Fast (flexible and friendly) statistical functions (mainly from collapse) for matrix-like and data frame objects
Source:R/fast_functions.R
fstat_functions.RdThe fast statistical function, or fast-flexible-friendly
statistical functions are prefixed with "f". These vectorized functions
supersede the no-f functions, bringing the capacity to work smoothly on
matrix-like and data frame objects. Most of them are defined in the
{collapse} package
For instance, base mean() operates on a vector, but not on a data frame. A
matrix is recognized as a vector and a single mean is returned. On, the
contrary, fmean() calculates one mean per column. It does the same for a
data frame, and it does so usually quicker than base functions. No need for
colMeans(), a separate function to do so. Fast statistical functions also
recognize grouping with fgroup_by(), sgroup_by() or group_by() and
calculate the mean by group in this case. Again, no need for a different
function like stats::ave().
Finally, these functions also have a TRA= argument that computes, for
instance, if TRA = "-", (x f(x)) very efficiently (for instance to
calculate residuals by subtracting the mean).
Another particularity is the na.rm= argument that is TRUE by default,
while it is FALSE by default for mean().
These are generic functions with methods for matrix, data.frame,
grouped_df and a default method used for simple numeric vectors. Most
of them are defined in the {collapse} package, but there are a couple more
here, together with an alternate syntax to replace TRA= with %_f%.
Usage
list_fstat_functions()
fn(x, ...)
fna(x, ...)
x %replacef% expr
x %replace_fillf% expr
x %-f% expr
x %+f% expr
x %-+f% expr
x %/f% expr
x %/*100f% expr
x %*f% expr
x %modf% expr
x %-modf% exprArguments
- x
A numeric vector, matrix, data frame or grouped data frame (class 'grouped_df').
- ...
Further arguments passed to the method, like
w=, a numeric vector of (non-negative) weights that may contain missing values, orTRA=, a quoted operator indicating the transformation to perform:"replace"to get a vector of same size ofxwith results,"replace_fill"idem but also replace missing data,"-"to subtract,"+"to add,"-+"to subtract and add the global statistic,"/"to divide,"%"to divide and multiply by 100 (percent),"*"to multiply,"%%"to take the modulus (remainder from division by the statistic) and"-%%"to subtract modulus ('i.e., to floor the data by the statistic), seecollapse::TRA(). Alsona.rm=, a logical indicating if we skip missing values inxifTRUE(by default). IfFALSEfor any missing data inx,NAis returned. For details and other arguments, see the corresponding help page in the collapse package.- expr
The expression to evaluate as RHS of the
%__f%operators.
Value
The number of all observations for fn() or the number of
missing observations for fna(). list_fstat_functions() returns a list of
all the known fast statistical functions.
Note
The page collapse::fast-statistical-functions gives more details.
fn() count all observations, including NAs, fna() counts
only NAs, where fnobs() counts non-missing observations.
Instead of TRA= one can use the %__f% functions where __ is replace,
replace_fill, -, +, -+, /, /*100 for TRA="%", *, mod for
TRA="%%", or -mod for TRA="-%%". See example.
