HaselgroveSequence

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../../_images/openturns-HaselgroveSequence-1.png
class HaselgroveSequence(*args)

Haselgrove sequence.

Available constructors:

HaselgroveSequence(dimension=1)

HaselgroveSequence(base)

Parameters
dimensionpositive int

Dimension of the points.

basesequence of positive float

Sequence of positive real values linearly independent over the integer ring, i.e. no linear combination with integer coefficients of these values can be zero excepted if all the coefficients are zero. The dimension of the sequence is given by the dimension of the base.

Examples

>>> import openturns as ot
>>> sequence = ot.HaselgroveSequence(2)
>>> print(sequence.generate(5))
0 : [ 0.414214  0.732051  ]
1 : [ 0.828427  0.464102  ]
2 : [ 0.242641  0.196152  ]
3 : [ 0.656854  0.928203  ]
4 : [ 0.0710678 0.660254  ]

Methods

ComputeStarDiscrepancy(sample)

Compute the star discrepancy of a sample uniformly distributed over [0, 1).

generate(*args)

Generate a sample of pseudo-random vectors of numbers uniformly distributed over [0, 1).

getClassName()

Accessor to the object's name.

getDimension()

Accessor to the dimension of the points of the low discrepancy sequence.

getId()

Accessor to the object's id.

getName()

Accessor to the object's name.

getScramblingState()

Accessor to the linear congruential generator (LCG) used to scramble the sequences.

getShadowedId()

Accessor to the object's shadowed id.

getVisibility()

Accessor to the object's visibility state.

hasName()

Test if the object is named.

hasVisibleName()

Test if the object has a distinguishable name.

initialize(dimension)

Initialize the sequence.

setName(name)

Accessor to the object's name.

setScramblingState(state)

Accessor to the linear congruential generator (LCG) used to scramble the sequences.

setShadowedId(id)

Accessor to the object's shadowed id.

setVisibility(visible)

Accessor to the object's visibility state.
__init__(*args)
static ComputeStarDiscrepancy(sample)

Compute the star discrepancy of a sample uniformly distributed over [0, 1).

Parameters
sample2-d sequence of float
Returns
starDiscrepancyfloat

Star discrepancy of a sample uniformly distributed over [0, 1).

Examples

>>> import openturns as ot
>>> # Create a sequence of 3 points of 2 dimensions
>>> sequence = ot.LowDiscrepancySequence(ot.SobolSequence(2))
>>> sample = sequence.generate(16)
>>> print(sequence.computeStarDiscrepancy(sample))
0.12890625
>>> sample = sequence.generate(64)
>>> print(sequence.computeStarDiscrepancy(sample))
0.0537109375
generate(*args)

Generate a sample of pseudo-random vectors of numbers uniformly distributed over [0, 1).

Parameters
sizeint

Number of points to be generated. Default is 1.

Returns
sampleSample

Sample of pseudo-random vectors of numbers uniformly distributed over [0, 1).

Examples

>>> import openturns as ot
>>> # Create a sequence of 3 points of 2 dimensions
>>> sequence = ot.LowDiscrepancySequence(ot.SobolSequence(2))
>>> print(sequence.generate(3))
0 : [ 0.5  0.5  ]
1 : [ 0.75 0.25 ]
2 : [ 0.25 0.75 ]
getClassName()

Accessor to the object’s name.

Returns
class_namestr

The object class name (object.__class__.__name__).

getDimension()

Accessor to the dimension of the points of the low discrepancy sequence.

Returns
dimensionint

Dimension of the points of the low discrepancy sequence.

getId()

Accessor to the object’s id.

Returns
idint

Internal unique identifier.

getName()

Accessor to the object’s name.

Returns
namestr

The name of the object.

getScramblingState()

Accessor to the linear congruential generator (LCG) used to scramble the sequences.

Returns
stateint

The state of the LCG, defined by the recursion x_{n+1}=(2862933555777941757 * x_n + 3037000493)\mbox{ mod }2^{64}.

getShadowedId()

Accessor to the object’s shadowed id.

Returns
idint

Internal unique identifier.

getVisibility()

Accessor to the object’s visibility state.

Returns
visiblebool

Visibility flag.

hasName()

Test if the object is named.

Returns
hasNamebool

True if the name is not empty.

hasVisibleName()

Test if the object has a distinguishable name.

Returns
hasVisibleNamebool

True if the name is not empty and not the default one.

initialize(dimension)

Initialize the sequence.

Parameters
dimensionint

Dimension of the points of the low discrepancy sequence.

Examples

>>> import openturns as ot
>>> # Create a sequence of 3 points of 2 dimensions
>>> sequence = ot.LowDiscrepancySequence(ot.SobolSequence(2))
>>> print(sequence.generate(3))
0 : [ 0.5  0.5  ]
1 : [ 0.75 0.25 ]
2 : [ 0.25 0.75 ]
>>> print(sequence.generate(3))
0 : [ 0.375 0.375 ]
1 : [ 0.875 0.875 ]
2 : [ 0.625 0.125 ]
>>> sequence.initialize(2)
>>> print(sequence.generate(3))
0 : [ 0.5  0.5  ]
1 : [ 0.75 0.25 ]
2 : [ 0.25 0.75 ]
setName(name)

Accessor to the object’s name.

Parameters
namestr

The name of the object.

setScramblingState(state)

Accessor to the linear congruential generator (LCG) used to scramble the sequences.

Parameters
stateint

The state of the LCG, defined by the recursion x_{n+1}=2862933555777941757 * x_n + 3037000493\mbox{ mod }2^{64}.

setShadowedId(id)

Accessor to the object’s shadowed id.

Parameters
idint

Internal unique identifier.

setVisibility(visible)

Accessor to the object’s visibility state.

Parameters
visiblebool

Visibility flag.