tf-Class: Definition | tf-class | Example Data | tf subclass: tfd | tf subclass: tfb | tfb_spline: spline basis | Penalization: | tfb FPC-based | tf-Class: Methods | subset & subassign: | compare & compute: | summarize across a vector of functions: | summarize each function over its domain: | Methods for "functional" operations | evaluate: | (simple, local) smoothing | differentiate & integrate: | query | zoom & query

1. A quick tour of vector-valued functional data | What is a vector-valued function? | The tf_mv classes: tfd_mv and tfb_mv | Constructing tf_mv objects | Geometry on the bundle: speed, arc length, reparametrization | Aligning vector-valued curves: a ladder | 2. How variable is a "normal" gait cycle? | Pointwise mean and standard deviation | Most- and least-varied subjects | A ladder of registrations | Rung 1 -- arc-length reparametrization | Rung 2 -- alignment to a 1-d reference signal | Rung 3 -- joint multivariate reparametrization (srvf_mv) | Rung 4 -- full elastic shape registration | Quantifying the alignment | Shape registration and its quotient spaces | Modes of variation via FPC | Joint modes of variation via MFPCA | 3. Atlantic storms as 4-dimensional curves | Movement workflow: regularize, then describe | A single 4-d curve: Hurricane Katrina (2005) | Track map, faceted by peak intensity | Scalar features extracted from the 4-d object | Intensity and forward-speed life-cycles per category | Smoothing on normalised time | 4. Recap | References

Plotting with ggplot2 | tf_ggplot with standard geoms | Using with other ggplot2 features | Multivariate functional data (tf_mv) | Functional data boxplots with geom_fboxplot | Heatmaps for functional data: gglasagna | geom_capellini | Plotting with base R

Conversion from matrices | Conversion to tf from a data frame | ... in "long" format | ... in "wide" format | Changing representation with tf_rebase | Splitting and combining functions | Conversion from fda objects | Reversing the conversion | Conversion from tf to data frames | Converting back to a matrix or data frame

Registration: Template, Warp, Domain | What Is the Template? | What is a Warping Function? | Domain-Preserving vs Non-domain-preserving Warps | Example: Shift Registration with Explicit Template | Choosing a Registration Method | Evidence-Based Method Selection | Pitfalls and Likely Failure Modes | Structured shape variation | Noise dominates phase signal | Sparse or irregular grids | Boundary and overlap artifacts | Over-warping | Lambda penalization | Unsuitable template | Practical Diagnostics Workflow | Step 1: Register and inspect summary | Step 2: Visual inspection via plot() | Step 3: Quantify alignment of specific features | Step 4: Compare with an alternative method | Theoretical Background 101 | SRVF Framework | CC (Continuous Registration Criterion) | Affine (Shift / Scale) | Landmark | Worked Examples | Pinch Data: Cross-method Comparison | Growth Data: Deeper Real-data Workflow | Data representation matters | Penalization | Landmark registration | References

Data manipulation using tidyfun | Example datasets | Existing tidyverse functions | tf helper functions in tidy workflows | Working with data.table

Why use tidyfun | Thoughts on design | Using tidyfun in new functions | Keep us informed!