Examples
library(collapse)
#> collapse 2.0.13, see ?`collapse-package` or ?`collapse-documentation`
#>
#> Attaching package: ‘collapse’
#> The following object is masked from ‘package:data.table’:
#>
#> fdroplevels
#> The following object is masked from ‘package:stats’:
#>
#> D
data(iris)
iris_num <- iris[, -5] # Only numerical variables
mean(iris$Sepal.Length) # OK, but mean(iris_num does not work)
#> [1] 5.843333
colMeans(iris_num)
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> 5.843333 3.057333 3.758000 1.199333
# Same
fmean(iris_num)
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> 5.843333 3.057333 3.758000 1.199333
# Idem, but mean by group for all 4 numerical variables
iris |> fgroup_by(Species) |> fmean()
#> Species Sepal.Length Sepal.Width Petal.Length Petal.Width
#> 1 setosa 5.006 3.428 1.462 0.246
#> 2 versicolor 5.936 2.770 4.260 1.326
#> 3 virginica 6.588 2.974 5.552 2.026
# Residuals (x - mean(x)) by group
iris |> fgroup_by(Species) |> fmean(TRA = "-")
#> Species Sepal.Length Sepal.Width Petal.Length Petal.Width
#> 1 setosa 0.094 0.072 -0.062 -0.046
#> 2 setosa -0.106 -0.428 -0.062 -0.046
#> 3 setosa -0.306 -0.228 -0.162 -0.046
#> 4 setosa -0.406 -0.328 0.038 -0.046
#> 5 setosa -0.006 0.172 -0.062 -0.046
#> 6 setosa 0.394 0.472 0.238 0.154
#> 7 setosa -0.406 -0.028 -0.062 0.054
#> 8 setosa -0.006 -0.028 0.038 -0.046
#> 9 setosa -0.606 -0.528 -0.062 -0.046
#> 10 setosa -0.106 -0.328 0.038 -0.146
#> 11 setosa 0.394 0.272 0.038 -0.046
#> 12 setosa -0.206 -0.028 0.138 -0.046
#> 13 setosa -0.206 -0.428 -0.062 -0.146
#> 14 setosa -0.706 -0.428 -0.362 -0.146
#> 15 setosa 0.794 0.572 -0.262 -0.046
#> 16 setosa 0.694 0.972 0.038 0.154
#> 17 setosa 0.394 0.472 -0.162 0.154
#> 18 setosa 0.094 0.072 -0.062 0.054
#> 19 setosa 0.694 0.372 0.238 0.054
#> 20 setosa 0.094 0.372 0.038 0.054
#> 21 setosa 0.394 -0.028 0.238 -0.046
#> 22 setosa 0.094 0.272 0.038 0.154
#> 23 setosa -0.406 0.172 -0.462 -0.046
#> 24 setosa 0.094 -0.128 0.238 0.254
#> 25 setosa -0.206 -0.028 0.438 -0.046
#> 26 setosa -0.006 -0.428 0.138 -0.046
#> 27 setosa -0.006 -0.028 0.138 0.154
#> 28 setosa 0.194 0.072 0.038 -0.046
#> 29 setosa 0.194 -0.028 -0.062 -0.046
#> 30 setosa -0.306 -0.228 0.138 -0.046
#> 31 setosa -0.206 -0.328 0.138 -0.046
#> 32 setosa 0.394 -0.028 0.038 0.154
#> 33 setosa 0.194 0.672 0.038 -0.146
#> 34 setosa 0.494 0.772 -0.062 -0.046
#> 35 setosa -0.106 -0.328 0.038 -0.046
#> 36 setosa -0.006 -0.228 -0.262 -0.046
#> 37 setosa 0.494 0.072 -0.162 -0.046
#> 38 setosa -0.106 0.172 -0.062 -0.146
#> 39 setosa -0.606 -0.428 -0.162 -0.046
#> 40 setosa 0.094 -0.028 0.038 -0.046
#> 41 setosa -0.006 0.072 -0.162 0.054
#> 42 setosa -0.506 -1.128 -0.162 0.054
