# freq2d: Bivariate (Two-Dimensional) Frequency Distribution In r2d2: Bivariate (Two-Dimensional) Confidence Region and Frequency Distribution

## Description

Calculate a frequency distribution for two continuous variables.

## Usage

 ```1 2 3 4 5 6 7``` ```freq2d(x, ...) ## S3 method for class 'formula' freq2d(formula, data, subset, ...) ## Default S3 method: freq2d(x, y, n=20, pad=0, layout=1, print=TRUE, dnn=NULL, ...) ```

## Arguments

 `x` a vector of x values, or a data frame whose first two columns contain the x and y values. `y` a vector of y values. `formula` a `formula`, such as `y~x`. `data` a `data.frame`, `matrix`, or `list` from which the variables in `formula` should be taken. `subset` an optional vector specifying a subset of observations to be used. `n` the desired number of bins for the output, a scalar or a vector of length 2. `pad` number of rows and columns to add to each margin, containing only zeros. `layout` one of three layouts for the output: `1`, `2`, or `3`. `print` whether to display the resulting matrix on the screen using dots for zeros. `dnn` the names to be given to the dimensions in the result. `...` named arguments to be passed to the default method.

## Details

The exact number of bins is determined by the `pretty` function, based on the value of `n`.

Padding the margins with zeros can be helpful for subsequent analysis, such as smoothing.

The `print` logical flag only has an effect when `layout=1`.

## Value

The `layout` argument specifies one of the following formats for the binned frequency output:

1. `matrix` that is easy to read, aligned like a scatterplot.

2. `list` with three elements (x, y, matrix) that can be passed to various plotting functions.

3. `data.frame` with three columns (x, y, frequency) that can be analyzed further.

## Author(s)

Arni Magnusson.

`cut`, `table`, and `print.table` are the basic underlying functions.

`hist2d` in the gplots package is a related function with graphical capabilities.

`conf2d` calculates a bivariate empirical confidence region, a smooth polygon.

`r2d2-package` gives an overview of the package.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```freq2d(Ushape) freq2d(quakes\$long, quakes\$lat, dnn="") freq2d(lat~long, quakes, n=c(10,20), pad=1) # Supress display freq2d(saithe) range(freq2d(saithe, print=FALSE)) # Layout, plot freq2d(saithe, layout=2) freq2d(saithe, layout=3) contour(freq2d(saithe, layout=2)) lattice::contourplot(Freq~Bio+HR, freq2d(saithe,layout=3)) ```

### Example output

```    x
y     8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
29  .  .  .  .  .  .  1  1  .  .  .  .  .  .  .  .  .  1  .  1  2  .  .  .  .
28  .  .  .  3  1  1  .  .  .  .  .  .  .  .  .  .  .  .  3  3  3  2  .  .  .
27  .  .  .  5  6  7  1  1  .  .  .  .  .  .  .  .  .  .  5  6  4  2  .  .  .
26  .  2  .  5  5  7  3  1  .  .  .  .  .  .  .  .  .  .  3  3  6  4  4  .  .
25  .  2  6  6  5  5  3  .  .  .  .  .  .  .  .  .  .  .  2  5  8  6  3  6  .
24  .  4  7  1  4  1  .  .  .  .  .  .  .  .  .  .  .  .  .  .  5  6  5  1  .
23  .  1  8  6  5  1  .  .  .  .  .  .  .  .  .  .  .  .  .  1  5  8  5  4  .
22  2  6  6  5  7  .  .  .  .  .  .  .  .  .  .  .  .  .  .  1  .  6  3  5  2
21  1  2  4  5  4  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  2 10  7 10  .
20  3  7  5  4  1  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  4  7  3  8  2
19  1  4  6  8  4  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  1  9  4  6  4
18  .  6  4  7  3  .  .  .  .  .  .  .  .  .  .  .  .  .  .  1  8  5  5  5  .
