Pyleoclim Utilities API (pyleoclim.utils)

Utilities upon which Pyleoclim depends for higher-level functionalities accessible to users.

Pyleoclim makes extensive use of functions from numpy, Pandas, Scipy, Matplotlib, Statsmodels, and scikit-learn. Please note that some default parameter values for these functions have been changed to values more appropriate for paleoclimate datasets.

Causality

Utilities for Liang and Granger causality analysis

pyleoclim.utils.causality.granger_causality(y1, y2, maxlag=1, addconst=True, verbose=True)[source]

Granger causality tests

Four tests for the Granger non-causality of 2 time series.

All four tests give similar results. params_ftest and ssr_ftest are equivalent based on F test which is identical to lmtest:grangertest in R.

Wrapper for the functions described in statsmodels (https://www.statsmodels.org/stable/generated/statsmodels.tsa.stattools.grangercausalitytests.html)

Parameters:

y1 (array) – vectors of (real) numbers with identical length, no NaNs allowed
y2 (array) – vectors of (real) numbers with identical length, no NaNs allowed
maxlag (int or int iterable, optional) – If an integer, computes the test for all lags up to maxlag. If an iterable, computes the tests only for the lags in maxlag.
addconst (bool, optional) – Include a constant in the model.
verbose (bool, optional) – Print results

Returns:

All test results, dictionary keys are the number of lags. For each lag the values are a tuple, with the first element a dictionary with test statistic, pvalues, degrees of freedom, the second element are the OLS estimation results for the restricted model, the unrestricted model and the restriction (contrast) matrix for the parameter f_test.

Return type:

dict

Notes

The null hypothesis for Granger causality tests is that y2, does NOT Granger cause y1. Granger causality means that past values of y2 have a statistically significant effect on the current value of y1, taking past values of y1 into account as regressors. We reject the null hypothesis that y2 does not Granger cause y1 if the p-values are below a desired threshold (e.g. 0.05).

The null hypothesis for all four test is that the coefficients corresponding to past values of the second time series are zero.

‘params_ftest’, ‘ssr_ftest’ are based on the F distribution

‘ssr_chi2test’, ‘lrtest’ are based on the chi-square distribution

See also

pyleoclim.utils.causality.liang_causality: information flow estimated using the Liang algorithm
pyleoclim.utils.causality.signif_isopersist: significance test with AR(1) with same persistence
pyleoclim.utils.causality.signif_isospec: significance test with surrogates with randomized phases

References

Granger, C. W. J. (1969). Investigating causal relations by econometric models and cross-spectral methods. Econometrica, 37(3), 424-438.

Granger, C. W. J. (1980). Testing for causality: A personal viewpoont. Journal of Economic Dynamics and Control, 2, 329-352.

Granger, C. W. J. (1988). Some recent development in a concept of causality. Journal of Econometrics, 39(1-2), 199-211.

pyleoclim.utils.causality.liang(y1, y2, npt=1)[source]

Estimate the Liang information transfer from series y2 to series y1

Parameters:

y1 (array) – Vectors of (real) numbers with identical length, no NaNs allowed
y2 (array) – Vectors of (real) numbers with identical length, no NaNs allowed
npt (int >=1) – Time advance in performing Euler forward differencing, e.g., 1, 2. Unless the series are generated with a highly chaotic deterministic system, npt=1 should be used

Returns:

res –

A dictionary of results including:

T21float: information flow from y2 to y1 (Note: not y1 -> y2!)
tau21float: the standardized information flow from y2 to y1
Zfloat: the total information flow from y2 to y1
dH1_starfloat: dH*/dt (Liang, 2016)

dH1_noise : float

Return type:

dict

See also

pyleoclim.utils.causality.liang_causality: information flow estimated using the Liang algorithm
pyleoclim.utils.causality.granger_causality: information flow estimated using the Granger algorithm
pyleoclim.utils.causality.signif_isopersist: significance test with AR(1) with same persistence
pyleoclim.utils.causality.signif_isospec: significance test with surrogates with randomized phases

References

Liang, X.S. (2013) The Liang-Kleeman Information Flow: Theory and: Applications. Entropy, 15, 327-360, doi:10.3390/e15010327
Liang, X.S. (2014) Unraveling the cause-effect relation between timeseries.: Physical review, E 90, 052150
Liang, X.S. (2015) Normalizing the causality between time series.: Physical review, E 92, 022126
Liang, X.S. (2016) Information flow and causality as rigorous notions ab initio.: Physical review, E 94, 052201

pyleoclim.utils.causality.liang_causality(y1, y2, npt=1, signif_test='isospec', nsim=1000, qs=[0.005, 0.025, 0.05, 0.95, 0.975, 0.995])[source]

Liang-Kleeman information flow

Estimate the Liang information transfer from series y2 to series y1 with significance estimates using either an AR(1) tests with series with the same persistence or surrogates with randomized phases.

Parameters:

y1 (array) – vectors of (real) numbers with identical length, no NaNs allowed
y2 (array) – vectors of (real) numbers with identical length, no NaNs allowed
npt (int >=1) – time advance in performing Euler forward differencing, e.g., 1, 2. Unless the series are generated with a highly chaotic deterministic system, npt=1 should be used
signif_test (str; {'isopersist', 'isospec'}) – the method for significance test see signif_isospec and signif_isopersist for details.
nsim (int) – the number of AR(1) surrogates for significance test
qs (list) – the quantiles for significance test

Returns:

res –

A dictionary of results including:

T21float: information flow from y2 to y1 (Note: not y1 -> y2!)
tau21float: the standardized information flow from y2 to y1
Zfloat: the total information flow from y2 to y1
dH1_starfloat: dH*/dt (Liang, 2016)

dH1_noise : float signif_qs :

the quantiles for significance test

T21_noiselist: the quantiles of the information flow from noise2 to noise1 for significance testing
tau21_noiselist: the quantiles of the standardized information flow from noise2 to noise1 for significance testing

Return type:

dict

See also

pyleoclim.utils.causality.liang: information flow estimated using the Liang algorithm
pyleoclim.utils.causality.granger_causality: information flow estimated using the Granger algorithm
pyleoclim.utils.causality.signif_isopersist: significance test with AR(1) with same persistence
pyleoclim.utils.causality.causality.signif_isospec: significance test with surrogates with randomized phases

References

Liang, X.S. (2013) The Liang-Kleeman Information Flow: Theory and Applications. Entropy, 15, 327-360, doi:10.3390/e15010327

Liang, X.S. (2014) Unraveling the cause-effect relation between timeseries. Physical review, E 90, 052150

Liang, X.S. (2015) Normalizing the causality between time series. Physical review, E 92, 022126

Liang, X.S. (2016) Information flow and causality as rigorous notions ab initio. Physical review, E 94, 052201

pyleoclim.utils.causality.signif_isopersist(y1, y2, method, nsim=1000, qs=[0.005, 0.025, 0.05, 0.95, 0.975, 0.995], **kwargs)[source]

significance test with AR(1) with same persistence

Parameters:

y1 (array) – vectors of (real) numbers with identical length, no NaNs allowed
y2 (array) – vectors of (real) numbers with identical length, no NaNs allowed
method (str; {'liang'}) – estimates for the Liang method
nsim (int) – the number of AR(1) surrogates for significance test
qs (list) – the quantiles for significance test

Returns:

res_dict –

A dictionary with the following information:

T21_noise_qslist: the quantiles of the information flow from noise2 to noise1 for significance testing
tau21_noise_qslist: the quantiles of the standardized information flow from noise2 to noise1 for significance testing

Return type:

dict

See also

pyleoclim.utils.causality.liang_causality: information flow estimated using the Liang algorithm
pyleoclim.utils.causality.granger_causality: information flow estimated using the Granger algorithm
pyleoclim.utils.causality.signif_isospec: significance test with surrogates with randomized phases

pyleoclim.utils.causality.signif_isospec(y1, y2, method, nsim=1000, qs=[0.005, 0.025, 0.05, 0.95, 0.975, 0.995], **kwargs)[source]

significance test with surrogates with randomized phases

Parameters:

y1 (array) – vectors of (real) numbers with identical length, no NaNs allowed
y2 (array) – vectors of (real) numbers with identical length, no NaNs allowed
method (str; {'liang'}) – estimates for the Liang method
nsim (int) – the number of surrogates for significance test
qs (list) – the quantiles for significance test
kwargs (dict) – keyword arguments for the causality method (e.g. npt for Liang-Kleeman)

Returns:

res_dict –

A dictionary with the following information:

T21_noise_qslist: the quantiles of the information flow from noise2 to noise1 for significance testing
tau21_noise_qslist: the quantiles of the standardized information flow from noise2 to noise1 for significance testing

Return type:

dict

See also

pyleoclim.utils.causality.liang_causality: information flow estimated using the Liang algorithm
pyleoclim.utils.causality.granger_causality: information flow estimated using the Granger algorithm
pyleoclim.utils.causality.signif_isopersist: significance test with AR(1) with same persistence

Correlation

Relevant functions for correlation analysis

pyleoclim.utils.correlation.corr_isopersist(y1, y2, alpha=0.05, nsim=1000)[source]

Computes the Pearson’s correlation between two timeseries, and their significance using Ar(1) modeling.

The significance is gauged via a non-parametric (Monte Carlo) simulation of correlations with nsim AR(1) processes with identical persistence properties as x and y ; the measure of which is the lag-1 autocorrelation (g).

Parameters:

y1 (array) – vectors of (real) numbers with identical length, no NaNs allowed
y2 (array) – vectors of (real) numbers with identical length, no NaNs allowed
alpha (float) – significance level for critical value estimation [default: 0.05]
nsim (int) – number of simulations [default: 1000]

Returns:

r (float) – correlation between x and y
signif (bool) – true (1) if significant; false (0) otherwise
pval (float) – test p-value (the probability of the test statstic exceeding the observed one by chance alone)

Notes

The probability of obtaining a test statistic at least as extreme as the one actually observed, assuming that the null hypothesis is true. The test is 1 tailed on |r|: Ho = { |r| = 0 }, Ha = { |r| > 0 } The test is rejected (signif = 1) if pval <= alpha, otherwise signif=0; (Some Rights Reserved) Hepta Technologies, 2009 v1.0 USC, Aug 10 2012, based on corr_signif.

See also

pyleoclim.utils.correlation.corr_sig: Estimates the Pearson’s correlation and associated significance between two non IID time series
pyleoclim.utils.correlation.corr_ttest: Estimates Pearson’s correlation and associated significance using a t-test
pyleoclim.utils.correlation.corr_isospec: Estimates Pearson’s correlation and associated significance using
pyleoclim.utils.correlation.fdr: Determine significance based on the false discovery rate

pyleoclim.utils.correlation.corr_isospec(y1, y2, alpha=0.05, nsim=1000)[source]

Estimates the significance of the correlation using phase randomization

Estimates the significance of correlations between non IID time series by phase randomization of original inputs. This function creates ‘nsim’ random time series that have the same power spectrum as the original time series but random phases.

Parameters:

y1 (array) – vectors of (real) numbers with identical length, no NaNs allowed
y2 (array) – vectors of (real) numbers with identical length, no NaNs allowed
alpha (float) – significance level for critical value estimation [default: 0.05]
nsim (int) – number of simulations [default: 1000]

Returns:

r (float) – correlation between y1 and y2
signif (bool) – true (1) if significant; false (0) otherwise
F (float) – Fraction of time series with higher correlation coefficents than observed (approximates the p-value).

See also

pyleoclim.utils.correlation.corr_sig: Estimates the Pearson’s correlation and associated significance between two non IID time series
pyleoclim.utils.correlation.corr_ttest: Estimates Pearson’s correlation and associated significance using a t-test
pyleoclim.utils.correlation.corr_isopersist: Estimates Pearson’s correlation and associated significance using AR(1) simulations
pyleoclim.utils.correlation.fdr: Determine significance based on the false discovery rate

References

Ebisuzaki, W, 1997: A method to estimate the statistical

significance of a correlation when the data are serially correlated. J. of Climate, 10, 2147-2153.

Prichard, D., Theiler, J. Generating Surrogate Data for Time Series

with Several Simultaneously Measured Variables (1994) Physical Review Letters, Vol 73, Number 7 (Some Rights Reserved) USC Climate Dynamics Lab, 2012.

pyleoclim.utils.correlation.corr_sig(y1, y2, nsim=1000, method='isospectral', alpha=0.05)[source]

Estimates the Pearson’s correlation and associated significance between two non IID time series

The significance of the correlation is assessed using one of the following methods:

‘ttest’: T-test adjusted for effective sample size.
This is a parametric test (data are Gaussian and identically distributed) with a rather ad-hoc adjustment. It is instantaneous but makes a lot of assumptions about the data, many of which may not be met.
‘isopersistent’: AR(1) modeling of x and y.
This is a parametric test as well (series follow an AR(1) model) but solves the issue by direct simulation.
‘isospectral’: phase randomization of original inputs. (default)
This is a non-parametric method, assuming only wide-sense stationarity

For 2 and 3, computational requirements scale with nsim. When possible, nsim should be at least 1000.

Parameters:

y1 (array) – vector of (real) numbers of same length as y2, no NaNs allowed
y2 (array) – vector of (real) numbers of same length as y1, no NaNs allowed
nsim (int) – the number of simulations [default: 1000]
method (str; {'ttest','isopersistent','isospectral' (default)}) – method for significance testing
alpha (float) – significance level for critical value estimation [default: 0.05]

Returns:

res – the result dictionary, containing

rfloat
correlation coefficient
pfloat
the p-value
signifbool
true if significant; false otherwise Note that signif = True if and only if p <= alpha.

Return type:

dict

See also

pyleoclim.utils.correlation.corr_ttest: Estimates the significance of correlations between 2 time series using the classical T-test adjusted for effective sample size
pyleoclim.utils.correlation.corr_isopersist: Computes correlation between two timeseries, and their significance using Ar(1) modeling
pyleoclim.utils.correlation.corr_isospec: Estimates the significance of the correlation using phase randomization
pyleoclim.utils.correlation.fdr: Determine significance based on the false discovery rate

pyleoclim.utils.correlation.corr_ttest(y1, y2, alpha=0.05)[source]

Estimates the significance of correlations between 2 time series using the classical T-test adjusted for effective sample size.

The degrees of freedom are adjusted following n_eff=n(1-g)/(1+g) where g is the lag-1 autocorrelation.

Parameters:

y1 (array) – vectors of (real) numbers with identical length, no NaNs allowed
y2 (array) – vectors of (real) numbers with identical length, no NaNs allowed
alpha (float) – significance level for critical value estimation [default: 0.05]

Returns:

r (float) – correlation between x and y
signif (bool) – true (1) if significant; false (0) otherwise
pval (float) – test p-value (the probability of the test statistic exceeding the observed one by chance alone)

See also

pyleoclim.utils.correlation.corr_sig: Estimates the Pearson’s correlation and associated significance between two non IID time series
pyleoclim.utils.correlation.corr_isopersist: Estimate Pearson’s correlation and associated significance using AR(1)
pyleoclim.utils.correlation.corr_isospec: Estimate Pearson’s correlation and associated significance using phase randomization
pyleoclim.utils.correlation.fdr: Determine significance based on the false discovery rate

pyleoclim.utils.correlation.fdr(pvals, qlevel=0.05, method='original', adj_method=None, adj_args={})[source]

Determine significance based on the false discovery rate

The false discovery rate is a method of conceptualizing the rate of type I errors in null hypothesis testing when conducting multiple comparisons. Translated from fdr.R by Dr. Chris Paciorek

Parameters:

pvals (list or array) – A vector of p-values on which to conduct the multiple testing.
qlevel (float) – The proportion of false positives desired.
method ({'original', 'general'}) –
Method for performing the testing.
- ’original’ follows Benjamini & Hochberg (1995);
- ’general’ is much more conservative, requiring no assumptions on the p-values (see Benjamini & Yekutieli (2001)).
’original’ is recommended, and if desired, using ‘adj_method=”mean”’ to increase power.
adj_method ({'mean', 'storey', 'two-stage'}) –
Method for increasing the power of the procedure by estimating the proportion of alternative p-values.
- ’mean’, the modified Storey estimator in Ventura et al. (2004)
- ’storey’, the method of Storey (2002)
- ’two-stage’, the iterative approach of Benjamini et al. (2001)
adj_args (dict) – Arguments for adj_method; see prop_alt() for description, but note that for “two-stage”, qlevel and fdr_method are taken from the qlevel and method arguments for fdr()

Returns:

fdr_res – A vector of the indices of the significant tests; None if no significant tests

Return type:

array or None

See also

pyleoclim.utils.correlation.corr_sig: Estimates the Pearson’s correlation and associated significance between two non IID time series

References

fdr.R by Dr. Chris Paciorek: https://www.stat.berkeley.edu/~paciorek/research/code/code.html

pyleoclim.utils.correlation.fdr_basic(pvals, qlevel=0.05)[source]

The basic FDR of Benjamini & Hochberg (1995).

Parameters:

pvals (list or array) – A vector of p-values on which to conduct the multiple testing.
qlevel (float) – The proportion of false positives desired.

Returns:

fdr_res – A vector of the indices of the significant tests; None if no significant tests

Return type:

array or None

See also

pyleoclim.utils.correlation.corr_sig: Estimates the Pearson’s correlation and associated significance between two non IID time series
pyleoclim.utils.correlation.fdf: Determine significance based on the false discovery rate

References

Benjamini, Yoav; Hochberg, Yosef (1995). “Controlling the false discovery rate: a practical and powerful approach to multiple testing”. Journal of the Royal Statistical Society, Series B. 57 (1): 289–300. MR 1325392

pyleoclim.utils.correlation.fdr_master(pvals, qlevel=0.05, method='original')[source]

Perform various versions of the FDR procedure

Parameters:

pvals (list or array) – A vector of p-values on which to conduct the multiple testing.
qlevel (float) – The proportion of false positives desired.
method ({'original', 'general'}) – Method for performing the testing. - ‘original’ follows Benjamini & Hochberg (1995); - ‘general’ is much more conservative, requiring no assumptions on the p-values (see Benjamini & Yekutieli (2001)). We recommend using ‘original’, and if desired, using ‘adj_method=”mean”’ to increase power.

Returns:

fdr_res – A vector of the indices of the significant tests; None if no significant tests

Return type:

array or None

See also

pyleoclim.utils.correlation.corr_sig: Estimates the Pearson’s correlation and associated significance between two non IID time series
pyleoclim.utils.correlation.fdf: Determine significance based on the false discovery rate

References

Benjamini, Yoav; Hochberg, Yosef (1995). “Controlling the false discovery rate: a practical and powerful approach to multiple testing”. Journal of the Royal Statistical Society, Series B. 57 (1): 289–300. MR 1325392
Benjamini, Yoav; Yekutieli, Daniel (2001). “The control of the false discovery rate in multiple testing under dependency”. Annals of Statistics. 29 (4): 1165–1188. doi:10.1214/aos/1013699998

pyleoclim.utils.correlation.isopersistent_rn(X, p)[source]

Generates p realization of a red noise [i.e. AR(1)] process with same persistence properties as X (Mean and variance are also preserved).

Parameters:

X (array) – vector of (real) numbers as a time series, no NaNs allowed
p (int) – number of simulations

Returns:

red (numpy array) – n rows by p columns matrix of an AR1 process, where n is the size of X
g (float) – lag-1 autocorrelation coefficient

See also

pyleoclim.utils.correlation.corr_sig: Estimates the Pearson’s correlation and associated significance between two non IID time series
pyleoclim.utils.correlation.fdr: Determine significance based on the false discovery rate

Notes

(Some Rights Reserved) Hepta Technologies, 2008

pyleoclim.utils.correlation.phaseran(recblk, nsurr)[source]

Simultaneous phase randomization of a set of time series

It creates blocks of surrogate data with the same second order properties as the original time series dataset by transforming the oriinal data into the frequency domain, randomizing the phases simultaneoulsy across the time series and converting the data back into the time domain.

Written by Carlos Gias for MATLAB

http://www.mathworks.nl/matlabcentral/fileexchange/32621-phase-randomization/content/phaseran.m

Parameters:

recblk (numpy array) – 2D array , Row: time sample. Column: recording. An odd number of time samples (height) is expected. If that is not the case, recblock is reduced by 1 sample before the surrogate data is created. The class must be double and it must be nonsparse.
nsurr (int) – is the number of image block surrogates that you want to generate.

Returns:

surrblk – 3D multidimensional array image block with the surrogate datasets along the third dimension

Return type:

numpy array

See also

pyleoclim.utils.correlation.corr_sig: Estimates the Pearson’s correlation and associated significance between two non IID time series
pyleoclim.utils.correlation.fdf: Determine significance based on the false discovery rate

References

Prichard, D., Theiler, J. Generating Surrogate Data for Time Series with Several Simultaneously Measured Variables (1994)

Physical Review Letters, Vol 73, Number 7

Carlos Gias (2020). Phase randomization, MATLAB Central File Exchange

pyleoclim.utils.correlation.prop_alt(pvals, adj_method='mean', adj_args={'edf_lower': 0.8, 'num_steps': 20})[source]

Calculate an estimate of a, the proportion of alternative hypotheses, using one of several methods

Parameters:: pvals (list or array) – A vector of p-values on which to estimate a

adj_method: str; {‘mean’, ‘storey’, ‘two-stage’}

Method for increasing the power of the procedure by estimating the proportion of alternative p-values. - ‘mean’, the modified Storey estimator that we suggest in Ventura et al. (2004) - ‘storey’, the method of Storey (2002) - ‘two-stage’, the iterative approach of Benjamini et al. (2001)

adj_argsdict

for “mean”, specify “edf_lower”, the smallest quantile at which to estimate a, and “num_steps”, the number of quantiles to use the approach uses the average of the Storey (2002) estimator for the num_steps quantiles starting at “edf_lower” and finishing just less than 1
for “storey”, specify “edf_quantile”, the quantile at which to calculate the estimator
for “two-stage”, the method uses a standard FDR approach to estimate which p-values are significant this number is the estimate of a; therefore the method requires specification of qlevel, the proportion of false positives and “fdr_method” (‘original’ or ‘general’), the FDR method to be used. We do not recommend ‘general’ as this is very conservative and will underestimate a.

