### Add source code of examples and make GitLab happy with a LICENSE file

parent 7b8b9dbd
 ^.*\.Rproj\$ ^\.Rproj\.user\$ R/RcppExports.R LICENSE examples.r
LICENSE 0 → 120000
 GPL-2 \ No newline at end of file
examples.r 0 → 100644
 library("Langevin") # Load library used for plotting library("plotrix") # Set the number of bins to estimate drift and diffusion on bins <- 40 # Set the time lags for computing the conditional moments steps <- c(1:3) # Set the sampling frequency sf <- 1000 ########################################## # One dimensional example ########################################## # Generate the time series set.seed(4711) Ux <- timeseries1D(N = 1e7, d11 = 1, d13 = -1, d22 = 1, d20 = 1, sf = sf) # Plot time series and probability density function (PDF) par(mar = c(4.2, 5.4, 0.5, 0.5)) layout(matrix(c(1, 1, 2), 1, 3)) plot((1:1e5)/sf, Ux[1:1e5], xlab = "t [s]", ylab = "x [a.u.]", t = 'l') plot(density(Ux), xlab = "x [a.u.]", ylab = "density", t = 'l',main = "") # Esitmate drift and diffusion coefficients ests <- Langevin1D(Ux, bins, steps) attach(ests) # Plot drift and diffusion coefficients with errors and theoretical expecations # for comparison par(mar = c(4.2, 5.4, 0.5, 0.5)) par(mfrow = c(1, 2)) plotCI(mean_bin, D1, uiw = eD1, xlab = "x [a.u.]", ylab = expression(paste("Drift coefficient ", D^(1), "(x) [",1/s,"]")), pch = 20) lines(mean_bin, mean_bin - mean_bin^3, col = 'red', lty = 2) plotCI(mean_bin, D2, uiw = eD2, xlab = "x [a.u.]", ylab = expression(paste("Diffusion coefficient ", D^(2), "(x) [",1/s^2,"]")), pch = 20) lines(mean_bin, mean_bin^2 + 1, col = 'red', lty = 2) # Fit polynomials to the estimated drift and diffusion coefficients estD1 <- coef(lm(D1 ~ mean_bin + I(mean_bin^2) + I(mean_bin^3), weights = 1/eD1)) estD2 <- coef(lm(D2 ~ mean_bin + I(mean_bin^2), weights = 1/eD2)) # Generate a time series from the reconstructed coefficients set.seed(5048); rec_x <- timeseries1D(N = 1e7, d10 = estD1, d11 = estD1, d12 = estD1, d13 = estD1, d20 = estD2, d21 = estD2, d22 = estD2, sf = sf) # Compute and plot the increment PDFs for the original and the reconstructed # time series for four different time lags par(mar = c(4.2, 5.4, 0.5, 0.5)) par(mfrow = c(1, 1)); plot(1, 1, log = "y", type = "n", xlim = c(-11, 12), ylim = c(1e-8, 5), xlab = expression(Delta[tau]/sigma[Delta[tau]]), ylab = "density") tau <- c(1, 10, 100, 1000) for(i in 1:4) { delta <- diff(Ux, lag = tau[i]) rec_delta <- diff(rec_x, lag = tau[i]) den <- density(delta) den\$x <- den\$x/sd(delta, na.rm = TRUE) rec_den <- density(rec_delta) rec_den\$x <- rec_den\$x/sd(rec_delta, na.rm = TRUE) lines(den, col = i) lines(rec_den, lty = 2, col = i) } ########################################## # Two dimensional example ########################################## # Construct the drift matrices D1_1 <- matrix(0, nrow = 4,ncol = 4) D1_1[1, 2] = 1 D1_2 <- matrix(0, nrow = 4,ncol = 4) D1_2[2, 1] = 0.02 D1_2[4, 1] = -1 D1_2[1, 2] = 0.03 D1_2[3, 2] = -1 # Construct the diffusion matrices g_11 <- matrix(0, nrow = 3, ncol = 3) g_12 <- matrix(0, nrow = 3, ncol = 3) g_21 <- matrix(0, nrow = 3, ncol = 3) g_22 <- matrix(0, nrow = 3, ncol = 3) # Generate the time series without noise (only for plotting) set.seed(4711) Ux1 <- timeseries2D(N = 1e6, 0.145, 0.0002, D1_1, D1_2, g_11, g_12, g_21, g_22, sf = sf) # Add the noise g_11[1, 1] <- 0.0025 g_22[1, 1] <- 0.0025 # Generate time series with added noise set.seed(4711) Ux <- timeseries2D(N = 1e8, 0.145, 0.0002, D1_1, D1_2, g_11, g_12, g_21, g_22, sf = sf) # Plot trajectories of the time series without and with noise par(mar = c(4.2, 5.4, 0.5, 0.5)) par(mfrow = c(1, 2)) plot(Ux1[1:1e6, 1], Ux1[1:1e6, 2], xlab = expression(paste(X," [a.u.]")), ylab = expression(paste(X," [a.u.]")), t = 'l') plot(Ux[1:1e5, 1], Ux[1:1e5, 2], xlab = expression(paste(X," [a.u.]")), ylab = expression(paste(X," [a.u.]")), t = 'l') # Estimate drift and diffusion coefficients ests <- Langevin2D(Ux, bins, steps) attach(ests) # Compute the mids of the bins for plotting bin_mids <- matrix(NA, nrow = 40, ncol = 2) bin_mids[,1] <- U[1:40, 1] + diff(U[,1])/2 bin_mids[,2] <- U[1:40, 2] + diff(U[,2])/2 # Plot drift and diffusion coefficients par(mar = c(4.2, 5.4, 0.5, 0.5)) layout(matrix(c(1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5), 2, 6, byrow = TRUE)) pmat <- perspx(x = bin_mids[,1], y = bin_mids[,2], z = D1[,,1], xlab = "", ylab = "", zlab = "", ticktype = "detailed", theta = 30, main = "") attr(pmat, "ranges") <- list(x = range(bin_mids[,1]), y = range(bin_mids[,2]), z = range(D1[,,1], na.rm = TRUE)) mtext3d("X", pmat, expression(X)) mpos<-plotrix:::get_axispos3d("Y", pmat, at = 0, dist = .3) mpos[1,] <- -mpos[1,] ptext3d(mpos[1,], mpos[2,], mpos[3,], pmat = pmat, xpd = NA, texts = expression(X)) mtext3d("Z", pmat, expression(D[x]^(1)), at = 0) pmat <- perspx(x = bin_mids[,1], y = bin_mids[,2], z = D1[,,2], xlab = "", ylab = "", zlab = "", ticktype = "detailed", theta = 30, main = "") attr(pmat, "ranges") <- list(x = range(bin_mids[,1]), y = range(bin_mids[,2]), z = range(D1[,,2], na.rm = TRUE)) mtext3d("X", pmat, expression(X)) mpos<-plotrix:::get_axispos3d("Y", pmat, at = 0, dist = .3) mpos[1,] <- -mpos[1,] ptext3d(mpos[1,], mpos[2,], mpos[3,], pmat = pmat, xpd = NA, texts = expression(X)); mtext3d("Z", pmat, expression(D[y]^(1)), at = 0) pmat <- perspx(x = bin_mids[,1], y = bin_mids[,2], z = D2[,,1], xlab = "", ylab = "", zlab = "", ticktype = "detailed", theta = 30, main = "") attr(pmat, "ranges") <- list(x = range(bin_mids[,1]), y = range(bin_mids[,2]), z = range(D2[,,1], na.rm = TRUE)) mtext3d("X", pmat, expression(X)) mpos<-plotrix:::get_axispos3d("Y", pmat, at = 0, dist = .3) mpos[1,] <- -mpos[1,] ptext3d(mpos[1,], mpos[2,], mpos[3,], pmat = pmat, xpd = NA, texts = expression(X)); mtext3d("Z", pmat, expression(D[xx]^(2)), at = 0.0025) pmat <- perspx(x = bin_mids[,1], y = bin_mids[,2], z = D2[,,3], xlab = "", ylab = "", zlab = "", ticktype = "detailed", theta = 30, main = "") attr(pmat, "ranges") <- list(x = range(bin_mids[,1]), y = range(bin_mids[,2]), z = range(D2[,,3], na.rm = TRUE)) mtext3d("X", pmat, expression(X)) mpos<-plotrix:::get_axispos3d("Y", pmat, at = 0, dist = .3) mpos[1,] <- -mpos[1,] ptext3d(mpos[1,], mpos[2,], mpos[3,], pmat = pmat, xpd = NA, texts = expression(X)); mtext3d("Z", pmat, expression(D[yy]^(2)), at = 0.00225) pmat <- perspx(x = bin_mids[,1], y = bin_mids[,2], z = D2[,,2], xlab = "", ylab = "", zlab = "", ticktype = "detailed", theta = 30, main = "") attr(pmat, "ranges") <- list(x = range(bin_mids[,1]), y = range(bin_mids[,2]), z = range(D2[,,2], na.rm = TRUE)) mtext3d("X", pmat, expression(X)) mpos<-plotrix:::get_axispos3d("Y", pmat, at = 0, dist = .3) mpos[1,] <- -mpos[1,] ptext3d(mpos[1,], mpos[2,], mpos[3,], pmat = pmat, xpd = NA, texts = expression(X)) mtext3d("Z", pmat, expression(D[xy]^(2)), at = -2.5e-4)
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