This function takes in a dataframe of multi-species data and rescales them so that the value in the starting year is the same. This function accounts for species that have no data at the beginning of the period or those that have no data at teh end of the period.
Arguments
- Data
A matrix, the first column, named year, gives the year. Subsequent named columns give the species. Values in the table are the yearly values to be rescaled.
- index
The index value for the first year, defaults to 100.
- max
The upper limit allowed for scaled values. Values greater than this will be set equal to
max.- min
The upper limit allowed for scaled values. Values greater than this will be set equal to
min.
Value
A matrix. In each row we have the year, the species and the scaled value. There is also an additional column, 'geomean' giving the geometric mean for each year.
Examples
# We will create fake data which will mimic a summarised output from a sparta package occupancy detection model. Please see the vignette for more details.
# Create a matrix with random data using set.seed for reproducibility
set.seed(123)
data <- matrix(rnorm(50 * 27), nrow = 50, ncol = 27)
# Assign column names
col_names <- c("year", letters[1:26])
dimnames(data) <- list(NULL, col_names)
# Create the 'trends_summary' object
trends_summary <- data
# Re-scale the data so that the value for all species in the first year is the same (all defaults used).
# This function accounts for species that have no data at the beginning of the dataset by entering them at the geometric mean for that year, this stops them dramatically changing the indicator value in the year they join the dataset.
# It also accounts for species that leave the dataset before the end by holding them at their last value.
# Finally it limits the species values that can be given, preventing extremely high or low values biasing the indicator.
rescale_species(Data = trends_summary)
#> year a b c d e
#> [1,] -0.56047565 100.00000 100.000000 100.000000 100.000000 100.00000
#> [2,] -0.23017749 1.00000 1.000000 97.626548 59.687411 149.59320
#> [3,] 1.55870831 1.00000 34.725450 42.171664 1.000000 91.56406
#> [4,] 0.07050839 540.26935 48.921648 1.000000 24.703998 1.00000
#> [5,] 0.12928774 1.00000 133.954079 1.000000 1.000000 1.00000
#> [6,] 1.71506499 598.64184 6.338304 1.000000 1.000000 23.57946
#> [7,] 0.46091621 1.00000 110.486658 71.469058 1.000000 1.00000
#> [8,] -1.26506123 230.78209 234.786955 1.000000 1.000000 1.00000
#> [9,] -0.68685285 48.89269 53.522383 124.022497 75.081849 30.25533
#> [10,] -0.44566197 85.24508 1.000000 1.000000 1.000000 408.11775
#> [11,] 1.22408180 149.86646 80.988407 133.637115 5.423171 138.74157
#> [12,] 0.35981383 1.00000 1.000000 1.000000 11.082694 130.42245
#> [13,] 0.40077145 1.00000 227.740394 1.000000 56.051941 1.00000
#> [14,] 0.11068272 1.00000 7.821150 411.435839 1.000000 1.00000
#> [15,] -0.55584113 1.00000 1.000000 1.000000 1.000000 1.00000
#> [16,] 1.78691314 119.82095 1.000000 37.858688 76.209253 1.00000
#> [17,] 0.49785048 176.93526 1.000000 80.809735 1.000000 35.44993
#> [18,] -1.96661716 20.92395 90.188639 1.000000 1.000000 467.65548
#> [19,] 0.70135590 364.07425 119.608178 65.613375 1.000000 103.50822
#> [20,] -0.47279141 809.29130 144.160941 46.838432 1.000000 1.00000
#> [21,] -1.06782371 1.00000 1.000000 1.000000 1.000000 1.00000
#> [22,] -0.21797491 1.00000 133.370757 8.288665 28.105462 1.00000
#> [23,] -1.02600445 397.02527 69.053056 1.000000 50.474937 1.00000
#> [24,] -0.72889123 1.00000 36.048680 270.197656 32.180509 371.47595
#> [25,] -0.62503927 1.00000 1.000000 1.000000 1.000000 1.00000
#> [26,] -1.68669331 404.85449 91.771379 1.000000 2.717376 118.89079
#> [27,] 0.83778704 1.00000 1.000000 4.797072 1.000000 1.00000
#> [28,] 0.15337312 1.00000 1.000000 39.414173 1.000000 1.00000
#> [29,] -1.13813694 71.57135 135.395235 55.414746 40.233142 1.00000
#> [30,] 1.25381492 1.00000 10.037645 1.000000 1.000000 1.00000
#> [31,] 0.42646422 2.27547 1.000000 1.000000 88.925085 443.94631
#> [32,] -0.29507148 152.09327 1.000000 160.355831 1.000000 1.00000
#> [33,] 0.89512566 1.00000 1.000000 1.000000 9.757041 1.00000
#> [34,] 0.87813349 254.37404 59.472541 1.000000 1.000000 70.72673
#> [35,] 0.82158108 1.00000 289.024247 1.000000 1.000000 1.00000
#> [36,] 0.68864025 130.97423 1.000000 1.000000 1.000000 1.00000
