Geospatial Analytics for Social Good

1. OVERVIEW

The main aim of this project is to use the water point related data from rural areas at the water point or small water scheme level available from the WPdx Data Repository to explore the applicable geospatial analysis tools in water resources management for Nigeria.

1.1 Problem Statement

To address the issue of providing clean and sustainable water supply to the rural community.

1.2 Objectives

Apply appropriate global and local measures of spatial Association techniques to reveals the spatial patterns of Not Functional water points.

1.3 Scope of Works

Below are the list of tasks to be completed :

• Import the shapefile into R and save it in a simple feature data frame format with appropriate sf method.

  note : Nigeria (NGA) has 3 Projected Coordinate Systems, EPSG: 26391, 26392, and 26303.

• Derive the proportion of functional and non-functional water point at LGA level with appropriate tidyr and dplyr methods,

• Combine the geospatial and aspatial data frame into simple feature data frame.

• Performe outliers / clusters analysis by using appropriate local measures of spatial association methods.

• Perform hotspot areas analysis by using appropriate local measures of spatial association methods.

• Plot 2 main types of maps below :

  1. Thematic Mapping

     Plot maps to show the spatial distribution of functional and non-functional water point rate at LGA level by using appropriate thematic mapping technique provided by tmap package.

  2. Analytical Mapping

     Plot hotspot areas and outliers / clusters maps of functional and non-functional water point rate at LGA level by using appropriate thematic mapping technique provided by tmap package.

2. R PACKAGE REQUIRED

Following are the packages require for this exercise :

• pacman package : to install and load the following R packages into R environment.

• sf package :

  • st_read( ) = import and save the shapefiles into simple feature data table.
  • st_geometry( ) = get geometry from an sf object.
  • st_centroid( ) - takes a polygon or multipolygon and returns the geometric center of the bounding box of the polygon or multipolygon as a point.

• tidyverse package :

  • dplyr:

    • filter( ) - extract water point records of Nigeria.
    • glimpse( ) - list all columns in a data frame.
    • mutate( ) - edit variables’ values.

  • readr :

    • write_rds( ) - save the extracted sf data table into an output file in rds data format.

  • stringr :

    • str_replace( ) - replace some characters with some other characters in a string.

• tmap package :

  • qtm( ) - to plot quick thematic map.

  • tm_shape( ) - specify the shape object.

• spdep package :

  • poly2nb( ) - compute contiguity weight matrices for the study area.

  • nb2listw( ) - supplements a neighbours list with spatial weights for the chosen coding scheme.

  • moran.test( ) - for spatial autocorrelation using a spatial weights matrix in weights list form.

  • moran.mc( ) - for permutation test with Moran’s I statistic.

  • geary.test( ) - for spatial autocorrelation using a spatial weights matrix in weights list form.

  • geary.mc( ) - for permutation test with Geary’s C statistic.

  • sp.correlogram( ) - spatial correlograms for Moran’s I and the autocorrelation coefficient.

  • localmoran( ) - to calculate local spatial statistics for each zone based on the spatial weights object used.

  • moran.plot( ) - plot of spatial data against its spatially lagged values.

  • knearneigh ( ) - return matrix with the indices of points belonging to the set of the k nearest neighbours of each other.

  • knn2nb( ) - convert knn object to a neighbours list of class nb.

  • nbdist( ) - return the length of neighbour relationship edges.

  • dnearneigh( ) - derive distance-based weight matrices.

  • localG( ) - calculate local spatial statistic G for each zone based on the spatial weights object used.

• funModeling package :

  • freq( ) = retrieves the frequency and percentage for input.

• janitor package :

  • get_dupes( ) = search duplicated records during data wrangling.

2.1 Load R Packages into R Environment

Use the code chunk below.

Show the code

pacman::p_load(sf, tidyverse, tmap, spdep, funModeling, janitor, maps)

3. GEOSPATIAL DATA

3.1 Acquire Data Source

• Aspatial Data

  1. Download the Nigeria data set in shapefile format via Access WPdx+ Global Data Repository from WPdx Global Data Repositories.
  2. Rename the title of the data set to “geo_export”.

• Geospatial Data

  1. Download the Nigeria geoBoundaries data set at ADM2 level from geoBoundaries.org or the Humanitarian Data Exchange portal.
  2. Rename the title of the data set to “nga_admbnda_adm2_osgof_20190417”

3.2 Import Aspatial Data - Water Point Shapefile

Use the code chunk below.

Note :

• st_read( ) to import geo_export data set.

• #| eval: false to display the code chunks without the output.

Show the code

wp <- st_read(dsn = "/jephOstan/ISSS624/class_project/project_1/data/geodata",
              layer = "geo_export",
              crs = 4326) %>%
  filter(clean_coun == "Nigeria")

3.2.1 Review Imported Aspatial Shapefile

-- retrieve geometry list-column

Use the code chunk below.

Note :

st_geometry( ) to get the geometry summary of a class data.frame or sf object.

Show the code

st_geometry(wp)

-- identify associated attribute

Use the code chunk below.

Note :

glimpse( ) to swtich columns to rows, features to columns.

Show the code

glimpse(wp)

Avoid performing transformation 
if going to use st_intersects() 
in geoprocessing stage. This is 
because st_intersects() only 
works correctly if the geospatial 
data are in geographic coordinate 
system (i.e. wgs84)

3.2.2 Write “wp” in RDS Format

Use the code chunk below.

Notes :

• write_rds( ) to save the extracted sf data table, i.e. “wp” into an output file in rds data format.

The output file is called “wp_nga.rds” and it is saved in geodata sub-folder.”

Show the code

write_rds(wp, "/jephOstan/ISSS624/class_project/project_1/data/geodata/wp_nga.rds")

3.3 Import Geospatial Data - Nigeria LGA Boundary Data

Use the code chunk below.

Notes :

• st_read( ) to import geo_export data set.

Show the code

nga <- st_read(dsn = "/jephOstan/ISSS624/class_project/project_1/data/geodata",
               layer = "nga_admbnda_adm2_osgof_20190417",
               crs = 4326)

3.3.1 Review Imported Geospatial Shapefile

-- retrieve geometry list-column

Use the code chunk below.

Note :

st_geometry( ) to get the geometry summary of a class data.frame or sf object.

Show the code

st_geometry(nga)

-- identify associated attribute

Use the code chunk below.

Note :

glimpse( ) to swtich columns to rows, features to columns.

Show the code

glimpse(nga)

3.4 Data Wrangling and Exploratory Data Analysis (EDA)

3.4.1 Recode NA Values into String

Use the code chunk below.

Note :

glimpse( ) to recode all the NA values in status_cle field into Unknown.

Show the code

wp_nga <- read_rds("/jephOstan/ISSS624/class_project/project_1/data/geodata/wp_nga.rds") %>%
  mutate(status_cle = replace_na(status_cle, "Unknown"))

3.4.2 Search Duplicate Rows

Use the code chunk below.

Note :

get_dupes( ) to review rows that have duplicates. Specify the data.frame and the variable combination to search for duplicates and get back the duplicated rows.

Assumption :

For the same value of clean_adm2, each observation has unique pair of lat_deg and lon_deg.

Show the code

duplicates <- wp_nga %>% 
                janitor::get_dupes(clean_adm2,lat_deg,lon_deg)

duplicates

3.4.3 Exploratory Data Analysis

Before proceed to analysis stage, sense the data with EDA.

Use the code chunk below.

Note :

freq( ) to display the distribution of status_cle field in wp_nga.

Show the code

freq(data=wp_nga, 
     input = 'status_cle')

Remarks :

During the first round of EDA, noticed there are 2 values of “Non-functional due to dry season”.

Use mutate( ) with str_replace to combine both values, thereafter update the dataset.

Show the code

wp_nga <- wp_nga %>%
  mutate(status_cle = str_replace(status_cle,"Non functional due to dry season"  ,"Non-Functional due to dry season"))

3.4.4 Explore Variables and Values for “Non-Functional”

Use the code chunk below.

Note :

filter( ) to get the data tables based on values associated with “Non-Functional” under “status_clean” variable.

-- retrieve based on “Non-Functional”

Show the code

wp_nfc <- filter(wp_nga, status_cle == "Non-Functional")
wp_nfc

-- retrieve based on “Non-Functional due to dry season”

Show the code

wp_nfcD <- filter(wp_nga, status_cle == "Non-Functional due to dry season")
wp_nfcD

According to the variables’ definition from the waterpointdata.org :

• usage_cap (usage_capacity) = recommended maximum users per water point :

  • 1,000 people per mechanised well
  • 500 people per hand pump / undefined shallow well (all hand pumps)
  • 400 people per open hand well (rope & bucket)
  • 250 people per tap (tapstand, kiosk, rainwater catchment)

• local_popu (local_population_1km) = number of people living within a 1km radius of the water point.

• served_pop (water_point_population) = number of people currently or potentially served by a specific water point.

  • For non-functional water points, this number represents users who would gain access if the point was functional.

• pressure (pressure_score) = the pressure score ( 0 - 100% ) is calculated based on the ratio of the number of people assigned to that water point over the theoretical maximum population which can be served based on the technology.

  • If a point is serving less than the recommended maximum, the pressure score will be less than 100% (i.e., 250/500 = 0.5).
  • If serving more than the recommended maximum, the pressure score will be over 100% (i.e. 750/500 = 150%).

• crucialness (crucialness_score) = the crucialness score ( 0 - 100% ) is the ratio is likely current users to the total local population within a 1km radius of the water point.

  • For non-functional water points, the crucialness score shows how important the water point would be if it were to be rehabilitated.

3.4.5 Plot Preliminary Visualisation for Non-Functional Water Points

Show the code

plot(wp_nfc["crucialnes"])

Remarks :

1. Visually, noticeable of clusters.
   • This suggests new installation or more resources required to upgrade or rehabilitate the existing facility in order to support population for those light.

3.4.6 Plot Preliminary Visualisation for Non-Functional due to Dry Season Water Points

Show the code

plot(wp_nfcD["crucialnes"])

3.4.7 Plot Preliminary Visualisation for Distribution of Urban & Non-Urban

Show the code

plot(wp_nga["is_urban"])

3.5 Water Point Data Extraction

3.5.1 Extract Non-functional Water Point

Use the code chunk below.

Note :

filter( ) to get water points that associated to the variation of “Non-Functional”.

Show the code

wpt_nonfunctional <- wp_nga %>%
  filter(status_cle %in%
           c("Abandoned/Decommissioned", 
             "Abandoned",
             "Non-Functional",
             "Non-Functional due to dry season"))

Show the code

freq(data=wpt_nonfunctional, 
     input = 'status_cle')

3.5.2 Extract Functional Water Point

Use the code chunk below.

Note :

filter( ) to get water points that associated to the variation of “Functional”.

Show the code

wpt_functional <- wp_nga %>%
  filter(status_cle %in%
           c("Functional", 
             "Functional but not in use",
             "Functional but needs repair"))

Show the code

freq(data=wpt_functional, 
     input = 'status_cle')

3.5.3 Extract Unknown Water Point

Use the code chunk below.

Note :

filter( ) to get water points that associated to the variation of “Unknown”.

Show the code

wpt_unknown <- wp_nga %>%
  filter(status_cle == "Unknown")

3.5.4 Perform Point-In-Polygon Count

Use the code chunk below.

Show the code

nga_wp <- nga %>% 
  mutate(`total_wpt` = lengths(
    st_intersects(nga, wp_nga))) %>%
  mutate(`wpt_functional` = lengths(
    st_intersects(nga, wpt_functional))) %>%
  mutate(`wpt_nonFunctional` = lengths(
    st_intersects(nga, wpt_nonfunctional))) %>%
  mutate(`wpt_unknown` = lengths(
    st_intersects(nga, wpt_unknown)))

3.5.5 Add New Variables

Use the code chunk below.

Note :

mutate( ) to add “pct_functional” and “pct_non-functional”.

write_rds( ) to save the sf data table into rds format.

Show the code

nga_wp <- nga_wp %>%
  mutate(pct_functional = `wpt_functional`/`total_wpt`) %>%
  mutate(`pct_non-functional` = `wpt_nonFunctional`/`total_wpt`)

Show the code

write_rds(nga_wp, "/jephOstan/ISSS624/class_project/project_1/data/geodata/nga_wp.rds")

3.5.6 Spatial Distribution of Water Points Visualisation

Show the code

nga_wp <- read_rds("/jephOstan/ISSS624/class_project/project_1/data/geodata/nga_wp.rds")

Show the code

total <- qtm(nga_wp, "total_wpt") + 
  tm_layout(legend.height = 0.3, legend.width = 0.3)

wp_functional <- qtm(nga_wp, "wpt_functional") +
  tm_layout(legend.height = 0.3, legend.width = 0.3)

wp_nonfunctional <- qtm(nga_wp, "wpt_nonFunctional") + 
  tm_layout(legend.height = 0.3, legend.width = 0.3)

unknown <- qtm(nga_wp, "wpt_unknown") + tm_layout(legend.height = 0.3, legend.width = 0.3)

tmap_arrange(total, wp_functional, wp_nonfunctional, unknown, asp=1.5, ncol=2)

3.6 Exploratory Spatial Data Analysis

Determine autocorrelation for non-functional water points data.

3.6.1 Contiguity Weight Matrices (CWM)

Compute Contiguity Weight Matrices (CWM) first before compute the Global Spatial Autocorrelation statistics.

3.6.1.1 compute Contiguity Weight Matrices

Determine the adjacency with 2 methods, Queen and Rook methods and derive W_q and W_r from the methods respectively.

-- compute QUEEN contiguity based neighbours

Use the code chunk below.

Note :

poly2nb( ) to return a list of first order neighbours based on Queen criteria.

Show the code

nga_wpQ <- poly2nb(nga_wp, queen=TRUE)
summary(nga_wpQ)

-- compute ROOK contiguity based neighbours

Use the code chunk below.

Note :

poly2nb( ) to return a list of first order neighbours based on Queen criteria.

Show the code

nga_wpR <- poly2nb(nga_wp, queen = FALSE)
summary(nga_wpR)

-- Compare Queen and Rook Contiguity Matrices

	Wq	Wr
Number of regions without links	1 link (#86)	1 link (#86)
Number of regions with the most links	14 links (#508)	14 links (#508)
Number of regions with 1 link	#138, #560	#138, #560
Average number of links per region	5.736	5.711

Both methods have relatively similar performance, only have 1 region without links.

