pylbm.stencil.Stencil¶

class pylbm.stencil.Stencil(dico, need_validation=True)¶

Create the stencil of velocities used by the scheme(s).

The numbering of the velocities follows the convention for 1D and 2D.

Parameters

dicoa dictionary that contains the following key:value

dim : the value of the spatial dimension (1, 2 or 3)
schemesa list of dictionaries that contain
the key:value velocities

[
    {
        'velocities': [...]
    },
    {
        'velocities': [...]
    },
    {
        'velocities': [...]
    },
    ...
]

Notes

The velocities for each schemes are defined as a Python list.

Examples

>>> s = Stencil({'dim': 1,
...              'schemes':[{'velocities': list(range(9))},],
...             })
>>> s
+---------------------+
| Stencil information |
+---------------------+
    - spatial dimension: 1
    - minimal velocity in each direction: [-4]
    - maximal velocity in each direction: [4]
    - information for each elementary stencil:
        stencil 0
            - number of velocities: 9
            - velocities
                (0: 0)
                (1: 1)
                (2: -1)
                (3: 2)
                (4: -2)
                (5: 3)
                (6: -3)
                (7: 4)
                (8: -4)
>>> s = Stencil({'dim': 2,
...              'schemes':[
                               {'velocities': list(range(9))},
...                            {'velocities': list(range(49))},
...                        ],
...            })
>>> s
+---------------------+
| Stencil information |
+---------------------+
    - spatial dimension: 2
    - minimal velocity in each direction: [-3 -3]
    - maximal velocity in each direction: [3 3]
    - information for each elementary stencil:
        stencil 0
            - number of velocities: 9
            - velocities
                (0: 0, 0)
                (1: 1, 0)
                (2: 0, 1)
                (3: -1, 0)
                (4: 0, -1)
                (5: 1, 1)
                (6: -1, 1)
                (7: -1, -1)
                (8: 1, -1)
        stencil 1
            - number of velocities: 49
            - velocities
                (0: 0, 0)
                (1: 1, 0)
                (2: 0, 1)
                (3: -1, 0)
                (4: 0, -1)
                (5: 1, 1)
                (6: -1, 1)
                (7: -1, -1)
                (8: 1, -1)
                (9: 2, 0)
                (10: 0, 2)
                (11: -2, 0)
                (12: 0, -2)
                (13: 2, 2)
                (14: -2, 2)
                (15: -2, -2)
                (16: 2, -2)
                (17: 2, 1)
                (18: 1, 2)
                (19: -1, 2)
                (20: -2, 1)
                (21: -2, -1)
                (22: -1, -2)
                (23: 1, -2)
                (24: 2, -1)
                (25: 3, 0)
                (26: 0, 3)
                (27: -3, 0)
                (28: 0, -3)
                (29: 3, 3)
                (30: -3, 3)
                (31: -3, -3)
                (32: 3, -3)
                (33: 3, 1)
                (34: 1, 3)
                (35: -1, 3)
                (36: -3, 1)
                (37: -3, -1)
                (38: -1, -3)
                (39: 1, -3)
                (40: 3, -1)
                (41: 3, 2)
                (42: 2, 3)
                (43: -2, 3)
                (44: -3, 2)
                (45: -3, -2)
                (46: -2, -3)
                (47: 2, -3)
                (48: 3, -2)

get the x component of the unique velocities

>>> s.uvx
array([ 0,  1,  0, -1,  0,  1, -1, -1,  1,  2,  0, -2,  0,  2, -2, -2,  2,
        2,  1, -1, -2, -2, -1,  1,  2,  3,  0, -3,  0,  3, -3, -3,  3,  3,
        1, -1, -3, -3, -1,  1,  3,  3,  2, -2, -3, -3, -2,  2,  3])

get the y component of the velocity for the second stencil

>>> s.vy[1]
array([ 0,  0,  1,  0, -1,  1,  1, -1, -1,  0,  2,  0, -2,  2,  2, -2, -2,
        1,  2,  2,  1, -1, -2, -2, -1,  0,  3,  0, -3,  3,  3, -3, -3,  1,
        3,  3,  1, -1, -3, -3, -1,  2,  3,  3,  2, -2, -3, -3, -2])

Attributes

dimint: the spatial dimension (1, 2 or 3).
unique_velocitiesNumPy array: array of all velocities involved in the stencils. Each unique velocity appeared only once.
uvxNumPy array: the x component of the unique velocities.
uvyNumPy array: the y component of the unique velocities.
uvzNumPy array: the z component of the unique velocities.
unumNumPy array: the numbering of the unique velocities.
vmaxint: the maximal velocity in norm for each spatial direction.
vminint: the minimal velocity in norm for each spatial direction.
vmax_fullint: the maximal velocity in norm for each spatial direction.
nstencilsint: the number of elementary stencils.
nvlist of integers: the number of velocities for each elementary stencil.
vlist of velocities: list of all the velocities for each elementary stencil.
vxNumPy array: vx[k] the x component of the velocities for the stencil k.
vyNumPy array: vy[k] the y component of the velocities for the stencil k.
vzNumPy array: vz[k] the z component of the velocities for the stencil k.
numNumPy array: num[k] the numbering of the velocities for the stencil k.
nv_ptrlist of integers: used to obtain the list of the velocities involved in a stencil. For instance, the list for the kth stencil is v[nv_ptr[k]:nv_ptr[k+1]]
unvtotint: the number of unique velocities involved in the stencils.

Methods

`append`(object)
`clear`()
`copy`()
`count`(value)
`extend`(iterable)
`extract_dim`(dico)	Extract the dimension from the dictionary
`get_all_velocities`([scheme_id])	get all the velocities for all the stencils in one array
`get_symmetric`([axis])	get the symmetric velocities.
`index`(value, [start, [stop]])	Raises ValueError if the value is not present.
`insert`	L.insert(index, object) – insert object before index
`is_symmetric`()	check if all the velocities have their symmetric.
`pop`([index])	Raises IndexError if list is empty or index is out of range.
`remove`(value)	Raises ValueError if the value is not present.
`reverse`	L.reverse() – reverse IN PLACE
`sort`([key, reverse])
`visualize`([viewer_mod, k, …])	plot the velocities

Attributes

`num`	num[k] the numbering of the velocities for the stencil k.
`unum`	the numbering of the unique velocities.
`unvtot`	the number of unique velocities involved in the stencils.
`uvx`	the x component of the unique velocities.
`uvy`	the y component of the unique velocities.
`uvz`	the z component of the unique velocities.
`vmax`	the maximal velocity in norm for each spatial direction.
`vmax_full`	the maximal velocity in norm for each spatial direction.
`vmin`	the minimal velocity in norm for each spatial direction.
`vx`	vx[k] the x component of the velocities for the stencil k.
`vy`	vy[k] the y component of the velocities for the stencil k.
`vz`	vz[k] the z component of the velocities for the stencil k.