# Sample¶

class Sample(*args)

Sample of real vectors.

Available constructors:

Sample(size, dim)

Sample(size, point)

Sample(other, first, last)

Parameters:
sizeint, , optional

The sample size. Default creates an empty sample with dimension 1.

dimensionint, , optional

The real vectors dimension. Default creates an empty sample with dimension 1.

pointPoint or flat (1d) array, list or tuple of floats, optional

The point that will be repeated along the sample. Default creates a sample filled with zeros (null vectors).

otherSample

The sample contains points to copy.

firstint,

The index of the first point to copy.

lastint, , optional

The index after the last point to copy.

Examples

Create a Sample

>>> import openturns as ot
>>> import numpy as np
>>> sample = ot.Sample(3, 2)
>>> print(sample)
0 : [ 0 0 ]
1 : [ 0 0 ]
2 : [ 0 0 ]
>>> sample = ot.Sample(3, [1.0, 2.0])
>>> print(sample)
0 : [ 1 2 ]
1 : [ 1 2 ]
2 : [ 1 2 ]


Create a Sample from a (2d) array, list or tuple

>>> import numpy as np
>>> sample = ot.Sample(np.array([(1.0, 2.0), (3.0, 4.0), (5.0, 6.0)]))


and back

>>> z = np.array(sample)


Eventually samples may also be generated from probability distributions or experiments

>>> random_sample = ot.Normal(2).getSample(10)
>>> experiment = ot.LHSExperiment(ot.Normal(2), 10).generate()


Translation: addition or subtraction of a (compatible) sample or a point, or a scalar which is promoted into a point of compatible dimension with equal components

>>> print(sample + sample)
0 : [  2  4 ]
1 : [  6  8 ]
2 : [ 10 12 ]
>>> print(sample - sample)
0 : [ 0 0 ]
1 : [ 0 0 ]
2 : [ 0 0 ]
>>> print(sample - sample[0])
0 : [ 0 0 ]
1 : [ 2 2 ]
2 : [ 4 4 ]
>>> print(sample - sample[0, 0])
0 : [ 0 1 ]
1 : [ 2 3 ]
2 : [ 4 5 ]


Methods

 Convert a pandas DataFrame to Sample. BuildFromPoint(point) Static method for building a sample from a sequence of float. ImportFromCSVFile(*args) Static method for building a sample from a CSV file. ImportFromTextFile(*args) Static method for building a sample from a text file. add(*args) Append a sample (in-place). argsort([isIncreasing]) Returns indices of sorted sample. Convert to pandas DataFrame. Accessor to the internal linear storage for 1D sample. Erase all values. Estimate componentwise central moments. Estimate the covariance matrix. computeEmpiricalCDF(point[, tail]) Estimate the empirical cumulative distribution function (ECDF). Estimate the Kendall coefficients matrix. Estimate the componentwise kurtosis (4th order central normalized moment). (ditch me?) Estimate the mean vector. Estimate the componentwise medians (50%-quantiles). Estimate the Pearson correlation matrix. computeQuantile(*args) Estimate the quantile of the joint distribution underlying the sample. Estimate the componentwise quantiles. Compute the range per component. Compute the raw (non-central) moment per component. Estimate the componentwise skewness (3rd order central normalized moment). Estimate the Spearman correlation matrix. Estimate the componentwise standard deviations. Estimate the componentwise variances. erase(*args) Erase point(s) at or between index(es) (in-place). exportToCSVFile(*args) Dump the sample to a CSV file. find(point) Get the position of a point in the sample. Accessor to the object's name. Accessor to the componentwise description. Accessor to the sample's dimension. Accessor to the object's id. Accessor to the underlying implementation. getMarginal(*args) Accessor to sample marginal(s) (column(s)). Accessor to the componentwise maximum values. Accessor to the componentwise minimum values. Accessor to the object's name. Accessor to the sample size. rank(*args) Compute the sample (componentwise) ranks. select(indices) Select points in a sample. setDescription(description) Accessor to the componentwise description. setName(name) Accessor to the object's name. sort(*args) Sort the sample. Sort the sample according to the given component. Sort the sample in place according to the given component. Sort the sample in place. Sort the sample and remove duplicate points. Sort the sample in place and remove duplicate points. split(index) Trunk the sample. stack(sample) Stack (horizontally) the given sample to the current one (in-place).
__init__(*args)
BuildFromDataFrame()

Convert a pandas DataFrame to Sample.

Parameters:
dfpandas DataFrame

The data to convert

Returns:
sampleSample

The converted sample

static BuildFromPoint(point)

Static method for building a sample from a sequence of float.

Parameters:
data1d array-like

Data.

Returns:
sampleSample

Sample generated from sequence

Examples

>>> import openturns as ot
>>> n = 20
>>> x = ot.Sample.BuildFromPoint(range(n))
>>> data = [2.0, 2.0, 1.0, 1.0, 2.0, 3.0, 1.0, 2.0, 2.0, 1.0]
>>> sample = ot.Sample.BuildFromPoint(data)

static ImportFromCSVFile(*args)

Static method for building a sample from a CSV file.