Returns:: a – estimate of a, the number of alternative hypotheses
Return type:: int

See also

pyleoclim.utils.correlation.corr_sig: Estimates the Pearson’s correlation and associated significance between two non IID time series
pyleoclim.utils.correlation.fdf: Determine significance based on the false discovery rate

References

Storey, J.D. (2002). A direct approach to False Discovery Rates. Journal of the Royal Statistical Society, Series B, 64, 3, 479-498
Benjamini, Yoav; Yekutieli, Daniel (2001). “The control of the false discovery rate in multiple testing under dependency”. Annals of Statistics. 29 (4): 1165–1188. doi:10.1214/aos/1013699998
Ventura, V., Paciorek, C., Risbey, J.S. (2004). Controlling the proportion of falsely rejected hypotheses when conducting multiple tests with climatological data. Journal of climate, 17, 4343-4356

pyleoclim.utils.correlation.sm_ar1_sim(n, p, g, sig)[source]

Produce p realizations of an AR1 process of length n with lag-1 autocorrelation g using statsmodels

Parameters:

n (int) – row dimensions
p (int) – column dimensions
g (float) – lag-1 autocorrelation coefficient
sig (float) – the standard deviation of the original time series

Returns:

red – n rows by p columns matrix of an AR1 process

Return type:

numpy matrix

See also

pyleoclim.utils.correlation.corr_sig: Estimates the Pearson’s correlation and associated significance between two non IID time series
pyleoclim.utils.correlation.fdr: Determine significance based on the false discovery rate

pyleoclim.utils.correlation.storey(edf_quantile, pvals)[source]

The basic Storey (2002) estimator of a, the proportion of alternative hypotheses.

Parameters:

edf_quantile (float) – The quantile of the empirical distribution function at which to estimate a.
pvals (list or array) – A vector of p-values on which to estimate a

Returns:

a – estimate of a, the number of alternative hypotheses

Return type:

int

See also

pyleoclim.utils.correlation.corr_sig: Estimates the Pearson’s correlation and associated significance between two non IID time series
pyleoclim.utils.correlation.fdf: Determine significance based on the false discovery rate

References

Storey, J.D., 2002, A direct approach to False Discovery Rates. Journal of the Royal Statistical Society, Series B, 64, 3, 479-498

Decomposition

Eigendecomposition methods: Singular Spectrum Analysis (SSA). soon: Monte-Carlo Principal Component Analysis, Multi-Channel SSA

pyleoclim.utils.decomposition.ssa(y, M=None, nMC=0, f=0.5, trunc=None, var_thresh=80)[source]

Singular spectrum analysis

Nonparametric eigendecomposition of timeseries into orthogonal oscillations. This implementation uses the method of [1], with applications presented in [2]. Optionally (nMC>0), the significance of eigenvalues is assessed by Monte-Carlo simulations of an AR(1) model fit to X, using [3]. The method expects regular spacing, but is tolerant to missing values, up to a fraction 0<f<1 (see [4]).

Parameters:

y (array of length N) – time series (evenly-spaced, possibly with up to f*N NaNs)
M (int) – window size (default: 10% of N)
nMC (int) – Number of iterations in the Monte-Carlo simulation (default nMC=0, bypasses Monte Carlo SSA) Currently only supported for evenly-spaced, gap-free data.
f (float) – maximum allowable fraction of missing values. (Default is 0.5)
trunc (str) –
if present, truncates the expansion to a level K < M owing to one of 3 criteria:
1. ’kaiser’: variant of the Kaiser-Guttman rule, retaining eigenvalues larger than the median
2. ’mcssa’: Monte-Carlo SSA (use modes above the 95% quantile from an AR(1) process)
3. ’var’: first K modes that explain at least var_thresh % of the variance.
Default is None, which bypasses truncation (K = M)
var_thresh (float) – variance threshold for reconstruction (only impactful if trunc is set to ‘var’)

Returns:

res –

eigvals : (M, ) array of eigenvalues
eigvecs : (M, M) Matrix of temporal eigenvectors (T-EOFs)
PC : (N - M + 1, M) array of principal components (T-PCs)
RCmat : (N, M) array of reconstructed components
RCseries : (N,) reconstructed series, with mean and variance restored
pctvar: (M, ) array of the fraction of variance (%) associated with each mode
eigvals_q : (M, 2) array containting the 5% and 95% quantiles of the Monte-Carlo eigenvalue spectrum [ if nMC >0 ]
mode_idx : array of indices of eigenvalues >=eigvals_q

Return type:

dict containing:

References

[1]_ Vautard, R., and M. Ghil (1989), Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series, Physica D, 35, 395–424.

[2]_ Ghil, M., R. M. Allen, M. D. Dettinger, K. Ide, D. Kondrashov, M. E. Mann, A. Robertson, A. Saunders, Y. Tian, F. Varadi, and P. Yiou (2002), Advanced spectral methods for climatic time series, Rev. Geophys., 40(1), 1003–1052, doi:10.1029/2000RG000092.

[3]_ Allen, M. R., and L. A. Smith (1996), Monte Carlo SSA: Detecting irregular oscillations in the presence of coloured noise, J. Clim., 9, 3373–3404.

[4]_ Schoellhamer, D. H. (2001), Singular spectrum analysis for time series with missing data, Geophysical Research Letters, 28(16), 3187–3190, doi:10.1029/2000GL012698.

See also

pyleoclim.core.series.Series.ssa: Singular Spectrum Analysis for timeseries objects
pyleoclim.core.ssares.SsaRes.modeplot: plot SSA modes
pyleoclim.core.ssares.SsaRes.screeplot: plot SSA eigenvalue spectrum

Filter

Utilities to filter arrayed timeseries data, leveraging SciPy

pyleoclim.utils.filter.butterworth(ys, fc, fs=1, filter_order=3, pad='reflect', reflect_type='odd', params=(1, 0, 0), padFrac=0.1)[source]

Applies a Butterworth filter with frequency fc, with padding: Supports both lowpass and band-pass filtering.

Parameters:

ys (numpy array) – Timeseries
fc (float or list) – cutoff frequency. If scalar, it is interpreted as a low-frequency cutoff (lowpass) If fc is a list, it is interpreted as a frequency band (f1, f2), with f1 < f2 (bandpass)
fs (float) – sampling frequency
filter_order (int) – order n of Butterworth filter
pad (str) – Indicates if padding is needed. - ‘reflect’: Reflects the timeseries - ‘ARIMA’: Uses an ARIMA model for the padding - None: No padding.
params (tuple) – model parameters for ARIMA model (if pad = ‘ARIMA’)
padFrac (float) – fraction of the series to be padded

Returns:

yf – filtered array

Return type:

array

See also

pyleoclim.utils.filter.ts_pad: Pad a timeseries based on timeseries model predictions
pyleoclim.utils.filter.firwin: Applies a Finite Impulse Response filter with frequency fc, with padding
pyleoclim.utils.filter.savitzky_golay: Smooth (and optionally differentiate) data with a Savitzky-Golay filter
pyleoclim.utils.filter.lanczos: Applies a Lanczos filter with frequency fc, with padding

pyleoclim.utils.filter.firwin(ys, fc, numtaps=None, fs=1, pad='reflect', window='hamming', reflect_type='odd', params=(1, 0, 0), padFrac=0.1, **kwargs)[source]

Applies a Finite Impulse Response filter design with window method and frequency fc, with padding

Parameters:

ys (numpy array) – Timeseries
fc (float or list) – cutoff frequency. If scalar, it is interpreted as a low-frequency cutoff (lowpass) If fc is a list, it is interpreted as a frequency band (f1, f2), with f1 < f2 (bandpass)
numptaps (int) – Length of the filter (number of coefficients, i.e. the filter order + 1). numtaps must be odd if a passband includes the Nyquist frequency. If None, will use the largest number that is smaller than 1/3 of the the data length.
fs (float) – sampling frequency
window (str or tuple of string and parameter values, optional) – Desired window to use. See scipy.signal.get_window for a list of windows and required parameters.
pad (str) – Indicates if padding is needed. - ‘reflect’: Reflects the timeseries - ‘ARIMA’: Uses an ARIMA model for the padding - None: No padding.
params (tuple) – model parameters for ARIMA model (if pad = True)
padFrac (float) – fraction of the series to be padded
kwargs (dict) – a dictionary of keyword arguments for scipy.signal.firwin

Returns:

yf – filtered array

Return type:

array

See also

scipy.signal.firwin: FIR filter design using the window method
pyleoclim.utils.filter.ts_pad: Pad a timeseries based on timeseries model predictions
pyleoclim.utils.filter.butterworth: Applies a Butterworth filter with frequency fc, with padding
pyleoclim.utils.filter.lanczos: Applies a Lanczos filter with frequency fc, with padding
pyleoclim.utils.filter.savitzky_golay: Smooth (and optionally differentiate) data with a Savitzky-Golay filter

pyleoclim.utils.filter.lanczos(ys, fc, fs=1, pad='reflect', reflect_type='odd', params=(1, 0, 0), padFrac=0.1)[source]

Applies a Lanczos (lowpass) filter with frequency fc, with optional padding

Parameters:

ys (numpy array) – Timeseries
fc (float) – cutoff frequency
fs (float) – sampling frequency
pad (str) – Indicates if padding is needed - ‘reflect’: Reflects the timeseries - ‘ARIMA’: Uses an ARIMA model for the padding - None: No padding
params (tuple) – model parameters for ARIMA model (if pad = ‘ARIMA’). May require fiddling
padFrac (float) – fraction of the series to be padded

Returns:

yf – filtered array

Return type:

array

See also

pyleoclim.utils.filter.ts_pad: Pad a timeseries based on timeseries model predictions
pyleoclim.utils.filter.butterworth: Applies a Butterworth filter with frequency fc, with padding
pyleoclim.utils.filter.firwin: Applies a Finite Impulse Response filter with frequency fc, with padding
pyleoclim.utils.filter.savitzky_golay: Smooth (and optionally differentiate) data with a Savitzky-Golay filter

References

Filter design from http://scitools.org.uk/iris/docs/v1.2/examples/graphics/SOI_filtering.html

pyleoclim.utils.filter.savitzky_golay(ys, window_length=None, polyorder=2, deriv=0, delta=1, axis=-1, mode='mirror', cval=0)[source]

Smooth (and optionally differentiate) data with a Savitzky-Golay filter.

The Savitzky-Golay filter removes high frequency noise from data. It has the advantage of preserving the original shape and features of the signal better than other types of filtering approaches, such as moving averages techniques.

The Savitzky-Golay is a type of low-pass filter, particularly suited for smoothing noisy data. The main idea behind this approach is to make for each point a least-square fit with a polynomial of high order over a odd-sized window centered at the point.

Uses the implementation from scipy.signal: https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.savgol_filter.html

Parameters:

ys (array) – the values of the signal to be filtered
window_length (int) –

The length of the filter window. Must be a positive integer.
If mode is ‘interp’, window_length must be less than or equal to the size of ys. Default is the size of ys.
polyorder (int) –

The order of the polynomial used to fit the samples. polyorder Must be less than window_length.
Default is 2
deriv (int) –

The order of the derivative to compute.
This must be a nonnegative integer. The default is 0, which means to filter the data without differentiating
delta (float) –

The spacing of the samples to which the filter will be applied.
This is only used if deriv>0. Default is 1.0
axis (int) – The axis of the array ys along which the filter will be applied. Default is -1
mode (str) – Must be ‘mirror’ (the default), ‘constant’, ‘nearest’, ‘wrap’ or ‘interp’. This determines the type of extension to use for the padded signal to which the filter is applied. When mode is ‘constant’, the padding value is given by cval. See the Notes for more details on ‘mirror’, ‘constant’, ‘wrap’, and ‘nearest’. When the ‘interp’ mode is selected, no extension is used. Instead, a degree polyorder polynomial is fit to the last window_length values of the edges, and this polynomial is used to evaluate the last window_length // 2 output values.
cval (scalar) – Value to fill past the edges of the input if mode is ‘constant’. Default is 0.0.

Returns:

yf – ndarray of shape (N), the smoothed signal (or it’s n-th derivative).

Return type:

array

See also

pyleoclim.utils.filter.butterworth: Applies a Butterworth filter with frequency fc, with padding
pyleoclim.utils.filter.lanczos: Applies a Lanczos filter with frequency fc, with padding
pyleoclim.utils.filter.firwin: Applies a Finite Impulse Response filter with frequency fc, with padding

References

Savitzky, M. J. E. Golay, Smoothing and Differentiation of
Data by Simplified Least Squares Procedures. Analytical Chemistry, 1964, 36 (8), pp 1627-1639.

Numerical Recipes 3rd Edition: The Art of Scientific Computing: W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery Cambridge University Press ISBN-13: 9780521880688

SciPy Cookbook: shttps://github.com/scipy/scipy-cookbook/blob/master/ipython/SavitzkyGolay.ipynb

Notes

Details on the mode option:

‘mirror’: Repeats the values at the edges in reverse order. The value closest to the edge is not included.

‘nearest’: The extension contains the nearest input value.

‘constant’: The extension contains the value given by the cval argument.

‘wrap’: The extension contains the values from the other end of the array.

pyleoclim.utils.filter.ts_pad(ys, ts, method='reflect', params=(1, 0, 0), reflect_type='odd', padFrac=0.1)[source]

Pad a timeseries based on timeseries model predictions

Parameters:

ys (numpy array) – Evenly-spaced timeseries
ts (numpy array) – Time axis
method (str) – the method to use to pad the series - ARIMA: uses a fitted ARIMA model - reflect (default): Reflects the time series around either end.
params (tuple) – the ARIMA model order parameters (p,d,q), Default corresponds to an AR(1) model
reflect_type (str; {‘even’, ‘odd’}, optional) – Used in ‘reflect’, and ‘symmetric’. The ‘even’ style is the default with an unaltered reflection around the edge value. For the ‘odd’ style, the extented part of the array is created by subtracting the reflected values from two times the edge value. For more details, see np.lib.pad()
padFrac (float) – padding fraction (scalar) such that padLength = padFrac*length(series)

Returns:

yp (array) – padded timeseries
tp (array) – augmented time axis

See also

pyleoclim.utils.filter.butterworth: Applies a Butterworth filter with frequency fc, with padding
pyleoclim.utils.filter.lanczos: Applies a Lanczos filter with frequency fc, with padding
pyleoclim.utils.filter.firwin: Applies a Finite Impulse Response filter with frequency fc, with padding

Mapping

Mapping utilities for geolocated objects, leveraging Cartopy.

pyleoclim.utils.mapping.compute_dist(lat_r, lon_r, lat_c, lon_c)[source]

Computes the distance in (km) between a reference point and an array of other coordinates.

Parameters:

lat_r (float) – The reference latitude, in deg
lon_r (float) – The reference longitude, in deg
lat_c (list) – A list of latitudes for the comparison points, in deg
lon_c (list) – A list of longitudes for the comparison points, in deg

See also

pyleoclim.utils.mapping.dist_sphere: calculate distance on a sphere

Returns:: dist – A list of distances in km.
Return type:: list

pyleoclim.utils.mapping.dist_sphere(lat1, lon1, lat2, lon2)[source]

Uses the harversine formula to calculate distance on a sphere

Parameters:

lat1 (float) – Latitude of the first point, in radians
lon1 (float) – Longitude of the first point, in radians
lat2 (float) – Latitude of the second point, in radians
lon2 (float) – Longitude of the second point, in radians

Returns:

dist – The distance between the two point in km

Return type:

float

pyleoclim.utils.mapping.map(lat, lon, criteria, marker=None, color=None, projection='Robinson', proj_default=True, background=True, borders=False, rivers=False, lakes=False, figsize=None, ax=None, scatter_kwargs=None, legend=True, lgd_kwargs=None, savefig_settings=None)[source]

Map the location of all lat/lon according to some criteria

Map the location of all lat/lon according to some criteria. Based on functions defined in the Cartopy package.

Parameters:

lat (list) – a list of latitudes.
lon (list) – a list of longitudes.
criteria (list) – a list of unique criteria for plotting purposes. For instance, a map by the types of archive present in the dataset or proxy observations. Should have the same length as lon/lat.
marker (list) – a list of possible markers for each criterion. If None, will use pyleoclim default
color (list) – a list of possible colors for each criterion. If None, will use pyleoclim default
projection (string) – the map projection. Available projections: ‘Robinson’ (default), ‘PlateCarree’, ‘AlbertsEqualArea’, ‘AzimuthalEquidistant’,’EquidistantConic’,’LambertConformal’, ‘LambertCylindrical’,’Mercator’,’Miller’,’Mollweide’,’Orthographic’, ‘Sinusoidal’,’Stereographic’,’TransverseMercator’,’UTM’, ‘InterruptedGoodeHomolosine’,’RotatedPole’,’OSGB’,’EuroPP’, ‘Geostationary’,’NearsidePerspective’,’EckertI’,’EckertII’, ‘EckertIII’,’EckertIV’,’EckertV’,’EckertVI’,’EqualEarth’,’Gnomonic’, ‘LambertAzimuthalEqualArea’,’NorthPolarStereo’,’OSNI’,’SouthPolarStereo’
proj_default (bool) –
If True, uses the standard projection attributes. Enter new attributes in a dictionary to change them. Lists of attributes can be found in the Cartopy documentation:

https://scitools.org.uk/cartopy/docs/latest/crs/projections.html#eckertiv
background (bool) – If True, uses a shaded relief background (only one available in Cartopy)
borders (bool) – Draws the countries border. Defaults is off (False).
rivers (bool) – Draws major rivers. Default is off (False).
lakes (bool) – Draws major lakes. Default is off (False).
figsize (list) – the size for the figure
ax (axis,optional) – Return as axis instead of figure (useful to integrate plot into a subplot)
scatter_kwargs (dict) – Dictionary of arguments available in matplotlib.pyplot.scatter (https://matplotlib.org/3.2.1/api/_as_gen/matplotlib.pyplot.scatter.html).
legend (bool) – Whether the draw a legend on the figure
lgd_kwargs (dict) – Dictionary of arguments for matplotlib.pyplot.legend (https://matplotlib.org/3.2.1/api/_as_gen/matplotlib.pyplot.legend.html)
savefig_settings (dict) –
Dictionary of arguments for matplotlib.pyplot.saveFig. - “path” must be specified; it can be any existed or non-existed path,

with or without a suffix; if the suffix is not given in “path”, it will follow “format”
- ”format” can be one of {“pdf”, “eps”, “png”, “ps”}

Returns:

ax

Return type:

The figure, or axis if ax specified

See also

pyleoclim.utils.mapping.set_proj: Set the projection for Cartopy-based maps

pyleoclim.utils.mapping.set_proj(projection='Robinson', proj_default=True)[source]

Set the projection for Cartopy.

Parameters:

projection (string) – the map projection. Available projections: ‘Robinson’ (default), ‘PlateCarree’, ‘AlbertsEqualArea’, ‘AzimuthalEquidistant’,’EquidistantConic’,’LambertConformal’, ‘LambertCylindrical’,’Mercator’,’Miller’,’Mollweide’,’Orthographic’, ‘Sinusoidal’,’Stereographic’,’TransverseMercator’,’UTM’, ‘InterruptedGoodeHomolosine’,’RotatedPole’,’OSGB’,’EuroPP’, ‘Geostationary’,’NearsidePerspective’,’EckertI’,’EckertII’, ‘EckertIII’,’EckertIV’,’EckertV’,’EckertVI’,’EqualEarth’,’Gnomonic’, ‘LambertAzimuthalEqualArea’,’NorthPolarStereo’,’OSNI’,’SouthPolarStereo’
proj_default (bool; {True,False}) –
If True, uses the standard projection attributes from Cartopy. Enter new attributes in a dictionary to change them. Lists of attributes can be found in the Cartopy documentation:

https://scitools.org.uk/cartopy/docs/latest/crs/projections.html#eckertiv

Returns:

proj

Return type:

the Cartopy projection object

See also

pyleoclim.utils.mapping.map: mapping function making use of the projection

pyleoclim.utils.mapping.within_distance(distance, radius)[source]

Returns the index of the records that are within a certain distance

Parameters:

distance (list) – A list containing the distance
radius (float) – The radius to be considered

Returns:

idx – a list of index

Return type:

list

Plotting

Plotting utilities, leveraging Matplotlib.

pyleoclim.utils.plotting.closefig(fig=None)[source]

Close the figure

Parameters:: fig (matplotlib.pyplot.figure) – The matplotlib figure object

pyleoclim.utils.plotting.plot_scatter_xy(x1, y1, x2, y2, figsize=None, xlabel=None, ylabel=None, title=None, xlim=None, ylim=None, savefig_settings=None, ax=None, legend=True, plot_kwargs=None, lgd_kwargs=None)[source]

Plot a scatter on top of a line plot.