17  .  3  8  6  3  1  .  .  .  .  .  .  .  .  .  .  .  .  .  .  3  3  8  1  1
16  .  1  7  7  4  .  1  .  .  .  .  .  .  .  .  .  .  .  .  2  5  4  3  4  .
15  .  3  6  5 10  4  1  .  .  .  .  .  .  .  .  .  .  .  2  7  6  3  3  3  .
14  .  1  7  6  8  7  3  4  .  .  .  .  .  .  .  .  .  2  5  8  5  4  4  .  .
13  .  .  .  3  4  4  4  2  1  2  .  .  .  .  1  .  3  6 14  6  7  5  2  .  .
12  .  .  .  .  2  7  8  8  3  3  2  4  4  2  6  6  6  4  7  4  2  1  .  .  .
11  .  .  .  .  2  4 10  7  6  5  3  5  3  5  2  8  5  3  4  2  1  .  .  .  .
10  .  .  .  .  1  2  2  7  3  3  6  6  .  4  8  6  6  3  4  2  1  .  .  .  .
9  .  .  .  .  .  .  1  3  3  4  9  5 10  6  5  4  1  1  .  .  .  .  .  .  .
8  .  .  .  .  .  .  .  .  .  1  2  2  5  1  3  .  .  .  .  .  .  .  .  .  .

166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183
-11  13   3   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .
-12  16  11   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .
-13   4  12   .   3   4   .   1   1   .   .   .   .   .   .   .   .   .   .
-14   3  14   .   .   1   1   2   1   .   .   .   .   .   .   .   .   .   .
-15   1  14   3   .   .   2   .   .   .   .   .   .   .   .   .   1   1   1
-16   .  16   9   .   .   .   .   .   .   .   .   .   1   .   .   1   .   3
-17   .   .   1   1   .   .   .   .   .   .   .   .   .   .   1   8   3   4
-18   .   .   1   3   .   .   .   .   .   .   .   1   .   .   2  49  42   4
-19   .   .   .  21   3   .   .   .   .   .   .   .   .   .   .   3  15   8
-20   .   .   .   7   2   .   .   .   1   .   .   .   .   1   1   7  33   5
-21   .   .   .   .   5   .   .   1   1   .   .   .   .   .   .  49  26   2
-22   .   .   .   .   3   7   4   .   .   .   .   .   .   .  16  15   5   6
-23   .   .   .   .   2   3   1   3   .   .   .   .   .   4  18   3   .   5
-24   .   .   .   .   .   .   .   .   .   .   .   .   .   5  39   2   1   8
-25   .   .   .   .   .   .   .   .   .   .   .   .   2   1  16   5   .   6
-26   .   .   .   .   .   .   .   .   .   .   .   .   6   3   7   1   7   2
-27   .   .   .   .   .   .   .   .   .   .   .   .   2   1   .   2  12   7
-28   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .  14   7
-29   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   1   3   4
-30   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   8   7   .
-31   .   .   .   .   .   .   .   .   .   .   .   .   .   .   2   4   3   .
-32   .   .   .   .   .   .   .   .   .   .   .   .   .   .   4   4   .   .
-33   .   .   .   .   .   .   .   .   .   .   .   .   .   .   2   4   5   .
-34   .   .   .   .   .   .   .   .   .   .   .   .   .   1   2   1   2   .
-35   .   .   .   .   .   .   .   .   .   .   .   .   .   1   2   1   .   .
-36   .   .   .   .   .   .   .   .   .   .   .   .   .   1   1   .   .   .
-37   .   .   .   .   .   .   .   .   .   .   .   1   2   .   .   .   .   .
-38   .   .   .   .   .   .   .   .   .   .   1   2   .   .   .   .   .   .
-39   .   .   .   .   .   .   .   .   .   .   1   .   .   .   .   .   .   .

184 185 186 187 188
-11   .   .   .   .   .
-12   .   .   .   .   .
-13   .   .   .   .   .
-14   .   .   .   .   .
-15   1   7  10   7   1
-16   4  15   8   8   2
-17   .   4   8   5   1
-18   1   8   .   3   1
-19  12   5   4   3   1
-20  19   6   5   2   .
