[Rcpp-commits] r4220 - in pkg/RcppArmadillo/inst/examples: . kalman
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Sun Jan 20 03:46:15 CET 2013
Author: edd
Date: 2013-01-20 03:46:12 +0100 (Sun, 20 Jan 2013)
New Revision: 4220
Added:
pkg/RcppArmadillo/inst/examples/kalman/
pkg/RcppArmadillo/inst/examples/kalman/FirstKalmanR.R
pkg/RcppArmadillo/inst/examples/kalman/Kalman.cpp
pkg/RcppArmadillo/inst/examples/kalman/KalmanCpp.R
pkg/RcppArmadillo/inst/examples/kalman/KalmanR.R
pkg/RcppArmadillo/inst/examples/kalman/KalmanRimp.R
pkg/RcppArmadillo/inst/examples/kalman/benchmark.R
pkg/RcppArmadillo/inst/examples/kalman/firstExample.R
pkg/RcppArmadillo/inst/examples/kalman/kalmanExample.m
pkg/RcppArmadillo/inst/examples/kalman/kalmanM.m
pkg/RcppArmadillo/inst/examples/kalman/kalmanfilter.m
pkg/RcppArmadillo/inst/examples/kalman/pos.txt
Log:
cleaned up code from vignette / paper
Added: pkg/RcppArmadillo/inst/examples/kalman/FirstKalmanR.R
===================================================================
--- pkg/RcppArmadillo/inst/examples/kalman/FirstKalmanR.R (rev 0)
+++ pkg/RcppArmadillo/inst/examples/kalman/FirstKalmanR.R 2013-01-20 02:46:12 UTC (rev 4220)
@@ -0,0 +1,37 @@
+FirstKalmanR <- function(pos) {
+
+ kalmanfilter <- function(z) {
+ dt <- 1
+ A <- matrix(c( 1, 0, dt, 0, 0, 0, 0, 1, 0, dt, 0, 0, # x, y
+ 0, 0, 1, 0, dt, 0, 0, 0, 0, 1, 0, dt, # Vx, Vy
+ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1), # Ax, Ay
+ 6, 6, byrow=TRUE)
+ H <- matrix( c(1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0),
+ 2, 6, byrow=TRUE)
+ Q <- diag(6)
+ R <- 1000 * diag(2)
+
+ xprd <- A %*% xest # predicted state and covriance
+ pprd <- A %*% pest %*% t(A) + Q
+
+ S <- H %*% t(pprd) %*% t(H) + R # estimation
+ B <- H %*% t(pprd)
+ kalmangain <- t(solve(S, B))
+
+ ## estimated state and covariance, assign to vars in parent env
+ xest <<- xprd + kalmangain %*% (z - H %*% xprd)
+ pest <<- pprd - kalmangain %*% H %*% pprd
+
+ ## compute the estimated measurements
+ y <- H %*% xest
+ }
+ xest <- matrix(0, 6, 1)
+ pest <- matrix(0, 6, 6)
+
+ N <- nrow(pos)
+ y <- matrix(NA, N, 2)
+ for (i in 1:N) {
+ y[i,] <- kalmanfilter(t(pos[i,,drop=FALSE]))
+ }
+ invisible(y)
+}
Added: pkg/RcppArmadillo/inst/examples/kalman/Kalman.cpp
===================================================================
--- pkg/RcppArmadillo/inst/examples/kalman/Kalman.cpp (rev 0)
+++ pkg/RcppArmadillo/inst/examples/kalman/Kalman.cpp 2013-01-20 02:46:12 UTC (rev 4220)
@@ -0,0 +1,46 @@
+using namespace arma;
+
+class Kalman {
+private:
+ mat A, H, Q, R, xest, pest;
+ double dt;
+
+public:
+ // constructor, sets up data structures
+ Kalman() : dt(1.0) {
+ A.eye(6,6);
+ A(0,2) = A(1,3) = A(2,4) = A(3,5) = dt;
+ H.zeros(2,6);
+ H(0,0) = H(1,1) = 1.0;
+ Q.eye(6,6);
+ R = 1000 * eye(2,2);
+ xest.zeros(6,1);
+ pest.zeros(6,6);
+ }
+
+ // sole member function: estimate model
+ mat estimate(const mat & Z) {
+ unsigned int n = Z.n_rows, k = Z.n_cols;
+ mat Y = zeros(n, k);
+ mat xprd, pprd, S, B, kalmangain;
