基于空间自相关，R语言克里金插值
library(gstat)
Warning message:
In scan(file = file, what = what, sep = sep, quote = quote, dec = dec, :
EOF within quoted string
library(sp)
data(meuse)
head(meuse)
x y cadmium copper lead zinc elev dist om ffreq soil lime landuse
1 181072 333611 11.7 85 299 1022 7.909 0.00135803 13.6 1 1 1 Ah
2 181025 333558 8.6 81 277 1141 6.983 0.01222430 14.0 1 1 1 Ah
3 181165 333537 6.5 68 199 640 7.800 0.10302900 13.0 1 1 1 Ah
4 181298 333484 2.6 81 116 257 7.655 0.19009400 8.0 1 2 0 Ga
5 181307 333330 2.8 48 117 269 7.480 0.27709000 8.7 1 2 0 Ah
6 181390 333260 3.0 61 137 281 7.791 0.36406700 7.8 1 2 0 Ga
dist.m
1 50
2 30
3 150
4 270
5 380
6 470
数据框转空间数据
coordinates(meuse) <- c("x","y")#定义坐标
class(meuse)
[1] "SpatialPointsDataFrame"
attr(,"package")
[1] "sp"
spplot(meuse,"cadmium")
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" alt="" />
In strsplit(code, "\n", fixed = TRUE) :
input string 1 is invalid in this locale
v
np dist gamma dir.hor dir.ver id
1 57 79.29244 0.6650872 0 0 var1
2 299 163.97367 0.8584648 0 0 var1
3 419 267.36483 1.0064382 0 0 var1
4 457 372.73542 1.1567136 0 0 var1
5 547 478.47670 1.3064732 0 0 var1
6 533 585.34058 1.5135658 0 0 var1
7 574 693.14526 1.6040086 0 0 var1
8 564 796.18365 1.7096998 0 0 var1
9 589 903.14650 1.7706890 0 0 var1
10 543 1011.29177 1.9875659 0 0 var1
11 500 1117.86235 1.8259154 0 0 var1
12 477 1221.32810 1.8852099 0 0 var1
13 452 1329.16407 1.9145967 0 0 var1
14 457 1437.25620 1.8505336 0 0 var1
15 415 1543.20248 1.8523791 0 0 var1
np点对数量，dist距离，gamma两点协方差
半变异函数画图
plot(v,plot.number = T)
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" alt="" />
设置半变异计算时点对距离
v <- variogram(log(meuse$cadmium) ~ 1,meuse, width = 100)
plot(v, plot.number = T)