#> [37,] 0.55391765 432.98810 205.606218 140.899524 1.000000 1.00000
#> [38,] -0.06191171 171.79222 1.000000 10.757028 19.054959 1.00000
#> [39,] -0.30596266 1.00000 1.000000 95.723829 14.749082 58.31968
#> [40,] -0.38047100 453.50322 203.248849 1.000000 1.000000 1.00000
#> [41,] -0.69470698 392.19552 1.000000 27.222894 1.000000 1.00000
#> [42,] -0.20791728 216.48515 36.908089 1.000000 1.000000 1.00000
#> [43,] -1.26539635 94.24172 221.302032 12.006965 68.039550 1.00000
#> [44,] 2.16895597 1.00000 213.211382 1.000000 1.000000 153.74430
#> [45,] 1.20796200 537.13107 225.439383 1.000000 1.000000 1.00000
#> [46,] -1.12310858 1.00000 74.732773 253.537501 86.517776 1.00000
#> [47,] -0.40288484 863.47143 205.763243 76.257357 1.000000 1.00000
#> [48,] -0.46665535 605.01327 1.000000 1.000000 1.000000 359.66250
#> [49,] 0.77996512 1.00000 1.000000 1.000000 1.000000 1.00000
#> [50,] -0.08336907 1.00000 181.168157 1.000000 22.078302 1.00000
#> f g h i j k
#> [1,] 100.000000 100.000000 100.00000 100.000000 100.00000 100.000000
#> [2,] 105.235539 1.000000 1588.79102 73.170241 165.09560 1.000000
#> [3,] 131.219707 1.000000 862.94537 30.431225 1.00000 131.460036
#> [4,] 147.154810 11.492001 39.21032 49.998409 1.00000 29.568406
#> [5,] 61.120491 1.000000 1.00000 64.120065 250.73675 195.515102
#> [6,] 1.000000 32.898684 2243.93131 1.000000 15.80804 1.000000
#> [7,] 281.612373 40.537237 475.49370 77.619916 148.85504 1.000000
#> [8,] 1.000000 1.000000 1.00000 1.000000 344.03982 1.000000
#> [9,] 1.000000 1.000000 732.51539 16.122515 1.00000 1.000000
#> [10,] 1.000000 253.359815 1.00000 1.000000 13.16043 1.000000
#> [11,] 1.000000 1.000000 1.00000 60.959419 16.17718 1.000000
#> [12,] 1.000000 64.160566 1.00000 1.000000 1.00000 68.495617
#> [13,] 241.418981 26.973578 1.00000 36.248806 1.00000 1.000000
#> [14,] 84.098326 100.958680 166.82341 1.000000 1.00000 175.644867
#> [15,] 49.220594 80.562091 562.39655 1.000000 102.41621 1.000000
#> [16,] 1.000000 1.000000 3593.38227 84.592319 122.08141 11.963385
#> [17,] 14.774203 37.259995 126.35406 51.796616 21.89805 63.082804
#> [18,] 175.975166 1.000000 1.00000 120.543863 1.00000 69.444004
#> [19,] 1.000000 84.430639 1.00000 4.554937 172.73512 1.000000
#> [20,] 1.000000 1.000000 754.90539 78.649392 30.62154 9.409586
#> [21,] 1.000000 238.119081 1.00000 138.102336 1.00000 113.771964
#> [22,] 1.000000 1.000000 1.00000 1.000000 17.98993 1.000000
#> [23,] 187.177758 1.000000 1.00000 1.000000 116.03738 1.000000
#> [24,] 1.000000 81.322766 1.00000 1.000000 45.84623 37.921731
#> [25,] 73.109834 50.262178 976.76061 1.000000 1.00000 1.000000
#> [26,] 1.000000 1.000000 612.23898 10.604045 1.00000 162.149026
#> [27,] 8.503687 1.000000 1.00000 119.707926 1.00000 79.684044
#> [28,] 1.000000 14.234857 1.00000 1.000000 1.00000 8.541412
#> [29,] 1.000000 1.000000 1.00000 26.076905 1.00000 1.000000
#> [30,] 1.000000 1.000000 1955.66136 1.000000 92.78344 3.089134
#> [31,] 1.000000 3.404237 259.00913 1.429717 1.00000 1.000000
#> [32,] 166.158269 18.742952 1.00000 21.955897 84.12354 1.000000
#> [33,] 100.889524 17.215387 1.00000 92.856021 236.01635 1.000000
#> [34,] 1.000000 1.000000 1367.17059 8.481416 1.00000 59.019475
#> [35,] 1.000000 46.912309 1.00000 49.835092 1.00000 1.000000
#> [36,] 286.926982 135.827323 1464.76205 54.450416 1.00000 1.000000
#> [37,] 190.709871 44.951916 1.00000 63.952165 1.00000 45.144267
#> [38,] 28.071752 1.000000 1.00000 1.000000 1.00000 1.000000
#> [39,] 1.000000 1.000000 3024.88868 113.735917 101.10723 69.000885
#> [40,] 14.244581 34.100788 1.00000 1.000000 33.60081 1.000000
#> [41,] 1.000000 1.000000 1687.20998 1.000000 45.39813 1.000000
#> [42,] 1.000000 1.000000 1.00000 98.157716 77.87097 55.032034
#> [43,] 1.000000 87.123185 1.00000 90.469924 1.00000 99.483443
#> [44,] 1.000000 1.000000 271.75183 1.000000 198.93300 1.000000
#> [45,] 7.267735 1.000000 877.03762 1.000000 1.00000 59.666673
#> [46,] 245.124993 148.175844 1.00000 1.000000 1.00000 1.000000
#> [47,] 1.000000 1.000000 1.00000 12.713010 199.14215 1.000000
#> [48,] 79.951947 83.327970 1.00000 11.524091 1.00000 1.000000
#> [49,] 136.178989 1.000000 2790.16865 25.455403 1.00000 139.800564
#> [50,] 25.153191 1.000000 2224.67078 38.601567 92.57719 220.132741
#> l m n o p q r
#> [1,] 100.00000 100.000000 100.000000 100.00000 100.00000 100.00000 100.000000
#> [2,] 1.00000 1.000000 211.535564 1.00000 1.00000 1.00000 78.030058
