API Reference

AbstractCoordinateSystem

Base abstract type for all coordinate system implementations.

AbstractCoordinateVector

Base abstract type to represent coordinates in a coordinate systems.

A variable v of a type derived from AbstractDataVariable should at least implement:

• Base.parent(v): the parent array of the variable

Optional:

• times(v): the timestamps of the variable
• units(v): the units of the variable
• meta(v): the metadata of the variable
• name(v): the name of the variable

DataSet <: AbstractDataSet

A concrete dataset with a name, data (parameters), and metadata.

Construct a DataSet from a name and data, with optional metadata.

DataSet(ld::LDataSet; kwargs...)

Create a concrete DataSet from a Dataset template with specified data.

See also: LDataSet

Instrument <: AbstractInstrument

Fields

• name: The name of the instrument
• metadata: Additional metadata
• datasets: Collection of datasets

Construct an Instrument from a dictionary.

keyword-based constructor

LDataSet <: AbstractDataSet

A template for generating datasets with parameterized naming patterns.

Fields

• format: Format string pattern for the dataset name
• data: Dictionary of variable patterns
• metadata: Additional metadata

Examples

using SPEDAS.MMS

# Access FPI dataset specification
lds = mms.datasets.fpi_moms

# Create a concrete dataset with specific parameters
ds = DataSet(lds; probe=1, data_rate="fast", data_type="des")

The format string and variable patterns use placeholders like {probe}, {data_rate}, which are replaced with actual values when creating a concrete DataSet.

Construct a LDataSet from a dictionary.

NoMetadata

Indicates an object has no metadata. But unlike using nothing, get, keys and haskey will still work on it, get always returning the fallback argument. keys returns () while haskey always returns false.

Project <: AbstractProject

A representation of a project or mission containing instruments and datasets.

Fields

• name: The name of the project
• metadata: Additional metadata
• instruments: Collection of instruments
• datasets: Collection of datasets

keyword-based constructor

Create a new product with the composed function

_getfield(v, name, default)

Return the field from a composite v for the given name, or the given default if no field is present.

See also: getfield.

abbr(p)

Get the abbreviation (abbr) of p.

getcsys(x)

Get the coordinate system of x.

If x is a instance of AbstractCoordinateSystem, return x itself. If x is a type of AbstractCoordinateSystem, return an instance of the coordinate system, i.e. x().

This is a generic function, packages should extend it for their own types.

Check if a string is in Day of Year format (YYYY-DDD).

@get(collection, key, default)

Short-circuiting version of get. See also @something.

Short-circuiting version of _getfield.

cotrans(A, in, out)
cotrans(A, out; in=get_coord(A))

Transform the data to the out coordinate system from the in coordinate system.

This function automatically choose between Julia's GeoCotrans (if available) and Fortran's IRBEM implementation.

References:

• IRBEM-LIB: compute magnetic coordinates and perform coordinate conversions (Documentation, IRBEM.jl)
• SPEDAS Cotrans

Debouncer

A struct that creates a debounced version of a function f.

The debounced function will only execute after a specified delay (in seconds) of inactivity. If called again before the delay expires, the timer resets.

DualAxisData(data1, data2; meta=nothing)

A type for handling dual-axis data where each field represents data for a different axis. The first field is plotted against the left y-axis and the second field against the right y-axis.

Fields

• data1: Data for the left y-axis
• data2: Data for the right y-axis
• metadata: Metadata for the data (e.g., title)

DualPlot is the plot type associated with plotting function dualplot. Check the docstring for dualplot for further information.

FunctionPlot is the plot type associated with plotting function functionplot. Check the docstring for functionplot for further information.

LinesPlot is the plot type associated with plotting function linesplot. Check the docstring for linesplot for further information.

MultiPlot is the plot type associated with plotting function multiplot. Check the docstring for multiplot for further information.

PanelPlot is the plot type associated with plotting function panelplot. Check the docstring for panelplot for further information.

SpecPlot is the plot type associated with plotting function specplot. Check the docstring for specplot for further information.

Convert the vector of vectors into a single vector of curves

Add labels to a figure, automatically searching for blocks to label.

Notes

• https://github.com/brendanjohnharris/Foresight.jl/blob/main/src/Layouts.jl#L2

Add labels to a grid of layouts

Notes

• See tag_facet in egg for reference

Only add legend when the axis contains multiple labels

Only add legend when the axis contains multiple labels

auto_figure_size(tas)

Calculate an appropriate figure size based on the number of plots in the list. Returns a tuple of (width, height) in pixels.

