikits_odes_sundials.CVODESolveFailed(soln)[source]
+

CVODE.solve failed to reach endpoint

+
+ +
+
+exception scikits_odes_sundials.CVODESolveFoundRoot(soln)[source]
+

CVODE.solve found a root

+
+ +
+
+exception scikits_odes_sundials.CVODESolveReachedTSTOP(soln)[source]
+

CVODE.solve reached the endpoint specified by tstop.

+
+ +
+
+exception scikits_odes_sundials.IDASolveException(soln)[source]
+

Base class for exceptions raised by IDA.validate_flags.

+
+ +
+
+exception scikits_odes_sundials.IDASolveFailed(soln)[source]
+

IDA.solve failed to reach endpoint

+
+ +
+
+exception scikits_odes_sundials.IDASolveFoundRoot(soln)[source]
+

IDA.solve found a root

+
+ +
+
+exception scikits_odes_sundials.IDASolveReachedTSTOP(soln)[source]
+

IDA.solve reached the endpoint specified by tstop.

+
+ +
+
+

scikits_odes_sundials.cvode

+
+
+class scikits_odes_sundials.cvode.CV_ContinuationFunction
+

Simple wrapper for functions called when ROOT or TSTOP are returned.

+
+
+evaluate(self, DTYPE_t t, ndarray y, CVODE solver) → int
+
+ +
+ +
+
+class scikits_odes_sundials.cvode.CV_JacRhsFunction
+

Prototype for jacobian function.

+

Note that evaluate must return a integer, 0 for success, positive for +recoverable failure, negative for unrecoverable failure (as per CVODE +documentation).

+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray fy, ndarray J) → int
+

Returns the Jacobi matrix of the right hand side function, as:

+
+

d(rhs)/d y

+
+

(for dense the full matrix, for band only bands). Result has to be +stored in the variable J, which is preallocated to the corresponding +size.

+

This is a generic class, you should subclass is for the problem specific +purposes.

+
+ +
+ +
+
+class scikits_odes_sundials.cvode.CV_JacTimesSetupFunction
+

Prototype for jacobian times setup function.

+

Note that evaluate must return a integer, 0 for success, non-zero for error +(as per CVODE documentation), with >0 a recoverable error (step is retried).

+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray fy, userdata=None) → int
+

This function calculates the product of the Jacobian with a given vector v. +Use the userdata object to expose Jacobian related data to the solve function.

+

This is a generic class, you should subclass it for the problem specific +purposes.

+
+ +
+ +
+
+class scikits_odes_sundials.cvode.CV_JacTimesVecFunction
+

Prototype for jacobian times vector function.

+

Note that evaluate must return a integer, 0 for success, non-zero for error +(as per CVODE documentation).

+
+
+evaluate(self, ndarray v, ndarray Jv, DTYPE_t t, ndarray y, userdata=None) → int
+

This function calculates the product of the Jacobian with a given vector v. +Use the userdata object to expose Jacobian related data to the solve function.

+

This is a generic class, you should subclass it for the problem specific +purposes.

+
+ +
+ +
+
+class scikits_odes_sundials.cvode.CV_PrecSetupFunction
+

Prototype for preconditioning setup function.

+

Note that evaluate must return a integer, 0 for success, positive for +recoverable failure, negative for unrecoverable failure (as per CVODE +documentation).

+
+
+evaluate(self, DTYPE_t t, ndarray y, bool jok, jcurPtr, DTYPE_t gamma, userdata=None) → int
+

This function preprocesses and/or evaluates Jacobian-related data +needed by the preconditioner. Use the userdata object to expose +the preprocessed data to the solve function.

+

This is a generic class, you should subclass it for the problem specific +purposes.

+
+ +
+ +
+
+class scikits_odes_sundials.cvode.CV_PrecSolveFunction
+

Prototype for precondititioning solution function.

+

Note that evaluate must return a integer, 0 for success, positive for +recoverable failure, negative for unrecoverable failure (as per CVODE +documentation).

+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray r, ndarray z, DTYPE_t gamma, DTYPE_t delta, int lr, userdata=None) → int
+

This function solves the preconditioned system P*z = r, where P may be +either a left or right preconditioner matrix. Here P should approximate +(at least crudely) the Newton matrix M = I − gamma*J, where J is the +Jacobian of the system. If preconditioning is done on both sides, +the product of the two preconditioner matrices should approximate M.

+

This is a generic class, you should subclass it for the problem specific +purposes.

+
+ +
+ +
+
+class scikits_odes_sundials.cvode.CV_RhsFunction
+

Prototype for rhs function.

+

Note that evaluate must return a integer, 0 for success, positive for +recoverable failure, negative for unrecoverable failure (as per CVODE +documentation).

+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray ydot, userdata=None) → int
+
+ +
+ +
+
+class scikits_odes_sundials.cvode.CV_RootFunction
+

Prototype for root function.

+

Note that evaluate must return a integer, 0 for success, non-zero if error +(as per CVODE documentation).

+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray g, userdata=None) → int
+
+ +
+ +
+
+class scikits_odes_sundials.cvode.CV_WrapJacRhsFunction
+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray fy, ndarray J) → int
+

Returns the Jacobi matrix (for dense the full matrix, for band only +bands. Result has to be stored in the variable J, which is preallocated +to the corresponding size.

+
+ +
+
+set_jacfn(self, jacfn)
+

Set some jacobian equations as a JacRhsFunction executable class.

+
+ +
+ +
+
+class scikits_odes_sundials.cvode.CV_WrapJacTimesSetupFunction
+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray fy, userdata=None) → int
+
+ +
+
+set_jac_times_setupfn(self, jac_times_setupfn)
+

Set some CV_JacTimesSetupFn executable class.

+
+ +
+ +
+
+class scikits_odes_sundials.cvode.CV_WrapJacTimesVecFunction
+
+
+evaluate(self, ndarray v, ndarray Jv, DTYPE_t t, ndarray y, userdata=None) → int
+
+ +
+
+set_jac_times_vecfn(self, jac_times_vecfn)
+

Set some CV_JacTimesVecFn executable class.