+ colvec z, y;
+
+ for (unsigned int i = 0; i<n; i++) {
+ z = Z.row(i).t();
+ // predicted state and covariance
+ xprd = A * xest;
+ pprd = A * pest * A.t() + Q;
+ // estimation
+ S = H * pprd.t() * H.t() + R;
+ B = H * pprd.t();
+ kalmangain = (solve(S, B)).t();
+ // estimated state and covariance
+ xest = xprd + kalmangain * (z - H * xprd);
+ pest = pprd - kalmangain * H * pprd;
+ // compute the estimated measurements
+ y = H * xest;
+ Y.row(i) = y.t();
+ }
+ return Y;
+ }
+};
Added: pkg/RcppArmadillo/inst/examples/kalman/KalmanCpp.R
===================================================================
--- pkg/RcppArmadillo/inst/examples/kalman/KalmanCpp.R (rev 0)
+++ pkg/RcppArmadillo/inst/examples/kalman/KalmanCpp.R 2013-01-20 02:46:12 UTC (rev 4220)
@@ -0,0 +1,59 @@
+kalmanClass <- '
+using namespace arma;
+
+class Kalman {
+private:
+ mat A, H, Q, R, xest, pest;
+ double dt;
+
+public:
+ // constructor, sets up data structures
+ Kalman() : dt(1.0) {
+ A.eye(6,6);
+ A(0,2) = A(1,3) = A(2,4) = A(3,5) = dt;
+ H.zeros(2,6);
+ H(0,0) = H(1,1) = 1.0;
+ Q.eye(6,6);
+ R = 1000 * eye(2,2);
+ xest.zeros(6,1);
+ pest.zeros(6,6);
+ }
+
+ // sole member function: estimate model
+ mat estimate(const mat & Z) {
+ unsigned int n = Z.n_rows, k = Z.n_cols;
+ mat Y = zeros(n, k);
+ mat xprd, pprd, S, B, kalmangain;
+ colvec z, y;
+
+ for (unsigned int i = 0; i<n; i++) {
+ z = Z.row(i).t();
+ // predicted state and covariance
+ xprd = A * xest;
+ pprd = A * pest * A.t() + Q;
+ // estimation
+ S = H * pprd.t() * H.t() + R;
+ B = H * pprd.t();
+ kalmangain = (solve(S, B)).t();
+ // estimated state and covariance
+ xest = xprd + kalmangain * (z - H * xprd);
+ pest = pprd - kalmangain * H * pprd;
+ // compute the estimated measurements
+ y = H * xest;
+ Y.row(i) = y.t();
+ }
+ return Y;
+ }
+};
+'
+
+suppressMessages(library(inline))
+kalmanSrc <- '
+ mat Z = as<mat>(ZS); // passed from R
+ Kalman K;
+ mat Y = K.estimate(Z);
+ return wrap(Y);'
+
+KalmanCpp <- cxxfunction(signature(ZS="numeric"),
+ body=kalmanSrc, include=kalmanClass,
+ plugin="RcppArmadillo")
Added: pkg/RcppArmadillo/inst/examples/kalman/KalmanR.R
===================================================================
--- pkg/RcppArmadillo/inst/examples/kalman/KalmanR.R (rev 0)
+++ pkg/RcppArmadillo/inst/examples/kalman/KalmanR.R 2013-01-20 02:46:12 UTC (rev 4220)
@@ -0,0 +1,46 @@
+KalmanR <- function(pos) {
+
+ kalmanfilter <- function(z) {
+ ## predicted state and covariance
+ xprd <- A %*% xest
+ pprd <- A %*% pest %*% t(A) + Q
+
+ ## estimation
+ S <- H %*% t(pprd) %*% t(H) + R
+ B <- H %*% t(pprd)
+
+ kalmangain <- t(solve(S, B))
+
+ ## estimated state and covariance
+ ## assigned to vars in parent env
+ xest <<- xprd + kalmangain %*% (z - H %*% xprd)
+ pest <<- pprd - kalmangain %*% H %*% pprd
+
+ ## compute the estimated measurements
+ y <- H %*% xest
+ }
+
+ dt <- 1
+ A <- matrix( c( 1, 0, dt, 0, 0, 0, # x
+ 0, 1, 0, dt, 0, 0, # y
+ 0, 0, 1, 0, dt, 0, # Vx
+ 0, 0, 0, 1, 0, dt, # Vy