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Huv/46sUIe8SKnQnteszb0/s/jR6EQL3IqFK8xePe6TwZcpNQB24F4UVqhqTKzKv/ud+Z5UVLWePdbe5LCTJM1VXX69D/iRU6cHoYs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oUs4oWs28RbAeWUjTfr73J7bPdN5d5s4lUkut3EmxPbfVPEmxPbfVPEmxPbfVPEmxPbfVPEmxPbfVPzjBe4A+KFLOKFLOKFLOKFLOKFLOKFLOKFLOKFrDXGu3uqqoe3w/tL9fn7IbzM3+5Lv7VC2243u8wf+RrjbTf2pd6Yf8LL7O235i98vNEC2+42u8wf+RrjrZ/N2/3XV7NX8C/33qafaqo/uq0cb7TAtrvNLvRHvsJ43/96NS8714J/ufdG/dS/b2ZLxxstsO1uswv9ka8w3v3XX6tPr2rxur96uXhDsUX+yFcY7+6X18P+z+9KAVjC8Rb6I19hvIZYAJZwvEaBzV5vvDoHPV74O5c6YBvFywHbh7Wfuz3Y729C002O/fuWmyqzm13oj3yF8R6ays6R77fDl/mz8Y43WmHb7WaX+SNfY7xYCOKFLOKFLOKFLOKFLOKFLOKFLOKFLOKFLOKFLOKFLOKFLOKFLOKFLOKFLOKFLOItof30ut9+G/z42/lfi2TEW0IX7/CHo5CRDfGWQLw3Qby5NVX16b9+2GDWl6u++VXmavO+Kfk/W/uO+ZXVxr8+33uzFRFvZvXn74e2cvHunrpG2+qbDdncL9t0e+T9tnvT+H/322f7unui3usRb16210Pt4m39PbLmfbvKhvlZ06t5x77anzSv7ezvAp4h4s3LRehnG9zynv2YtzXDBfuD7o3LPIyPw49wBeLNqxnGa1ZRjr2apQv+9zSI9xd3UNcVbRHv1Yg3r9Ge16oH49/d07k9LxIQb14uyWYQb/dOHP+2g2FDP+Zln5uIeDMzcwdhtsHuVO1e+NnvdKvnGK/9le8vG/tq9s/33nI9xJvbcJ7XjGdtmtXDm/n4qx9DxFFwnOdlsiEB8UIW8UIW8UIW8UIW8UIW8UIW8UIW8UIW8UIW8UIW8UIW8UIW8UIW8UIW8UIW8ULW/wFP10FLsp8RnAAAAABJRU5ErkJggg==" alt="" />
半变异函数值越大协方差越小。Nugget表示不确定性，Sill最大gamma值，Range半变异gamma不再增加的点。 PSill= sill - nugget. 球形曲线、高斯曲线
经验半变异函数对象
m1 <- vgm(psill = 1.5,
model = "Sph",#Sph球形曲线
range = 1400,
nugget = 0.5)
Warning messages:
1: In scan(file = file, what = what, sep = sep, quote = quote, dec = dec, :
EOF within quoted string
2: In strsplit(code, "\n", fixed = TRUE) :
input string 1 is invalid in this locale
m2 <- fit.variogram(v,m1)#拟合半变异函数"
plot(v,model = m2)
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" alt="" />
拟合计算出的模型参数
m2
model psill range
1 Nug 0.5855785 0.000
2 Sph 1.3253037 1224.936
开始空间插值
数据准备
data(meuse.grid)
data(meuse)
head(meuse.grid)
x y part.a part.b dist soil ffreq
1 181180 333740 1 0 0.0000000 1 1
2 181140 333700 1 0 0.0000000 1 1
3 181180 333700 1 0 0.0122243 1 1
4 181220 333700 1 0 0.0434678 1 1
5 181100 333660 1 0 0.0000000 1 1
6 181140 333660 1 0 0.0122243 1 1
普通克里金插值
kr <- krige(log(meuse$cadmium) ~ 1,
loc = ~ x+y, #位置信息
data = meuse,
newdata = meuse.grid,
model = m2)
[using ordinary kriging]
head(kr)
