Compute Multi Entry Perturbation Expectation
This function takes a jacobian matrix and computes the multi-entry perturbation expectation.
In this example we take the IGP.csv matrix and use the default num_iterates and interval_length values.
The IGP.csv file is an example dataset that is included in the PressPurt package.
infile <- system.file("extdata", "Modules", "IGP.csv", package = "PressPurt")
MultiPert <- ComputeMultiEntryPerturbationExpectation(input_file = infile)
MultiPert
#> [1] 0.266
PreprocessMatrix
This function pre-processes a matrix by figuring out what the intervals of asymptotic stability are, as well as finding which perturbation values lead to a sign switch.
In this example we use a max_bound of 10, don’t perturb zero entries and use 2 threads.
PreProsMatrix <- PreprocessMatrix(input_file = infile,
max_bound = 10,
zero_perturb = FALSE,
threads = 2)
Output
The output is a list of 9 objects which includes: original_matrix, matrix_size, column_names, row_names, non_zero, num_switch_functions_py, asymptotic_stability_start, asymptotic_stability_end, num_switch_funcs_r
Matrix
This includes the original matrix and information about that matrix:
# Original Matrix
PreProsMatrix$original_matrix
#> [,1] [,2] [,3] [,4]
#> [1,] -0.237 -1.000 0.000 0.000
#> [2,] 0.100 -0.015 -1.000 -1.000
#> [3,] 0.000 0.100 -0.015 -1.000
#> [4,] 0.000 0.045 0.100 -0.015
# Matrix size
PreProsMatrix$matrix_size
#> [1] 4
# row names
PreProsMatrix$row_names
#> [1] "0" "1" "2" "3"
# column names
PreProsMatrix$column_names
#> [1] "0" "1" "2" "3"
# number of entries that aren't zero
PreProsMatrix$non_zero
#> [1] 12
Asymptotic of Stability intervals
The asymptotic of stability intervals are divided up into two matrices: start and stop.
# Start
PreProsMatrix$asymptotic_stability_start
#> [,1] [,2] [,3] [,4]
#> [1,] -0.08298658 -9.99999999 0.00000000 0.000000
#> [2,] -0.02593439 -9.99999999 -0.25212423 -7.117953
#> [3,] 0.00000000 -0.08404049 -9.99999999 -1.448616
#> [4,] 0.00000000 -0.04499999 -0.02042571 -10.000000
# End
PreProsMatrix$asymptotic_stability_end
#> [,1] [,2] [,3] [,4]
#> [1,] 0.1090182 0.25934395 0.00000000 0.00000000
#> [2,] 10.0000000 0.01499999 0.99999999 0.99999999
#> [3,] 0.0000000 0.91947448 0.01499999 0.99999999
#> [4,] 0.0000000 0.01113441 0.63448010 0.01499999
# To access entry 1,1:
PreProsMatrix$asymptotic_stability_start[1,1]
#> [1] -0.08298658
PreProsMatrix$asymptotic_stability_end[1,1]
#> [1] 0.1090182
Num Switch
The num_switch_funcs object is a list of each non-zero entry in the matrix and the corresponding perturbation values that leads to a sign switch.
For example, entry 1,1 has 1 sign switch and 2,2 has 2.
# get the length of the list, see it's
# the same as the non-zero entries
length(PreProsMatrix$num_switch_funcs_r)
#> [1] 12
# see the names of the entries
names(PreProsMatrix$num_switch_funcs_r)
#> [1] "(1, 1)" "(1, 2)" "(2, 1)" "(2, 2)" "(2, 3)" "(2, 4)" "(3, 2)" "(3, 3)"
#> [9] "(3, 4)" "(4, 2)" "(4, 3)" "(4, 4)"
# num switch function for 1,1
PreProsMatrix$num_switch_funcs_r$`(1, 1)`
#> num_switch_val start end
#> 1 1 0.007114943 0.1090182
# num switch function for 2,2
PreProsMatrix$num_switch_funcs_r$`(2, 2)`
#> num_switch_val start end
#> 1 1 -0.3125131 -0.01305907
#> 2 2 -10.0000000 -0.31251310
You can ignore the num_switch_functions_py object as it is a python dictionary that is passed to the next step.
Compute Entry Wise Perturbation Expectation
This function computes the expected number of sign switches from perturbing each entry individually.
In this example, the PreProsMatrix object is passed, “truncnorm” distribution is used, input_a is 0 and input_b is -2.