+ 0, 0, 0, 0, 1, 0, # Ax
+ 0, 0, 0, 0, 0, 1), # Ay
+ 6, 6, byrow=TRUE)
+ H <- matrix( c(1, 0, 0, 0, 0, 0,
+ 0, 1, 0, 0, 0, 0),
+ 2, 6, byrow=TRUE)
+ Q <- diag(6)
+ R <- 1000 * diag(2)
+ N <- nrow(pos)
+ Y <- matrix(NA, N, 2)
+
+ xest <- matrix(0, 6, 1)
+ pest <- matrix(0, 6, 6)
+
+ for (i in 1:N) {
+ Y[i,] <- kalmanfilter(t(pos[i,,drop=FALSE]))
+ }
+ invisible(Y)
+}
Added: pkg/RcppArmadillo/inst/examples/kalman/KalmanRimp.R
===================================================================
--- pkg/RcppArmadillo/inst/examples/kalman/KalmanRimp.R (rev 0)
+++ pkg/RcppArmadillo/inst/examples/kalman/KalmanRimp.R 2013-01-20 02:46:12 UTC (rev 4220)
@@ -0,0 +1,49 @@
+## Improved version supplied by one referee, not shown in paper
+KalmanRimp <- function(pos) {
+
+ kalmanfilter <- function(z) {
+ ## predicted state and covriance
+ xprd <- xest %*% A
+ pprd <- crossprod(pest %*% A, A) + Q
+
+ ## estimation
+ B <- crossprod(H, pprd)
+ S <- B %*% H + R
+
+ ## kalmangain <- (S \ B)'
+ kalmangain <- solve(S, B)
+
+ ## estimated state and covariance, assign to vars in parent env
+ xest <<- xprd + (z - xprd %*% H) %*% kalmangain
+ pest <<- pprd - pprd %*% H %*% kalmangain
+
+ ## compute the estimated measurements
+ y <- xest %*% H
+ }
+
+ dt <- 1
+ A <- matrix( c( 1, 0, dt, 0, 0, 0, # x
+ 0, 1, 0, dt, 0, 0, # y
+ 0, 0, 1, 0, dt, 0, # Vx
+ 0, 0, 0, 1, 0, dt, # Vy
+ 0, 0, 0, 0, 1, 0, # Ax
+ 0, 0, 0, 0, 0, 1), # Ay
+ 6, 6, byrow=FALSE)
+ H <- matrix( c(1, 0, 0, 0, 0, 0,
+ 0, 1, 0, 0, 0, 0),
+ 6, 2, byrow=FALSE)
+ Q <- diag(6)
+ R <- 1000 * diag(2)
+
+ N <- nrow(pos)
+ y <- matrix(NA, N, 2)
+
+ xest <- matrix(0, 1, 6)
+ pest <- matrix(0, 6, 6)
+
+ for (i in 1:N) {
+ y[i,] <- kalmanfilter(pos[i,,drop=FALSE])
+ }
+
+ invisible(y)
+}
Added: pkg/RcppArmadillo/inst/examples/kalman/benchmark.R
===================================================================
--- pkg/RcppArmadillo/inst/examples/kalman/benchmark.R (rev 0)
+++ pkg/RcppArmadillo/inst/examples/kalman/benchmark.R 2013-01-20 02:46:12 UTC (rev 4220)
@@ -0,0 +1,35 @@
+
+suppressMessages(library(Rcpp))
+suppressMessages(library(inline))
+suppressMessages(library(rbenchmark))
+suppressMessages(library(compiler))
+
+source("FirstKalmanR.R")
+source("KalmanR.R")
+source("KalmanRimp.R")
+source("KalmanCpp.R")
+
+FirstKalmanRC <- cmpfun(FirstKalmanR)
+KalmanRC <- cmpfun(KalmanR)
+KalmanRimpC <- cmpfun(KalmanRimp)
+
+## Read data, ensure identical results
+pos <- as.matrix(read.table("pos.txt", header=FALSE,
+ col.names=c("x","y")))
+stopifnot(all.equal(KalmanR(pos), KalmanRC(pos)),
+ all.equal(KalmanRC(pos), KalmanCpp(pos)),
+ all.equal(KalmanCpp(pos), FirstKalmanRC(pos)),
+ all.equal(KalmanCpp(pos), FirstKalmanR(pos)),
+ all.equal(KalmanCpp(pos), KalmanRimp(pos)),
+ all.equal(KalmanCpp(pos), KalmanRimpC(pos)))
+
+res <- benchmark(KalmanR(pos), KalmanRC(pos),
+ KalmanRimp(pos), KalmanRimpC(pos),
+ FirstKalmanR(pos), FirstKalmanRC(pos),
+ KalmanCpp(pos),
+ columns = c("test", "replications",
+ "elapsed", "relative"),