#> 43 setosa -0.606 -0.228 -0.162 -0.046
#> 44 setosa -0.006 0.072 0.138 0.354
#> 45 setosa 0.094 0.372 0.438 0.154
#> 46 setosa -0.206 -0.428 -0.062 0.054
#> 47 setosa 0.094 0.372 0.138 -0.046
#> 48 setosa -0.406 -0.228 -0.062 -0.046
#> 49 setosa 0.294 0.272 0.038 -0.046
#> 50 setosa -0.006 -0.128 -0.062 -0.046
#> 51 versicolor 1.064 0.430 0.440 0.074
#> 52 versicolor 0.464 0.430 0.240 0.174
#> 53 versicolor 0.964 0.330 0.640 0.174
#> 54 versicolor -0.436 -0.470 -0.260 -0.026
#> 55 versicolor 0.564 0.030 0.340 0.174
#> 56 versicolor -0.236 0.030 0.240 -0.026
#> 57 versicolor 0.364 0.530 0.440 0.274
#> 58 versicolor -1.036 -0.370 -0.960 -0.326
#> 59 versicolor 0.664 0.130 0.340 -0.026
#> 60 versicolor -0.736 -0.070 -0.360 0.074
#> 61 versicolor -0.936 -0.770 -0.760 -0.326
#> 62 versicolor -0.036 0.230 -0.060 0.174
#> 63 versicolor 0.064 -0.570 -0.260 -0.326
#> 64 versicolor 0.164 0.130 0.440 0.074
#> 65 versicolor -0.336 0.130 -0.660 -0.026
#> 66 versicolor 0.764 0.330 0.140 0.074
#> 67 versicolor -0.336 0.230 0.240 0.174
#> 68 versicolor -0.136 -0.070 -0.160 -0.326
#> 69 versicolor 0.264 -0.570 0.240 0.174
#> 70 versicolor -0.336 -0.270 -0.360 -0.226
#> 71 versicolor -0.036 0.430 0.540 0.474
#> 72 versicolor 0.164 0.030 -0.260 -0.026
#> 73 versicolor 0.364 -0.270 0.640 0.174
#> 74 versicolor 0.164 0.030 0.440 -0.126
#> 75 versicolor 0.464 0.130 0.040 -0.026
#> 76 versicolor 0.664 0.230 0.140 0.074
#> 77 versicolor 0.864 0.030 0.540 0.074
#> 78 versicolor 0.764 0.230 0.740 0.374
#> 79 versicolor 0.064 0.130 0.240 0.174
#> 80 versicolor -0.236 -0.170 -0.760 -0.326
#> 81 versicolor -0.436 -0.370 -0.460 -0.226
#> 82 versicolor -0.436 -0.370 -0.560 -0.326
#> 83 versicolor -0.136 -0.070 -0.360 -0.126
#> 84 versicolor 0.064 -0.070 0.840 0.274
#> 85 versicolor -0.536 0.230 0.240 0.174
#> 86 versicolor 0.064 0.630 0.240 0.274
#> 87 versicolor 0.764 0.330 0.440 0.174
#> 88 versicolor 0.364 -0.470 0.140 -0.026
#> 89 versicolor -0.336 0.230 -0.160 -0.026
#> 90 versicolor -0.436 -0.270 -0.260 -0.026
#> 91 versicolor -0.436 -0.170 0.140 -0.126
#> 92 versicolor 0.164 0.230 0.340 0.074
#> 93 versicolor -0.136 -0.170 -0.260 -0.126
#> 94 versicolor -0.936 -0.470 -0.960 -0.326
#> 95 versicolor -0.336 -0.070 -0.060 -0.026
#> 96 versicolor -0.236 0.230 -0.060 -0.126
#> 97 versicolor -0.236 0.130 -0.060 -0.026
#> 98 versicolor 0.264 0.130 0.040 -0.026
#> 99 versicolor -0.836 -0.270 -1.260 -0.226
#> 100 versicolor -0.236 0.030 -0.160 -0.026
#> 101 virginica -0.288 0.326 0.448 0.474
#> 102 virginica -0.788 -0.274 -0.452 -0.126
#> 103 virginica 0.512 0.026 0.348 0.074
#> 104 virginica -0.288 -0.074 0.048 -0.226
#> 105 virginica -0.088 0.026 0.248 0.174
