Creation of basis functions

fourier_2d() and polynomial_2d() creates a list of basis functions to be used as the fixed effect in fit_ghm.

fourier_2d(max_freqs, lattice_dim)

polynomial_2d(poly_deg, lattice_dim)

Arguments

max_freqs

A length 2 numeric vector with maximum frequencies considered (x-axis and y-axis direction, respectively).

lattice_dim

A length 2 numeric vector with lattice dimensions (N,M) to be used.

poly_deg

A length 2 numeric vector with degrees of the bivariate polynomial to be considered.

Value

A list of functions.

Details

fourier_2d() is for 2-dimensional Fourier transform.

See also

A paper with detailed description of the package can be found at doi: 10.18637/jss.v101.i08 .

Author

Victor Freguglia

Examples

# \donttest{
fourier_2d(c(10,10), dim(Z_potts))
#> $`2`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c235f40>
#> 
#> $`3`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c235d48>
#> 
#> $`4`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c235b18>
#> 
#> $`5`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c235920>
#> 
#> $`6`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c235680>
#> 
#> $`7`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c235488>
#> 
#> $`8`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c235290>
#> 
#> $`9`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c235098>
#> 
#> $`10`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c234e68>
#> 
#> $`11`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c1668e0>
#> 
#> $`12`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c1666e8>
#> 
#> $`13`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c1664f0>
#> 
#> $`14`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c1662c0>
#> 
#> $`15`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c166058>
#> 
#> $`16`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c165e28>
#> 
#> $`17`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c165a38>
#> 
#> $`18`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c165798>
#> 
#> $`19`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c165488>
#> 
#> $`20`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c168e20>
#> 
#> $`21`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c168c28>
#> 
#> $`22`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c168a30>
#> 
#> $`23`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c168838>
#> 
#> $`24`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c168608>
#> 
#> $`25`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c168100>
#> 
#> $`26`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c167b88>
#> 
#> $`27`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c167798>
#> 
#> $`28`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c16b0f8>
#> 
#> $`29`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c16ab48>
#> 
#> $`30`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c16a528>
#> 
#> $`31`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c16a1a8>
#> 
#> $`32`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c169610>
#> 
#> $`33`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c1749c0>
#> 
#> $`34`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c1744b8>
#> 
#> $`35`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c1741a8>
#> 
#> $`36`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c173fb0>
#> 
#> $`37`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c173db8>
#> 
#> $`38`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c173b18>
#> 
#> $`39`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c173920>
#> 
#> $`40`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c173728>
#> 
#> $`41`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c173530>
#> 
#> $`42`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c173300>
#> 
#> $`43`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c173108>
#> 
#> $`44`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c172f10>
#> 
#> $`45`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c144208>
#> 
#> $`46`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c144010>
#> 
#> $`47`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c143e18>
#> 
#> $`48`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c143be8>
#> 
#> $`49`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c1439f0>
#> 
#> $`50`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c1437f8>
#> 
#> $`51`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c143248>
#> 
#> $`52`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c143050>
#> 
#> $`53`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c142a30>
#> 
#> $`54`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c145de0>
#> 
#> $`55`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c145be8>
#> 
#> $`56`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14a330>
#> 
#> $`57`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14a138>
#> 
#> $`58`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14dd70>
#> 
#> $`59`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14db78>
#> 
#> $`60`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14d980>
#> 
#> $`61`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14d788>
#> 
#> $`62`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14d590>
#> 
#> $`63`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14d398>
#> 
#> $`64`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14d1a0>
#> 
#> $`65`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14cfa8>
#> 
#> $`66`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14cdb0>
#> 
#> $`67`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14cbb8>
#> 
#> $`68`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14c9c0>
#> 
#> $`69`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14c7c8>
#> 
#> $`70`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14c5d0>
#> 
#> $`71`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14c3d8>
#> 
#> $`72`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14c1e0>
#> 
#> $`73`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14bfe8>
#> 
#> $`74`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14fbe8>
#> 
#> $`75`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14f9f0>
#> 