-21   7   8   8   .   .
-22   8   8   1   .   .
-23   7   6   1   .   .
-24   7   5   .   .   .
-25   .   .   .   .   .
-26   2   .   .   .   .
-27   4   .   .   .   .
-28   1   .   .   .   .
-29   1   .   .   .   .
-30   .   .   .   .   .
-31   .   .   .   .   .
-32   .   .   .   .   .
-33   .   .   .   .   .
-34   .   .   .   .   .
-35   .   .   .   .   .
-36   .   .   .   .   .
-37   .   .   .   .   .
-38   .   .   .   .   .
-39   .   .   .   .   .
long
lat   164 166 168 170 172 174 176 178 180 182 184 186 188 190
-9    .   .   .   .   .   .   .   .   .   .   .   .   .   .
-11   .  14   2   .   .   .   .   .   .   .   .   .   .   .
-12   .  20   7   .   .   .   .   .   .   .   .   .   .   .
-13   .   9   7   7   2   .   .   .   .   .   .   .   .   .
-14   .   9   8   2   2   1   .   .   .   .   .   .   .   .
-15   .   4  14   .   2   .   .   .   .   2   5  20   2   .
-16   .   8  17   .   .   .   .   1   1   3   8  23   6   .
-17   .   .   2   .   .   .   .   .   2  14   1  15   2   .
-18   .   .   3   1   .   .   .   1  12  81   8   7   2   .
-19   .   .   2  22   .   .   .   .   2  22  17   9   1   .
-20   .   .   4   5   .   1   .   1   3  41  24  10   .   .
-21   .   .   .   5   .   2   .   .  17  59  12  12   .   .
-22   .   .   .   5   9   .   .   .  29   9  15   6   .   .
-23   .   .   .   5   3   1   .   .  24   3  16   1   .   .
-24   .   .   .   .   .   .   .   1  45   8  13   .   .   .
-25   .   .   .   .   .   .   .   2  21   5   2   .   .   .
-26   .   .   .   .   .   .   .   7   9  10   2   .   .   .
-27   .   .   .   .   .   .   .   3   1  17   7   .   .   .
-28   .   .   .   .   .   .   .   .   .  17   5   .   .   .
-29   .   .   .   .   .   .   .   .   .   6   3   .   .   .
-30   .   .   .   .   .   .   .   .   3  12   .   .   .   .
-31   .   .   .   .   .   .   .   .   4   5   .   .   .   .
-32   .   .   .   .   .   .   .   .   6   2   .   .   .   .
-33   .   .   .   .   .   .   .   .   4   7   .   .   .   .
-34   .   .   .   .   .   .   .   .   4   2   .   .   .   .
-35   .   .   .   .   .   .   .   .   4   .   .   .   .   .
-36   .   .   .   .   .   .   .   1   1   .   .   .   .   .
-37   .   .   .   .   .   .   1   2   .   .   .   .   .   .
-38   .   .   .   .   .   .   1   2   .   .   .   .   .   .
-39   .   .   .   .   .   .   1   .   .   .   .   .   .   .
-41   .   .   .   .   .   .   .   .   .   .   .   .   .   .
Bio
HR     0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
1.60   1   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .
1.55   1   1   .   .   .   .   .   .   .   .   .   .   .   .   .   .
1.50   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .   .
1.45   .   .   .   1   .   .   .   .   .   .   .   .   .   .   .   .
1.40   .   1   .   .   .   .   .   .   .   .   .   .   .   .   .   .
1.35   .   2   1   .   .   .   .   .   .   .   .   .   .   .   .   .
1.30   .   3   5   .   .   .   .   .   .   .   .   .   .   .   .   .
1.25   .   2   2   .   .   .   .   .   .   .   .   .   .   .   .   .
1.20   .   1   9   6   .   .   .   .   .   .   .   .   .   .   .   .
1.15   .   2   9   3   4   .   .   .   .   .   .   .   .   .   .   .
