fipy.variables.scharfetterGummelFaceVariable

Classes

ScharfetterGummelFaceVariable(*args, **kwds)

param mesh: the mesh that defines the geometry of this Variable

class fipy.variables.scharfetterGummelFaceVariable.ScharfetterGummelFaceVariable(*args, **kwds)

Bases: _CellToFaceVariable

Parameters:

• mesh (Mesh) – the mesh that defines the geometry of this Variable

• name (str) – the user-readable name of the Variable

• value (float or array_like) – the initial value

• rank (int) – the rank (number of dimensions) of each element of this Variable. Default: 0

• elementshape (tuple of int) – the shape of each element of this variable Default: rank * (mesh.dim,)

• unit (str or PhysicalUnit) – The physical units of the variable

__abs__()

Following test it to fix a bug with C inline string using abs() instead of fabs()

>>> print(abs(Variable(2.3) - Variable(1.2)))
1.1

Check representation works with different versions of numpy

>>> print(repr(abs(Variable(2.3))))
numerix.fabs(Variable(value=array(2.3)))

__and__(other)

This test case has been added due to a weird bug that was appearing.

>>> a = Variable(value=(0, 0, 1, 1))
>>> b = Variable(value=(0, 1, 0, 1))
>>> print(numerix.equal((a == 0) & (b == 1), [False,  True, False, False]).all())
True
>>> print(a & b)
[0 0 0 1]
>>> from fipy.meshes import Grid1D
>>> mesh = Grid1D(nx=4)
>>> from fipy.variables.cellVariable import CellVariable
>>> a = CellVariable(value=(0, 0, 1, 1), mesh=mesh)
>>> b = CellVariable(value=(0, 1, 0, 1), mesh=mesh)
>>> print(numerix.allequal((a == 0) & (b == 1), [False,  True, False, False]))
True
>>> print(a & b)
[0 0 0 1]

__array__(dtype=None, copy=None)

Attempt to convert the Variable to a numerix array object

>>> v = Variable(value=[2, 3])
>>> print(numerix.array(v))
[2 3]

A dimensional Variable will convert to the numeric value in its base units

>>> v = Variable(value=[2, 3], unit="mm")
>>> numerix.array(v)
array([ 0.002,  0.003])

__array_wrap__(arr, context=None, return_scalar=False)

Required to prevent numpy not calling the reverse binary operations. Both the following tests are examples ufuncs.

>>> print(type(numerix.array([1.0, 2.0]) * Variable([1.0, 2.0]))) 
<class 'fipy.variables.binaryOperatorVariable...binOp'>

>>> from scipy.special import gamma as Gamma 
>>> print(type(Gamma(Variable([1.0, 2.0])))) 
<class 'fipy.variables.unaryOperatorVariable...unOp'>

__bool__()

>>> print(bool(Variable(value=0)))
0
>>> print(bool(Variable(value=(0, 0, 1, 1))))
Traceback (most recent call last):
    ...
ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()

__call__()

“Evaluate” the Variable and return its value

>>> a = Variable(value=3)
>>> print(a())
3
>>> b = a + 4
>>> b
(Variable(value=array(3)) + 4)
>>> b()
7

__eq__(other)

Test if a Variable is equal to another quantity

>>> a = Variable(value=3)
>>> b = (a == 4)
>>> b
(Variable(value=array(3)) == 4)
>>> b()
0

__ge__(other)

Test if a Variable is greater than or equal to another quantity

>>> a = Variable(value=3)
>>> b = (a >= 4)
>>> b
(Variable(value=array(3)) >= 4)
>>> b()
0
>>> a.value = 4
>>> print(b())
1
>>> a.value = 5
>>> print(b())
1

__getitem__(index)

“Evaluate” the Variable and return the specified element

>>> a = Variable(value=((3., 4.), (5., 6.)), unit="m") + "4 m"
>>> print(a[1, 1])
10.0 m

It is an error to slice a Variable whose value is not sliceable

>>> Variable(value=3)[2]
Traceback (most recent call last):
      ...
IndexError: 0-d arrays can't be indexed

__getstate__()

Used internally to collect the necessary information to pickle the MeshVariable to persistent storage.

__gt__(other)

Test if a Variable is greater than another quantity

>>> a = Variable(value=3)
>>> b = (a > 4)
>>> b
(Variable(value=array(3)) > 4)
>>> print(b())
0
>>> a.value = 5
>>> print(b())
1

__hash__()

Return hash(self).