#> $`76`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14f7f8>
#> 
#> $`77`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14f600>
#> 
#> $`78`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14f088>
#> 
#> $`79`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14ee90>
#> 
#> $`80`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c14e870>
#> 
#> $`81`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0982c0>
#> 
#> $`82`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0980c8>
#> 
#> $`83`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09a1e0>
#> 
#> $`84`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c099fe8>
#> 
#> $`85`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c099df0>
#> 
#> $`86`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c099bf8>
#> 
#> $`87`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c099a00>
#> 
#> $`88`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09d638>
#> 
#> $`89`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09d408>
#> 
#> $`90`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09d210>
#> 
#> $`91`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09d018>
#> 
#> $`92`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09ce20>
#> 
#> $`93`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09cc28>
#> 
#> $`94`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09ca30>
#> 
#> $`95`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09c838>
#> 
#> $`96`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09c640>
#> 
#> $`97`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09c448>
#> 
#> $`98`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09c250>
#> 
#> $`99`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09c058>
#> 
#> $`100`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09be60>
#> 
#> $`101`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09bc68>
#> 
#> $`102`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09ba70>
#> 
#> $`103`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09b878>
#> 
#> $`104`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09f4b0>
#> 
#> $`105`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09f2b8>
#> 
#> $`106`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09f0c0>
#> 
#> $`107`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09eec8>
#> 
#> $`108`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09ecd0>
#> 
#> $`109`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09ead8>
#> 
#> $`110`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09e8e0>
#> 
#> $`111`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09e6e8>
#> 
#> $`112`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09e4f0>
#> 
#> $`113`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09e2f8>
#> 
#> $`114`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09e100>
#> 
#> $`115`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09df08>
#> 
#> $`116`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09dd10>
#> 
#> $`117`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09db18>
#> 
#> $`118`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09d920>
#> 
#> $`119`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09d728>
#> 
#> $`120`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a1328>
#> 
#> $`121`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a1130>
#> 
#> $`2`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdc5a0>
#> 
#> $`3`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdc290>
#> 
#> $`4`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdc098>
#> 
#> $`5`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdbea0>
#> 
#> $`6`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdbca8>
#> 
#> $`7`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdbab0>
#> 
#> $`8`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdb8b8>
#> 
#> $`9`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdb6c0>
#> 
#> $`10`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdb4c8>
#> 
#> $`11`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdb2d0>
#> 
#> $`12`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdb0d8>
#> 
#> $`13`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdaee0>
#> 
#> $`14`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdace8>
#> 
#> $`15`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdaaf0>
#> 
#> $`16`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcde728>
#> 
#> $`17`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcde530>
#> 
#> $`18`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcde338>
#> 
#> $`19`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcde140>
#> 
#> $`20`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcddf48>
#> 
#> $`21`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcddd50>
#> 
#> $`22`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcddb58>
#> 
#> $`23`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdd960>
#> 
#> $`24`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdd768>
#> 
#> $`25`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdd538>
#> 
#> $`26`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdd340>
#> 
#> $`27`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdd148>
#> 
#> $`28`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdcf50>
#> 
#> $`29`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdcd58>
#> 
#> $`30`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdcb60>
#> 
#> $`31`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bce0760>
#> 
#> $`32`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bce04c0>
#> 
#> $`33`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bce02c8>
#> 
#> $`34`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bce00d0>
#> 
#> $`35`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdfed8>
#> 
#> $`36`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdfce0>
#> 
#> $`37`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdf5e0>
#> 
#> $`38`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdefc0>
#> 
#> $`39`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdecb0>
#> 
#> $`40`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc14b8>
#> 
#> $`41`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc11a8>
#> 