3.6.1.2 compute Distance-Based Neighbours

Identify neighbours of region points by Euclidean distance with a distance band.

-- compute “coords”

Use the code chunk below.

Note :

cbind( ) to combine both longitude and latitude

Show the code

longitude <- wp_nga$lon_deg
latitude <- wp_nga$lat_deg
coords <- cbind(longitude, latitude)
head(coords)

-- determine the upper limit for distance band

Use the code chunk below.

Note :

knn2nb( ) to convert knn objects that returned by knearneigh( ) into a neighbours list of class nb.

nbdist( ) to return the length of neighbour relationship edges.

unlist( ) to remove the list structure of the returned object.

Show the code

k3 <- knn2nb(knearneigh(coords,k = 3))
k3dists <- unlist(nbdists(k3, coords, longlat = TRUE))
summary(k3dists)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  13.86   34.82   42.98   45.71   56.00   94.18 

Show the code

upper_threshold3 <- unlist(nbdists(k3, coords, longlat = TRUE))

Remarks :

The largest first nearest neighbour distance is 39.085 km, using this as the upper threshold gives certainty that all units will have at least one neighbour.

Show the code

k5 <- knn2nb(knearneigh(coords,k = 5))
k5dists <- unlist(nbdists(k5, coords, longlat = TRUE))
summary(k5dists)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  13.86   39.06   50.48   54.58   65.14  147.41 

Show the code

upper_threshold5 <- unlist(nbdists(k5, coords, longlat = TRUE))

Show the code

k6 <- knn2nb(knearneigh(coords,k = 6))
k6dists <- unlist(nbdists(k6, coords, longlat = TRUE))
summary(k6dists)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  13.86   41.11   52.45   59.26   72.44  192.60 

Show the code

upper_threshold6 <- unlist(nbdists(k6, coords, longlat = TRUE))

Show the code

k8 <- knn2nb(knearneigh(coords,k = 8))
k8dists <- unlist(nbdists(k8, coords, longlat = TRUE))
summary(k8dists)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  13.86   44.66   58.06   69.16   84.49  267.15 

Show the code

upper_threshold8 <- unlist(nbdists(k8, coords, longlat = TRUE))

-- compute fixed distance weight matrix

Use the code chunk below.

Note :

dnearneigh( ) to derive distance-based weight matrices.

Show the code

wm_d39 <- dnearneigh(coords, 0, upper_threshold3, longlat = TRUE)
wm_d39

Show the code

wm_d40 <- dnearneigh(coords, 0, upper_threshold5, longlat = TRUE)
wm_d40

Show the code

wm_d43 <- dnearneigh(coords, 0, upper_threshold6, longlat = TRUE)
wm_d43

Show the code

wm_d45 <- dnearneigh(coords, 0, upper_threshold8, longlat = TRUE)
wm_d45

3.6.1.3 list all fixed distance weight matrix

Show the code

str(wm_d43)

-- plot Fixed Distance Weight Matrix

Show the code

plot(nga_wp$geometry, border="lightgrey")
plot(wm_d43, coords, add = TRUE)
plot(k1, coords, add = TRUE, col = "red", length = 0.08)

	Wd=3	Wd=5	Wd=6	Wd=8
Largest first nearest neighbour distance	39.08489	40.08029	42.28107	44.87575

3.6.1.4 compute Adaptive Distance Weight Matrix

Show the code

knn6 <- knn2nb(knearneigh(coords, k=6))
knn6

Neighbour list object:
Number of regions: 49 
Number of nonzero links: 294 
Percentage nonzero weights: 12.2449 
Average number of links: 6 
Non-symmetric neighbours list

-- plot Adaptive Distance Weight Matrix

Show the code

plot(nga_wp$geometry, border="lightgrey")
plot(knn6, coords, pch = 5, cex = 0.3, add = TRUE, col = "red")

3.6.2 Global Spatial Autocorrelation (GSA)

3.6.2.1 compute row-standardised weights matrix

Use the code chunk below.

Note :

nb2listw( ) to assign weights to each neighboring polygon. Each neighboring polygon will be assigned equal weight by explore with different input for style i.e. “W”, “B” and “C”.

Show the code

wm_q <- poly2nb(nga_wp, queen = TRUE)
wm_q

Neighbour list object:
Number of regions: 774 
Number of nonzero links: 4440 
Percentage nonzero weights: 0.7411414 
Average number of links: 5.736434 
1 region with no links:
86

Show the code

set.ZeroPolicyOption(TRUE)

[1] FALSE

Show the code

ngaWp_rswmQW <- nb2listw(wm_q, style = "W", zero.policy = TRUE)
ngaWp_rswmQW

Characteristics of weights list object:
Neighbour list object:
Number of regions: 774 
Number of nonzero links: 4440 
Percentage nonzero weights: 0.7411414 
Average number of links: 5.736434 
1 region with no links:
86

Weights style: W 
Weights constants summary:
    n     nn  S0       S1       S2
W 773 597529 773 285.0658 3198.414

Show the code

set.ZeroPolicyOption(TRUE)

[1] TRUE

Show the code

ngaWp_rswmQB <- nb2listw(wm_q, style = "B", zero.policy = TRUE)
ngaWp_rswmQB

Characteristics of weights list object:
Neighbour list object:
Number of regions: 774 
Number of nonzero links: 4440 
Percentage nonzero weights: 0.7411414 
Average number of links: 5.736434 
1 region with no links:
86

Weights style: B 
Weights constants summary:
    n     nn   S0   S1     S2
B 773 597529 4440 8880 112368

Show the code

set.ZeroPolicyOption(TRUE)

[1] TRUE

Show the code

ngaWp_rswmQC <- nb2listw(wm_q, style = "C", zero.policy = TRUE)
ngaWp_rswmQC

Characteristics of weights list object:
Neighbour list object:
Number of regions: 774 
Number of nonzero links: 4440 
Percentage nonzero weights: 0.7411414 
Average number of links: 5.736434 
1 region with no links:
86

Weights style: C 
Weights constants summary:
    n     nn  S0       S1      S2
C 773 597529 773 269.1572 3405.93

Regardless of which input for the style, all have the same result of 1 region without links while the average number of links is 5.736434.

3.6.2.2 GSA : Moran’s I method

Use the code chunk below.

Note :

moran.test( ) to calculates the Moran’s I Index value and both a a z-score and p-value to evaluate the significance of that Index.

moran.mc( ) to do a permutation test to evaluate the rank of the observed statistic in relation to the statistic of simulated values.

Show the code

moran.test(nga_wp$wpt_nonFunctional, listw = ngaWp_rswmQW, zero.policy = TRUE, na.action = na.omit)

    Moran I test under randomisation

data:  nga_wp$wpt_nonFunctional  
weights: ngaWp_rswmQW  n reduced by no-neighbour observations
  

Moran I statistic standard deviate = 20.043, p-value < 2.2e-16
alternative hypothesis: greater
sample estimates:
Moran I statistic       Expectation          Variance 
      0.433932927      -0.001295337       0.000471516 

Show the code

set.seed(1234)
bperm_m = moran.mc(nga_wp$wpt_nonFunctional,
                 listw = ngaWp_rswmQW,
                 nsim = 999,
                 zero.policy = TRUE,
                 na.action = na.omit)
bperm_m

    Monte-Carlo simulation of Moran I

data:  nga_wp$wpt_nonFunctional 
weights: ngaWp_rswmQW  
number of simulations + 1: 1000 

statistic = 0.43393, observed rank = 1000, p-value = 0.001
alternative hypothesis: greater

Remarks :

• The value for both actual and random Moran’s I almost the same, i.e. 0.43393, which means the non-functional water points are positively autocorrelated with the data spatially cluster.

• There is a statistical significant with p-value (2.2e-16) < 0.001, smaller than the alpha value to support the rejection of null hypothesis for the test i.e. the non-functional water points are not randomly spatial.

-- visualise Monte Carlo Moran’s I

Use the code chunk below.

Note :

hist( ) to examine the simulated Moran’s I test statistics by plotting the distribution of the statistical values as a histogram.

Show the code

hist(bperm_m$res, 
     freq=TRUE, 
     breaks=20, 
     xlab="Simulated Moran's I")
abline(v=0, 
       col="red") 

3.6.2.3 GSA : Geary’s C method

Show the code

geary.test(nga_wp$wpt_nonFunctional, listw=ngaWp_rswmQW)

    Geary C test under randomisation

data:  nga_wp$wpt_nonFunctional 
weights: ngaWp_rswmQW 

Geary C statistic standard deviate = 14.457, p-value < 2.2e-16
alternative hypothesis: Expectation greater than statistic
sample estimates:
Geary C statistic       Expectation          Variance 
     0.6170907765      1.0000000000      0.0007014859 

Show the code

set.seed(1234)
bperm_c = geary.mc(nga_wp$wpt_nonFunctional,
               listw = ngaWp_rswmQW, 
               nsim = 999)
bperm_c

    Monte-Carlo simulation of Geary C

data:  nga_wp$wpt_nonFunctional 
weights: ngaWp_rswmQW 
number of simulations + 1: 1000 

statistic = 0.61709, observed rank = 1, p-value = 0.001
alternative hypothesis: greater

Remarks :

• The value for both actual and random Geary’s C almost the same, i.e. 0.61709, which means the non-functional water points are positively autocorrelated with the data spatially cluster.

• There is a statistical significant with p-value (2.2e-16) < 0.001, smaller than the alpha value to support the rejection of null hypothesis for the test i.e. the non-functional water points are not randomly spatial.

• The Geary’s C value is greater than the Moran’s I value. However, since both values are less than 1, the observations tend to be clustered and similar.

3.7 Cluster and Outlier Analysis

Use Local Indicators for Spatial Association (LISA) method, especially local Moran’s I to detect cluster and / or outlier.

3.7.1 Compute Local Moran’s I

Use the code chunk below.

Show the code

fips <- order(nga_wp$shapeName)
localMI <- localmoran(nga_wp$wpt_nonFunctional, ngaWp_rswmQW)
head(localMI)

           Ii          E.Ii       Var.Ii        Z.Ii Pr(z != E(Ii))
1 -0.32365786 -9.995243e-04 1.924638e-01 -0.73547576     0.46204980
2  0.07000542 -4.092463e-05 1.053077e-02  0.68258288     0.49487045
3  1.25819985 -1.627684e-03 4.181728e-01  1.94819847     0.05139122
4 -0.03537489 -5.427505e-05 5.954304e-03 -0.45773361     0.64714384
5  0.01201533 -2.590965e-04 3.988998e-02  0.06145673     0.95099547
6  0.00768085 -1.538445e-07 1.687859e-05  1.86960486     0.06153871

3.7.1.1 list the local Moran matrix derived

Use the code chunk below.

Show the code

printCoefmat(data.frame(localMI[fips,], nga_wp$shapeName[fips]), check.names=FALSE)

