Generates a comprehensive summary of a gradient flow basin complex, including detailed information about extrema, basins, basin overlaps, and cell complex structure.
Usage
# S3 method for class 'basin_cx'
summary(object, ...)Arguments
- object
An object of class "basin_cx" as created by
create.basin.cx.- ...
Additional arguments (currently unused).
Value
An object of class "summary.basin_cx" containing:
- n_extrema
Total number of local extrema
- n_minima
Number of local minima
- n_maxima
Number of local maxima
- minima
Data frame of local minima information
- maxima
Data frame of local maxima information
- n_ascending_basins
Number of merged ascending basins (minima)
- n_descending_basins
Number of merged descending basins (maxima)
- ascending_basin_sizes
Summary statistics of ascending basin sizes
- descending_basin_sizes
Summary statistics of descending basin sizes
- minima_info
Detailed information about each minimum basin including vertex, label, size, and function value
- maxima_info
Detailed information about each maximum basin including vertex, label, size, and function value
- ascending_basins_jaccard_index
Matrix of Jaccard indices between pairs of ascending basins
- descending_basins_jaccard_index
Matrix of Jaccard indices between pairs of descending basins
- cells_summary
Summary of cell complex structure
- messages
Any messages generated during basin complex creation
Details
The summary method computes several key statistics and relationships:
Extrema Analysis: Counts and details of all local minima and maxima in the original function.
Basin Statistics: For both ascending (minimum) and descending (maximum) basins, provides counts, size distributions, and detailed information including the representative vertex, label, size (number of vertices), and function value.
Basin Overlap: Computes Jaccard indices between all pairs of basins of the same type. The Jaccard index measures the overlap between two basins as the ratio of their intersection size to their union size, ranging from 0 (no overlap) to 1 (complete overlap).
Cell Complex: Summarizes the structure of cells representing intersections between basins.
See also
create.basin.cx for creating basin complex objects,
print.basin_cx for basic basin complex information,
print.summary.basin_cx for printing summary objects
Examples
basin_cx <- list(
basins = list(
ascending = list(
m1 = list(vertex = 2L, value = 0.7, vertices = c(1L, 2L)),
m2 = list(vertex = 5L, value = 1.1, vertices = c(4L, 5L))
),
descending = list(
M1 = list(vertex = 3L, value = 3.2, vertices = c(2L, 3L, 4L))
)
),
local_extrema = data.frame(
vertex_index = c(2L, 5L, 3L),
label = c("m1", "m2", "M1"),
is_maximum = c(0, 0, 1),
fn_value = c(0.7, 1.1, 3.2)
),
original_y = c(2.5, 0.7, 3.2, 1.8, 1.1),
cells = list(
asc_desc_cells = list(c1 = list(vertices = c(2L, 3L))),
asc_asc_cells = list(),
desc_desc_cells = list()
)
)
class(basin_cx) <- "basin_cx"
basin_summary <- summary(basin_cx)
basin_summary$minima_info
basin_summary$cells_summary$total_cells