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Package esys :: Package escript :: Module pdetools :: Class Defect
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Class Defect

object --+
         |
        Defect
Defines a non-linear defect F(x) of a variable x.
Instance Methods [hide private]
 
__call__(self, x)
 
__init__(self)
Initializes defect.
float
bilinearform(self, x0, x1)
Returns the inner product of x0 and x1
 
derivative(self, F0, x0, v, v_is_normalised=True)
Returns the directional derivative at x0 in the direction of v.
 
eval(self, x)
Returns the value F of a given x.
 
getDerivativeIncrementLength(self)
Returns the relative increment length used to approximate the derivative of the defect.
float
norm(self, x)
Returns the norm of argument x.
 
setDerivativeIncrementLength(self, inc=1.49011611938e-05)
Sets the relative length of the increment used to approximate the derivative of the defect.

Inherited from object: __delattr__, __format__, __getattribute__, __hash__, __new__, __reduce__, __reduce_ex__, __repr__, __setattr__, __sizeof__, __str__, __subclasshook__

Properties [hide private]

Inherited from object: __class__

Method Details [hide private]

__init__(self)
(Constructor)

 
Initializes defect.
Overrides: object.__init__

bilinearform(self, x0, x1)

 
Returns the inner product of x0 and x1
Parameters:
  • x0 - value for x0
  • x1 - value for x1
Returns: float
the inner product of x0 and x1

derivative(self, F0, x0, v, v_is_normalised=True)

 
Returns the directional derivative at x0 in the direction of v.
Parameters:
  • F0 - value of this defect at x0
  • x0 - value at which derivative is calculated
  • v - direction
  • v_is_normalised - True to indicate that v is nomalized (self.norm(v)=0)
Returns:
derivative of this defect at x0 in the direction of v

Note: by default numerical evaluation (self.eval(x0+eps*v)-F0)/eps is used but this method maybe overwritten to use exact evaluation.

eval(self, x)

 
Returns the value F of a given x.
Parameters:
  • x - value for which the defect F is evaluated
Returns:
value of the defect at x

getDerivativeIncrementLength(self)

 
Returns the relative increment length used to approximate the derivative of the defect. :return: value of the defect at x :rtype: positive float

norm(self, x)

 
Returns the norm of argument x.
Parameters:
  • x - a value
Returns: float
norm of argument x

Note: by default sqrt(self.bilinearform(x,x) is returned.

setDerivativeIncrementLength(self, inc=1.49011611938e-05)

 
Sets the relative length of the increment used to approximate the derivative of the defect. The increment is inc*norm(x)/norm(v)*v in the direction of v with x as a starting point.
Parameters:
  • inc (positive float) - relative increment length

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