1 Mesh Matrices, Arrays and Scalars

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  • r expand.grid meshed array to matrix
  • r meshgrid
  • r array to matrix
  • r reshape array to matrix
  • dplyr permuations rows of matrix and element of array
  • tidyr expand_grid mesh matrix and vector

1.1 Mesh Two or More Vectors with expand_grid

In the example below, we have a matrix that is 2 by 2 (endogenous states), a vector that is 3 by 1 (choices), and another matrix that is 4 by 3 (exogenous states shocks).

We want to generate a tibble dataset that meshes the matrix and the vector, so that all combinations show up. Additionally, we want to add some additional values that are common across all rows to the meshed dataframe.

Note expand_grid is a from tidyr 1.0.0.

# A. Generate the 5 by 2 Matrix (ENDO STATES)
# it_child_count = N, the number of children
it_N_child_cnt = 2
# P fixed parameters, nN is N dimensional, nP is P dimensional
ar_nN_A = seq(-2, 2, length.out = it_N_child_cnt)
ar_nN_alpha = seq(0.1, 0.9, length.out = it_N_child_cnt)
fl_rho = 0.1
fl_lambda = 1.1
mt_nP_A_alpha = cbind(ar_nN_A, ar_nN_alpha, fl_rho, fl_lambda)
ar_st_varnames <- c('s_A', 's_alpha', 'p_rho', 'p_lambda')
tb_states_endo <- as_tibble(mt_nP_A_alpha) %>%
  rename_all(~c(ar_st_varnames)) %>%
  rowid_to_column(var = "state_id")

# B. Choice Grid
it_N_choice_cnt = 3
fl_max = 10
fl_min = 0
ar_nN_d = seq(fl_min, fl_max, length.out = it_N_choice_cnt)
ar_st_varnames <- c('c_food')
tb_choices <- as_tibble(ar_nN_d) %>%
  rename_all(~c(ar_st_varnames)) %>%
  rowid_to_column(var = "choice_id")

# C. Shock Grid
set.seed(123)
it_N_shock_cnt = 4
ar_nQ_shocks = exp(rnorm(it_N_shock_cnt, mean=0, sd=1))
ar_st_varnames <- c('s_eps')
tb_states_exo <- as_tibble(ar_nQ_shocks) %>%
  rename_all(~c(ar_st_varnames)) %>%
  rowid_to_column(var = "shock_id")

# dataframe expand with other non expanded variables
ar_st_varnames <-
tb_states_shk_choices <- tb_states_endo %>%
  expand_grid(tb_choices) %>%
  expand_grid(tb_states_exo) %>%
  select(state_id, choice_id, shock_id,
         s_A, s_alpha, s_eps, c_food,
         p_rho, p_lambda)

# display
kable(tb_states_shk_choices) %>% kable_styling_fc()
state_id choice_id shock_id s_A s_alpha s_eps c_food p_rho p_lambda
1 1 1 -2 0.1 0.5709374 0 0.1 1.1
1 1 2 -2 0.1 0.7943926 0 0.1 1.1
1 1 3 -2 0.1 4.7526783 0 0.1 1.1
1 1 4 -2 0.1 1.0730536 0 0.1 1.1
1 2 1 -2 0.1 0.5709374 5 0.1 1.1
1 2 2 -2 0.1 0.7943926 5 0.1 1.1
1 2 3 -2 0.1 4.7526783 5 0.1 1.1
1 2 4 -2 0.1 1.0730536 5 0.1 1.1
1 3 1 -2 0.1 0.5709374 10 0.1 1.1
1 3 2 -2 0.1 0.7943926 10 0.1 1.1
1 3 3 -2 0.1 4.7526783 10 0.1 1.1
1 3 4 -2 0.1 1.0730536 10 0.1 1.1
2 1 1 2 0.9 0.5709374 0 0.1 1.1
2 1 2 2 0.9 0.7943926 0 0.1 1.1
2 1 3 2 0.9 4.7526783 0 0.1 1.1
2 1 4 2 0.9 1.0730536 0 0.1 1.1
2 2 1 2 0.9 0.5709374 5 0.1 1.1
2 2 2 2 0.9 0.7943926 5 0.1 1.1
2 2 3 2 0.9 4.7526783 5 0.1 1.1
2 2 4 2 0.9 1.0730536 5 0.1 1.1
2 3 1 2 0.9 0.5709374 10 0.1 1.1
2 3 2 2 0.9 0.7943926 10 0.1 1.1
2 3 3 2 0.9 4.7526783 10 0.1 1.1
2 3 4 2 0.9 1.0730536 10 0.1 1.1

Using expand_grid directly over arrays

# expand grid with dplyr
expand_grid(x = 1:3, y = 1:2, z = -3:-1)

1.2 Mesh Arrays with expand.grid

Given two arrays, mesh the two arrays together.

# use expand.grid to generate all combinations of two arrays

it_ar_A = 5
it_ar_alpha = 10

ar_A = seq(-2, 2, length.out=it_ar_A)
ar_alpha = seq(0.1, 0.9, length.out=it_ar_alpha)

mt_A_alpha = expand.grid(A = ar_A, alpha = ar_alpha)

mt_A_meshed = mt_A_alpha[,1]
dim(mt_A_meshed) = c(it_ar_A, it_ar_alpha)

mt_alpha_meshed = mt_A_alpha[,2]
dim(mt_alpha_meshed) = c(it_ar_A, it_ar_alpha)

# display
kable(mt_A_meshed) %>%
  kable_styling_fc()
-2 -2 -2 -2 -2 -2 -2 -2 -2 -2
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1
0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1
2 2 2 2 2 2 2 2 2 2 
kable(mt_alpha_meshed) %>%
  kable_styling_fc_wide()
0.1 0.1888889 0.2777778 0.3666667 0.4555556 0.5444444 0.6333333 0.7222222 0.8111111 0.9
0.1 0.1888889 0.2777778 0.3666667 0.4555556 0.5444444 0.6333333 0.7222222 0.8111111 0.9
0.1 0.1888889 0.2777778 0.3666667 0.4555556 0.5444444 0.6333333 0.7222222 0.8111111 0.9
0.1 0.1888889 0.2777778 0.3666667 0.4555556 0.5444444 0.6333333 0.7222222 0.8111111 0.9
0.1 0.1888889 0.2777778 0.3666667 0.4555556 0.5444444 0.6333333 0.7222222 0.8111111 0.9

Two Identical Arrays, individual attributes, each column is an individual for a matrix, and each row is also an individual.

# use expand.grid to generate all combinations of two arrays

it_ar_A = 5

ar_A = seq(-2, 2, length.out=it_ar_A)
mt_A_A = expand.grid(Arow = ar_A, Arow = ar_A)
mt_Arow = mt_A_A[,1]
dim(mt_Arow) = c(it_ar_A, it_ar_A)
mt_Acol = mt_A_A[,2]
dim(mt_Acol) = c(it_ar_A, it_ar_A)

# display
kable(mt_Arow) %>%
  kable_styling_fc()
-2 -2 -2 -2 -2
-1 -1 -1 -1 -1
0 0 0 0 0
1 1 1 1 1
2 2 2 2 2 
kable(mt_Acol) %>%
  kable_styling_fc()
-2 -1 0 1 2
-2 -1 0 1 2
-2 -1 0 1 2
-2 -1 0 1 2
-2 -1 0 1 2