+
+ +
+ +
+
+class scikits_odes_sundials.cvode.CV_WrapPrecSetupFunction
+
+
+evaluate(self, DTYPE_t t, ndarray y, bool jok, jcurPtr, DTYPE_t gamma, userdata=None) → int
+
+ +
+
+set_prec_setupfn(self, prec_setupfn)
+

set a precondititioning setup method as a CV_PrecSetupFunction +executable class

+
+ +
+ +
+
+class scikits_odes_sundials.cvode.CV_WrapPrecSolveFunction
+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray r, ndarray z, DTYPE_t gamma, DTYPE_t delta, int lr, userdata=None) → int
+
+ +
+
+set_prec_solvefn(self, prec_solvefn)
+

set a precondititioning solve method as a CV_PrecSolveFunction +executable class

+
+ +
+ +
+
+class scikits_odes_sundials.cvode.CV_WrapRhsFunction
+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray ydot, userdata=None) → int
+
+ +
+
+set_rhsfn(self, rhsfn)
+

set some rhs equations as a RhsFunction executable class

+
+ +
+
+with_userdata
+

‘int’

+
+
Type:
+

with_userdata

+
+
+
+ +
+ +
+
+class scikits_odes_sundials.cvode.CV_WrapRootFunction
+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray g, userdata=None) → int
+
+ +
+
+set_rootfn(self, rootfn)
+

set root-ing condition(equations) as a RootFunction executable class

+
+ +
+ +
+
+class scikits_odes_sundials.cvode.StatusEnum(value, names=None, *, module=None, qualname=None, type=None, start=1, boundary=None)
+
+ +
+
+scikits_odes_sundials.cvode.no_continue_fn(t, y, solver)
+
+ +
+
+

scikits_odes_sundials.ida

+
+
+class scikits_odes_sundials.ida.IDA_ContinuationFunction
+

Simple wrapper for functions called when ROOT or TSTOP are returned.

+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray yp, IDA solver) → int
+
+ +
+ +
+
+class scikits_odes_sundials.ida.IDA_JacRhsFunction
+

Prototype for jacobian function.

+

Note that evaluate must return a integer, 0 for success, positive for +recoverable failure, negative for unrecoverable failure (as per IDA +documentation).

+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray ydot, ndarray residual, DTYPE_t cj, ndarray J, userdata=None) → int
+

Returns the Jacobi matrix of the residual function, as:

+
+

d(res)/d y + cj d(res)/d ydot

+
+

(for dense the full matrix, for band only bands). Result has to be +stored in the variable J, which is preallocated to the corresponding +size.

+

This is a generic class, you should subclass is for the problem specific +purposes.”

+
+ +
+ +
+
+class scikits_odes_sundials.ida.IDA_JacTimesSetupFunction
+

Prototype for jacobian times setup function.

+

Note that evaluate must return a integer, 0 for success, non-zero for error +(as per CVODE documentation), with >0 a recoverable error (step is retried).

+
+
+evaluate(self, DTYPE_t tt, ndarray yy, ndarray yp, ndarray rr, DTYPE_t cj, userdata=None) → int
+

This function calculates the product of the Jacobian with a given vector v. +Use the userdata object to expose Jacobian related data to the solve function.

+

This is a generic class, you should subclass it for the problem specific +purposes.

+
+ +
+ +
+
+class scikits_odes_sundials.ida.IDA_JacTimesVecFunction
+

Prototype for jacobian times vector function.

+

Note that evaluate must return a integer, 0 for success, non-zero for error +(as per IDA documentation).

+
+
+evaluate(self, DTYPE_t t, ndarray yy, ndarray yp, ndarray rr, ndarray v, ndarray Jv, DTYPE_t cj, userdata=None) → int
+

This function calculates the product of the Jacobian with a given vector v. +Use the userdata object to expose Jacobian related data to the solve function.

+

This is a generic class, you should subclass it for the problem specific +purposes.

+
+ +
+ +
+
+class scikits_odes_sundials.ida.IDA_PrecSetupFunction
+

Prototype for preconditioning setup function.

+

Note that evaluate must return a integer, 0 for success, positive for +recoverable failure, negative for unrecoverable failure (as per CVODE +documentation).

+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray yp, ndarray rr, DTYPE_t cj, userdata=None) → int
+

This function preprocesses and/or evaluates Jacobian-related data +needed by the preconditioner. Use the userdata object to expose +the preprocessed data to the solve function.

+

This is a generic class, you should subclass it for the problem specific +purposes.

+
+ +
+ +
+
+class scikits_odes_sundials.ida.IDA_PrecSolveFunction
+

Prototype for precondititioning solution function.

+

Note that evaluate must return a integer, 0 for success, positive for +recoverable failure, negative for unrecoverable failure (as per CVODE +documentation).

+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray yp, ndarray r, ndarray rvec, ndarray z, DTYPE_t cj, DTYPE_t delta, userdata=None) → int
+

This function solves the preconditioned system P*z = r, where P may be +either a left or right preconditioner matrix. Here P should approximate +(at least crudely) the Newton matrix M = I − gamma*J, where J is the +Jacobian of the system. If preconditioning is done on both sides, +the product of the two preconditioner matrices should approximate M.

+

This is a generic class, you should subclass it for the problem specific +purposes.

+
+ +
+ +
+
+class scikits_odes_sundials.ida.IDA_RhsFunction
+

Prototype for rhs function.

+

Note that evaluate must return a integer, 0 for success, positive for +recoverable failure, negative for unrecoverable failure (as per IDA +documentation).

+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray ydot, ndarray result, userdata=None) → int
+
+ +
+ +
+
+class scikits_odes_sundials.ida.IDA_RootFunction
+

Prototype for root function.

+

Note that evaluate must return a integer, 0 for success, non-zero for error +(as per IDA documentation).