1.10   .   2   2  14   1   .   .   .   .   .   .   .   .   .   .   .
1.05   .   1   7  15   7   4   .   .   .   .   .   .   .   .   .   .
1.00   .   2   9  14  19   3   2   .   .   .   .   .   .   .   .   .
0.95   .   1   5  21  19  12   .   .   .   .   .   .   .   .   .   .
0.90   .   .   2  20  22  19   5   5   .   .   .   .   .   .   .   .
0.85   .   .   3  12  38  29  19   8   .   .   .   .   .   .   .   .
0.80   .   .   .   7  19  32  31   8   4   .   1   .   .   .   .   .
0.75   .   .   .   1  15  41  31  19   5   1   .   .   .   .   .   .
0.70   .   .   .   .   8  38  25  32  12   2   1   .   .   .   .   .
0.65   .   .   .   .   3  20  16  33  16   5   1   1   .   .   .   .
0.60   .   .   .   .   .   5  12  22  29  10   6   1   1   .   1   .
0.55   .   .   .   .   .   1   3  14  11  11  10   1   .   .   .   .
0.50   .   .   .   .   .   .   1   5   4   6   3   2   2   2   .   .
0.45   .   .   .   .   .   .   .   .   1   1   1   1   1   1   2   1
0.40   .   .   .   .   .   .   .   .   .   .   1   .   .   .   1   2
[1]  0 41
\$x
[1] 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0

\$y
[1] 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10
[16] 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60

\$z
HR
Bio   0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05
0.5    0    0    0    0    0    0    0    0    0    0    0    0    0    0
0.6    0    0    0    0    0    0    0    0    0    0    0    1    2    1
0.7    0    0    0    0    0    0    0    0    0    3    2    5    9    7
0.8    0    0    0    0    0    0    0    1    7   12   20   21   14   15
0.9    0    0    0    0    0    3    8   15   19   38   22   19   19    7
1.0    0    0    0    1    5   20   38   41   32   29   19   12    3    4
1.1    0    0    1    3   12   16   25   31   31   19    5    0    2    0
1.2    0    0    5   14   22   33   32   19    8    8    5    0    0    0
1.3    0    1    4   11   29   16   12    5    4    0    0    0    0    0
1.4    0    1    6   11   10    5    2    1    0    0    0    0    0    0
1.5    1    1    3   10    6    1    1    0    1    0    0    0    0    0
1.6    0    1    2    1    1    1    0    0    0    0    0    0    0    0
1.7    0    1    2    0    1    0    0    0    0    0    0    0    0    0
1.8    0    1    2    0    0    0    0    0    0    0    0    0    0    0
1.9    1    2    0    0    1    0    0    0    0    0    0    0    0    0
2.0    2    1    0    0    0    0    0    0    0    0    0    0    0    0
HR
Bio   1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60
0.5    0    0    0    0    0    0    0    0    0    1    1
0.6    2    2    1    2    3    2    1    0    0    1    0