Get the default orientation for a legend based on the position

No docstring defined.

Plot type

The plot type alias for the dualplot function is DualPlot.

Attributes

color2 = (Makie.wong_colors())[end - 1] — No docs available.

linestyle2 = :dash — No docs available.

marker2 = :rect — No docs available.

plotfunc = scatterlines! — No docs available.

dualplot! is the mutating variant of plotting function dualplot. Check the docstring for dualplot for further information.

Setup the panel with both primary and secondary y-axes

Format datetime ticks with time on top and date on bottom.

No docstring defined.

Plot type

The plot type alias for the functionplot function is FunctionPlot.

Attributes

plotfunc = tplot_panel! — No docs available.

functionplot! is the mutating variant of plotting function functionplot. Check the docstring for functionplot for further information.

functionplot!(ax, f, tmin, tmax; kwargs...)

Interactive plot of a function f on ax for a time range from tmin to tmax

functionplot(gp, f, tmin, tmax; kwargs...)

Interactively plot a function over a time range on a grid position

No docstring defined.

Plot type

The plot type alias for the linesplot function is LinesPlot.

Attributes

labels = nothing — No docs available.

linesplot! is the mutating variant of plotting function linesplot. Check the docstring for linesplot for further information.

linesplot(gp, ta)

Plot a multivariate time series on a panel

Create and configure a secondary y-axis

No docstring defined.

Plot type

The plot type alias for the multiplot function is MultiPlot.

Attributes

plotfunc = plot! — No docs available.

multiplot! is the mutating variant of plotting function multiplot. Check the docstring for multiplot for further information.

multiplot!(ax, fs, t0, t1; plotfunc=plot2spec, kwargs...)

Specialized multiplot function for functionplot. Merge specs before plotting so as to cycle through them.

multiplot(gp, tas::MultiPlottable, args...; axis=(;), kwargs...)

Setup the panel on a position and plot multiple time series on it

No docstring defined.

Plot type

The plot type alias for the panelplot function is PanelPlot.

Attributes

cycle = [:color] — No docs available.

plot = (;) — No docs available.

plotfunc = plot! — No docs available.

panelplot! is the mutating variant of plotting function panelplot. Check the docstring for panelplot for further information.

Plot attributes for a time array (axis + labels)

Determine the plotting function for a given data type. Extend this for custom data types to integrate with the plotting system.

Determine the plotting function for a given data type. Extend this for custom data types to integrate with the plotting system.

Plot attributes for a time array (labels)

Set an attribute if all values are equal and non-empty

No docstring defined.

Plot type

The plot type alias for the specplot function is SpecPlot.

Attributes

specplot! is the mutating variant of plotting function specplot. Check the docstring for specplot for further information.

Plot heatmap of a time series on the same axis

specplot(gp, ta)

Plot a spectrogram on a panel

spectrogram_y_values(ta; check=false, center=false, transform=identity)

Get y-axis values from a spectrogram array. Can return either bin centers or edges. By default, return bin edges for better compatibility.

Arguments

• check: If true, check if values are constant along time
• center: If true, return bin centers instead of edges
• transform: Optional transform function for edge calculation (e.g., log for logarithmic bins)

Reference: Makie.edges

Add vertical lines to a plot

tplot(f, tas; legend=(; position=Right()), link_xaxes=true, link_yaxes=false, rowgap=5, transform=transform_pipeline, kwargs...)

Lay out multiple time series across different panels (rows) on one Figure / GridPosition f

If legend is nothing, no legend will be added to the plot. Otherwise, legend can be a NamedTuple containing options for legend placement and styling. By default, the time series are transformed via transform_pipeline, which is extensible via transform.

See also: tplot_panel, transform_pipeline, transform

tplot_panel!(ax, args...; kwargs...)

Generic entry point for adding plots to an existing axis ax.

Transforms the arguments to appropriate types and calls the plotting function. Dispatches to appropriate implementation based on the plotting trait of the transformed arguments.

tplot_panel(gp, args...; kwargs...)

Generic entry point for plotting different types of data on a grid position gp.

Transforms the arguments to appropriate types and calls the plotting function. Dispatches to appropriate implementation based on the plotting trait of the transformed arguments.

tplot_panel_s!(ax::Axis, data; kwargs...)

Plot data on an axis.

transform(args...; kwargs...)

Transform data into plottable format (e.g., DimArray).