+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray ydot, ndarray g, userdata=None) → int
+
+ +
+ +
+
+class scikits_odes_sundials.ida.IDA_WrapJacRhsFunction
+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray ydot, ndarray residual, DTYPE_t cj, ndarray J, userdata=None) → int
+

Returns the Jacobi matrix (for dense the full matrix, for band only +bands. Result has to be stored in the variable J, which is preallocated +to the corresponding size.

+
+ +
+
+set_jacfn(self, jacfn)
+

Set some jacobian equations as a JacResFunction executable class.

+
+ +
+ +
+
+class scikits_odes_sundials.ida.IDA_WrapJacTimesSetupFunction
+
+
+evaluate(self, DTYPE_t tt, ndarray yy, ndarray yp, ndarray rr, DTYPE_t cj, userdata=None) → int
+
+ +
+
+set_jac_times_setupfn(self, jac_times_setupfn)
+

Set some IDA_JacTimesSetupFn executable class.

+
+ +
+ +
+
+class scikits_odes_sundials.ida.IDA_WrapJacTimesVecFunction
+
+
+evaluate(self, DTYPE_t t, ndarray yy, ndarray yp, ndarray rr, ndarray v, ndarray Jv, DTYPE_t cj, userdata=None) → int
+
+ +
+
+set_jac_times_vecfn(self, jac_times_vecfn)
+

Set some IDA_JacTimesVecFn executable class.

+
+ +
+ +
+
+class scikits_odes_sundials.ida.IDA_WrapPrecSetupFunction
+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray yp, ndarray rr, DTYPE_t cj, userdata=None) → int
+
+ +
+
+set_prec_setupfn(self, prec_setupfn)
+

set a precondititioning setup method as a IDA_PrecSetupFunction +executable class

+
+ +
+ +
+
+class scikits_odes_sundials.ida.IDA_WrapPrecSolveFunction
+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray yp, ndarray r, ndarray rvec, ndarray z, DTYPE_t cj, DTYPE_t delta, userdata=None) → int
+
+ +
+
+set_prec_solvefn(self, prec_solvefn)
+

set a precondititioning solve method as a IDA_PrecSolveFunction +executable class

+
+ +
+ +
+
+class scikits_odes_sundials.ida.IDA_WrapRhsFunction
+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray ydot, ndarray result, userdata=None) → int
+
+ +
+
+set_resfn(self, resfn)
+

set some residual equations as a ResFunction executable class

+
+ +
+ +
+
+class scikits_odes_sundials.ida.IDA_WrapRootFunction
+
+
+evaluate(self, DTYPE_t t, ndarray y, ndarray ydot, ndarray g, userdata=None) → int
+
+ +
+
+set_rootfn(self, rootfn)
+

set root-ing condition(equations) as a RootFunction executable class

+
+ +
+ +
+
+class scikits_odes_sundials.ida.StatusEnumIDA(value, names=None, *, module=None, qualname=None, type=None, start=1, boundary=None)
+
+ +
+
+scikits_odes_sundials.ida.no_continue_fn(t, y, yp, solver)
+
+ +
+
+ + +
+ +
+
+ +
+
+
+ ©2016, B. Malengier. + + | + Powered by Sphinx 7.3.7 + & Alabaster 0.7.16 + + | + Page source +
+ + + + + + \ No newline at end of file diff --git a/v3.0.0a3/dae.html b/v3.0.0a3/dae.html new file mode 100644 index 0000000..40fef16 --- /dev/null +++ b/v3.0.0a3/dae.html @@ -0,0 +1,433 @@ + + + + + + + + DAE Solvers — Odes 3.0.0a3 documentation + + + + + + + + + + + + + + + + + + + + + + + +
+
+
+ + +
+ +
+

DAE Solvers

+
+
+class scikits.odes.dae.dae(integrator_name, eqsres, **options)[source]
+

A generic interface class to differential algebraic equations.

+

Define equation res = G(t,y,y’) which can eg be G = f(y,t) - A y’ when +solving A y’ = f(y,t), and where (optional) jac is the jacobian matrix of +the nonlinear system see fortran source code), so d res/dy + scaling * d +res/dy’ or d res/dy depending on the backend.

+
+
Parameters:
+
    +

  • integrator_name ('ida', 'ddaspk' or 'lsodi') – The integrator solver to use.

    • +

  • eqsres (residual function) –

    Residual of the DAE. The signature of this function depends on the +solver used, see the solver documentation for details. +Generally however, you can assume the following signature to work:

    +
    +

    eqsres(x, y, yprime, return_residual)

    +
    +

    with +x : independent variable, eg the time, float +y : array of n unknowns in x +yprime : dy/dx array of n unknowns in x, dimension = dim(y) +return_residual: array that must be updated with the value of the residuals, so G(t,y,y’). The dimension is equal to dim(y) +return value: integer, 0 for success. It is not guaranteed that a solver takes this status into account

    +

    Some solvers will allow userdata to be passed to eqsres, or optional +formats that are more performant.

    +

    • +

  • options (mapping) – Additional options for initialization, solver dependent +See set_options method of the integrator_name you selected for +details.

    • +
+
+
+
+

See also

+
+
odeint

an ODE integrator with a simpler interface based on lsoda from ODEPACK

+
+
ode

class around vode ODE integrator

+
+
+
+

Notes

+

Possible future solvers

+

ddaskr: Not included, starting hints: +http://osdir.com/ml/python.f2py.user/2005-07/msg00014.html +Modified Extended Backward Differentiation Formulae (MEBDF): Not included. +Fortran codes: http://www.ma.ic.ac.uk/~jcash/IVP_software/readme.html

+

Examples

+

DAE arise in many applications of dynamical systems, as well as in +discritisations of PDE (eg moving mesh combined with method of +lines). +As an easy example, consider the simple oscillator, which we write as +G(y,y’,t) = 0 instead of the normal ode, and solve as a DAE.