             Ii        E.Ii      Var.Ii        Z.Ii Pr.z....E.Ii..
1   -3.2366e-01 -9.9952e-04  1.9246e-01 -7.3548e-01     4.6205e-01
2    7.0005e-02 -4.0925e-05  1.0531e-02  6.8258e-01     4.9487e-01
3    1.2582e+00 -1.6277e-03  4.1817e-01  1.9482e+00     5.1391e-02
4   -3.5375e-02 -5.4275e-05  5.9543e-03 -4.5773e-01     6.4714e-01
5    1.2015e-02 -2.5910e-04  3.9890e-02  6.1457e-02     9.5100e-01
6    7.6808e-03 -1.5384e-07  1.6879e-05  1.8696e+00     6.1539e-02
7    2.3716e-01 -6.6542e-04  8.5226e-02  8.1464e-01     4.1528e-01
8    1.3499e-01 -6.9507e-05  1.3396e-02  1.1669e+00     2.4326e-01
9    5.8469e-01 -3.9167e-04  6.0293e-02  2.3828e+00     1.7183e-02
10   1.9145e-01 -2.2881e-04  2.5098e-02  1.2099e+00     2.2630e-01
11   6.7485e-01 -7.6926e-04  8.4332e-02  2.3265e+00     1.9992e-02
12   1.3484e-01 -9.2780e-04  8.8869e-02  4.5543e-01     6.4880e-01
13   1.6286e-02 -4.0925e-05  6.3021e-03  2.0567e-01     8.3705e-01
14  -3.1655e-02 -2.9456e-05  2.8239e-03 -5.9514e-01     5.5175e-01
15  -3.1637e-01 -1.0254e-02  1.1135e+00 -2.9010e-01     7.7174e-01
16   6.8612e-02 -9.2780e-04  1.4275e-01  1.8406e-01     8.5397e-01
17   2.4270e-02 -1.9868e-05  5.1126e-03  3.3971e-01     7.3408e-01
18   5.8712e-01 -1.1792e-03  1.8138e-01  1.3814e+00     1.6717e-01
19  -8.6368e-03 -8.6620e-05  1.1101e-02 -8.1152e-02     9.3532e-01
20  -2.1125e-02 -1.8249e-05  2.8103e-03 -3.9815e-01     6.9052e-01
21  -6.1300e-02 -1.4475e-04  2.2288e-02 -4.0963e-01     6.8208e-01
22   2.8968e-01 -1.3297e-03  3.4172e-01  4.9782e-01     6.1861e-01
23   8.3857e-01 -1.1920e-03  1.8334e-01  1.9612e+00     4.9856e-02
24   1.5893e-03 -2.7477e-05  5.2960e-03  2.2217e-02     9.8228e-01
25   1.3175e-01 -8.6620e-05  9.5025e-03  1.3525e+00     1.7623e-01
26   8.0063e-01 -9.3914e-04  1.8085e-01  1.8849e+00     5.9446e-02
27   8.4077e-01 -1.6277e-03  2.5025e-01  1.6840e+00     9.2191e-02
28  -1.9940e-03 -1.2099e-02  1.3113e+00  8.8241e-03     9.9296e-01
29   3.0859e-01 -2.2324e-04  2.4486e-02  1.9735e+00     4.8442e-02
30   2.5468e-01 -3.1865e-04  3.0540e-02  1.4592e+00     1.4452e-01
31   9.3035e-03 -6.3380e-06  8.1230e-04  3.2665e-01     7.4393e-01
32   1.0902e+00 -1.5504e-03  3.9834e-01  1.7298e+00     8.3669e-02
33   8.0526e-02 -1.9868e-05  2.5464e-03  1.5962e+00     1.1045e-01
34   2.2617e-01 -2.7477e-05  3.0145e-03  4.1198e+00     3.7925e-05
35  -1.7370e-01 -3.5422e-04  3.8849e-02 -8.7950e-01     3.7913e-01
36   3.6215e+00 -1.7248e-02  1.6251e+00  2.8544e+00     4.3117e-03
37  -9.7994e-02 -6.9507e-05  4.8271e-03 -1.4094e+00     1.5870e-01
38   2.6132e+00 -5.7830e-03  6.3080e-01  3.2975e+00     9.7543e-04
39   1.8731e+00 -1.5753e-02  2.9886e+00  1.0926e+00     2.7457e-01
40   2.9695e+00 -3.9022e-03  7.4920e-01  3.4353e+00     5.9197e-04
41   4.0806e+00 -1.3638e-02  2.0716e+00  2.8446e+00     4.4471e-03
42   7.7463e-01 -8.2075e-03  1.5690e+00  6.2497e-01     5.3199e-01
43   7.5445e-01 -1.3297e-03  3.4172e-01  1.2929e+00     1.9605e-01
44  -9.4511e-02 -2.0041e-04  2.5680e-02 -5.8852e-01     5.5619e-01
45  -4.0892e-01 -1.0618e-03  2.7294e-01 -7.8067e-01     4.3500e-01
46   1.7264e-02 -1.8555e-06  3.5764e-04  9.1300e-01     3.6124e-01
47  -6.0666e-01 -4.4019e-03  6.7490e-01 -7.3309e-01     4.6350e-01
48   3.8136e-02 -1.0903e-05  2.1016e-03  8.3213e-01     4.0533e-01
49  -2.6481e-01 -9.2780e-04  1.0170e-01 -8.2749e-01     4.0796e-01
50  -3.6486e-01 -1.7389e-04  1.6668e-02 -2.8247e+00     4.7319e-03
51   6.4059e-01 -1.0618e-03  1.0169e-01  2.0122e+00     4.4203e-02
52   5.2295e-01 -6.1632e-04  7.8942e-02  1.8634e+00     6.2399e-02
53   5.1817e-01 -5.6910e-04  5.4530e-02  2.2214e+00     2.6324e-02
54   6.8852e-01 -7.1640e-04  7.8541e-02  2.4593e+00     1.3920e-02
55   7.4747e-01 -8.8063e-04  2.2641e-01  1.5727e+00     1.1578e-01
56   5.8669e-01 -1.6277e-03  2.5025e-01  1.1760e+00     2.3958e-01
57   9.1402e-01 -1.2599e-03  2.4254e-01  1.8585e+00     6.3096e-02
58   7.1930e-01 -1.3297e-03  1.4569e-01  1.8880e+00     5.9027e-02
59  -3.0961e-02 -5.2377e-04  8.0617e-02 -1.0720e-01     9.1463e-01
60   3.2899e-03 -3.3373e-07  3.6614e-05  5.4375e-01     5.8662e-01
61   7.1599e-02 -2.9126e-04  4.4841e-02  3.3949e-01     7.3424e-01
62   1.1170e+00 -1.6277e-03  2.0827e-01  2.4512e+00     1.4236e-02
63   5.9556e-01 -6.0715e-04  7.7767e-02  2.1378e+00     3.2531e-02
64  -7.0312e-02 -2.9456e-05  2.8239e-03 -1.3226e+00     1.8597e-01
65   4.0210e-02 -3.1865e-04  4.9056e-02  1.8298e-01     8.5481e-01
66   9.0458e-02 -1.1259e-03  1.4414e-01  2.4123e-01     8.0938e-01
67   6.6358e-02 -1.8555e-06  2.0357e-04  4.6511e+00     3.3019e-06
68   9.9615e-01 -1.1259e-03  4.3469e-01  1.5126e+00     1.3038e-01
69   9.5142e-01 -1.1259e-03  9.5720e-02  3.0788e+00     2.0782e-03
70   1.5763e+00 -2.3901e-03  3.6719e-01  2.6053e+00     9.1806e-03
71   1.3676e+00 -3.5471e-03  3.0082e-01  2.4999e+00     1.2422e-02
72   9.2471e-02 -1.4925e-04  1.4307e-02  7.7435e-01     4.3873e-01
73  -3.7128e-02 -8.3203e-05  1.0663e-02 -3.5875e-01     7.1978e-01
74  -3.1518e-02 -1.2649e-04  1.6210e-02 -2.4656e-01     8.0525e-01
75  -9.2317e-03 -1.9519e-04  2.1411e-02 -6.1757e-02     9.5076e-01
76  -3.8035e-02 -2.3951e-06  2.2963e-04 -2.5098e+00     1.2079e-02
77   7.1490e-01 -1.0618e-03  1.3594e-01  1.9419e+00     5.2155e-02
78   8.4336e-01 -1.6277e-03  1.7829e-01  2.0012e+00     4.5369e-02
79   7.2523e-01 -9.9952e-04  1.5377e-01  1.8520e+00     6.4030e-02
80   5.3888e-01 -4.8031e-04  7.3931e-02  1.9837e+00     4.7294e-02
81   3.4904e+00 -9.4838e-03  1.4466e+00  2.9099e+00     3.6157e-03
82   1.1262e+00 -3.3198e-03  8.5145e-01  1.2241e+00     2.2090e-01
83  -4.1318e-01 -3.9167e-04  7.5464e-02 -1.5026e+00     1.3293e-01
84  -1.6794e-01 -5.4275e-05  8.3578e-03 -1.8364e+00     6.6298e-02
85  -1.0457e-01 -3.8586e-05  4.2332e-03 -1.6066e+00     1.0814e-01
86   0.0000e+00  0.0000e+00  0.0000e+00         NaN            NaN
87   9.7051e-02 -1.4925e-04  1.9126e-02  7.0284e-01     4.8215e-01
88   1.3239e-01 -1.1259e-03  1.4414e-01  3.5167e-01     7.2509e-01
89   8.6819e-01 -5.3489e-03  5.8371e-01  1.1434e+00     2.5289e-01
90   2.8316e-01 -1.6128e-03  1.3704e-01  7.6927e-01     4.4173e-01
91   1.2582e+00 -1.6277e-03  3.1322e-01  2.2510e+00     2.4382e-02
92   1.5674e+00 -3.2090e-03  4.0996e-01  2.4530e+00     1.4167e-02
93   1.5345e-02 -2.7477e-05  3.5215e-03  2.5904e-01     7.9560e-01
94   6.5838e-03 -9.8783e-04  9.4613e-02  2.4616e-02     9.8036e-01
95   7.6830e-02 -6.6449e-05  8.5158e-03  8.3329e-01     4.0468e-01
96   1.0339e-01 -8.3203e-05  9.1276e-03  1.0831e+00     2.7876e-01
97   1.3652e-02 -1.0184e-04  1.5681e-02  1.0983e-01     9.1254e-01
98   1.1441e-01 -8.6620e-05  1.3338e-02  9.9137e-01     3.2151e-01
99   1.7511e+00 -5.0690e-03  7.7665e-01  1.9927e+00     4.6290e-02
100  2.3957e-01 -3.9905e-04  6.1428e-02  9.6821e-01     3.3294e-01
101 -3.3289e-02 -9.9952e-04  1.5377e-01 -8.2343e-02     9.3437e-01
102  1.3164e+00 -1.5358e-03  2.3615e-01  2.7122e+00     6.6840e-03
103  4.0316e-01 -6.6542e-04  6.3753e-02  1.5994e+00     1.0974e-01
104  1.8824e-01 -2.5316e-04  2.4265e-02  1.2100e+00     2.2626e-01
105 -1.4448e-01 -1.0184e-04  1.3051e-02 -1.2638e+00     2.0630e-01
106 -2.7746e-01 -1.2649e-04  4.8883e-02 -1.2544e+00     2.0971e-01
107  2.5014e+00 -3.3198e-03  6.3776e-01  3.1364e+00     1.7103e-03
108 -6.5757e-02 -1.2235e-04  1.5680e-02 -5.2416e-01     6.0017e-01
109 -1.5657e-01 -3.5422e-04  4.5383e-02 -7.3329e-01     4.6338e-01
110 -4.0714e-01 -7.5196e-03  9.5649e-01 -4.0861e-01     6.8283e-01
111 -5.2572e-04 -5.6910e-04  5.4530e-02  1.8579e-04     9.9985e-01
112  1.4369e+00 -5.3489e-03  4.0699e-01  2.2607e+00     2.3777e-02
113 -3.8910e-01 -6.1632e-04  7.8942e-02 -1.3827e+00     1.6677e-01
114  2.8350e-01 -3.9905e-04  5.1123e-02  1.2556e+00     2.0926e-01
115  1.1070e+00 -1.6277e-03  1.5580e-01  2.8086e+00     4.9757e-03
116 -3.9128e-03 -2.7477e-05  4.2313e-03 -5.9730e-02     9.5237e-01
117 -2.2763e-01 -2.2881e-04  5.8867e-02 -9.3725e-01     3.4863e-01
118  2.6518e+00 -7.0234e-03  1.0740e+00  2.5656e+00     1.0298e-02
119  5.0676e-01 -2.2324e-04  2.8605e-02  2.9976e+00     2.7211e-03
120  3.1906e-01 -8.3203e-05  1.6036e-02  2.5203e+00     1.1727e-02
121  6.1173e-01 -1.4014e-03  2.1550e-01  1.3208e+00     1.8658e-01
122  1.0868e+00 -1.6277e-03  2.0827e-01  2.3850e+00     1.7081e-02
123 -1.6043e-01 -2.5910e-04  2.2046e-02 -1.0787e+00     2.8070e-01
124  1.1122e+00 -1.7723e-03  2.2675e-01  2.3395e+00     1.9311e-02
125 -2.0497e-02 -1.4925e-04  1.9126e-02 -1.4713e-01     8.8303e-01
126  2.9959e-01 -6.1632e-04  2.3806e-01  6.1529e-01     5.3837e-01
127  4.5026e-03 -3.3373e-07  5.1394e-05  6.2812e-01     5.2993e-01
128 -3.1431e-02 -2.5910e-04  3.9890e-02 -1.5607e-01     8.7598e-01
129  2.0237e-01 -8.8063e-04  1.1277e-01  6.0526e-01     5.4501e-01
130  3.6342e-02 -1.2649e-04  1.3876e-02  3.0959e-01     7.5687e-01
131  8.8429e-01 -2.5835e-03  3.9683e-01  1.4079e+00     1.5917e-01
132  4.7994e-01 -5.2377e-04  5.0189e-02  2.1447e+00     3.1980e-02
133  5.0409e-01 -7.5901e-04  9.7204e-02  1.6193e+00     1.0539e-01
134  8.0259e-01 -1.4014e-03  2.6973e-01  1.5480e+00     1.2161e-01
135  3.2095e-01 -2.5316e-04  4.8784e-02  1.4543e+00     1.4587e-01
136 -5.6408e-01 -2.2881e-04  5.8867e-02 -2.3240e+00     2.0127e-02
137  1.0900e-01 -3.8586e-05  7.4371e-03  1.2644e+00     2.0609e-01
138  1.4615e-02 -2.3951e-06  1.8538e-03  3.3950e-01     7.3423e-01
139  5.5125e-02 -5.1577e-05  6.6100e-03  6.7866e-01     4.9735e-01
140  9.5921e-01 -1.0618e-03  2.7294e-01  1.8380e+00     6.6055e-02
141 -9.5427e-01 -1.3297e-03  1.2731e-01 -2.6707e+00     7.5682e-03
142 -1.5215e-01 -1.2235e-04  2.3581e-02 -9.8999e-01     3.2218e-01
143  1.0215e+00 -1.4014e-03  2.1550e-01  2.2035e+00     2.7561e-02
144  1.7310e-02 -1.8249e-05  2.3389e-03  3.5830e-01     7.2012e-01
145  5.8823e-01 -8.6966e-04  1.3381e-01  1.6104e+00     1.0730e-01
146  1.2015e+00 -1.6277e-03  1.5580e-01  3.0481e+00     2.3030e-03
147  1.9828e-01 -1.1259e-03  1.2339e-01  5.6767e-01     5.7026e-01
148  6.0353e-01 -5.2080e-03  9.9861e-01  6.0916e-01     5.4242e-01
149  2.5690e-02 -1.8555e-06  3.5764e-04  1.3585e+00     1.7430e-01
150  8.6937e-02 -1.2649e-04  1.3876e-02  7.3910e-01     4.5985e-01
151 -2.5042e-01 -2.9126e-04  3.7319e-02 -1.2948e+00     1.9539e-01
152  5.2452e-03 -1.0903e-05  1.1962e-03  1.5197e-01     8.7921e-01
153  2.4361e-01 -3.6124e-04  1.3957e-01  6.5305e-01     5.1372e-01