0.7    2    9    9    2    5    1    0    0    0    0    0
0.8   14    3    6    0    0    0    0    1    0    0    0
0.9    1    4    0    0    0    0    0    0    0    0    0
1.0    0    0    0    0    0    0    0    0    0    0    0
1.1    0    0    0    0    0    0    0    0    0    0    0
1.2    0    0    0    0    0    0    0    0    0    0    0
1.3    0    0    0    0    0    0    0    0    0    0    0
1.4    0    0    0    0    0    0    0    0    0    0    0
1.5    0    0    0    0    0    0    0    0    0    0    0
1.6    0    0    0    0    0    0    0    0    0    0    0
1.7    0    0    0    0    0    0    0    0    0    0    0
1.8    0    0    0    0    0    0    0    0    0    0    0
1.9    0    0    0    0    0    0    0    0    0    0    0
2.0    0    0    0    0    0    0    0    0    0    0    0

Bio   HR Freq
1   0.5 0.40    0
2   0.6 0.40    0
3   0.7 0.40    0
4   0.8 0.40    0
5   0.9 0.40    0
6   1.0 0.40    0
7   1.1 0.40    0
8   1.2 0.40    0
9   1.3 0.40    0
10  1.4 0.40    0
11  1.5 0.40    1
12  1.6 0.40    0
13  1.7 0.40    0
14  1.8 0.40    0
15  1.9 0.40    1
16  2.0 0.40    2
17  0.5 0.45    0
18  0.6 0.45    0
19  0.7 0.45    0
20  0.8 0.45    0
21  0.9 0.45    0
22  1.0 0.45    0
23  1.1 0.45    0
24  1.2 0.45    0
25  1.3 0.45    1
26  1.4 0.45    1
27  1.5 0.45    1
28  1.6 0.45    1
29  1.7 0.45    1
30  1.8 0.45    1
31  1.9 0.45    2
32  2.0 0.45    1
33  0.5 0.50    0
34  0.6 0.50    0
35  0.7 0.50    0
36  0.8 0.50    0
37  0.9 0.50    0
38  1.0 0.50    0
39  1.1 0.50    1
40  1.2 0.50    5
41  1.3 0.50    4
42  1.4 0.50    6
43  1.5 0.50    3
44  1.6 0.50    2
45  1.7 0.50    2
46  1.8 0.50    2
47  1.9 0.50    0
48  2.0 0.50    0
49  0.5 0.55    0
50  0.6 0.55    0
51  0.7 0.55    0
52  0.8 0.55    0
53  0.9 0.55    0
54  1.0 0.55    1
55  1.1 0.55    3
56  1.2 0.55   14
57  1.3 0.55   11
58  1.4 0.55   11
59  1.5 0.55   10
60  1.6 0.55    1
61  1.7 0.55    0
62  1.8 0.55    0
63  1.9 0.55    0
64  2.0 0.55    0
65  0.5 0.60    0
66  0.6 0.60    0
67  0.7 0.60    0
68  0.8 0.60    0
69  0.9 0.60    0
70  1.0 0.60    5
71  1.1 0.60   12
72  1.2 0.60   22
73  1.3 0.60   29
74  1.4 0.60   10
75  1.5 0.60    6
76  1.6 0.60    1
77  1.7 0.60    1
78  1.8 0.60    0
79  1.9 0.60    1
80  2.0 0.60    0
81  0.5 0.65    0
82  0.6 0.65    0
83  0.7 0.65    0
84  0.8 0.65    0
85  0.9 0.65    3
86  1.0 0.65   20
87  1.1 0.65   16
88  1.2 0.65   33
89  1.3 0.65   16
90  1.4 0.65    5
91  1.5 0.65    1
92  1.6 0.65    1
93  1.7 0.65    0
94  1.8 0.65    0
95  1.9 0.65    0
96  2.0 0.65    0
97  0.5 0.70    0
98  0.6 0.70    0
99  0.7 0.70    0
100 0.8 0.70    0
101 0.9 0.70    8
102 1.0 0.70   38
103 1.1 0.70   25
104 1.2 0.70   32