Extend with transform(x::MyType) for custom types.

transform_pipeline(x)

Transform data for plotting with the following pipeline:

1. Custom transformations (transform(x))
2. String -> SpeasyProduct

See also: transform

Convert x to DateTime

Reference:

• https://docs.makie.org/dev/explanations/dim-converts#Makie.DateTimeConversion
• https://github.com/MakieOrg/Makie.jl/issues/442
• https://github.com/MakieOrg/Makie.jl/blob/master/src/dim-converts/dates-integration.jl

Julia-based Space Physics Environment Data Analysis Software

See the Documentation for more information.

SPEDAS.DEFAULTS

A global constant that holds default parameters:

• add_title::Bool defaults to false.
• add_colorbar::Bool defaults to true.
• delay : in seconds, the time interval between updates. Default is 0.25.
• resample::Int : the number of points to resample to. Default is 6070.

Calculate the composite statistical error estimate for ⟨B·x₃⟩: |Δ⟨B·x₃⟩| = √(λ₃/(M-1) + (Δφ₃₂⟨B⟩·x₂)² + (Δφ₃₁⟨B⟩·x₁)²)

Parameters:

• λ₁, λ₂, λ₃: eigenvalues in descending order
• M: number of samples
• B: mean magnetic field vector
• x₁, x₂, x₃: eigenvectors

Constant Thickness Approach (CTA) for determining boundary normal and velocity. Based on the method described in Haaland et al., Annales Geophysicae, 2004.

ConstantVelocityApproach(positions, times, durations)

Given durations of the boundary crossings, calculate the thickness of the boundary

CVA(positions, times)

Constant Velocity Approach (CVA) for determining boundary normal and velocity. Solve timing equation: $D * m = Δts$

Parameters:

• positions: Positions of 4 spacecraft (4×3 array)
• times: Times of boundary crossing for each spacecraft

Discontinuity Analyzer (DA) for analyzing properties of discontinuities using multi-spacecraft measurements.

_linear_binedges(centers)

Calculate bin edges assuming linear spacing.

amap(f, a, b)

Apply a function f to the intersection of a and b.

https://github.com/rafaqz/DimensionalData.jl/issues/914

Return the angle between two vectors.

binedges(centers; transform=identity)

Calculate bin edges from bin centers.

• For linear spacing, edges are placed halfway between centers.
• For transformed spacing, edges are placed halfway between transformed centers.

Arguments

• transform: Function to transform the space (e.g., log for logarithmic spacing)

Example

centers = [1.0, 2.0, 3.0]
edges = binedges(centers)               # Returns [0.5, 1.5, 2.5, 3.5]
edges = binedges(centers, transform=log)  # Returns edges in log space

check_mva_eigen(F; r=5, verbose=false)

Check the quality of the MVA result.

If λ₁ ≥ λ₂ ≥ λ₃ are 3 eigenvalues of the constructed matrix M, then a good indicator of nice fitting LMN coordinate system should have λ₂ / λ₃ > r.

cotrans(A, in, out)
cotrans(A, out; in=get_coord(A))

Transform the data to the out coordinate system from the in coordinate system.

This function automatically choose between Julia's GeoCotrans (if available) and Fortran's IRBEM implementation.

References:

• IRBEM-LIB: compute magnetic coordinates and perform coordinate conversions (Documentation, IRBEM.jl)
• SPEDAS Cotrans

current_density(B, V)

Calculate the current density time series from the magnetic field (B) and plasma velocity (V) time series.

Assume 1-D structure along the z-direction. Remember to transform the coordinates of B and V first (e.g. using mva

dimarrayify(x)

Convert x or values of x to DimArray(s).

Transform matrix-like A to n×m shape

fac_mat(vec::AbstractVector; xref=[1.0, 0.0, 0.0])

Generates a field-aligned coordinate (FAC) transformation matrix for a vector.

Arguments

• vec: A 3-element vector representing the magnetic field

fill_gaps(times, data; resolution, margin)

Given a sorted vector of time stamps times and corresponding data values, this function inserts missing time stamps with a value of NaN if the gap between consecutive time stamps is larger than resolution + margin.

• If the gap is only slightly larger (within margin of the resolution), no gap is inserted.
• The function supports numeric times or DateTime (with appropriate resolution types).

Arguments

• times: Sorted vector of time stamps.
• resolution: The expected time difference between consecutive time stamps.
• margin: Allowed deviation from resolution before inserting missing time stamps.

Returns

A tuple (full_times, full_values) where:

• full_times is a vector containing all time stamps (original and inserted).
• full_values is a vector of data values with NaN for inserted gaps.