#> 106 virginica 1.012 0.026 1.048 0.074
#> 107 virginica -1.688 -0.474 -1.052 -0.326
#> 108 virginica 0.712 -0.074 0.748 -0.226
#> 109 virginica 0.112 -0.474 0.248 -0.226
#> 110 virginica 0.612 0.626 0.548 0.474
#> 111 virginica -0.088 0.226 -0.452 -0.026
#> 112 virginica -0.188 -0.274 -0.252 -0.126
#> 113 virginica 0.212 0.026 -0.052 0.074
#> 114 virginica -0.888 -0.474 -0.552 -0.026
#> 115 virginica -0.788 -0.174 -0.452 0.374
#> 116 virginica -0.188 0.226 -0.252 0.274
#> 117 virginica -0.088 0.026 -0.052 -0.226
#> 118 virginica 1.112 0.826 1.148 0.174
#> 119 virginica 1.112 -0.374 1.348 0.274
#> 120 virginica -0.588 -0.774 -0.552 -0.526
#> 121 virginica 0.312 0.226 0.148 0.274
#> 122 virginica -0.988 -0.174 -0.652 -0.026
#> 123 virginica 1.112 -0.174 1.148 -0.026
#> 124 virginica -0.288 -0.274 -0.652 -0.226
#> 125 virginica 0.112 0.326 0.148 0.074
#> 126 virginica 0.612 0.226 0.448 -0.226
#> 127 virginica -0.388 -0.174 -0.752 -0.226
#> 128 virginica -0.488 0.026 -0.652 -0.226
#> 129 virginica -0.188 -0.174 0.048 0.074
#> 130 virginica 0.612 0.026 0.248 -0.426
#> 131 virginica 0.812 -0.174 0.548 -0.126
#> 132 virginica 1.312 0.826 0.848 -0.026
#> 133 virginica -0.188 -0.174 0.048 0.174
#> 134 virginica -0.288 -0.174 -0.452 -0.526
#> 135 virginica -0.488 -0.374 0.048 -0.626
#> 136 virginica 1.112 0.026 0.548 0.274
#> 137 virginica -0.288 0.426 0.048 0.374
#> 138 virginica -0.188 0.126 -0.052 -0.226
#> 139 virginica -0.588 0.026 -0.752 -0.226
#> 140 virginica 0.312 0.126 -0.152 0.074
#> 141 virginica 0.112 0.126 0.048 0.374
#> 142 virginica 0.312 0.126 -0.452 0.274
#> 143 virginica -0.788 -0.274 -0.452 -0.126
#> 144 virginica 0.212 0.226 0.348 0.274
#> 145 virginica 0.112 0.326 0.148 0.474
#> 146 virginica 0.112 0.026 -0.352 0.274
#> 147 virginica -0.288 -0.474 -0.552 -0.126
#> 148 virginica -0.088 0.026 -0.352 -0.026
#> 149 virginica -0.388 0.426 -0.152 0.274
#> 150 virginica -0.688 0.026 -0.452 -0.226
#>
#> Grouped by: Species [3 | 50 (0)]
# The same calculation, in a little bit more expressive way
iris |> fgroup_by(Species) %-f% fmean()
#> Species Sepal.Length Sepal.Width Petal.Length Petal.Width
#> 1 setosa 0.094 0.072 -0.062 -0.046
#> 2 setosa -0.106 -0.428 -0.062 -0.046
#> 3 setosa -0.306 -0.228 -0.162 -0.046
#> 4 setosa -0.406 -0.328 0.038 -0.046
#> 5 setosa -0.006 0.172 -0.062 -0.046
#> 6 setosa 0.394 0.472 0.238 0.154
#> 7 setosa -0.406 -0.028 -0.062 0.054
#> 8 setosa -0.006 -0.028 0.038 -0.046
#> 9 setosa -0.606 -0.528 -0.062 -0.046
#> 10 setosa -0.106 -0.328 0.038 -0.146
#> 11 setosa 0.394 0.272 0.038 -0.046
#> 12 setosa -0.206 -0.028 0.138 -0.046
#> 13 setosa -0.206 -0.428 -0.062 -0.146
