# Plot of the absolute values of the graph Fourier coefficients vs the eigenvalues This function displays the absolute values of the graph Fourier coefficients vs the eigenvalues. ```r gftplot(graph, signal = NULL, K = NULL, size = 1, plot=TRUE) ``` ## Arguments - `graph`: an `igraph` graph object with vertex attributes of coordinates `x`, `y`, a signal `z`, and edge attribute of `weight`. - `signal`: specifies a signal for the graph Fourier transform. When `signal=NULL`, a signal `z` of object `graph` is used. - `K`: specifies the number of frequency components. - `size`: specifies point size. - `plot`: specifies whether plot is displayed. ## Details This function displays the absolute values of the graph Fourier coefficients vs the eigenvalues for `signal`. The red color denotes the nonnegative graph Fourier coefficients, and the blue color indicates the negative graph Fourier coefficients. ## Returns If `plot=TRUE`, plot of the absolute values of the graph Fourier coefficients vs the eigenvalues for `signal` over a graph using package `ggplot2`. If `plot=FALSE`, a list with components: - **absgFCoeffs**: the absolute values of the graph Fourier coefficients in decreasing order. - **eigenvalues**: the eigenvalues according to the absolute values of the graph Fourier coefficients. ## See Also `gsignal`, `gfdecomp`. ## Examples ```r #### example : composite of two components having different frequencies ## define vertex coordinate x <- y <- seq(0, 1, length=30) xy <- expand.grid(x=x, y=y) ## weighted adjacency matrix by Gaussian kernel ## for connecting vertices within distance 0.04 A <- adjmatrix(xy, method = "dist", 0.04) ## signal # high-frequency component signal1 <- rep(sin(12.5*pi*x - 1.25*pi), 30) # low-frequency component signal2 <- rep(sin(5*pi*x - 0.5*pi), 30) # composite signal signal0 <- signal1 + signal2 # noisy signal with SNR(signal-to-noise ratio)=5 signal <- signal0 + rnorm(900, 0, sqrt(var(signal0) / 5)) # graph with signal gsig <- gsignal(vertex = cbind(xy, signal), edge = A, edgetype = "matrix") # display a signal over graph gplot(gsig, size=3) # display of absolute values of the graph Fourier coefficients vs the eigenvalues # for signal gftplot(gsig) gftplot(gsig, K=5, size=3) out <- gftplot(gsig, K=5, plot=FALSE) names(out) ## signal3 # high-frequency component signal11 <- c(outer(sin(6*pi*x - 0.5*pi), sin(6*pi*y - 0.5*pi))) # low-frequency component signal22 <- c(outer(sin(2*pi*x - 0.5*pi), sin(2*pi*y - 0.5*pi))) # composite signal signal00 <- signal11 + signal22 # noisy signal signal3 <- signal00 + rnorm(900, 0, sqrt(var(signal00) / 5)) # display signal3 over graph gplot(gsig, signal=signal3, size=3) # display of absolute values of the graph Fourier coefficients vs the eigenvalues # for signal3 gftplot(gsig, signal=signal3) gftplot(gsig, signal=signal3, K=10, size=2) ```

gftplot function