__invert__()

Returns logical “not” of the Variable

>>> a = Variable(value=True)
>>> print(~a)
False

__le__(other)

Test if a Variable is less than or equal to another quantity

>>> a = Variable(value=3)
>>> b = (a <= 4)
>>> b
(Variable(value=array(3)) <= 4)
>>> b()
1
>>> a.value = 4
>>> print(b())
1
>>> a.value = 5
>>> print(b())
0

__lt__(other)

Test if a Variable is less than another quantity

>>> a = Variable(value=3)
>>> b = (a < 4)
>>> b
(Variable(value=array(3)) < 4)
>>> b()
1
>>> a.value = 4
>>> print(b())
0
>>> print(1000000000000000000 * Variable(1) < 1.)
0
>>> print(1000 * Variable(1) < 1.)
0

Python automatically reverses the arguments when necessary

>>> 4 > Variable(value=3)
(Variable(value=array(3)) < 4)

__ne__(other)

Test if a Variable is not equal to another quantity

>>> a = Variable(value=3)
>>> b = (a != 4)
>>> b
(Variable(value=array(3)) != 4)
>>> b()
1

static __new__(cls, *args, **kwds)

__nonzero__()

>>> print(bool(Variable(value=0)))
0
>>> print(bool(Variable(value=(0, 0, 1, 1))))
Traceback (most recent call last):
    ...
ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()

__or__(other)

This test case has been added due to a weird bug that was appearing.

>>> a = Variable(value=(0, 0, 1, 1))
>>> b = Variable(value=(0, 1, 0, 1))
>>> print(numerix.equal((a == 0) | (b == 1), [True,  True, False, True]).all())
True
>>> print(a | b)
[0 1 1 1]
>>> from fipy.meshes import Grid1D
>>> mesh = Grid1D(nx=4)
>>> from fipy.variables.cellVariable import CellVariable
>>> a = CellVariable(value=(0, 0, 1, 1), mesh=mesh)
>>> b = CellVariable(value=(0, 1, 0, 1), mesh=mesh)
>>> print(numerix.allequal((a == 0) | (b == 1), [True,  True, False, True]))
True
>>> print(a | b)
[0 1 1 1]

__pow__(other)

return self**other, or self raised to power other

>>> print(Variable(1, "mol/l")**3)
1.0 mol**3/l**3
>>> print((Variable(1, "mol/l")**3).unit)
<PhysicalUnit mol**3/l**3>

__repr__()

Return repr(self).

__setstate__(dict)

Used internally to create a new Variable from pickled persistent storage.

__str__()

Return str(self).

all(axis=None)

>>> print(Variable(value=(0, 0, 1, 1)).all())
0
>>> print(Variable(value=(1, 1, 1, 1)).all())
1

allclose(other, rtol=1e-05, atol=1e-08)

>>> var = Variable((1, 1))
>>> print(var.allclose((1, 1)))
1
>>> print(var.allclose((1,)))
1

The following test is to check that the system does not run out of memory.

>>> from fipy.tools import numerix
>>> var = Variable(numerix.ones(10000))
>>> print(var.allclose(numerix.zeros(10000, 'l')))
False

any(axis=None)

>>> print(Variable(value=0).any())
0
>>> print(Variable(value=(0, 0, 1, 1)).any())
1

constrain(value, where=None)

Constrain the Variable to have a value at an index or mask location specified by where.

>>> v = Variable((0, 1, 2, 3))
>>> v.constrain(2, numerix.array((True, False, False, False)))
>>> print(v)
[2 1 2 3]
>>> v[:] = 10
>>> print(v)
[ 2 10 10 10]
>>> v.constrain(5, numerix.array((False, False, True, False)))
>>> print(v)
[ 2 10  5 10]
>>> v[:] = 6
>>> print(v)
[2 6 5 6]
>>> v.constrain(8)
>>> print(v)
[8 8 8 8]
>>> v[:] = 10
>>> print(v)
[8 8 8 8]
>>> del v.constraints[2]
>>> print(v)
[ 2 10  5 10]

>>> from fipy.variables.cellVariable import CellVariable
>>> from fipy.meshes import Grid2D
>>> m = Grid2D(nx=2, ny=2)
>>> x, y = m.cellCenters
>>> v = CellVariable(mesh=m, rank=1, value=(x, y))
>>> v.constrain(((0.,), (-1.,)), where=m.facesLeft)
>>> print(v.faceValue)
[[ 0.5  1.5  0.5  1.5  0.5  1.5  0.   1.   1.5  0.   1.   1.5]
 [ 0.5  0.5  1.   1.   1.5  1.5 -1.   0.5  0.5 -1.   1.5  1.5]]

Parameters:

• value (float or array_like) – The value of the constraint

• where (array_like of bool) – The constraint mask or index specifying the location of the constraint

property constraintMask

Test that constraintMask returns a Variable that updates itself whenever the constraints change.

