R/FFT2FS_2D.R

In FPCA2D: Two Dimensional Functional Principal Component Analysis

FFT2FS_2D <-
function(A) {
  ##calculate the dimension of the matrix
  n1 <- dim(A)[1]
  n2 <- dim(A)[2]
  ## calculate the 
  X <- fft(A)/(n1*n2)
  
  ## partition the X matrix into four parts
  F11 <- X[1,1]
  F12 <- X[1,-1]
  F21 <- X[-1,1]
  F22 <- X[-1,-1]
  
  C11 <- as.matrix(Re(F11),nrow=1)
  ## Calculation of C12
  C12_r <- matrix(Re(F12),nrow=1)
  C12_i <- matrix(-Im(F12),nrow=1)
  colnames(C12_r) <- seq(1,2*(n2-1),by=2)
  colnames(C12_i) <- seq(2,2*(n2-1),by=2)
  C12 <- cbind(C12_r,C12_i)   
  C12 <- C12[1, as.character(sort(as.numeric(colnames(C12))))]
  ## Calculation of C21
  C21_r <- matrix(Re(F21),ncol=1)
  C21_i <- matrix(-Im(F21),ncol=1)
  rownames(C21_r) <- seq(1,2*(n1-1),by=2)
  rownames(C21_i) <- seq(2,2*(n1-1),by=2)
  C21 <- rbind(C21_r,C21_i)
  C21 <- C21[as.character(sort(as.numeric(rownames(C21)))),1]
  ## Calculation of C22
  C22_1 <- Re(F22)
  C22_2 <- -Im(F22)
  C22_3 <- -Im(F22)
  C22_4 <- -Re(F22)
  # Calculation of C22_odd
  colnames(C22_1) <- seq(1,2*(n2-1),by=2)
  colnames(C22_2) <- seq(2,2*(n2-1),by=2)
  C22_odd <- cbind(C22_1,C22_2)
  C22_odd <- C22_odd[,as.character(sort(as.numeric(colnames(C22_odd))))]
  rownames(C22_odd) <- seq(1,2*(n1-1),by=2)
  
  # Calculate of the C22_even
  colnames(C22_3) <- seq(1,2*(n2-1),by=2)
  colnames(C22_4) <- seq(2,2*(n2-1),by=2)
  C22_even <- cbind(C22_3,C22_4)
  C22_even <- C22_even[,as.character(sort(as.numeric(colnames(C22_even))))]
  rownames(C22_even) <- seq(2,2*(n1-1),by=2)
  
  #Build the C22 matrix
  C22 <- rbind(C22_odd,C22_even)
  C22 <- C22[as.character(sort(as.numeric(rownames(C22)))),]
  
  ###calculations of the C matrix
  C_1 <- matrix(c(C11,C12),nrow=1)
  C_2 <- cbind(C21,C22)
  C <- rbind(C_1,C_2)
  ### return the C matrix
  return(C)
}