Details on Broadcasted Operators

Description

Base ‘R’ comes with relational, arithmetic and logical/bit-wise (&, |) operators.
‘broadcast’ provides 2 ways to use these operators with broadcasting.

The first (and simple) way is to use the broadcaster class, which comes with it’s own method dispatch for the above mentioned operators.
This approach supports operator precedence, and for the average ‘R’ user, this is sufficient.

The second way is to use the large set of bc.- functions.
These offer much greater control and more operators than the previous method, and has less risk of running into conflicting methods.
But they do not support operator precedence.

Operators Overloaded via Broadcaster Class

The ‘broadcast’ package provides the broadcaster class, which comes with its own method dispatch for the base operators.
If at least one of the 2 arguments of the base operators has the broadcaster class attribute, and no other class (like bit64) interferes, broadcasting will be used.

The following operators have a ‘broadcaster’ method:

+, -, *, /, ^, %%, %/%
==, !=, <, >, <=, >=
&, |

See also the Examples section below.

Available bc. functions

‘broadcast’ provides a set of functions for broadcasted element-wise binary operations with broadcasting.
These functions use an API similar to the outer function.

The following functions for simple operations are available:

  • bc.rel: General relational operations (==, !=, <, >, <=, >=).
    The various other bc. methods below have specialised relational operators available for specialised needs.

  • bc.b: Boolean (i.e. logical) operations;

  • bc.i: integer arithmetic operations;

  • bc.d: decimal arithmetic operations;

  • bc.cplx: complex arithmetic operations;

  • bc.str: string (in)equality, concatenation, and distance operations;

  • bc.raw: operations that take in arrays of type raw and return an array of type raw;

  • bc.bit: BIT-WISE operations, supporting the raw and integer types;

  • bc.list: apply any ‘R’ function to 2 recursive arrays with broadcasting.

Attribute Handling

The bc. functions and the overloaded operators generally do not preserve attributes, unlike the base ‘R’ operators, except for names, dimnames, comment (if appropriate), and the broadcaster class attribute (and related attributes).

Broadcasting often results in an object with more dimensions, larger dimensions, and/or larger length than the original objects.
This is relevant as some class-specific attributes are only appropriate for certain dimensions or lengths.
Custom matrix classes, for example, presumes an object to have exactly 2 dimensions.
And the various classes provided by the ‘bit’ package have length-related attributes.
So class attributes cannot be guaranteed to hold for the resulting objects when broadcasting is involved.


Almost all functions provided by ‘broadcast’ are S3 or S4 generics;
methods can be written for them for specific classes, so that class-specific attributes can be supported when needed.

Unary operations (i.e. + x, - x) return the original object, with only the sign adjusted.


Examples

library("broadcast")


# maths ====

x <- 1:10
y <- 1:10
dim(x) <- c(10, 1)
dim(y) <- c(1, 10)
broadcaster(x) <- TRUE
broadcaster(y) <- TRUE



x + y / x
#>            [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]
#>  [1,]  2.000000  3.000000  4.000000  5.000000  6.000000  7.000000  8.000000
#>  [2,]  2.500000  3.000000  3.500000  4.000000  4.500000  5.000000  5.500000
#>  [3,]  3.333333  3.666667  4.000000  4.333333  4.666667  5.000000  5.333333
#>  [4,]  4.250000  4.500000  4.750000  5.000000  5.250000  5.500000  5.750000
#>  [5,]  5.200000  5.400000  5.600000  5.800000  6.000000  6.200000  6.400000
#>  [6,]  6.166667  6.333333  6.500000  6.666667  6.833333  7.000000  7.166667
#>  [7,]  7.142857  7.285714  7.428571  7.571429  7.714286  7.857143  8.000000
#>  [8,]  8.125000  8.250000  8.375000  8.500000  8.625000  8.750000  8.875000
#>  [9,]  9.111111  9.222222  9.333333  9.444444  9.555556  9.666667  9.777778
#> [10,] 10.100000 10.200000 10.300000 10.400000 10.500000 10.600000 10.700000
#>            [,8]      [,9]     [,10]
#>  [1,]  9.000000 10.000000 11.000000
#>  [2,]  6.000000  6.500000  7.000000
#>  [3,]  5.666667  6.000000  6.333333
#>  [4,]  6.000000  6.250000  6.500000
#>  [5,]  6.600000  6.800000  7.000000
#>  [6,]  7.333333  7.500000  7.666667
#>  [7,]  8.142857  8.285714  8.428571
#>  [8,]  9.000000  9.125000  9.250000
#>  [9,]  9.888889 10.000000 10.111111
#> [10,] 10.800000 10.900000 11.000000
#> broadcaster
(x + y) / x
#>           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]     [,8]
#>  [1,] 2.000000 3.000000 4.000000 5.000000 6.000000 7.000000 8.000000 9.000000
#>  [2,] 1.500000 2.000000 2.500000 3.000000 3.500000 4.000000 4.500000 5.000000
#>  [3,] 1.333333 1.666667 2.000000 2.333333 2.666667 3.000000 3.333333 3.666667
#>  [4,] 1.250000 1.500000 1.750000 2.000000 2.250000 2.500000 2.750000 3.000000
#>  [5,] 1.200000 1.400000 1.600000 1.800000 2.000000 2.200000 2.400000 2.600000
#>  [6,] 1.166667 1.333333 1.500000 1.666667 1.833333 2.000000 2.166667 2.333333
#>  [7,] 1.142857 1.285714 1.428571 1.571429 1.714286 1.857143 2.000000 2.142857
#>  [8,] 1.125000 1.250000 1.375000 1.500000 1.625000 1.750000 1.875000 2.000000
#>  [9,] 1.111111 1.222222 1.333333 1.444444 1.555556 1.666667 1.777778 1.888889
#> [10,] 1.100000 1.200000 1.300000 1.400000 1.500000 1.600000 1.700000 1.800000
#>            [,9]     [,10]
#>  [1,] 10.000000 11.000000
#>  [2,]  5.500000  6.000000
#>  [3,]  4.000000  4.333333
#>  [4,]  3.250000  3.500000
#>  [5,]  2.800000  3.000000
#>  [6,]  2.500000  2.666667
#>  [7,]  2.285714  2.428571
#>  [8,]  2.125000  2.250000
#>  [9,]  2.000000  2.111111
#> [10,]  1.900000  2.000000
#> broadcaster