>>> from fipy import *

>>> m = Grid2D(nx=2, ny=2)
>>> x, y = m.cellCenters
>>> v0 = CellVariable(mesh=m)
>>> v0.constrain(1., where=m.facesLeft)
>>> print(v0.faceValue.constraintMask)
[False False False False False False  True False False  True False False]
>>> print(v0.faceValue)
[ 0.  0.  0.  0.  0.  0.  1.  0.  0.  1.  0.  0.]
>>> v0.constrain(3., where=m.facesRight)
>>> print(v0.faceValue.constraintMask)
[False False False False False False  True False  True  True False  True]
>>> print(v0.faceValue)
[ 0.  0.  0.  0.  0.  0.  1.  0.  3.  1.  0.  3.]
>>> v1 = CellVariable(mesh=m)
>>> v1.constrain(1., where=(x < 1) & (y < 1))
>>> print(v1.constraintMask)
[ True False False False]
>>> print(v1)
[ 1.  0.  0.  0.]
>>> v1.constrain(3., where=(x > 1) & (y > 1))
>>> print(v1.constraintMask)
[ True False False  True]
>>> print(v1)
[ 1.  0.  0.  3.]

copy()

Make an duplicate of the Variable

>>> a = Variable(value=3)
>>> b = a.copy()
>>> b
Variable(value=array(3))

The duplicate will not reflect changes made to the original

>>> a.setValue(5)
>>> b
Variable(value=array(3))

Check that this works for arrays.

>>> a = Variable(value=numerix.array((0, 1, 2)))
>>> b = a.copy()
>>> b
Variable(value=array([0, 1, 2]))
>>> a[1] = 3
>>> b
Variable(value=array([0, 1, 2]))

property divergence

the divergence of self, \(\vec{u}\),

\[\nabla\cdot\vec{u} \approx \frac{\sum_f (\vec{u}\cdot\hat{n})_f A_f}{V_P}\]

Returns:

divergence – one rank lower than self

Return type:

fipy.variables.cellVariable.CellVariable

Examples

>>> from fipy.meshes import Grid2D
>>> from fipy.variables.cellVariable import CellVariable
>>> mesh = Grid2D(nx=3, ny=2)
>>> from builtins import range
>>> var = CellVariable(mesh=mesh, value=list(range(3*2)))
>>> print(var.faceGrad.divergence)
[ 4.  3.  2. -2. -3. -4.]

dot(other, opShape=None, operatorClass=None)

Return the mesh-element–by–mesh-element (cell-by-cell, face-by-face, etc.) scalar product

\[ext{self} \cdot ext{other}\]

Both self and other can be of arbitrary rank, and other does not need to be a MeshVariable.

property dtype

Returns the Numpy dtype of the underlying array.

>>> issubclass(Variable(1).dtype.type, numerix.integer)
True
>>> issubclass(Variable(1.).dtype.type, numerix.floating)
True
>>> issubclass(Variable((1, 1.)).dtype.type, numerix.floating)
True

inBaseUnits()

Return the value of the Variable with all units reduced to their base SI elements.

>>> e = Variable(value="2.7 Hartree*Nav")
>>> print(e.inBaseUnits().allclose("7088849.01085 kg*m**2/s**2/mol"))
1

inUnitsOf(*units)

Returns one or more Variable objects that express the same physical quantity in different units. The units are specified by strings containing their names. The units must be compatible with the unit of the object. If one unit is specified, the return value is a single Variable.

>>> freeze = Variable('0 degC')
>>> print(freeze.inUnitsOf('degF').allclose("32.0 degF"))
1

If several units are specified, the return value is a tuple of Variable instances with with one element per unit such that the sum of all quantities in the tuple equals the the original quantity and all the values except for the last one are integers. This is used to convert to irregular unit systems like hour/minute/second. The original object will not be changed.