References

• https://pyspedas.readthedocs.io/en/latest/modules/pytplot/tplotmath/degap.html

find_continuous_timeranges(x, max_dt)

Find continuous time ranges for x (e.g. times or DimArray). max_dt is the maximum time gap between consecutive times.

interpolate_nans(da; interp=LinearInterpolation)

Interpolate only the NaN values in da along the specified dimension dims. Non-NaN values are preserved exactly as they are.

The default interpolation method interp is LinearInterpolation.

lingradest(
    Bx1, Bx2, Bx3, Bx4,
    By1, By2, By3, By4,
    Bz1, Bz2, Bz3, Bz4,
    R1, R2, R3, R4
)

SPEDAS-argument-compatible version of lingradest.

lingradest(B1, B2, B3, B4, R1, R2, R3, R4)

Compute spatial derivatives such as grad, div, curl and curvature using reciprocal vector technique (linear interpolation).

Arguments

• B1, B2, B3, B4: 3-element vectors giving magnetic field measurements at each probe
• R1, R2, R3, R4: 3-element vectors giving the probe positions

Returns

A named tuple containing: • Rbary: Barycenter position • Bbc: Magnetic field at the barycenter • Bmag: Magnetic field magnitude at the barycenter • LGBx, LGBy, LGBz: Linear gradient estimators for each component • LD: Linear divergence estimator • LCB: Linear curl estimator • curvature: Field‐line curvature vector • R_c: Field‐line curvature radius

References

Based on the method of Chanteur (ISSI, 1998, Ch. 11).

• lingradest.pro
• lingradest.py

lingradest(B1::AbstractDimArray, args...)

Method for handling dimensional arrays. Takes AbstractDimArray inputs with a time dimension and returns a DimStack containing all computed quantities.

lingradest(B1::MatrixLike, args...)

Vectorized method for simplified usage. Returns a StructArray containing the results.

Convert slowness vector $𝐦 = 𝐧/V$ to normal vector and velocity

mva(V, B=V; kwargs...)

Rotate a timeseries V into the LMN coordinates based on the reference field B.

Arguments

• V: The timeseries data to be transformed, where each column represents a component
• B: The reference field used to determine the minimum variance directions, where each column represents a component

See also: mva_eigen, rotate

mva_eigen(B::AbstractMatrix; sort=(;), check=false) -> F::Eigen

Perform minimum variance analysis, returning Eigen factorization object F which contains the eigenvalues in F.values and the eigenvectors in the columns of the matrix F.vectors.

Set check=true to check the reliability of the result.

The kth eigenvector can be obtained from the slice F.vectors[:, k].

nt2ds(nt_arr, dim; fields=propertynames(first(nt_arr)))

Convert a NamedTuple array to a DimStack of DimArrays.

Phase factor exp (i φ) satisfies the following equation

$\exp (4 i φ) = \exp (-2 i γ)$

where

$γ = \arctan (2 Re(𝐮)^𝐓 Im(𝐮) /(Re(𝐮)^2-Im(𝐮)^2))$

polarization(S0, S1, S2, S3)
polarization(S::StokesVector)

Compute the degree of polarization (p) from Stoke parameters or a Stokes vector.

Reference

• Wikipedia
• Stokes parameters

polarization(S)

Compute the degree of polarization (DOP) p^2 from spectral matrix S.

\[\begin{aligned} p^2 &= 1-\frac{(tr 𝐒)^2-(tr 𝐒^2)}{(tr 𝐒)^2-n^{-1}(tr 𝐒)^2} \\ &= \frac{n(tr 𝐒^2)-(tr 𝐒)^2}{(n-1)(tr 𝐒)^2} \end{aligned}\]

\[𝐑 = ∑_α (𝐫_α-𝐫_b) (𝐫_α-𝐫_b)' = ∑_α 𝐫_α 𝐫_α'-𝐫_b 𝐫_b'\]

with $𝐫_b = ∑_α 𝐫_α / N$ and N is the number of positions.

References

• Paschmann and Daly [2] Paschmann & Daly, 2008. Section 4.7

pspectrum(x::AbstractDimArray, spec::Spectrogram)
pspectrum(x::AbstractDimArray; nfft=256, noverlap=128, window=hamming)

Compute the power spectrum (time-frequency representation) of a time series using the short-time Fourier transform.

Returns a DimArray with frequency and original time dimensions.

See also: DSP.Spectrogram, DSP.stft

Reference

• Matlab

reciprocal_vector(rα, rβ, rγ, rλ)

Compute the reciprocal vector $𝒌_α$ for a vertex of a tetrahedron given the position vectors of all vertices.