#> [3,] 1.00000 1.000000 95.176658 33.24628 240.03429 180.77792 1.000000
#> [4,] 1.00000 74.842445 1.000000 13.90755 323.60093 1.00000 1.000000
#> [5,] 73.59184 1.000000 187.403686 1.00000 77.54349 412.76810 1.000000
#> [6,] 1.00000 42.722325 1.000000 1.00000 40.44665 1.00000 61.587491
#> [7,] 1.00000 1.000000 1.000000 65.83557 1.00000 1.00000 1.000000
#> [8,] 1.00000 1.000000 124.167989 1.00000 606.65644 1.00000 4.789239
#> [9,] 1.00000 1.000000 1.000000 1.00000 77.55500 26.09230 1.000000
#> [10,] 1.00000 1.000000 1.000000 1.00000 1.00000 288.76321 1.000000
#> [11,] 1.00000 1.000000 1.000000 35.08710 1.00000 162.05986 1.000000
#> [12,] 1.00000 1.000000 29.228604 40.07044 1.00000 25.33642 116.879227
#> [13,] 157.12944 1.000000 12.858327 40.07772 1.00000 1.00000 1.000000
#> [14,] 1.00000 1.464792 11.907698 1.00000 57.90168 1.00000 175.520404
#> [15,] 100.08685 116.019894 1.000000 23.96872 77.71131 1.00000 1.000000
#> [16,] 1.00000 1.000000 1.000000 62.91213 230.57681 454.05911 1.000000
#> [17,] 1.00000 1.000000 1.000000 82.97930 1.00000 1.00000 1.000000
#> [18,] 1.00000 8.013669 39.458014 1.00000 340.90530 201.15958 189.835159
#> [19,] 1.00000 1.000000 1.000000 1.00000 1.00000 1.00000 1.000000
#> [20,] 144.00293 1.000000 1.000000 96.71143 1.00000 296.29871 1.000000
#> [21,] 1.00000 26.720721 143.043938 1.00000 1.00000 1.00000 40.825370
#> [22,] 29.64494 15.171247 237.333035 1.00000 208.34458 25.54358 20.919788
#> [23,] 78.81067 1.000000 1.000000 29.73564 1.00000 1.00000 3.602871
#> [24,] 16.59108 28.383926 210.006921 1.00000 221.68253 160.69161 1.000000
#> [25,] 1.00000 1.000000 1.000000 18.17618 1.00000 263.89217 1.000000
#> [26,] 87.63083 101.196948 1.000000 122.06365 1.00000 346.93834 1.000000
#> [27,] 15.88325 57.771318 1.000000 1.00000 1.00000 141.85434 9.415862
#> [28,] 1.00000 68.493797 1.000000 1.00000 1.00000 327.82737 1.000000
#> [29,] 1.00000 44.035163 100.636442 30.86989 1.00000 221.67816 1.000000
#> [30,] 194.29177 35.764913 1.000000 1.00000 1.00000 1.00000 1.000000
#> [31,] 1.00000 1.000000 1.000000 52.87210 295.92241 84.84171 1.000000
#> [32,] 1.00000 1.000000 1.000000 58.78950 1.00000 1.00000 132.356214
#> [33,] 49.65114 37.522918 266.904682 1.00000 221.58203 1.00000 1.000000
#> [34,] 28.88517 51.423088 1.000000 1.00000 425.64173 217.15003 21.824579
#> [35,] 1.00000 53.736721 7.697676 1.00000 1.00000 96.26811 1.089210
#> [36,] 1.00000 21.387037 1.000000 1.00000 79.67785 81.34161 56.740913
#> [37,] 1.00000 12.330590 1.000000 51.83079 1.00000 1.00000 67.725673
#> [38,] 106.08783 1.000000 13.277058 1.00000 1.00000 1.00000 71.074210
#> [39,] 59.22875 16.575912 10.335241 1.00000 15.77813 1.00000 21.151910
#> [40,] 1.00000 107.221265 1.000000 1.00000 83.94636 70.30390 1.000000
#> [41,] 1.00000 4.716743 1.000000 25.63619 1.00000 1.00000 1.000000
#> [42,] 25.23870 1.000000 1.000000 1.00000 753.57410 99.95981 35.496508
#> [43,] 14.65098 1.000000 1.000000 57.63986 1.00000 1.00000 166.245232
#> [44,] 58.63171 40.699577 1.000000 21.66949 18.03159 325.20659 83.282874
#> [45,] 1.00000 79.843837 1.000000 1.00000 182.38065 81.91679 45.138954
#> [46,] 83.73778 1.000000 303.567028 53.22491 1.00000 1.00000 1.000000
#> [47,] 1.00000 8.378723 1.000000 25.24425 1.00000 42.87034 65.338528
#> [48,] 1.00000 5.027135 66.281812 1.00000 293.39167 1.00000 1.000000
#> [49,] 68.97636 1.000000 1.000000 15.02278 453.44396 66.00916 26.847819
#> [50,] 92.17508 83.262086 1.000000 42.08923 1.00000 43.31262 119.704911
#> s t u v w x
#> [1,] 100.00000 100.000000 100.00000 100.000000 100.00000 100.00000
#> [2,] 711.71250 104.434261 1.00000 87.404945 1681.30668 1.00000
#> [3,] 1.00000 1.805610 141.95652 1.000000 1.00000 137.37591
#> [4,] 1.00000 13.273278 1.00000 1.000000 1.00000 1.00000
#> [5,] 1.00000 256.009845 349.36340 17.497700 1.00000 101.67617
#> [6,] 1148.12267 1.000000 176.41659 1.000000 1.00000 176.92369
#> [7,] 1.00000 1.000000 1.00000 1.000000 581.96007 1.00000
#> [8,] 1.00000 1.000000 16.45974 9.162817 1.00000 178.75210
#> [9,] 1006.01074 1.000000 216.13074 1.000000 2081.06116 1.00000
#> [10,] 1.00000 44.884503 168.27794 17.601283 1467.23929 47.48784
#> [11,] 1.00000 1.000000 447.12740 1.000000 1.00000 32.56231
#> [12,] 1.00000 1.000000 1.00000 104.494822 584.72491 1.00000
#> [13,] 1.00000 122.385356 336.75944 264.684516 115.78081 43.25286
#> [14,] 1.00000 1.000000 312.74606 1.000000 202.24790 1.00000