#> $`42`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc0fb0>
#> 
#> $`43`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc0db8>
#> 
#> $`44`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc0b18>
#> 
#> $`45`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc0920>
#> 
#> $`46`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc0728>
#> 
#> $`47`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc0530>
#> 
#> $`48`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc0338>
#> 
#> $`49`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc0140>
#> 
#> $`50`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcbff48>
#> 
#> $`51`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcbfd50>
#> 
#> $`52`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcbfb58>
#> 
#> $`53`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcbf960>
#> 
#> $`54`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcbf768>
#> 
#> $`55`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc33a0>
#> 
#> $`56`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc31a8>
#> 
#> $`57`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc2f78>
#> 
#> $`58`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc2d80>
#> 
#> $`59`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc2b88>
#> 
#> $`60`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc2990>
#> 
#> $`61`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc2798>
#> 
#> $`62`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc25a0>
#> 
#> $`63`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc23a8>
#> 
#> $`64`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc21b0>
#> 
#> $`65`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc1fb8>
#> 
#> $`66`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc1dc0>
#> 
#> $`67`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc1bc8>
#> 
#> $`68`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc19d0>
#> 
#> $`69`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc17d8>
#> 
#> $`70`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc5410>
#> 
#> $`71`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc5218>
#> 
#> $`72`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc4fe8>
#> 
#> $`73`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc4df0>
#> 
#> $`74`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc4bc0>
#> 
#> $`75`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc49c8>
#> 
#> $`76`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc4680>
#> 
#> $`77`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc4488>
#> 
#> $`78`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc4290>
#> 
#> $`79`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc4098>
#> 
#> $`80`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc3ea0>
#> 
#> $`81`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc3ca8>
#> 
#> $`82`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc3ab0>
#> 
#> $`83`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc38b8>
#> 
#> $`84`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc36c0>
#> 
#> $`85`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc72f8>
#> 
#> $`86`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc7100>
#> 
#> $`87`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc6f08>
#> 
#> $`88`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc6d10>
#> 
#> $`89`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc6b18>
#> 
#> $`90`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc6920>
#> 
#> $`91`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc6728>
#> 
#> $`92`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc6530>
#> 
#> $`93`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc6338>
#> 
#> $`94`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc6140>
#> 
#> $`95`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc5f48>
#> 
#> $`96`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc5d50>
#> 
#> $`97`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc5b58>
#> 
#> $`98`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc5960>
#> 
#> $`99`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc5768>
#> 
#> $`100`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc5570>
#> 
#> $`101`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc91a8>
#> 
#> $`102`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc8f78>
#> 
#> $`103`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc8d80>
#> 
#> $`104`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc8b18>
#> 
#> $`105`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc8878>
#> 
#> $`106`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc8680>
#> 
#> $`107`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc8488>
#> 
#> $`108`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc8290>
#> 
#> $`109`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc8098>
#> 
#> $`110`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc7bc8>
#> 
#> $`111`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc76c0>
#> 
#> $`112`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bccaed0>
#> 
#> $`113`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcca840>
#> 
#> $`114`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcca290>
#> 
#> $`115`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc9c38>
#> 
#> $`116`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc9768>
#> 
#> $`117`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcc9308>
#> 
#> $`118`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcccb18>
#> 
#> $`119`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bccc680>
#> 
#> $`120`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bccbf80>
#> 
#> $`121`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bccbae8>
#> 
#> $`2`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a08a8>
#> 
#> $`3`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a06b0>
#> 
#> $`4`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a04b8>
#> 
#> $`5`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a02c0>
#> 
#> $`6`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a00c8>
#> 
#> $`7`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09fed0>
#> 
#> $`8`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09fca0>