Parameters:

x1 (array) – x axis of timeseries1 - plotted as a line
y1 (array) – values of timeseries1 - plotted as a line
x2 (array) – x axis of scatter points
y2 (array) – y of scatter points
figsize (list) – a list of two integers indicating the figure size
xlabel (str) – label for x-axis
ylabel (str) – label for y-axis
title (str) – the title for the figure
xlim (list) – set the limits of the x axis
ylim (list) – set the limits of the y axis
ax (pyplot.axis) – the pyplot.axis object
legend (bool) – plot legend or not
lgd_kwargs (dict) – the keyword arguments for ax.legend()
plot_kwargs (dict) – the keyword arguments for ax.plot()
savefig_settings (dict) –
the dictionary of arguments for plt.savefig(); some notes below: - “path” must be specified; it can be any existing or non-existing path,

with or without a suffix; if the suffix is not given in “path”, it will follow “format”
- ”format” can be one of {“pdf”, “eps”, “png”, “ps”}

Returns:

ax

Return type:

the pyplot.axis object

See also

pyleoclim.utils.plotting.set_style: set different styles for the figures. Should be set before invoking the plotting functions
pyleoclim.utils.plotting.savefig: save figures

pyleoclim.utils.plotting.plot_xy(x, y, figsize=None, xlabel=None, ylabel=None, title=None, xlim=None, ylim=None, savefig_settings=None, ax=None, legend=True, plot_kwargs=None, lgd_kwargs=None, invert_xaxis=False, invert_yaxis=False)[source]

Plot a timeseries

Parameters:

x (array) – The time axis for the timeseries
y (array) – The values of the timeseries
figsize (list) – a list of two integers indicating the figure size
xlabel (str) – label for x-axis
ylabel (str) – label for y-axis
title (str) – the title for the figure
xlim (list) – set the limits of the x axis
ylim (list) – set the limits of the y axis
ax (pyplot.axis) – the pyplot.axis object
legend (bool) – plot legend or not
lgd_kwargs (dict) – the keyword arguments for ax.legend()
plot_kwargs (dict) – the keyword arguments for ax.plot()
mute (bool) –
if True, the plot will not show; recommend to turn on when more modifications are going to be made on ax

(going to be deprecated)
savefig_settings (dict) –
the dictionary of arguments for plt.savefig(); some notes below: - “path” must be specified; it can be any existing or non-existing path,

with or without a suffix; if the suffix is not given in “path”, it will follow “format”
- ”format” can be one of {“pdf”, “eps”, “png”, “ps”}
invert_xaxis (bool, optional) – if True, the x-axis of the plot will be inverted
invert_yaxis (bool, optional) – if True, the y-axis of the plot will be inverted

Returns:

ax

Return type:

the pyplot.axis object

See also

pyleoclim.utils.plotting.set_style: set different styles for the figures. Should be set before invoking the plotting functions
pyleoclim.utils.plotting.savefig: save figures

pyleoclim.utils.plotting.savefig(fig, path=None, dpi=300, settings={}, verbose=True)[source]

Save a figure to a path

Parameters:

fig (matplotlib.pyplot.figure) – the figure to save
path (str) – the path to save the figure, can be ignored and specify in “settings” instead
dpi (int) – resolution in dot (pixels) per inch. Default: 300.
settings (dict) –
the dictionary of arguments for plt.savefig(); some notes below: - “path” must be specified in settings if not assigned with the keyword argument;

it can be any existing or non-existing path, with or without a suffix; if the suffix is not given in “path”, it will follow “format”
- ”format” can be one of {“pdf”, “eps”, “png”, “ps”}
verbose (bool, {True,False}) – If True, print the path of the saved file.

pyleoclim.utils.plotting.scatter_xy(x, y, c=None, figsize=None, xlabel=None, ylabel=None, title=None, xlim=None, ylim=None, savefig_settings=None, ax=None, legend=True, plot_kwargs=None, lgd_kwargs=None)[source]

Make scatter plot.

Parameters:

x (numpy.array) – x value
y (numpy.array) – y value
c (TYPE, optional) – DESCRIPTION. The default is None.
figsize (list, optional) – A list of two integers indicating the dimension of the figure. The default is None.
xlabel (str, optional) – x-axis label. The default is None.
ylabel (str, optional) – y-axis label. The default is None.
title (str, optional) – Title for the plot. The default is None.
xlim (list, optional) – Limits for the x-axis. The default is None.
ylim (list, optional) – Limits for the y-axis. The default is None.
savefig_settings (dict, optional) –
the dictionary of arguments for plt.savefig(); some notes below:
- ”path” must be specified; it can be any existing or non-existing path, with or without a suffix; if the suffix is not given in “path”, it will follow “format”
- ”format” can be one of {“pdf”, “eps”, “png”, “ps”}
The default is None.
ax (pyplot.axis, optional) – The axis object. The default is None.
legend (bool, optional) – Whether to include a legend. The default is True.
plot_kwargs (dict, optional) – the keyword arguments for ax.plot(). The default is None.
lgd_kwargs (dict, optional) – the keyword arguments for ax.legend(). The default is None.

Returns:

ax

Return type:

the pyplot.axis object

pyleoclim.utils.plotting.set_style(style='journal', font_scale=1.0, dpi=300)[source]

Modify the visualization style

This function is inspired by [Seaborn](https://github.com/mwaskom/seaborn).

Parameters:

style ({journal,web,matplotlib,_spines, _nospines,_grid,_nogrid}) –
set the styles for the figure:
- journal (default): fonts appropriate for paper
- web: web-like font (e.g. ggplot)
- matplotlib: the original matplotlib style
In addition, the following options are available: - _spines/_nospines: allow to show/hide spines - _grid/_nogrid: allow to show gridlines (default: _grid)
font_scale (float) – Default is 1. Corresponding to 12 Font Size.

pyleoclim.utils.plotting.stripes_xy(x, y, ref_period, thickness=1.0, LIM=0.75, figsize=None, xlabel=None, ylabel=None, title=None, xlim=None, savefig_settings=None, ax=None, x_offset=0.05, label_size=None, show_xaxis=False, invert_xaxis=False, top_label=None, bottom_label=None, label_color=None)[source]

Represent y as an Ed Hawkins “warming stripes” pattern, as a function of x

Credit: https://matplotlib.org/matplotblog/posts/warming-stripes/

Parameters:

x (array) – Independent variable
y (array) – Dependent variable
ref_period (2-tuple or 2-vector) – indices of the reference period, in the form “(first, last)”
thickness (float, optional) – vertical thickness of the stripe . The default is 1.0
LIM (float, optional) – size of the y-value range (default: 0.7)
figsize (list) – a list of two integers indicating the figure size
top_label (str) – the “title” label for the stripe
bottom_label (str) – the “ylabel” explaining which variable is being plotted
label_size (int) – size of the text in labels (in points). Default is the Matplotlib ‘axes.labelsize’] rcParams
xlim (list) – set the limits of the x axis
x_offset (float) – value controlling the horizontal offset between stripes and labels (default = 0.05)
show_xaxis (bool) – flag indicating whether or not the x-axis should be shown (default = False)
ax (pyplot.axis) – the pyplot.axis object
savefig_settings (dict) –
the dictionary of arguments for plt.savefig(); some notes below: - “path” must be specified; it can be any existing or non-existing path,

with or without a suffix; if the suffix is not given in “path”, it will follow “format”
- ”format” can be one of {“pdf”, “eps”, “png”, “ps”}
invert_xaxis (bool, optional) – if True, the x-axis of the plot will be inverted

Return type:

ax, or fig, ax (if no axes were provided)

Spectral

Utilities for spectral analysis, including WWZ, CWT, Lomb-Scargle, MTM, and Welch. Designed for NumPy arrays, either evenly spaced or not (method-dependent).

All spectral methods must return a dictionary containing one vector for the frequency axis and the power spectral density (PSD).

Additional utilities help compute an optimal frequency vector or estimate scaling exponents.

pyleoclim.utils.spectral.beta2Hurst(beta)[source]

Translates spectral slope to Hurst exponent

Parameters:: beta (float) – the estimated slope of a power spectral density :math: S(f) propto 1/f^{eta}
Returns:: H – Hurst index, should be in (0, 1)
Return type:: float

References

Equation 2 in http://www.bearcave.com/misl/misl_tech/wavelets/hurst/

See also

pyleoclim.utils.spectral.beta_estimation: Estimate the scaling exponent of a power spectral density.

pyleoclim.utils.spectral.beta_estimation(psd, freq, fmin=None, fmax=None, logf_binning_step='max', verbose=False)[source]

Estimate the scaling exponent of a power spectral density.

Models the spectrum as :math: S(f) propto 1/f^{eta}. For instance: - :math: eta = 0 corresponds to white noise - :math: eta = 1 corresponds to pink noise - :math: eta = 2 corresponds to red noise (Brownian motion)

Parameters:

psd (array) – the power spectral density
freq (array) – the frequency vector
fmin (float) – the min of frequency range for beta estimation
fmax (float) – the max of frequency range for beta estimation
verbose (bool) – if True, will print out debug information

Returns:

beta (float) – the estimated slope
f_binned (array) – binned frequency vector
psd_binned (array) – binned power spectral density
Y_reg (array) – prediction based on linear regression

pyleoclim.utils.spectral.cwt_psd(ys, ts, freq=None, freq_method='log', freq_kwargs=None, scale=None, detrend=False, sg_kwargs={}, gaussianize=False, standardize=True, pad=False, mother='MORLET', param=None, cwt_res=None)[source]

Spectral estimation using the continuous wavelet transform Uses the Torrence and Compo [1998] continuous wavelet transform implementation

Parameters:

ys (numpy.array) – the time series.
ts (numpy.array) – the time axis.
freq (numpy.array, optional) – The frequency vector. The default is None, which will prompt the use of one the underlying functions
freq_method (string, optional) – The method by which to obtain the frequency vector. The default is ‘log’. Options are ‘log’ (default), ‘nfft’, ‘lomb_scargle’, ‘welch’, and ‘scale’
freq_kwargs (dict, optional) – Optional parameters for the choice of the frequency vector. See make_freq_vector and additional methods for details. The default is {}.
scale (numpy.array) – Optional scale vector in place of a frequency vector. Default is None. If scale is not None, frequency method and attached arguments will be ignored.
detrend (bool, string, {'linear', 'constant', 'savitzy-golay', 'emd'}) – Whether to detrend and with which option. The default is False.
sg_kwargs (dict, optional) – Additional parameters for the savitzy-golay method. The default is {}.
gaussianize (bool, optional) – Whether to gaussianize. The default is False.
standardize (bool, optional) – Whether to standardize. The default is True.
pad (bool, optional) – Whether or not to pad the timeseries. with zeroes to get N up to the next higher power of 2. This prevents wraparound from the end of the time series to the beginning, and also speeds up the FFT’s used to do the wavelet transform. This will not eliminate all edge effects. The default is False.
mother (string, optional) – the mother wavelet function. The default is ‘MORLET’. Options are: ‘MORLET’, ‘PAUL’, or ‘DOG’
param (flaot, optional) –
the mother wavelet parameter. The default is None since it varies for each mother
- For ‘MORLET’ this is k0 (wavenumber), default is 6.
- For ‘PAUL’ this is m (order), default is 4.
- For ‘DOG’ this is m (m-th derivative), default is 2.
cwt_res (dict) – Results from pyleoclim.utils.wavelet.cwt

Returns:

res –

Dictionary containing:

psd: the power density function
freq: frequency vector
scale: the scale vector
mother: the mother wavelet
param : the wavelet parameter

Return type:

dict

See also

pyleoclim.utils.wavelet.make_freq_vector: make the frequency vector with various methods
pyleoclim.utils.wavelet.cwt: Torrence and Compo implementation of the continuous wavelet transform
pyleoclim.utils.spectral.periodogram: Spectral estimation using Blackman-Tukey’s periodogram
pyleoclim.utils.spectral.mtm: Spectral estimation using the multi-taper method
pyleoclim.utils.spectral.lomb_scargle: Spectral estimation using the lomb-scargle periodogram
pyleoclim.utils.spectral.welch: Spectral estimation using Welch’s periodogram
pyleoclim.utils.spectral.wwz_psd: Spectral estimation using the Weighted Wavelet Z-transform
pyleoclim.utils.tsutils.detrend: detrending functionalities using 4 possible methods
pyleoclim.utils.tsutils.gaussianize_1d: Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.standardize: Centers and normalizes a given time series.

References

Torrence, C. and G. P. Compo, 1998: A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc., 79, 61-78. Python routines available at http://paos.colorado.edu/research/wavelets/

pyleoclim.utils.spectral.lomb_scargle(ys, ts, freq=None, freq_method='lomb_scargle', freq_kwargs=None, n50=3, window='hann', detrend=None, sg_kwargs=None, gaussianize=False, standardize=True, average='mean')[source]

Lomb-scargle priodogram

Appropriate for unevenly-spaced arrays. Uses the lomb-scargle implementation from scipy.signal: https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.lombscargle.html

Parameters:

ys (array) – a time series
ts (array) – time axis of the time series
freq (str or array) – vector of frequency. If string, uses the following method:
freq_method (str) –
Method to generate the frequency vector if not set directly. The following options are avialable:
- log
- lomb_scargle (default)
- welch
- scale
- nfft
See utils.wavelet.make_freq_vector for details
freq_kwargs (dict) – Arguments for the method chosen in freq_method. See specific functions in utils.wavelet for details By default, uses dt=median(ts), ofac=4 and hifac=1 for Lomb-Scargle
n50 (int) – The number of 50% overlapping segment to apply
window (str or tuple) –
Desired window to use. Possible values:
boxcar

triang

blackman

hamming

hann (default)

bartlett

flattop

parzen

bohman

blackmanharris

nuttail

barthann

kaiser (needs beta)

gaussian (needs standard deviation)

general_gaussian (needs power, width)

slepian (needs width)

dpss (needs normalized half-bandwidth)

chebwin (needs attenuation)

exponential (needs decay scale)

tukey (needs taper fraction)
If the window requires no parameters, then window can be a string. If the window requires parameters, then window must be a tuple with the first argument the string name of the window, and the next arguments the needed parameters. If window is a floating point number, it is interpreted as the beta parameter of the kaiser window.
detrendstr
If None, no detrending is applied. Available detrending methods:

None - no detrending will be applied (default);

linear - a linear least-squares fit to ys is subtracted;

constant - the mean of ys is subtracted

savitzy-golay - ys is filtered using the Savitzky-Golay filters and the resulting filtered series is subtracted from y.

emd - Empirical mode decomposition
sg_kwargsdict
The parameters for the Savitzky-Golay filters. see pyleoclim.utils.filter.savitzy_golay for details.

gaussianizebool
If True, gaussianizes the timeseries

standardizebool
If True, standardizes the timeseriesprep_args : dict

average{‘mean’,’median’}
Method to use when averaging periodograms. Defaults to ‘mean’.

Returns:

res_dict – the result dictionary, including - freq (array): the frequency vector - psd (array): the spectral density vector

Return type:

dict

See also

pyleoclim.utils.spectral.periodogram: Estimate power spectral density using a periodogram
pyleoclim.utils.spectral.mtm: Retuns spectral density using a multi-taper method
pyleoclim.utils.spectral.welch: Returns power spectral density using the Welch method
pyleoclim.utils.spectral.wwz_psd: Spectral estimation using the Weighted Wavelet Z-transform
pyleoclim.utils.spectral.cwt_psd: Spectral estimation using the Continuous Wavelet Transform
pyleoclim.utils.filter.savitzy_golay: Filtering using Savitzy-Golay
pyleoclim.utils.tsutils.detrend: detrending functionalities using 4 possible methods
pyleoclim.utils.tsutils.gaussianize_1d: Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.standardize: Centers and normalizes a given time series.

References

Lomb, N. R. (1976). Least-squares frequency analysis of unequally spaced data. Astrophysics and Space Science 39, 447-462.

Scargle, J. D. (1982). Studies in astronomical time series analysis. II. Statistical aspects of spectral analyis of unvenly spaced data. The Astrophysical Journal, 263(2), 835-853.

pyleoclim.utils.spectral.mtm(ys, ts, NW=None, BW=None, detrend=None, sg_kwargs=None, gaussianize=False, standardize=True, adaptive=False, jackknife=True, low_bias=True, sides='default', nfft=None)[source]

Spectral density using the multi-taper method.

If the NW product, or the BW and Fs in Hz are not specified by the user, a bandwidth of 4 times the fundamental frequency, corresponding to NW = 4 will be used.

Based on the nitime package: http://nipy.org/nitime/api/generated/nitime.algorithms.spectral.html

Parameters:

ys (array) – a time series
ts (array) – time axis of the time series
NW (float) – The time-bandwidth product NW governs the width (and therefore, height) of a peak, which can take the values [2, 5/2, 3, 7/2, 4]. This product controls the classical bias-variance tradeoff inherent to spectral estimation: a large product limits the variance but increases leakage out of harmonic line. In other words, small values of NW mean high spectral resolution, low bias, but high variance. Large values of the parameter mean lower resolution, higher bias, but reduced variance. There is no automated way to choose this parameter, and the default (NW=4) corresponds to a conservative choice with low variance. For a demonstration on the effect of this parameter, see the spectral analysis notebook in our tutorials: https://pyleoclim-util.readthedocs.io/en/master/tutorials.html.
BW (float) – The sampling-relative bandwidth of the data tapers
detrend (str) –
If None, no detrending is applied. Available detrending methods:
None - no detrending will be applied (default);

linear - a linear least-squares fit to ys is subtracted;

constant - the mean of ys is subtracted

savitzy-golay - ys is filtered using the Savitzky-Golay filters and the resulting filtered series is subtracted from y.

emd - Empirical mode decomposition
sg_kwargsdict
The parameters for the Savitzky-Golay filters. see pyleoclim.utils.filter.savitzy_golay for details.

gaussianizebool
If True, gaussianizes the timeseries

standardizebool
If True, standardizes the timeseries

adaptive{True/False}
Use an adaptive weighting routine to combine the PSD estimates of different tapers.

jackknife{True/False}
Use the jackknife method to make an estimate of the PSD variance at each point.

low_bias{True/False}
Rather than use 2NW tapers, only use the tapers that have better than 90% spectral concentration within the bandwidth (still using a maximum of 2NW tapers)

sidesstr (optional) [ ‘default’ | ‘onesided’ | ‘twosided’ ]
This determines which sides of the spectrum to return. For complex-valued inputs, the default is two-sided, for real-valued inputs, default is one-sided Indicates whether to return a one-sided or two-sided

Returns:

res_dict – the result dictionary, including - freq (array): the frequency vector - psd (array): the spectral density vector

Return type:

dict

See also

pyleoclim.utils.spectral.periodogram: Spectral density estimation using a Blackman-Tukey periodogram
pyleoclim.utils.spectral.welch: spectral estimation using Welch’s periodogram
pyleoclim.utils.spectral.lomb_scargle: Lomb-scargle priodogram
pyleoclim.utils.spectral.wwz_psd: Spectral estimation using the Weighted Wavelet Z-transform
pyleoclim.utils.spectral.cwt_psd: Spectral estimation using the Continuous Wavelet Transform
pyleoclim.utils.filter.savitzy_golay: Filtering using Savitzy-Golay
pyleoclim.utils.tsutils.detrend: detrending functionalities using 4 possible methods
pyleoclim.utils.tsutils.gaussianize_1d: Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.standardize: Centers and normalizes a given time series.

pyleoclim.utils.spectral.periodogram(ys, ts, window='hann', nfft=None, return_onesided=True, detrend=None, sg_kwargs=None, gaussianize=False, standardize=True, scaling='density')[source]

Spectral density estimation using a Blackman-Tukey periodogram

Based on the function from scipy: https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.periodogram.html

Parameters:

ys (array) – a time series
ts (array) – time axis of the time series
window (string or tuple) –
Desired window to use. Possible values:
boxcar (default)

triang

blackman

hamming

hann

bartlett

flattop

parzen

bohman

blackmanharris

nuttail

barthann

kaiser (needs beta)

gaussian (needs standard deviation)

general_gaussian (needs power, width)

slepian (needs width)

dpss (needs normalized half-bandwidth)

chebwin (needs attenuation)

exponential (needs decay scale)

tukey (needs taper fraction)
If the window requires no parameters, then window can be a string. If the window requires parameters, then window must be a tuple with the first argument the string name of the window, and the next arguments the needed parameters. If window is a floating point number, it is interpreted as the beta parameter of the kaiser window.
nfft: int
Length of the FFT used, if a zero padded FFT is desired. If None, the FFT length is nperseg

return_onesidedbool
If True, return a one-sided spectrum for real data. If False return a two-sided spectrum. Defaults to True, but for complex data, a two-sided spectrum is always returned.

detrendstr
If None, no detrending is applied. Available detrending methods:
None - no detrending will be applied (default);

linear - a linear least-squares fit to ys is subtracted;

constant - the mean of ys is subtracted

savitzy-golay - ys is filtered using the Savitzky-Golay filters and the resulting filtered series is subtracted from y.

emd - Empirical mode decomposition
sg_kwargsdict
The parameters for the Savitzky-Golay filters. see pyleoclim.utils.filter.savitzy_golay for details.

gaussianizebool
If True, gaussianizes the timeseries

standardizebool
If True, standardizes the timeseries

scaling{“density,”spectrum}
Selects between computing the power spectral density (‘density’) where Pxx has units of V**2/Hz and computing the power spectrum (‘spectrum’) where Pxx has units of V**2, if x is measured in V and fs is measured in Hz. Defaults to ‘density’

Returns:

res_dict – the result dictionary, including - freq (array): the frequency vector - psd (array): the spectral density vector

Return type:

dict

See also

pyleoclim.utils.spectral.welch: Estimate power spectral density using the welch method
pyleoclim.utils.spectral.mtm: Retuns spectral density using a multi-taper method
pyleoclim.utils.spectral.lomb_scargle: Return the computed periodogram using lomb-scargle algorithm
pyleoclim.utils.spectral.wwz_psd: Spectral estimation using the Weighted Wavelet Z-transform
pyleoclim.utils.spectral.cwt_psd: Spectral estimation using the Continuous Wavelet Transform
pyleoclim.utils.filter.savitzy_golay: Filtering using Savitzy-Golay
pyleoclim.utils.tsutils.detrend: detrending functionalities using 4 possible methods
pyleoclim.utils.tsutils.gaussianize_1d: Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.standardize: Centers and normalizes a given time series.

pyleoclim.utils.spectral.psd_ar(var_noise, freq, ar_params, f_sampling)[source]

Theoretical power spectral density (PSD) of an autoregressive model

Parameters:

var_noise (float) – the variance of the noise of the AR process
freq (array) – vector of frequency
ar_params (array) – autoregressive coefficients, not including zero-lag
f_sampling (float) – sampling frequency

Returns:

psd – power spectral density

Return type:

array

pyleoclim.utils.spectral.psd_fBM(freq, ts, H)[source]

Theoretical power spectral density of a fractional Brownian motion

Parameters:

freq (array) – vector of frequency
ts (array) – the time axis of the time series
H (float) – Hurst exponent, should be in (0, 1)

Returns:

psd – power spectral density

Return type:

array

References

Flandrin, P. On the spectrum of fractional Brownian motions. IEEE Transactions on Information Theory 35, 197–199 (1989).

pyleoclim.utils.spectral.welch(ys, ts, window='hann', nperseg=None, noverlap=None, nfft=None, return_onesided=True, detrend=None, sg_kwargs=None, gaussianize=False, standardize=True, scaling='density', average='mean')[source]

Estimate power spectral density using Welch’s periodogram

Wrapper for the function implemented in scipy.signal.welch See https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.welch.html for details.

