Package PyDSTool :: Package Toolbox :: Module phaseplane :: Class mesh_patch_2D

Class mesh_patch_2D

object --+
         |
        mesh_patch_2D

2D mesh patch generator (for 4 or 8 points of a fixed distance from a central point). i.e., total number of mesh points may be 5 or 9.

Once either 5 or 9 points have been selected, this is fixed for the mesh patch instance. The central point p0 and radii r of the mesh points are mutable using the 'update' method. If shape='circle' (default), mesh points are equidistant from p0. If shape='square', mesh points are distributed around the corners and mid-sides of a square of side length 2*r.

The points are in the order p0 followed by points in 'clockwise' order in the phase plane defined by the two variable names in p0.

Functions / callable objects can be applied to all points in the mesh patch by calling the mesh patch's 'eval' method with the function. It returns an a dictionary of mesh points -> function return values.

The direction of minimum (interpolated) gradient of a functional over the mesh can be determined from the 'min_gradient_dir' method. A similar method 'max_gradient_dir' also exists.

Highly experimental class!

Rob Clewley, Jan 2007

Instance Methods

[hide private]

__init__(self, p0, r, n=5, shape='circle')
p0 should be of type Point, r must be either a scalar or a Point giving weighted radius in each of two directions, n must be 5 or 9. source code

make_mesh(self, makelocalmesh=False)

source code

update(self, p0=None, r=None)
Change the central point p0 or patch radius r

source code

derive_angles(self)

source code

__getitem__(self, ix)

source code

eval(self, f)
Evaluate the function or callable object f at the mesh patch points.

source code

setup_grad(self, valdict, orient, dir)

source code

min_gradient_dir(self, valdict, orient=None, dir=None)
Find the direction of any local minima of a functional over the mesh patch, whose dictionary of mesh point index -> function value is given by valdict.

source code

min_gradient_mesh(self, valdict, orient=None, dir=None)
Find the direction of any local minima of a functional over the mesh patch, whose dictionary of mesh point index -> function value is given by valdict.

source code

__min_grad(self, valdict, orient, dir, return_type)

source code

max_gradient_dir(self, valdict, orient=None, dir=None)
Find the direction of maximum gradient of a functional over the mesh patch, whose dictionary of mesh point index -> function value is given by valdict.

source code

max_gradient_mesh(self, valdict, orient=None, dir=None)
Find the direction of maximum gradient of a functional over the mesh patch, whose dictionary of mesh point index -> function value is given by valdict.

source code

__max_grad(self, valdict, orient, dir, return_type)

source code

__repr__(self)
str(x)

source code

__str__(self)
str(x)

source code

Inherited from object: __delattr__, __getattribute__, __hash__, __new__, __reduce__, __reduce_ex__, __setattr__

Class Variables

[hide private]

_s2 = 0.70710678118654757

_mesh5 = [(0, 0), (0, 1), (1, 0), (0, -1), (-1, 0)]

_mesh9s = [(0, 0), (0, 1), (1, 1), (1, 0), (1, -1), (0, -1), (...

_mesh9c = [(0, 0), (0, 1), (0.70710678118654757, 0.70710678118...

Properties

[hide private]

Inherited from object: __class__

Method Details

[hide private]

init(self, p0, r, n=5, shape=`'circle'`)
(Constructor)

source code

p0 should be of type Point, r must be either a scalar or a Point giving weighted radius in each of two directions, n must be 5 or 9.

Overrides: object.__init__

eval(self, f)

source code

Evaluate the function or callable object f at the mesh patch points.
Returns a dictionary of
    mesh point index -> function value
Indices are always in the same order as the Pointset attribute 'mesh'

min_gradient_dir(self, valdict, orient=None, dir=None)

source code

Find the direction of any local minima of a functional over
the mesh patch, whose dictionary of
    mesh point index -> function value
is given by valdict. The magnitudes of these values are
compared. The direction is indicated by a Point object, a
relative position at the patch's characteristic radius from
p0.

If the functional is constant everywhere on the patch (degenerate)
then a random direction is returned. If the functional is constant
everywhere except at the centre, then the vector (0,0) is returned
if the centre has lower value; a random vector is returned
otherwise.