#> [15,] 1.00000 21.213817 1.00000 115.466522 1141.84048 1.00000
#> [16,] 1.00000 1.000000 1.00000 90.082629 3543.39081 133.22429
#> [17,] 1308.54437 1.000000 1.00000 1.000000 1.00000 1.00000
#> [18,] 1183.00033 126.722442 138.12295 1.000000 1.00000 1.00000
#> [19,] 54.89027 1.000000 1.00000 171.978315 2262.07506 1.00000
#> [20,] 411.34090 1.000000 536.78878 1.000000 1.00000 1.00000
#> [21,] 1.00000 16.478230 161.46120 1.000000 1.00000 67.69105
#> [22,] 1494.53639 16.361410 1.00000 1.000000 1.00000 1.00000
#> [23,] 1060.93700 1.000000 1.00000 152.328115 1680.11498 1.00000
#> [24,] 779.74638 1.000000 1.00000 1.000000 1.00000 1.00000
#> [25,] 1.00000 165.544982 103.45589 1.000000 175.55384 1.00000
#> [26,] 777.62731 1.000000 1.00000 347.606122 1.00000 138.22463
#> [27,] 565.98047 1.000000 155.15291 1.000000 1010.80248 1.00000
#> [28,] 1.00000 1.000000 1.00000 1.000000 17.72438 187.35002
#> [29,] 228.47398 1.000000 1.00000 32.736665 3122.06860 64.26759
#> [30,] 1.00000 1.000000 1.00000 1.000000 1364.95376 58.45803
#> [31,] 1.00000 120.198508 574.78753 53.526953 1.00000 1.00000
#> [32,] 796.11332 1.000000 100.35824 1.000000 1239.80143 315.18394
#> [33,] 216.24369 95.847576 69.58651 51.149474 76.47723 1.00000
#> [34,] 365.81695 45.995045 1.00000 1.000000 821.34736 1.00000
#> [35,] 1.00000 1.000000 199.07164 1.000000 1.00000 1.00000
#> [36,] 544.72275 114.168966 1.00000 1.000000 1.00000 1.00000
#> [37,] 58.10979 1.000000 1.00000 1.000000 1443.73127 1.00000
#> [38,] 1.00000 1.000000 277.08083 141.818912 538.93923 1.00000
#> [39,] 749.38225 1.000000 1.00000 172.397298 1.00000 109.99913
#> [40,] 1.00000 1.000000 1.00000 1.000000 3859.75540 162.86135
#> [41,] 1.00000 102.666061 534.01340 1.000000 561.40915 1.00000
#> [42,] 760.43696 1.000000 1.00000 1.000000 1.00000 130.04901
#> [43,] 1.00000 8.930577 172.82803 7.558633 1.00000 229.78510
#> [44,] 151.00134 26.193270 306.92326 10.579157 1.00000 1.00000
#> [45,] 1.00000 1.000000 1.00000 31.663417 1515.88706 1.00000
#> [46,] 63.69395 102.470566 134.04977 1.000000 1.00000 104.98964
#> [47,] 1.00000 131.899237 132.49391 1.000000 1145.81057 29.53101
#> [48,] 956.45163 49.656709 313.97560 130.686468 1.00000 88.53350
#> [49,] 369.96333 1.000000 146.06190 1.000000 1415.61365 226.61678
#> [50,] 176.40350 1.000000 1.00000 33.083878 1.00000 62.44786
#> y z indicator
#> [1,] 100.000000 100.00000 100.000000
#> [2,] 59.228365 42.89649 18.434784
#> [3,] 41.230376 153.09207 14.593365
#> [4,] 36.710466 1.00000 7.030356
#> [5,] 122.784230 1.00000 13.449395
#> [6,] 1.000000 1.00000 8.085288
#> [7,] 1.000000 162.70082 6.706895
#> [8,] 56.284614 1.00000 5.384031
#> [9,] 1.000000 125.92040 10.927643
#> [10,] 7.036714 1.00000 6.618135
#> [11,] 70.483644 1.00000 6.922303
#> [12,] 71.626332 67.16126 6.900736
#> [13,] 1.000000 1.00000 9.254198
#> [14,] 1.000000 99.99237 8.342027
#> [15,] 6.998053 63.82710 8.984141
#> [16,] 101.076020 1.00000 15.079417
#> [17,] 40.507747 90.58142 8.378396
#> [18,] 136.256136 227.14503 19.490218
#> [19,] 1.000000 1.00000 6.211307
#> [20,] 107.033018 1.00000 11.895386
#> [21,] 83.959422 77.84705 6.330338
#> [22,] 58.199365 265.97442 8.679146
#> [23,] 39.431416 1.00000 8.705079
#> [24,] 1.000000 1.00000 9.699392
#> [25,] 1.000000 1.00000 4.393866
#> [26,] 21.811849 1.00000 15.012011
#> [27,] 4.648553 1.00000 6.033059
#> [28,] 89.685588 93.60815 3.937974
#> [29,] 1.000000 46.84329 11.003278
#> [30,] 1.000000 230.36703 4.861715
#> [31,] 1.000000 98.24635 7.490526
#> [32,] 1.000000 1.00000 9.594441
#> [33,] 1.000000 38.77631 11.887064
#> [34,] 1.000000 28.57198 14.172596
#> [35,] 1.000000 15.01343 3.437549
#> [36,] 1.000000 248.57982 9.733159
#> [37,] 1.000000 1.00000 8.415488
#> [38,] 1.000000 192.53611 6.202011
#> [39,] 1.000000 27.81953 13.540560
#> [40,] 1.000000 58.49652 7.363468
#> [41,] 62.137014 29.15650 6.858212
#> [42,] 168.606683 1.00000 8.816510
#> [43,] 1.000000 77.63637 10.537778
#> [44,] 141.978039 104.45120 15.475271
#> [45,] 7.894082 202.69464 10.250864
#> [46,] 10.985259 107.46570 11.875874
#> [47,] 30.885701 155.54817 12.770525
#> [48,] 1.000000 1.00000 10.406502
#> [49,] 1.000000 115.10932 14.701704
#> [50,] 86.378872 1.00000 15.526217
# Now, I have 'messed up' the data a bit by including two species with data missing at the beginning and one species with data missing at the end. We also have one species with some very high values.