The vertices (α, β, γ, λ) must form a cyclic permutation of (1, 2, 3, 4).

reciprocal_vector(rα, r0s::AbstractVector{<:AbstractVector})

Generalised reciprocal vector for N != 4

\[𝐪_α = 𝐑^{-1} 𝐫_α\]

See also: reciprocal_vector, position_tensor

reciprocal_vector(r_βα, r_βγ, r_βλ)

Compute the reciprocal vector $𝒌_α$ for a vertex of a tetrahedron given the relative position vectors.

\[𝒌_α = \frac{𝐫_{βγ} × 𝐫_{βλ}}{𝐫_{βα} ⋅ (𝐫_{βγ} × 𝐫_{βλ})}\]

where $𝐫_{αβ} = r_β - r_α$ are relative position vectors.

References

• Multi-spacecraft analysis methods revisited : 4.3 Properties of reciprocal vectors

Compute the set of reciprocal vectors {$𝒌_α$}, which is also called the reciprocal base of the tetrahedron.

See also: reciprocal_vector

resample(arr, n=DEFAULTS.resample; dim=1, verbose=false)

Resample an array along the dimension dim to n points. If the original length is less than or equal to n, the original array is returned unchanged.

rotate(ts::AbstractMatrix, mat::AbstractMatrix)

Coordinate-aware transformation of vector/matrix by rotation matrix(s) mat(s). Assume ts is a matrix of shape (n, 3).

Set the coordinate system.

Updates legend names and axis labels if they include the coordinate system. Also updates the dimension name if it contains the coordinate system.

Reference:

• https://pyspedas.readthedocs.io/en/latest/modules/pytplot/dataattgetterssetters.html#set_coords

smooth_spectral_matrix!(S_smooth, S, aa)

In-place version of smooth_spectral_matrix that writes results to a pre-allocated array.

smooth_spectral_matrix(S, aa)

Smooth the spectral matrix $S(f)$ by applying a weighted average over frequency. The smoothing uses a symmetric window aa (for example, a Hamming window) of length M.

Arguments

• S: Spectral matrix array of size $N_{freq}, n, n$ where n is the number of components.
• aa: Weighting vector of length M.

spectral_matrix(Xf)

Compute the spectral matrix $S$ defined by

\[S_{ij}(f) = X_i(f) X_j^*(f),\]

where $X_i(f)$=Xf[f, i] is the FFT of the i-th component and * denotes complex conjugation.

spectral_matrix(X, window)

Compute the spectral matrix $S(f)$ given the time series data X.

Returns a 3-D array of size $N_{freq}, n, n$, where $N_{freq} = \lfloor N/2 \rfloor$ and n is the dimensionality (number of components).

Arguments

• X: Matrix where each column is a component of the multivariate time series, or a vector of vectors.
• window: A window function (optional). If not provided, a rectangular window (no windowing) is used.

Calculate tetrahedron quality factors

tinterp(A, t; interp=LinearInterpolation)

Interpolate time series A at time point(s) t using interp (default: LinearInterpolation) method. Returns interpolated value for single time point or DimArray for multiple time points.

See DataInterpolations.jl for available interpolation methods.

Examples

# Interpolate at a single time point
tinterp(time_series, DateTime("2023-01-01T12:00:00"))

# Interpolate at multiple time points using cubic spline interpolation
new_times = DateTime("2023-01-01"):Hour(1):DateTime("2023-01-02")
tinterp(time_series, new_times; interp = CubicSpline)

tinterp(A, B; interp=LinearInterpolation)

Interpolate A to times in B

tinterp_nans(da::AbstractDimArray; query=timeDimType, kwargs...)

Interpolate only the NaN values in da along the specified dimensions query. Non-NaN values are preserved exactly as they are.

See also interpolate_nans

tresample(da::DimArray, n=DEFAULTS.resample; dimtype=Ti)

Resample a DimArray specifically along its dimension of type dimtype to n points. Throws an error if no dimension of type dimtype is found in the array.

tstack(vectors::AbstractVector{<:AbstractVector{T}})

Stack a time series of vectors into a matrix.

By default, each row in the output matrix represents a time point from the input vector of vectors.

tsync(A, Bs...)

Synchronize multiple time series to have the same time points.

This function aligns the time series Bs... to match the time points of A by:

1. Finding the common time range between all input time series
2. Extracting the subset of A within this common range
3. Interpolating each series in Bs... to match the time points of the subset of A

Returns a tuple containing the synchronized time series, with the first element being the subset of A and subsequent elements being the interpolated versions of Bs....

Examples

A_sync, B_sync, C_sync = tsync(A, B, C)

See also: tinterp, common_timerange

twavpol(x)

A convenience wrapper around wavpol that works with DimensionalData arrays.