#> 14 setosa -0.706 -0.428 -0.362 -0.146
#> 15 setosa 0.794 0.572 -0.262 -0.046
#> 16 setosa 0.694 0.972 0.038 0.154
#> 17 setosa 0.394 0.472 -0.162 0.154
#> 18 setosa 0.094 0.072 -0.062 0.054
#> 19 setosa 0.694 0.372 0.238 0.054
#> 20 setosa 0.094 0.372 0.038 0.054
#> 21 setosa 0.394 -0.028 0.238 -0.046
#> 22 setosa 0.094 0.272 0.038 0.154
#> 23 setosa -0.406 0.172 -0.462 -0.046
#> 24 setosa 0.094 -0.128 0.238 0.254
#> 25 setosa -0.206 -0.028 0.438 -0.046
#> 26 setosa -0.006 -0.428 0.138 -0.046
#> 27 setosa -0.006 -0.028 0.138 0.154
#> 28 setosa 0.194 0.072 0.038 -0.046
#> 29 setosa 0.194 -0.028 -0.062 -0.046
#> 30 setosa -0.306 -0.228 0.138 -0.046
#> 31 setosa -0.206 -0.328 0.138 -0.046
#> 32 setosa 0.394 -0.028 0.038 0.154
#> 33 setosa 0.194 0.672 0.038 -0.146
#> 34 setosa 0.494 0.772 -0.062 -0.046
#> 35 setosa -0.106 -0.328 0.038 -0.046
#> 36 setosa -0.006 -0.228 -0.262 -0.046
#> 37 setosa 0.494 0.072 -0.162 -0.046
#> 38 setosa -0.106 0.172 -0.062 -0.146
#> 39 setosa -0.606 -0.428 -0.162 -0.046
#> 40 setosa 0.094 -0.028 0.038 -0.046
#> 41 setosa -0.006 0.072 -0.162 0.054
#> 42 setosa -0.506 -1.128 -0.162 0.054
#> 43 setosa -0.606 -0.228 -0.162 -0.046
#> 44 setosa -0.006 0.072 0.138 0.354
#> 45 setosa 0.094 0.372 0.438 0.154
#> 46 setosa -0.206 -0.428 -0.062 0.054
#> 47 setosa 0.094 0.372 0.138 -0.046
#> 48 setosa -0.406 -0.228 -0.062 -0.046
#> 49 setosa 0.294 0.272 0.038 -0.046
#> 50 setosa -0.006 -0.128 -0.062 -0.046
#> 51 versicolor 1.064 0.430 0.440 0.074
#> 52 versicolor 0.464 0.430 0.240 0.174
#> 53 versicolor 0.964 0.330 0.640 0.174
#> 54 versicolor -0.436 -0.470 -0.260 -0.026
#> 55 versicolor 0.564 0.030 0.340 0.174
#> 56 versicolor -0.236 0.030 0.240 -0.026
#> 57 versicolor 0.364 0.530 0.440 0.274
#> 58 versicolor -1.036 -0.370 -0.960 -0.326
#> 59 versicolor 0.664 0.130 0.340 -0.026
#> 60 versicolor -0.736 -0.070 -0.360 0.074
#> 61 versicolor -0.936 -0.770 -0.760 -0.326
#> 62 versicolor -0.036 0.230 -0.060 0.174
#> 63 versicolor 0.064 -0.570 -0.260 -0.326
#> 64 versicolor 0.164 0.130 0.440 0.074
#> 65 versicolor -0.336 0.130 -0.660 -0.026
#> 66 versicolor 0.764 0.330 0.140 0.074
#> 67 versicolor -0.336 0.230 0.240 0.174
#> 68 versicolor -0.136 -0.070 -0.160 -0.326
#> 69 versicolor 0.264 -0.570 0.240 0.174
#> 70 versicolor -0.336 -0.270 -0.360 -0.226
#> 71 versicolor -0.036 0.430 0.540 0.474
#> 72 versicolor 0.164 0.030 -0.260 -0.026
#> 73 versicolor 0.364 -0.270 0.640 0.174
#> 74 versicolor 0.164 0.030 0.440 -0.126
#> 75 versicolor 0.464 0.130 0.040 -0.026
#> 76 versicolor 0.664 0.230 0.140 0.074
#> 77 versicolor 0.864 0.030 0.540 0.074
#> 78 versicolor 0.764 0.230 0.740 0.374
#> 79 versicolor 0.064 0.130 0.240 0.174