Parameters:
file_namestr

Path to CSV file.

separatorstr

Separating string. Default uses csv-file-separator from the ResourceMap.

Returns:
sampleSample

Sample loaded from the CSV file.

Notes

The file may or may not contain a header line (columns spanned with strings delimited with quotes). If it does contain such a header line, it will be used for setting the sample description using setDescription().

The implementation follows the RFC 4180: https://tools.ietf.org/html/rfc4180.

Examples

>>> import openturns as ot


Let’s first create a sample CSV file

>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(30)
>>> sample.exportToCSVFile('sample.csv')


And load it back

>>> loaded_sample = ot.Sample.ImportFromCSVFile('sample.csv')
>>> assert sample == loaded_sample

static ImportFromTextFile(*args)

Static method for building a sample from a text file.

Parameters:
file_namestr

Path to text file.

separatorstr

Separating string. Default uses a blank space.

skipped_linesint

Number of lines skipped. Default is 0.

numSeparatorstr

Decimal separator. Default is dot.

Returns:
sampleSample

Sample loaded from the text file.

Notes

The file may or may not contain a header line (columns spanned with strings delimited with quotes). If it does contain such a header line, it will be used for setting the sample description using setDescription(). It can also contain some comments, if a line starts with one of the characters contained in Sample-CommentsMarker from the ResourceMap.

Examples

>>> import openturns as ot


Let’s first create a sample text file

>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(30)
>>> sample.exportToCSVFile('sample.txt', ' ')


And load it back

>>> loaded_sample = ot.Sample.ImportFromTextFile('sample.txt')
>>> assert sample == loaded_sample


Append a sample (in-place).

Parameters:
point or samplesequence or 2-d sequence of float

The point(s) to append.

Examples

Append an existing sample with a single point.

>>> import openturns as ot
>>> sample = ot.Sample(3, 2)
>>> print(sample)
0 : [ 0 0 ]
1 : [ 0 0 ]
2 : [ 0 0 ]
3 : [ 1 2 ]


Append an existing sample with another sample.

>>> sample.add(ot.Sample(2, [2.0, 1.0]))
>>> print(sample)
0 : [ 0 0 ]
1 : [ 0 0 ]
2 : [ 0 0 ]
3 : [ 1 2 ]
4 : [ 2 1 ]
5 : [ 2 1 ]

argsort(isIncreasing=True)

Returns indices of sorted sample.

The algorithm sorts the points in the sample in the lexicographic order.

Returns:
indicesIndices

The indices which sorts the sample.

isIncreasingbool, optional

If True, sort in increasing order. If False, sort in decreasing order. Default is True.

Examples

>>> import openturns as ot
>>> sample = ot.Sample(
...     [[-1.0, 1.0, 0.0], [-1.0, 1.0, 1.0], [-1.0, 0.0, 1.0], [-1.0, 0.0, -1.0]]
... )
>>> print(sample)
0 : [ -1  1  0 ]
1 : [ -1  1  1 ]
2 : [ -1  0  1 ]
3 : [ -1  0 -1 ]
>>> indices = sample.argsort()
>>> print(indices)
[3,2,0,1]
>>> print(sample[indices])
[ v0 v1 v2 ]
0 : [ -1  0 -1 ]
1 : [ -1  0  1 ]
2 : [ -1  1  0 ]
3 : [ -1  1  1 ]
>>> indices = sample.argsort(False)
>>> print(indices)
[1,0,2,3]

asDataFrame()

Convert to pandas DataFrame.

Returns:
dfpandas DataFrame

The converted data

asPoint()

Accessor to the internal linear storage for 1D sample.

Returns:
valuesPoint

Flat internal representation of the sample.

Notes

Available only for 1D sample.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal().getSample(5)
>>> print(sample)
[ X0        ]
0 : [  0.608202 ]
1 : [ -1.26617  ]
2 : [ -0.438266 ]
3 : [  1.20548  ]
4 : [ -2.18139  ]
>>> print(sample.asPoint())
[0.608202,-1.26617,-0.438266,1.20548,-2.18139]

clear()

Erase all values.

computeCentralMoment(k)

Estimate componentwise central moments.

Parameters:
kint

The central moment’s order.

Returns:
mPoint

Componentwise central moment of order estimated from the sample.

Notes

The central moment of order is estimated as follows:

where is the estimator of the mean.

These estimators are the natural (possibly biased) estimators. For unbiased estimators use the other dedicated methods such as computeVariance() for the variance.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(30)
>>> print(sample.computeCentralMoment(2))
[0.915126,0.873119]

computeCovariance()

Estimate the covariance matrix.

Returns:
covarianceCovarianceMatrix

Covariance matrix estimated from the sample.