Entrywise <- ComputeEntryWisePerturbationExpectation(PreProsMatrix = PreProsMatrix,
distribution_type="truncnorm",
input_a=0, input_b=-2, threads=1)
Output
The output includes the same object that were found in PreProsMatrix with 3 additions: original_matrix, matrix_size, column_names, row_names, non_zero, num_switch_functions_py, asymptotic_stability_start, asymptotic_stability_end, num_switch_funcs_r, expected_num_switch, distributions_object, ns_object_plot
Expected num switch
This is a data frame of expected sign switches.
Entrywise$expected_num_switch
#> 0 1 2 3
#> 0 0.03155098 0.05964785 0.00000000 0.000000000
#> 1 0.06219858 0.12130032 0.05215649 0.021873797
#> 2 0.00000000 0.03050608 0.15946639 0.008706269
#> 3 0.00000000 0.05350997 0.08104533 0.174734087
Distributions Object
This object gets the probability density distribution into a plot ready format for each non-zero interval in the matrix. By default there are 250 points in the distribution.
# distributions object of each non-zero entry in the matrix
names(Entrywise$distributions_object)
#> [1] "(1, 1)" "(1, 2)" "(2, 1)" "(2, 2)" "(2, 3)" "(2, 4)" "(3, 2)" "(3, 3)"
#> [9] "(3, 4)" "(4, 2)" "(4, 3)" "(4, 4)"
# position in the matrix
Entrywise$distributions_object$`(1, 1)`[1]
#> $position
#> [1] 1 1
# Interval of asymptotic of stability
Entrywise$distributions_object$`(1, 1)`[2]
#> $interval
#> [1] -0.08298658 0.10901820
# ready to plot probability density distribution dataframe
head(Entrywise$distributions_object$`(1, 1)`[[3]], n = 10)
#> x_range dist_vals
#> 1 -0.08375460 0.000000
#> 2 -0.08297733 4.217092
#> 3 -0.08220006 4.246567
#> 4 -0.08142278 4.275968
#> 5 -0.08064551 4.305290
#> 6 -0.07986824 4.334529
#> 7 -0.07909097 4.363681
#> 8 -0.07831369 4.392740
#> 9 -0.07753642 4.421704
#> 10 -0.07675915 4.450566
Num Switch Object
The ns_object_plot is the Num Switch functions that have been converted into step functions and are ready to plot!
# Step function for each non-zero entry in the matrix
names(Entrywise$ns_object_plot)
#> [1] "(1, 1)" "(1, 2)" "(2, 1)" "(2, 2)" "(2, 3)" "(2, 4)" "(3, 2)" "(3, 3)"
#> [9] "(3, 4)" "(4, 2)" "(4, 3)" "(4, 4)"
# entry 1,1
Entrywise$ns_object_plot$`(1, 1)`
#> nsx nsy
#> 1 -0.082986581 0
#> 2 0.007114943 0
#> 3 0.109018199 1
# entry 4,2
Entrywise$ns_object_plot$`(4, 2)`
#> nsx nsy
#> 6 -0.044999990 4
#> 5 -0.043500000 4
#> 4 -0.043500000 3
#> 3 -0.031798604 2
#> 2 -0.001305907 1
#> 1 0.011134411 0
The y-0 position has been added to the step function:
# Before
Entrywise$num_switch_funcs_r$`(1, 1)`
#> num_switch_val start end
#> 1 1 0.007114943 0.1090182
# After - step function
Entrywise$ns_object_plot$`(1, 1)`
#> nsx nsy
#> 1 -0.082986581 0
#> 2 0.007114943 0
#> 3 0.109018199 1
Generate Entry Wise Figures
The GenerateEntryWiseFigures function plots the Num Switch step function on the Y-axis in black and the probability density on the Y-axis in grey.
One may plot individual entries or a list of entries with the list_of_numswitch_to_plot option:
list_of_numswitch_to_plot <- list(c(1, 1), c(1, 2))
GenerateEntryWiseFigures(EntryWise=Entrywise,
all_numswitch_plots = FALSE,
list_of_numswitch_to_plot=list_of_numswitch_to_plot)
Or plot all figures with all_numswitch_plots.
For large matrices it is not recommended that you plot them all in one plot.
GenerateEntryWiseFigures(EntryWise=Entrywise,
all_numswitch_plots = TRUE)