154  4.0067e-01 -8.1339e-04  2.0914e-01  8.7790e-01     3.8000e-01
155 -1.3898e-01 -4.3100e-04  5.5216e-02 -5.8963e-01     5.5544e-01
156  5.3574e-01 -1.0618e-03  1.3594e-01  1.4559e+00     1.4541e-01
157  8.9537e-01 -1.4749e-03  1.4120e-01  2.3867e+00     1.6999e-02
158  1.9339e-02 -8.1339e-04  1.5665e-01  5.0915e-02     9.5939e-01
159  7.6650e-01 -1.4014e-03  1.5353e-01  1.9598e+00     5.0021e-02
160  1.2582e+00 -1.6277e-03  2.0827e-01  2.7606e+00     5.7704e-03
161 -8.4890e-03 -1.0903e-05  1.3974e-03 -2.2680e-01     8.2058e-01
162 -6.3606e-02 -5.4275e-05  4.6190e-03 -9.3509e-01     3.4974e-01
163  1.1977e+00 -1.6128e-03  1.5437e-01  3.0525e+00     2.2691e-03
164  2.0702e+00 -5.2080e-03  5.6841e-01  2.7528e+00     5.9085e-03
165  5.5459e-01 -6.1632e-04  9.4853e-02  1.8027e+00     7.1432e-02
166 -2.2400e-01 -1.4749e-03  1.4120e-01 -5.9220e-01     5.5372e-01
167 -2.0141e-01 -2.0041e-04  2.1983e-02 -1.3571e+00     1.7476e-01
168 -6.0268e-02 -6.0715e-04  7.7767e-02 -2.1394e-01     8.3060e-01
169  1.3772e-01 -3.9905e-04  6.1428e-02  5.5729e-01     5.7733e-01
170 -8.3981e-03 -2.3951e-06  3.0697e-04 -4.7919e-01     6.3180e-01
171  3.9793e-01 -1.6916e-03  6.5269e-01  4.9464e-01     6.2085e-01
172  5.9514e-02 -6.6449e-05  1.7098e-02  4.5565e-01     6.4864e-01
173 -8.1927e-02 -6.3380e-06  5.3942e-04 -3.5272e+00     4.1996e-04
174  5.1947e+00 -7.3523e-03  1.1239e+00  4.9069e+00     9.2505e-07
175 -6.0047e-01 -3.2531e-04  6.2682e-02 -2.3971e+00     1.6526e-02
176  4.1374e-01 -3.2531e-04  5.0081e-02  1.8503e+00     6.4277e-02
177 -5.1956e-02 -1.4749e-03  2.2680e-01 -1.0600e-01     9.1558e-01
178 -5.0841e-02 -5.4275e-05  8.3578e-03 -5.5552e-01     5.7854e-01
179  1.4958e-01 -5.1577e-05  4.9446e-03  2.1279e+00     3.3345e-02
180  8.7695e-02 -2.0041e-04  5.1562e-02  3.8708e-01     6.9869e-01
181  2.6769e-01 -3.2531e-04  5.0081e-02  1.1976e+00     2.3106e-01
182  6.3460e-01 -7.8598e-03  8.5553e-01  6.9459e-01     4.8731e-01
183  2.1155e-01 -1.4925e-04  2.8763e-02  1.2482e+00     2.1195e-01
184  2.1926e-02 -1.0562e-04  2.0355e-02  1.5442e-01     8.7728e-01
185  1.3996e+00 -5.9315e-03  7.5570e-01  1.6168e+00     1.0592e-01
186 -1.0664e+00 -1.3297e-03  2.0450e-01 -2.3552e+00     1.8515e-02
187  6.1959e-01 -1.2468e-03  1.3661e-01  1.6797e+00     9.3016e-02
188  6.6563e-01 -1.5358e-03  1.4701e-01  1.7400e+00     8.1854e-02
189  8.4749e-01 -1.4014e-03  2.1550e-01  1.8286e+00     6.7455e-02
190  9.4563e-01 -1.6277e-03  2.0827e-01  2.0757e+00     3.7926e-02
191  6.9021e-01 -1.4749e-03  1.4120e-01  1.8408e+00     6.5657e-02
192 -7.7908e-01 -5.2377e-04  8.0617e-02 -2.7421e+00     6.1053e-03
193  7.7086e-01 -1.3297e-03  2.0450e-01  1.7076e+00     8.7716e-02
194  9.2093e-01 -1.5504e-03  2.3838e-01  1.8894e+00     5.8840e-02
195  7.6545e-01 -1.5504e-03  3.9834e-01  1.2153e+00     2.2427e-01
196 -3.6995e-01 -1.7723e-03  1.6962e-01 -8.9396e-01     3.7134e-01
197  3.0774e-01 -4.3874e-04  8.4529e-02  1.0600e+00     2.8916e-01
198  2.7947e-01 -4.3874e-04  6.7535e-02  1.0771e+00     2.8144e-01
199  3.0774e-01 -4.3874e-04  3.7324e-02  1.5952e+00     1.1068e-01
200  2.5330e-01 -5.2377e-04  6.7093e-02  9.7994e-01     3.2712e-01
201 -1.1965e-01 -8.1339e-04  1.2516e-01 -3.3591e-01     7.3694e-01
202 -6.6417e-02 -2.2324e-04  2.8605e-02 -3.9138e-01     6.9552e-01
203 -9.9313e-03 -6.3380e-06  6.9535e-04 -3.7638e-01     7.0663e-01
204  3.5951e-01 -9.9952e-04  1.0955e-01  1.0892e+00     2.7606e-01
205  1.7751e-01 -7.1640e-04  1.3799e-01  4.7979e-01     6.3137e-01
206  2.3959e-01 -5.6910e-04  8.7591e-02  8.1148e-01     4.1709e-01
207  3.5680e-01 -1.6277e-03  2.5025e-01  7.1649e-01     4.7369e-01
208  5.9762e-04 -6.9507e-05  8.9077e-03  7.0684e-03     9.9436e-01
209 -5.3116e-02 -2.0041e-04  3.0857e-02 -3.0124e-01     7.6323e-01
210  1.7582e-01 -1.4925e-04  2.2981e-02  1.1608e+00     2.4572e-01
211  1.5230e-01 -3.2531e-04  2.7678e-02  9.1739e-01     3.5894e-01
212  2.4259e-01 -3.6124e-04  3.9618e-02  1.2206e+00     2.2223e-01
213  1.4001e+00 -1.6916e-03  4.3457e-01  2.1265e+00     3.3464e-02
214  5.2532e-01 -7.6926e-04  9.8516e-02  1.6761e+00     9.3712e-02
215  7.5812e-01 -9.3914e-04  1.4449e-01  1.9969e+00     4.5835e-02
216  1.6424e-01 -4.8031e-04  7.3931e-02  6.0582e-01     5.4464e-01
217  5.8749e-01 -8.6966e-04  1.1136e-01  1.7631e+00     7.7886e-02
218  3.6410e-01 -3.1865e-04  4.9056e-02  1.6453e+00     9.9906e-02
219  1.8579e-01 -1.3297e-03  2.0450e-01  4.1378e-01     6.7903e-01
220 -3.2768e-01 -9.3914e-04  1.0294e-01 -1.0184e+00     3.0849e-01
221  2.4600e-02 -1.3162e-03  1.2602e-01  7.3004e-02     9.4180e-01
222  1.7425e-01 -1.3297e-03  1.1302e-01  5.2226e-01     6.0149e-01
223  1.1271e+00 -1.6277e-03  2.0827e-01  2.4733e+00     1.3386e-02
224  9.0870e-01 -4.5316e-03  6.9469e-01  1.0957e+00     2.7322e-01
225  5.8078e-01 -4.8031e-04  4.6027e-02  2.7094e+00     6.7411e-03
226 -3.7568e-01 -5.6910e-04  8.7591e-02 -1.2675e+00     2.0499e-01
227 -1.2497e-01 -1.3297e-03  1.7019e-01 -2.9970e-01     7.6440e-01
228 -1.3336e-01 -3.9905e-04  7.6885e-02 -4.7953e-01     6.3156e-01
229 -2.0255e-01 -6.9507e-05  8.9077e-03 -2.1454e+00     3.1923e-02
230 -7.6106e-01 -1.0452e-02  1.3256e+00 -6.5195e-01     5.1444e-01
231  2.7157e-02 -8.8063e-04  8.4354e-02  9.6537e-02     9.2309e-01
232  5.0818e-01 -1.2599e-03  2.4254e-01  1.0344e+00     3.0093e-01
233  2.6512e-01 -1.9394e-03  1.8558e-01  6.1993e-01     5.3531e-01
234 -5.3344e-01 -8.8063e-04  9.6531e-02 -1.7141e+00     8.6510e-02
235 -1.6336e-02 -1.8555e-06  2.8574e-04 -9.6630e-01     3.3389e-01
236  1.1751e-01 -5.1531e-04  9.9274e-02  3.7459e-01     7.0796e-01
237  1.3117e+00 -3.6636e-03  4.6782e-01  1.9231e+00     5.4466e-02
238 -1.3765e-01 -1.4014e-03  2.6973e-01 -2.6234e-01     7.9306e-01
239  4.2520e-02 -9.8783e-04  1.5197e-01  1.1160e-01     9.1114e-01
240  7.7837e-01 -8.6966e-04  1.3381e-01  2.1302e+00     3.3151e-02
241  1.1322e+00 -1.6277e-03  2.0827e-01  2.4844e+00     1.2978e-02
242 -6.3029e-01 -2.3901e-03  3.6719e-01 -1.0362e+00     3.0011e-01
243  4.9513e-02 -8.6620e-05  1.6694e-02  3.8387e-01     7.0107e-01
244  1.0825e+00 -1.4749e-03  2.2680e-01  2.2762e+00     2.2835e-02
245  3.8218e+00 -8.7432e-03  7.3761e-01  4.4601e+00     8.1903e-06
246  1.0730e+00 -1.5504e-03  2.9837e-01  1.9672e+00     4.9166e-02
247 -1.8102e-01 -6.3380e-06  2.4496e-03 -3.6574e+00     2.5483e-04
248  7.0598e-01 -6.1632e-04  7.8942e-02  2.5149e+00     1.1907e-02
249  1.6376e-01 -2.0041e-04  2.5680e-02  1.0232e+00     3.0623e-01
250  1.2461e+00 -1.6277e-03  2.5025e-01  2.4942e+00     1.2624e-02
251 -5.9560e-02 -3.2531e-04  8.3685e-02 -2.0476e-01     8.3776e-01
252  1.1415e+00 -1.6277e-03  1.7829e-01  2.7074e+00     6.7820e-03
253 -2.9028e-01 -1.5504e-03  1.6983e-01 -7.0062e-01     4.8354e-01
254  2.0483e-01 -3.5422e-04  3.0137e-02  1.1819e+00     2.3724e-01
255  3.8132e-01 -1.0059e-02  2.5625e+00  2.4450e-01     8.0685e-01
256  6.0271e-02 -3.9905e-04  4.3763e-02  2.9001e-01     7.7181e-01
257 -1.8991e-02 -3.2531e-04  3.5679e-02 -9.8820e-02     9.2128e-01
258 -2.6016e-01 -4.8031e-04  5.2671e-02 -1.1315e+00     2.5785e-01
259 -1.5029e-02 -6.9507e-05  6.6634e-03 -1.8326e-01     8.5459e-01
260  2.5243e-01 -8.8063e-04  1.6959e-01  6.1511e-01     5.3848e-01
261  1.2582e+00 -1.6277e-03  2.0827e-01  2.7606e+00     5.7704e-03
262 -1.6611e-02 -8.3203e-05  1.0663e-02 -1.6006e-01     8.7283e-01
263  4.4939e-02 -8.3203e-05  1.0663e-02  4.3600e-01     6.6283e-01
264  1.2976e-01 -3.2531e-04  6.2682e-02  5.1958e-01     6.0336e-01
265  3.3150e-02 -2.3901e-03  4.5958e-01  5.2424e-02     9.5819e-01
266  1.7154e-01 -8.2400e-04  7.8934e-02  6.1351e-01     5.3954e-01
267  4.4473e-01 -9.9952e-04  1.2798e-01  1.2460e+00     2.1277e-01
268  1.9014e-01 -1.2468e-03  1.0598e-01  5.8789e-01     5.5661e-01
269 -3.5537e-02 -5.2377e-04  6.7093e-02 -1.3517e-01     8.9247e-01
270  1.5685e-01 -3.9167e-04  5.0179e-02  7.0197e-01     4.8270e-01
271  1.2582e+00 -1.6277e-03  3.1322e-01  2.2510e+00     2.4382e-02
272  4.8530e-01 -1.6916e-03  4.3457e-01  7.3874e-01     4.6007e-01
273  1.0595e+00 -1.4749e-03  2.2680e-01  2.2278e+00     2.5892e-02
274  1.0249e+00 -1.4749e-03  1.8875e-01  2.3625e+00     1.8151e-02
275 -1.6524e-02 -1.3297e-03  2.0450e-01 -3.3600e-02     9.7320e-01
276 -2.9120e-02 -1.0903e-05  1.3974e-03 -7.7869e-01     4.3616e-01
277  2.3890e-01 -2.5910e-04  3.9890e-02  1.1974e+00     2.3113e-01
278  1.9144e-01 -1.1920e-03  1.8334e-01  4.4987e-01     6.5280e-01
279  2.6967e-01 -2.5910e-04  4.9927e-02  1.2081e+00     2.2703e-01
280  2.2770e-01 -2.0041e-04  2.1983e-02  1.5371e+00     1.2427e-01
281 -2.2712e-01 -7.5901e-04  1.1680e-01 -6.6235e-01     5.0774e-01
282  1.8845e-02 -4.0925e-05  5.2449e-03  2.6077e-01     7.9427e-01
283 -3.8965e-02 -5.6029e-04  8.6235e-02 -1.3078e-01     8.9595e-01
284  2.2390e-03 -1.0903e-05  4.2140e-03  3.4659e-02     9.7235e-01
285  1.2904e-01 -8.2400e-04  1.2679e-01  3.6470e-01     7.1534e-01
286 -9.1998e-03 -1.4925e-04  2.2981e-02 -5.9702e-02     9.5239e-01
287 -4.0001e-01 -2.9126e-04  3.1946e-02 -2.2364e+00     2.5326e-02
288  1.3579e-02 -1.0562e-04  1.3535e-02  1.1762e-01     9.0637e-01
289  6.7715e-02 -1.9868e-05  5.1126e-03  9.4731e-01     3.4348e-01
290  2.5630e-01 -1.6903e-04  1.4384e-02  2.1384e+00     3.2481e-02
291  8.9115e-01 -1.3297e-03  1.2731e-01  2.5013e+00     1.2374e-02
292  8.3080e-01 -1.1920e-03  2.2948e-01  1.7368e+00     8.2423e-02
293  8.3572e-01 -1.4749e-03  1.6158e-01  2.0827e+00     3.7274e-02
294  9.4127e-01 -1.3297e-03  1.7019e-01  2.2849e+00     2.2321e-02
295  1.3369e-01 -1.4925e-04  1.4307e-02  1.1189e+00     2.6316e-01
296 -2.6395e-01 -1.4014e-03  2.1550e-01 -5.6557e-01     5.7169e-01
297 -8.5516e-02 -4.8031e-04  7.3931e-02 -3.1274e-01     7.5448e-01
298  1.2702e+00 -2.3901e-03  4.5958e-01  1.8772e+00     6.0487e-02
299  1.8042e+00 -3.5471e-03  6.8127e-01  2.1902e+00     2.8513e-02
300  5.3311e-01 -3.1865e-04  3.4949e-02  2.8534e+00     4.3255e-03
301  1.1625e+00 -9.2780e-04  1.1880e-01  3.3755e+00     7.3685e-04
302 -2.4336e-01 -4.0925e-05  5.2449e-03 -3.3597e+00     7.8028e-04
303  6.2924e-01 -2.4859e-03  2.7205e-01  1.2112e+00     2.2583e-01
304  7.9307e+00 -5.2576e-02  3.4595e+00  4.2921e+00     1.7698e-05
305  1.2027e+00 -1.1135e-03  2.8623e-01  2.2501e+00     2.4444e-02
306  1.2091e-01 -9.3914e-04  7.9854e-02  4.3119e-01     6.6633e-01