trends_summary[1:3, 'a'] <- NA
trends_summary[1:5, 'b'] <- NA
trends_summary[2:4, 'c'] <- 1000
trends_summary[45:50, 'd'] <- NA
# Let's run this data again through our scaling function (all defaults used)
rescale_species(Data = trends_summary)
#> year a b c d e
#> [1,] -0.56047565 NA NA 100.000000 100.000000 100.00000
#> [2,] -0.23017749 NA NA 10000.000000 59.687411 149.59320
#> [3,] 1.55870831 NA NA 10000.000000 1.000000 91.56406
#> [4,] 0.07050839 7.942748 NA 10000.000000 24.703998 1.00000
#> [5,] 0.12928774 1.000000 NA 1.000000 1.000000 1.00000
#> [6,] 1.71506499 8.800908 6.896343 1.000000 1.000000 23.57946
#> [7,] 0.46091621 1.000000 120.214163 71.469058 1.000000 1.00000
#> [8,] -1.26506123 3.392833 255.458150 1.000000 1.000000 1.00000
#> [9,] -0.68685285 1.000000 58.234619 124.022497 75.081849 30.25533
#> [10,] -0.44566197 1.253227 1.000000 1.000000 1.000000 408.11775
#> [11,] 1.22408180 2.203256 88.118817 133.637115 5.423171 138.74157
#> [12,] 0.35981383 1.000000 1.000000 1.000000 11.082694 130.42245
#> [13,] 0.40077145 1.000000 247.791193 1.000000 56.051941 1.00000
#> [14,] 0.11068272 1.000000 8.509743 411.435839 1.000000 1.00000
#> [15,] -0.55584113 1.000000 1.000000 1.000000 1.000000 1.00000
#> [16,] 1.78691314 1.761543 1.000000 37.858688 76.209253 1.00000
#> [17,] 0.49785048 2.601207 1.000000 80.809735 1.000000 35.44993
#> [18,] -1.96661716 1.000000 98.129058 1.000000 1.000000 467.65548
#> [19,] 0.70135590 5.352423 130.138763 65.613375 1.000000 103.50822
#> [20,] -0.47279141 11.897763 156.853209 46.838432 1.000000 1.00000
#> [21,] -1.06782371 1.000000 1.000000 1.000000 1.000000 1.00000
#> [22,] -0.21797491 1.000000 145.113032 8.288665 28.105462 1.00000
#> [23,] -1.02600445 5.836851 75.132649 1.000000 50.474937 1.00000
#> [24,] -0.72889123 1.000000 39.222491 270.197656 32.180509 371.47595
#> [25,] -0.62503927 1.000000 1.000000 1.000000 1.000000 1.00000
#> [26,] -1.68669331 5.951952 99.851147 1.000000 2.717376 118.89079
#> [27,] 0.83778704 1.000000 1.000000 4.797072 1.000000 1.00000
#> [28,] 0.15337312 1.000000 1.000000 39.414173 1.000000 1.00000
#> [29,] -1.13813694 1.052203 147.315749 55.414746 40.233142 1.00000
#> [30,] 1.25381492 1.000000 10.921382 1.000000 1.000000 1.00000
#> [31,] 0.42646422 1.000000 1.000000 1.000000 88.925085 443.94631
#> [32,] -0.29507148 2.235993 1.000000 160.355831 1.000000 1.00000
#> [33,] 0.89512566 1.000000 1.000000 1.000000 9.757041 1.00000
#> [34,] 0.87813349 3.739670 64.708643 1.000000 1.000000 70.72673
#> [35,] 0.82158108 1.000000 314.470621 1.000000 1.000000 1.00000
#> [36,] 0.68864025 1.925512 1.000000 1.000000 1.000000 1.00000
#> [37,] 0.55391765 6.365557 223.708273 140.899524 1.000000 1.00000
#> [38,] -0.06191171 2.525596 1.000000 10.757028 19.054959 1.00000
#> [39,] -0.30596266 1.000000 1.000000 95.723829 14.749082 58.31968
#> [40,] -0.38047100 6.667159 221.143355 1.000000 1.000000 1.00000
#> [41,] -0.69470698 5.765846 1.000000 27.222894 1.000000 1.00000
#> [42,] -0.20791728 3.182648 40.157564 1.000000 1.000000 1.00000
#> [43,] -1.26539635 1.385491 240.785983 12.006965 68.039550 1.00000
#> [44,] 2.16895597 1.000000 231.983013 1.000000 1.000000 153.74430
#> [45,] 1.20796200 7.896610 245.287596 1.000000 1.000000 1.00000
#> [46,] -1.12310858 1.000000 81.312422 253.537501 1.000000 1.00000
#> [47,] -0.40288484 12.694290 223.879122 76.257357 1.000000 1.00000
#> [48,] -0.46665535 8.894578 1.000000 1.000000 1.000000 359.66250
#> [49,] 0.77996512 1.000000 1.000000 1.000000 1.000000 1.00000
#> [50,] -0.08336907 1.000000 197.118627 1.000000 1.000000 1.00000
#> f g h i j k
#> [1,] 100.000000 100.000000 100.00000 100.000000 100.00000 100.000000
#> [2,] 105.235539 1.000000 1588.79102 73.170241 165.09560 1.000000
#> [3,] 131.219707 1.000000 862.94537 30.431225 1.00000 131.460036
#> [4,] 147.154810 11.492001 39.21032 49.998409 1.00000 29.568406
#> [5,] 61.120491 1.000000 1.00000 64.120065 250.73675 195.515102