Notes

The covariance matrix is estimated as follows:

where denotes the estimate of the mean.

This is an unbiased estimator.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(30)
>>> print(sample.computeCovariance())
[[ 0.946682  0.0182104 ]
[ 0.0182104 0.903226  ]]

computeEmpiricalCDF(point, tail=False)

Estimate the empirical cumulative distribution function (ECDF).

Parameters:
xsequence of float

CDF input.

survivalbool, optional

A flag telling whether this should estimate the empirical cumulative distribution function or the empirical survival function. Default is False and estimates the CDF.

Returns:
pfloat,

Empirical CDF or SF value at point x.

Notes

The empirical cumulative distribution function (CDF) is estimated as follows:

The empirical survival function (SF) is estimated in a similar way:

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(30)
>>> print(sample.computeEmpiricalCDF(sample[0]))
0.1

computeKendallTau()

Estimate the Kendall coefficients matrix.

Returns:
tauCorrelationMatrix

Kendall coefficients matrix estimated from the sample.

Notes

This uses an external implementation provided under the Boost Software License by David Simcha based on the paper by [knight1966]. It actually switches between two implementations depending on the sample size:

• The most basic implementation performing in is used when the sample size is less than SampleImplementation-SmallKendallTau from the ResourceMap.

• The other more complex implementation performing in is used for larger samples.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(30)
>>> print(sample.computeKendallTau())
[[ 1          0.00689655 ]
[ 0.00689655 1          ]]

computeKurtosis()

Estimate the componentwise kurtosis (4th order central normalized moment).

Returns:
kurtosisPoint

Componentwise kurtosis estimated from the sample.

Notes

The componentwise kurtosis are estimated as follows:

where is the estimate of the mean.

This estimator is unbiased.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(30)
>>> print(sample.computeKurtosis())
[3.27647,2.40275]

computeLinearCorrelation()

(ditch me?)

computeMean()

Estimate the mean vector.

Returns:
meanPoint

Mean vector estimated from the sample.

Notes

The mean is estimated as follows:

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(30)
>>> print(sample.computeMean())
[-0.0512622,0.136653]

computeMedian()

Estimate the componentwise medians (50%-quantiles).

Returns:
medianPoint

Median vector estimated from the sample.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(30)
>>> print(sample.computeMedian())
[0.221141,0.108703]

computePearsonCorrelation()

Estimate the Pearson correlation matrix.

Returns:
rhoCorrelationMatrix

Pearson correlation matrix estimated from the sample.

Notes

The Pearson correlation matrix is estimated as follows:

where denotes the estimate of the covariance.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(30)
>>> print(sample.computePearsonCorrelation())
[[ 1         0.0196933 ]
[ 0.0196933 1         ]]

computeQuantile(*args)

Estimate the quantile of the joint distribution underlying the sample.

Parameters:
pfloat, , or sequence of float

Input probability level.

Returns:
quantile

Quantile of the joint distribution at probability level , estimated from the sample.

Raises:
NotImplementedYetErrorIf the dimension is greater than 1.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(1).getSample(30)
>>> print(sample.computeQuantile(.2))
[-0.947394]

computeQuantilePerComponent(*args)

Estimate the componentwise quantiles.

Parameters:
pfloat, , or sequence of float

Input probability level.

Returns:
quantile

Componentwise quantile at probability level , estimated from the sample.

Notes

The present implementation interpolates the quantile between the two adjacent empirical quantiles ( and ):

where .

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(30)
>>> print(sample.computeQuantilePerComponent(0.2))
[-0.696412,-0.767092]

computeRange()

Compute the range per component.

Returns:
rangePoint

Componentwise ranges estimated from the sample.

Notes

The statistical range is defined as the deviation between the maximal and the minimal value of the sample.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(30)
>>> print(sample.computeRange())
[4.02827,3.49949]

computeRawMoment(k)

Compute the raw (non-central) moment per component.

Parameters:
kint,

Componentwise moment’s order.

Returns:
momentsPoint

Componentwise moments estimated from the sample.

Notes

The (raw) moment of order is estimated as follows:

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(30)
>>> print(sample.computeRawMoment(2))
[0.917754,0.891793]

computeSkewness()

Estimate the componentwise skewness (3rd order central normalized moment).

Returns:
skewnessPoint

Componentwise skewness estimated from the sample.

Notes

The componentwise skewnesses are estimated as follows:

where is the estimate of the mean.

This is an unbiased estimator.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(30)
>>> print(sample.computeSkewness())
[-0.69393,0.231931]

computeSpearmanCorrelation()

Estimate the Spearman correlation matrix.

Returns:
rhoCorrelationMatrix

Spearman correlation matrix estimated from the sample.

Notes

The Spearman correlation matrix is estimated as the Pearson correlation matrix of the ranks sample (i.e. using self.rank().computePearsonCorrelation()).