#> 
#> $`9`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09faa8>
#> 
#> $`10`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09f8b0>
#> 
#> $`11`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c09f6b8>
#> 
#> $`12`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a32f0>
#> 
#> $`13`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a30f8>
#> 
#> $`14`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a2f00>
#> 
#> $`15`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a2d08>
#> 
#> $`16`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a2a68>
#> 
#> $`17`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a2870>
#> 
#> $`18`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a2678>
#> 
#> $`19`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a2480>
#> 
#> $`20`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a2288>
#> 
#> $`21`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a2090>
#> 
#> $`22`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a1e98>
#> 
#> $`23`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a1ca0>
#> 
#> $`24`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a1a70>
#> 
#> $`25`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a1878>
#> 
#> $`26`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a1648>
#> 
#> $`27`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a5210>
#> 
#> $`28`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a4fe0>
#> 
#> $`29`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a4db0>
#> 
#> $`30`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a4bb8>
#> 
#> $`31`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a4988>
#> 
#> $`32`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a4790>
#> 
#> $`33`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a4560>
#> 
#> $`34`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a4330>
#> 
#> $`35`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a4138>
#> 
#> $`36`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a3f08>
#> 
#> $`37`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a3d10>
#> 
#> $`38`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a3b18>
#> 
#> $`39`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a38b0>
#> 
#> $`40`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a3680>
#> 
#> $`41`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233c0a3488>
#> 
#> $`42`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf6e5b0>
#> 
#> $`43`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf6dfc8>
#> 
#> $`44`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf6d9a8>
#> 
#> $`45`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf6d7b0>
#> 
#> $`46`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf73078>
#> 
#> $`47`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf753c0>
#> 
#> $`48`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf75158>
#> 
#> $`49`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf74f28>
#> 
#> $`50`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf74d30>
#> 
#> $`51`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf74b38>
#> 
#> $`52`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf74908>
#> 
#> $`53`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf74710>
#> 
#> $`54`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf74518>
#> 
#> $`55`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf78150>
#> 
#> $`56`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf77f20>
#> 
#> $`57`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf77d28>
#> 
#> $`58`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf77b30>
#> 
#> $`59`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf77938>
#> 
#> $`60`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf77740>
#> 
#> $`61`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf77510>
#> 
#> $`62`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf772a8>
#> 
#> $`63`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf770b0>
#> 
#> $`64`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf76eb8>
#> 
#> $`65`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf76cc0>
#> 
#> $`66`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf76ac8>
#> 
#> $`67`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf768d0>
#> 
#> $`68`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf766d8>
#> 
#> $`69`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf764a8>
#> 
#> $`70`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf7a0e0>
#> 
#> $`71`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf79eb0>
#> 
#> $`72`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf79cb8>
#> 
#> $`73`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf79a88>
#> 
#> $`74`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf79890>
#> 
#> $`75`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf79698>
#> 
#> $`76`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf794a0>
#> 
#> $`77`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf792a8>
#> 
#> $`78`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf79078>
#> 
#> $`79`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf78e80>
#> 
#> $`80`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf78c50>
#> 
#> $`81`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf78a58>
#> 
#> $`82`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf787b8>
#> 
#> $`83`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf785c0>
#> 
#> $`84`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf78390>
#> 
#> $`85`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf7bfc8>
#> 
#> $`86`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf7bdd0>
#> 
#> $`87`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf7bbd8>
#> 
#> $`88`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf7b9e0>
#> 
#> $`89`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf7b7e8>
#> 
#> $`90`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf7b5f0>
#> 
#> $`91`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf7b3f8>
#> 
#> $`92`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf7b200>
#> 
#> $`93`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf7b008>
#> 
#> $`94`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf7ae10>