#> [6,] 1.000000 32.898684 2243.93131 1.000000 15.80804 1.000000
#> [7,] 281.612373 40.537237 475.49370 77.619916 148.85504 1.000000
#> [8,] 1.000000 1.000000 1.00000 1.000000 344.03982 1.000000
#> [9,] 1.000000 1.000000 732.51539 16.122515 1.00000 1.000000
#> [10,] 1.000000 253.359815 1.00000 1.000000 13.16043 1.000000
#> [11,] 1.000000 1.000000 1.00000 60.959419 16.17718 1.000000
#> [12,] 1.000000 64.160566 1.00000 1.000000 1.00000 68.495617
#> [13,] 241.418981 26.973578 1.00000 36.248806 1.00000 1.000000
#> [14,] 84.098326 100.958680 166.82341 1.000000 1.00000 175.644867
#> [15,] 49.220594 80.562091 562.39655 1.000000 102.41621 1.000000
#> [16,] 1.000000 1.000000 3593.38227 84.592319 122.08141 11.963385
#> [17,] 14.774203 37.259995 126.35406 51.796616 21.89805 63.082804
#> [18,] 175.975166 1.000000 1.00000 120.543863 1.00000 69.444004
#> [19,] 1.000000 84.430639 1.00000 4.554937 172.73512 1.000000
#> [20,] 1.000000 1.000000 754.90539 78.649392 30.62154 9.409586
#> [21,] 1.000000 238.119081 1.00000 138.102336 1.00000 113.771964
#> [22,] 1.000000 1.000000 1.00000 1.000000 17.98993 1.000000
#> [23,] 187.177758 1.000000 1.00000 1.000000 116.03738 1.000000
#> [24,] 1.000000 81.322766 1.00000 1.000000 45.84623 37.921731
#> [25,] 73.109834 50.262178 976.76061 1.000000 1.00000 1.000000
#> [26,] 1.000000 1.000000 612.23898 10.604045 1.00000 162.149026
#> [27,] 8.503687 1.000000 1.00000 119.707926 1.00000 79.684044
#> [28,] 1.000000 14.234857 1.00000 1.000000 1.00000 8.541412
#> [29,] 1.000000 1.000000 1.00000 26.076905 1.00000 1.000000
#> [30,] 1.000000 1.000000 1955.66136 1.000000 92.78344 3.089134
#> [31,] 1.000000 3.404237 259.00913 1.429717 1.00000 1.000000
#> [32,] 166.158269 18.742952 1.00000 21.955897 84.12354 1.000000
#> [33,] 100.889524 17.215387 1.00000 92.856021 236.01635 1.000000
#> [34,] 1.000000 1.000000 1367.17059 8.481416 1.00000 59.019475
#> [35,] 1.000000 46.912309 1.00000 49.835092 1.00000 1.000000
#> [36,] 286.926982 135.827323 1464.76205 54.450416 1.00000 1.000000
#> [37,] 190.709871 44.951916 1.00000 63.952165 1.00000 45.144267
#> [38,] 28.071752 1.000000 1.00000 1.000000 1.00000 1.000000
#> [39,] 1.000000 1.000000 3024.88868 113.735917 101.10723 69.000885
#> [40,] 14.244581 34.100788 1.00000 1.000000 33.60081 1.000000
#> [41,] 1.000000 1.000000 1687.20998 1.000000 45.39813 1.000000
#> [42,] 1.000000 1.000000 1.00000 98.157716 77.87097 55.032034
#> [43,] 1.000000 87.123185 1.00000 90.469924 1.00000 99.483443
#> [44,] 1.000000 1.000000 271.75183 1.000000 198.93300 1.000000
#> [45,] 7.267735 1.000000 877.03762 1.000000 1.00000 59.666673
#> [46,] 245.124993 148.175844 1.00000 1.000000 1.00000 1.000000
#> [47,] 1.000000 1.000000 1.00000 12.713010 199.14215 1.000000
#> [48,] 79.951947 83.327970 1.00000 11.524091 1.00000 1.000000
#> [49,] 136.178989 1.000000 2790.16865 25.455403 1.00000 139.800564
#> [50,] 25.153191 1.000000 2224.67078 38.601567 92.57719 220.132741
#> l m n o p q r
#> [1,] 100.00000 100.000000 100.000000 100.00000 100.00000 100.00000 100.000000
#> [2,] 1.00000 1.000000 211.535564 1.00000 1.00000 1.00000 78.030058
#> [3,] 1.00000 1.000000 95.176658 33.24628 240.03429 180.77792 1.000000
#> [4,] 1.00000 74.842445 1.000000 13.90755 323.60093 1.00000 1.000000
#> [5,] 73.59184 1.000000 187.403686 1.00000 77.54349 412.76810 1.000000
#> [6,] 1.00000 42.722325 1.000000 1.00000 40.44665 1.00000 61.587491
#> [7,] 1.00000 1.000000 1.000000 65.83557 1.00000 1.00000 1.000000
#> [8,] 1.00000 1.000000 124.167989 1.00000 606.65644 1.00000 4.789239
#> [9,] 1.00000 1.000000 1.000000 1.00000 77.55500 26.09230 1.000000
#> [10,] 1.00000 1.000000 1.000000 1.00000 1.00000 288.76321 1.000000
#> [11,] 1.00000 1.000000 1.000000 35.08710 1.00000 162.05986 1.000000
#> [12,] 1.00000 1.000000 29.228604 40.07044 1.00000 25.33642 116.879227
#> [13,] 157.12944 1.000000 12.858327 40.07772 1.00000 1.00000 1.000000
