Random walk

ffpack.lsg.randomWalk.randomWalkUniform(numSteps, dim=1, randomSeed=None)

Generate load sequence by a random walk.

Parameters

  • numSteps (integer) – Number of steps for generating.

  • dim (scalar, optional) – Data dimension.

  • randomSeed (integer, optional) – Random seed. If randomSeed is none or is not an integer, the random seed in global config will be used.

Returns

rst – A 2d (numSteps by dim) matrix holding the coordinates of the position at each step.

Return type

2d array

Raises

ValueError – If the numSteps is less than 1 or the dim is less than 1.

Examples

>>> from ffpack.lsg import randomWalkUniform
>>> rst = randomWalkUniform( 5 )

Autoregressive moving average

ffpack.lsg.autoregressiveMovingAverage.arNormal(numSteps, obs, phis, mu, sigma, randomSeed=None)

Generate load sequence by an autoregressive model.

The white noise is generated by the normal distribution.

Parameters

  • numSteps (integer) – Number of steps for generating.

  • obs (1d array) – Initial observed values.

  • phis (1d array) – Coefficients for the autoregressive model.

  • mu (scalar) – Mean of the white noise.

  • sigma (scalar) – Standard deviation of the white noise.

  • randomSeed (integer, optional) – Random seed. If randomSeed is none or is not an integer, the random seed in global config will be used.

Returns

rst – Generated sequence includes the observed values.

Return type

1d array

Raises

ValueError – If the numSteps is less than 1. If lengths of obs and phis are not equal.

Examples

>>> from ffpack.lsg import arNormal
>>> obs = [ 0, 1 ]
>>> phis = [ 0.5, 0.3 ]
>>> rst = arNormal( 500, obs, phis, 0, 0.5 )
ffpack.lsg.autoregressiveMovingAverage.arimaNormal(numSteps, c, phis, thetas, mu, sigma, randomSeed=None)

Generate load sequence by an autoregressive integrated moving average model.

The white noise is generated by the normal distribution.

First-order diference is used in this function.

Parameters

  • numSteps (integer) – Number of steps for generating.

  • c (scalar) – Mean of the series.

  • phis (1d array) – Coefficients for the autoregressive part.

  • thetas (1d array) – Coefficients for the white noise for the moving-average part.

  • mu (scalar) – Mean of the white noise.

  • sigma (scalar) – Standard deviation of the white noise.

  • randomSeed (integer, optional) – Random seed. If randomSeed is none or is not an integer, the random seed in global config will be used.

Returns

rst – Generated sequence with the autoregressive integrated moving average model.

Return type

1d array

Raises

ValueError – If the numSteps is less than 1. If mean of the series is not a scalar. If the phis is empty. If the thetas is empty.

Examples

>>> from ffpack.lsg import arimaNormal
>>> phis = [ 0.5, 0.3 ]
>>> thetas = [ 0.8, 0.5 ]
>>> rst = arimaNormal( 500, 0.0, phis, thetas, 0, 0.5 )
ffpack.lsg.autoregressiveMovingAverage.armaNormal(numSteps, obs, phis, thetas, mu, sigma, randomSeed=None)

Generate load sequence by an autoregressive-moving-average model.

The white noise is generated by the normal distribution.

Parameters

  • numSteps (integer) – Number of steps for generating.

  • obs (1d array) – Initial observed values, could be empty.

  • phis (1d array) – Coefficients for the autoregressive part.

  • thetas (1d array) – Coefficients for the white noise for the moving-average part.

  • mu (scalar) – Mean of the white noise.

  • sigma (scalar) – Standard deviation of the white noise.

  • randomSeed (integer, optional) – Random seed. If randomSeed is none or is not an integer, the random seed in global config will be used.

Returns

rst – Generated sequence includes the observed values.

Return type

1d array

Raises

ValueError – If the numSteps is less than 1. If the phis is empty. If the thetas is empty.

Examples

>>> from ffpack.lsg import armaNormal
>>> obs = [ 0, 1 ]
>>> phis = [ 0.5, 0.3 ]
>>> thetas = [ 0.8, 0.5 ]
>>> rst = armaNormal( 500, obs, phis, thetas, 0, 0.5 )
ffpack.lsg.autoregressiveMovingAverage.maNormal(numSteps, c, thetas, mu, sigma, randomSeed=None)

Generate load sequence by a moving-average model.

The white noise is generated by the normal distribution.

Parameters

  • numSteps (integer) – Number of steps for generating.

  • c (scalar) – Mean of the series.

  • thetas (1d array) – Coefficients for the white noise in the moving-average model.

  • mu (scalar) – Mean of the white noise.

  • sigma (scalar) – Standard deviation of the white noise.

  • randomSeed (integer, optional) – Random seed. If randomSeed is none or is not an integer, the random seed in global config will be used.

Returns

rst – Generated sequence with moving-average model.

Return type

1d array

Raises

ValueError – If the numSteps is less than 1. If mean of the series is not a scalar. If the thetas is empty.

Examples

>>> from ffpack.lsg import maNormal
>>> thetas = [ 0.8, 0.5 ]
>>> rst = maNormal( 500, 0, thetas, 0, 0.5 )

Sequence from spectrum

ffpack.lsg.sequenceFromSpectrum.spectralRepresentation(fs, time, freq, psd, freqBandwidth=None, randomSeed=None)

Generate a sequence from a given power spectrum density with spectral representation method.

Parameters

  • fs (scalar) – Sampling frequency.

  • time (scalar) – Total sampling time.

  • freq (1darray) – Frequency array for psd. The freq array should be in equally spaced increasing.

  • psd (1darray) – Power spectrum density array.

  • freqBandwidth (scalar, optional) – Frequency bandwidth used to generate the time series from psd. Default to None, every frequency in freq will be used.

  • randomSeed (integer, optional) – Random seed. If randomSeed is none or is not an integer, the random seed in global config will be used.

Returns

  • ts (1darray) – Array containing all the time data for the time series.

  • amps (1darray) – Amplitude array containing the amplitudes of the time series corresponding to ts.

Raises

ValueError – If the fs or time is not a scalar. If freq or psd is not a 1darray or has less than 3 elements. If freq and psd are in different lengths. If freq contains negative elements. If freq is not equally spaced increasing.

Examples

>>> from ffpack.lsg import spectralRepresentation
>>> fs = 100
>>> time = 10
>>> freq = [ 0, 0.1, 0.2, 0.3, 0.4, 0.5 ]
>>> psd = [ 0.01, 2, 0.05, 0.04, 0.01, 0.03 ]
>>> ts, amps = spectralRepresentation( fs, time, freq, psd, freqBandwidth=None )