Welch’s method is an approach for spectral density estimation. It computes an estimate of the power spectral density by dividing the data into overlapping segments, computing a modified periodogram for each segment and averaging the periodograms to lower the estimator’s variance.

Parameters:

ys (array) – a time series
ts (array) – time axis of the time series
window (string or tuple) –
Desired window to use. Possible values:
boxcar

triang

blackman

hamming

hann (default)

bartlett

flattop

parzen

bohman

blackmanharris

nuttail

barthann

kaiser (needs beta)

gaussian (needs standard deviation)

general_gaussian (needs power, width)

slepian (needs width)

dpss (needs normalized half-bandwidth)

chebwin (needs attenuation)

exponential (needs decay scale)

tukey (needs taper fraction)
If the window requires no parameters, then window can be a string. If the window requires parameters, then window must be a tuple with the first argument the string name of the window, and the next arguments the needed parameters. If window is a floating point number, it is interpreted as the beta parameter of the kaiser window.
npersegint
Length of each segment. If none, nperseg=len(ys)/2. Default to None This will give three segments with 50% overlap

noverlapint
Number of points to overlap. If None, noverlap=nperseg//2. Defaults to None, represents 50% overlap

nfft: int
Length of the FFT used, if a zero padded FFT is desired. If None, the FFT length is nperseg

return_onesidedbool
If True, return a one-sided spectrum for real data. If False return a two-sided spectrum. Defaults to True, but for complex data, a two-sided spectrum is always returned.

detrendstr
If None, no detrending is applied. Available detrending methods:
None - no detrending will be applied (default);

linear - a linear least-squares fit to ys is subtracted;

constant - the mean of ys is subtracted

savitzy-golay - ys is filtered using the Savitzky-Golay filters and the resulting filtered series is subtracted from y.

emd - Empirical mode decomposition
sg_kwargsdict
The parameters for the Savitzky-Golay filters. see pyleoclim.utils.filter.savitzy_golay for details.

gaussianizebool
If True, gaussianizes the timeseries

standardizebool
If True, standardizes the timeseries

scaling{“density,”spectrum}
Selects between computing the power spectral density (‘density’) where Pxx has units of V**2/Hz and computing the power spectrum (‘spectrum’) where Pxx has units of V**2, if x is measured in V and fs is measured in Hz. Defaults to ‘density’

average{‘mean’,’median’}
Method to use when combining periodograms. Defaults to ‘mean’.

Returns:

res_dict – the result dictionary, including - freq (array): the frequency vector - psd (array): the spectral density vector

Return type:

dict

See also

pyleoclim.utils.spectral.periodogram: Spectral density estimation using a Blackman-Tukey periodogram
pyleoclim.utils.spectral.mtm: Spectral density estimation using the multi-taper method
pyleoclim.utils.spectral.lomb_scargle: Lomb-scargle priodogram
pyleoclim.utils.spectral.wwz_psd: Spectral estimation using the Weighted Wavelet Z-transform
pyleoclim.utils.spectral.cwt_psd: Spectral estimation using the Continuous Wavelet Transform
pyleoclim.utils.filter.savitzy_golay: Filtering using Savitzy-Golay
pyleoclim.utils.tsutils.detrend: detrending functionalities using 4 possible methods
pyleoclim.utils.tsutils.gaussianize_1d: Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.standardize: Centers and normalizes a given time series.

References

Welch, “The use of the fast Fourier transform for the estimation of power spectra:
A method based on time averaging over short, modified periodograms”, IEEE Trans. Audio Electroacoust. vol. 15, pp. 70-73, 1967.

pyleoclim.utils.spectral.wwz_psd(ys, ts, freq=None, freq_method='log', freq_kwargs=None, tau=None, c=0.001, nproc=8, detrend=False, sg_kwargs=None, gaussianize=False, standardize=True, Neff_threshold=3, anti_alias=False, avgs=2, method='Kirchner_numba', wwa=None, wwz_Neffs=None, wwz_freq=None)[source]

Spectral estimation using the Weighted Wavelet Z-transform

The Weighted wavelet Z-transform (WWZ) is based on Morlet wavelet spectral estimation, using least squares minimization to suppress the energy leakage caused by data gaps. WWZ does not rely on interpolation or detrending, and is appropriate for unevenly-spaced datasets. In particular, we use the variant of Kirchner & Neal (2013), in which basis rotations mitigate the numerical instability that occurs in pathological cases with the original algorithm (Foster, 1996). The WWZ method has one adjustable parameter, a decay constant c that balances the time and frequency resolutions of the analysis. The smaller this constant is, the sharper the peaks. The default value is 1e-3 to obtain smooth spectra that lend themselves to better scaling exponent estimation, while still capturing the main periodicities.

Note that scalogram applications use the larger value (8π2)−1, justified elsewhere (Foster, 1996).

Parameters:

ys (array) – a time series, NaNs will be deleted automatically
ts (array) – the time points, if ys contains any NaNs, some of the time points will be deleted accordingly
freq (array) – vector of frequency
freq_method (str, {'log', 'lomb_scargle', 'welch', 'scale', 'nfft'}) –
Method to generate the frequency vector if not set directly. The following options are avialable:
- ’log’ (default)
- ’lomb_scargle’
- ’welch’
- ’scale’
- ’nfft’
See pyleoclim.utils.wavelet.make_freq_vector() for details
freq_kwargs (dict) – Arguments for the method chosen in freq_method. See specific functions in pyleoclim.utils.wavelet for details
tau (array) – the evenly-spaced time vector for the analysis, namely the time shift for wavelet analysis
c (float) – the decay constant that will determine the analytical resolution of frequency for analysis, the smaller the higher resolution; the default value 1e-3 is good for most of the spectral analysis cases
nproc (int) – the number of processes for multiprocessing
detrend (str, {None, 'linear', 'constant', 'savitzy-golay'}) –
available methods for detrending, including
- None: the original time series is assumed to have no trend;
- ’linear’: a linear least-squares fit to ys is subtracted;
- ’constant’: the mean of ys is subtracted
- ’savitzy-golay’: ys is filtered using the Savitzky-Golay filters and the resulting filtered series is subtracted from y.
sg_kwargs (dict) – The parameters for the Savitzky-Golay filters. See pyleoclim.utils.filter.savitzky_golay() for details.
gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries
method (string, {'Foster', 'Kirchner', 'Kirchner_f2py', 'Kirchner_numba'}) –
available specific implementation of WWZ, including
- ’Foster’: the original WWZ method;
- ’Kirchner’: the method Kirchner adapted from Foster;
- ’Kirchner_f2py’: the method Kirchner adapted from Foster, implemented with f2py for acceleration;
- ’Kirchner_numba’: the method Kirchner adapted from Foster, implemented with Numba for acceleration (default);
Neff_threshold (int) – threshold for the effective number of points
anti_alias (bool) – If True, uses anti-aliasing
avgs (int) – flag for whether spectrum is derived from instantaneous point measurements (avgs<>1) OR from measurements averaged over each sampling interval (avgs==1)
wwa (array) – the weighted wavelet amplitude, returned from pyleoclim.utils.wavelet.wwz
wwz_Neffs (array) – the matrix of effective number of points in the time-scale coordinates, returned from pyleoclim.utils.wavelet.wwz
wwz_freq (array) – the returned frequency vector from pyleoclim.utils.wavelet.wwz

Returns:

res – a namedtuple that includes below items

psdarray: power spectral density
freqarray: vector of frequency

Return type:

namedtuple

See also

pyleoclim.utils.spectral.periodogram: Estimate power spectral density using a periodogram
pyleoclim.utils.spectral.mtm: Retuns spectral density using a multi-taper method
pyleoclim.utils.spectral.lomb_scargle: Return the computed periodogram using lomb-scargle algorithm
pyleoclim.utils.spectral.welch: Estimate power spectral density using the Welch method
pyleoclim.utils.spectral.cwt_psd: Spectral estimation using the Continuous Wavelet Transform
pyleoclim.utils.filter.savitzy_golay: Filtering using Savitzy-Golay
pyleoclim.utils.tsutils.detrend: detrending functionalities using 4 possible methods
pyleoclim.utils.tsutils.gaussianize_1d: Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.standardize: Centers and normalizes a given time series.

References

Foster, G. (1996). Wavelets for period analysis of unevenly sampled time series. The Astronomical Journal, 112(4), 1709-1729.
Kirchner, J. W. (2005). Aliasin in 1/f^a noise spectra: origins, consequences, and remedies. Physical Review E covering statistical, nonlinear, biological, and soft matter physics, 71, 66110.
Kirchner, J. W. and Neal, C. (2013). Universal fractal scaling in stream chemistry and its impli-cations for solute transport and water quality trend detection. Proc Natl Acad Sci USA 110:12213–12218.

Tsmodel

Module for timeseries modeling

pyleoclim.utils.tsmodel.ar1_fit(y, t=None)[source]

Return lag-1 autocorrelation

Returns the lag-1 autocorrelation from AR(1) fit OR persistence from tauest.

Parameters:

y (array) – The time series
t (array) – The time axis of that series

Returns:

g – Lag-1 autocorrelation coefficient (for evenly-spaced time series) OR estimated persistence (for unevenly-spaced time series)

Return type:

float

See also

pyleoclim.utils.tsbase.is_evenly_spaced: Check if a time axis is evenly spaced, within a given tolerance
pyleoclim.utils.tsmodel.tau_estimation: Estimates the temporal decay scale of an (un)evenly spaced time series.

pyleoclim.utils.tsmodel.ar1_fit_evenly(y)[source]

Returns the lag-1 autocorrelation from AR(1) fit.

Uses [statsmodels.tsa.arima.model.ARIMA](https://www.statsmodels.org/devel/generated/statsmodels.tsa.arima.model.ARIMA.html) to calculate lag-1 autocorrelation

Parameters:: y (array) – Vector of (float) numbers as a time series
Returns:: g – Lag-1 autocorrelation coefficient
Return type:: float

pyleoclim.utils.tsmodel.ar1_model(t, tau, output_sigma=1)[source]

Simulate AR(1) process with REDFIT

Simulate a (possibly irregularly-sampled) AR(1) process with given decay constant tau, à la REDFIT.

Parameters:

t (array) – Time axis of the time series
tau (float) – The averaged persistence

Returns:

y – The AR(1) time series

Return type:

array

References

Schulz, M. & Mudelsee, M. REDFIT: estimating red-noise spectra directly from unevenly spaced: paleoclimatic time series. Computers & Geosciences 28, 421–426 (2002).

pyleoclim.utils.tsmodel.ar1_sim(y, p, t=None)[source]

Simulate AR(1) process(es) with sample autocorrelation value

Produce p realizations of an AR(1) process of length n with lag-1 autocorrelation g calculated from y and (if provided) t

Parameters:

y (array) – a time series; NaNs not allowed
p (int) – column dimension (number of surrogates)
t (array) – the time axis of the series

Returns:

ysim – n by p matrix of simulated AR(1) vector

Return type:

array

See also

pyleoclim.utils.tsmodel.ar1_model: Simulates a (possibly irregularly-sampled) AR(1) process with given decay constant tau, à la REDFIT.
pyleoclim.utils.tsmodel.ar1_fit: Returns the lag-1 autocorrelation from AR(1) fit OR persistence from tauest.
pyleoclim.utils.tsmodel.ar1_fit_evenly: Returns the lag-1 autocorrelation from AR(1) fit assuming even temporal spacing.
pyleoclim.utils.tsmodel.tau_estimation: Estimates the temporal decay scale of an (un)evenly spaced time series.

pyleoclim.utils.tsmodel.colored_noise(alpha, t, f0=None, m=None, seed=None)[source]

Generate a colored noise timeseries

Parameters:

alpha (float) – exponent of the 1/f^alpha noise
t (float) – time vector of the generated noise
f0 (float) – fundamental frequency
m (int) – maximum number of the waves, which determines the highest frequency of the components in the synthetic noise

Returns:

y – the generated 1/f^alpha noise

Return type:

array

See also

pyleoclim.utils.tsmodel.gen_ts: Generate pyleoclim.Series with timeseries models

References

Eq. (15) in Kirchner, J. W. Aliasing in 1/f(alpha) noise spectra: origins, consequences, and remedies.: Phys Rev E Stat Nonlin Soft Matter Phys 71, 066110 (2005).

pyleoclim.utils.tsmodel.colored_noise_2regimes(alpha1, alpha2, f_break, t, f0=None, m=None, seed=None)[source]

Generate a colored noise timeseries with two regimes

Parameters:

alpha1 (float) – the exponent of the 1/f^alpha noise
alpha2 (float) – the exponent of the 1/f^alpha noise
f_break (float) – the frequency where the scaling breaks
t (float) – time vector of the generated noise
f0 (float) – fundamental frequency
m (int) – maximum number of the waves, which determines the highest frequency of the components in the synthetic noise

Returns:

y – the generated 1/f^alpha noise

Return type:

array

See also

pyleoclim.utils.tsmodel.gen_ts: Generate pyleoclim.Series with timeseries models

References

Eq. (15) in Kirchner, J. W. Aliasing in 1/f(alpha) noise spectra: origins, consequences, and remedies.: Phys Rev E Stat Nonlin Soft Matter Phys 71, 066110 (2005).

pyleoclim.utils.tsmodel.gen_ar1_evenly(t, g, scale=1, burnin=50)[source]

Generate AR(1) series samples

Wrapper for the function [statsmodels.tsa.arima_process.arma_generate_sample](https://www.statsmodels.org/stable/generated/statsmodels.tsa.arima_process.arma_generate_sample.html) used to generate an ARMA

Parameters:

t (array) – the time axis
g (float) – lag-1 autocorrelation
scale (float) – The standard deviation of noise.
burnin (int) – Number of observation at the beginning of the sample to drop. Used to reduce dependence on initial values.

Returns:

y – the generated AR(1) series

Return type:

array

See also

pyleoclim.utils.tsmodel.gen_ts: Generate pyleoclim.Series with timeseries models

pyleoclim.utils.tsmodel.gen_ts(model, t=None, nt=1000, **kwargs)[source]

Generate pyleoclim.Series with timeseries models

Parameters:

model (str, {'colored_noise', 'colored_noise_2regimes', 'ar1'}) – the timeseries model to use - colored_noise : colored noise with one scaling slope - colored_noise_2regimes : colored noise with two regimes of two different scaling slopes - ar1 : AR(1) series
t (array) – the time axis
nt (number of time points) – only works if ‘t’ is None, and it will use an evenly-spaced vector with nt points
kwargs (dict) – the keyward arguments for the specified timeseries model

Returns:

t, v – time axis and values

Return type:

NumPy arrays

See also

pyleoclim.utils.tsmodel.colored_noise: Generate a colored noise timeseries
pyleoclim.utils.tsmodel.colored_noise_2regimes: Generate a colored noise timeseries with two regimes
pyleoclim.utils.tsmodel.gen_ar1_evenly: Generate an AR(1) series

pyleoclim.utils.tsmodel.tau_estimation(y, t)[source]

Estimates the temporal decay scale of an (un)evenly spaced time series.

Esimtates the temporal decay scale of an (un)evenly spaced time series. Uses [scipy.optimize.minimize_scalar](https://docs.scipy.org/doc/scipy/reference/optimize.minimize_scalar-bounded.html)

Parameters:

y (array) – A time series
t (array) – Time axis of the time series

Returns:

tau_est – The estimated persistence

Return type:

float

References

Mudelsee, M. TAUEST: A Computer Program for Estimating Persistence in Unevenly Spaced Weather/Climate Time Series.: Comput. Geosci. 28, 69–72 (2002).

Wavelet

Utilities for wavelet analysis, including Weighted Wavelet Z-transform (WWZ) and Continuous Wavelet Transform (CWT) à la Torrence & Compo 1998.

Includes multiple options for WWZ (Fortran via f2py, numba, multiprocessing) and enables cross-wavelet transform with either WWZ or CWT.

Designed for NumPy arrays, either evenly spaced or not (method-dependent)

class pyleoclim.utils.wavelet.AliasFilter[source]

Performing anti-alias filter on a psd

experimental: Use at your own risk

@author: fzhu

Methods

alias_filter(freq, pwr, fs, fc, f_limit, avgs)

The anti-aliasing filter

alias
misfit
model

alias_filter(freq, pwr, fs, fc, f_limit, avgs)[source]

The anti-aliasing filter

Parameters:

freq (array) – vector of frequencies in power spectrum
pwr (array) – vector of spectral power corresponding to frequencies “freq”
fs (float) – sampling frequency
fc (float) – corner frequency for 1/f^2 steepening of power spectrum
f_limit (float) – lower frequency limit for estimating misfit of model-plus-alias spectrum vs. measured power
avgs (int) – flag for whether spectrum is derived from instantaneous point measurements (avgs<>1) OR from measurements averaged over each sampling interval (avgs==1)

Returns:

alpha (float) – best-fit exponent of power-law model
filtered_pwr (array) – vector of alias-filtered spectral power
model_pwr (array) – vector of modeled spectral power
aliased_pwr (array) – vector of modeled spectral power, plus aliases

References

Kirchner, J. W. Aliasing in 1/f(alpha) noise spectra: origins, consequences, and remedies. Phys Rev E Stat Nonlin Soft Matter Phys 71, 66110 (2005).

pyleoclim.utils.wavelet.angle_sig(theta, nMC=1000, level=0.05)[source]

Calculates the mean angle and assesses the significance of its statistics.

In general, a consistent phase relationship will have low circular standard deviation (sigma <= sigma_lo) and high concentration (kappa >= kappa_hi).

Parameters:

theta (numpy.array) – array of phase angles
nMC (int) – number of Monte Carlo simulations to assess angle confidence interval if None, the simulation is not performed.
level (float) – significance level against which to gauge sigma and kappa. default: 0.05

Returns:

angle_mean (float) – mean angle
sigma (float) – circular standard deviation
kappa (float) – an estimate of the Von Mises distribution’s kappa parameter. kappa is a measure of concentration (a reciprocal measure of dispersion, so 1/kappa is analogous to the variance).
sigma_lo (float) – alpha-level quantile for sigma
kappa_hi (float) – (1-alpha)-level quantile for kappa

References

_[1] Grinsted, A., J. C. Moore, and S. Jevrejeva (2004), Application of the cross wavelet transform and wavelet coherence to geophysical time series, Nonlinear Processes in Geophysics, 11, 561–566.

_[2] Huber, R., Dutra, L. V., & da Costa Freitas, C. (2001, July). SAR interferogram phase filtering based on the Von Mises distribution. In IGARSS 2001. Scanning the Present and Resolving the Future. Proceedings. IEEE 2001 International Geoscience and Remote Sensing Symposium (Cat. No. 01CH37217) (Vol. 6, pp. 2816-2818). IEEE.

See also

pyleoclim.utils.wavelet.angle_stats: phase angle statistics

pyleoclim.utils.wavelet.angle_stats(theta)[source]

Statistics of a phase angle

Parameters:

theta (numpy.array) – array of phase angles

Returns:

mean_theta (float) – mean angle
sigma (float) – circular standard deviation
kappa (float) – an estimate of the Von Mises distribution’s kappa parameter

References

_[1] Huber, R., Dutra, L. V., & da Costa Freitas, C. (2001, July). SAR interferogram phase filtering based on the Von Mises distribution. In IGARSS 2001. Scanning the Present and Resolving the Future. Proceedings. IEEE 2001 International Geoscience and Remote Sensing Symposium (Cat. No. 01CH37217) (Vol. 6, pp. 2816-2818). IEEE.

See also

pyleoclim.utils.wavelet.angle_sig: significance of phase angle statistics

pyleoclim.utils.wavelet.assertPositiveInt(*args)[source]

Assert that the arguments are all integers larger than unity

Parameters:: args –

pyleoclim.utils.wavelet.chisquare_inv(P, V)[source]

Returns the inverse of chi-square CDF with V degrees of freedom at fraction P

Parameters:

P (float) – fraction
V (float) – degress of freedom

Returns:

X – Inverse chi-square

Return type:

float

References

Torrence, C. and G. P. Compo, 1998: A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc., 79, 61-78. Python routines available at http://paos.colorado.edu/research/wavelets/

pyleoclim.utils.wavelet.chisquare_solve(XGUESS, P, V)[source]

Given XGUESS, a percentile P, and degrees-of-freedom V, return the difference between calculated percentile and P.