#> [14,] 1.00000 1.464792 11.907698 1.00000 57.90168 1.00000 175.520404
#> [15,] 100.08685 116.019894 1.000000 23.96872 77.71131 1.00000 1.000000
#> [16,] 1.00000 1.000000 1.000000 62.91213 230.57681 454.05911 1.000000
#> [17,] 1.00000 1.000000 1.000000 82.97930 1.00000 1.00000 1.000000
#> [18,] 1.00000 8.013669 39.458014 1.00000 340.90530 201.15958 189.835159
#> [19,] 1.00000 1.000000 1.000000 1.00000 1.00000 1.00000 1.000000
#> [20,] 144.00293 1.000000 1.000000 96.71143 1.00000 296.29871 1.000000
#> [21,] 1.00000 26.720721 143.043938 1.00000 1.00000 1.00000 40.825370
#> [22,] 29.64494 15.171247 237.333035 1.00000 208.34458 25.54358 20.919788
#> [23,] 78.81067 1.000000 1.000000 29.73564 1.00000 1.00000 3.602871
#> [24,] 16.59108 28.383926 210.006921 1.00000 221.68253 160.69161 1.000000
#> [25,] 1.00000 1.000000 1.000000 18.17618 1.00000 263.89217 1.000000
#> [26,] 87.63083 101.196948 1.000000 122.06365 1.00000 346.93834 1.000000
#> [27,] 15.88325 57.771318 1.000000 1.00000 1.00000 141.85434 9.415862
#> [28,] 1.00000 68.493797 1.000000 1.00000 1.00000 327.82737 1.000000
#> [29,] 1.00000 44.035163 100.636442 30.86989 1.00000 221.67816 1.000000
#> [30,] 194.29177 35.764913 1.000000 1.00000 1.00000 1.00000 1.000000
#> [31,] 1.00000 1.000000 1.000000 52.87210 295.92241 84.84171 1.000000
#> [32,] 1.00000 1.000000 1.000000 58.78950 1.00000 1.00000 132.356214
#> [33,] 49.65114 37.522918 266.904682 1.00000 221.58203 1.00000 1.000000
#> [34,] 28.88517 51.423088 1.000000 1.00000 425.64173 217.15003 21.824579
#> [35,] 1.00000 53.736721 7.697676 1.00000 1.00000 96.26811 1.089210
#> [36,] 1.00000 21.387037 1.000000 1.00000 79.67785 81.34161 56.740913
#> [37,] 1.00000 12.330590 1.000000 51.83079 1.00000 1.00000 67.725673
#> [38,] 106.08783 1.000000 13.277058 1.00000 1.00000 1.00000 71.074210
#> [39,] 59.22875 16.575912 10.335241 1.00000 15.77813 1.00000 21.151910
#> [40,] 1.00000 107.221265 1.000000 1.00000 83.94636 70.30390 1.000000
#> [41,] 1.00000 4.716743 1.000000 25.63619 1.00000 1.00000 1.000000
#> [42,] 25.23870 1.000000 1.000000 1.00000 753.57410 99.95981 35.496508
#> [43,] 14.65098 1.000000 1.000000 57.63986 1.00000 1.00000 166.245232
#> [44,] 58.63171 40.699577 1.000000 21.66949 18.03159 325.20659 83.282874
#> [45,] 1.00000 79.843837 1.000000 1.00000 182.38065 81.91679 45.138954
#> [46,] 83.73778 1.000000 303.567028 53.22491 1.00000 1.00000 1.000000
#> [47,] 1.00000 8.378723 1.000000 25.24425 1.00000 42.87034 65.338528
#> [48,] 1.00000 5.027135 66.281812 1.00000 293.39167 1.00000 1.000000
#> [49,] 68.97636 1.000000 1.000000 15.02278 453.44396 66.00916 26.847819
#> [50,] 92.17508 83.262086 1.000000 42.08923 1.00000 43.31262 119.704911
#> s t u v w x
#> [1,] 100.00000 100.000000 100.00000 100.000000 100.00000 100.00000
#> [2,] 711.71250 104.434261 1.00000 87.404945 1681.30668 1.00000
#> [3,] 1.00000 1.805610 141.95652 1.000000 1.00000 137.37591
#> [4,] 1.00000 13.273278 1.00000 1.000000 1.00000 1.00000
#> [5,] 1.00000 256.009845 349.36340 17.497700 1.00000 101.67617
#> [6,] 1148.12267 1.000000 176.41659 1.000000 1.00000 176.92369
#> [7,] 1.00000 1.000000 1.00000 1.000000 581.96007 1.00000
#> [8,] 1.00000 1.000000 16.45974 9.162817 1.00000 178.75210
#> [9,] 1006.01074 1.000000 216.13074 1.000000 2081.06116 1.00000
#> [10,] 1.00000 44.884503 168.27794 17.601283 1467.23929 47.48784
#> [11,] 1.00000 1.000000 447.12740 1.000000 1.00000 32.56231
#> [12,] 1.00000 1.000000 1.00000 104.494822 584.72491 1.00000
#> [13,] 1.00000 122.385356 336.75944 264.684516 115.78081 43.25286
#> [14,] 1.00000 1.000000 312.74606 1.000000 202.24790 1.00000
#> [15,] 1.00000 21.213817 1.00000 115.466522 1141.84048 1.00000
#> [16,] 1.00000 1.000000 1.00000 90.082629 3543.39081 133.22429
#> [17,] 1308.54437 1.000000 1.00000 1.000000 1.00000 1.00000
#> [18,] 1183.00033 126.722442 138.12295 1.000000 1.00000 1.00000
