Instruction for BOOOM
My Nguyen
2024-05-07
Optimization problem
Install package
library(devtools)
install_github("hamy12398/ballsdMN")### Load package
library("BOOOM")
library(Rcpp)
library(testthat)
library(RcppArmadillo)
library(pracma)Function augment
BOOOM_opt(Mat, func,
desired_min = -10^(60),
s_init = 1,
no_runs = 1000,
max_iter = 10000,
rho = 2,
phi = 10^(-20),
tol_fun = 10^(-6),
tol_fun_2 = 10^(-15),
desired_improv_rate = 10^(-20),
improv_rate_period = 20,
total_iter = 10000000,
print_output = 0
)Mat = List of multiple orthognal matrix input
func = The interested function to ooptimize
s_init = Initial Global Step Size. Default Value is 1.
no_runs = Number of Runs. Default Value is 1,000.
max_iter = Max Number Of Iterations In each Run. Default Value is 10,000.
rho = Factor by which step-size value is decremented to enable jumps of smaller step-sizes. Default Value is 2.
phi = Value of the smallest step-size. Default Value is .
tol_fun = Termination Tolerance on the function value. Default Value is .
tol_fun_2 = Termination Tolerance on the difference of solutions in two consecutive runs. Default Value is .
improv_rate_period = The number of iteration of a Run to control the rate of decrement of objective function value.
Example
Create function
Firstly, we need to have the function of multiple row orthognal matrices that needs to be optimized. For example, we generate a function: finds an row orthogonal A that minimize the least square difference (L2 norm) between A and a given constant matrix (B)
## Create constant matrix B dimension 5x5
Mat_B = list()
for ( i in 1:3){
mat <- randortho(5)
Mat_B[[i]] <- mat
}
Mat_B## [[1]]
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.2154170 0.2004185 0.1873450 -0.6851848 -0.63941503
## [2,] -0.6804706 0.0247309 0.4102292 0.3606922 -0.48781275
## [3,] -0.5935054 0.1055514 -0.7247361 -0.3329649 -0.02241095
## [4,] 0.2623309 -0.6178461 -0.4207463 0.2885350 -0.53774422
## [5,] -0.2636078 -0.7525596 0.3071548 -0.4542080 0.25202389
##
## [[2]]
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.1254617 -0.08544999 0.8974851 -0.4129853 0.03035201
## [2,] 0.3066282 0.28370281 -0.2884925 -0.5433525 0.66860449
## [3,] 0.3675769 0.46814763 -0.1424442 -0.3469806 -0.71066101
## [4,] -0.5616959 0.78133357 0.2078460 0.1281943 0.11992441
## [5,] -0.6630410 -0.28734418 -0.2186371 -0.6303823 -0.18062627
##
## [[3]]
## [,1] [,2] [,3] [,4] [,5]
## [1,] -0.11066919 -0.07499812 -0.3909510 0.8456838 0.3377926
## [2,] 0.39614187 0.56470133 -0.1090162 -0.2204696 0.6809498
## [3,] -0.07888133 -0.74005095 0.1458765 -0.2490960 0.6023069
## [4,] 0.25222943 -0.24239749 -0.8631336 -0.3134572 -0.1853878
## [5,] -0.87234282 0.26278459 -0.2626654 -0.2755138 0.1583075## Create function need to be optimized
calculate_l2_norm_mm <- function(matrices1) {
## identify number of matrix and dimension
sum_squares <- 0
set.seed(1)
# Initialize sum of squared differences
for (i in 1:3) {
# Calculate the difference between corresponding matrices
diff_matrix <- matrices1[[i]] - Mat_B[[i]]
# Calculate the sum of squared differences for this pair
sum_squares <- sum_squares + sum(diff_matrix^2)
}
# Calculate the square root of the sum of squared differences
l2_norm <- sqrt(sum_squares)