#> 80 versicolor -0.236 -0.170 -0.760 -0.326
#> 81 versicolor -0.436 -0.370 -0.460 -0.226
#> 82 versicolor -0.436 -0.370 -0.560 -0.326
#> 83 versicolor -0.136 -0.070 -0.360 -0.126
#> 84 versicolor 0.064 -0.070 0.840 0.274
#> 85 versicolor -0.536 0.230 0.240 0.174
#> 86 versicolor 0.064 0.630 0.240 0.274
#> 87 versicolor 0.764 0.330 0.440 0.174
#> 88 versicolor 0.364 -0.470 0.140 -0.026
#> 89 versicolor -0.336 0.230 -0.160 -0.026
#> 90 versicolor -0.436 -0.270 -0.260 -0.026
#> 91 versicolor -0.436 -0.170 0.140 -0.126
#> 92 versicolor 0.164 0.230 0.340 0.074
#> 93 versicolor -0.136 -0.170 -0.260 -0.126
#> 94 versicolor -0.936 -0.470 -0.960 -0.326
#> 95 versicolor -0.336 -0.070 -0.060 -0.026
#> 96 versicolor -0.236 0.230 -0.060 -0.126
#> 97 versicolor -0.236 0.130 -0.060 -0.026
#> 98 versicolor 0.264 0.130 0.040 -0.026
#> 99 versicolor -0.836 -0.270 -1.260 -0.226
#> 100 versicolor -0.236 0.030 -0.160 -0.026
#> 101 virginica -0.288 0.326 0.448 0.474
#> 102 virginica -0.788 -0.274 -0.452 -0.126
#> 103 virginica 0.512 0.026 0.348 0.074
#> 104 virginica -0.288 -0.074 0.048 -0.226
#> 105 virginica -0.088 0.026 0.248 0.174
#> 106 virginica 1.012 0.026 1.048 0.074
#> 107 virginica -1.688 -0.474 -1.052 -0.326
#> 108 virginica 0.712 -0.074 0.748 -0.226
#> 109 virginica 0.112 -0.474 0.248 -0.226
#> 110 virginica 0.612 0.626 0.548 0.474
#> 111 virginica -0.088 0.226 -0.452 -0.026
#> 112 virginica -0.188 -0.274 -0.252 -0.126
#> 113 virginica 0.212 0.026 -0.052 0.074
#> 114 virginica -0.888 -0.474 -0.552 -0.026
#> 115 virginica -0.788 -0.174 -0.452 0.374
#> 116 virginica -0.188 0.226 -0.252 0.274
#> 117 virginica -0.088 0.026 -0.052 -0.226
#> 118 virginica 1.112 0.826 1.148 0.174
#> 119 virginica 1.112 -0.374 1.348 0.274
#> 120 virginica -0.588 -0.774 -0.552 -0.526
#> 121 virginica 0.312 0.226 0.148 0.274
#> 122 virginica -0.988 -0.174 -0.652 -0.026
#> 123 virginica 1.112 -0.174 1.148 -0.026
#> 124 virginica -0.288 -0.274 -0.652 -0.226
#> 125 virginica 0.112 0.326 0.148 0.074
#> 126 virginica 0.612 0.226 0.448 -0.226
#> 127 virginica -0.388 -0.174 -0.752 -0.226
#> 128 virginica -0.488 0.026 -0.652 -0.226
#> 129 virginica -0.188 -0.174 0.048 0.074
#> 130 virginica 0.612 0.026 0.248 -0.426
#> 131 virginica 0.812 -0.174 0.548 -0.126
#> 132 virginica 1.312 0.826 0.848 -0.026
#> 133 virginica -0.188 -0.174 0.048 0.174
#> 134 virginica -0.288 -0.174 -0.452 -0.526
#> 135 virginica -0.488 -0.374 0.048 -0.626
#> 136 virginica 1.112 0.026 0.548 0.274
#> 137 virginica -0.288 0.426 0.048 0.374
#> 138 virginica -0.188 0.126 -0.052 -0.226
#> 139 virginica -0.588 0.026 -0.752 -0.226
#> 140 virginica 0.312 0.126 -0.152 0.074
#> 141 virginica 0.112 0.126 0.048 0.374