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(30)
>>> print(sample.computeSpearmanCorrelation())
[[  1          -0.00556174 ]
[ -0.00556174  1          ]]

computeStandardDeviation()

Estimate the componentwise standard deviations.

Returns:
standard_deviationsPoint

Componentwise standard deviation estimated from the sample.

Notes

The componentwise standard deviations are estimated as the square root of the componentwise variances.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(30)
>>> print(sample.computeStandardDeviation())
[0.972976,0.950382]

computeVariance()

Estimate the componentwise variances.

Returns:
variancesPoint

Componentwise variances estimated from the sample.

Notes

The componentwise variances are estimated as follows:

where is the estimate of the mean.

This estimator is unbiased.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(30)
>>> print(sample.computeVariance())
[0.946682,0.903226]

erase(*args)

Erase point(s) at or between index(es) (in-place).

Parameters:
fint,

The index of the first point to erase.

lint, , optional

The index after the last point to erase. Default uses l = f + 1 and only removes sample[f].

Examples

>>> import openturns as ot
>>> sample = ot.Sample([[i] for i in range(5)])
>>> print(sample)
0 : [ 0 ]
1 : [ 1 ]
2 : [ 2 ]
3 : [ 3 ]
4 : [ 4 ]
>>> sample.erase(1, 3)
>>> print(sample)
0 : [ 0 ]
1 : [ 3 ]
2 : [ 4 ]

exportToCSVFile(*args)

Dump the sample to a CSV file.

Parameters:
file_namestr

Path to CSV file.

separatorstr

Separating string. Default uses csv-file-separator from the ResourceMap.

numSeparatorstr, default=’.’

Decimal separator.

precisionint

Numerical precision Default takes Sample-CSVPrecision entry from ResourceMap.

formatstr

Floating-point formatting, one of:

• scientific: exponent notation

• fixed: constant number of digits

• defaultfloat: variable number of digits

Default takes Sample-CSVFormat entry from ResourceMap.

Notes

This will create a header line with componentwise descriptions (obtained from getDescription()) between quotes as column names. In scientific formatting the number of significant digits is .

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(30)
>>> sample.exportToCSVFile('sample.csv', '; ')

find(point)

Get the position of a point in the sample.

Parameters:
pointsequence of float

The wanted point.

Returns:
indexint,

Returns if the point does not belong to the sample.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(30)
>>> print(sample.find(sample[10]))
10
>>> print(sample.find([0.0, 0.0]))
30

getClassName()

Accessor to the object’s name.

Returns:
class_namestr

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

getDescription()

Accessor to the componentwise description.

Returns:
descriptionDescription

Description of the sample’s components.

getDimension()

Accessor to the sample’s dimension.

Returns:
nint

The number of components of the points in the sample.

getId()

Accessor to the object’s id.

Returns:
idint

Internal unique identifier.

getImplementation()

Accessor to the underlying implementation.

Returns:
implImplementation

A copy of the underlying implementation object.

getMarginal(*args)

Accessor to sample marginal(s) (column(s)).

Parameters:
indicesint, sequence of int, or sequence of str

The identifiers of the wanted marginal(s). When the description contains duplicate labels, the first marginal is picked up.

Returns:
sampleSample

A subsample of the present sample with the requested marginal(s).

Notes

The Sample also implements slicing in its __getitem__ method.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(10).getSample(3)
>>> print(sample.getMarginal([1, 4]))
[ X1        X4        ]
0 : [ -1.26617  -2.18139  ]
1 : [  0.261018 -1.31178  ]
2 : [  0.445785  0.473617 ]

getMax()

Accessor to the componentwise maximum values.

Returns:
maximum_valuesPoint

Componentwise maximum values.

getMin()

Accessor to the componentwise minimum values.

Returns:
minimum_valuesPoint

Componentwise minimum values.

getName()

Accessor to the object’s name.

Returns:
namestr

The name of the object.

getSize()

Accessor to the sample size.

Returns:
mint

The number points in the sample.

rank(*args)

Compute the sample (componentwise) ranks.

Parameters:
marginal_indexint, , optional

The component whose ranks are wanted. Default computes the ranks of all the components.

Returns:
ranksSample

The requested ranks.

Notes

The ranks of a 1d sample is a list of indices that sorts the points in the ascending order. Ties (equal points) are averaged.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(3)
>>> print(sample)
[ X0        X1        ]
0 : [  0.608202 -1.26617  ]
1 : [ -0.438266  1.20548  ]
2 : [ -2.18139   0.350042 ]
>>> print(sample.rank())
[ X0 X1 ]
0 : [ 2  0  ]
1 : [ 1  2  ]
2 : [ 0  1  ]

select(indices)

Select points in a sample.

It selects the points at given locations and returns them as a new sample.

Parameters:
indicessequence of int,

The selected indices.