+ order="relative",
+ replications=500)
+
+print(res[,1:4])
Added: pkg/RcppArmadillo/inst/examples/kalman/firstExample.R
===================================================================
--- pkg/RcppArmadillo/inst/examples/kalman/firstExample.R (rev 0)
+++ pkg/RcppArmadillo/inst/examples/kalman/firstExample.R 2013-01-20 02:46:12 UTC (rev 4220)
@@ -0,0 +1,12 @@
+
+library(inline)
+
+g <- cxxfunction(signature(vs="numeric"), plugin="RcppArmadillo", body='
+ arma::colvec v = Rcpp::as<arma::colvec>(vs);
+ arma::mat op = v * v.t();
+ double ip = arma::as_scalar(v.t() * v);
+ return Rcpp::List::create(Rcpp::Named("outer")=op,
+ Rcpp::Named("inner")=ip);
+')
+
+g(7:11)
Added: pkg/RcppArmadillo/inst/examples/kalman/kalmanExample.m
===================================================================
--- pkg/RcppArmadillo/inst/examples/kalman/kalmanExample.m (rev 0)
+++ pkg/RcppArmadillo/inst/examples/kalman/kalmanExample.m 2013-01-20 02:46:12 UTC (rev 4220)
@@ -0,0 +1,4 @@
+function x = kalmanExample
+ load pos.txt; # renamed here
+ x = kalmanM(pos);
+end
\ No newline at end of file
Added: pkg/RcppArmadillo/inst/examples/kalman/kalmanM.m
===================================================================
--- pkg/RcppArmadillo/inst/examples/kalman/kalmanM.m (rev 0)
+++ pkg/RcppArmadillo/inst/examples/kalman/kalmanM.m 2013-01-20 02:46:12 UTC (rev 4220)
@@ -0,0 +1,36 @@
+function Y = kalmanM(pos)
+ dt=1;
+ %% Initialize state transition matrix
+ A=[ 1 0 dt 0 0 0;... % [x ]
+ 0 1 0 dt 0 0;... % [y ]
+ 0 0 1 0 dt 0;... % [Vx]
+ 0 0 0 1 0 dt;... % [Vy]
+ 0 0 0 0 1 0 ;... % [Ax]
+ 0 0 0 0 0 1 ]; % [Ay]
+ H = [ 1 0 0 0 0 0; 0 1 0 0 0 0 ]; % Initialize measurement matrix
+ Q = eye(6);
+ R = 1000 * eye(2);
+ x_est = zeros(6, 1); % x_est=[x,y,Vx,Vy,Ax,Ay]'
+ p_est = zeros(6, 6);
+
+ numPts = size(pos,1);
+ Y = zeros(numPts, 2);
+
+ for idx = 1:numPts
+ z = pos(idx, :)';
+
+ %% Predicted state and covariance
+ x_prd = A * x_est;
+ p_prd = A * p_est * A' + Q;
+ %% Estimation
+ S = H * p_prd' * H' + R;
+ B = H * p_prd';
+ klm_gain = (S \ B)';
+ %% Estimated state and covariance
+ x_est = x_prd + klm_gain * (z - H * x_prd);
+ p_est = p_prd - klm_gain * H * p_prd;
+ %% Compute the estimated measurements
+ Y(idx, :) = H * x_est;
+ end % of the function
+
+end % of the function
Added: pkg/RcppArmadillo/inst/examples/kalman/kalmanfilter.m
===================================================================
--- pkg/RcppArmadillo/inst/examples/kalman/kalmanfilter.m (rev 0)
+++ pkg/RcppArmadillo/inst/examples/kalman/kalmanfilter.m 2013-01-20 02:46:12 UTC (rev 4220)
@@ -0,0 +1,28 @@
+% Copyright 2010 The MathWorks, Inc.
+function y = kalmanfilter(z)
+ dt=1;
+ % Initialize state transition matrix
+ A=[ 1 0 dt 0 0 0; 0 1 0 dt 0 0;... % [x ], [y ]
+ 0 0 1 0 dt 0; 0 0 0 1 0 dt;... % [Vx], [Vy]
+ 0 0 0 0 1 0 ; 0 0 0 0 0 1 ]; % [Ax], [Ay]
+ H = [ 1 0 0 0 0 0; 0 1 0 0 0 0 ]; % Init. measuremnt mat
+ Q = eye(6);
+ R = 1000 * eye(2);
+ persistent x_est p_est % Init. state cond.