It automatically extracts the time dimension and returns the results as a DimStack with properly labeled dimensions.

Wave normal angle is the angle between (wnx, wny) and the vertical |wnz| Use the imaginary parts of off-diagonals. Define:$A = Im(S₁₂), B = Im(S₁₃), C = Im(S₂₃)$

wavpol(X, fs=1; nfft=256, noverlap=div(nfft, 2), smooth_t=_smooth_t(nfft), smooth_f=hamming(3), nbuffers=Threads.nthreads())

Perform polarization analysis of n-component time series data.

For each FFT window (with specified overlap), the routine:

1. Applies a time-domain window function and computes the FFT to construct the spectral matrix $S(f)$
2. Applies frequency smoothing using a window function
3. Computes wave parameters: power, degree of polarization, wave normal angle, ellipticity, and helicity

The analysis assumes the data are in a right-handed, field-aligned coordinate system (with Z along the ambient magnetic field).

Arguments

• X: Matrix where each column is a component of the multivariate time series
• fs: Sampling frequency (default: 1)

Keywords

• nfft: Number of points for FFT (default: 256)
• noverlap: Number of overlapping points between windows (default: nfft÷2)
• smooth_t: Time domain window function (default: Hann window)
• smooth_f: Frequency domain smoothing window (default: 3-point Hamming window)
• nbuffers: Number of pre-allocated buffers for parallel processing (default: number of threads)

Returns

A named tuple containing:

• indices: Time indices for each FFT window
• freqs: Frequency array
• power: Power spectral density, normalized by frequency bin width and window function
• degpol: Degree of polarization [0,1]
• waveangle: Wave normal angle [0,π/2]
• ellipticity: Wave ellipticity [-1,1], negative for left-hand polarized
• helicity: Wave helicity

See also: polarization, wave_normal_angle, wpol_helicity

wpol_helicity(S, waveangle)

Compute helicity and ellipticity for a single frequency.

Arguments

• S: Spectral matrix for a single frequency, size (3,3)
• waveangle: Wave normal angle for this frequency

Returns

• helicity: Average helicity across the three components
• ellipticity: Average ellipticity across the three components

permutedims is needed for series in Makie

Δφij(λᵢ, λⱼ, λ₃, M)

Calculate the phase error between components i and j according to: |Δφᵢⱼ| = |Δφⱼᵢ| = √(λ₃/(M-1) * (λᵢ + λⱼ - λ₃)/(λᵢ - λⱼ)²)

Parameters:

• λᵢ: eigenvalue i
• λⱼ: eigenvalue j
• λ₃: smallest eigenvalue (λ₃)
• M: number of samples

Convert angular frequency to frequency

Reference: https://www.wikiwand.com/en/articles/Angular_frequency

@load_project_config(file)

Load configuration from a file and export all key-value pairs as constants. The macro evaluates in the calling module's context.

TimeseriesUtilities

A collection of utilities to simplify common time series analysis.

From data cleaning to arithmetic operations (e.g. linear algebra) to common time series operations (e.g. resampling, filtering).

Data Cleaning

• find_outliers, find_outliers_median, find_outliers_mean
• replace_outliers, replace_outliers!

Query

• times, time_grid
• timerange, common_timerange

(Windowed) Statistics

• tstat
• tmean
• tmedian
• tsum
• tvar
• tstd
• tsem

Algebra

• tcross
• tdot
• tnorm
• tsproj, tproj, toproj
• tsubtract
• tderiv

Time-Domain Operations

• tselect
• tclip, tclips
• tview
• tmask and tmask!
• tshift
• tsplit
• tgroupby

Time-Frequency Domain Operations

• tfilter

DiffQ(v, t; dim=1)

Difference quotient of v with respect to t.

To avoid undefined behavior for division by Date/DateTime, we convert the time difference to a Unitful.Quantity if eltype(v) is not a Unitful.Quantity.

common_timerange(x1, xs...)

Get the common time range (intersection) across multiple arrays. If there is no overlap, returns nothing.

dimnum(x, query)

Get the number(s) of Dimension(s) as ordered in the dimensions of an object.

Extend the function for custom type x. By default, we fall back to DimensionalData.dimnum.

dropna(A; dim=nothing)
dropna(A::AbstractDimArray; dim=nothing, query=nothing)

Remove slices containing NaN values along along the dim dimension.

find_outliers(A, [method, window]; dim = 1, kw...)

Find outliers in data A along the specified dim dimension.