+
>>> from __future__ import print_function
+>>> from numpy import cos, sin, sqrt
+>>> k = 4.0
+>>> m = 1.0
+>>> initx = [1, 0.1]
+>>> initxp = [initx[1], -k/m*initx[0]]
+>>> def reseqn(t, x, xdot, result):
+    ... # we create residual equations for the problem
+    ... result[0] = m*xdot[1] + k*x[0]
+    ... result[1] = xdot[0] - x[1]
+>>> from scikits.odes import dae
+>>> solver = dae('ida', reseqn)
+>>> result = solver.solve([0., 1., 2.], initx, initxp)
+
+
+
+
+init_step(t0, y0, yp0, y_ic0_retn=None, yp_ic0_retn=None)[source]
+

Initializes the solver and allocates memory. It is not needed to +call this method if solve is used to compute the solution. In the case +step is used, init_step must be called first.

+
+
Parameters:
+
    +

  • t0 (number) – initial time

    • +

  • y0 (list/array) – initial condition for y

    • +

  • yp0 (list/array) – initial condition for yp

    • +

  • y_ic0 (numpy array) – (optional) returns the calculated consistent initial condition for y

    • +

  • yp_ic0 (numpy array) – (optional) returns the calculated consistent initial condition for y +derivated.

    • +
+
+
Returns:
+

    +

  • old_api is False (namedtuple) – namedtuple with the following attributes

    + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    An integer flag (StatusEnumXXX)

    values

    Named tuple with entries t and y and ydot. y will correspond to y_retn value and ydot to yp_retn!

    errors

    Named tuple with entries t and y and ydot

    roots

    Named tuple with entries t and y and ydot

    tstop

    Named tuple with entries t and y and ydot

    message

    String with message in case of an error

    +
    • +

  • old_api is True (tuple) – tuple with the following elements in order

    + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    status of the computation (successful or error occurred)

    t_out

    time, where the solver stopped (when no error occurred, t_out == t)

    +
    • +
+

+
+
+
+ +
+
+set_options(**options)[source]
+

Set specific options for the solver. +See the solver documentation for details.

+

Calling set_options a second time, normally resets the solver.

+
+ +
+
+solve(tspan, y0, yp0)[source]
+

Runs the solver.

+
+
Parameters:
+
    +

  • tspan (list/array) – A list of times at which the computed value will be returned. Must +contain the start time as first entry.

    • +

  • y0 (list/array) – list array of initial values

    • +

  • yp0 (list/array) – list array of initial values of derivatives

    • +
+
+
Returns:
+

    +

  • old_api is False (namedtuple) – namedtuple with the following attributes

    + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    An integer flag (StatusEnumXXX)

    values

    Named tuple with entries array t and array y and array ydot. y will correspond to y_retn value and ydot to yp_retn!

    errors

    Named tuple with entries t and y and ydot of error

    roots

    Named tuple with entries array t and array y and array ydot

    tstop

    Named tuple with entries array t and array y and array ydot

    message

    String with message in case of an error

    +
    • +

  • old_api is True (tuple) – tuple with the following elements in order

    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    indicating return status of the solver

    t

    numpy array of times at which the computations were successful

    y

    numpy array of values corresponding to times t (values of y[i, :] ~ t[i])

    yp

    numpy array of derivatives corresponding to times t (values of yp[i, :] ~ t[i])

    t_err

    float or None - if recoverable error occurred (for example reached maximum number of allowed iterations), this is the time at which it happened

    y_err

    numpy array of values corresponding to time t_err

    yp_err

    numpy array of derivatives corresponding to time t_err

    +
    • +
+

+
+
+
+ +
+
+step(t, y_retn=None, yp_retn=None)[source]
+

Method for calling successive next step of the IDA solver to allow +more precise control over the IDA solver. The ‘init_step’ method has to +be called before the ‘step’ method.

+

A step is done towards time t, and output at t returned. This time can +be higher or lower than the previous time. If option +‘one_step_compute’==True, and the solver supports it, only one internal +solver step is done in the direction of t starting at the current step.

+

If old_api=True, the old behavior is used: if t>0.0 then integration is +performed until this time and results at this time are returned in +y_retn; else if if t<0.0 only one internal step is performed towards time +abs(t) and results after this one time step are returned.

+
+
Parameters:
+
    +

  • t (number)

    • +

  • y_retn (numpy array (ndim = 1) or None.) – (Needs to be preallocated) If not None, will be filled with y at +time t. If None y_retn is not used.

    • +

  • yp_retn (numpy array (ndim = 1) or None.) – (Needs to be preallocated) If not None, will be filled with +derivatives of y at time t. If None yp_retn is not used.

    • +
+
+
Returns:
+

    +

  • old_api is False (namedtuple) – namedtuple with the following attributes

    + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    An integer flag (StatusEnumXXX)

    values

    Named tuple with entries t and y and ydot. y will correspond to y_retn value and ydot to yp_retn!

    errors

    Named tuple with entries t and y and ydot

    roots

    Named tuple with entries t and y and ydot

    tstop

    Named tuple with entries t and y and ydot

    message

    String with message in case of an error

    +
    • +

  • old_api is True (tuple) – tuple with the following elements in order

    + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    status of the computation (successful or error occurred)

    t_out

    time, where the solver stopped (when no error occurred, t_out == t)

    +
    • +
+

+
+
+
+ +
+ +
+ + +
+ +
+
+ +
+
+
+ ©2016, B. Malengier. + + | + Powered by Sphinx 7.3.7 + & Alabaster 0.7.16 + + | + Page source +
+ + + + + + \ No newline at end of file diff --git a/v3.0.0a3/genindex.html b/v3.0.0a3/genindex.html new file mode 100644 index 0000000..8c2c517 --- /dev/null +++ b/v3.0.0a3/genindex.html @@ -0,0 +1,702 @@ + + + + + + + Index — Odes 3.0.0a3 documentation + + + + + + + + + + + + + + + + + + + + + +
+
+
+ + +
+ + +