Parameters:

XGUESS (float) – sig level
P (float) – percentile
V (float) – degrees of freedom

Returns:

PDIFF – difference between calculated percentile and P

Return type:

float

References

Torrence, C. and G. P. Compo, 1998: A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc., 79, 61-78. Python routines available at http://paos.colorado.edu/research/wavelets/

pyleoclim.utils.wavelet.cwt(ys, ts, freq=None, freq_method='log', freq_kwargs={}, scale=None, detrend=False, sg_kwargs={}, gaussianize=False, standardize=True, pad=False, mother='MORLET', param=None)[source]

Wrapper function to implement Torrence and Compo continuous wavelet transform

Parameters:

ys (numpy.array) – the time series.
ts (numpy.array) – the time axis.
freq (numpy.array, optional) – The frequency vector. The default is None, which will prompt the use of one the underlying functions
freq_method (string, optional) – The method by which to obtain the frequency vector. The default is ‘log’. Options are ‘log’ (default), ‘nfft’, ‘lomb_scargle’, ‘welch’, and ‘scale’
freq_kwargs (dict, optional) – Optional parameters for the choice of the frequency vector. See make_freq_vector and additional methods for details. The default is {}.
scale (numpy.array) – Optional scale vector in place of a frequency vector. Default is None. If scale is not None, frequency method and attached arguments will be ignored.
detrend (bool, string, {'linear', 'constant', 'savitzy-golay', 'emd'}) – Whether to detrend and with which option. The default is False.
sg_kwargs (dict, optional) – Additional parameters for the savitzy-golay method. The default is {}.
gaussianize (bool, optional) – Whether to gaussianize. The default is False.
standardize (bool, optional) – Whether to standardize. The default is True.
pad (bool, optional) – Whether or not to pad the timeseries. with zeroes to get N up to the next higher power of 2. This prevents wraparound from the end of the time series to the beginning, and also speeds up the FFT’s used to do the wavelet transform. This will not eliminate all edge effects. The default is False.
mother (string, optional) – the mother wavelet function. The default is ‘MORLET’. Options are: ‘MORLET’, ‘PAUL’, or ‘DOG’
param (flaot, optional) –
the mother wavelet parameter. The default is None since it varies for each mother
- For ‘MORLET’ this is k0 (wavenumber), default is 6.
- For ‘PAUL’ this is m (order), default is 4.
- For ‘DOG’ this is m (m-th derivative), default is 2.

Returns:

res –

Dictionary containing:

amplitude: the wavelet amplitude
coi: cone of influence
freq: frequency vector
coeff: the wavelet coefficients
scale: the scale vector
time: the time vector
mother: the mother wavelet
param : the wavelet parameter

Return type:

dict

See also

pyleoclim.utils.wavelet.make_freq_vector: make the frequency vector with various methods
pyleoclim.utils.wavelet.tc_wavelet: the underlying wavelet function by Torrence and Compo
pyleoclim.utils.tsutils.detrend: detrending functionalities
pyleoclim.utils.tsutils.gaussianize_1d: Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.preprocess: pre-processes a times series using Gaussianization and detrending.

References

Torrence, C. and G. P. Compo, 1998: A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc., 79, 61-78. Python routines available at http://paos.colorado.edu/research/wavelets/

pyleoclim.utils.wavelet.cwt_coherence(ys1, ts1, ys2, ts2, freq=None, freq_method='log', freq_kwargs={}, scale=None, detrend=False, sg_kwargs={}, pad=False, standardize=True, gaussianize=False, tau=None, Neff_threshold=3, mother='MORLET', param=None, smooth_factor=0.25)[source]

Returns the wavelet transform coherency of two time series using the CWT.

Parameters:

ys1 (array) – first of two time series
ys2 (array) – second of the two time series
ts1 (array) – time axis of first time series
ts2 (array) – time axis of the second time series (should be = ts1)
tau (array) – evenly-spaced time points at which to evaluate coherence Defaults to None, which uses ts1
freq (array) – vector of frequency
freq_method (string, optional) – The method by which to obtain the frequency vector. The default is ‘log’. Options are ‘log’ (default), ‘nfft’, ‘lomb_scargle’, ‘welch’, and ‘scale’
freq_kwargs (dict, optional) – Optional parameters for the choice of the frequency vector. See make_freq_vector and additional methods for details. The default is {}.
scale (numpy.array) – Optional scale vector in place of a frequency vector. Default is None. If scale is not None, frequency method and attached arguments will be ignored.
detrend (bool, string, {'linear', 'constant', 'savitzy-golay', 'emd'}) – Whether to detrend and with which option. The default is False.
sg_kwargs (dict, optional) – Additional parameters for the savitzy-golay method. The default is {}.
gaussianize (bool, optional) – Whether to gaussianize. The default is False.
standardize (bool, optional) – Whether to standardize. The default is True.
pad (bool, optional) – Whether or not to pad the timeseries with zeroes to increase N to the next higher power of 2. This prevents wraparound from the end of the time series to the beginning, and also speeds up the FFT used to do the wavelet transform. This will not eliminate all edge effects. The default is False.
mother (string, optional) – the mother wavelet function. The default is ‘MORLET’. Options are: ‘MORLET’, ‘PAUL’, or ‘DOG’
param (flaot, optional) –
the mother wavelet parameter. The default is None since it varies for each mother
- For ‘MORLET’ this is k0 (wavenumber), default is 6.
- For ‘PAUL’ this is m (order), default is 4.
- For ‘DOG’ this is m (m-th derivative), default is 2.
smooth_factor (float) – smoothing factor for the WTC (default: 0.25)
Neff_threshold (int) – threshold for the effective number of points (3 by default, see make_coi())

Returns:

res – contains the cross wavelet coherence (WTC), cross-wavelet transform (XWT), cross-wavelet phase, vector of frequency, evenly-spaced time points, nMC AR1 scalograms, cone of influence.

Return type:

dict

References

Grinsted, A., J. C. Moore, and S. Jevrejeva (2004), Application of the cross wavelet transform and wavelet coherence to geophysical time series, Nonlinear Processes in Geophysics, 11, 561–566.

See also

pyleoclim.utils.wavelet.cwt: Continuous Wavelet Transform (Torrence & Compo 1998)
pyleoclim.utils.filter.savitzky_golay: Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
pyleoclim.utils.wavelet.make_freq_vector: Makes frequency vector
pyleoclim.utils.tsutils.gaussianize_1d: Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.detrend: detrending functionalities
pyleoclim.utils.tsutils.preprocess: pre-processes a times series using Gaussianization and detrending.

pyleoclim.utils.wavelet.freq_vector_log(ts, nfreq=None)[source]

Return the frequency vector based on logspace

Parameters:

ts (array) – time axis of the time series
nv (int) – the parameter that controls the number of freq points

Returns:

freq – the frequency vector

Return type:

array

See also

pyleoclim.utils.wavelet.freq_vector_lomb_scargle: Return the frequency vector based on the REDFIT recommendation.
pyleoclim.utils.wavelet.freq_vector_welch: Return the frequency vector based on the Welch’s method.
pyleoclim.utils.wavelet.freq_vector_nfft: Return the frequency vector based on NFFT
pyleoclim.utils.wavelet.freq_vector_scale: Return the frequency vector based on scales
pyleoclim.utils.wavelet.make_freq_vector: Make frequency vector

pyleoclim.utils.wavelet.freq_vector_lomb_scargle(ts, dt=None, nf=None, ofac=4, hifac=1)[source]

Return the frequency vector based on the REDFIT recommendation.

Parameters:

ts (array) – time axis of the time series
dt (float) – The resolution of the data. If None, uses the median resolution. Defaults to None.
nf (int) – Number of frequency points. If None, calculated as the difference between the highest and lowest frequencies (set by hifac and ofac) divided by resolution. Defaults to None
ofac (float) –

Oversampling rate that influences the resolution of the frequency axis,
when equals to 1, it means no oversamling (should be >= 1). The default value 4 is usually a good value.
hifac (float) – fhi/fnyq (should be <= 1), where fhi is the highest frequency that can be analyzed by the Lomb-Scargle algorithm and fnyq is the Nyquist frequency.

Returns:

freq – the frequency vector

Return type:

array

References

Trauth, M. H. MATLAB® Recipes for Earth Sciences. (Springer, 2015). pp 181.

See also

pyleoclim.utils.wavelet.freq_vector_welch: Return the frequency vector based on the Welch’s method.
pyleoclim.utils.wavelet.freq_vector_nfft: Return the frequency vector based on NFFT
pyleoclim.utils.wavelet.freq_vector_scale: Return the frequency vector based on scales
pyleoclim.utils.wavelet.freq_vector_log: Return the frequency vector based on logspace
pyleoclim.utils.wavelet.make_freq_vector: Make frequency vector

pyleoclim.utils.wavelet.freq_vector_nfft(ts)[source]

Return the frequency vector based on NFFT

Parameters:: ts (array) – time axis of the time series
Returns:: freq – the frequency vector
Return type:: array

See also

pyleoclim.utils.wavelet.freq_vector_lomb_scargle: Return the frequency vector based on the REDFIT recommendation.
pyleoclim.utils.wavelet.freq_vector_welch: Return the frequency vector based on the Welch’s method.
pyleoclim.utils.wavelet.freq_vector_scale: Return the frequency vector based on scales
pyleoclim.utils.wavelet.freq_vector_log: Return the frequency vector based on logspace
pyleoclim.utils.wavelet.make_freq_vector: Make frequency vector

pyleoclim.utils.wavelet.freq_vector_scale(ts, dj=0.25, s0=None, j1=None, mother='MORLET', param=None)[source]

Return the frequency vector based on scales for wavelet analysis. This function is adapted from Torrence and Compo

Parameters:

ts (numpy.array) – The time axis for the timeseries
dj (float, optional) – The spacing between discrete scales. The default is 0.25. A smaller number will give better scale resolution, but be slower to plot.
s0 (float, optional) – the smallest scale of the wavelet. The default is None, representing 2*dT.
j1 (float, optional) – the number of scales minus one. Scales range from S0 up to S0*2**(J1*DJ), to give a total of (J1+1) scales. The default is None, which represents (LOG2(N DT/S0))/DJ.
mother (string, optional) – the mother wavelet function. The default is ‘MORLET’. Options are: ‘MORLET’, ‘PAUL’, or ‘DOG’
param (flaot, optional) –
the mother wavelet parameter. The default is None since it varies for each mother
- For ‘MORLET’ this is k0 (wavenumber), default is 6.
- For ‘PAUL’ this is m (order), default is 4.
- For ‘DOG’ this is m (m-th derivative), default is 2.

Returns:

freq – the frequency vector

Return type:

array

See also

pyleoclim.utils.wavelet.freq_vector_lomb_scargle: Return the frequency vector based on the REDFIT recommendation.
pyleoclim.utils.wavelet.freq_vector_welch: Return the frequency vector based on the Welch’s method.
pyleoclim.utils.wavelet.freq_vector_nfft: Return the frequency vector based on NFFT
pyleoclim.utils.wavelet.freq_vector_log: Return the frequency vector based on logspace
pyleoclim.utils.wavelet.make_freq_vector: Make frequency vector

References

Torrence, C. and G. P. Compo, 1998: A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc., 79, 61-78. Python routines available at http://paos.colorado.edu/research/wavelets/

pyleoclim.utils.wavelet.freq_vector_welch(ts)[source]

Return the frequency vector based on Welch’s method.

Parameters:: ts (array) – time axis of the time series
Returns:: freq – the frequency vector
Return type:: array

References

https://github.com/scipy/scipy/blob/v0.14.0/scipy/signal/Spectral.py

See also

pyleoclim.utils.wavelet.freq_vector_lomb_scargle: Return the frequency vector based on the REDFIT recommendation.
pyleoclim.utils.wavelet.freq_vector_nfft: Return the frequency vector based on NFFT
pyleoclim.utils.wavelet.freq_vector_scale: Return the frequency vector based on scales
pyleoclim.utils.wavelet.freq_vector_log: Return the frequency vector based on logspace
pyleoclim.utils.wavelet.make_freq_vector: Make frequency vector

pyleoclim.utils.wavelet.get_wwz_func(nproc, method)[source]

Return the wwz function to use.

Parameters:

nproc (int) – the number of processes for multiprocessing
method (string) – ‘Foster’ - the original WWZ method; ‘Kirchner’ - the method Kirchner adapted from Foster; ‘Kirchner_f2py’ - the method Kirchner adapted from Foster with f2py ‘Kirchner_numba’ - Kirchner’s algorithm with Numba support for acceleration (default)

Returns:

wwz_func – the wwz function to use

Return type:

function

pyleoclim.utils.wavelet.kirchner_basic(ys, ts, freq, tau, c=0.012665147955292222, Neff_threshold=3, nproc=1, detrend=False, sg_kwargs=None, gaussianize=False, standardize=False)[source]

Return the weighted wavelet amplitude (WWA) modified by Kirchner.

Method modified by Kirchner. No multiprocessing.

Parameters:

ys (array) – a time series
ts (array) – time axis of the time series
freq (array) – vector of frequency
tau (array) – the evenly-spaced time points, namely the time shift for wavelet analysis
c (float) – the decay constant that determines the analytical resolution of frequency for analysis, the smaller the higher resolution; the default value 1/(8*np.pi**2) is good for most of the wavelet analysis cases
Neff_threshold (int) – the threshold of the number of effective degrees of freedom
nproc (int) – fake argument for convenience, for parameter consistency between functions, does not need to be specified
detrend (string) – None - the original time series is assumed to have no trend; Types of detrending: - “linear” : the result of a linear least-squares fit to y is subtracted from y. - “constant” : only the mean of data is subtracted. - “savitzky-golay” : y is filtered using the Savitzky-Golay filter and the resulting filtered series is subtracted from y. - “emd” : Empirical mode decomposition. The last mode is assumed to be the trend and removed from the series
sg_kwargs (dict) – The parameters for the Savitzky-Golay filter. see pyleoclim.utils.filter.savitzy_golay for details.
gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries

Returns:

wwa (array) – the weighted wavelet amplitude
phase (array) – the weighted wavelet phase
Neffs (array) – the matrix of effective number of points in the time-scale coordinates
coeff (array) – the wavelet transform coefficients (a0, a1, a2)

References

Foster, G. Wavelets for period analysis of unevenly sampled time series. The Astronomical Journal 112, 1709 (1996).
Witt, A. & Schumann, A. Y. Holocene climate variability on millennial scales recorded in Greenland ice cores.

Nonlinear Processes in Geophysics 12, 345–352 (2005).

See also

pyleoclim.utils.wavelet.wwz_basic: Returns the weighted wavelet amplitude using the original method from Kirchner. No multiprocessing
pyleoclim.utils.wavelet.wwz_nproc: Returns the weighted wavelet amplitude using the original method from Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_nproc: Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_numba: Return the weighted wavelet amplitude (WWA) modified by Kirchner using Numba package.
pyleoclim.utils.wavelet.kirchner_f2py: Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Uses Fortran. Fastest method but requires a compiler.
pyleoclim.utils.filter.savitzky_golay: Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
pyleoclim.utils.tsutils.preprocess: pre-processes a times series using Gaussianization and detrending.
pyleoclim.utils.tsutils.detrend: detrending functionalities
pyleoclim.utils.tsutils.gaussianize_1d: Quantile maps a 1D array to a Gaussian distribution

pyleoclim.utils.wavelet.kirchner_f2py(ys, ts, freq, tau, c=0.012665147955292222, Neff_threshold=3, nproc=8, detrend=False, sg_kwargs=None, gaussianize=False, standardize=False)[source]

Returns the weighted wavelet amplitude (WWA) modified by Kirchner.

Fastest method. Calls Fortran libraries.

Parameters:

ys (array) – a time series
ts (array) – time axis of the time series
freq (array) – vector of frequency
tau (array) – the evenly-spaced time points, namely the time shift for wavelet analysis
c (float) – the decay constant that determines the analytical resolution of frequency for analysis, the smaller the higher resolution; the default value 1/(8*np.pi**2) is good for most of the wavelet analysis cases
Neff_threshold (int) – the threshold of the number of effective degrees of freedom
nproc (int) – fake argument, just for convenience
detrend (string) – None - the original time series is assumed to have no trend; Types of detrending: - “linear” : the result of a linear least-squares fit to y is subtracted from y. - “constant” : only the mean of data is subtracted. - “savitzky-golay” : y is filtered using the Savitzky-Golay filter and the resulting filtered series is subtracted from y. - “emd” : Empirical mode decomposition. The last mode is assumed to be the trend and removed from the series
sg_kwargs (dict) – The parameters for the Savitzky-Golay filter. see pyleoclim.utils.filter.savitzy_golay for details.
gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries

Returns:

wwa (array) – the weighted wavelet amplitude
phase (array) – the weighted wavelet phase
Neffs (array) – the matrix of effective number of points in the time-scale coordinates
coeff (array) – the wavelet transform coefficients (a0, a1, a2)

See also

pyleoclim.utils.wavelet.wwz_basic: Returns the weighted wavelet amplitude using the original method from Kirchner. No multiprocessing
pyleoclim.utils.wavelet.wwz_nproc: Returns the weighted wavelet amplitude using the original method from Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_basic: Return the weighted wavelet amplitude (WWA) modified by Kirchner. No multiprocessing
pyleoclim.utils.wavelet.kirchner_nproc: Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_numba: Return the weighted wavelet amplitude (WWA) modified by Kirchner using Numba package.
pyleoclim.utils.filter.savitzky_golay: Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
pyleoclim.utils.tsutils.preprocess: pre-processes a times series using Gaussianization and detrending.
pyleoclim.utils.tsutils.detrend: detrending functionalities
pyleoclim.utils.tsutils.gaussianize_1d: Quantile maps a 1D array to a Gaussian distribution

pyleoclim.utils.wavelet.kirchner_nproc(ys, ts, freq, tau, c=0.012665147955292222, Neff_threshold=3, nproc=8, detrend=False, sg_kwargs=None, gaussianize=False, standardize=False)[source]

Return the weighted wavelet amplitude (WWA) modified by Kirchner.

Method modified by kirchner. Supports multiprocessing.

Parameters:

ys (array) – a time series
ts (array) – time axis of the time series
freq (array) – vector of frequency
tau (array) – the evenly-spaced time points, namely the time shift for wavelet analysis
c (float) – the decay constant that determines the analytical resolution of frequency for analysis, the smaller the higher resolution; the default value 1/(8*np.pi**2) is good for most of the wavelet analysis cases
Neff_threshold (int) – the threshold of the number of effective degrees of freedom
nproc (int) – the number of processes for multiprocessing
detrend (string) – Types of detrending: - “linear” : the result of a linear least-squares fit to y is subtracted from y. - “constant” : only the mean of data is subtracted. - “savitzky-golay” : y is filtered using the Savitzky-Golay filter and the resulting filtered series is subtracted from y. - “emd” : Empirical mode decomposition. The last mode is assumed to be the trend and removed from the series
sg_kwargs (dict) – The parameters for the Savitzky-Golay filter. see pyleoclim.utils.filter.savitzy_golay for details.
gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries

Returns:

wwa (array) (the weighted wavelet amplitude)
phase (array) (the weighted wavelet phase)
Neffs (array) (the matrix of effective number of points in the time-scale coordinates)
coeff (array) (the wavelet transform coefficients (a0, a1, a2))

See also

pyleoclim.utils.wavelet.wwz_basic: Returns the weighted wavelet amplitude using the original method from Kirchner. No multiprocessing
pyleoclim.utils.wavelet.wwz_nproc: Returns the weighted wavelet amplitude using the original method from Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_basic: Return the weighted wavelet amplitude (WWA) modified by Kirchner. No multiprocessing
pyleoclim.utils.wavelet.kirchner_numba: Return the weighted wavelet amplitude (WWA) modified by Kirchner using Numba package.
pyleoclim.utils.wavelet.kirchner_f2py: Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Uses Fortran. Fastest method but requires a compiler.
pyleoclim.utils.filter.savitzky_golay: Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
pyleoclim.utils.tsutils.preprocess: pre-processes a times series using Gaussianization and detrending.
pyleoclim.utils.tsutils.detrend: detrending functionalities
pyleoclim.utils.tsutils.gaussianize_1d: Quantile maps a 1D array to a Gaussian distribution

pyleoclim.utils.wavelet.kirchner_numba(ys, ts, freq, tau, c=0.012665147955292222, Neff_threshold=3, detrend=False, sg_kwargs=None, gaussianize=False, standardize=False, nproc=1)[source]

Return the weighted wavelet amplitude (WWA) modified by Kirchner.

Using numba.

Parameters:

ys (array) – a time series
ts (array) – time axis of the time series
freq (array) – vector of frequency
tau (array) – the evenly-spaced time points, namely the time shift for wavelet analysis
c (float) – the decay constant that determines the analytical resolution of frequency for analysis, the smaller the higher resolution; the default value 1/(8*np.pi**2) is good for most of the wavelet analysis cases
Neff_threshold (int) – the threshold of the number of effective degrees of freedom
nproc (int) – fake argument, just for convenience
detrend (string) – None - the original time series is assumed to have no trend; Types of detrending: - “linear” : the result of a linear least-squares fit to y is subtracted from y. - “constant” : only the mean of data is subtracted. - “savitzky-golay” : y is filtered using the Savitzky-Golay filter and the resulting filtered series is subtracted from y. - “emd” : Empirical mode decomposition. The last mode is assumed to be the trend and removed from the series
sg_kwargs (dict) – The parameters for the Savitzky-Golay filter. see pyleoclim.utils.filter.savitzy_golay for details.
gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries

Returns:

wwa (array) – the weighted wavelet amplitude
phase (array) – the weighted wavelet phase
Neffs (array) – the matrix of effective number of points in the time-scale coordinates
coeff (array) – the wavelet transform coefficients (a0, a1, a2)

References

Foster, G. Wavelets for period analysis of unevenly sampled time series. The Astronomical Journal 112, 1709 (1996). Witt, A. & Schumann, A. Y. Holocene climate variability on millennial scales recorded in Greenland ice cores. Nonlinear Processes in Geophysics 12, 345–352 (2005).