Returns a Boolean array whose elements are true when an outlier is detected in the corresponding element of A.

The default method is :median (other option is :mean), which uses the median absolute deviation (MAD) to detect outliers. When the length of A is greater than 256, it uses a moving window of size 16.

See also: find_outliers_median, find_outliers_mean, isoutlier - MATLAB

find_outliers_mean(x::AbstractVector, window; threshold = 3)

Find outliers that are defined as elements more than three standard deviations from the mean.

This method is faster but less robust than find_outliers_median.

find_outliers_median(x, window; threshold=3)

Find outliers that are defined as elements more than threshold=3 times the scaled median absolute deviation (MAD) from the median.

When window is set to a integer, a moving window of that size is used to compute local MAD. Otherwise, global statistics are used.

References

• Median absolute deviation - Wikipedia

Group x into windows based on every and period.

interpolate_outliers!(x, t, outliers)

Interpolate outliers in x using interpolation of neighboring non-outlier values.

Vector rejection

proj(a, b)

Vector projection of a vector a on (or onto) a nonzero vector b.

References: Wikipedia

See also: sproj, oproj

Rectify the time step of a DimArray to be uniform.

replace_outliers!(A, s, [find_method, window]; kwargs...)

Finds outliers in A and replaces them with s (by default: NaN).

See also: find_outliers, filloutliers - MATLAB

replace_outliers!(A, method, [find_method, window]; kwargs...)
replace_outliers!(A, method, outliers; kwargs...)

Replaces outliers in A with values determined by the specified method.

Outliers can be detected using find_outliers with optional find_method and window parameters or specified directly as a Boolean array outliers.

method can be one of the following:

• :linear: Linear interpolation of neighboring, nonoutlier values
• :previous: Previous nonoutlier value
• :next: Next nonoutlier value
• :nearest: Nearest nonoutlier value

See also: filloutliers - MATLAB

replace_outliers(A; args...; kw...)

Non-mutable version of replace_outliers!.

smooth(da::AbstractDimArray, window; dim=Ti, suffix="_smoothed", kwargs...)

Smooths a time series by computing a moving average over a sliding window.

The size of the sliding window can be either:

• Quantity: A time duration that will be converted to number of samples based on data resolution
• Integer: Number of samples directly

Arguments

• dims=Ti: Dimension along which to perform smoothing (default: time dimension)
• suffix="_smoothed": Suffix to append to the variable name in output
• kwargs...: Additional arguments passed to RollingWindowArrays.rolling

Scalar projection

tclip(A, t0, t1; query=nothing, sort=false)

Clip a Dimension or DimArray A to a time range [t0, t1].

For unordered dimensions, the dimension should be sorted before clipping (see tsort).

tclips(xs...; trange=common_timerange(xs...))

Clip multiple arrays to a common time range trange.

If trange is not provided, automatically finds the common time range across all input arrays.

tcross(x, y; dim = nothing, query=nothing)

Compute the cross product of two (arrays of) vectors along the specified dimension dim or query.

References:

• https://docs.xarray.dev/en/stable/generated/xarray.cross.html

tderiv(A, times; dim=1)
tderiv(A; dim = nothing, query = nothing)

Compute the time derivative of A. Set lazy=true for lazy evaluation.

See also: deriv_data - PySPEDAS

tdot(x, y; dim=nothing, query=nothing)

Dot product of two arrays x and y along the dim dimension.

tfilter(da, Wn1, Wn2=samplingrate(da) / 2; designmethod=nothing)

By default, the max frequency corresponding to the Nyquist frequency is used.

References

• https://docs.juliadsp.org/stable/filters/
• https://www.mathworks.com/help/signal/ref/filtfilt.html
• https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.filtfilt.html

Issues

• DSP.jl and Unitful.jl: https://github.com/JuliaDSP/DSP.jl/issues/431

tgroupby(x, every, period = every, start_by = :window)

Group x into windows based on every and period.

time_grid(x, dt)

Create a time grid from the minimum to maximum time in x with the step size dt.

Examples

# Create hourly time grid
time_grid(x, Hour(1))
time_grid(x, 1u"hr")

# Create 1-s intervals
time_grid(x, Second(1))
time_grid(x, 1u"second")
time_grid(x, 1u"Hz")

timerange(times)
timerange(x1, xs...)

Get the time range (minimum and maximum) of time series data.

For a single argument, returns a tuple (tmin, tmax) containing the minimum and maximum times. For multiple arguments, returns the common time range (intersection) across all arrays - equivalent to common_timerange(x1, xs...).