#> 
#> $`95`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf7ac18>
#> 
#> $`96`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf7aa20>
#> 
#> $`97`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf7a828>
#> 
#> $`98`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf7a630>
#> 
#> $`99`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bf7a400>
#> 
#> $`100`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcd458>
#> 
#> $`101`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcd260>
#> 
#> $`102`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcd068>
#> 
#> $`103`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdccd58>
#> 
#> $`104`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdccb60>
#> 
#> $`105`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcc968>
#> 
#> $`106`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcc738>
#> 
#> $`107`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcc540>
#> 
#> $`108`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcc348>
#> 
#> $`109`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcc150>
#> 
#> $`110`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcbf58>
#> 
#> $`111`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcbd60>
#> 
#> $`112`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcbb68>
#> 
#> $`113`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcb970>
#> 
#> $`114`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcb778>
#> 
#> $`115`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcf3b0>
#> 
#> $`116`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcf1b8>
#> 
#> $`117`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcefc0>
#> 
#> $`118`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcedc8>
#> 
#> $`119`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcebd0>
#> 
#> $`120`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdce9d8>
#> 
#> $`121`
#> function(x, y, N, M) cos(2*(x-1)*pi*nm[1,1]/N)*sin(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdce7e0>
#> 
#> $`2`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcdf58>
#> 
#> $`3`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcdd28>
#> 
#> $`4`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcdb30>
#> 
#> $`5`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcd938>
#> 
#> $`6`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcd740>
#> 
#> $`7`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcd510>
#> 
#> $`8`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd10a0>
#> 
#> $`9`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd0ea8>
#> 
#> $`10`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd0cb0>
#> 
#> $`11`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd0ab8>
#> 
#> $`12`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd08c0>
#> 
#> $`13`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd0620>
#> 
#> $`14`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcfeb0>
#> 
#> $`15`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcfb30>
#> 
#> $`16`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdcf3f8>
#> 
#> $`17`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd2b98>
#> 
#> $`18`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd2690>
#> 
#> $`19`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd2380>
#> 
#> $`20`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd1fc8>
#> 
#> $`21`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd1820>
#> 
#> $`22`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd4c40>
#> 
#> $`23`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd4658>
#> 
#> $`24`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd42a0>
#> 
#> $`25`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd34d8>
#> 
#> $`26`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd6dc8>
#> 
#> $`27`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd64d0>
#> 
#> $`28`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd60a8>
#> 
#> $`29`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd5cf0>
#> 
#> $`30`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd5820>
#> 
#> $`31`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd53f8>
#> 
#> $`32`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd8ea8>
#> 
#> $`33`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd8bd0>
#> 
#> $`34`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd87a8>
#> 
#> $`35`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd82d8>
#> 
#> $`36`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd7f20>
#> 
#> $`37`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bddad20>
#> 
#> $`38`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdda4d0>
#> 
#> $`39`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdda188>
#> 
#> $`40`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd9d28>
#> 
#> $`41`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd93c0>
#> 
#> $`42`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bdd90b0>
#> 
#> $`43`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd94a38>
#> 
#> $`44`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd94760>
#> 
#> $`45`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd941e8>
#> 
#> $`46`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd93ed8>
#> 
#> $`47`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd93a40>
#> 
#> $`48`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd93768>
#> 
#> $`49`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd92fc0>
#> 
#> $`50`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd96a38>
#> 
#> $`51`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd96300>
#> 
#> $`52`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd95c00>
#> 
#> $`53`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd95650>
#> 
#> $`54`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd950d8>
#> 
#> $`55`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd98b50>
#> 
#> $`56`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd982c8>
#> 
#> $`57`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd97f80>
#> 
#> $`58`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd979d0>
#> 
#> $`59`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd97688>
#> 
#> $`60`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd96e00>