105 1.3 0.70   12
106 1.4 0.70    2
107 1.5 0.70    1
108 1.6 0.70    0
109 1.7 0.70    0
110 1.8 0.70    0
111 1.9 0.70    0
112 2.0 0.70    0
113 0.5 0.75    0
114 0.6 0.75    0
115 0.7 0.75    0
116 0.8 0.75    1
117 0.9 0.75   15
118 1.0 0.75   41
119 1.1 0.75   31
120 1.2 0.75   19
121 1.3 0.75    5
122 1.4 0.75    1
123 1.5 0.75    0
124 1.6 0.75    0
125 1.7 0.75    0
126 1.8 0.75    0
127 1.9 0.75    0
128 2.0 0.75    0
129 0.5 0.80    0
130 0.6 0.80    0
131 0.7 0.80    0
132 0.8 0.80    7
133 0.9 0.80   19
134 1.0 0.80   32
135 1.1 0.80   31
136 1.2 0.80    8
137 1.3 0.80    4
138 1.4 0.80    0
139 1.5 0.80    1
140 1.6 0.80    0
141 1.7 0.80    0
142 1.8 0.80    0
143 1.9 0.80    0
144 2.0 0.80    0
145 0.5 0.85    0
146 0.6 0.85    0
147 0.7 0.85    3
148 0.8 0.85   12
149 0.9 0.85   38
150 1.0 0.85   29
151 1.1 0.85   19
152 1.2 0.85    8
153 1.3 0.85    0
154 1.4 0.85    0
155 1.5 0.85    0
156 1.6 0.85    0
157 1.7 0.85    0
158 1.8 0.85    0
159 1.9 0.85    0
160 2.0 0.85    0
161 0.5 0.90    0
162 0.6 0.90    0
163 0.7 0.90    2
164 0.8 0.90   20
165 0.9 0.90   22
166 1.0 0.90   19
167 1.1 0.90    5
168 1.2 0.90    5
169 1.3 0.90    0
170 1.4 0.90    0
171 1.5 0.90    0
172 1.6 0.90    0
173 1.7 0.90    0
174 1.8 0.90    0
175 1.9 0.90    0
176 2.0 0.90    0
177 0.5 0.95    0
178 0.6 0.95    1
179 0.7 0.95    5
180 0.8 0.95   21
181 0.9 0.95   19
182 1.0 0.95   12
183 1.1 0.95    0
184 1.2 0.95    0
185 1.3 0.95    0
186 1.4 0.95    0
187 1.5 0.95    0
188 1.6 0.95    0
189 1.7 0.95    0
190 1.8 0.95    0
191 1.9 0.95    0
192 2.0 0.95    0
193 0.5 1.00    0
194 0.6 1.00    2
195 0.7 1.00    9
196 0.8 1.00   14
197 0.9 1.00   19
198 1.0 1.00    3
199 1.1 1.00    2
200 1.2 1.00    0
201 1.3 1.00    0
202 1.4 1.00    0
203 1.5 1.00    0
204 1.6 1.00    0
205 1.7 1.00    0
206 1.8 1.00    0
207 1.9 1.00    0
208 2.0 1.00    0
209 0.5 1.05    0
210 0.6 1.05    1
211 0.7 1.05    7
212 0.8 1.05   15
213 0.9 1.05    7
214 1.0 1.05    4
215 1.1 1.05    0
216 1.2 1.05    0
217 1.3 1.05    0
218 1.4 1.05    0
219 1.5 1.05    0
220 1.6 1.05    0
221 1.7 1.05    0
222 1.8 1.05    0
223 1.9 1.05    0
224 2.0 1.05    0
225 0.5 1.10    0
226 0.6 1.10    2
227 0.7 1.10    2
228 0.8 1.10   14
229 0.9 1.10    1
230 1.0 1.10    0
231 1.1 1.10    0
232 1.2 1.10    0
233 1.3 1.10    0
234 1.4 1.10    0
235 1.5 1.10    0
236 1.6 1.10    0
237 1.7 1.10    0
238 1.8 1.10    0
239 1.9 1.10    0
240 2.0 1.10    0
241 0.5 1.15    0
242 0.6 1.15    2
243 0.7 1.15    9
244 0.8 1.15    3
245 0.9 1.15    4
246 1.0 1.15    0
247 1.1 1.15    0
248 1.2 1.15    0
249 1.3 1.15    0
250 1.4 1.15    0
251 1.5 1.15    0
252 1.6 1.15    0
253 1.7 1.15    0