307  4.7157e+00 -2.8615e-02  2.3657e+00  3.0846e+00     2.0384e-03
308  5.1810e-01 -7.1640e-04  6.0928e-02  2.1019e+00     3.5565e-02
309  6.0252e-01 -8.2400e-04  1.2679e-01  1.6944e+00     9.0185e-02
310  7.8575e-01 -1.4014e-03  2.1550e-01  1.6956e+00     8.9958e-02
311  9.7099e-01 -1.4014e-03  2.6973e-01  1.8723e+00     6.1166e-02
312  1.2618e-01 -1.7389e-04  2.2283e-02  8.4644e-01     3.9731e-01
313  2.4753e-01 -1.4925e-04  1.6372e-02  1.9357e+00     5.2905e-02
314  3.1114e-01 -5.6910e-04  8.7591e-02  1.0532e+00     2.9224e-01
315 -9.1066e-01 -1.4749e-03  1.2534e-01 -2.5680e+00     1.0228e-02
316 -2.1566e-02 -5.4275e-05  5.2032e-03 -2.9822e-01     7.6553e-01
317  1.0003e-02 -3.3373e-07  6.4326e-05  1.2473e+00     2.1229e-01
318  7.6232e-02 -6.1632e-04  1.1872e-01  2.2303e-01     8.2351e-01
319 -2.1311e-01 -2.9930e-03  4.5953e-01 -3.0996e-01     7.5659e-01
320  3.4728e-01 -3.9167e-04  3.7536e-02  1.7945e+00     7.2735e-02
321 -8.7294e-03 -3.3373e-07  6.4326e-05 -1.0884e+00     2.7643e-01
322  6.1088e-01 -1.6277e-03  2.5025e-01  1.2244e+00     2.2080e-01
323  3.7480e-01 -8.8063e-04  1.6959e-01  9.1226e-01     3.6163e-01
324 -3.3429e-01 -5.6910e-04  6.2402e-02 -1.3359e+00     1.8157e-01
325  2.8228e-01 -6.6542e-04  1.0240e-01  8.8420e-01     3.7659e-01
326  7.8513e-01 -1.5504e-03  1.4841e-01  2.0421e+00     4.1143e-02
327  2.9551e-01 -1.0618e-03  2.0444e-01  6.5590e-01     5.1189e-01
328  1.1550e-01 -1.4475e-04  2.2288e-02  7.7463e-01     4.3856e-01
329  3.1773e-01 -6.5588e-04  7.1911e-02  1.1873e+00     2.3512e-01
330  1.7514e+00 -1.8549e-03  2.3729e-01  3.5991e+00     3.1928e-04
331  2.8249e-02 -1.9868e-05  2.1798e-03  6.0548e-01     5.4486e-01
332 -7.1532e-02 -4.3100e-04  6.6345e-02 -2.7604e-01     7.8252e-01
333  4.7478e-02 -6.9507e-05  1.0703e-02  4.5959e-01     6.4581e-01
334  6.4821e-03 -8.6620e-05  2.2288e-02  4.3999e-02     9.6491e-01
335  3.1590e-02 -1.9868e-05  2.1798e-03  6.7706e-01     4.9837e-01
336  4.3466e-01 -1.4749e-03  2.8387e-01  8.1859e-01     4.1302e-01
337  1.6600e-01 -2.7477e-05  3.5215e-03  2.7978e+00     5.1457e-03
338 -1.4055e-02 -1.8555e-06  2.3780e-04 -9.1131e-01     3.6213e-01
339  1.0542e+00 -5.6029e-04  6.1436e-02  4.2556e+00     2.0849e-05
340 -4.6502e-02 -6.6542e-04  1.2817e-01 -1.2803e-01     8.9813e-01
341  1.7965e+00 -2.2962e-03  3.5280e-01  3.0285e+00     2.4580e-03
342 -2.0831e-01 -3.2531e-04  6.2682e-02 -8.3073e-01     4.0613e-01
343  4.5466e-01 -1.9519e-04  3.7616e-02  2.3452e+00     1.9016e-02
344  1.0931e-01 -1.0903e-05  2.1016e-03  2.3847e+00     1.7091e-02
345 -9.5441e-02 -1.0497e-03  2.6985e-01 -1.8171e-01     8.5581e-01
346 -3.2929e-01 -4.0925e-05  7.8878e-03 -3.7072e+00     2.0957e-04
347 -1.7755e-01 -1.2162e-05  2.3443e-03 -3.6668e+00     2.4556e-04
348  5.6912e-01 -2.2324e-04  3.4370e-02  3.0710e+00     2.1334e-03
349 -2.7842e-01 -1.6277e-03  2.5025e-01 -5.5330e-01     5.8006e-01
350 -2.2698e-02 -3.9905e-04  3.3949e-02 -1.2102e-01     9.0367e-01
351  2.3604e-01 -7.1640e-04  9.1751e-02  7.8162e-01     4.3444e-01
352 -3.1866e-01 -2.5910e-04  4.9927e-02 -1.4250e+00     1.5417e-01
353  3.4339e-01 -2.2324e-04  4.3019e-02  1.6567e+00     9.7579e-02
354 -2.1322e-02 -1.2162e-05  2.3443e-03 -4.4012e-01     6.5985e-01
355  6.6949e+00 -1.1886e-02  1.5053e+00  5.4665e+00     4.5908e-08
356  5.6083e-03 -1.5384e-07  3.9589e-05  8.9137e-01     3.7273e-01
357 -2.1211e-01 -1.2649e-04  1.2126e-02 -1.9251e+00     5.4218e-02
358  1.6871e-01 -6.6449e-05  1.0232e-02  1.6685e+00     9.5219e-02
359  2.2350e-01 -9.9952e-04  1.2798e-01  6.2755e-01     5.3030e-01
360 -3.6619e-01 -1.5504e-03  1.9839e-01 -8.1866e-01     4.1298e-01
361 -6.0131e-03 -8.2400e-04  7.8934e-02 -1.8470e-02     9.8526e-01
362  4.5740e-01 -1.6916e-03  1.8527e-01  1.0666e+00     2.8617e-01
363 -1.8197e-02 -1.8555e-06  1.5792e-04 -1.4479e+00     1.4764e-01
364  6.1303e-03 -1.0562e-04  1.6263e-02  4.8899e-02     9.6100e-01
365 -2.2750e-02 -5.4275e-05  5.9543e-03 -2.9412e-01     7.6867e-01
366  1.3585e-01 -5.4275e-05  6.9558e-03  1.6296e+00     1.0319e-01
367  1.6027e+00 -2.2324e-04  5.7433e-02  6.6885e+00     2.2541e-11
368  4.3276e-01 -5.6910e-04  8.7591e-02  1.4642e+00     1.4315e-01
369  1.3356e-01 -5.1577e-05  7.9423e-03  1.4992e+00     1.3381e-01
370  1.8036e-01 -2.9126e-04  5.6124e-02  7.6255e-01     4.4573e-01
371  2.2985e-01 -5.2377e-04  8.0617e-02  8.1138e-01     4.1715e-01
372  8.0179e-01 -1.4749e-03  2.8387e-01  1.5076e+00     1.3165e-01
373 -1.3378e-02 -2.3951e-06  2.2963e-04 -8.8267e-01     3.7741e-01
374 -1.9886e-01 -1.1259e-03  2.1678e-01 -4.2469e-01     6.7106e-01
375  2.5139e-02 -1.0903e-05  2.1016e-03  5.4861e-01     5.8327e-01
376  2.9981e-01 -5.6910e-04  7.2897e-02  1.1125e+00     2.6591e-01
377 -2.7264e-01 -1.3875e-03  1.7758e-01 -6.4368e-01     5.1978e-01
378  2.9537e-04 -1.5384e-07  2.3692e-05  6.0714e-02     9.5159e-01
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380  1.8019e+00 -2.4859e-03  3.8186e-01  2.9200e+00     3.5001e-03
381  1.0926e+00 -1.4014e-03  3.6011e-01  1.8231e+00     6.8292e-02
382  4.1537e-02 -1.9868e-05  2.5464e-03  8.2353e-01     4.1021e-01
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388  1.3567e-01 -1.9868e-05  3.8295e-03  2.1926e+00     2.8333e-02
389 -1.3819e-01 -8.6620e-05  1.3338e-02 -1.1958e+00     2.3176e-01
390  1.5263e-01 -1.2235e-04  1.5680e-02  1.2199e+00     2.2250e-01
391 -1.3166e-01 -2.0041e-04  3.8621e-02 -6.6893e-01     5.0354e-01
392  7.8292e-01 -1.7723e-03  2.7245e-01  1.5033e+00     1.3275e-01
393 -4.1586e-02 -1.2162e-05  1.5588e-03 -1.0530e+00     2.9234e-01
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395  3.6773e-01 -1.4607e-03  1.6002e-01  9.2290e-01     3.5606e-01
396  7.0376e-01 -7.5901e-04  1.9517e-01  1.5947e+00     1.1077e-01
397 -1.3855e+00 -1.1259e-03  2.8941e-01 -2.5733e+00     1.0074e-02
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401  6.9862e-01 -7.0234e-03  7.6514e-01  8.0671e-01     4.1983e-01
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404 -8.3787e-02 -1.6903e-04  4.3490e-02 -4.0097e-01     6.8845e-01
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406  1.2582e+00 -1.6277e-03  4.1817e-01  1.9482e+00     5.1391e-02
407  2.6952e-01 -8.1339e-04  1.2516e-01  7.6413e-01     4.4479e-01
408  2.4358e+00 -1.4607e-03  2.2462e-01  5.1426e+00     2.7103e-07
409  3.0479e-01 -1.0497e-03  1.1505e-01  9.0170e-01     3.6722e-01
410  1.1181e-01 -2.9126e-04  3.1946e-02  6.2722e-01     5.3052e-01
411  7.3786e-01 -2.1140e-03  3.2487e-01  1.2983e+00     1.9419e-01
412  4.7488e-03 -2.9456e-05  3.2316e-03  8.4055e-02     9.3301e-01
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414  2.6079e-01 -7.1640e-04  1.1024e-01  7.8760e-01     4.3093e-01
415 -4.5621e-02 -3.8586e-05  5.9420e-03 -5.9133e-01     5.5430e-01
416  5.2632e-01 -8.6966e-04  6.6469e-02  2.0448e+00     4.0872e-02
417  6.3472e-01 -5.1531e-04  4.3835e-02  3.0341e+00     2.4128e-03
418 -3.6917e-02 -1.2162e-05  1.3343e-03 -1.0103e+00     3.1236e-01
419 -2.1227e-01 -6.1632e-04  9.4853e-02 -6.8723e-01     4.9194e-01
420  2.5970e-01 -3.1865e-04  8.1973e-02  9.0818e-01     3.6378e-01
421  2.7703e-01 -1.2235e-04  1.3422e-02  2.3923e+00     1.6744e-02
422 -2.6231e-02 -1.0562e-04  1.0125e-02 -2.5965e-01     7.9514e-01
423  3.8165e-01 -2.8497e-04  5.4911e-02  1.6299e+00     1.0312e-01
424  2.5215e-01 -4.8031e-04  9.2535e-02  8.3049e-01     4.0626e-01
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426  1.4889e+00 -4.1483e-03  4.5323e-01  2.2178e+00     2.6571e-02
427 -9.4618e-03 -2.3951e-06  4.6165e-04 -4.4025e-01     6.5975e-01
428 -8.3087e-02 -1.4925e-04  1.9126e-02 -5.9971e-01     5.4870e-01
429 -2.3081e-01 -5.6910e-04  2.1983e-01 -4.9106e-01     6.2339e-01
430  4.3336e-01 -4.8031e-04  4.0859e-02  2.1463e+00     3.1853e-02
431  2.9650e-03 -3.3373e-07  6.4326e-05  3.6973e-01     7.1158e-01
432 -8.1591e-02 -1.2162e-05  1.8730e-03 -1.8850e+00     5.9429e-02
433  7.6751e-01 -3.2090e-03  4.0996e-01  1.2037e+00     2.2870e-01
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435 -8.1356e-01 -2.3901e-03  3.6719e-01 -1.3387e+00     1.8068e-01
436 -6.4567e-04 -1.5384e-07  2.3692e-05 -1.3262e-01     8.9449e-01
437 -1.7906e-02 -3.1000e-03  3.9608e-01 -2.3526e-02     9.8123e-01
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439  4.1120e-01 -1.5504e-03  3.9834e-01  6.5397e-01     5.1313e-01
440  1.1281e+00 -1.6277e-03  1.2431e-01  3.2043e+00     1.3540e-03
441  1.0935e+00 -1.9394e-03  2.1236e-01  2.3771e+00     1.7448e-02
442 -3.9073e-02 -1.0562e-04  2.7175e-02 -2.3638e-01     8.1314e-01
443  5.7842e-01 -1.1920e-03  2.2948e-01  1.2099e+00     2.2630e-01
444 -3.1227e-01 -4.8031e-04  7.3931e-02 -1.1467e+00     2.5151e-01
445  1.7688e+00 -1.9394e-03  2.4808e-01  3.5552e+00     3.7773e-04
446  3.2529e-01 -9.8783e-04  1.5197e-01  8.3697e-01     4.0261e-01
447  1.2582e+00 -1.6277e-03  4.1817e-01  1.9482e+00     5.1391e-02
448  2.9856e-01 -9.9952e-04  7.6385e-02  1.0839e+00     2.7842e-01
449  6.7138e-02 -7.1640e-04  1.3799e-01  1.8267e-01     8.5506e-01
450 -1.8849e-03 -1.8555e-06  3.5764e-04 -9.9571e-02     9.2068e-01
451  1.2681e-01 -6.5588e-04  1.0094e-01  4.0121e-01     6.8826e-01
452  7.5819e-01 -1.5358e-03  2.3615e-01  1.5634e+00     1.1796e-01
453  1.0092e-01 -1.4014e-03  2.6973e-01  1.9701e-01     8.4382e-01
454  2.6045e-01 -9.2780e-04  2.3853e-01  5.3517e-01     5.9253e-01
455  2.1905e+00 -2.9930e-03  3.8244e-01  3.5469e+00     3.8973e-04
456  3.4467e-01 -1.9519e-04  2.5012e-02  2.1806e+00     2.9213e-02
457 -9.2051e-02 -5.1577e-05  4.9446e-03 -1.3083e+00     1.9076e-01
458  1.0582e+00 -1.5504e-03  2.9837e-01  1.9401e+00     5.2364e-02
459  6.2038e-01 -2.5835e-03  2.4705e-01  1.2534e+00     2.1008e-01
460  1.7886e-03 -8.3203e-05  9.1276e-03  1.9592e-02     9.8437e-01
461  8.6984e-01 -8.8063e-04  1.6959e-01  2.1144e+00     3.4484e-02
462  1.0537e+00 -1.4749e-03  2.2680e-01  2.2157e+00     2.6710e-02
463 -1.5843e-01 -1.6277e-03  2.0827e-01 -3.4359e-01     7.3115e-01
464  1.4196e+00 -2.4859e-03  2.7205e-01  2.7264e+00     6.4020e-03
465 -1.1870e-02 -3.3373e-07  6.4326e-05 -1.4799e+00     1.3890e-01
466  8.4157e-02 -2.0041e-04  2.5680e-02  5.2641e-01     5.9860e-01
467 -2.5992e-01 -1.1792e-03  1.1292e-01 -7.6999e-01     4.4131e-01
468 -1.3204e-01 -5.4275e-05  1.0461e-02 -1.2904e+00     1.9690e-01
469 -2.5568e-01 -9.2780e-04  1.4275e-01 -6.7426e-01     5.0014e-01