Index

+ +
+ C + | D + | E + | F + | G + | I + | M + | N + | O + | R + | S + | T + | V + | W + | Y + +
+

C

+ + + +
+ +

D

+ + + +
+ +

E

+ + +
+ +

F

+ + +
+ +

G

+ + +
+ +

I

+ + + +
+ +

M

+ + +
+ +

N

+ + +
+ +

O

+ + + +
+ +

R

+ + +
+ +

S

+ + + +
+ +

T

+ + + +
+ +

V

+ + + +
+ +

W

+ + +
+ +

Y

+ + +
+ + + +
+ +
+
+ +
+
+
+ ©2016, B. Malengier. + + | + Powered by Sphinx 7.3.7 + & Alabaster 0.7.16 + +
+ + + + + + \ No newline at end of file diff --git a/v3.0.0a3/index.html b/v3.0.0a3/index.html new file mode 100644 index 0000000..3c318df --- /dev/null +++ b/v3.0.0a3/index.html @@ -0,0 +1,268 @@ + + + + + + + + Welcome to the ODES scikit API Documentation — Odes 3.0.0a3 documentation + + + + + + + + + + + + + + + + + + + + + + + +
+
+
+ + +
+ +
+

Welcome to the ODES scikit API Documentation

+

The ODES scikit provides access to Ordinary Differential Equation (ODE) solvers and Differential Algebraic Equation (DAE) solvers.

+

This is the generated API documentation for version 3.0.0a3, see https://scikits-odes.readthedocs.io/en/latest/ for the main documentation and user guide.

+

For other versions of the API documentation, see https://bmcage.github.io/odes.

+

Contents:

+
+ +
+
+
+

Indices and tables

+ +
+ + +
+ +
+
+ +
+
+
+ ©2016, B. Malengier. + + | + Powered by Sphinx 7.3.7 + & Alabaster 0.7.16 + + | + Page source +
+ + + + + + \ No newline at end of file diff --git a/v3.0.0a3/objects.inv b/v3.0.0a3/objects.inv new file mode 100644 index 0000000..1d2329c Binary files /dev/null and b/v3.0.0a3/objects.inv differ diff --git a/v3.0.0a3/ode.html b/v3.0.0a3/ode.html new file mode 100644 index 0000000..0734530 --- /dev/null +++ b/v3.0.0a3/ode.html @@ -0,0 +1,682 @@ + + + + + + + + ODE Solvers — Odes 3.0.0a3 documentation + + + + + + + + + + + + + + + + + + + + + + + + +
+
+
+ + +
+ +
+

ODE Solvers

+

scikits.odes contains two main routines for solving ODEs: the simpler +scikits.odes.odeint.odeint(), and the more configurable +scikits.odes.ode.ode. Both these routines allow selection of the +solver and solution method used. Additionally, it is also possible to directly +use the low level interface to individual solvers.

+
+
+scikits.odes.odeint.odeint(rhsfun, tout, y0, method='bdf', **options)[source]
+

Integrate a system of ordinary differential equations. +odeint is a wrapper around the ode class, as a convenience function to +quickly integrate a system of ode. +Solves the initial value problem for stiff or non-stiff systems +of first order ode’s:

+
+

rhs = dy/dt = fun(t, y)

+
+

where y can be a vector, then rhsfun must be a function computing rhs with +signature:

+
+

rhsfun(t, y, rhs)

+
+

storing the computed dy/dt in the rhs array passed to the function

+
+
Parameters:
+
    +

  • rhsfun (callable(t, y, out)) – Computes the derivative at dy/dt in terms of t and y, and stores in out

    • +

  • 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.

    • +

  • method (string, solution method to use.) –

    Available are all the ode class solvers as well as some convenience +shorthands:

    + + + + + + + + + + + + + + + + + + + + +

    Method

    Meaning

    bdf

    This uses the ‘cvode’ solver in default from, which is a +variable step, variable coefficient Backward Differentiation +Formula solver, good for stiff ODE. Newton iterations are +used to solve the nonlinear system.

    admo

    This uses the ‘cvode’ solver with option lmm_type=’ADAMS’, +which is a variable step Adams-Moulton method (linear +multistep method), good for non-stiff ODE. Functional +iterations are used to solve the nonlinear system.

    rk5

    This uses the ‘dopri5’ solver, which is a variable step +Runge-Kutta method of order (4)5 (use for non-stiff ODE)

    rk8

    This uses the ‘dop853’ solver, which is a variable step +Runge-Kutta method of order 8(5,3)

    +

    For educational purposes, you can also access following methods:

    + + + + + + + + + + + + + + +

    Method

    Meaning

    beuler

    This is the Implicit Euler (backward Euler) method (order 1), +which is obtained via the ‘bdf’ method, setting the order +option to 1, setting large tolerances, and fixing the +stepsize. +Use option ‘step’ to change stepsize, default: step=0.05. +Use option ‘rtol’ and ‘atol’ to use more strict tolerances +Note: this is not completely the backward Euler method, as +the cvode solver has added control options!

    trapz

    This is the Trapezoidal Rule method (order 2), which is +obtained via the ‘admo’ method, setting option order to 2, +setting large tolerances and fixing the stepsize. +Use option ‘step’ to change stepsize, default: step=0.05. +Use option ‘rtol’ and ‘atol’ to use more strict tolerances +Note: The cvode solver might change the order to 1 internally +in which case this becomes beuler method. Set atol, rtol +options as strict as possible.

    +

    You can also access the solvers of ode via their names:

    + + + + + + + + + + + + + + + + + +

    Method

    Meaning

    cvode

    This uses the ‘cvode’ solver

    dopri5

    This uses the ‘dopri5’ solver

    dop853

    This uses the ‘dop853’ solver

    +

    • +

  • options (extra solver options, optional) – Every solver has it’s own extra options, see the ode class and the +details of the solvers available there to know the options possible per +solver

    • +
+
+
Returns:
+

solution – A single named tuple is returned containing the result of the +integration.