Examples

# Single time series
times = [1, 2, 3, 4, 5]
timerange(times)  # (1, 5)

# Multiple time series - find common range
x1_times = [1, 2, 3, 4]
x2_times = [2, 3, 4, 5]
timerange(x1_times, x2_times)  # (2, 4)

See also: common_timerange, tminimum, tmaximum

Returns the time indices of x.

tmask!(da, t0, t1)
tmask!(da, it::Interval)
tmask!(da, its)

Mask all data values within the specified time range(s) (t0, t1) / it / its with NaN.

tmask(da, args...; kwargs...)

Non-mutable version of tmask!. See also tmask!.

tmaximum(x)

Get the maximum timestamp of x.

tmean(x, [dt]; dim=nothing, query=nothing)

Calculate the arithmetic mean of x along the dim dimension, optionally grouped by dt.

It returns a value if x is a vector along the dim dimension, otherwise returns a DimArray with the specified dimension dropped.

If dim is not specified, it defaults to the query dimension (dimension of type TimeDim by default).

tmedian(x, [dt]; dim=nothing, query=nothing)

Calculate the median of x along the dim dimension, optionally grouped by dt.

It returns a value if x is a vector along the dim dimension, otherwise returns a DimArray with the specified dimension dropped.

If dim is not specified, it defaults to the query dimension (dimension of type TimeDim by default).

tminimum(x)

Get the minimum timestamp of x.

tnorm(A; dim=nothing, query=nothing)

Compute the norm of each slice in A along the specified dimension dim or query.

See also: tnorm_combine

tnorm_combine(x; dim=nothing, name=:magnitude)

Calculate the norm of each slice along query dimension and combine it with the original components.

toproj(A, B; dim=nothing, query=nothing)

Compute vector rejection (orthogonal projection) of array A from B along specified dimension dim or query.

tproj(A, B; dim=nothing, query=nothing)

Compute vector projection of A onto B along specified dimension dim or query.

tselect(A, t, [δt]; query=nothing)

Select the value of A closest to time t within the time range [t-δt, t+δt].

Similar to DimensionalData.Dimensions.Lookups.At but choose the closest value and return missing if the time range is empty.

tsem(x, [dt]; dim=nothing, query=nothing)

Calculate the standard error of the mean of x along the dim dimension, optionally grouped by dt.

It returns a value if x is a vector along the dim dimension, otherwise returns a DimArray with the specified dimension dropped.

If dim is not specified, it defaults to the query dimension (dimension of type TimeDim by default).

tshift(x; dim=TimeDim, t0=nothing, new_dim=nothing)

Shift the dim of x by t0.

tsort(A; query=nothing, rev=false)

Sort a DimArray A along the query dimension.

tsplit(da::AbstractDimArray, dim=Ti)

Splits up data along dimension dim.

tsproj(A, B; dim=nothing, query=nothing)

Compute scalar projection of A onto B along specified dimension dim or query.

tstat(f, x, [dt]; dim = nothing)

Calculate the statistic f of x along the dim dimension, optionally grouped by dt.

See also: groupby_dynamic

tstd(x, [dt]; dim=nothing, query=nothing)

Calculate the standard deviation of x along the dim dimension, optionally grouped by dt.

It returns a value if x is a vector along the dim dimension, otherwise returns a DimArray with the specified dimension dropped.

If dim is not specified, it defaults to the query dimension (dimension of type TimeDim by default).

tsubtract(x, f=nanmedian; dims=timedim(x))

Subtract a statistic (default function f: nanmedian) along dimensions (default: time dimension) from x.

tsum(x, [dt]; dim=nothing, query=nothing)

Calculate the sum of x along the dim dimension, optionally grouped by dt.

It returns a value if x is a vector along the dim dimension, otherwise returns a DimArray with the specified dimension dropped.

If dim is not specified, it defaults to the query dimension (dimension of type TimeDim by default).

tvar(x, [dt]; dim=nothing, query=nothing)

Calculate the variance of x along the dim dimension, optionally grouped by dt.

It returns a value if x is a vector along the dim dimension, otherwise returns a DimArray with the specified dimension dropped.

If dim is not specified, it defaults to the query dimension (dimension of type TimeDim by default).

tview(d, t0, t1)

View a dimension or DimArray in time range [t0, t1].

unwrap(x)

Return the innermost object of the wrapped object x with similar behavior as x (e.g. same size, same type, etc.)

window_bf_sizes(window)

Converts a window specification to backward and forward window sizes.

When window is a positive integer scalar, the window is centered about the current element and contains window-1 neighboring elements. If window is even, then the window is centered about the current and previous elements.