470  4.0363e-01 -3.5422e-04  5.4530e-02  1.7300e+00     8.3627e-02
471 -2.3647e-01 -6.1632e-04  4.7118e-02 -1.0865e+00     2.7724e-01
472 -2.0137e-01 -1.1259e-03  1.7320e-01 -4.8117e-01     6.3040e-01
473  1.1675e+00 -1.6277e-03  3.1322e-01  2.0889e+00     3.6716e-02
474  1.8047e-01 -3.2531e-04  3.1178e-02  1.0239e+00     3.0588e-01
475  1.0717e+00 -1.6277e-03  2.0827e-01  2.3518e+00     1.8682e-02
476  1.0032e-02 -5.4386e-06  6.9703e-04  3.8020e-01     7.0380e-01
477  1.1648e+00 -1.4749e-03  1.6158e-01  2.9014e+00     3.7150e-03
478  1.3145e-01 -4.5316e-03  6.9469e-01  1.6314e-01     8.7040e-01
479  6.3142e-01 -1.3297e-03  5.1324e-01  8.8323e-01     3.7711e-01
480  4.2948e-03 -1.5384e-07  2.3692e-05  8.8239e-01     3.7757e-01
481  1.0689e+00 -1.3297e-03  2.5595e-01  2.1153e+00     3.4402e-02
482  2.4269e-01 -1.4475e-04  1.8549e-02  1.7830e+00     7.4589e-02
483 -1.7618e-01 -1.4749e-03  1.6158e-01 -4.3463e-01     6.6383e-01
484 -2.0568e-02 -1.9868e-05  3.8295e-03 -3.3204e-01     7.3986e-01
485 -7.2227e-01 -6.1632e-04  9.4853e-02 -2.3432e+00     1.9121e-02
486  3.5764e-01 -5.6910e-04  8.7591e-02  1.2103e+00     2.2615e-01
487  1.3249e+00 -3.1000e-03  3.9608e-01  2.1101e+00     3.4852e-02
488  8.6679e-02 -2.2324e-04  2.8605e-02  5.1382e-01     6.0738e-01
489  1.2453e-01 -1.4925e-04  1.2701e-02  1.1063e+00     2.6859e-01
490  2.2996e-01 -3.1865e-04  2.7112e-02  1.3986e+00     1.6195e-01
491 -1.1691e+00 -1.4014e-03  2.6973e-01 -2.2484e+00     2.4553e-02
492  1.2582e+00 -1.6277e-03  3.1322e-01  2.2510e+00     2.4382e-02
493  3.2091e-02 -5.1577e-05  4.3894e-03  4.8516e-01     6.2757e-01
494 -2.2500e-02 -2.9456e-05  2.8239e-03 -4.2285e-01     6.7241e-01
495  4.0696e-01 -2.8497e-04  5.4911e-02  1.7379e+00     8.2226e-02
496 -4.1196e-02 -3.8586e-05  7.4371e-03 -4.7726e-01     6.3318e-01
497  2.5996e-01 -1.4014e-03  1.1910e-01  7.5733e-01     4.4885e-01
498  4.1673e-01 -7.6926e-04  6.5421e-02  1.6323e+00     1.0262e-01
499  2.4038e-02 -6.9507e-05  1.3396e-02  2.0828e-01     8.3501e-01
500  1.0360e+00 -1.2599e-03  3.2380e-01  1.8228e+00     6.8330e-02
501  5.3008e-02 -1.5504e-03  2.3838e-01  1.1174e-01     9.1103e-01
502  2.2082e+00 -2.4859e-03  6.3810e-01  2.7674e+00     5.6503e-03
503  5.4171e-02 -1.4749e-03  1.6158e-01  1.3843e-01     8.8990e-01
504  1.8292e-02 -1.2162e-05  1.8730e-03  4.2294e-01     6.7234e-01
505 -1.6085e-01 -1.1135e-03  1.4256e-01 -4.2306e-01     6.7225e-01
506 -1.7727e-01 -8.6620e-05  1.1101e-02 -1.6817e+00     9.2627e-02
507  1.2582e+00 -1.6277e-03  2.5025e-01  2.5184e+00     1.1789e-02
508  4.1411e-01 -1.0497e-03  5.6999e-02  1.7389e+00     8.2048e-02
509  1.2582e+00 -1.6277e-03  2.5025e-01  2.5184e+00     1.1789e-02
510  6.8447e-02 -2.5316e-04  6.5130e-02  2.6920e-01     7.8778e-01
511  8.4196e-01 -6.5588e-04  5.5785e-02  3.5675e+00     3.6035e-04
512  1.1172e+00 -1.5504e-03  2.9837e-01  2.0482e+00     4.0538e-02
513  1.1591e+00 -1.5504e-03  3.9834e-01  1.8389e+00     6.5927e-02
514  2.3732e-01 -3.9905e-04  3.8242e-02  1.2156e+00     2.2413e-01
515  1.0431e+00 -1.2599e-03  1.9378e-01  2.3724e+00     1.7671e-02
516 -1.1309e-03 -1.5384e-07  2.9653e-05 -2.0765e-01     8.3550e-01
517  7.4541e-01 -1.3162e-03  2.5336e-01  1.4835e+00     1.3794e-01
518  9.0273e-02 -9.3914e-04  1.2025e-01  2.6303e-01     7.9253e-01
519 -6.4231e-02 -5.1577e-05  6.6100e-03 -7.8940e-01     4.2988e-01
520  1.9796e-01 -5.6029e-04  5.3686e-02  8.5677e-01     3.9157e-01
521  3.1335e-01 -8.1339e-04  1.5665e-01  7.9377e-01     4.2733e-01
522 -7.1570e-02 -1.8249e-05  1.7496e-03 -1.7106e+00     8.7150e-02
523  1.1464e-01 -1.7389e-04  1.9074e-02  8.3134e-01     4.0578e-01
524  2.8016e-01 -2.0041e-04  3.0857e-02  1.5960e+00     1.1048e-01
525  1.2582e+00 -1.6277e-03  4.1817e-01  1.9482e+00     5.1391e-02
526  1.0897e+00 -1.6277e-03  1.7829e-01  2.5846e+00     9.7504e-03
527  5.1373e-02 -1.9519e-04  2.5012e-02  3.2607e-01     7.4437e-01
528  3.8138e-01 -8.2400e-04  7.8934e-02  1.3604e+00     1.7371e-01
529  1.2072e-02 -6.3380e-06  9.7603e-04  3.8661e-01     6.9905e-01
530 -9.8898e-02 -5.6910e-04  5.4530e-02 -4.2108e-01     6.7370e-01
531  7.6469e-01 -1.1259e-03  1.7320e-01  1.8402e+00     6.5746e-02
532  6.2583e-01 -7.6926e-04  9.8516e-02  1.9964e+00     4.5896e-02
533  9.3026e-02 -1.5504e-03  1.3174e-01  2.6056e-01     7.9443e-01
534  1.5217e-01 -2.9456e-05  4.5360e-03  2.2598e+00     2.3833e-02
535  5.7646e-01 -5.2377e-04  6.7093e-02  2.2275e+00     2.5912e-02
536  8.8679e-01 -9.3914e-04  2.4144e-01  1.8066e+00     7.0818e-02
537  9.2056e-01 -1.4749e-03  1.4120e-01  2.4538e+00     1.4136e-02
538  1.1681e-03 -1.0184e-04  1.9627e-02  9.0651e-03     9.9277e-01
539  4.3614e-02 -2.2881e-04  4.4093e-02  2.0879e-01     8.3461e-01
540 -2.0447e-02 -6.6449e-05  6.3702e-03 -2.5536e-01     7.9845e-01
541  6.7234e-01 -9.3914e-04  1.2025e-01  1.9416e+00     5.2190e-02
542  6.2298e-01 -1.6277e-03  3.1322e-01  1.1160e+00     2.6440e-01
543  4.9715e-01 -5.6910e-04  8.7591e-02  1.6817e+00     9.2621e-02
544  3.2338e-01 -6.6542e-04  6.3753e-02  1.2834e+00     1.9936e-01
545  9.3118e-01 -6.0715e-04  1.5614e-01  2.3581e+00     1.8371e-02
546  1.4691e-02 -3.8586e-05  7.4371e-03  1.7080e-01     8.6438e-01
547  1.6951e-01 -4.7222e-04  9.0976e-02  5.6357e-01     5.7305e-01
548 -2.4197e-01 -4.9318e-03  4.1767e-01 -3.6678e-01     7.1378e-01
549 -6.5236e-02 -5.4386e-06  5.9668e-04 -2.6704e+00     7.5757e-03
550  8.4506e-01 -1.6916e-03  1.4373e-01  2.2335e+00     2.5516e-02
551  9.9888e-03 -1.8249e-05  2.0021e-03  2.2364e-01     8.2303e-01
552  1.9787e-01 -2.5910e-04  3.9890e-02  9.9200e-01     3.2120e-01
553  1.4982e+00 -5.2080e-03  5.6841e-01  1.9941e+00     4.6137e-02
554  1.3832e+00 -2.3901e-03  3.0559e-01  2.5066e+00     1.2191e-02
555  3.6842e-02 -1.9868e-05  2.1798e-03  7.8954e-01     4.2980e-01
556  4.0670e-01 -7.8598e-03  8.5553e-01  4.4820e-01     6.5401e-01
557  2.6021e+00 -5.4918e-03  5.9920e-01  3.3686e+00     7.5543e-04
558  8.4874e-03 -3.6124e-04  3.4620e-02  4.7556e-02     9.6207e-01
559  1.1578e-01 -2.2962e-03  1.5911e-01  2.9601e-01     7.6722e-01
560  6.6227e+00 -3.9022e-03  3.0085e+00  3.8204e+00     1.3321e-04
561  2.7372e-02 -3.2531e-04  3.5679e-02  1.4664e-01     8.8342e-01
562  3.2130e-01 -8.2400e-04  7.0072e-02  1.2169e+00     2.2365e-01
563  1.1029e-01 -4.0925e-05  6.3021e-03  1.3899e+00     1.6457e-01
564  5.2719e-01 -8.2400e-04  6.2983e-02  2.1040e+00     3.5382e-02
565  4.2386e-01 -4.8031e-04  7.3931e-02  1.5606e+00     1.1861e-01
566 -2.0503e-01 -1.7389e-04  4.4739e-02 -9.6850e-01     3.3279e-01
567  2.0166e-01 -2.5316e-04  4.8784e-02  9.1416e-01     3.6063e-01
568  7.3130e-01 -1.1792e-03  1.8138e-01  1.7199e+00     8.5452e-02
569  2.0417e+00 -2.2042e-03  3.3869e-01  3.5121e+00     4.4456e-04
570  7.1880e-03 -2.5910e-04  1.0011e-01  2.3536e-02     9.8122e-01
571  1.2340e+00 -1.6277e-03  2.5025e-01  2.4700e+00     1.3511e-02
572 -1.4659e-01 -1.4925e-04  2.2981e-02 -9.6603e-01     3.3403e-01
573 -2.9739e-01 -3.1865e-04  3.0540e-02 -1.6999e+00     8.9146e-02
574  2.2340e-01 -4.8031e-04  9.2535e-02  7.3597e-01     4.6175e-01
575 -1.7016e-01 -8.3203e-05  9.1276e-03 -1.7802e+00     7.5043e-02
576 -8.4012e-02 -8.1339e-04  1.0416e-01 -2.5779e-01     7.9657e-01
577  5.0585e-01 -1.6916e-03  3.2550e-01  8.8961e-01     3.7368e-01
578  2.9012e-02 -1.2162e-05  2.3443e-03  5.9946e-01     5.4887e-01
579  6.6482e-01 -7.6926e-04  7.3694e-02  2.4518e+00     1.4213e-02
580 -2.8194e-01 -8.6620e-05  1.6694e-02 -2.1814e+00     2.9154e-02
581 -1.6483e-01 -1.2649e-04  1.3876e-02 -1.3982e+00     1.6205e-01
582  3.8743e+00 -6.0818e-03  6.6319e-01  4.7649e+00     1.8891e-06
583 -4.3259e-02 -1.4475e-04  2.2288e-02 -2.8879e-01     7.7274e-01
584 -5.7052e-02 -5.1577e-05  7.9423e-03 -6.3959e-01     5.2244e-01
585  3.6430e-01 -2.9126e-04  2.7916e-02  2.1821e+00     2.9101e-02
586  1.6093e-01 -1.2235e-04  1.8840e-02  1.1733e+00     2.4067e-01
587  3.1158e-02 -3.8586e-05  4.2332e-03  4.7948e-01     6.3160e-01
588  4.8875e-01 -1.1920e-03  1.3062e-01  1.3556e+00     1.7522e-01
589  6.1094e-02 -1.0562e-04  1.3535e-02  5.2604e-01     5.9886e-01
590  1.1394e+00 -1.5504e-03  2.3838e-01  2.3368e+00     1.9449e-02
591 -4.7970e-01 -7.1640e-04  1.3799e-01 -1.2895e+00     1.9724e-01
592  2.9334e-01 -6.6542e-04  7.2956e-02  1.0885e+00     2.7638e-01
593  5.8173e-01 -5.6029e-04  5.3686e-02  2.5131e+00     1.1967e-02
594 -4.9347e-02 -1.0562e-04  1.1586e-02 -4.5747e-01     6.4734e-01
595  2.4317e-01 -5.6910e-04  5.4530e-02  1.0438e+00     2.9659e-01
596 -9.3535e-02 -8.6620e-05  1.1101e-02 -8.8695e-01     3.7511e-01
597  3.8428e-01 -1.1920e-03  2.2948e-01  8.0468e-01     4.2100e-01
598 -1.3621e-01 -2.8497e-04  3.6512e-02 -7.1136e-01     4.7686e-01
599  1.5652e+00 -1.9394e-03  2.9809e-01  2.8704e+00     4.0999e-03
600  1.4039e+00 -3.9022e-03  4.2644e-01  2.1558e+00     3.1097e-02
601  7.3697e-01 -3.1000e-03  2.9629e-01  1.3596e+00     1.7395e-01
602  8.5261e-01 -1.5504e-03  1.6983e-01  2.0727e+00     3.8202e-02
603  9.5775e-01 -1.4749e-03  3.7898e-01  1.5582e+00     1.1920e-01
604  2.2091e-02 -2.9456e-05  3.7751e-03  3.6003e-01     7.1883e-01
605  5.4810e-01 -1.2599e-03  2.4254e-01  1.1155e+00     2.6464e-01
606  7.8103e-02 -1.2649e-04  3.2546e-02  4.3363e-01     6.6456e-01
607  8.6743e-03 -6.3380e-06  9.7603e-04  2.7786e-01     7.8112e-01
608 -3.8818e-01 -6.0715e-04  3.8579e-02 -1.9732e+00     4.8469e-02
609 -2.3074e-02 -1.9868e-05  1.9048e-03 -5.2823e-01     5.9734e-01
610  1.3380e+00 -3.2090e-03  2.4469e-01  2.7115e+00     6.6989e-03
611  6.6415e-01 -7.1640e-04  9.1751e-02  2.1950e+00     2.8166e-02
612  3.8157e-01 -6.0715e-04  1.1696e-01  1.1175e+00     2.6377e-01
613 -2.9816e-01 -1.0618e-03  1.6334e-01 -7.3512e-01     4.6227e-01
614  7.5463e-01 -1.1259e-03  1.7320e-01  1.8160e+00     6.9374e-02
615  5.1528e-01 -9.9952e-04  1.0955e-01  1.5598e+00     1.1880e-01
616  2.1165e-01 -9.9952e-04  2.5695e-01  4.1950e-01     6.7485e-01
617 -2.0130e-02 -5.1577e-05  5.6583e-03 -2.6692e-01     7.8953e-01
618  5.9947e-01 -6.6542e-04  1.0240e-01  1.8754e+00     6.0742e-02
619  6.4364e-01 -8.8063e-04  1.1277e-01  1.9193e+00     5.4942e-02
620  1.3031e+00 -3.7819e-03  4.1335e-01  2.0327e+00     4.2086e-02
621  7.9825e-01 -1.2599e-03  1.9378e-01  1.8163e+00     6.9332e-02
622  6.2773e-01 -8.2400e-04  9.0329e-02  2.0914e+00     3.6495e-02