x y var1.pred var1.var
1 181180 333740 1.831241 1.1606001
2 181140 333700 1.905750 1.0508440
3 181180 333700 1.834357 1.0788180
4 181220 333700 1.760312 1.1129144
5 181100 333660 1.985888 0.9396745
6 181140 333660 1.909244 0.9662369
var1.var 估计值的方差，越大越不可靠。
显示插值结果图
In strsplit(code, "\n", fixed = TRUE) :
input string 1 is invalid in this locale
levelplot(var1.pred ~ x + y,kr )
aaarticlea/png;base64,iVBORw0KGgoAAAANSUhEUgAAArwAAAGwCAMAAAB8TkaXAAAAk1BMVEUAAAAAADoAAGYAOpAAZrY6AAA6ADo6AGY6OgA6OpA6ZmY6kLY6kNtmAABmADpmAGZmZmZmtv+A//+QOgCQOjqQ2/+R//+h//+z//+2ZgC2/7a2///C///U///bkDrbtrbb/9vb///m///1////gP//kf//of//s///tmb/wv//1P//25D/5v//9f///7b//9v///9QM0KDAAAACXBIWXMAAA7DAAAOwwHHb6hkAAAUp0lEQVR4nO3dD3vT1hWAcQGlg47AspCmGdRdytZ6pHH8/T/dLOs61rWPdP9L91jv++yZoE6OhfLDyLItNVsipTVzrwBRbOAltYGX1AZeUht4SW3gJbWBl9QGXlIbeElt4CW1gZfUBl5SG3hJbeAltYGX1AZeUht4SW3gJbWBl9QGXlIbeElt4CW1gZfUBl5SG3hJbeAltYGX1AZeUht4SW3gJbWBl9QGXlIbeElt4CW1gZfUBl5SG3hJbeAltU2FN//9MLHSidM9HoKXibUPnP2eFGx0JlY6cPZ7UrDRmVjpwNnvScFGZ2KFAx/fNs318ZdvHord00gKNjoT6xu4ubrerl/d7n+9/qHkPY2lYKMzsb6B691D7fNN99B7/6HkPZ3X0KKL03HyZe2j767nz7dnA7JBFVev6HQq292+hAEuvP8UOyW86nZ0Nx/fNa9sv+CloebCa3/V6vWX/fLxx9vt5tOXgPmJgVdld/1+6YqZkwPvqv9ou/loPfSCl86qCO/hcbcLvOSqHrztvoJpvWP8+H7C47zgVdbdebPivd8/d7veHyZbNY31MAxesqoNb9L8xMCrLPBONZ3y9XPXMN4YwuClKQLvxNMpX+CdeDrlaFCtzbbra5fnaPBS2cA7y3TKEXhnmU5JSV4H1R7YgpdqCLxzTqekwDvndIprWO3Ibq7Vr12uOwIv5Q68FUynuKrB+7MYeGm4KK+WWvDSTIG3gukUF3grmE6heR4JG/EqNHx34KV8gTcg8NYVeAMCbyWN7OXGePU0DF7KEHjDA28lgTc88FaSxDbM6++uhHsFL2UIvOGBt5LAGx54Z29YbQJUT8LgpaTAGxt4Zw+8sYF39gS22aSCl4qmHG/vOmzPN5zidGHpxtu/Dtv9D+3/AuYnBt7Z0423dx229pT+j3/jgiqLyHk0d1jgN1eehl145c/RnV7KylyHrYXLNSkWkl68J19mrsMG3gV1KXhfrsMG3uXk69UpNb4ceF+uwwbeBXUZeI/XYeMJ24K6CLy967BxqGxBWV4LCi2Kt38dts0VL1IspYvA6xiQuInmnE5jgTcx8M6RtbNr4X1KzZdttyLgpdDAmyXwzhF4swTeSZNeTcuL15dytz7gJe/AK7VumvZVOnth3hxsL2KmU6bAK9S+zrF+/cVeHF7xsBcR0ylXFlvrBTSJ3l9deSVb61MF3jbznojjwrzWbC9ip1OOwDuQeVflcWHe5WMvYqdTjsAr9vh2/860/mIUb3P6dngqmvCZdgnvX66SCVtr1YwzmO6Rd909HTsueOStqErxjq9084vYFPu84K0o8I7GE7aaEw6SReFNICysVRV4232Fx/cP9oJDZRUF3uFWzf4VCHth3hxsL2KmU3LgzR94S2d9Rnj4RTXL5ncr8M4yncBbMPCWDrzFAm/pwvB+F0re9R1eOfDSWOAtFnhLB95igbd0nnifLMOegZeKBt5igbd04C0WeItl3j/oxBvzCpsvXtc6gpfEwAtetYEXvGpz4vX9GBB4Z5m+6BaD9+Vd4u0l2bpPUHrOTwy8xVoK3s3V4Z2264nfLg7eAnVXK5sA7zBhzzV14f0qZn3Xqvnp8MjbnmA6aH5i4C3QxePtf+L4t4fDbsPz59NPSIJXXxeP1/6qA97Nx3fNK9sveNXlxCt8DEh6uc3TcC1427OMbT5xNSDdLRRvG9dh0x54PecnBt6cWddGz4bXRThGrSkr3sMZF/znJwbenC0Yb3uYzJxxwX9+YuDN2TLxxs9PDLx5ktiCF7wqAm/M/MTAmyfwxsxPDLyJ/SxkqS2JN4FtF3gXHXgT5icG3sTAmzA/MfBG9899zp1d8BYLvNGBN3l+YuCNDrzJ8xMDb3jDu7kSW+vHbrPNhDfhjwLepQXeXPMTA294C8L7qxh4Nea7g3uuVtzbjcebvLNrAu9yAi941QZe8Ooryqug1sL7TSgMb/KfC7wLCLzgVRt4waui4R1bp1f5Z93zGrOzC955pqsMvMebwass8B5vBm/NSa+W9dk692k9oY6wjcGb648PXs2Bd/Rm8NYceEdvBu/83Z03smcrsI3xKh0JC/MqsQXvVNNrCbwDgbf+wDsQeCvJKTAsYf/W9901UUT91GZj2wXeSgJveFnwvpyf9/mGs0RGBt7wcuA9Xsrq/of2fwHzE7sIvJ70nMk/qrOG1WaGOj9e+Uif9V3HS1m1Z0XvnyXdPT8x8IJ35GYPvMdLWbVLTusfGnhji8Tbvw5b72pA4A1p2GuYQAmi/HPzYusLMagiGzDDIy94IwNvYuCdL/AmlhUvT9g8c3l1apPodUrMb4a/ejKvyvByqMwz8GYpH972UlabK16k8Am8WcqCN35+YlrxWl6dRGOOUFlf5qn2e0zzsO0C7xyBN0vgnSPwZqkOvOumeXX7snh82zTXL+/ysRcx0yvK2sG1vIbZHOY2TNjp9X/DJXguuDWrwPv442170W2z2Fxdb9c7xObQhb2ImF5T4M1ZFXjbzIsbu8X6zcPucfbaHDS2F7HTawm8OasG72pH9rjYPfqal+vsxcvYk3dXaMnazTU7oX4oA/N0P+I1WXL5rdmMM5gK7+Pbdmf3sNgbHsUbNr2ewJuzah55193TsW6x2v0/eMHrqBq8x33end39MYcLxmvt5lo/8ShNEbLMHf3pWcz9ld+aNeJd7R99L/IJG3hzVgXedl/h8f2DWbRHzNou8VAZeHPmwiu94vPtW+5H3lWzfwWiW9zvn0BeH97lYy9ipldRd4zs9/7errT36avJj9mwWvvu/jgvgfBk27QOvLGBF7wjN4M3U+DNH3gnynpRzXqtS8ArYBILkmzneUeeU8EbHnjBO3IzeDMF3vyBd6KG8fYx/RmGN0abdBf/7ec5VfobMfE2Be9EgTd/4J0o8OYPvBPVf2ntm/XS2rApCVgMXilBbRjhOdWawDtR4M0feCcKvPkDb+mG38Jr74QKeIdpDTvzVOt7D+AtFnjBO3IzeFMDb7GmxLu5as7ekZuWOrzWJ3gtvH8IJbO1D2RZd5T8F2NWtl3TPvKumqb5ELOaXtPrDLzFmny3Iatf8IJ35GYPvL0TMbUnaupOvDAyv+V7/qGIqBTh7Tac9cmfBLzSVw+ztW5ZEF7pnCtPT9Z39T5dtnZ+ymy9/4TP841NPDbwgnfkZjfe/ud67892CKz5u2ds5oF5neehF7zgHbl5AG/vLDu9Myo8fz49scLJ0YZXZ7enBV7wjtzsfuTt4d18fNec+OQ4r+fH1jzVSmyH1ZbEO/d23WbG255xYfOJqwFZgbdYWfG2cR22k8BbrLxP2LbgPWapld5INjVe37tYEN7eoTJzvqaA+YmBF7wjN3vgNSdiag+Trc5efgAveIuVAW/K/MQU4bVOvDu8KzosS1DrxPtn2F144p17w74E3mKBt3TgLRZ4SwfeAgkfc3+aCq+Uc/Z/9oE3bH5i4AXvyM3gjQi80wTeAgkfc/fFG8Y2JukehrO+de7tehp4CwTeaQJvgcA7TeDN2df+yfutY2TWO3Ls19mE/dIyxav9o7KdXRN4cwbeSXPh/UsMvHLgnTTw5umXfRJeaZ+3PN4gqG68c29eOfDmCbwzBN48gXeGwJvYL/0MXuehsqrxWnNqe1HNCryJgXe+wJsYeOcLvNHd7RvGK30M6K++4TC8w2+1SZc8/K1zbmBn4I0OvHMH3ujAO3fgDe+u3wR4E9jGV/XOrgm84YG3ksAbHngrCbwh3Z1ns70EvArUmsAbEnirCrwhgbeqwBuSc29XwGt9iDgK71RZf0km3rJRgTck8FYVeEMCb1VlwNu7Dlvvl37zE5sM789dLry/9rPxWp8Jqgbvn0JTbdP0XHi/i1nf1bsOW++XfvMTAy94R2524+2d1v/kDP8e8xMDL3hHbh7AK1+H7eTaKh7zE5sMb9DObhRe3yNhYV8dxnYheHtfAl7wzhR4vQJvjYHXK88X1SS2nq+wReFNIKxarYknbF6Bt8bqOFS2bvbXLDaL7iH8cNDYXgStfb7AW2MZ8Pauw2Z+6T+/q71m8fr1F7Nox+wHdn8T7EXQ2mfoTmDrVPutn3WGQglvGOFktoJacxWW4hszdxnwpsw/9nLh+NvtqvnJ7DzvHoHtRez06MBbcdXgXb15OCx+e2iZmmd/9iJ2enTgrbhK8D6+3e/smsXWibfpv0ySuTsh6ejY8P6toHbkpCOeeCV0yXj/p5RtVzPOYLpH3nW3s9wtZn3kBa+WKnnktfZ5wQter+rFO+UTNsmroNZ++40nW+u9pGF4Ja/gPVYF3nZf4fH9g1lszXHeCQ+VgVdlVeDdrpr98WGzMHjNQWN7ETPdHXhVVgfe2NKnO7167uYOe3WyFfD6FuPVZgve+PmJgRe8IzcLm3kXeMFbQYvFKxGVvLpeRxv2Kv+jFYLXU3eCWrM++X4ikwZe8II3bn5i4AXvyM2Lwvv1vF8FttZurlvqoNeoPPEOe7XY5vtRzBF4was28IJXbQvEKxCV8tzNLSJUcmb9p+Ed4BG1wl+p3D+QaQMveNUGXvCqbUl4w7wKr6ZJ5yktytaV02uXoPZ792co9HOZKPCCV23gBa/aFoHXE6qU9PabKLyeznI17FWq6A+pXOAFL3jj5icG3qHAeyl4PaGKbF14PaGOlMumJ9cnoaI/pHKBF7zgjZufGHjBO3KzJ97eCUgf3zZNd94xj/mJOacnq50AryfhKKnDXpeAV97SZ9/VO6vC2jq7AnjBW6w8ePvns2nP0+s9PzHwgnfkZj+8vTOJPX+u4poU6V4FtU9F8MawjYL6bbCiP6RyReI9ObNkD+/m4ztzbn6f+YmBF7wjNwc/8rbn5t98ejkxE3jBW6x0vKum+eHkBKT9s0BnX2Nr9YT/liBVYmvhtZgk43WqlfC6vA4LdVb0R1Wi/E/YtuAF7zRlP1R2PE+pz/zEwAvekZs98fYuZ/VynlKf+YlZ0xOghuG1MIXh9fXqUuv0GvMnLvqjKlEmvLHzEwMveEduBi94q+2C8CZAHVYbhTe57zFshT9K1J5/0Z9Y1sALXvDGzU8MvOAduVkF3oJsLSs23pJeY9SOSA1KD2Hwghe8cfMTAy94R25eBl5pN7c8XsmroNbJ1qLnPLNK2Keni/74UgMveMEbNz8x8IJ35Gb5Qh0XgHfYqy/eBMK+bPt4BbW/W3g7lJ5nfA+UXPSnGB14wQveuPmJgRe8IzdfIF5Ptp54wwzHqB3e2f29r/brMF5PyeoIgxe84I2bnxh4wTty83LxPglZtMIID7MV8D452Q7iHdlayYaL/iwjAi94wRs3PzHwgnfk5gXildR64o3KtbM78qJaru0YtgOc616TAy94wRs3PzHw5gm8MfMTa8LYxuMVgKXjlYa61JpKblTwes5PDLwFAq/n/MTAWyDwes5PbIF4i27P88BbLPCWDrzFAm/pwFusIu/n9cWbIDlIranohnSlE+9/xYTvejm3dO+SbO75iYF3oi4b7+bqILZ3STb3/MTAO1EXjXfV/GQeeU/O8A9e8BYrE97fHg5gT66tMgnebpuWxOtr2OVZ+jrhfipiW3OReE+uw7Y97vOCF7xTlf0JWxTedbO/8KBZmKd84kJce/Aus3S87XXYtml42wsPrl9/MYvDUz5xIa69cCwywfAI3gjC7obZ+my7JZf9kTf2CdvL1V9vzQRxIa89eJdZ/uO8kYfKVm8ezMI8dosLee3Bu8zy4m2vw2YuyeY3/+W73+4vtr1f+OBtrKeM0muYQYYDd30zsZYmoDagphGOHPRu9sY7NN/3C9ed+HbXN8cjL3gXULZH3rj5x477vOAFr18V4g1/wtaVTDju8FmM60G17OyGVAVec7HtwzW3gw+VdYF3aVWB93CxbbMwT/nExch08C6tOvDG5ok3jPIw4RHJCcZhGxt4was28IJXbQvE60fYV7Jvw15RGxt4was2F97/iIEXvBV0QXhNYYaDJOejDNscgRe8agMveNV2eXi7YggHSk6WXnTTLCHwgldt4AWv2i4VrynBcBHQpqIbZTmBF7xqAy941XbheK1ySY7SXWgLLDrwgldt4AWv2paE1zQV4dx/WDoNvOBVG3jBq7YF4hVK8JppDSgi8LaBV2XgbQOvypTjpUUXp8OfVyLP+e6HiZVOnIoUeJkI3hnuh4mVTgQvE9VOBC8T1U4ELxPVTgQvE9VOvDy8RNkDL6kNvKQ28JLawEtqAy+pDbykNvCS2sBLatOCt72u8Xr/VuUP28e3zZuH7fb5Zn/NTXuRNHG3aJcpE9sZr24HVi7HxIzraH6XuI4zpgTv5sps0fXrL5urD9uV37WPAyeuuwEpEzdX19vVbul/febAiRnX0WyDtHWcMx14V81P3RXl2+3ePlwMXXw+aeL2/sP+v6RMHFu5HBMzrqP5Xdo6zpoOvL89mA262v2Laba9uEia+Pz55d/S6InPN9fb9ZuHjOtoT8y4juZ3aes4azrwmr2z/Wbv/tVrrlM3+vnEzcd37b5g2sTdPmOuv2DSxIzraH4H3uJ11Mz/v23+fpMJrzXxx9vt5tOXpIn73efXXzLiPZmYbx234J2oDtnq8FQi16OaNVEcHDhxTG2OiRnXcWyNAybOmC683bOV7repTzTOJ7aLsydbgRNzPmGTJmZcx+3LrjNP2Mpm9tV2O6jdcYHkw1DCxPXun9LH9w9JE59vPuQ7VCZMzLmOZhtwqKx0+81s/j1b7w/T73bdmu5gZX+RNHHVpE80LwCIK5djYsZ1PGyDtHWcMS14ic4CL6kNvKQ28JLawEtqAy+pDbykNvCS2sBLagMvqQ28pDbwktrAS2oDL6kNvKQ28JLawEtqAy+pDbykNvCWavW6O0MCFQu8pdp/Rrc7MQ2VCbzFWr/+l5azdygNvOW6b7ScAEFp4C3XurmeexUuO/AW6/nmH2pO36Ez8BZr9ebfNxxsKBl4S9We9HfNQ2/JwFuq+/1lT3jKVjDwktrAS2oDL6kNvKQ28JLawEtqAy+pDbykNvCS2sBLagMvqQ28pDbwktrAS2oDL6kNvKS2/wOxzk+Cwzl3igAAAABJRU5ErkJggg==" alt="" />
地理探测器，基于异质性，R语言插值
thead>tr>th {
border: none;
border-bottom: 2px solid #dddddd;
}
.kable-table table>thead {
background-color: #fff;
}
-->