See also

pyleoclim.utils.wavelet.wwz_basic: Returns the weighted wavelet amplitude using the original method from Kirchner. No multiprocessing
pyleoclim.utils.wavelet.wwz_nproc: Returns the weighted wavelet amplitude using the original method from Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_basic: Return the weighted wavelet amplitude (WWA) modified by Kirchner. No multiprocessing
pyleoclim.utils.wavelet.kirchner_nproc: Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_f2py: Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Uses Fortran. Fastest method but requires a compiler.
pyleoclim.utils.filter.savitzky_golay: Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
pyleoclim.utils.tsutils.preprocess: pre-processes a times series using Gaussianization and detrending.
pyleoclim.utils.tsutils.detrend: detrending functionalities
pyleoclim.utils.tsutils.gaussianize_1d: Quantile maps a 1D array to a Gaussian distribution

pyleoclim.utils.wavelet.make_coi(tau, Neff_threshold=3)[source]

Return the cone of influence.

Parameters:

tau (array) – the evenly-spaced time points, namely the time shift for wavelet analysis
Neff_threshold (int) – the threshold of the number of effective samples (default: 3)

Returns:

coi – cone of influence

Return type:

array

References

wave_signif() in http://paos.colorado.edu/research/wavelets/wave_python/waveletFunctions.py

pyleoclim.utils.wavelet.make_freq_vector(ts, method='log', **kwargs)[source]

Make frequency vector

This function selects among five methods to obtain the frequency vector.

Parameters:

ts (array) – Time axis of the time series
method (string) – The method to use. Options are ‘log’ (default), ‘nfft’, ‘lomb_scargle’, ‘welch’, and ‘scale’
kwargs (dict, optional) –
For Lomb_Scargle, additional parameters may be passed: - nf (int): number of frequency points - ofac (float): Oversampling rate that influences the resolution of the frequency axis,

when equals to 1, it means no oversamling (should be >= 1). The default value 4 is usaually a good value.
- hifac (float): fhi/fnyq (should be >= 1), where fhi is the highest frequency that
  can be analyzed by the Lomb-Scargle algorithm and fnyq is the Nyquist frequency.

Returns:

freq – the frequency vector

Return type:

array

See also

pyleoclim.utils.wavelet.freq_vector_lomb_scargle: Return the frequency vector based on the REDFIT recommendation.
pyleoclim.utils.wavelet.freq_vector_welch: Return the frequency vector based on the Welch’s method.
pyleoclim.utils.wavelet.freq_vector_nfft: Return the frequency vector based on NFFT
pyleoclim.utils.wavelet.freq_vector_scale: Return the frequency vector based on scales
pyleoclim.utils.wavelet.freq_vector_log: Return the frequency vector based on logspace

pyleoclim.utils.wavelet.make_omega(ts, freq)[source]

Return the angular frequency based on the time axis and given frequency vector

Parameters:

ys (array) – a time series
ts (array) – time axis of the time series
freq (array) – vector of frequency

Returns:

omega – the angular frequency vector

Return type:

array

pyleoclim.utils.wavelet.prepare_wwz(ys, ts, freq=None, freq_method='log', freq_kwargs=None, tau=None, len_bd=0, bc_mode='reflect', reflect_type='odd', **kwargs)[source]

Return the truncated time series with NaNs deleted and estimate frequency vector and tau

Parameters:

ys (array) – a time series, NaNs will be deleted automatically
ts (array) – the time points, if ys contains any NaNs, some of the time points will be deleted accordingly
freq (array) – vector of frequency. If None, will be generated according to freq_method. may be set.
freq_method (str) – when freq=None, freq will be ganerated according to freq_method
freq_kwargs (str) – used when freq=None for certain methods
tau (array) – The evenly-spaced time points, namely the time shift for wavelet analysis. If the boundaries of tau are not exactly on two of the time axis points, then tau will be adjusted to be so. If None, at most 50 tau points will be generated from the input time span.
len_bd (int) – the number of the ghost grid points desired on each boundary
bc_mode (string) – {‘constant’, ‘edge’, ‘linear_ramp’, ‘maximum’, ‘mean’, ‘median’, ‘minimum’, ‘reflect’ , ‘symmetric’, ‘wrap’} For more details, see np.lib.pad()
reflect_type (string) – {‘even’, ‘odd’}, optional Used in ‘reflect’, and ‘symmetric’. The ‘even’ style is the default with an unaltered reflection around the edge value. For the ‘odd’ style, the extented part of the array is created by subtracting the reflected values from two times the edge value. For more details, see np.lib.pad()

Returns:

ys_cut (array) – the truncated time series with NaNs deleted
ts_cut (array) – the truncated time axis of the original time series with NaNs deleted
freq (array) – vector of frequency
tau (array) – the evenly-spaced time points, namely the time shift for wavelet analysis

pyleoclim.utils.wavelet.tc_wave_bases(mother, k, scale, param)[source]

WAVE_BASES 1D Wavelet functions Morlet, Paul, or DOG

Parameters:

mother (string) – equal to ‘MORLET’ or ‘PAUL’ or ‘DOG’
k (numpy.array) – the Fourier frequencies at which to calculate the wavelet
scale (float) – The wavelet scale
param (float) – the nondimensional parameter for the wavelet function

Returns:

daughter (numpy.array) – a vector, the wavelet function
fourier_factor (float) – the ratio of Fourier period to scale
coi (float) – the cone-of-influence size at the scale
dofmin (float) –

degrees of freedom for each point in the wavelet power
(either 2 for Morlet and Paul, or 1 for the DOG)

References

Torrence, C. and G. P. Compo, 1998: A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc., 79, 61-78. Python routines available at http://paos.colorado.edu/research/wavelets/

pyleoclim.utils.wavelet.tc_wave_signif(ys, ts, scale, mother, param, sigtest='chi-square', qs=[0.95], dof=None, gws=None)[source]

Asymptotic singificance testing.

Parameters:

ys (numpy.array) – Values for the timeseries
ts (numpy.array) – time vector.
scale (numpy.array) – vector of scale
mother (str) – Type of mother wavelet
param (int) – mother wavelet parameter
sigtest ({'chi-square','time-average','scale-average'}, optional) –
Type of significance test to perform . The default is ‘chi-square’. - chi-square: a regular chi-square test Eq(18) from Torrence and Compo - time-average: DOF should be set to NA, the number of local wavelet spectra that were averaged together.

For the Global Wavelet Spectrum, this would be NA=N, where N is the number of points in your time series. Eq23 in Torrence and Compo

-scale-average: In this case, DOF should be set to a two-element vector [S1,S2], which gives the scale range that was averaged together.
e.g. if one scale-averaged scales between 2 and 8, then DOF=[2,8].
qs (list, optional) – Significance level. The default is [0.95].
dof (None, optional) –
Degrees of freedon for signif test. The default is None, which will automatically assign:
- chi-square: DOF = 2 (or 1 for MOTHER=’DOG’)
- time-average: DOF = NA, the number of times averaged together.
-scale-average: DOF = [S1,S2], the range of scales averaged.
gws (np.array, optional) – Global wavelet spectrum. a vector of the same length as scale. If input then this is used as the theoretical background spectrum, rather than white or red noise. The default is None.

Returns:

signif_level – Array of values for significance level

Return type:

numpy.array

References

Torrence, C. and G. P. Compo, 1998: A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc., 79, 61-78. Python routines available at http://paos.colorado.edu/research/wavelets/

See also

pyleoclim.utils.wavelet.chisquare_inv: inverse of chi-square CDF
pyleoclim.utils.wavelet.chisquare_solve: return the difference between calculated percentile and true P

pyleoclim.utils.wavelet.tc_wavelet(Y, dt, scale, mother, param, pad=False)[source]

WAVELET 1D Wavelet transform. Adapted from Torrence and Compo to fit existing Pyleoclim functionalities

Computes the wavelet transform of the vector Y (length N), with sampling rate DT.

By default, the Morlet wavelet (k0=6) is used. The wavelet basis is normalized to have total energy=1 at all scales.

Parameters:

Y (numpy.array) – the time series of length N.
dt (float) – the sampling time
mother (string, optional) – the mother wavelet function. The default is ‘MORLET’. Options are: ‘MORLET’, ‘PAUL’, or ‘DOG’
param (flaot, optional) –
the mother wavelet parameter. The default is None since it varies for each mother
- For ‘MORLET’ this is k0 (wavenumber), default is 6.
- For ‘PAUL’ this is m (order), default is 4.
- For ‘DOG’ this is m (m-th derivative), default is 2.
pad ({True,False}, optional) – Whether or not to pad the timeseries. with zeroes to get N up to the next higher power of 2. This prevents wraparound from the end of the time series to the beginning, and also speeds up the FFT’s used to do the wavelet transform. This will not eliminate all edge effects. The default is False.

Returns:

wave (numpy.array) – The wavelet coefficients
coi (numpy.array) – The cone of influence. Periods greater than this are subject to edge effects.

See also

pyleoclim.utils.wavelet.tc_wave_bases: 1D wavelet functions Morlet, Paul or Dog

References

Torrence, C. and G. P. Compo, 1998: A Practical Guide to Wavelet Analysis. Bull. Amer. Meteor. Soc., 79, 61-78. Python routines available at http://paos.colorado.edu/research/wavelets/

pyleoclim.utils.wavelet.wtc(coeff1, coeff2, scales, tau, smooth_factor=0.25)[source]

Return the wavelet transform coherency (WTC).

Parameters:

coeff1 (array) – the first of two sets of wavelet transform coefficients in the form of a1 + a2*1j
coeff2 (array) – the second of two sets of wavelet transform coefficients in the form of a1 + a2*1j
scales (array) – vector of scales (period for WWZ; more complicated dependence for CWT)
tau (array') – the evenly-spaced time points, namely the time shift for wavelet analysis

Returns:

xw_coherence – the cross wavelet coherence

Return type:

array

References

Grinsted, A., Moore, J. C. & Jevrejeva, S. Application of the cross wavelet transform and
wavelet coherence to geophysical time series. Nonlin. Processes Geophys. 11, 561–566 (2004).
Matlab code by Grinsted (https://github.com/grinsted/wavelet-coherence)
Python code by Sebastian Krieger (https://github.com/regeirk/pycwt)

pyleoclim.utils.wavelet.wwa2psd(wwa, ts, Neffs, freq=None, Neff_threshold=3, anti_alias=False, avgs=2)[source]

Return the power spectral density (PSD) using the weighted wavelet amplitude (WWA).

Parameters:

wwa (array) – the weighted wavelet amplitude.
ts (array) – the time points, should be pre-truncated so that the span is exactly what is used for wwz
Neffs (array) – the matrix of effective number of points in the time-scale coordinates obtained from wwz
freq (array) – vector of frequency from wwz
Neff_threshold (int) – the threshold of the number of effective samples
anti_alias (bool) – whether to apply anti-alias filter
avgs (int) – flag for whether spectrum is derived from instantaneous point measurements (avgs<>1) OR from measurements averaged over each sampling interval (avgs==1)

Returns:

psd – power spectral density

Return type:

array

References

Kirchner’s C code for weighted psd calculation (see https://www.pnas.org/doi/full/10.1073/pnas.1304328110#supplementary-materials)

pyleoclim.utils.wavelet.wwz(ys, ts, tau=None, ntau=None, freq=None, freq_method='log', freq_kwargs={}, c=0.012665147955292222, Neff_threshold=3, Neff_coi=3, nproc=8, detrend=False, sg_kwargs=None, method='Kirchner_numba', gaussianize=False, standardize=True, len_bd=0, bc_mode='reflect', reflect_type='odd')[source]

Weighted wavelet Z transform (WWZ) for unevenly-spaced data

Parameters:

ys (array) – a time series, NaNs will be deleted automatically
ts (array) – the time points, if ys contains any NaNs, some of the time points will be deleted accordingly
tau (array) – the evenly-spaced time vector for the analysis, namely the time shift for wavelet analysis
freq (array) – vector of frequency
freq_method (str) –
Method to generate the frequency vector if not set directly. The following options are avialable:
- ’log’ (default)
- ’lomb_scargle’
- ’welch’
- ’scale’
- ’nfft’
See pyleoclim.utils.wavelet.make_freq_vector() for details
freq_kwargs (str) – used when freq=None for certain methods
c (float) – the decay constant that determines the analytical resolution of frequency for analysis, the smaller the higher resolution; the default value 1/(8*np.pi**2) is good for most of the wavelet analysis cases
Neff_threshold (int) – threshold for the effective number of points
nproc (int) – the number of processes for multiprocessing
detrend (string, {None, 'linear', 'constant', 'savitzy-golay'}) –
available methods for detrending, including
- None: the original time series is assumed to have no trend;
- ’linear’: a linear least-squares fit to ys is subtracted;
- ’constant’: the mean of ys is subtracted
- ’savitzy-golay’: ys is filtered using the Savitzky-Golay filter and the resulting filtered series is subtracted from y.
Empirical mode decomposition. The last mode is assumed to be the trend and removed from the series
sg_kwargs (dict) – The parameters for the Savitzky-Golay filter. See pyleoclim.utils.filter.savitzky_golay() for details.
method (string, {'Foster', 'Kirchner', 'Kirchner_f2py', 'Kirchner_numba'}) –
available specific implementation of WWZ, including
- ’Foster’: the original WWZ method;
- ’Kirchner’: the method Kirchner adapted from Foster;
- ’Kirchner_f2py’: the method Kirchner adapted from Foster, implemented with f2py for acceleration;
- ’Kirchner_numba’: the method Kirchner adapted from Foster, implemented with Numba for acceleration (default);
len_bd (int) – the number of the ghost grids want to creat on each boundary
bc_mode (string, {'constant', 'edge', 'linear_ramp', 'maximum', 'mean', 'median', 'minimum', 'reflect' , 'symmetric', 'wrap'}) – For more details, see np.lib.pad()
reflect_type (string, optional, {‘even’, ‘odd’}) – Used in ‘reflect’, and ‘symmetric’. The ‘even’ style is the default with an unaltered reflection around the edge value. For the ‘odd’ style, the extented part of the array is created by subtracting the reflected values from two times the edge value. For more details, see np.lib.pad()

Returns:

res – a namedtuple that includes below items

wwaarray: the weighted wavelet amplitude.
coiarray: cone of influence
freqarray: vector of frequency
tauarray: the evenly-spaced time points, namely the time shift for wavelet analysis
Neffsarray: the matrix of effective number of points in the time-scale coordinates
coeffarray: the wavelet transform coefficients

Return type:

namedtuple

See also

pyleoclim.utils.wavelet.wwz_basic: Returns the weighted wavelet amplitude using the original method from Kirchner. No multiprocessing
pyleoclim.utils.wavelet.wwz_nproc: Returns the weighted wavelet amplitude using the original method from Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_basic: Return the weighted wavelet amplitude (WWA) modified by Kirchner. No multiprocessing
pyleoclim.utils.wavelet.kirchner_nproc: Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_numba: Return the weighted wavelet amplitude (WWA) modified by Kirchner using Numba package.
pyleoclim.utils.wavelet.kirchner_f2py: Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Uses Fortran. Fastest method but requires a compiler.
pyleoclim.utils.filter.savitzky_golay: Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
pyleoclim.utils.wavelet.make_freq_vector: Make frequency vector
pyleoclim.utils.tsutils.detrend: detrending functionalities
pyleoclim.utils.tsutils.gaussianize_1d: Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.preprocess: pre-processes a times series using Gaussianization and detrending.

Examples

We perform an ideal test below. We use a sine wave with a period of 50 yrs as the signal for test. Then performing wavelet analysis should return an energy band around period of 50 yrs in the scalogram.

In [1]: from pyleoclim import utils

In [2]: import matplotlib.pyplot as plt

In [3]: from matplotlib.ticker import ScalarFormatter, FormatStrFormatter

In [4]: import numpy as np

# Create a signal
In [5]: time = np.arange(2001)

In [6]: f = 1/50  # the period is then 1/f = 50

In [7]: signal = np.cos(2*np.pi*f*time)

# Wavelet Analysis
In [8]: res = utils.wwz(signal, time)

# Visualization
In [9]: fig, ax = plt.subplots()

In [10]: contourf_args = {'cmap': 'magma', 'origin': 'lower', 'levels': 11}

In [11]: cbar_args = {'drawedges': False, 'orientation': 'vertical', 'fraction': 0.15, 'pad': 0.05}

In [12]: cont = ax.contourf(res.time, 1/res.freq, res.amplitude.T, **contourf_args)

In [13]: ax.plot(res.time, res.coi, 'k--')  # plot the cone of influence
Out[13]: [<matplotlib.lines.Line2D at 0x7f17eb6c47f0>]

In [14]: ax.set_yscale('log')

In [15]: ax.set_yticks([2, 5, 10, 20, 50, 100, 200, 500, 1000])
Out[15]: 
[<matplotlib.axis.YTick at 0x7f17e9c79000>,
 <matplotlib.axis.YTick at 0x7f17d591f550>,
 <matplotlib.axis.YTick at 0x7f17d2ddcd90>,
 <matplotlib.axis.YTick at 0x7f17d5952170>,
 <matplotlib.axis.YTick at 0x7f17d5953fd0>,
 <matplotlib.axis.YTick at 0x7f17e86f4730>,
 <matplotlib.axis.YTick at 0x7f17d4f1f190>,
 <matplotlib.axis.YTick at 0x7f17d4f1ecb0>,
 <matplotlib.axis.YTick at 0x7f17d4f1d6f0>]

In [16]: ax.set_ylim([2, 1000])
Out[16]: (2.0, 1000.0)

In [17]: ax.yaxis.set_major_formatter(ScalarFormatter())

In [18]: ax.yaxis.set_major_formatter(FormatStrFormatter('%g'))

In [19]: ax.set_xlabel('Time (yr)')
Out[19]: Text(0.5, 0, 'Time (yr)')

In [20]: ax.set_ylabel('Period (yrs)')
Out[20]: Text(0, 0.5, 'Period (yrs)')

In [21]: cb = plt.colorbar(cont, **cbar_args)

In [22]: plt.show()

pyleoclim.utils.wavelet.wwz_basic(ys, ts, freq, tau, c=0.012665147955292222, Neff_threshold=3, nproc=1, detrend=False, sg_kwargs=None, gaussianize=False, standardize=False)[source]

Return the weighted wavelet amplitude (WWA).

The Weighted wavelet Z-transform (WWZ) is based on Morlet wavelet estimation, using least squares minimization to suppress the energy leakage caused by data gaps. WWZ does not rely on interpolation or detrending, and is appropriate for unevenly-spaced datasets. In particular, we use the variant of Kirchner & Neal (2013), in which basis rotations mitigate the numerical instability that occurs in pathological cases with the original algorithm (Foster, 1996). The WWZ method has one adjustable parameter, a decay constant c that balances the time and frequency resolutions of the analysis. This application uses the larger value 1/(8π^2), justified elsewhere (Witt & Schumann, 2005).

No multiprocessing is applied by Default.

Parameters:

ys (array) – a time series
ts (array) – time axis of the time series
freq (array) – vector of frequency
tau (array) – the evenly-spaced time points, namely the time shift for wavelet analysis
c (float) – the decay constant that determines the analytical resolution of frequency for analysis, the smaller the higher resolution; the default value 1/(8*np.pi**2) is good for most of the wavelet analysis cases
Neff_threshold (int) – the threshold of the number of effective degrees of freedom
nproc (int) – fake argument, just for convenience
detrend (string) – None - the original time series is assumed to have no trend (default); Types of detrending: - “linear” : the result of a linear least-squares fit to y is subtracted from y. - “constant” : only the mean of data is subtracted. - “savitzky-golay” : y is filtered using the Savitzky-Golay filter and the resulting filtered series is subtracted from y. - “emd” : Empirical mode decomposition. The last mode is assumed to be the trend and removed from the series
sg_kwargs (dict) – The parameters for the Savitzky-Golay filter. see pyleoclim.utils.filter.savitzy_golay for details.
gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries

Returns:

wwa (array) – the weighted wavelet amplitude
phase (array) – the weighted wavelet phase
Neffs (array) – the matrix of effective number of points in the time-scale coordinates
coeff (array) – the wavelet transform coefficients (a0, a1, a2)

References

Foster, G. Wavelets for period analysis of unevenly sampled time series. The Astronomical Journal 112, 1709 (1996).
Witt, A. & Schumann, A. Y. Holocene climate variability on millennial scales recorded in Greenland ice cores.

Nonlinear Processes in Geophysics 12, 345–352 (2005). - Kirchner, J. W. and Neal, C. (2013). Universal fractal scaling in stream chemistry and its implications for solute transport and water quality trend detection. Proc Natl Acad Sci USA 110:12213–12218.

See also

pyleoclim.utils.wavelet.wwz_nproc: Returns the weighted wavelet amplitude using the original method from Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_basic: Return the weighted wavelet amplitude (WWA) modified by Kirchner. No multiprocessing
pyleoclim.utils.wavelet.kirchner_nproc: Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_numba: Return the weighted wavelet amplitude (WWA) modified by Kirchner using Numba package.
pyleoclim.utils.wavelet.kirchner_f2py: Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Uses Fortran. Fastest method but requires a compiler.
pyleoclim.utils.filter.savitzky_golay: Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
pyleoclim.utils.tsutils.preprocess: pre-processes a times series using Gaussianization and detrending.
pyleoclim.utils.tsutils.detrend: detrending functionalities using 4 possible methods
pyleoclim.utils.tsutils.gaussianize_1d: Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.standardize: Centers and normalizes a given time series.

pyleoclim.utils.wavelet.wwz_coherence(ys1, ts1, ys2, ts2, smooth_factor=0.25, tau=None, freq=None, freq_method='log', freq_kwargs=None, c=0.012665147955292222, Neff_threshold=3, nproc=8, detrend=False, sg_kwargs=None, verbose=False, method='Kirchner_numba', gaussianize=False, standardize=True)[source]

Returns the wavelet coherence of two time series (WWZ method).