#> 142 virginica 0.312 0.126 -0.452 0.274
#> 143 virginica -0.788 -0.274 -0.452 -0.126
#> 144 virginica 0.212 0.226 0.348 0.274
#> 145 virginica 0.112 0.326 0.148 0.474
#> 146 virginica 0.112 0.026 -0.352 0.274
#> 147 virginica -0.288 -0.474 -0.552 -0.126
#> 148 virginica -0.088 0.026 -0.352 -0.026
#> 149 virginica -0.388 0.426 -0.152 0.274
#> 150 virginica -0.688 0.026 -0.452 -0.226
#>
#> Grouped by: Species [3 | 50 (0)]
# or:
iris_num %-f% fmean(g = iris$Species)
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> 1 0.094 0.072 -0.062 -0.046
#> 2 -0.106 -0.428 -0.062 -0.046
#> 3 -0.306 -0.228 -0.162 -0.046
#> 4 -0.406 -0.328 0.038 -0.046
#> 5 -0.006 0.172 -0.062 -0.046
#> 6 0.394 0.472 0.238 0.154
#> 7 -0.406 -0.028 -0.062 0.054
#> 8 -0.006 -0.028 0.038 -0.046
#> 9 -0.606 -0.528 -0.062 -0.046
#> 10 -0.106 -0.328 0.038 -0.146
#> 11 0.394 0.272 0.038 -0.046
#> 12 -0.206 -0.028 0.138 -0.046
#> 13 -0.206 -0.428 -0.062 -0.146
#> 14 -0.706 -0.428 -0.362 -0.146
#> 15 0.794 0.572 -0.262 -0.046
#> 16 0.694 0.972 0.038 0.154
#> 17 0.394 0.472 -0.162 0.154
#> 18 0.094 0.072 -0.062 0.054
#> 19 0.694 0.372 0.238 0.054
#> 20 0.094 0.372 0.038 0.054
#> 21 0.394 -0.028 0.238 -0.046
#> 22 0.094 0.272 0.038 0.154
#> 23 -0.406 0.172 -0.462 -0.046
#> 24 0.094 -0.128 0.238 0.254
#> 25 -0.206 -0.028 0.438 -0.046
#> 26 -0.006 -0.428 0.138 -0.046
#> 27 -0.006 -0.028 0.138 0.154
#> 28 0.194 0.072 0.038 -0.046
#> 29 0.194 -0.028 -0.062 -0.046
#> 30 -0.306 -0.228 0.138 -0.046
#> 31 -0.206 -0.328 0.138 -0.046
#> 32 0.394 -0.028 0.038 0.154
#> 33 0.194 0.672 0.038 -0.146
#> 34 0.494 0.772 -0.062 -0.046
#> 35 -0.106 -0.328 0.038 -0.046
#> 36 -0.006 -0.228 -0.262 -0.046
#> 37 0.494 0.072 -0.162 -0.046
#> 38 -0.106 0.172 -0.062 -0.146
#> 39 -0.606 -0.428 -0.162 -0.046
#> 40 0.094 -0.028 0.038 -0.046
#> 41 -0.006 0.072 -0.162 0.054
#> 42 -0.506 -1.128 -0.162 0.054
#> 43 -0.606 -0.228 -0.162 -0.046
#> 44 -0.006 0.072 0.138 0.354
#> 45 0.094 0.372 0.438 0.154
#> 46 -0.206 -0.428 -0.062 0.054
#> 47 0.094 0.372 0.138 -0.046
#> 48 -0.406 -0.228 -0.062 -0.046
#> 49 0.294 0.272 0.038 -0.046
#> 50 -0.006 -0.128 -0.062 -0.046
#> 51 1.064 0.430 0.440 0.074
#> 52 0.464 0.430 0.240 0.174
#> 53 0.964 0.330 0.640 0.174
#> 54 -0.436 -0.470 -0.260 -0.026
#> 55 0.564 0.030 0.340 0.174
#> 56 -0.236 0.030 0.240 -0.026
#> 57 0.364 0.530 0.440 0.274
#> 58 -1.036 -0.370 -0.960 -0.326
#> 59 0.664 0.130 0.340 -0.026
#> 60 -0.736 -0.070 -0.360 0.074
#> 61 -0.936 -0.770 -0.760 -0.326
#> 62 -0.036 0.230 -0.060 0.174
#> 63 0.064 -0.570 -0.260 -0.326
#> 64 0.164 0.130 0.440 0.074
#> 65 -0.336 0.130 -0.660 -0.026
#> 66 0.764 0.330 0.140 0.074
#> 67 -0.336 0.230 0.240 0.174
#> 68 -0.136 -0.070 -0.160 -0.326