return(l2_norm)
}Initial input matrix
### Generate an inital input (row of orthognal)
matrix1 <- randortho(5)
matrix2 <- randortho(5)
matrix3 <- randortho(5)
Mat_A=list(matrix1,matrix2,matrix3)
Mat_A## [[1]]
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.5757865 0.65012057 0.4736613 0.008831053 0.1462196
## [2,] 0.5159878 -0.14196822 -0.3009820 -0.689603118 -0.3840039
## [3,] -0.2610782 0.69130273 -0.6589617 -0.103109918 0.0952707
## [4,] 0.2720606 -0.26504580 -0.2375228 -0.130698910 0.8844402
## [5,] 0.5099487 -0.09507647 -0.4409163 0.704738031 -0.1996243
##
## [[2]]
## [,1] [,2] [,3] [,4] [,5]
## [1,] -0.312845540 -0.6087234167 -0.72088713 -0.06956638 -0.08405795
## [2,] -0.037213247 0.0009997181 -0.09244646 0.98944201 0.10522518
## [3,] 0.291402949 -0.7356257294 0.52138693 0.09292943 -0.30571048
## [4,] -0.004809744 -0.2961196118 0.15088119 -0.08567149 0.93924720
## [5,] 0.903218706 0.0249552449 -0.42091084 -0.01376760 0.07885254
##
## [[3]]
## [,1] [,2] [,3] [,4] [,5]
## [1,] -0.7120219 0.6865112 0.04274324 -0.1381982 -0.02831116
## [2,] -0.5404552 -0.4218094 0.11527032 0.6731502 0.25212415
## [3,] -0.3336773 -0.3775701 -0.47614259 -0.1597454 -0.70275880
## [4,] 0.2268370 0.3886419 -0.71697121 0.5301682 0.04874884
## [5,] 0.1952882 0.2391182 0.49409137 0.4702906 -0.66286160#### a Mat A matrix is an row orthognal matrix where the off-diagonal elements close to 0
Mat_A[[1]] %*% t(Mat_A[[1]])## [,1] [,2] [,3] [,4] [,5]
## [1,] 1.000000e+00 -8.326673e-17 1.578598e-16 -1.942890e-16 -2.324529e-16
## [2,] -8.326673e-17 1.000000e+00 -6.938894e-18 2.220446e-16 0.000000e+00
## [3,] 1.578598e-16 -6.938894e-18 1.000000e+00 -1.387779e-17 2.428613e-17
## [4,] -1.942890e-16 2.220446e-16 -1.387779e-17 1.000000e+00 -1.110223e-16
## [5,] -2.324529e-16 0.000000e+00 2.428613e-17 -1.110223e-16 1.000000e+00Result
The optimized matrices list should be closed to the constant matrix B above, as their square of difference goes to 0.
result = BOOOM_opt((Mat_A), calculate_l2_norm_mm)## ********** TASK COMPLETE ****************
## Final Obj function value :2.82985result## [[1]]
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.30777642 0.4679596 -0.31557418 -0.5633424 -0.5189854
## [2,] -0.53910028 0.4342436 -0.35956585 0.5471907 -0.3034767
## [3,] -0.74369205 -0.3294997 0.09306586 -0.5310940 -0.2182428
## [4,] 0.24146948 -0.6782762 -0.30715074 0.2610141 -0.5649459
## [5,] -0.05708933 -0.1543298 -0.81738761 -0.1817647 0.5213082
##
## [[2]]
## [,1] [,2] [,3] [,4] [,5]
## [1,] 0.1116870 -0.07261373 0.8900034 -0.4359786 0.008364309
## [2,] 0.2930043 0.28885258 -0.2860755 -0.5441317 0.672899823
## [3,] 0.3969191 0.43610657 -0.1748889 -0.3416045 -0.710624038
## [4,] -0.5432051 0.80240653 0.1957783 0.1283791 0.079130344
## [5,] -0.6701178 -0.27793210 -0.2390387 -0.6169835 -0.189440574
##
## [[3]]
## [,1] [,2] [,3] [,4] [,5]
## [1,] -0.53600621 -0.41722691 -0.3940861 0.60744402 -0.11969531
## [2,] -0.53945894 -0.18808525 -0.1159158 -0.74451846 -0.32536717
## [3,] 0.02691869 -0.65492543 0.1466574 -0.18983512 0.71610215
## [4,] 0.46014259 -0.07511051 -0.8616008 -0.19699996 0.03824095
## [5,] -0.45741182 0.59663786 -0.2596063 -0.04310079 0.60460282