Returns:
selected_sampleSample

The selected points as a sample.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(3)
>>> print(sample)
[ X0        X1        ]
0 : [  0.608202 -1.26617  ]
1 : [ -0.438266  1.20548  ]
2 : [ -2.18139   0.350042 ]
>>> selected_sample = sample.select([1, 0, 1])
>>> print(selected_sample)
[ X0        X1        ]
0 : [ -0.438266  1.20548  ]
1 : [  0.608202 -1.26617  ]
2 : [ -0.438266  1.20548  ]

setDescription(description)

Accessor to the componentwise description.

Parameters:
descriptionsequence of str

Description of the sample’s components.

setName(name)

Accessor to the object’s name.

Parameters:
namestr

The name of the object.

sort(*args)

Sort the sample.

The ordering is based on the comparison operator of the Point. Hence, the sort method orders the points in the sample according to lexicographic order.

Parameters:
marginal_indexint, , optional

The index of the component to sort. Default sorts the whole sample, i.e. the returned sorted sample has the same dimension as the input sample. If marginal_index is provided, then the returned sorted sample has dimension 1: the corresponding marginal sample is sorted and returned.

Returns:
sorted_sampleSample

The requested sorted sample.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(3)
>>> print(sample)
[ X0        X1        ]
0 : [  0.608202 -1.26617  ]
1 : [ -0.438266  1.20548  ]
2 : [ -2.18139   0.350042 ]
>>> print(sample.sort())
[ X0        X1        ]
0 : [ -2.18139   0.350042 ]
1 : [ -0.438266  1.20548  ]
2 : [  0.608202 -1.26617  ]
>>> print(sample.sort(1))
0 : [ -1.26617  ]
1 : [  0.350042 ]
2 : [  1.20548  ]


In the following sample, the first component of all points is equal to -1, which creates a tie where the other components must be used to make a difference in the comparison. The algorithm sorts the points taking into account all the components in the points. This shows that the algorithm uses lexicographic ordering, since using only the first component would leave the sample unchanged.

>>> import openturns as ot
>>> sample = ot.Sample(
...     [[-1.0, 1.0, 1.0], [-1.0, 1.0, 0.0], [-1.0, 0.0, 1.0], [-1.0, 0.0, -1.0]]
... )
>>> print(sample)
0 : [ -1  1  1 ]
1 : [ -1  1  0 ]
2 : [ -1  0  1 ]
3 : [ -1  0 -1 ]
>>> print(sample.sort())
0 : [ -1  0 -1 ]
1 : [ -1  0  1 ]
2 : [ -1  1  0 ]
3 : [ -1  1  1 ]

sortAccordingToAComponent(index)

Sort the sample according to the given component.

Parameters:
marginal_indexint,

The component to use for sorting the sample.

Returns:
sorted_sampleSample

The sample sorted according to the given component.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(3)
>>> print(sample)
[ X0        X1        ]
0 : [  0.608202 -1.26617  ]
1 : [ -0.438266  1.20548  ]
2 : [ -2.18139   0.350042 ]
>>> print(sample.sortAccordingToAComponent(0))
[ X0        X1        ]
0 : [ -2.18139   0.350042 ]
1 : [ -0.438266  1.20548  ]
2 : [  0.608202 -1.26617  ]

sortAccordingToAComponentInPlace(index)

Sort the sample in place according to the given component.

Parameters:
marginal_indexint,

The component to use for sorting the sample.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(3)
>>> print(sample)
[ X0        X1        ]
0 : [  0.608202 -1.26617  ]
1 : [ -0.438266  1.20548  ]
2 : [ -2.18139   0.350042 ]
>>> sample.sortAccordingToAComponentInPlace(0)
>>> print(sample)
[ X0        X1        ]
0 : [ -2.18139   0.350042 ]
1 : [ -0.438266  1.20548  ]
2 : [  0.608202 -1.26617  ]

sortInPlace()

Sort the sample in place.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(3)
>>> print(sample)
[ X0        X1        ]
0 : [  0.608202 -1.26617  ]
1 : [ -0.438266  1.20548  ]
2 : [ -2.18139   0.350042 ]
>>> sample.sortInPlace()
>>> print(sample)
[ X0        X1        ]
0 : [ -2.18139   0.350042 ]
1 : [ -0.438266  1.20548  ]
2 : [  0.608202 -1.26617  ]

sortUnique()

Sort the sample and remove duplicate points.

Returns:
unique_sampleSample

The requested sorted sample with duplicate points removed.

Examples

>>> import openturns as ot
>>> sample = ot.Sample([[3, 0, 3], [1, 1, 0], [0, 2, 2], [1, 1, 0]])
>>> print(sample)
0 : [ 3 0 3 ]
1 : [ 1 1 0 ]
2 : [ 0 2 2 ]
3 : [ 1 1 0 ]
>>> print(sample.sortUnique())
0 : [ 0 2 2 ]
1 : [ 1 1 0 ]
2 : [ 3 0 3 ]

sortUniqueInPlace()

Sort the sample in place and remove duplicate points.