#> 69 0.264 -0.570 0.240 0.174
#> 70 -0.336 -0.270 -0.360 -0.226
#> 71 -0.036 0.430 0.540 0.474
#> 72 0.164 0.030 -0.260 -0.026
#> 73 0.364 -0.270 0.640 0.174
#> 74 0.164 0.030 0.440 -0.126
#> 75 0.464 0.130 0.040 -0.026
#> 76 0.664 0.230 0.140 0.074
#> 77 0.864 0.030 0.540 0.074
#> 78 0.764 0.230 0.740 0.374
#> 79 0.064 0.130 0.240 0.174
#> 80 -0.236 -0.170 -0.760 -0.326
#> 81 -0.436 -0.370 -0.460 -0.226
#> 82 -0.436 -0.370 -0.560 -0.326
#> 83 -0.136 -0.070 -0.360 -0.126
#> 84 0.064 -0.070 0.840 0.274
#> 85 -0.536 0.230 0.240 0.174
#> 86 0.064 0.630 0.240 0.274
#> 87 0.764 0.330 0.440 0.174
#> 88 0.364 -0.470 0.140 -0.026
#> 89 -0.336 0.230 -0.160 -0.026
#> 90 -0.436 -0.270 -0.260 -0.026
#> 91 -0.436 -0.170 0.140 -0.126
#> 92 0.164 0.230 0.340 0.074
#> 93 -0.136 -0.170 -0.260 -0.126
#> 94 -0.936 -0.470 -0.960 -0.326
#> 95 -0.336 -0.070 -0.060 -0.026
#> 96 -0.236 0.230 -0.060 -0.126
#> 97 -0.236 0.130 -0.060 -0.026
#> 98 0.264 0.130 0.040 -0.026
#> 99 -0.836 -0.270 -1.260 -0.226
#> 100 -0.236 0.030 -0.160 -0.026
#> 101 -0.288 0.326 0.448 0.474
#> 102 -0.788 -0.274 -0.452 -0.126
#> 103 0.512 0.026 0.348 0.074
#> 104 -0.288 -0.074 0.048 -0.226
#> 105 -0.088 0.026 0.248 0.174
#> 106 1.012 0.026 1.048 0.074
#> 107 -1.688 -0.474 -1.052 -0.326
#> 108 0.712 -0.074 0.748 -0.226
#> 109 0.112 -0.474 0.248 -0.226
#> 110 0.612 0.626 0.548 0.474
#> 111 -0.088 0.226 -0.452 -0.026
#> 112 -0.188 -0.274 -0.252 -0.126
#> 113 0.212 0.026 -0.052 0.074
#> 114 -0.888 -0.474 -0.552 -0.026
#> 115 -0.788 -0.174 -0.452 0.374
#> 116 -0.188 0.226 -0.252 0.274
#> 117 -0.088 0.026 -0.052 -0.226
#> 118 1.112 0.826 1.148 0.174
#> 119 1.112 -0.374 1.348 0.274
#> 120 -0.588 -0.774 -0.552 -0.526
#> 121 0.312 0.226 0.148 0.274
#> 122 -0.988 -0.174 -0.652 -0.026
#> 123 1.112 -0.174 1.148 -0.026
#> 124 -0.288 -0.274 -0.652 -0.226
#> 125 0.112 0.326 0.148 0.074
#> 126 0.612 0.226 0.448 -0.226
#> 127 -0.388 -0.174 -0.752 -0.226
#> 128 -0.488 0.026 -0.652 -0.226
#> 129 -0.188 -0.174 0.048 0.074
#> 130 0.612 0.026 0.248 -0.426
#> 131 0.812 -0.174 0.548 -0.126
#> 132 1.312 0.826 0.848 -0.026
#> 133 -0.188 -0.174 0.048 0.174
#> 134 -0.288 -0.174 -0.452 -0.526
#> 135 -0.488 -0.374 0.048 -0.626
#> 136 1.112 0.026 0.548 0.274
#> 137 -0.288 0.426 0.048 0.374
#> 138 -0.188 0.126 -0.052 -0.226
#> 139 -0.588 0.026 -0.752 -0.226
#> 140 0.312 0.126 -0.152 0.074
#> 141 0.112 0.126 0.048 0.374
#> 142 0.312 0.126 -0.452 0.274
#> 143 -0.788 -0.274 -0.452 -0.126
#> 144 0.212 0.226 0.348 0.274
#> 145 0.112 0.326 0.148 0.474
#> 146 0.112 0.026 -0.352 0.274
#> 147 -0.288 -0.474 -0.552 -0.126
#> 148 -0.088 0.026 -0.352 -0.026
#> 149 -0.388 0.426 -0.152 0.274
#> 150 -0.688 0.026 -0.452 -0.226