Sparse vector generation example (MPS row, column, value format) using tidyverse

[sbmack]

Here is an example for creating a sparse row, column, value data frame (tibble) from a dense data table using the tidyverse:

library(tidyverse)
set.seed(7)
data <- sample(c(0, 0, 1), 70, replace = TRUE)
data <- matrix(data, nrow = 7)
data
data2 <- as_tibble(data)
data2
data3 <- rownames_to_column(data2)
data3
data4 <- pivot_longer(data3, !rowname, names_to = "var")
data4
data5 <- filter(data4, value != 0)
data5

• data3 tibble represents a common fully dense representation of a data table, i.e., many zero (or NA) values
• data4 tibble creates the row, column, value format tibble
• data5 tibble removes the zero value row, column pairs resulting in a sparse representation, i.e. MPS format

If the sparse object must be a matrix then the column names could be the column numbers converted into integers (as.integer) and the sparse tibble then converted to a matrix. The user of course could write a generic function to execute all of the conversion steps and return a sparse object. ROI also has a "simple_triplet_matrix" class. Could that be integrated into MIPModel2?

[dirkschumacher]

If you have that kind of input data, then my feeling is you should use ROI directly and build a matrix for the constraints instead of using an algebraic framework.

However, with the new MIPModel you can also use that input and build your model:

library(tidyverse)
library(ompr)
set.seed(7)
data <- sample(c(0, 0, 1), 70, replace = TRUE)
data <- matrix(data, nrow = 7)
data2 <- as_tibble(data)
data3 <- rownames_to_column(data2)
data4 <- pivot_longer(data3, !rowname, names_to = "var")
data5 <- filter(data4, value != 0)
data5
#> # A tibble: 24 × 3
#>    rowname var   value
#>    <chr>   <chr> <dbl>
#>  1 1       V4        1
#>  2 1       V8        1
#>  3 2       V1        1
#>  4 2       V2        1
#>  5 2       V3        1
#>  6 2       V5        1
#>  7 3       V1        1
#>  8 3       V3        1
#>  9 3       V8        1
#> 10 3       V9        1
#> # … with 14 more rows

model <- MIPModel() |> 
  add_variable(x[i], i = sort(unique(data5$var))) |> 
  add_constraint(
    sum_over(
      data5$value[data5$rowname == j & data5$var == i] * x[i], 
      i = data5$var[data5$rowname == j]
    ) == 1, j = unique(data5$rowname))

extract_constraints(model) # note, the second column is V10, not V2
#> $matrix
#> 7 x 10 sparse Matrix of class "dgCMatrix"
#>                         
#> [1,] . . . . 1 . . . 1 .
#> [2,] 1 . 1 1 . 1 . . . .
#> [3,] 1 . . 1 . . . . 1 1
#> [4,] 1 1 1 . 1 . . 1 . .
#> [5,] . . 1 . . 1 1 . . .
#> [6,] 1 . . 1 . . . . 1 .
#> [7,] . . 1 . 1 . 1 . . .
#> 
#> $sense
#> [1] "==" "==" "==" "==" "==" "==" "=="
#> 
#> $rhs
#> [1] 1 1 1 1 1 1 1

^{Created on 2022-01-07 by the reprex package (v2.0.1)}