254 1.8 1.15    0
255 1.9 1.15    0
256 2.0 1.15    0
257 0.5 1.20    0
258 0.6 1.20    1
259 0.7 1.20    9
260 0.8 1.20    6
261 0.9 1.20    0
262 1.0 1.20    0
263 1.1 1.20    0
264 1.2 1.20    0
265 1.3 1.20    0
266 1.4 1.20    0
267 1.5 1.20    0
268 1.6 1.20    0
269 1.7 1.20    0
270 1.8 1.20    0
271 1.9 1.20    0
272 2.0 1.20    0
273 0.5 1.25    0
274 0.6 1.25    2
275 0.7 1.25    2
276 0.8 1.25    0
277 0.9 1.25    0
278 1.0 1.25    0
279 1.1 1.25    0
280 1.2 1.25    0
281 1.3 1.25    0
282 1.4 1.25    0
283 1.5 1.25    0
284 1.6 1.25    0
285 1.7 1.25    0
286 1.8 1.25    0
287 1.9 1.25    0
288 2.0 1.25    0
289 0.5 1.30    0
290 0.6 1.30    3
291 0.7 1.30    5
292 0.8 1.30    0
293 0.9 1.30    0
294 1.0 1.30    0
295 1.1 1.30    0
296 1.2 1.30    0
297 1.3 1.30    0
298 1.4 1.30    0
299 1.5 1.30    0
300 1.6 1.30    0
301 1.7 1.30    0
302 1.8 1.30    0
303 1.9 1.30    0
304 2.0 1.30    0
305 0.5 1.35    0
306 0.6 1.35    2
307 0.7 1.35    1
308 0.8 1.35    0
309 0.9 1.35    0
310 1.0 1.35    0
311 1.1 1.35    0
312 1.2 1.35    0
313 1.3 1.35    0
314 1.4 1.35    0
315 1.5 1.35    0
316 1.6 1.35    0
317 1.7 1.35    0
318 1.8 1.35    0
319 1.9 1.35    0
320 2.0 1.35    0
321 0.5 1.40    0
322 0.6 1.40    1
323 0.7 1.40    0
324 0.8 1.40    0
325 0.9 1.40    0
326 1.0 1.40    0
327 1.1 1.40    0
328 1.2 1.40    0
329 1.3 1.40    0
330 1.4 1.40    0
331 1.5 1.40    0
332 1.6 1.40    0
333 1.7 1.40    0
334 1.8 1.40    0
335 1.9 1.40    0
336 2.0 1.40    0
337 0.5 1.45    0
338 0.6 1.45    0
339 0.7 1.45    0
340 0.8 1.45    1
341 0.9 1.45    0
342 1.0 1.45    0
343 1.1 1.45    0
344 1.2 1.45    0
345 1.3 1.45    0
346 1.4 1.45    0
347 1.5 1.45    0
348 1.6 1.45    0
349 1.7 1.45    0
350 1.8 1.45    0
351 1.9 1.45    0
352 2.0 1.45    0
353 0.5 1.50    0
354 0.6 1.50    0
355 0.7 1.50    0
356 0.8 1.50    0
357 0.9 1.50    0
358 1.0 1.50    0
359 1.1 1.50    0
360 1.2 1.50    0
361 1.3 1.50    0
362 1.4 1.50    0
363 1.5 1.50    0
364 1.6 1.50    0
365 1.7 1.50    0
366 1.8 1.50    0
367 1.9 1.50    0
368 2.0 1.50    0
369 0.5 1.55    1
370 0.6 1.55    1
371 0.7 1.55    0
372 0.8 1.55    0
373 0.9 1.55    0
374 1.0 1.55    0
375 1.1 1.55    0
376 1.2 1.55    0
377 1.3 1.55    0
378 1.4 1.55    0
379 1.5 1.55    0
380 1.6 1.55    0
381 1.7 1.55    0
382 1.8 1.55    0
383 1.9 1.55    0
384 2.0 1.55    0
385 0.5 1.60    1
386 0.6 1.60    0
387 0.7 1.60    0
388 0.8 1.60    0
389 0.9 1.60    0
390 1.0 1.60    0
391 1.1 1.60    0
392 1.2 1.60    0
393 1.3 1.60    0
394 1.4 1.60    0
395 1.5 1.60    0
396 1.6 1.60    0
397 1.7 1.60    0
398 1.8 1.60    0
399 1.9 1.60    0
400 2.0 1.60    0
```

r2d2 documentation built on May 2, 2019, 2:38 a.m.