#> [19,] 54.89027 1.000000 1.00000 171.978315 2262.07506 1.00000
#> [20,] 411.34090 1.000000 536.78878 1.000000 1.00000 1.00000
#> [21,] 1.00000 16.478230 161.46120 1.000000 1.00000 67.69105
#> [22,] 1494.53639 16.361410 1.00000 1.000000 1.00000 1.00000
#> [23,] 1060.93700 1.000000 1.00000 152.328115 1680.11498 1.00000
#> [24,] 779.74638 1.000000 1.00000 1.000000 1.00000 1.00000
#> [25,] 1.00000 165.544982 103.45589 1.000000 175.55384 1.00000
#> [26,] 777.62731 1.000000 1.00000 347.606122 1.00000 138.22463
#> [27,] 565.98047 1.000000 155.15291 1.000000 1010.80248 1.00000
#> [28,] 1.00000 1.000000 1.00000 1.000000 17.72438 187.35002
#> [29,] 228.47398 1.000000 1.00000 32.736665 3122.06860 64.26759
#> [30,] 1.00000 1.000000 1.00000 1.000000 1364.95376 58.45803
#> [31,] 1.00000 120.198508 574.78753 53.526953 1.00000 1.00000
#> [32,] 796.11332 1.000000 100.35824 1.000000 1239.80143 315.18394
#> [33,] 216.24369 95.847576 69.58651 51.149474 76.47723 1.00000
#> [34,] 365.81695 45.995045 1.00000 1.000000 821.34736 1.00000
#> [35,] 1.00000 1.000000 199.07164 1.000000 1.00000 1.00000
#> [36,] 544.72275 114.168966 1.00000 1.000000 1.00000 1.00000
#> [37,] 58.10979 1.000000 1.00000 1.000000 1443.73127 1.00000
#> [38,] 1.00000 1.000000 277.08083 141.818912 538.93923 1.00000
#> [39,] 749.38225 1.000000 1.00000 172.397298 1.00000 109.99913
#> [40,] 1.00000 1.000000 1.00000 1.000000 3859.75540 162.86135
#> [41,] 1.00000 102.666061 534.01340 1.000000 561.40915 1.00000
#> [42,] 760.43696 1.000000 1.00000 1.000000 1.00000 130.04901
#> [43,] 1.00000 8.930577 172.82803 7.558633 1.00000 229.78510
#> [44,] 151.00134 26.193270 306.92326 10.579157 1.00000 1.00000
#> [45,] 1.00000 1.000000 1.00000 31.663417 1515.88706 1.00000
#> [46,] 63.69395 102.470566 134.04977 1.000000 1.00000 104.98964
#> [47,] 1.00000 131.899237 132.49391 1.000000 1145.81057 29.53101
#> [48,] 956.45163 49.656709 313.97560 130.686468 1.00000 88.53350
#> [49,] 369.96333 1.000000 146.06190 1.000000 1415.61365 226.61678
#> [50,] 176.40350 1.000000 1.00000 33.083878 1.00000 62.44786
#> y z indicator
#> [1,] 100.000000 100.00000 100.000000
#> [2,] 59.228365 42.89649 28.502036
#> [3,] 41.230376 153.09207 19.766610
#> [4,] 36.710466 1.00000 7.942748
#> [5,] 122.784230 1.00000 12.267967
#> [6,] 1.000000 1.00000 6.896343
#> [7,] 1.000000 162.70082 6.728697
#> [8,] 56.284614 1.00000 4.592307
#> [9,] 1.000000 125.92040 9.439848
#> [10,] 7.036714 1.00000 5.626644
#> [11,] 70.483644 1.00000 5.904375
#> [12,] 71.626332 67.16126 6.900736
#> [13,] 1.000000 1.00000 9.284280
#> [14,] 1.000000 99.99237 8.369144
#> [15,] 6.998053 63.82710 8.984141
#> [16,] 101.076020 1.00000 12.820306
#> [17,] 40.507747 90.58142 7.123193
#> [18,] 136.256136 227.14503 17.395310
#> [19,] 1.000000 1.00000 5.297931
#> [20,] 107.033018 1.00000 10.146164
#> [21,] 83.959422 77.84705 6.330338
#> [22,] 58.199365 265.97442 8.707359
#> [23,] 39.431416 1.00000 7.424993
#> [24,] 1.000000 1.00000 9.730921
#> [25,] 1.000000 1.00000 4.393866
#> [26,] 21.811849 1.00000 12.804487
#> [27,] 4.648553 1.00000 6.033059
#> [28,] 89.685588 93.60815 3.937974
#> [29,] 1.000000 46.84329 9.385240
#> [30,] 1.000000 230.36703 4.877519
#> [31,] 1.000000 98.24635 7.257362
#> [32,] 1.000000 1.00000 8.157058
#> [33,] 1.000000 38.77631 11.887064
#> [34,] 1.000000 28.57198 12.088508
#> [35,] 1.000000 15.01343 3.448723
#> [36,] 1.000000 248.57982 8.274994
#> [37,] 1.000000 1.00000 7.177986
#> [38,] 1.000000 192.53611 5.272862
#> [39,] 1.000000 27.81953 13.540560
#> [40,] 1.000000 58.49652 6.280666
#> [41,] 62.137014 29.15650 5.830755
#> [42,] 168.606683 1.00000 7.520038
#> [43,] 1.000000 77.63637 8.988192
#> [44,] 141.978039 104.45120 15.525576
#> [45,] 7.894082 202.69464 8.743469
#> [46,] 10.985259 107.46570 10.036238
#> [47,] 30.885701 155.54817 10.892613
#> [48,] 1.000000 1.00000 8.847461
#> [49,] 1.000000 115.10932 14.701704
#> [50,] 86.378872 1.00000 13.828788