623  6.9558e-01 -1.6277e-03  2.5025e-01  1.3937e+00     1.6340e-01
624  8.0750e-03 -5.2377e-04  5.0189e-02  3.8383e-02     9.6938e-01
625  4.6860e-01 -5.6029e-04  6.1436e-02  1.8928e+00     5.8383e-02
626  1.1250e-02 -4.0925e-05  3.9234e-03  1.8026e-01     8.5694e-01
627 -2.9406e-02 -6.9507e-05  5.3168e-03 -4.0233e-01     6.8744e-01
628 -1.4238e-01 -8.6620e-05  1.1101e-02 -1.3506e+00     1.7684e-01
629 -7.3679e-03 -1.4925e-04  2.2981e-02 -4.7618e-02     9.6202e-01
630 -5.5478e-03 -5.4275e-05  8.3578e-03 -6.0090e-02     9.5208e-01
631  4.7785e-01 -1.4749e-03  5.6921e-01  6.3532e-01     5.2522e-01
632  2.2707e-01 -1.2649e-04  1.6210e-02  1.7845e+00     7.4339e-02
633  2.1351e-01 -4.3874e-04  5.6206e-02  9.0244e-01     3.6682e-01
634  5.7511e-01 -2.3901e-03  2.6159e-01  1.1291e+00     2.5885e-01
635  1.6371e-01 -8.6966e-04  1.3381e-01  4.4992e-01     6.5277e-01
636  3.1633e-01 -1.7389e-04  2.6774e-02  1.9343e+00     5.3075e-02
637  3.4468e-01 -1.4749e-03  1.4120e-01  9.2121e-01     3.5694e-01
638 -6.3373e-02 -1.2649e-04  1.0764e-02 -6.0960e-01     5.4212e-01
639  1.7885e-01 -8.2400e-04  9.0329e-02  5.9781e-01     5.4997e-01
640  8.3120e+00 -1.8811e-02  2.0249e+00  5.8544e+00     4.7869e-09
641 -2.0520e-03 -3.3373e-07  2.8403e-05 -3.8497e-01     7.0026e-01
642  1.9527e+00 -3.2090e-03  3.5093e-01  3.3016e+00     9.6119e-04
643  5.2612e-01 -9.9952e-04  1.5377e-01  1.3442e+00     1.7888e-01
644  1.1201e+00 -4.7965e-03  6.1179e-01  1.4382e+00     1.5039e-01
645  6.2063e-01 -7.6926e-04  1.4816e-01  1.6144e+00     1.0644e-01
646  7.9197e-01 -1.1920e-03  3.0637e-01  1.4330e+00     1.5186e-01
647  2.0377e+00 -4.2742e-03  5.4546e-01  2.7648e+00     5.6957e-03
648  4.4925e-01 -1.2599e-03  1.3805e-01  1.2125e+00     2.2532e-01
649 -8.4046e-03 -3.3373e-07  5.1394e-05 -1.1723e+00     2.4107e-01
650  2.6986e-02 -3.2531e-04  5.0081e-02  1.2204e-01     9.0287e-01
651  3.6799e-01 -4.8031e-04  7.3931e-02  1.3552e+00     1.7536e-01
652  1.7095e-01 -1.1135e-03  1.2203e-01  4.9256e-01     6.2232e-01
653 -8.3028e-02 -2.9456e-05  4.5360e-03 -1.2324e+00     2.1782e-01
654  6.5987e-01 -1.2599e-03  1.9378e-01  1.5019e+00     1.3313e-01
655  3.8028e-02 -1.2599e-03  1.6127e-01  9.7831e-02     9.2207e-01
656  1.5301e+00 -3.4325e-03  3.7530e-01  2.5032e+00     1.2307e-02
657 -1.1049e-01 -8.1339e-04  8.9166e-02 -3.6728e-01     7.1341e-01
658 -5.1784e-03 -1.2468e-03  1.9176e-01 -8.9783e-03     9.9284e-01
659  9.0495e+00 -1.7248e-02  3.2672e+00  5.0161e+00     5.2740e-07
660 -1.2167e-01 -5.1577e-05  1.3272e-02 -1.0557e+00     2.9113e-01
661 -3.2913e-01 -6.9507e-05  1.3396e-02 -2.8430e+00     4.4688e-03
662 -2.2388e-02 -3.6124e-04  4.6281e-02 -1.0239e-01     9.1845e-01
663 -4.2228e-02 -5.4386e-06  4.6287e-04 -1.9625e+00     4.9702e-02
664  3.1197e-01 -7.0651e-04  1.3608e-01  8.4761e-01     3.9666e-01
665 -1.6296e-03 -2.3951e-06  3.6884e-04 -8.4725e-02     9.3248e-01
666  2.3715e-02 -5.1577e-05  1.3272e-02  2.0631e-01     8.3655e-01
667  1.3349e-02 -1.8555e-06  2.3780e-04  8.6577e-01     3.8661e-01
668  8.4485e-01 -1.0497e-03  1.0054e-01  2.6678e+00     7.6342e-03
669  5.7035e-01 -1.0618e-03  2.0444e-01  1.2638e+00     2.0632e-01
670 -3.1543e-01 -1.7389e-04  6.7196e-02 -1.2162e+00     2.2392e-01
671 -1.1518e-01 -3.9167e-04  5.0179e-02 -5.1242e-01     6.0836e-01
672 -9.6663e-02 -5.6910e-04  8.7591e-02 -3.2469e-01     7.4542e-01
673  8.0602e-02 -9.2780e-04  8.8869e-02  2.7349e-01     7.8448e-01
674  1.3145e-01 -1.6277e-03  1.5580e-01  3.3715e-01     7.3601e-01
675  2.2983e-01 -3.2531e-04  5.0081e-02  1.0284e+00     3.0374e-01
676  9.9270e-01 -1.3297e-03  1.4569e-01  2.6043e+00     9.2072e-03
677  1.4623e+00 -4.2742e-03  4.6692e-01  2.1463e+00     3.1852e-02
678  2.6920e-02 -6.3380e-06  1.6310e-03  6.6675e-01     5.0493e-01
679 -5.8645e-02 -6.6449e-05  1.0232e-02 -5.7910e-01     5.6252e-01
680 -8.5911e-02 -2.5910e-04  2.8419e-02 -5.0808e-01     6.1140e-01
681  1.9560e+00 -4.6631e-03  7.1476e-01  2.3191e+00     2.0389e-02
682  1.0692e+00 -1.4014e-03  2.6973e-01  2.0614e+00     3.9261e-02
683 -6.5842e-02 -6.6542e-04  1.2817e-01 -1.8205e-01     8.5554e-01
684  3.6742e+00 -1.2747e-02  1.2065e+00  3.3566e+00     7.8921e-04
685  2.9738e-01 -1.4014e-03  3.6011e-01  4.9790e-01     6.1855e-01
686  3.0015e-01 -1.1920e-03  2.2948e-01  6.2907e-01     5.2931e-01
687  9.3505e-01 -1.1259e-03  1.2339e-01  2.6651e+00     7.6963e-03
688  2.5622e-01 -2.9126e-04  3.1946e-02  1.4352e+00     1.5124e-01
689  8.9191e-01 -5.1531e-04  6.6011e-02  3.4735e+00     5.1377e-04
690  6.1243e-02 -8.2400e-04  1.5869e-01  1.5580e-01     8.7619e-01
691  1.6924e-01 -8.6966e-04  1.6748e-01  4.1567e-01     6.7765e-01
692  1.4857e-01 -2.7477e-05  4.2313e-03  2.2845e+00     2.2343e-02
693  1.0077e+00 -1.1920e-03  1.5259e-01  2.5827e+00     9.8023e-03
694  1.3377e+00 -2.3901e-03  1.6560e-01  3.2931e+00     9.9086e-04
695 -4.2032e-01 -1.0618e-03  1.6334e-01 -1.0374e+00     2.9957e-01
696 -2.0376e-01 -3.9905e-04  3.0514e-02 -1.1641e+00     2.4436e-01
697  1.0710e+00 -1.4749e-03  2.2680e-01  2.2520e+00     2.4322e-02
698 -1.3067e-01 -2.5835e-03  3.3026e-01 -2.2289e-01     8.2362e-01
699  7.9880e-01 -1.6916e-03  3.2550e-01  1.4031e+00     1.6059e-01
700 -3.1578e-01 -7.0651e-04  1.3608e-01 -8.5411e-01     3.9305e-01
701  2.4912e-02 -5.1577e-05  4.3894e-03  3.7679e-01     7.0633e-01
702 -3.4236e-03 -3.3373e-07  4.2772e-05 -5.2343e-01     6.0067e-01
703  3.3251e-01 -1.1920e-03  2.2948e-01  6.9661e-01     4.8605e-01
704  1.9596e-01 -8.3203e-05  1.6036e-02  1.5482e+00     1.2158e-01
705  8.8341e-01 -1.2599e-03  1.9378e-01  2.0097e+00     4.4462e-02
706 -2.1826e-01 -9.8783e-04  1.2648e-01 -6.1094e-01     5.4124e-01
707  7.3790e-01 -1.5504e-03  2.3838e-01  1.5145e+00     1.2990e-01
708  6.4220e-02 -1.7389e-04  1.3300e-02  5.5837e-01     5.7659e-01
709  6.0549e-02 -1.8249e-05  2.3389e-03  1.2524e+00     2.1044e-01
710 -2.7763e-01 -1.5504e-03  3.9834e-01 -4.3743e-01     6.6180e-01
711 -8.4724e-03 -5.4386e-06  1.0483e-03 -2.6151e-01     7.9370e-01
712 -3.6620e-03 -1.5384e-07  1.6879e-05 -8.9133e-01     3.7275e-01
713 -2.3849e-01 -1.0497e-03  8.9248e-02 -7.9480e-01     4.2673e-01
714 -3.3298e-01 -6.0715e-04  6.6571e-02 -1.2882e+00     1.9767e-01
715  6.7295e-01 -1.5504e-03  2.3838e-01  1.3815e+00     1.6713e-01
716  7.3616e-01 -9.3914e-04  7.9854e-02  2.6084e+00     9.0956e-03
717  7.6129e-01 -1.3297e-03  2.5595e-01  1.5074e+00     1.3171e-01
718 -4.2922e-03 -1.5384e-07  3.9589e-05 -6.8215e-01     4.9515e-01
719  3.2251e-01 -5.2377e-04  4.0046e-02  1.6142e+00     1.0648e-01
720  6.8852e-01 -7.1640e-04  7.8541e-02  2.4593e+00     1.3920e-02
721  8.3329e-02 -1.4475e-04  1.8549e-02  6.1289e-01     5.3995e-01
722  5.3675e-02 -1.7389e-04  2.2283e-02  3.6074e-01     7.1830e-01
723  4.8583e-02 -5.4275e-05  8.3578e-03  5.3201e-01     5.9472e-01
724  7.1148e-01 -9.2780e-04  1.7867e-01  1.6854e+00     9.1907e-02
725  1.1053e-01 -3.5422e-04  3.8849e-02  5.6258e-01     5.7372e-01
726 -3.1866e-01 -6.5588e-04  8.4006e-02 -1.0972e+00     2.7257e-01
727  1.1424e-02 -2.3951e-06  4.6165e-04  5.3181e-01     5.9486e-01
728  5.7671e-01 -7.1640e-04  7.8541e-02  2.0604e+00     3.9362e-02
729  2.7894e-01 -5.6910e-04  6.2402e-02  1.1189e+00     2.6317e-01
730  6.0619e-03 -3.3373e-07  5.1394e-05  8.4562e-01     3.9776e-01
731  3.0813e-01 -7.6926e-04  6.5421e-02  1.2077e+00     2.2716e-01
732  6.7941e-01 -1.4749e-03  1.6158e-01  1.6939e+00     9.0288e-02
733 -1.1686e-02 -2.3951e-06  3.0697e-04 -6.6684e-01     5.0488e-01
734  4.6362e-03 -2.3951e-06  3.6884e-04  2.4153e-01     8.0915e-01
735  9.6682e-01 -2.9930e-03  3.8244e-01  1.5682e+00     1.1683e-01
736  1.0961e+00 -1.2468e-03  3.2043e-01  1.9386e+00     5.2554e-02
737  6.7907e-01 -1.0618e-03  1.6334e-01  1.6828e+00     9.2404e-02
738 -7.6637e-03 -1.0903e-05  8.3406e-04 -2.6499e-01     7.9102e-01
739  7.8882e-01 -1.5504e-03  1.4841e-01  2.0517e+00     4.0203e-02
740  3.4338e-01 -1.2235e-04  1.8840e-02  2.5026e+00     1.2329e-02
741  2.0732e-02 -1.2162e-05  1.0351e-03  6.4477e-01     5.1908e-01
742  4.6167e-02 -5.4386e-06  8.3753e-04  1.5955e+00     1.1061e-01
743 -2.1810e-04 -1.4475e-04  1.5879e-02 -5.8210e-04     9.9954e-01
744  1.3116e-01 -4.0925e-05  7.8878e-03  1.4773e+00     1.3961e-01
745  1.9287e-01 -3.2531e-04  2.7678e-02  1.1612e+00     2.4555e-01
746  3.4420e-01 -2.0041e-04  2.5680e-02  2.1491e+00     3.1624e-02
747  7.0914e-01 -1.1920e-03  1.8334e-01  1.6589e+00     9.7129e-02
748 -7.6487e-02 -5.6029e-04  6.1436e-02 -3.0633e-01     7.5936e-01
749  1.1859e-01 -6.6449e-05  1.0232e-02  1.1731e+00     2.4077e-01
750 -8.0353e-03 -1.9868e-05  2.1798e-03 -1.7168e-01     8.6369e-01
751  8.4291e-01 -2.5835e-03  2.8271e-01  1.5902e+00     1.1180e-01
752  1.2249e-01 -3.6124e-04  6.9603e-02  4.6565e-01     6.4147e-01
753  6.0254e-02 -6.0715e-04  6.6571e-02  2.3588e-01     8.1352e-01
754 -6.1064e-02 -8.3203e-05  1.0663e-02 -5.9055e-01     5.5482e-01
755  5.4543e-03 -1.5384e-07  1.6879e-05  1.3276e+00     1.8430e-01
756  2.2042e+00 -1.2468e-03  1.3661e-01  5.9669e+00     2.4176e-09
757  1.4624e+00 -6.3882e-03  9.7748e-01  1.4856e+00     1.3738e-01
758  1.4254e+00 -4.4019e-03  4.2017e-01  2.2058e+00     2.7401e-02
759  1.7873e+00 -6.7020e-03  7.3036e-01  2.0992e+00     3.5802e-02
760 -1.1477e-01 -2.9456e-05  4.5360e-03 -1.7036e+00     8.8453e-02
761 -3.4257e-01 -7.1640e-04  1.8422e-01 -7.9648e-01     4.2575e-01
762  4.8213e-01 -6.6542e-04  8.5226e-02  1.6538e+00     9.8170e-02
763  1.0412e+00 -1.4014e-03  5.4087e-01  1.4176e+00     1.5631e-01
764  9.9111e-01 -1.1259e-03  1.7320e-01  2.3842e+00     1.7116e-02
765  9.1919e-02 -5.1577e-05  6.6100e-03  1.1312e+00     2.5796e-01
766  1.0843e+00 -1.6277e-03  3.1322e-01  1.9403e+00     5.2346e-02
767  6.9180e-01 -1.2599e-03  1.9378e-01  1.5744e+00     1.1539e-01
768  8.1963e-02 -1.0184e-04  1.1172e-02  7.7642e-01     4.3750e-01
769 -5.1902e-01 -3.9905e-04  7.6885e-02 -1.8704e+00     6.1429e-02
770 -5.5710e-01 -4.8031e-04  6.1529e-02 -2.2440e+00     2.4834e-02
771  1.0395e+01 -1.1260e-02  2.1459e+00  7.1035e+00     1.2159e-12
772 -2.5409e-01 -4.7222e-04  1.8243e-01 -5.9380e-01     5.5265e-01
773 -2.3990e-02 -5.4386e-06  5.2141e-04 -1.0504e+00     2.9354e-01
774 -1.4493e-01 -2.0041e-04  3.8621e-02 -7.3644e-01     4.6146e-01
    nga_wp.shapeName.fips.
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-- append local Moran’s I dataframe