+ if isempty(x_est)
+ x_est = zeros(6, 1); % x_est=[x,y,Vx,Vy,Ax,Ay]'
+ p_est = zeros(6, 6);
+ end
+
+ x_prd = A * x_est; % Predicted state and covariance
+ p_prd = A * p_est * A' + Q;
+
+ S = H * p_prd' * H' + R; % Estimation
+ B = H * p_prd';
+ klm_gain = (S \ B)';
+
+ % Estimated state and covariance
+ x_est = x_prd + klm_gain * (z - H * x_prd);
+ p_est = p_prd - klm_gain * H * p_prd;
+ y = H * x_est; % Compute the estimated measurements
+end % of the function
Added: pkg/RcppArmadillo/inst/examples/kalman/pos.txt
===================================================================
--- pkg/RcppArmadillo/inst/examples/kalman/pos.txt (rev 0)
+++ pkg/RcppArmadillo/inst/examples/kalman/pos.txt 2013-01-20 02:46:12 UTC (rev 4220)
@@ -0,0 +1,310 @@
+ -4.76074274e-01 8.27344982e-01
+ -4.66073333e-01 8.25346801e-01
+ -4.56071632e-01 8.21349631e-01
+ -4.46068539e-01 8.15353570e-01
+ -4.36063422e-01 8.07358714e-01
+ -4.26055649e-01 7.97365162e-01
+ -4.16044587e-01 7.85373011e-01
+ -4.06029604e-01 7.71382359e-01
+ -3.96010067e-01 7.55393303e-01
+ -3.85985344e-01 7.37405941e-01
+ -3.75954804e-01 7.17420370e-01
+ -3.65917812e-01 6.95436687e-01
+ -3.55873738e-01 6.71454991e-01
+ -3.45821948e-01 6.45475379e-01
+ -3.35761811e-01 6.17497948e-01
+ -3.25692694e-01 5.87522796e-01
+ -3.15613964e-01 5.55550021e-01
+ -3.05524990e-01 5.21579720e-01
+ -2.95425138e-01 4.85611990e-01
+ -2.85313778e-01 4.47646929e-01
+ -2.75190275e-01 4.07684635e-01
+ -2.65053998e-01 3.65725205e-01
+ -2.54904315e-01 3.21768737e-01
+ -2.44740592e-01 2.75815328e-01
+ -2.34562199e-01 2.27865076e-01
+ -2.24368501e-01 1.77918079e-01
+ -2.14158868e-01 1.25974433e-01
+ -2.03932667e-01 7.20342366e-02
+ -1.93689265e-01 1.60975872e-02
+ -1.83428030e-01 -4.18354177e-02
+ -1.73148329e-01 -1.01764681e-01
+ -1.62849531e-01 -1.63690104e-01
+ -1.52531002e-01 -2.27611590e-01
+ -1.42192111e-01 -2.93529041e-01
+ -1.31832225e-01 -3.61442361e-01
+ -1.21450712e-01 -4.31351450e-01
+ -1.11046940e-01 -5.03256212e-01
+ -1.00620275e-01 -5.77156550e-01
+ -9.01700865e-02 -6.53052365e-01
+ -7.96957410e-02 -7.30943560e-01
+ -6.91966066e-02 -8.10830038e-01
+ -5.86720509e-02 -8.92711700e-01
+ -4.81214414e-02 -9.68723398e-01
+ -3.75441458e-02 -8.82849846e-01
+ -2.69395318e-02 -7.98971187e-01
+ -1.63069671e-02 -7.17087322e-01
+ -5.64581912e-03 -6.37198155e-01
+ 5.04454433e-03 -5.59303588e-01
+ 1.57647557e-02 -4.83403523e-01
+ 2.65154472e-02 -4.09497862e-01
+ 3.72972513e-02 -3.37586509e-01
+ 4.81108004e-02 -2.67669365e-01
+ 5.89567268e-02 -1.99746334e-01
+ 6.98356629e-02 -1.33817317e-01
+ 8.07482410e-02 -6.98822165e-02
+ 9.16950935e-02 -7.94093586e-03
+ 1.02676853e-01 5.20066229e-02
+ 1.13694151e-01 1.09960557e-01
+ 1.24747621e-01 1.65920965e-01
+ 1.35837894e-01 2.19887943e-01