(x + y) * x
#>       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
#>  [1,]    2    3    4    5    6    7    8    9   10    11
#>  [2,]    6    8   10   12   14   16   18   20   22    24
#>  [3,]   12   15   18   21   24   27   30   33   36    39
#>  [4,]   20   24   28   32   36   40   44   48   52    56
#>  [5,]   30   35   40   45   50   55   60   65   70    75
#>  [6,]   42   48   54   60   66   72   78   84   90    96
#>  [7,]   56   63   70   77   84   91   98  105  112   119
#>  [8,]   72   80   88   96  104  112  120  128  136   144
#>  [9,]   90   99  108  117  126  135  144  153  162   171
#> [10,]  110  120  130  140  150  160  170  180  190   200
#> broadcaster


# relational operators ====
x <- 1:10
y <- array(1:10, c(1, 10))
broadcaster(x) <- TRUE
broadcaster(y) <- TRUE

x == y
#>        [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10]
#>  [1,]  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [2,] FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [3,] FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [4,] FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [5,] FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE
#>  [6,] FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE
#>  [7,] FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE
#>  [8,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE
#>  [9,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE
#> [10,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE
#> broadcaster
x != y
#>        [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10]
#>  [1,] FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [2,]  TRUE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [3,]  TRUE  TRUE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [4,]  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [5,]  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [6,]  TRUE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE  TRUE
#>  [7,]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE
#>  [8,]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE
#>  [9,]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE
#> [10,]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE
#> broadcaster
x < y
#>        [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10]
#>  [1,] FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [2,] FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [3,] FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [4,] FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [5,] FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [6,] FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE
#>  [7,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE
#>  [8,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE
#>  [9,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE
#> [10,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#> broadcaster
x > y
#>        [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10]
#>  [1,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [2,]  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [3,]  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [4,]  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [5,]  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [6,]  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE
#>  [7,]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE
#>  [8,]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE
#>  [9,]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE
#> [10,]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE
#> broadcaster
x <= y
#>        [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10]
#>  [1,]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [2,] FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [3,] FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [4,] FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [5,] FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [6,] FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [7,] FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE
#>  [8,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE
#>  [9,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE
#> [10,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE
#> broadcaster
x >= y
#>       [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10]
#>  [1,] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [2,] TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [3,] TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [4,] TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [5,] TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE
#>  [6,] TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE
#>  [7,] TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE
#>  [8,] TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE
#>  [9,] TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE
#> [10,] TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#> broadcaster




# maths ====

x <- sample(1:10)
y <- sample(1:10)
dim(x) <- c(10, 1)
dim(y) <- c(1, 10)
mbroadcasters(c("x", "y"), TRUE)