Examples

>>> import openturns as ot
>>> sample = ot.Sample([[3, 0, 3], [1, 1, 0], [0, 2, 2], [1, 1, 0]])
>>> print(sample)
0 : [ 3 0 3 ]
1 : [ 1 1 0 ]
2 : [ 0 2 2 ]
3 : [ 1 1 0 ]
>>> sample.sortUniqueInPlace()
>>> print(sample)
0 : [ 0 2 2 ]
1 : [ 1 1 0 ]
2 : [ 3 0 3 ]

split(index)

Trunk the sample.

It splits the sample before the index passed as argument and returns the remainder as new sample.

Parameters:
indexint,

The truncation index.

Returns:
remainder_sampleSample

The remainder sample (everything that comes after the truncation index).

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(3)
>>> print(sample)
[ X0        X1        ]
0 : [  0.608202 -1.26617  ]
1 : [ -0.438266  1.20548  ]
2 : [ -2.18139   0.350042 ]
>>> remainder_sample = sample.split(1)
>>> print(sample)
[ X0        X1        ]
0 : [  0.608202 -1.26617  ]
>>> print(remainder_sample)
[ X0        X1        ]
0 : [ -0.438266  1.20548  ]
1 : [ -2.18139   0.350042 ]

stack(sample)

Stack (horizontally) the given sample to the current one (in-place).

Parameters:
sampleSample

Sample to stack with compatible size.

Examples

>>> import openturns as ot
>>> ot.RandomGenerator.SetSeed(0)
>>> sample = ot.Normal(2).getSample(3)
>>> print(sample)
[ X0        X1        ]
0 : [  0.608202 -1.26617  ]
1 : [ -0.438266  1.20548  ]
2 : [ -2.18139   0.350042 ]
>>> another_sample = ot.Normal(2).getSample(3)
>>> print(another_sample)
[ X0        X1        ]
0 : [ -0.355007  1.43725  ]
1 : [  0.810668  0.793156 ]
2 : [ -0.470526  0.261018 ]
>>> sample.stack(another_sample)
>>> print(sample)
[ X0        X1        X0        X1        ]
0 : [  0.608202 -1.26617  -0.355007  1.43725  ]
1 : [ -0.438266  1.20548   0.810668  0.793156 ]
2 : [ -2.18139   0.350042 -0.470526  0.261018 ]