+ 1.46965604e-01 2.71861590e-01
+ 1.58131383e-01 3.21842002e-01
+ 1.69335862e-01 3.69829278e-01
+ 1.80579674e-01 4.15823514e-01
+ 1.91863452e-01 4.59824809e-01
+ 2.03187829e-01 5.01833260e-01
+ 2.14553435e-01 5.41848965e-01
+ 2.25960904e-01 5.79872020e-01
+ 2.37410868e-01 6.15902524e-01
+ 2.48903960e-01 6.49940575e-01
+ 2.60440811e-01 6.81986269e-01
+ 2.72022055e-01 7.12039704e-01
+ 2.83648323e-01 7.40100978e-01
+ 2.95320248e-01 7.66170188e-01
+ 3.07038462e-01 7.90247432e-01
+ 3.18803597e-01 8.12332807e-01
+ 3.30616287e-01 8.32426411e-01
+ 3.42477163e-01 8.50528342e-01
+ 3.54386857e-01 8.66638696e-01
+ 3.66346003e-01 8.80757573e-01
+ 3.78355232e-01 8.92885068e-01
+ 3.90415176e-01 9.03021280e-01
+ 4.02526469e-01 9.11166306e-01
+ 4.14689742e-01 9.17320243e-01
+ 4.26905628e-01 9.21483190e-01
+ 4.39174759e-01 9.23655244e-01
+ 4.51497768e-01 9.23836502e-01
+ 4.63875286e-01 9.22027062e-01
+ 4.76307947e-01 9.18227021e-01
+ 4.88796383e-01 9.12436477e-01
+ 5.01341225e-01 9.04655528e-01
+ 5.13943106e-01 8.94884271e-01
+ 5.26602660e-01 8.83122803e-01
+ 5.39320517e-01 8.69371222e-01
+ 5.52097311e-01 8.53629626e-01
+ 5.64933673e-01 8.35898112e-01
+ 5.77830237e-01 8.16176778e-01
+ 5.90787634e-01 7.94465721e-01
+ 6.03806497e-01 7.70765039e-01
+ 6.16887458e-01 7.45074829e-01
+ 6.16887458e-01 7.45074829e-01
+ 2.43647025e-01 3.48142367e-01
+ -1.29593408e-01 -4.87900946e-02
+ -5.02833841e-01 -4.45722556e-01
+ -8.76074274e-01 -8.42655018e-01
+ -8.76074274e-01 -8.42655018e-01
+ -8.66073333e-01 -8.14653199e-01
+ -8.56071632e-01 -7.88650369e-01
+ -8.46068539e-01 -7.64646430e-01
+ -8.36063422e-01 -7.42641286e-01
+ -8.26055649e-01 -7.22634838e-01
+ -8.16044587e-01 -7.04626989e-01
+ -8.06029604e-01 -6.88617641e-01
+ -7.96010067e-01 -6.74606697e-01
+ -7.85985344e-01 -6.62594059e-01
+ -7.75954804e-01 -6.52579630e-01
+ -7.65917812e-01 -6.44563313e-01
+ -7.55873738e-01 -6.38545009e-01
+ -7.45821948e-01 -6.34524621e-01
+ -7.35761811e-01 -6.32502052e-01
+ -7.25692694e-01 -6.32477204e-01
+ -7.15613964e-01 -6.34449979e-01
+ -7.05524990e-01 -6.38420280e-01
+ -6.95425138e-01 -6.44388010e-01
+ -6.85313778e-01 -6.52353071e-01
+ -6.75190275e-01 -6.62315365e-01
+ -6.65053998e-01 -6.74274795e-01
+ -6.54904315e-01 -6.88231263e-01
+ -6.44740592e-01 -7.04184672e-01
+ -6.34562199e-01 -7.22134924e-01
+ -6.24368501e-01 -7.42081921e-01
+ -6.14158868e-01 -7.64025567e-01
+ -6.03932667e-01 -7.87965763e-01
+ -5.93689265e-01 -8.13902413e-01
+ -5.83428030e-01 -8.41835418e-01
+ -5.73148329e-01 -8.71764681e-01
+ -5.62849531e-01 -9.03690104e-01
+ -5.52531002e-01 -9.37611590e-01
+ -5.42192111e-01 -9.71782807e-01
+ -5.31832225e-01 -9.33867676e-01
+ -5.21450712e-01 -8.97948315e-01
+ -5.11046940e-01 -8.64024627e-01
+ -5.00620275e-01 -8.32096515e-01
+ -4.90170086e-01 -8.02163879e-01