Parameters:

ys1 (array) – first of two time series
ys2 (array) – second of the two time series
ts1 (array) – time axis of first time series
ts2 (array) – time axis of the second time series
tau (array) – the evenly-spaced time points
freq (array) – vector of frequency
c (float) – the decay constant that determines the analytical resolution of frequency for analysis, the smaller the higher resolution; the default value 1/(8*np.pi**2) is good for most of the wavelet analysis cases
Neff_threshold (int) – threshold for the effective number of points
nproc (int) – the number of processes for multiprocessing
detrend (string) –
- None: the original time series is assumed to have no trend;
- ’linear’: a linear least-squares fit to ys is subtracted;
- ’constant’: the mean of ys is subtracted
- ’savitzy-golay’: ys is filtered using the Savitzky-Golay filter and the resulting filtered series is subtracted from y.
Empirical mode decomposition. The last mode is assumed to be the trend and removed from the series
sg_kwargs (dict) – The parameters for the Savitzky-Golay filter. see pyleoclim.utils.filter.savitzy_golay for details.
gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries
method (string) –
- ‘Foster’: the original WWZ method;
- ’Kirchner’: the method Kirchner adapted from Foster;
- ’Kirchner_f2py’: the method Kirchner adapted from Foster with f2py
- ’Kirchner_numba’: Kirchner’s algorithm with Numba support for acceleration (default)
verbose (bool) – If True, print warning messages
smooth_factor (float) – smoothing factor for the WTC (default: 0.25)

Returns:

res – contains the cross wavelet coherence, cross-wavelet phase, vector of frequency, evenly-spaced time points, AR1 sims, cone of influence

Return type:

dict

References

Grinsted, A., J. C. Moore, and S. Jevrejeva (2004), Application of the cross wavelet transform and wavelet coherence to geophysical time series, Nonlinear Processes in Geophysics, 11, 561–566.

See also

pyleoclim.utils.wavelet.wwz_basic: Returns the weighted wavelet amplitude using the original method from Kirchner. No multiprocessing
pyleoclim.utils.wavelet.wwz_nproc: Returns the weighted wavelet amplitude using the original method from Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_basic: Return the weighted wavelet amplitude (WWA) modified by Kirchner. No multiprocessing
pyleoclim.utils.wavelet.kirchner_nproc: Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_numba: Return the weighted wavelet amplitude (WWA) modified by Kirchner using Numba package.
pyleoclim.utils.wavelet.kirchner_f2py: Returns the weighted wavelet amplitude (WWA) modified by Kirchner. Uses Fortran. Fastest method but requires a compiler.
pyleoclim.utils.filter.savitzky_golay: Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
pyleoclim.utils.wavelet.make_freq_vector: Make frequency vector
pyleoclim.utils.tsutils.detrend: detrending functionalities
pyleoclim.utils.tsutils.gaussianize_1d: Quantile maps a 1D array to a Gaussian distribution
pyleoclim.utils.tsutils.preprocess: pre-processes a times series using Gaussianization and detrending.

pyleoclim.utils.wavelet.wwz_nproc(ys, ts, freq, tau, c=0.012665147955292222, Neff_threshold=3, nproc=8, detrend=False, sg_kwargs=None, gaussianize=False, standardize=False)[source]

Return the weighted wavelet amplitude (WWA).

Original method from Foster (1996). Supports multiprocessing.

Parameters:

ys (array) – a time series
ts (array) – time axis of the time series
freq (array) – vector of frequency
tau (array) – the evenly-spaced time points, namely the time shift for wavelet analysis
c (float) – the decay constant that determines the analytical resolution of frequency for analysis, the smaller the higher resolution; the default value 1/(8*np.pi**2) is good for most of the wavelet analysis cases
Neff_threshold (int) – the threshold of the number of effective degrees of freedom [default = 3]
nproc (int) – the number of processes for multiprocessing [default = 8]
detrend (string) – False - the original time series is assumed to have no trend; Types of detrending: - “linear” : the result of a linear least-squares fit to y is subtracted from y. - “constant” : only the mean of data is subtracted. - “savitzky-golay” : y is filtered using the Savitzky-Golay filter and the resulting filtered series is subtracted from y. - “emd” : Empirical mode decomposition. The last mode is assumed to be the trend and removed from the series
sg_kwargs (dict) – The parameters for the Savitzky-Golay filter. see pyleoclim.utils.filter.savitzy_golay for details.
gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries

Returns:

wwa (array) – the weighted wavelet amplitude
phase (array) – the weighted wavelet phase
Neffs (array) – the matrix of effective number of points in the time-scale coordinates
coeff (array) – the wavelet transform coefficients (a0, a1, a2)

See also

pyleoclim.utils.wavelet.wwz_basic: weighted wavelet amplitude using the original method from Kirchner. No multiprocessing
pyleoclim.utils.wavelet.kirchner_basic: weighted wavelet amplitude (WWA) modified by Kirchner. No multiprocessing
pyleoclim.utils.wavelet.kirchner_nproc: weighted wavelet amplitude (WWA) modified by Kirchner. Supports multiprocessing
pyleoclim.utils.wavelet.kirchner_numba: weighted wavelet amplitude (WWA) modified by Kirchner using Numba package.
pyleoclim.utils.wavelet.kirchner_f2py: weighted wavelet amplitude (WWA) modified by Kirchner. Uses Fortran. Fastest method but requires a compiler.
pyleoclim.utils.tsutils.preprocess: pre-processes a times series using Gaussianization and detrending.
pyleoclim.utils.filter.savitzky_golay: Smooth (and optionally differentiate) data with a Savitzky-Golay filter.
pyleoclim.utils.tsutils.detrend: detrending functionalities
pyleoclim.utils.tsutils.gaussianize_1d: Quantile maps a 1D array to a Gaussian distribution

pyleoclim.utils.wavelet.xwt(coeff1, coeff2)[source]

Return the cross wavelet transform.

Parameters:

coeff1 (array) – the first of two sets of wavelet transform coefficients in the form of a1 + a2*1j
coeff2 (array) – the second of two sets of wavelet transform coefficients in the form of a1 + a2*1j
freq (array) – vector of frequency
tau (array) – evenly-spaced time axis (original ttime axis for CWT, time shift for WWZ).

Returns:

xw_t (array (complex)) – the cross wavelet transform
xw_amplitude (array) – the cross wavelet amplitude
xw_phase (array) – the cross wavelet phase

References

Grinsted, A., Moore, J. C. & Jevrejeva, S. Application of the cross wavelet transform and wavelet coherence to geophysical time series. Nonlin. Processes Geophys. 11, 561–566 (2004).

Tsutils

Utilities to manipulate timeseries - useful for preprocessing prior to analysis

pyleoclim.utils.tsutils.annualize(ys, ts)[source]

Annualize a time series whose time resolution is finer than 1 year

Parameters:

ys (array) – A time series, NaNs allowed
ts (array) – The time axis of the time series, NaNs allowed

Returns:

ys_ann (array) – the annualized time series
year_int (array) – The time axis of the annualized time series

pyleoclim.utils.tsutils.bin(x, y, bin_size=None, start=None, stop=None, evenly_spaced=True)[source]

Bin the values

Parameters:

x (array) – The x-axis series.
y (array) – The y-axis series.
bin_size (float) – The size of the bins. Default is the mean resolution if evenly_spaced is not True
start (float) – Where/when to start binning. Default is the minimum
stop (float) – When/where to stop binning. Default is the maximum
evenly_spaced ({True,False}) – Makes the series evenly-spaced. This option is ignored if bin_size is set to float

Returns:

binned_values (array) – The binned values
bins (array) – The bins (centered on the median, i.e., the 100-200 bin is 150)
n (array) – Number of data points in each bin
error (array) – The standard error on the mean in each bin

See also

pyleoclim.utils.tsutils.gkernel: Coarsen time resolution using a Gaussian kernel
pyleoclim.utils.tsutils.interp: Interpolate y onto a new x-axis

pyleoclim.utils.tsutils.calculate_distances(ys, n_neighbors=None, NN_kwargs=None)[source]

Uses the scikit-learn unsupervised learner for implementing neighbor searches and calculate the distance between a point and its nearest neighbors to estimate epsilon for DBSCAN.

Parameters:

ys (tnumpy.array) – the y-values for the timeseries
n_neighbors (int, optional) – Number of neighbors to use by default for kneighbors queries. The default is None.
NN_kwargs (dict, optional) – Other arguments for sklearn.neighbors.NearestNeighbors. The default is None. See: https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.NearestNeighbors.html#sklearn.neighbors.NearestNeighbors

Returns:

min_eps (int) – Minimum value for epsilon.
max_eps (int) – Maximum value for epsilon.

pyleoclim.utils.tsutils.center(y, axis=0)[source]

Centers array y (i.e. removes the sample mean)

Parameters:

y (array) – Vector of (real) numbers as a time series, NaNs allowed
axis (int or None) – Axis along which to operate, if None, compute over the whole array

Returns:

yc (array) – The centered time series, yc = (y - ybar), NaNs allowed
ybar (real) – The sampled mean of the original time series, y

References

Tapio Schneider’s MATLAB code: https://github.com/tapios/RegEM/blob/master/center.m

pyleoclim.utils.tsutils.detect_outliers_DBSCAN(ys, nbr_clusters=None, eps=None, min_samples=None, n_neighbors=None, metric='euclidean', NN_kwargs=None, DBSCAN_kwargs=None)[source]

Uses the unsupervised learning DBSCAN algorithm to identify outliers in timeseries data. The algorithm uses the silhouette score calculated over a range of epsilon and minimum sample values to determine the best clustering. In this case, we take the largest silhouette score (as close to 1 as possible).

The DBSCAN implementation used here is from scikit-learn: https://scikit-learn.org/stable/modules/generated/sklearn.cluster.DBSCAN.html

The Silhouette Coefficient is calculated using the mean intra-cluster distance (a) and the mean nearest-cluster distance (b) for each sample. The best value is 1 and the worst value is -1. Values near 0 indicate overlapping clusters. Negative values generally indicate that a sample has been assigned to the wrong cluster, as a different cluster is more similar. For additional details, see: https://scikit-learn.org/stable/modules/generated/sklearn.metrics.silhouette_score.html

Parameters:

ys (numpy.array) – The y-values for the timeseries data.
nbr_clusters (int, optional) – Number of clusters. Note that the DBSCAN algorithm calculates the number of clusters automatically. This paramater affects the optimization over the silhouette score. The default is None.
eps (float or list, optional) – epsilon. The default is None, which allows the algorithm to optimize for the best value of eps, using the silhouette score as the optimization criterion. The maximum distance between two samples for one to be considered as in the neighborhood of the other. This is not a maximum bound on the distances of points within a cluster. This is the most important DBSCAN parameter to choose appropriately for your data set and distance function.
min_samples (int or list, optional) – The number of samples (or total weight) in a neighborhood for a point to be considered as a core point. This includes the point itself.. The default is None and optimized using the silhouette score
n_neighbors (int, optional) – Number of neighbors to use by default for kneighbors queries, which can be used to calculate a range of plausible eps values. The default is None.
metric (str, optional) – The metric to use when calculating distance between instances in a feature array. The default is ‘euclidean’. See https://scikit-learn.org/stable/modules/generated/sklearn.cluster.DBSCAN.html for alternative values.
NN_kwargs (dict, optional) – Other arguments for sklearn.neighbors.NearestNeighbors. The default is None. See: https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.NearestNeighbors.html#sklearn.neighbors.NearestNeighbors
DBSCAN_kwargs (dict, optional) – Other arguments for sklearn.cluster.DBSCAN. The default is None. See: https://scikit-learn.org/stable/modules/generated/sklearn.cluster.DBSCAN.html

Returns:

indices (list) – list of indices that are considered outliers.
res (pandas.DataFrame) – Results of the clustering analysis. Contains information about eps value, min_samples value, number of clusters, the silhouette score, the indices of the outliers for each combination, and the cluster assignment for each point.

pyleoclim.utils.tsutils.detect_outliers_kmeans(ys, nbr_clusters=None, max_cluster=10, threshold=3, kmeans_kwargs=None)[source]

Outlier detection using the unsupervised alogrithm kmeans. The algorithm runs through various number of clusters and optimizes based on the silhouette score.

KMeans implementation: https://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html

The Silhouette Coefficient is calculated using the mean intra-cluster distance (a) and the mean nearest-cluster distance (b) for each sample. The best value is 1 and the worst value is -1. Values near 0 indicate overlapping clusters. Negative values generally indicate that a sample has been assigned to the wrong cluster, as a different cluster is more similar. For additional details, see: https://scikit-learn.org/stable/modules/generated/sklearn.metrics.silhouette_score.html

Parameters:

ys (numpy.array) – The y-values for the timeseries data
nbr_clusters (int or list, optional) – A user number of clusters to considered. The default is None.
max_cluster (int, optional) – The maximum number of clusters to consider in the optimization based on the Silhouette Score. The default is 10.
threshold (int, optional) – The algorithm uses the suclidean distance for each point in the cluster to identify the outliers. This parameter sets the threshold on the euclidean distance to define an outlier. The default is 3.
kmeans_kwargs (dict, optional) – Other parameters for the kmeans function. See: https://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html for details. The default is None.

Returns:

indices (list) – list of indices that are considered outliers.
res (pandas.DataFrame) – Results of the clustering analysis. Contains information about number of clusters, the silhouette score, the indices of the outliers for each combination, and the cluster assignment for each point.

pyleoclim.utils.tsutils.detrend(y, x=None, method='emd', n=1, sg_kwargs=None)[source]

Detrend a timeseries according to four methods

Detrending methods include: “linear”, “constant”, using a low-pass Savitzky-Golay filter, and Empirical Mode Decomposition (default). Linear and constant methods use [scipy.signal.detrend](https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.detrend.html), EMD uses [pyhht.emd.EMD](https://pyhht.readthedocs.io/en/stable/apiref/pyhht.html)

Parameters:

y (array) – The series to be detrended.
x (array) – Abscissa for array y. Necessary for use with the Savitzky-Golay method, since the series should be evenly spaced.
method (str) – The type of detrending: - “linear”: the result of a linear least-squares fit to y is subtracted from y. - “constant”: only the mean of data is subtracted. - “savitzky-golay”, y is filtered using the Savitzky-Golay filters and the resulting filtered series is subtracted from y. - “emd” (default): Empirical mode decomposition. The last mode is assumed to be the trend and removed from the series
n (int) – Works only if method == ‘emd’. The number of smoothest modes to remove.
sg_kwargs (dict) – The parameters for the Savitzky-Golay filters.

Returns:

ys (array) – The detrended version of y.
trend (array) – The removed trend. Only non-empty for EMD and Savitzy-Golay methods, since SciPy detrending does not retain the trends

See also

pyleoclim.utils.filter.savitzky_golay: Filtering using Savitzy-Golay
pyleoclim.utils.tsutils.preprocess: pre-processes a times series using standardization and detrending.

pyleoclim.utils.tsutils.eff_sample_size(y, detrend_flag=False)[source]

Effective Sample Size of timeseries y

Parameters:

y (float) – 1d array
detrend_flag (boolean) – if True (default), detrends y before estimation.

Returns:

neff – The effective sample size

Return type:

float

References

Thiébaux HJ and Zwiers FW, 1984: The interpretation and estimation of effective sample sizes. Journal of Climate and Applied Meteorology 23: 800–811.

pyleoclim.utils.tsutils.gauss(ys)

Maps a 1D array to a Gaussian distribution using the inverse Rosenblatt transform

The resulting array is mapped to a standard normal distribution, and therefore has zero mean and unit standard deviation. Using gaussianize() obviates the need for standardize().

Parameters:: ys (1D Array) – e.g. a timeseries
Returns:: yg – Gaussianized values of ys.
Return type:: 1D Array

References

van Albada, S., and P. Robinson (2007), Transformation of arbitrary: distributions to the normal distribution with application to EEG test-retest reliability, Journal of Neuroscience Methods, 161(2), 205 - 211, doi:10.1016/j.jneumeth.2006.11.004.

See also

pyleoclim.utils.tsutils.standardize: Centers and normalizes a time series

pyleoclim.utils.tsutils.gaussianize(ys)[source]

Maps a 1D array to a Gaussian distribution using the inverse Rosenblatt transform

The resulting array is mapped to a standard normal distribution, and therefore has zero mean and unit standard deviation. Using gaussianize() obviates the need for standardize().

Parameters:: ys (1D Array) – e.g. a timeseries
Returns:: yg – Gaussianized values of ys.
Return type:: 1D Array

References

van Albada, S., and P. Robinson (2007), Transformation of arbitrary: distributions to the normal distribution with application to EEG test-retest reliability, Journal of Neuroscience Methods, 161(2), 205 - 211, doi:10.1016/j.jneumeth.2006.11.004.

See also

pyleoclim.utils.tsutils.standardize: Centers and normalizes a time series

pyleoclim.utils.tsutils.gkernel(t, y, h=3.0, step=None, start=None, stop=None, step_style='max')[source]

Coarsen time resolution using a Gaussian kernel

Parameters:

t (1d array) – the original time axis
y (1d array) – values on the original time axis
h (float) – kernel e-folding scale
step (float) –
The interpolation step. Default is max spacing between consecutive points.

start : float where/when to start the interpolation. Default is min(t).
stop (float) – where/when to stop the interpolation. Default is max(t).
step_style (str) – step style to be applied from ‘increments’ [default = ‘max’]

Returns:

tc (1d array) – the coarse-grained time axis
yc (1d array) – The coarse-grained time series

References

Rehfeld, K., Marwan, N., Heitzig, J., and Kurths, J.: Comparison of correlation analysis techniques for irregularly sampled time series, Nonlin. Processes Geophys., 18, 389–404, doi:10.5194/npg-18-389-2011, 2011.

See also

pyleoclim.utils.tsutils.increments: Establishes the increments of a numerical array
pyleoclim.utils.tsutils.bin: Bin the values
pyleoclim.utils.tsutils.interp: Interpolate y onto a new x-axis

pyleoclim.utils.tsutils.increments(x, step_style='median')[source]

Establishes the increments of a numerical array: start, stop, and representative step.

Parameters:

x (array) –
step_style (str) –
Method to obtain a representative step if x is not evenly spaced. Valid entries: ‘median’ [default], ‘mean’, ‘mode’ or ‘max’ The mode is the most frequent entry in a dataset, and may be a good choice if the timeseries is nearly equally spaced but for a few gaps.

Max is a conservative choice, appropriate for binning methods and Gaussian kernel coarse-graining

Returns:

start (float) – min(x)
stop (float) – max(x)
step (float) – The representative spacing between consecutive values, computed as above

See also

pyleoclim.utils.tsutils.bin: Bin the values
pyleoclim.utils.tsutils.gkernel: Coarsen time resolution using a Gaussian kernel

pyleoclim.utils.tsutils.interp(x, y, interp_type='linear', step=None, start=None, stop=None, step_style='mean', **kwargs)[source]

Interpolate y onto a new x-axis

Largely a wrapper for [scipy.interpolate.interp1d](https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.interp1d.html)

Parameters:

x (array) – The x-axis
y (array) – The y-axis
interp_type (str) – Options include: ‘linear’, ‘nearest’, ‘zero’, ‘slinear’, ‘quadratic’, ‘cubic’, ‘previous’, ‘next’ where ‘zero’, ‘slinear’, ‘quadratic’ and ‘cubic’ refer to a spline interpolation of zeroth, first, second or third order; ‘previous’ and ‘next’ simply return the previous or next value of the point) or as an integer specifying the order of the spline interpolator to use. Default is ‘linear’.
step (float) – The interpolation step. Default is mean spacing between consecutive points.
start (float) – where/when to start the interpolation. Default is min..
stop (float) – where/when to stop the interpolation. Default is max.
kwargs (kwargs) – Aguments specific to interpolate.interp1D. If getting an error about extrapolation, you can use the arguments bound_errors=False and fill_value=”extrapolate” to allow for extrapolation.

Returns:

xi (array) – The interpolated x-axis
yi (array) – The interpolated y values

See also

pyleoclim.utils.tsutils.increments: Establishes the increments of a numerical array
pyleoclim.utils.tsutils.bin: Bin the values
pyleoclim.utils.tsutils.gkernel: Coarsen time resolution using a Gaussian kernel

pyleoclim.utils.tsutils.preprocess(ys, ts, detrend=False, sg_kwargs=None, gaussianize=False, standardize=True)[source]

Return the processed time series using detrend and standardization.

Parameters:

ys (array) – a time series
ts (array) – The time axis for the timeseries. Necessary for use with the Savitzky-Golay filters method since the series should be evenly spaced.
detrend (string) – ‘none’/False/None - no detrending will be applied; ‘emd’ - the last mode is assumed to be the trend and removed from the series ‘linear’ - a linear least-squares fit to ys is subtracted; ‘constant’ - the mean of ys is subtracted ‘savitzy-golay’ - ys is filtered using the Savitzky-Golay filter and the resulting filtered series is subtracted.
sg_kwargs (dict) – The parameters for the Savitzky-Golay filter.
gaussianize (bool) – If True, gaussianizes the timeseries
standardize (bool) – If True, standardizes the timeseries

Returns:

res – the processed time series

Return type:

array

See also

pyleoclim.utils.tsutils.detrend: Detrend a timeseries according to four methods
pyleoclim.utils.filter.savitzy_golay: Filtering using Savitzy-Golay method
pyleoclim.utils.tsutils.standardize: Centers and normalizes a given time series
pyleoclim.utils.tsutils.gaussianize_1d: Quantile maps a matrix to a Gaussian distribution

pyleoclim.utils.tsutils.remove_outliers(ts, ys, indices)[source]

Remove the outliers from timeseries data

Parameters:

ts (numpy.array) – The time axis for the timeseries data.
ys (numpy.array) – The y-values for the timeseries data.
indices (numpy.array) – The indices of the outliers to be removed.