>>> t = Variable(value=314159., unit='s')
>>> from builtins import zip
>>> print(numerix.allclose([e.allclose(v) for (e, v) in zip(t.inUnitsOf('d', 'h', 'min', 's'),
...                                                         ['3.0 d', '15.0 h', '15.0 min', '59.0 s'])],
...                        True))
1

property mag

The magnitude of the Variable, e.g., \(|\vec{\psi}| = \sqrt{\vec{\psi}\cdot\vec{\psi}}\).

max(axis=None)

Return the maximum along a given axis.

min(axis=None)

>>> from fipy import Grid2D, CellVariable
>>> mesh = Grid2D(nx=5, ny=5)
>>> x, y = mesh.cellCenters
>>> v = CellVariable(mesh=mesh, value=x*y)
>>> print(v.min())
0.25

rdot(other, opShape=None, operatorClass=None)

Return the mesh-element–by–mesh-element (cell-by-cell, face-by-face, etc.) scalar product

\[ext{other} \cdot ext{self}\]

Both self and other can be of arbitrary rank, and other does not need to be a MeshVariable.

release(constraint)

Remove constraint from self

>>> from fipy import *
>>> m = Grid1D(nx=3)
>>> v = CellVariable(mesh=m, value=m.cellCenters[0])
>>> c0 = Constraint(0., where=m.facesLeft)
>>> v.constrain(c0)
>>> c1 = Constraint(3., where=m.facesRight)
>>> v.faceValue.constrain(c1)
>>> print(v.faceValue)
[ 0.  1.  2.  3.]
>>> v.faceValue.release(constraint=c0)
>>> print(v.faceValue)
[ 0.5  1.   2.   3. ]
>>> v.faceValue.release(constraint=c1)
>>> print(v.faceValue)
[ 0.5  1.   2.   2.5]

setValue(value, unit=None, where=None)

Set the value of the Variable. Can take a masked array.

>>> a = Variable((1, 2, 3))
>>> a.setValue(5, where=(1, 0, 1))
>>> print(a)
[5 2 5]

>>> b = Variable((4, 5, 6))
>>> a.setValue(b, where=(1, 0, 1))
>>> print(a)
[4 2 6]
>>> print(b)
[4 5 6]
>>> a.value = 3
>>> print(a)
[3 3 3]

>>> b = numerix.array((3, 4, 5))
>>> a.value = b
>>> a[:] = 1
>>> print(b)
[3 4 5]

>>> a.setValue((4, 5, 6), where=(1, 0)) 
Traceback (most recent call last):
    ....
ValueError: shape mismatch: objects cannot be broadcast to a single shape

property shape

>>> from fipy.meshes import Grid2D
>>> from fipy.variables.cellVariable import CellVariable
>>> mesh = Grid2D(nx=2, ny=3)
>>> var = CellVariable(mesh=mesh)
>>> print(numerix.allequal(var.shape, (6,))) 
True
>>> print(numerix.allequal(var.arithmeticFaceValue.shape, (17,))) 
True
>>> print(numerix.allequal(var.grad.shape, (2, 6))) 
True
>>> print(numerix.allequal(var.faceGrad.shape, (2, 17))) 
True

Have to account for zero length arrays

>>> from fipy import Grid1D
>>> m = Grid1D(nx=0)
>>> v = CellVariable(mesh=m, elementshape=(2,))
>>> numerix.allequal((v * 1).shape, (2, 0))
True

std(axis=None, **kwargs)

Evaluate standard deviation of all the elements of a MeshVariable.

Adapted from http://mpitutorial.com/tutorials/mpi-reduce-and-allreduce/

>>> import fipy as fp
>>> mesh = fp.Grid2D(nx=2, ny=2, dx=2., dy=5.)
>>> var = fp.CellVariable(value=(1., 2., 3., 4.), mesh=mesh)
>>> print((var.std()**2).allclose(1.25))
True

property unit

Return the unit object of self.

>>> Variable(value="1 m").unit
<PhysicalUnit m>

property value

“Evaluate” the Variable and return its value (longhand)

>>> a = Variable(value=3)
>>> print(a.value)
3
>>> b = a + 4
>>> b
(Variable(value=array(3)) + 4)
>>> b.value
7

Last updated on Jun 26, 2024. Created using Sphinx 7.1.2.