+ -4.79695741e-01 -7.74226624e-01
+ -4.69196607e-01 -7.48284652e-01
+ -4.58672051e-01 -7.24337865e-01
+ -4.48121441e-01 -7.02386165e-01
+ -4.37544146e-01 -6.82429455e-01
+ -4.26939532e-01 -6.64467637e-01
+ -4.16306967e-01 -6.48500614e-01
+ -4.05645819e-01 -6.34528289e-01
+ -3.94955456e-01 -6.22550563e-01
+ -3.84235244e-01 -6.12567339e-01
+ -3.73484553e-01 -6.04578520e-01
+ -3.62702749e-01 -5.98584009e-01
+ -3.51889200e-01 -5.94583707e-01
+ -3.41043273e-01 -5.92577517e-01
+ -3.30164337e-01 -5.92565341e-01
+ -3.19251759e-01 -5.94547083e-01
+ -3.08304907e-01 -5.98522644e-01
+ -2.97323147e-01 -6.04491926e-01
+ -2.86305849e-01 -6.12454834e-01
+ -2.75252379e-01 -6.22411268e-01
+ -2.64162106e-01 -6.34361131e-01
+ -2.53034396e-01 -6.48304326e-01
+ -2.41868617e-01 -6.64240755e-01
+ -2.30664138e-01 -6.82170321e-01
+ -2.19420326e-01 -7.02092926e-01
+ -2.08136548e-01 -7.24008473e-01
+ -1.96812171e-01 -7.47916863e-01
+ -1.85446565e-01 -7.73818000e-01
+ -1.74039096e-01 -8.01711787e-01
+ -1.62589132e-01 -8.31598124e-01
+ -1.51096040e-01 -8.63476915e-01
+ -1.39559189e-01 -8.97348063e-01
+ -1.27977945e-01 -9.33211470e-01
+ -1.16351677e-01 -9.71067037e-01
+ -1.04679752e-01 -9.34397179e-01
+ -9.29615383e-02 -8.92555770e-01
+ -8.11964026e-02 -8.52706229e-01
+ -6.93837130e-02 -8.14848460e-01
+ -5.75228372e-02 -7.78982364e-01
+ -4.56131427e-02 -7.45107844e-01
+ -3.36539972e-02 -7.13224802e-01
+ -2.16447683e-02 -6.83333142e-01
+ -9.58482365e-03 -6.55432765e-01
+ 2.52646905e-03 -6.29523574e-01
+ 1.46897422e-02 -6.05605471e-01
+ 2.69056281e-02 -5.83678358e-01
+ 3.91747593e-02 -5.63742139e-01
+ 5.14977679e-02 -5.45796716e-01
+ 6.38752864e-02 -5.29841991e-01
+ 7.63079472e-02 -5.15877866e-01
+ 8.87963825e-02 -5.03904245e-01
+ 1.01341225e-01 -4.93921029e-01
+ 1.13943106e-01 -4.85928121e-01
+ 1.26602660e-01 -4.79925423e-01
+ 1.39320517e-01 -4.75912839e-01
+ 1.52097311e-01 -4.73890270e-01
+ 1.64933673e-01 -4.73857618e-01
+ 1.77830237e-01 -4.75814787e-01
+ 1.90787634e-01 -4.79761679e-01
+ 2.03806497e-01 -4.85698196e-01
+ 2.16887458e-01 -4.93624240e-01
+ 2.16887458e-01 -4.93624240e-01
+ 4.01147025e-01 -1.33381935e-01
+ 5.85406592e-01 2.26860371e-01
+ 7.69666159e-01 5.87102676e-01
+ 9.53925726e-01 9.47344982e-01
+ 9.53925726e-01 9.47344982e-01
+ 9.43926667e-01 9.15346801e-01
+ 9.33928368e-01 8.81349631e-01
+ 9.23931461e-01 8.45353570e-01
+ 9.13936578e-01 8.07358714e-01
+ 9.03944351e-01 7.67365162e-01
+ 8.93955413e-01 7.25373011e-01
+ 8.83970396e-01 6.81382359e-01
+ 8.73989933e-01 6.35393303e-01
+ 8.64014656e-01 5.87405941e-01
+ 8.54045196e-01 5.37420370e-01
+ 8.44082188e-01 4.85436687e-01
+ 8.34126262e-01 4.31454991e-01
+ 8.24178052e-01 3.75475379e-01
+ 8.14238189e-01 3.17497948e-01
+ 8.04307306e-01 2.57522796e-01
+ 7.94386036e-01 1.95550021e-01