+ + + + + + + + + + + + + + + + + + + + + + + + + + +

Field

Meaning

flag

An integer flag

values

Named tuple with fields t and y

errors

Named tuple with fields t and y

roots

Named tuple with fields t and y

tstop

Named tuple with fields t and y

message

String with message in case of an error

+

+
+
Return type:
+

named tuple

+
+
+
+

See also

+
+
scikits.odes.ode.ode

a more object-oriented integrator

+
+
scikits.odes.dae.dae

a solver for differential-algebraic equations

+
+
scipy.integrate.quad

for finding the area under a curve

+
+
+
+

Examples

+

The second order differential equation for the angle theta of a +pendulum acted on by gravity with friction can be written:

+
+\[\theta''(t) + b \theta'(t) + c \sin(\theta(t)) = 0\]
+

where b and c are positive constants, and a prime (’) denotes a +derivative. To solve this equation with odeint, we must first convert +it to a system of first order equations. By defining the angular +velocity omega(t) = theta'(t), we obtain the system:

+
+\[\theta'(t) = \omega(t) +\omega'(t) = -b \omega(t) - c \sin(\theta(t))\]
+

We assume the constants are b = 0.25 and c = 5.0:

+
>>> b = 0.25
+>>> c = 5.0
+
+
+

Let y be the vector [theta, omega]. We implement this system +in python as:

+
>>> def pend(t, y, out):
+ ...     theta, omega = y
+ ...     out[:] = [omega, -b*omega - c*np.sin(theta)]
+ ...
+
+
+

In case you want b and c easily changable, make pend a class method, and +consider attributes b and c accessible via self.b and self.c. +For initial conditions, we assume the pendulum is nearly vertical +with theta(0) = pi - 0.1, and it initially at rest, so +omega(0) = 0. Then the vector of initial conditions is

+
>>> y0 = [np.pi - 0.1, 0.0]
+
+
+

We generate a solution 101 evenly spaced samples in the interval +0 <= t <= 10. So our array of times is

+
>>> t = np.linspace(0, 10, 101)
+
+
+

Call odeint to generate the solution.

+
>>> from scikits.odes.odeint import odeint
+>>> sol = odeint(pend, t, y0)
+
+
+

The solution is a named tuple sol. sol.values.y is an array with shape (101, 2). +The first column is theta(t), and the second is omega(t). +The following code plots both components.

+
>>> import matplotlib.pyplot as plt
+>>> plt.plot(sol.values.t, sol.values.y[:, 0], 'b', label='theta(t)')
+>>> plt.plot(sol.values.t, sol.values.y[:, 1], 'g', label='omega(t)')
+>>> plt.legend(loc='best')
+>>> plt.xlabel('t')
+>>> plt.grid()
+>>> plt.show()
+
+
+
+ +
+
+class scikits.odes.ode.ode(integrator_name, eqsrhs, **options)[source]
+

A generic interface class to differential equation solvers.

+
+
Parameters:
+
    +

  • integrator_name ('cvode', 'dopri5' or 'dop853') –

    The solver to use.

    +

    'cvode' selects the CVODE solver from the SUNDIALS package. +See py:class:scikits.odes.sundials.cvode.CVODE for solver specific +options.

    +

    'dopri5' selects the Dormand & Prince Runge-Kutta order (4)5 +solver from scipy.

    +

    • +

  • eqsrhs (right-hand-side function) –

    Right-hand-side of a first order ode. +Generally, you can assume the following signature to work:

    +
    +

    eqsrhs(x, y, return_rhs)

    +
    +

    with

    +
    +

    x: independent variable, eg the time, float

    +

    y: array of n unknowns in x

    +

    return_rhs : array that must be updated with the value of the +right-hand-side, so f(t,y). The dimension is equal to +dim(y)

    +
    +
    +
    return value: An integer, 0 for success, 1 for failure.

    It is not guaranteed that a solver takes this status into account

    +
    +
    +

    Some solvers will allow userdata to be passed to eqsrhs, or optional +formats that are more performant.

    +

    • +

  • options (additional options of the solver) – See set_options method of the integrator_name you selected for +details. +Set option old_api=False to use the new API. In the future, this +will become the default!

    • +
+
+
+
+

See also

+
+
scikits.odes.odeint.odeint

an ODE integrator with a simpler interface

+
+
scipy.integrate

Methods in scipy for ODE integration

+
+
+
+

Examples

+

ODE arise in many applications of dynamical systems, as well as in +discritisations of PDE (eg moving mesh combined with method of +lines). +As an easy example, consider the simple oscillator,

+
>>> from __future__ import print_function
+>>> from numpy import cos, sin, sqrt
+>>> k = 4.0
+>>> m = 1.0
+>>> initx = [1, 0.1]
+>>> def rhseqn(t, x, xdot):
+        # we create rhs equations for the problem
+        xdot[0] = x[1]
+        xdot[1] = - k/m * x[0]
+
+
+
>>> from scikits.odes import ode
+>>> solver = ode('cvode', rhseqn, old_api=False)
+>>> result = solver.solve([0., 1., 2.], initx)
+>>> print('   t        Solution          Exact')
+>>> print('------------------------------------')
+>>> for t, u in zip(result.values.t, result.values.y):
+        print('%4.2f %15.6g %15.6g' % (t, u[0], initx[0]*cos(sqrt(k/m)*t)+initx[1]*sin(sqrt(k/m)*t)/sqrt(k/m)))
+
+
+

More examples in the Examples directory and IPython worksheets.

+
+
+get_info()[source]
+

Return additional information about the state of the integrator.

+
+
Returns:
+

    +

  • A dictionary filled with internal data as exposed by the integrator.

    • +

  • See the get_info method of your chosen integrator for details.

    • +
+

+
+
+
+ +
+
+init_step(t0, y0)[source]
+

Initializes the solver and allocates memory. It is not needed to +call this method if solve is used to compute the solution. In the case +step is used, init_step must be called first.

+
+
Parameters:
+
    +

  • t0 (number) – initial time

    • +

  • y0 (array) – initial condition for y (can be list or numpy array)

    • +
+
+
Returns:
+

    +

  • old_api is False (namedtuple) – namedtuple with the following attributes

    + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    An integer flag (StatusEnum)

    values

    Named tuple with entries t and y

    errors

    Named tuple with entries t and y

    roots

    Named tuple with entries t and y

    tstop

    Named tuple with entries t and y

    message

    String with message in case of an error

    +
    • +

  • old_api is True (tuple) – tuple with the following elements in order

    + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    boolean status of the computation (successful or error occured)

    t_out

    inititial time

    +
    • +
+

+
+
+
+ +
+
+set_options(**options)[source]
+

Set specific options for the solver. +See the solver documentation for details.