## Examples using the class¶

Link Pandas and OpenTURNS

Link Pandas and OpenTURNS

Randomize the lines of a Sample

Randomize the lines of a Sample

Import / export a sample via a CSV file

Import / export a sample via a CSV file

Estimate moments from sample

Estimate moments from sample

Sample manipulation

Sample manipulation

Sort a sample

Sort a sample

A quick start guide to the Point and Sample classes

A quick start guide to the Point and Sample classes

Estimate Wilks and empirical quantile

Estimate Wilks and empirical quantile

Build and validate a linear model

Build and validate a linear model

Estimate correlation coefficients

Estimate correlation coefficients

Draw an histogram

Draw an histogram

Draw the empirical CDF

Draw the empirical CDF

Compare unconditional and conditional histograms

Compare unconditional and conditional histograms

Compute SRC indices confidence intervals

Compute SRC indices confidence intervals

Draw a survival function

Draw a survival function

Fit a distribution by maximum likelihood

Fit a distribution by maximum likelihood

Fit a parametric distribution

Fit a parametric distribution

Model a singular multivariate distribution

Model a singular multivariate distribution

Get the asymptotic distribution of the estimators

Get the asymptotic distribution of the estimators

Estimate a GEV on the Venice sea-levels data

Estimate a GEV on the Venice sea-levels data

Bandwidth sensitivity in kernel smoothing

Bandwidth sensitivity in kernel smoothing

Fit an extreme value distribution

Fit an extreme value distribution

Estimate a conditional quantile

Estimate a conditional quantile

Estimate a multivariate distribution

Estimate a multivariate distribution

Fit a non parametric distribution

Fit a non parametric distribution

Estimate a GEV on the Port Pirie sea-levels data

Estimate a GEV on the Port Pirie sea-levels data

Estimate a GEV on the Fremantle sea-levels data

Estimate a GEV on the Fremantle sea-levels data

Estimate a GEV on race times data

Estimate a GEV on race times data

Test a discrete distribution

Test a discrete distribution

Draw the QQ-Plot

Draw the QQ-Plot

Use the Kolmogorov/Lilliefors test

Use the Kolmogorov/Lilliefors test

Test identical distributions

Test identical distributions

Select fitted distributions

Select fitted distributions

Test Normality

Test Normality

Test independence

Test independence

Test the copula

Test the copula

Kolmogorov-Smirnov : understand the statistics

Kolmogorov-Smirnov : understand the statistics

Kolmogorov-Smirnov : understand the p-value

Kolmogorov-Smirnov : understand the p-value

Kolmogorov-Smirnov : get the statistics distribution

Kolmogorov-Smirnov : get the statistics distribution

Fit a parametric copula

Fit a parametric copula

Fit a non parametric copula

Fit a non parametric copula

Estimate tail dependence coefficients on the wave-surge data

Estimate tail dependence coefficients on the wave-surge data

Estimate tail dependence coefficients on the wind data

Estimate tail dependence coefficients on the wind data

Estimate a spectral density function

Estimate a spectral density function

Estimate a stationary covariance function

Estimate a stationary covariance function

Visualize pairs

Visualize pairs

Visualize clouds

Visualize clouds

Visualize sensitivity

Visualize sensitivity

Create a Bayes distribution

Create a Bayes distribution

Create and draw scalar distributions

Create and draw scalar distributions

Truncate a distribution

Truncate a distribution

Create a random mixture

Create a random mixture

Create and draw multivariate distributions

Create and draw multivariate distributions

Generate random variates by inverting the CDF

Generate random variates by inverting the CDF

Quick start guide to distributions

Quick start guide to distributions

Draw minimum volume level sets

Draw minimum volume level sets

Export a field to VTK

Export a field to VTK

Manipulate a time series

Manipulate a time series

Create a stationary covariance model

Create a stationary covariance model

Create a spectral model

Create a spectral model

Draw a field

Draw a field

Create and manipulate an ARMA process

Create and manipulate an ARMA process

Trend computation

Trend computation

Create a mesh

Create a mesh

Create a linear least squares model

Create a linear least squares model

Create a general linear model metamodel

Create a general linear model metamodel

Create a linear model

Create a linear model

Mixture of experts

Mixture of experts

Perform stepwise regression

Perform stepwise regression

Over-fitting and model selection

Over-fitting and model selection

Apply a transform or inverse transform on your polynomial chaos

Apply a transform or inverse transform on your polynomial chaos

Fit a distribution from an input sample

Fit a distribution from an input sample

Polynomial chaos exploitation

Polynomial chaos exploitation

Polynomial chaos over database

Polynomial chaos over database

Compute grouped indices for the Ishigami function

Compute grouped indices for the Ishigami function

Validate a polynomial chaos

Validate a polynomial chaos

Create a polynomial chaos metamodel by integration on the cantilever beam

Create a polynomial chaos metamodel by integration on the cantilever beam

Advanced polynomial chaos construction

Advanced polynomial chaos construction

Create a polynomial chaos metamodel

Create a polynomial chaos metamodel

Create a polynomial chaos for the Ishigami function: a quick start guide to polynomial chaos

Create a polynomial chaos for the Ishigami function: a quick start guide to polynomial chaos

Plot enumeration rules

Plot enumeration rules

Polynomial chaos expansion cross-validation

Polynomial chaos expansion cross-validation

Polynomial chaos is sensitive to the degree

Polynomial chaos is sensitive to the degree

Create a sparse chaos by integration

Create a sparse chaos by integration

Compute Sobol’ indices confidence intervals

Compute Sobol' indices confidence intervals

Kriging: propagate uncertainties

Kriging: propagate uncertainties

Kriging : multiple input dimensions

Kriging : multiple input dimensions

Kriging : draw the likelihood

Kriging : draw the likelihood

Kriging : cantilever beam model

Kriging : cantilever beam model

Configuring an arbitrary trend in Kriging

Configuring an arbitrary trend in Kriging

Kriging the cantilever beam model using HMAT

Kriging the cantilever beam model using HMAT

Example of multi output Kriging on the fire satellite model

Example of multi output Kriging on the fire satellite model

Kriging : generate trajectories from a metamodel

Kriging : generate trajectories from a metamodel

Choose the trend basis of a kriging metamodel

Choose the trend basis of a kriging metamodel

Kriging with an isotropic covariance function

Kriging with an isotropic covariance function

Kriging: metamodel of the Branin-Hoo function

Kriging: metamodel of the Branin-Hoo function

Kriging : quick-start

Kriging : quick-start

Sequentially adding new points to a kriging

Sequentially adding new points to a kriging

Kriging :configure the optimization solver

Kriging :configure the optimization solver

Kriging : choose a trend vector space

Kriging : choose a trend vector space

Viscous free fall: metamodel of a field function

Viscous free fall: metamodel of a field function

Metamodel of a field function

Metamodel of a field function

Analyse the central tendency of a cantilever beam

Analyse the central tendency of a cantilever beam

Create a threshold event

Create a threshold event

Estimate a probability with Monte-Carlo on axial stressed beam: a quick start guide to reliability

Estimate a probability with Monte-Carlo on axial stressed beam: a quick start guide to reliability

Exploitation of simulation algorithm results

Exploitation of simulation algorithm results

Use the FORM algorithm in case of several design points

Use the FORM algorithm in case of several design points

Non parametric Adaptive Importance Sampling (NAIS)