+ 7.84475010e-01 1.31579720e-01
+ 7.74574862e-01 6.56119899e-02
+ 7.64686222e-01 -2.35307073e-03
+ 7.54809725e-01 -7.23153647e-02
+ 7.44946002e-01 -1.44274795e-01
+ 7.35095685e-01 -2.18231263e-01
+ 7.25259408e-01 -2.94184672e-01
+ 7.15437801e-01 -3.72134924e-01
+ 7.05631499e-01 -4.52081921e-01
+ 6.95841132e-01 -5.34025567e-01
+ 6.86067333e-01 -6.17965763e-01
+ 6.76310735e-01 -7.03902413e-01
+ 6.66571970e-01 -7.91835418e-01
+ 6.56851671e-01 -8.81764681e-01
+ 6.47150469e-01 -9.71621744e-01
+ 6.37468998e-01 -8.77698446e-01
+ 6.27807889e-01 -7.85771114e-01
+ 6.18167775e-01 -6.95839649e-01
+ 6.08549288e-01 -6.07903955e-01
+ 5.98953060e-01 -5.21963934e-01
+ 5.89379725e-01 -4.38019487e-01
+ 5.79829914e-01 -3.56070518e-01
+ 5.70304259e-01 -2.76116929e-01
+ 5.60803393e-01 -1.98158623e-01
+ 5.51327949e-01 -1.22195502e-01
+ 5.41878559e-01 -4.82274683e-02
+ 5.32455854e-01 2.37455755e-02
+ 5.23060468e-01 9.37237269e-02
+ 5.13693033e-01 1.61707083e-01
+ 5.04354181e-01 2.27695743e-01
+ 4.95044544e-01 2.91689802e-01
+ 4.85764756e-01 3.53689360e-01
+ 4.76515447e-01 4.13694512e-01
+ 4.67297251e-01 4.71705358e-01
+ 4.58110800e-01 5.27721993e-01
+ 4.48956727e-01 5.81744517e-01
+ 4.39835663e-01 6.33773026e-01
+ 4.30748241e-01 6.83807619e-01
+ 4.21695093e-01 7.31848392e-01
+ 4.12676853e-01 7.77895442e-01
+ 4.03694151e-01 8.21948869e-01
+ 3.94747621e-01 8.64008769e-01
+ 3.85837894e-01 9.04075239e-01
+ 3.76965604e-01 9.42148378e-01
+ 3.68131383e-01 9.78228282e-01
+ 3.59335862e-01 1.01231505e+00
+ 3.50579674e-01 1.01027937e+00
+ 3.41863452e-01 9.80180397e-01
+ 3.33187829e-01 9.48088578e-01
+ 3.24553435e-01 9.14004012e-01
+ 3.15960904e-01 8.77926796e-01
+ 3.07410868e-01 8.39857030e-01
+ 2.98903960e-01 7.99794810e-01
+ 2.90440811e-01 7.57740233e-01
+ 2.82022055e-01 7.13693397e-01
+ 2.73648323e-01 6.67654401e-01
+ 2.65320248e-01 6.19623340e-01
+ 2.57038462e-01 5.69600313e-01
+ 2.48803597e-01 5.17585418e-01
+ 2.40616287e-01 4.63578752e-01
+ 2.32477163e-01 4.07580412e-01
+ 2.24386857e-01 3.49590496e-01
+ 2.16346003e-01 2.89609102e-01
+ 2.08355232e-01 2.27636326e-01
+ 2.00415176e-01 1.63672267e-01
+ 1.92526469e-01 9.77170229e-02
+ 1.84689742e-01 2.97706900e-02
+ 1.76905628e-01 -4.01666337e-02
+ 1.69174759e-01 -1.12094851e-01
+ 1.61497768e-01 -1.86013863e-01
+ 1.53875286e-01 -2.61923574e-01
+ 1.46307947e-01 -3.39823885e-01
+ 1.38796383e-01 -4.19714700e-01
+ 1.31341225e-01 -5.01595920e-01
+ 1.23943106e-01 -5.85467448e-01
+ 1.16602660e-01 -6.71329186e-01
+ 1.09320517e-01 -7.59181037e-01
+ 1.02097311e-01 -8.49022904e-01
+ 9.49336734e-02 -9.40854688e-01
+ 8.78302370e-02 -9.10635555e-01
+ 8.07876341e-02 -8.14822416e-01
+ 7.38064970e-02 -7.20998902e-01
+ 6.68874582e-02 -6.29164916e-01
More information about the Rcpp-commits
mailing list