+

Calling set_options a second time, is only possible for options that +can change during runtime.

+
+ +
+
+set_tstop(tstop)[source]
+

Add a stop time to the integrator past which he is not allowed to +integrate.

+
+
Parameters:
+

tstop (float time) – Time point in the future where the integration must stop. You can +indicate like this that integration past this point is not allowed, +in order to avoid undefined behavior. +You can achieve the same result with a call to +set_options(tstop=tstop)

+
+
+
+ +
+
+solve(tspan, y0)[source]
+

Runs the solver.

+
+
Parameters:
+
    +

  • tspan (array (or similar)) – a list of times at which the computed value will be returned. Must +contain the start time as first entry.

    • +

  • y0 (array (or similar)) – a list of initial values

    • +
+
+
Returns:
+

    +

  • old_api is False (namedtuple) – namedtuple with the following attributes

    + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    An integer flag (StatusEnum)

    values

    Named tuple with entries t and y

    errors

    Named tuple with entries t and y

    roots

    Named tuple with entries t and y

    tstop

    Named tuple with entries t and y

    message

    String with message in case of an error

    +
    • +

  • old_api is True (tuple) – tuple with the following elements in order

    + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    indicating return status of the solver

    t

    numpy array of times at which the computations were successful

    y

    numpy array of values corresponding to times t (values of y[i, :] ~ t[i])

    t_err

    float or None - if recoverable error occured (for example reached maximum number of allowed iterations), this is the time at which it happened

    y_err

    numpy array of values corresponding to time t_err

    +
    • +
+

+
+
+
+ +
+
+step(t, y_retn=None)[source]
+

Method for calling successive next step of the ODE solver to allow +more precise control over the solver. The ‘init_step’ method has to +be called before the ‘step’ method.

+

A step is done towards time t, and output at t returned. This time can +be higher or lower than the previous time. If option +‘one_step_compute’==True, and the solver supports it, only one internal +solver step is done in the direction of t starting at the current step.

+

If old_api=True, the old behavior is used: if t>0.0 then integration is +performed until this time and results at this time are returned in +y_retn if t<0.0 only one internal step is perfomed towards time abs(t) +and results after this one time step are returned

+
+
Parameters:
+
    +

  • t (number)

    • +

  • y_retn (numpy vector (ndim = 1)) – in which the computed value will be stored (needs to be +preallocated). If None y_retn is not used.

    • +
+
+
Returns:
+

    +

  • old_api is False (namedtuple) – namedtuple with the following attributes

    + + + + + + + + + + + + + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    An integer flag (StatusEnum)

    values

    Named tuple with entries t and y

    errors

    Named tuple with entries t and y

    roots

    Named tuple with entries t and y

    tstop

    Named tuple with entries t and y

    message

    String with message in case of an error

    +
    • +

  • old_api is True (tuple) – tuple with the following elements in order

    + + + + + + + + + + + + + + +

    Field

    Meaning

    flag

    status of the computation (successful or error occured)

    t_out

    time, where the solver stopped (when no error occured, t_out == t)