If the functional is partially degenerate on some subset of
mesh points then the optional orient and dir arguments can
provide a means to select, provided the mesh resolution is
sufficiently high.

orient is a vector (Point object) relative to p0 orienting a
"positive" direction, such that the integer dir = -1 or +1
selects one half of the mesh points on which to conduct the
search.

min_gradient_mesh(self, valdict, orient=None, dir=None)

source code

Find the direction of any local minima of a functional over
the mesh patch, whose dictionary of
    mesh point index -> function value
is given by valdict. The magnitudes of these values are
compared. The direction is returned as a pair containing the two
closest mesh points to the direction (in mesh local coords).

If the functional is constant everywhere on the patch (degenerate)
then a random direction is returned. If the functional is constant
everywhere except at the centre, then the vector (0,0) is returned
if the centre has lower value; a random vector is returned
otherwise.

If the functional is partially degenerate on some subset of
mesh points then the optional orient and dir arguments can
provide a means to select, provided the mesh resolution is
sufficiently high.

orient is a vector (Point object) relative to p0 orienting a
"positive" direction, such that the integer dir = -1 or +1
selects one half of the mesh points on which to conduct the
search.

max_gradient_dir(self, valdict, orient=None, dir=None)

source code

Find the direction of maximum gradient of a functional over
the mesh patch, whose dictionary of
    mesh point index -> function value
is given by valdict. The magnitudes of the values are
compared. The direction is indicated by a Point object, a
relative position at the patch's characteristic radius from
p0.

If the functional is constant everywhere on the patch (degenerate)
then a random direction is returned. If the functional is constant
everywhere except at the centre, then the vector (0,0) is returned
if the centre has higher value; a random vector is returned
otherwise.

If the functional is partially degenerate on some subset of
mesh points then the optional orient and dir arguments can
provide a means to select, provided the mesh resolution is
sufficiently high.

orient is a vector (Point object) relative to p0 orienting a
"positive" direction, such that the integer dir = -1 or +1
selects one half of the mesh points on which to conduct the
search.

max_gradient_mesh(self, valdict, orient=None, dir=None)

source code

Find the direction of maximum gradient of a functional over
the mesh patch, whose dictionary of
    mesh point index -> function value
is given by valdict. The magnitudes of the values are
compared. The direction is returned as a pair containing the two
closest mesh points to the direction (in mesh local coords).

If the functional is constant everywhere on the patch (degenerate)
then a random direction is returned. If the functional is constant
everywhere except at the centre, then the vector (0,0) is returned
if the centre has higher value; a random vector is returned
otherwise.

If the functional is partially degenerate on some subset of
mesh points then the optional orient and dir arguments can
provide a means to select, provided the mesh resolution is
sufficiently high.

orient is a vector (Point object) relative to p0 orienting a
"positive" direction, such that the integer dir = -1 or +1
selects one half of the mesh points on which to conduct the
search.

repr(self)
(Representation operator)

source code

str(x)

Overrides: object.__repr__: (inherited documentation)

str(self)
(Informal representation operator)

source code

str(x)

Overrides: object.__str__: (inherited documentation)

Class Variable Details

[hide private]

_mesh9s

Value:

[(0, 0),
 (0, 1),
 (1, 1),
 (1, 0),
 (1, -1),
 (0, -1),
 (-1, -1),
 (-1, 0),
...

_mesh9c

Value:

[(0, 0),
 (0, 1),
 (0.70710678118654757, 0.70710678118654757),
 (1, 0),
 (0.70710678118654757, -0.70710678118654757),
 (0, -1),
 (-0.70710678118654757, -0.70710678118654757),
 (-1, 0),
...

Class mesh_patch_2D

__init__(self, p0, r, n=5, shape='circle') (Constructor)

eval(self, f)

min_gradient_dir(self, valdict, orient=None, dir=None)

min_gradient_mesh(self, valdict, orient=None, dir=None)

max_gradient_dir(self, valdict, orient=None, dir=None)

max_gradient_mesh(self, valdict, orient=None, dir=None)

__repr__(self) (Representation operator)

__str__(self) (Informal representation operator)

_mesh9s

_mesh9c

init(self, p0, r, n=5, shape=`'circle'`)
(Constructor)

repr(self)
(Representation operator)

str(self)
(Informal representation operator)