#> 
#> $`61`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd9a418>
#> 
#> $`62`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd99fb8>
#> 
#> $`63`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd99960>
#> 
#> $`64`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd99378>
#> 
#> $`65`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd98d20>
#> 
#> $`66`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd9c488>
#> 
#> $`67`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd9c108>
#> 
#> $`68`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd9bc38>
#> 
#> $`69`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd9b880>
#> 
#> $`70`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd9b030>
#> 
#> $`71`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd9ad20>
#> 
#> $`72`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd9e728>
#> 
#> $`73`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd9e220>
#> 
#> $`74`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd9df10>
#> 
#> $`75`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd9d8f0>
#> 
#> $`76`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bd9d298>
#> 
#> $`77`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bda08b0>
#> 
#> $`78`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bda0098>
#> 
#> $`79`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd0f18>
#> 
#> $`80`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd4728>
#> 
#> $`81`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd4338>
#> 
#> $`82`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd3b90>
#> 
#> $`83`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd3880>
#> 
#> $`84`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd3458>
#> 
#> $`85`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd6c30>
#> 
#> $`86`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd6878>
#> 
#> $`87`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd6568>
#> 
#> $`88`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd5ed8>
#> 
#> $`89`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd59d0>
#> 
#> $`90`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd5308>
#> 
#> $`91`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd5110>
#> 
#> $`92`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd4e00>
#> 
#> $`93`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd8a38>
#> 
#> $`94`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd8840>
#> 
#> $`95`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd85a0>
#> 
#> $`96`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd83a8>
#> 
#> $`97`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd81b0>
#> 
#> $`98`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd7fb8>
#> 
#> $`99`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd7dc0>
#> 
#> $`100`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd7bc8>
#> 
#> $`101`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd79d0>
#> 
#> $`102`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd77d8>
#> 
#> $`103`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd75e0>
#> 
#> $`104`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd73e8>
#> 
#> $`105`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd71f0>
#> 
#> $`106`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd6ff8>
#> 
#> $`107`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd6e00>
#> 
#> $`108`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcdaa00>
#> 
#> $`109`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcda808>
#> 
#> $`110`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcda610>
#> 
#> $`111`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcda418>
#> 
#> $`112`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcda220>
#> 
#> $`113`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcda028>
#> 
#> $`114`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd9e30>
#> 
#> $`115`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd9c38>
#> 
#> $`116`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd9a40>
#> 
#> $`117`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd9848>
#> 
#> $`118`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd9650>
#> 
#> $`119`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd9458>
#> 
#> $`120`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd9228>
#> 
#> $`121`
#> function(x, y, N, M) sin(2*(x-1)*pi*nm[1,1]/N)*cos(2*(y-1)*pi*nm[1,2]/M)
#> <environment: 0x56233bcd9030>
#> 
polynomial_2d(c(3,3), dim(Z_potts))
#> $`2`
#> function(x, y, N, M) return((x - N/2)^nm[1,1]*(y - M/2)^nm[1,2])
#> <environment: 0x56233c45edb0>
#> 
#> $`3`
#> function(x, y, N, M) return((x - N/2)^nm[1,1]*(y - M/2)^nm[1,2])
#> <environment: 0x56233c45ebb8>
#> 
#> $`4`
#> function(x, y, N, M) return((x - N/2)^nm[1,1]*(y - M/2)^nm[1,2])
#> <environment: 0x56233c45e9c0>
#> 
#> $`5`
#> function(x, y, N, M) return((x - N/2)^nm[1,1]*(y - M/2)^nm[1,2])
#> <environment: 0x56233c45e7c8>
#> 
#> $`6`
#> function(x, y, N, M) return((x - N/2)^nm[1,1]*(y - M/2)^nm[1,2])
#> <environment: 0x56233c45e5d0>
#> 
#> $`7`
#> function(x, y, N, M) return((x - N/2)^nm[1,1]*(y - M/2)^nm[1,2])
#> <environment: 0x56233c462208>
#> 
#> $`8`
#> function(x, y, N, M) return((x - N/2)^nm[1,1]*(y - M/2)^nm[1,2])
#> <environment: 0x56233c462010>
#> 
#> $`9`
#> function(x, y, N, M) return((x - N/2)^nm[1,1]*(y - M/2)^nm[1,2])
#> <environment: 0x56233c461e18>
#> 
#> $`10`
#> function(x, y, N, M) return((x - N/2)^nm[1,1]*(y - M/2)^nm[1,2])
#> <environment: 0x56233c461c20>
#> 
#> $`11`
#> function(x, y, N, M) return((x - N/2)^nm[1,1]*(y - M/2)^nm[1,2])
#> <environment: 0x56233c461a28>
#> 
#> $`12`
#> function(x, y, N, M) return((x - N/2)^nm[1,1]*(y - M/2)^nm[1,2])
#> <environment: 0x56233c461830>
#> 
#> $`13`
#> function(x, y, N, M) return((x - N/2)^nm[1,1]*(y - M/2)^nm[1,2])
#> <environment: 0x56233c461638>
#> 
#> $`14`
#> function(x, y, N, M) return((x - N/2)^nm[1,1]*(y - M/2)^nm[1,2])
#> <environment: 0x56233c461440>
#> 
#> $`15`
#> function(x, y, N, M) return((x - N/2)^nm[1,1]*(y - M/2)^nm[1,2])
#> <environment: 0x56233c461248>
#> 
#> $`16`
#> function(x, y, N, M) return((x - N/2)^nm[1,1]*(y - M/2)^nm[1,2])
#> <environment: 0x56233c461050>
#> 
# }