    +
    • +
+

+
+
+
+ +
+ +
+ + +
+ +
+
+ +
+
+
+ ©2016, B. Malengier. + + | + Powered by Sphinx 7.3.7 + & Alabaster 0.7.16 + + | + Page source +
+ + + + + + \ No newline at end of file diff --git a/v3.0.0a3/py-modindex.html b/v3.0.0a3/py-modindex.html new file mode 100644 index 0000000..c40cb65 --- /dev/null +++ b/v3.0.0a3/py-modindex.html @@ -0,0 +1,211 @@ + + + + + + + Python Module Index — Odes 3.0.0a3 documentation + + + + + + + + + + + + + + + + + + + + + + + + +
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+ scikits +
    + scikits.odes +
    + scikits.odes.dae +
    + scikits.odes.ddaspkint +
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    + scikits.odes.lsodiint +
    + scikits.odes.ode +
    + scikits.odes.sundials +
    + scikits.odes.sundials.cvode +
    + scikits.odes.sundials.ida +
+ scikits_odes +
    + scikits_odes.dae +
    + scikits_odes.dopri5 +
    + scikits_odes.ode +
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    + scikits_odes_sundials.ida +
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+ ©2016, B. Malengier. + + | + Powered by Sphinx 7.3.7 + & Alabaster 0.7.16 + +
+ + + + + + \ No newline at end of file diff --git a/v3.0.0a3/searchindex.js b/v3.0.0a3/searchindex.js new file mode 100644 index 0000000..52569cf --- /dev/null +++ b/v3.0.0a3/searchindex.js @@ -0,0 +1 @@ +Search.setIndex({"alltitles": {"DAE Solvers": [[6, "dae-solvers"]], "First-order DAE solver": [[4, "first-order-dae-solver"]], "First-order ODE solver": [[4, "first-order-ode-solver"]], "Indices and tables": [[7, "indices-and-tables"]], "Lower Level API": [[3, "lower-level-api"]], "Making scipy ode solvers available via the ode API": [[4, "making-scipy-ode-solvers-available-via-the-ode-api"]], "ODE Solvers": [[8, "ode-solvers"]], "Selecting Precision": [[9, "selecting-precision"]], "Sundials Solver Options": [[9, "sundials-solver-options"]], "Welcome to the ODES scikit API Documentation": [[7, "welcome-to-the-odes-scikit-api-documentation"]], "dop853": [[4, "dop853"]], "dopri5": [[4, "dopri5"]], "scikits-odes": [[4, "scikits-odes"]], "scikits-odes-core": [[1, "module-scikits_odes_core"]], "scikits-odes-daepack": [[2, "scikits-odes-daepack"]], "scikits-odes-sundials": [[5, "scikits-odes-sundials"]], "scikits.odes": [[0, "scikits-odes"], [0, "id1"]], "scikits.odes.dae": [[0, "module-scikits.odes.dae"]], "scikits.odes.ddaspkint": [[0, "module-scikits.odes.ddaspkint"]], "scikits.odes.dopri5": [[0, "module-scikits.odes.dopri5"]], "scikits.odes.lsodiint": [[0, "module-scikits.odes.lsodiint"]], "scikits.odes.ode": [[0, "module-scikits.odes.ode"]], "scikits.odes.sundials": [[0, "module-scikits.odes.sundials"]], "scikits.odes.sundials.cvode": [[0, "module-scikits.odes.sundials.cvode"]], "scikits.odes.sundials.ida": [[0, "module-scikits.odes.sundials.ida"]], "scikits_odes": [[4, "module-scikits_odes"]], "scikits_odes.dae": [[4, "module-scikits_odes.dae"]], "scikits_odes.dopri5": [[4, "module-scikits_odes.dopri5"]], "scikits_odes.ode": [[4, "module-scikits_odes.ode"]], "scikits_odes_sundials": [[5, "module-scikits_odes_sundials"]], "scikits_odes_sundials.cvode": [[5, "module-scikits_odes_sundials.cvode"]], "scikits_odes_sundials.ida": [[5, "module-scikits_odes_sundials.ida"]]}, "docnames": ["api/compat", "api/core", "api/daepack", "api/index", "api/main", "api/sundials", "dae", "index", "ode", "sundials"], "envversion": {"sphinx": 61, "sphinx.domains.c": 3, "sphinx.domains.changeset": 1, "sphinx.domains.citation": 1, "sphinx.domains.cpp": 9, "sphinx.domains.index": 1, "sphinx.domains.javascript": 3, "sphinx.domains.math": 2, "sphinx.domains.python": 4, "sphinx.domains.rst": 2, "sphinx.domains.std": 2, "sphinx.ext.intersphinx": 1, "sphinx.ext.viewcode": 1}, "filenames": ["api/compat.rst", "api/core.rst", "api/daepack.rst", "api/index.rst", "api/main.rst", "api/sundials.rst", "dae.rst", "index.rst", "ode.rst", "sundials.rst"], "indexentries": {"cv_continuationfunction (class in scikits_odes_sundials.cvode)": [[5, "scikits_odes_sundials.cvode.CV_ContinuationFunction", false]], "cv_jacrhsfunction (class in 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"xlabel": 8, "y": [1, 4, 5, 6, 8], "y0": [1, 4, 6, 8], "y_0": 4, "y_dot": 1, "y_err": [1, 4, 6, 8], "y_ic0": [1, 4, 6], "y_ic0_retn": [1, 4, 6], "y_retn": [1, 4, 6, 8], "y_root": 4, "y_tstop": 4, "ydot": [1, 4, 5, 6], "you": [4, 5, 6, 8, 9], "your": [4, 8], "yp": [1, 4, 5, 6], "yp0": [1, 4, 6], "yp_err": [1, 4, 6], "yp_ic0": [1, 4, 6], "yp_ic0_retn": [1, 4, 6], "yp_retn": [1, 4, 6], "yprime": [4, 6], "yprime0": 4, "yy": 5, "z": 5, "zero": 5, "zip": [4, 8]}, "titles": ["scikits.odes", "scikits-odes-core", "scikits-odes-daepack", "Lower Level API", "scikits-odes", "scikits-odes-sundials", "DAE Solvers", "Welcome to the ODES scikit API Documentation", "ODE Solvers", "Sundials Solver Options"], "titleterms": {"api": [3, 4, 7], "avail": 4, "core": 1, "cvode": [0, 5], "dae": [0, 4, 6], "daepack": 2, "ddaspkint": 0, "document": 7, "dop853": 4, "dopri5": [0, 4], "first": 4, "ida": [0, 5], "indic": 7, "level": 3, "lower": 3, "lsodiint": 0, "make": 4, "od": [0, 1, 2, 4, 5, 7, 8], "option": 9, "order": 4, "precis": 9, "scikit": [0, 1, 2, 4, 5, 7], "scikits_od": 4, "scikits_odes_sundi": 5, "scipi": 4, "select": 9, "solver": [4, 6, 8, 9], "sundial": [0, 5, 9], "tabl": 7, "via": 4, "welcom": 7}}) \ No newline at end of file diff --git a/v3.0.0a3/sundials.html b/v3.0.0a3/sundials.html new file mode 100644 index 0000000..06a9d6d --- /dev/null +++ b/v3.0.0a3/sundials.html @@ -0,0 +1,144 @@ + + + + + + + + Sundials Solver Options — Odes 3.0.0a3 documentation + + + + + + + + + + + + + + + + + + + + + + + +
+
+
+ + +
+ +
+

Sundials Solver Options

+
+

Selecting Precision

+

Sundials can be built with different precisions (currently ‘single’ which maps +to C ‘float’; ‘double’ (the default) which maps to C ‘double’; and +‘extended’ which maps to C ‘long double’), and scikits-odes-sundials +supports using whichever precision Sundials is built with. To take advantage of +this, you must first have sundials built and installed with the desired +precision setting.

+

Once you have done this, build scikits-odes-sundials against this particular +version of sundials (see the main documentation for how to do this). +scikits-odes-sundials will automatically detect the precision, and store this in +a variable called +DTYPE. DTYPE should be accessed from +scikits_odes_sundials (other modules may have DTYPE +defined, but scikits_odes_sundials should be preferred). Additionally +scikits_odes_sundials.precision contains the precision setting found +by scikits.odes.

+

To use DTYPE, treat it as a numpy dtype; use it whenever you need to +create an array:

+
np.array([1,2,3], dtype=DTYPE)
+
+
+

or when using scalars:

+
DTYPE(0.1) * DTYPE(0.1)
+
+
+
+
+ + +
+ +
+
+ +
+
+
+ ©2016, B. Malengier. + + | + Powered by Sphinx 7.3.7 + & Alabaster 0.7.16 + + | + Page source +
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