Non parametric Adaptive Importance Sampling (NAIS)

Subset Sampling

Subset Sampling

Create a domain event

Create a domain event

Test the design point with the Strong Maximum Test

Test the design point with the Strong Maximum Test

Time variant system reliability problem

Time variant system reliability problem

An illustrated example of a FORM probability estimate

An illustrated example of a FORM probability estimate

Cross Entropy Importance Sampling

Cross Entropy Importance Sampling

Estimate Sobol indices on a field to point function

Estimate Sobol indices on a field to point function

Parallel coordinates graph as sensitivity tool

Parallel coordinates graph as sensitivity tool

Estimate Sobol’ indices for a function with multivariate output

Estimate Sobol' indices for a function with multivariate output

Sobol’ sensitivity indices from chaos

Sobol' sensitivity indices from chaos

Use the ANCOVA indices

Use the ANCOVA indices

Estimate Sobol’ indices for the Ishigami function by a sampling method: a quick start guide to sensitivity analysis

Estimate Sobol' indices for the Ishigami function by a sampling method: a quick start guide to sensitivity analysis

The HSIC sensitivity indices: the Ishigami model

The HSIC sensitivity indices: the Ishigami model

Example of sensitivity analyses on the wing weight model

Example of sensitivity analyses on the wing weight model

Create a composite design of experiments

Create a composite design of experiments

Create a Monte Carlo design of experiments

Create a Monte Carlo design of experiments

Probabilistic design of experiments

Probabilistic design of experiments

Create a Gauss product design

Create a Gauss product design

Create a random design of experiments

Create a random design of experiments

Create mixed deterministic and probabilistic designs of experiments

Create mixed deterministic and probabilistic designs of experiments

Create a design of experiments with discrete and continuous variables

Create a design of experiments with discrete and continuous variables

The PlotDesign method

The PlotDesign method

Deterministic design of experiments

Deterministic design of experiments

Create a deterministic design of experiments

Create a deterministic design of experiments

Various design of experiments in OpenTURNS

Various design of experiments in OpenTURNS

Generate low discrepancy sequences

Generate low discrepancy sequences

Optimize an LHS design of experiments

Optimize an LHS design of experiments

Plot the Smolyak quadrature

Plot the Smolyak quadrature

Use the Smolyak quadrature

Use the Smolyak quadrature

Defining Python and symbolic functions: a quick start introduction to functions

Defining Python and symbolic functions: a quick start introduction to functions

Value function

Value function

Vertex value function

Vertex value function

Define a function with a field output: the viscous free fall example

Define a function with a field output: the viscous free fall example

Define a connection function with a field output

Define a connection function with a field output

Logistic growth model

Logistic growth model

Function manipulation

Function manipulation

Generate flooding model observations

Generate flooding model observations

Calibrate a parametric model: a quick-start guide to calibration

Calibrate a parametric model: a quick-start guide to calibration

Generate observations of the Chaboche mechanical model

Generate observations of the Chaboche mechanical model

Calibration without observed inputs

Calibration without observed inputs

Calibration of the logistic model

Calibration of the logistic model

Calibration of the deflection of a tube

Calibration of the deflection of a tube

Calibration of the flooding model

Calibration of the flooding model

Calibration of the Chaboche mechanical model

Calibration of the Chaboche mechanical model

Gibbs sampling of the posterior distribution

Gibbs sampling of the posterior distribution

Bayesian calibration of a computer code

Bayesian calibration of a computer code

Sampling from an unnormalized probability density

Sampling from an unnormalized probability density

Bayesian calibration of the flooding model

Bayesian calibration of the flooding model

Posterior sampling using a PythonDistribution

Posterior sampling using a PythonDistribution

Customize your Metropolis-Hastings algorithm

Customize your Metropolis-Hastings algorithm

Linear Regression with interval-censored observations

Linear Regression with interval-censored observations

Iterated Functions System

Iterated Functions System

Compute leave-one-out error of a polynomial chaos expansion

Compute leave-one-out error of a polynomial chaos expansion

Compute confidence intervals of a regression model from data

Compute confidence intervals of a regression model from data

Compute confidence intervals of a univariate noisy function

Compute confidence intervals of a univariate noisy function

Mix/max search and sensitivity from design

Mix/max search and sensitivity from design

Quick start guide to optimization

Quick start guide to optimization

Multi-objective optimization using Pagmo

Multi-objective optimization using Pagmo

Optimization of the Rastrigin test function

Optimization of the Rastrigin test function

EfficientGlobalOptimization examples

EfficientGlobalOptimization examples

Estimate moments iteratively

Estimate moments iteratively

Estimate extrema iteratively

Estimate extrema iteratively

Estimate threshold exceedance iteratively

Estimate threshold exceedance iteratively

How to fill an area

How to fill an area

Plot the log-likelihood contours of a distribution

Plot the log-likelihood contours of a distribution

A quick start guide to graphs

A quick start guide to graphs