x + y / x
#>            [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]
#>  [1,] 10.200000 10.500000 10.600000 10.100000 10.800000 10.300000 10.700000
#>  [2,]  3.000000  4.500000  5.000000  2.500000  6.000000  3.500000  5.500000
#>  [3,]  3.666667  4.666667  5.000000  3.333333  5.666667  4.000000  5.333333
#>  [4,]  7.285714  7.714286  7.857143  7.142857  8.142857  7.428571  8.000000
#>  [5,]  8.250000  8.625000  8.750000  8.125000  9.000000  8.375000  8.875000
#>  [6,]  6.333333  6.833333  7.000000  6.166667  7.333333  6.500000  7.166667
#>  [7,]  9.222222  9.555556  9.666667  9.111111  9.888889  9.333333  9.777778
#>  [8,]  5.400000  6.000000  6.200000  5.200000  6.600000  5.600000  6.400000
#>  [9,]  4.500000  5.250000  5.500000  4.250000  6.000000  4.750000  5.750000
#> [10,]  3.000000  6.000000  7.000000  2.000000  9.000000  4.000000  8.000000
#>            [,8]      [,9]     [,10]
#>  [1,] 10.900000 11.000000 10.400000
#>  [2,]  6.500000  7.000000  4.000000
#>  [3,]  6.000000  6.333333  4.333333
#>  [4,]  8.285714  8.428571  7.571429
#>  [5,]  9.125000  9.250000  8.500000
#>  [6,]  7.500000  7.666667  6.666667
#>  [7,] 10.000000 10.111111  9.444444
#>  [8,]  6.800000  7.000000  5.800000
#>  [9,]  6.250000  6.500000  5.000000
#> [10,] 10.000000 11.000000  5.000000
#> broadcaster
(x + y) / x
#>           [,1]     [,2]     [,3]     [,4]     [,5]     [,6]     [,7]      [,8]
#>  [1,] 1.200000 1.500000 1.600000 1.100000 1.800000 1.300000 1.700000  1.900000
#>  [2,] 2.000000 3.500000 4.000000 1.500000 5.000000 2.500000 4.500000  5.500000
#>  [3,] 1.666667 2.666667 3.000000 1.333333 3.666667 2.000000 3.333333  4.000000
#>  [4,] 1.285714 1.714286 1.857143 1.142857 2.142857 1.428571 2.000000  2.285714
#>  [5,] 1.250000 1.625000 1.750000 1.125000 2.000000 1.375000 1.875000  2.125000
#>  [6,] 1.333333 1.833333 2.000000 1.166667 2.333333 1.500000 2.166667  2.500000
#>  [7,] 1.222222 1.555556 1.666667 1.111111 1.888889 1.333333 1.777778  2.000000
#>  [8,] 1.400000 2.000000 2.200000 1.200000 2.600000 1.600000 2.400000  2.800000
#>  [9,] 1.500000 2.250000 2.500000 1.250000 3.000000 1.750000 2.750000  3.250000
#> [10,] 3.000000 6.000000 7.000000 2.000000 9.000000 4.000000 8.000000 10.000000
#>            [,9]    [,10]
#>  [1,]  2.000000 1.400000
#>  [2,]  6.000000 3.000000
#>  [3,]  4.333333 2.333333
#>  [4,]  2.428571 1.571429
#>  [5,]  2.250000 1.500000
#>  [6,]  2.666667 1.666667
#>  [7,]  2.111111 1.444444
#>  [8,]  3.000000 1.800000
#>  [9,]  3.500000 2.000000
#> [10,] 11.000000 5.000000
#> broadcaster

(x + y) * x
#>       [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
#>  [1,]  120  150  160  110  180  130  170  190  200   140
#>  [2,]    8   14   16    6   20   10   18   22   24    12
#>  [3,]   15   24   27   12   33   18   30   36   39    21
#>  [4,]   63   84   91   56  105   70   98  112  119    77
#>  [5,]   80  104  112   72  128   88  120  136  144    96
#>  [6,]   48   66   72   42   84   54   78   90   96    60
#>  [7,]   99  126  135   90  153  108  144  162  171   117
#>  [8,]   35   50   55   30   65   40   60   70   75    45
#>  [9,]   24   36   40   20   48   28   44   52   56    32
#> [10,]    3    6    7    2    9    4    8   10   11     5
#> broadcaster


# relational operators ====
x <- 1:10
y <- array(1:10, c(1, 10))
mbroadcasters(c("x", "y"), TRUE)

x == y
#>        [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10]
#>  [1,]  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [2,] FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [3,] FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [4,] FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [5,] FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE FALSE
#>  [6,] FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE FALSE
#>  [7,] FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE FALSE
#>  [8,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE FALSE
#>  [9,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE FALSE
#> [10,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE
#> broadcaster
x != y
#>        [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10]
#>  [1,] FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [2,]  TRUE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [3,]  TRUE  TRUE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [4,]  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [5,]  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [6,]  TRUE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE  TRUE
#>  [7,]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE
#>  [8,]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE
#>  [9,]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE
#> [10,]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE
#> broadcaster
x < y
#>        [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10]
#>  [1,] FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [2,] FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [3,] FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [4,] FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [5,] FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [6,] FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE
#>  [7,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE
#>  [8,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE
#>  [9,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE
#> [10,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#> broadcaster
x > y
#>        [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10]
#>  [1,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [2,]  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [3,]  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [4,]  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [5,]  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [6,]  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE
#>  [7,]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE
#>  [8,]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE
#>  [9,]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE
#> [10,]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE
#> broadcaster
x <= y
#>        [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10]
#>  [1,]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [2,] FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [3,] FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [4,] FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [5,] FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [6,] FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE  TRUE
#>  [7,] FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE  TRUE
#>  [8,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE  TRUE
#>  [9,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE  TRUE
#> [10,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE  TRUE
#> broadcaster
x >= y
#>       [,1]  [,2]  [,3]  [,4]  [,5]  [,6]  [,7]  [,8]  [,9] [,10]
#>  [1,] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [2,] TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [3,] TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [4,] TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE FALSE
#>  [5,] TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE FALSE
#>  [6,] TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE FALSE
#>  [7,] TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE FALSE
#>  [8,] TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE
#>  [9,] TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE
#> [10,] TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
#> broadcaster