Append local Moran’s I dataframe (i.e.localMI) before mapping the local Moran’s I map.

Show the code

nga_wp.localMI <- cbind(nga_wp,localMI) %>%
  rename(Pr.Ii = Pr.z....E.Ii..)

3.7.1.2 plot local Moran’s I values

Show the code

tm_shape(nga_wp.localMI) +
  tm_fill(col = "Ii", 
          style = "pretty",
          palette = "RdBu",
          title = "local moran statistics") +
  tm_borders(alpha = 0.5)

Variable(s) "Ii" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.

3.7.1.3 plot local Moran’s I p-value

Show the code

tm_shape(nga_wp.localMI) +
  tm_fill(col = "Pr.Ii", 
          breaks=c(-Inf, 0.001, 0.01, 0.05, 0.1, Inf),
          palette="-Blues", 
          title = "Local Moran's I p-value") +
  tm_borders(alpha = 0.5)

Show the code

localMI.map <- tm_shape(nga_wp.localMI) +
  tm_fill(col = "Ii", 
          style = "pretty",
          palette = "RdBu",
          title = "local moran statistics") +
  tm_borders(alpha = 0.5)  +
  tm_layout(legend.height = 0.3, legend.width = 0.3)


pvalue.map <- tm_shape(nga_wp.localMI) +
  tm_fill(col = "Pr.Ii", 
          breaks=c(-Inf, 0.001, 0.01, 0.05, 0.1, Inf),
          palette="-Blues", 
          title = "local Moran's I p-values") +
  tm_borders(alpha = 0.5) +
  tm_layout(legend.height = 0.26, legend.width = 0.3)

tmap_arrange(localMI.map, pvalue.map, asp=1.5, ncol=1)

Variable(s) "Ii" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.

3.8 Creating LISA Cluster Map

Plot the Moran scatterplot before generate the LISA cluster map.

3.8.1 Plot Moran Scatterplot

Use the code chunk below.

The Moran scatterplot is an illustration of the relationship between the values of the chosen attribute at each location and the average value of the same attribute at neighboring locations.

Show the code

nci <- moran.plot(nga_wp$wpt_nonFunctional, ngaWp_rswmQW,
                  labels=as.character(nga_wp$shapeName), 
                  xlab="Non-Functional Water Points", 
                  ylab="Spatially Lag wpt_nonFunctional")

3.8.1.1 plot Moran Scatterplot with Standardised Variable

Show the code

nga_wp$z.wpt_nonFunctional <- scale(nga_wp$wpt_nonFunctional) %>% as.vector 

3.8.1.2 plot Moran Scatterplot

Show the code

nci2 <- moran.plot(nga_wp$z.wpt_nonFunctional, ngaWp_rswmQW,
                   labels=as.character(nga_wp$shapeName),
                   xlab="z-wpt_nonFunctional", 
                   ylab="Spatially Lag z-wpt_nonFunctional")

3.8.2 Prepare LISA Map Classes

Use code chunk below.

Show the code

quadrant <- vector(mode="numeric",length=nrow(localMI))
DV <- nga_wp$wpt_nonFunctional - mean(nga_wp$wpt_nonFunctional)    
C_mI <- localMI[,1] - mean(localMI[,1])    
signif <- 0.05       
quadrant[DV >0 & C_mI>0] <- 4      
quadrant[DV <0 & C_mI<0] <- 1      
quadrant[DV <0 & C_mI>0] <- 2
quadrant[DV >0 & C_mI<0] <- 3
quadrant[localMI[,5]>signif] <- 0

3.8.3 Plot LISA Map

Show the code

nga_wp.localMI$quadrant <- quadrant
colors <- c("#ffffff", "#2c7bb6", "#abd9e9", "#fdae61", "#d7191c")
clusters <- c("insignificant", "low-low", "low-high", "high-low", "high-high")

tm_shape(nga_wp.localMI) +
  tm_fill(col = "quadrant", 
          style = "cat", 
          palette = colors[c(sort(unique(quadrant)))+1], 
          labels = clusters[c(sort(unique(quadrant)))+1],
          popup.vars = c("")) +
  tm_view(set.zoom.limits = c(11,17)) +
  tm_borders(alpha=0.5)

Show the code

wpt_nonFunctional <- qtm(nga_wp, "wpt_nonFunctional") +
  tm_layout(legend.height = 0.28, legend.width = 0.25)

nga_wp.localMI$quadrant <- quadrant 
colors <- c("#ffffff", "#2c7bb6", "#abd9e9", "#fdae61", "#d7191c")
clusters <- c("insignificant", "low-low", "low-high", "high-low", "high-high") 

LISAmap <- tm_shape(nga_wp.localMI) +
  tm_fill(col = "quadrant", 
          style = "cat", 
          palette = colors[c(sort(unique(quadrant)))+1], 
          labels = clusters[c(sort(unique(quadrant)))+1],
          popup.vars = c("")) +
  tm_view(set.zoom.limits = c(11,17)) +
  tm_borders(alpha=0.5) +
  tm_layout(legend.height = 0.35, legend.width = 0.3)

tmap_arrange(wpt_nonFunctional, LISAmap, asp=1.5, ncol=1)

3.9 Hot Spot and Cold Spot Area Analysis

3.9.1 Analyse with Getis and Ord’s G-Statistics

Show the code

k1 <- knn2nb(knearneigh(coords))
k1dists <- unlist(nbdists(k1, coords, longlat = TRUE))
summary(k1dists)

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  13.86   28.12   34.99   36.19   44.54   67.50 

Show the code

upper_threshold <- max(unlist(nbdists(k1, coords, longlat = TRUE)))

Show the code

wm_d39 <- dnearneigh(coords, 0, upper_threshold, longlat = TRUE)
wm_d39

Show the code

wm39_lw <- nb2listw(wm_d39, style = 'B')
summary(wm39_lw)

Show the code

knn <- knn2nb(knearneigh(coords, k=8))
knn

Show the code

knn_lw <- nb2listw(knn, style = 'B')
summary(knn_lw)

3.9.2 Compute Gi Statistics Using Fixed Distance

Show the code

fips <- order(nga_wp$shapeName)
gi.fixed <- localG(nga_wp$wpt_nonFunctional, wm39_lw)
gi.fixed

Show the code

nga_wp.gi <- cbind(nga_wp, as.matrix(gi.fixed)) %>%
  rename(gstat_fixed = as.matrix.gi.fixed.)

Show the code

wpt_nonFunctional <- qtm(nga_wp, "wpt_nonFunctional") +
  tm_layout(legend.height = 0.28, legend.width = 0.25)

Gimap <-tm_shape(nga_wp.gi) +
  tm_fill(col = "gstat_fixed", 
          style = "pretty",
          palette="-RdBu",
          title = "local Gi") +
  tm_borders(alpha = 0.5) +
  tm_layout(legend.height = 0.28, legend.width = 0.25)

tmap_arrange(nga_wp, Gimap, asp=1.5, ncol=1)

3.9.3 Compute Gi Statistics Using Adaptive Distance

Show the code

fips <- order(nga_wp$shapeName)
gi.adaptive <- localG(nga_wp$wpt_nonFunctional, knn_lw)
nga_wp.gi <- cbind(nga_wp, as.matrix(gi.adaptive)) %>%
  rename(gstat_adaptive = as.matrix.gi.adaptive.)

Show the code

wpt_nonFunctional <- qtm(nga_wp, "wpt_nonFunctional") +
  tm_layout(legend.height = 0.28, legend.width = 0.25)

Gimap <- tm_shape(nga_wp.gi) + 
  tm_fill(col = "gstat_adaptive", 
          style = "pretty", 
          palette="-RdBu", 
          title = "local Gi") + 
  tm_borders(alpha = 0.5) + 
  tm_layout(legend.height = 0.28, legend.width = 0.25)

tmap_arrange(wpt_nonFunctional,Gimap,asp=1.5,ncol=1)