Returns:

ys (numpy.array) – The time axis for the timeseries data after outliers removal
ts (numpy.array) – The y-values for the timeseries data after outliers removal

pyleoclim.utils.tsutils.simple_stats(y, axis=None)[source]

Computes simple statistics

Computes the mean, median, min, max, standard deviation, and interquartile range of a numpy array y, ignoring NaNs.

Parameters:

y (array) – A Numpy array
axis (int, tuple of ints) – Axis or Axes along which the means are computed, the default is to compute the mean of the flattened array. If a tuple of ints, performed over multiple axes

Returns:

mean (float) – mean of y, ignoring NaNs
median (float) – median of y, ignoring NaNs
min_ (float) – mininum value in y, ignoring NaNs
max_ (float) – max value in y, ignoring NaNs
std (float) – standard deviation of y, ignoring NaNs
IQR (float) – Interquartile range of y along specified axis, ignoring NaNs

pyleoclim.utils.tsutils.standardize(x, scale=1, axis=0, ddof=0, eps=0.001)[source]

Centers and normalizes a time series. Constant or nearly constant time series not rescaled.

Parameters:

x (array) – vector of (real) numbers as a time series, NaNs allowed
scale (real) – A scale factor used to scale a record to a match a given variance
axis (int or None) – axis along which to operate, if None, compute over the whole array
ddof (int) – degress of freedom correction in the calculation of the standard deviation
eps (real) – a threshold to determine if the standard deviation is too close to zero

Returns:

z (array) – The standardized time series (z-score), Z = (X - E[X])/std(X)*scale, NaNs allowed
mu (real) – The mean of the original time series, E[X]
sig (real) – The standard deviation of the original time series, std[X]

References

Tapio Schneider’s MATLAB code: https://github.com/tapios/RegEM/blob/master/standardize.m

The zscore function in SciPy: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.zscore.html

See also

pyleoclim.utils.tsutils.preprocess: pre-processes a times series using standardization and detrending.

pyleoclim.utils.tsutils.std(x, scale=1, axis=0, ddof=0, eps=0.001)

Centers and normalizes a time series. Constant or nearly constant time series not rescaled.

Parameters:

x (array) – vector of (real) numbers as a time series, NaNs allowed
scale (real) – A scale factor used to scale a record to a match a given variance
axis (int or None) – axis along which to operate, if None, compute over the whole array
ddof (int) – degress of freedom correction in the calculation of the standard deviation
eps (real) – a threshold to determine if the standard deviation is too close to zero

Returns:

z (array) – The standardized time series (z-score), Z = (X - E[X])/std(X)*scale, NaNs allowed
mu (real) – The mean of the original time series, E[X]
sig (real) – The standard deviation of the original time series, std[X]

References

Tapio Schneider’s MATLAB code: https://github.com/tapios/RegEM/blob/master/standardize.m

The zscore function in SciPy: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.zscore.html

See also

pyleoclim.utils.tsutils.preprocess: pre-processes a times series using standardization and detrending.

pyleoclim.utils.tsutils.ts2segments(ys, ts, factor=10)[source]

Chop a time series into several segments based on gap detection.

The rule of gap detection is very simple:: we define the intervals between time points as dts, then if dts[i] is larger than factor * dts[i-1], we think that the change of dts (or the gradient) is too large, and we regard it as a breaking point and chop the time series into two segments here

Parameters:

ys (array) – A time series, NaNs allowed
ts (array) – The time points
factor (float) – The factor that adjusts the threshold for gap detection

Returns:

seg_ys (list) – A list of several segments with potentially different lengths
seg_ts (list) – A list of the time axis of the several segments
n_segs (int) – The number of segments

Tsbase

Basic functionalities to clean timeseries data prior to analysis

pyleoclim.utils.tsbase.clean_ts(ys, ts, verbose=False)[source]

Cleaning the timeseries

Delete the NaNs in the time series and sort it with time axis ascending, duplicate timestamps will be reduced by averaging the values.

Parameters:

ys (array) – A time series, NaNs allowed
ts (array) – The time axis of the time series, NaNs allowed
verbose (bool) – If True, will print a warning message

Returns:

ys (array) – The time series without nans
ts (array) – The time axis of the time series without nans

See also

pyleoclim.utils.tsbase.dropna: Drop NaN values
pyleoclim.utils.tsbase.sort_ts: Sort timeseries
pyleoclim.utils.tsbase.reduce_duplicated_timestamps: Consolidate duplicated timestamps

pyleoclim.utils.tsbase.dropna(ys, ts, verbose=False)[source]

Drop NaN values

Remove entries of ys or ts that bear NaNs

Parameters:

ys (array) – A time series, NaNs allowed
ts (array) – The time axis of the time series, NaNs allowed
verbose (bool) – If True, will print a warning message

Returns:

ys (array) – The time series without nans
ts (array) – The time axis of the time series without nans

pyleoclim.utils.tsbase.is_evenly_spaced(ts, tol=0.0001)[source]

Check if a time axis is evenly spaced, within a given tolerance

Parameters:

ts (array) – The time axis of a time series
tol (float64) – Numerical tolerance for the relative difference

Returns:

check – True - evenly spaced; False - unevenly spaced.

Return type:

bool

pyleoclim.utils.tsbase.reduce_duplicated_timestamps(ys, ts, verbose=False)[source]

Consolidate duplicated timestamps

Reduce duplicated timestamps in a timeseries by averaging the values

Parameters:

ys (array) – Dependent variable
ts (array) – Independent variable
verbose (bool) – If True, will print a warning message

Returns:

ys (array) – Dependent variable
ts (array) – Independent variable, with duplicated timestamps reduced by averaging the values

pyleoclim.utils.tsbase.sort_ts(ys, ts, verbose=False)[source]

Sort timeseries

Sort ts values in ascending order

Parameters:

ys (array) – Dependent variable
ts (array) – Independent variable
verbose (bool) – If True, will print a warning message

Returns:

ys (array) – Dependent variable
ts (array) – Independent variable, sorted in ascending order

Lipdutils

Utilities to manipulate LiPD files and automate data transformation whenever possible. These functions are used throughout Pyleoclim but are not meant for direct interaction by users. Also handles integration with the LinkedEarth wiki and the LinkedEarth Ontology.

pyleoclim.utils.lipdutils.LipdToOntology(archiveType)[source]

standardize archiveType

Transform the archiveType from their LiPD name to their ontology counterpart

Parameters:: archiveType (string) – name of the archiveType from the LiPD file
Returns:: archiveType – archiveType according to the ontology
Return type:: string

pyleoclim.utils.lipdutils.checkTimeAxis(timeseries, x_axis=None)[source]

This function makes sure that time is available for the timeseries

Parameters:

timeseries (dict) – A LiPD timeseries object

Returns:

x (array) – the time values for the timeseries
label (string) – the time representation for the timeseries

pyleoclim.utils.lipdutils.checkXaxis(timeseries, x_axis=None)[source]

Check that a x-axis is present for the timeseries

Parameters:

timeseries (dict) – a timeseries
x_axis (string) – the x-axis representation, either depth, age or year

Returns:

x (array) – the values for the x-axis representation
label (string) – returns either “age”, “year”, or “depth”

pyleoclim.utils.lipdutils.enumerateLipds(lipds)[source]

Enumerate the LiPD files loaded in the workspace

Parameters:: lipds (dict) – A dictionary of LiPD files.

pyleoclim.utils.lipdutils.enumerateTs(timeseries_list)[source]

Enumerate the available time series objects

Parameters:: timeseries_list (list) – a list of available timeseries objects.

pyleoclim.utils.lipdutils.gen_dict_extract(key, var)[source]

Recursively searches for all the values in nested dictionaries corresponding to a particular key

Parameters:

key (str) – The key to search for
var (dict) – The dictionary to search

pyleoclim.utils.lipdutils.getEnsemble(csv_dict, csvName)[source]

Extracts the ensemble values and depth vector from the dictionary and returns them into two numpy arrays.

Parameters:

csv_dict (dict) – dictionary containing the availableTables
csvName (str) – Name of the csv

Returns:

depth (array) – Vector of depth
ensembleValues (array) – The matrix of Ensemble values

pyleoclim.utils.lipdutils.getLipd(lipds)[source]

Prompt for a LiPD file

Ask the user to select a LiPD file from a list Use this function in conjunction with enumerateLipds()

Parameters:: lipds (dict) – A dictionary of LiPD files. Can be obtained from pyleoclim.readLipd()
Returns:: select_lipd – The index of the LiPD file
Return type:: int

pyleoclim.utils.lipdutils.getMeasurement(csvName, lipd)[source]

Extract the dictionary corresponding to the measurement table

Parameters:

csvName (string) – The name of the csv file
lipd (dict) – The LiPD object from which to extract the data

Returns:

ts_list – A dictionary containing data and metadata for each column in the csv file.

Return type:

dict

pyleoclim.utils.lipdutils.getTs(timeseries_list, option=None)[source]

Get a specific timeseries object from a dictionary of timeseries

Parameters:

timeseries_list (list) – a list of available timeseries objects.
option (string) – An expression to filter the datasets. Uses lipd.filterTs()

Returns:

timeseries – A single timeseries object if not optional filter selected or a filtered list if optional arguments given

Return type:

single timeseries object or list of timeseries

See also

pyleoclim.utils.lipdutils.enumerateTs: Enumerate the available time series objects
pyleoclim.utils.lipdutils.promptForVariable: Prompt for a specific variable

pyleoclim.utils.lipdutils.isEnsemble(csv_dict)[source]

Check whether ensembles are available

Parameters:

csv_dict (dict) – Dictionary of available csv

Returns:

paleoEnsembleTables (list) – List of available paleoEnsembleTables
chronEnsembleTables (list) – List of availale chronEnsemble Tables

pyleoclim.utils.lipdutils.isMeasurement(csv_dict)[source]

Check whether measurement tables are available

Parameters:

csv_dict (dict) – Dictionary of available csv

Returns:

paleoMeasurementTables (list) – List of available paleoMeasurementTables
chronMeasurementTables (list) – List of available chronMeasurementTables

pyleoclim.utils.lipdutils.isModel(csvName, lipd)[source]

Check for the presence of a model in the same object as the measurement table

Parameters:

csvName (string) – The name of the csv file corresponding to the measurement table
lipd (dict) – A LiPD object

Returns:

model (list) – List of models already available
dataObject (string) – The name of the paleoData or ChronData object in which the model(s) are stored

pyleoclim.utils.lipdutils.mapAgeEnsembleToPaleoData(ensembleValues, depthEnsemble, depthPaleo)[source]

Map the depth for the ensemble age values to the paleo depth

Parameters:

ensembleValues (array) – A matrix of possible age models. Realizations should be stored in columns
depthEnsemble (array) – A vector of depth. The vector should have the same length as the number of rows in the ensembleValues
depthPaleo (array) – A vector corresponding to the depth at which there are paleodata information

Returns:

ensembleValuesToPaleo – A matrix of age ensemble on the PaleoData scale

Return type:

array

pyleoclim.utils.lipdutils.modelNumber(model)[source]

Assign a new or existing model number

Parameters:: model (list) – List of possible model number. Obtained from isModel
Returns:: modelNum – The number of the model
Return type:: int

pyleoclim.utils.lipdutils.pre_process_list(list_str)[source]

Pre-process a series of strings for capitalized letters, space, and punctuation

Parameters:: list_str (list) – A list of strings from which to strip capitals, spaces, and other characters
Returns:: res – A list of strings with capitalization, spaces, and punctuation removed
Return type:: list

pyleoclim.utils.lipdutils.pre_process_str(word)[source]

Pre-process a string for capitalized letters, space, and punctuation

Parameters:: string (str) – A string from which to strip capitals, spaces, and other characters
Returns:: res – A string with capitalization, spaces, and punctuation removed
Return type:: str

pyleoclim.utils.lipdutils.promptForVariable()[source]

Prompt for a specific variable

Ask the user to select the variable they are interested in. Use this function in conjunction with readHeaders() or getTSO()

Returns:: select_var – The index of the variable
Return type:: int

pyleoclim.utils.lipdutils.queryLinkedEarth(archiveType=[], proxyObsType=[], infVarType=[], sensorGenus=[], sensorSpecies=[], interpName=[], interpDetail=[], ageUnits=[], ageBound=[], ageBoundType=[], recordLength=[], resolution=[], lat=[], lon=[], alt=[], print_response=True, download_lipd=True, download_folder='default')[source]

This function allows to query the LinkedEarth wiki for records.

This function allows to query the LinkedEarth wiki for specific catagories. If you have more than one keyword per catagory, enter them in a list. If you don’t wish to use a particular terms, leave a blank in-between the brackets.

Parameters:

archiveType (list of strings) – The type of archive (enter all query terms, separated by a comma)
proxyObsType (list of strings) – The type of proxy observation (enter all query terms, separated by a comma)
infVarType (list of strings) – The type of inferred variable (enter all query terms, separated by a comma)
sensorGenus (list of strings) – The Genus of the sensor (enter all query terms, separated by a comma)
sensorSpecies (list of strings) – The Species of the sensor (enter all query terms, separated by a comma)
interpName (list of strings) – The name of the interpretation (enter all query terms, separated by a comma)
interpDetail (list of strings) – The detail of the interpretation (enter all query terms, separated by a comma)
ageUnits (list of strings) – The units of in which the age (year) is expressed in. Warning: Separate each query if need to run across multiple age queries (i.e., yr B.P. vs kyr B.P.). If the units are different but the meaning is the same (e.g., yr B.P. vs yr BP, enter all search terms separated by a comma).
ageBound (list of floats) – Enter the minimum and maximum age value to search for. Warning: You MUST enter a minimum AND maximum value. If you wish to perform a query such as “all ages before 2000 A.D.”, enter a minimum value of -99999 to cover all bases.
ageBoundType (list of strings) – The type of querying to perform. Possible values include: “any”, “entire”, and “entirely”. - any: Overlap any portions of matching datasets (default) - entirely: are entirely overlapped by matching datasets - entire: overlap entire matching datasets but dataset can be shorter than the bounds
recordLength (list of floats) – The minimum length the record needs to have while matching the ageBound criteria. For instance, “look for all records between 3000 and 6000 year BP with a record length of at least 1500 year”.
resolution (list of floats) – The maximum resolution of the resord. Resolution has the same units as age/year. For instance, “look for all records with a resolution of at least 100 years”. Warning: Resolution applies to specific variables rather than an entire dataset. Imagine the case where some measurements are made every cm while others are made every 5cm. If you require a specific variable to have the needed resolution, make sure that either the proxyObservationType, inferredVariableType, and/or Interpretation fields are completed.
lat (list of floats) – The minimum and maximum latitude. South is expressed with negative numbers. Warning: You MUST enter a minimum AND maximum value. If you wish to perform a query looking for records from the Northern Hemisphere, enter [0,90].
lon (list of floats) – The minimum and maximum longitude. West is expressed with negative numbers. Warning: You MUST enter a minimum AND a maximum value. If you wish to perform a query looking for records from the Western Hemisphere, enter [-180,0].
alt (list of floats) – The minimum and maximum altitude. Depth below sea level is expressed as negative numbers. Warning: You MUST enter a minimum AND a maximum value. If you wish to perform a query looking for records below a certain depth (e.g., 500), enter [-99999,-500].
print_response (bool) – If True, prints the URLs to the matching LiPD files
download_lipd (bool) – If True, download the matching LiPD files
download_folder (string) – Location to download the LiPD files. If “default”, will download in the current directory.

Returns:

res

Return type:

the response to the query

pyleoclim.utils.lipdutils.searchVar(timeseries_list, key, exact=True, override=True)[source]

This function searched for keywords (exact match) for a variable

Parameters:

timeseries_list (list) – A list of available series
key (list) – A list of keys to search
exact (bool) – if True, looks for an exact match.
override (bool) – if True, override the exact match if no match is found

Returns:

match – A list of keys for the timeseries that match the selection criteria.

Return type:

list

pyleoclim.utils.lipdutils.similar_string(list_str, search)[source]

Returns a list of indices for strings with similar values

Parameters:

list_str (list) – A list of strings
search (str) – A keyword search

Returns:

indices – A list of indices with similar value as the keyword

Return type:

list

pyleoclim.utils.lipdutils.timeUnitsCheck(units)[source]

This function attempts to make sense of the time units by checking for equivalence

Parameters:: units (string) – The units string for the timeseries
Returns:: unit_group – Whether the units belongs to age_units, kage_units, year_units, ma_units, or undefined
Return type:: string

pyleoclim.utils.lipdutils.whatArchives(print_response=True)[source]

Get the names for ArchiveType from LinkedEarth Ontology

Parameters:: print_response (bool) – Whether to print the results on the console. Default is True
Returns:: res
Return type:: JSON-object with the request from LinkedEarth wiki api

pyleoclim.utils.lipdutils.whatInferredVariables(print_response=True)[source]

Get the names for InferredVariables from LinkedEarth Ontology

Parameters:: print_response (bool) – Whether to print the results on the console. Default is True
Returns:: res
Return type:: JSON-object with the request from LinkedEarth wiki api

pyleoclim.utils.lipdutils.whatInterpretations(print_response=True)[source]

Get the names for interpretations from LinkedEarth Ontology

Parameters:: print_response (bool) – Whether to print the results on the console. Default is True
Returns:: res
Return type:: JSON-object with the request from LinkedEarth wiki api

pyleoclim.utils.lipdutils.whatProxyObservations(print_response=True)[source]

Get the names for ProxyObservations from LinkedEarth Ontology

Parameters:: print_response (bool) – Whether to print the results on the console. Default is True
Returns:: res
Return type:: JSON-object with the request from LinkedEarth wiki api

pyleoclim.utils.lipdutils.whatProxySensors(print_response=True)[source]

Get the names for ProxySensors from LinkedEarth Ontology

Parameters:: print_response (bool) – Whether to print the results on the console. Default is True
Returns:: res
Return type:: JSON-object with the request from LinkedEarth wiki api

pyleoclim.utils.lipdutils.whichEnsemble(ensembleTableList)[source]

Select an ensemble table from a list

Use in conjunction with the function isMeasurement

Parameters:

measurementTableList (list) – List of measurement tables contained in the LiPD file. Output from the isMeasurement function
csv_list (list) – Dictionary of available csv

Returns:

csvName – the name of the csv file

Return type:

string

pyleoclim.utils.lipdutils.whichMeasurement(measurementTableList)[source]

Select a measurement table from a list

Use in conjunction with the function isMeasurement

Parameters:: measurementTableList (list) – List of measurement tables contained in the LiPD file. Output from the isMeasurement function
Returns:: csvName – the name of the csv file
Return type:: string

pyleoclim.utils.lipdutils.xAxisTs(timeseries)[source]

Get the x-axis for the timeseries.

Parameters:

timeseries (dict) – a timeseries object

Returns:

x_axis (array) – the values for the x-axis representation
label (string) – returns either “age”, “year”, or “depth”

jsonutils

This module converts Pyleoclim objects to and from JSON files.

Useful for obtaining a human-readable output and keeping the results of an analysis. The JSON file can also be used to swap analysis results between programming languages.

These utilities are maintained on an as-needed basis and that not all objects are currently available.

pyleoclim.utils.jsonutils.PyleoObj_to_dict(obj)[source]

Transform a pyleoclim object into a dictionary.

The transformation ensures that all the objects are JSON serializable (i.e. all numpy arrays have been converted to lists.)

Parameters:: obj (pyleoclim.core.io) – A pyleoclim object from the UI module
Returns:: s – A JSON-encodable dictionary
Return type:: dict

See also

pyleoclim.utils.jsonutils.isPyleoclim: Whether an object is a valid Pyleoclim object

pyleoclim.utils.jsonutils.PyleoObj_to_json(obj, filename)[source]

Serializes a Pyleoclim object into a JSON file

Parameters:

obj (pyleoclim.core.ui) – A Pyleoclim object from the UI module
filename (str) – Filename or path to save the JSON to.

Return type:

None

See also

pyleoclim.utils.jsonutils.PyleoObj_to_dict: Encodes a Pyleoclim UI object into a dictionary that is JSON serializable

pyleoclim.utils.jsonutils.isPyleoclim(obj)[source]

Check whether an object is a valid type for Pyleoclim ui object

Parameters:: obj (pyleoclim.core.ui) – Object from the Pyleoclim UI module
Returns:: Bool
Return type:: {True,False}

pyleoclim.utils.jsonutils.json_to_PyleoObj(filename, objname)[source]

Reads a JSON serialized file into a Pyleoclim object

Parameters:

filename (str) – The filename/path/URL of the JSON-serialized object
objname (str) – Name of the object (e.g., Series, Scalogram, MultipleSeries…)

Returns:

pyleoObj – A Pyleoclim UI object

Return type:

pyleoclim.core.ui

See also

pyleoclim.utils.jsonutils.open_json: open a json file from a local source or URL
pyleoclim.utils.jsonutils.objename_to_obj: create a valid Pyleoclim object from a string

pyleoclim.utils.jsonutils.objname_to_obj(objname)[source]

Returns the correct obj type for the name of a Pyleoclim UI object

Parameters:: objname (str) – Name of the object (e.g., Series, Scalogram, MultipleSeries…)
Raises:: ValueError – If the name of the object is not valid
Returns:: obj – A valid Pyleoclim object for the UI module
Return type:: pyleoclim.core.ui

pyleoclim.utils.jsonutils.open_json(filename)[source]

Open a json file.

Parameters:: filename (str) – Path to the json file or URL
Returns:: t – A Python dictionary from the json
Return type:: dict