Make a matrix being symmetric

A symmetric matrix can be useful is many context and it is good to be able to generate such a matrix. Here are several solutions. The most complete function was symmetricize() available in the discontinuited package ENA. I copy the function from this package to my package HelpersMG to make it again available:

Matrix library

> library(Matrix)
> essai <- matrix(data = 1:25, nrow = 5)
> 
> forceSymmetric(x=essai, uplo="U")
5 x 5 Matrix of class "dsyMatrix"
     [,1] [,2] [,3] [,4] [,5]
[1,]    1    6   11   16   21
[2,]    6    7   12   17   22
[3,]   11   12   13   18   23
[4,]   16   17   18   19   24
[5,]   21   22   23   24   25

gdata library

> essai <- matrix(data = 1:25, nrow = 5)
> essai
     [,1] [,2] [,3] [,4] [,5]
[1,]    1    6   11   16   21
[2,]    2    7   12   17   22
[3,]    3    8   13   18   23
[4,]    4    9   14   19   24
[5,]    5   10   15   20   25
> 
> 
> diag(essai) <- 0
> library("gdata")
> lowerTriangle(essai, diag=FALSE, byrow=FALSE) <- upperTriangle(essai, diag=FALSE, byrow=TRUE)
> 
> essai
     [,1] [,2] [,3] [,4] [,5]
[1,]    0    6   11   16   21
[2,]    6    0   12   17   22
[3,]   11   12    0   18   23
[4,]   16   17   18    0   24
[5,]   21   22   23   24    0

ENA and now HelpersMG library

A function symmetricize() was present in the package ENA, but this package is no more available (some dependencies do not exist anymore).

symmetricize {ENA}

Make a matrix symmetric 

Package: 

 ENA 

Version: 

 1.3-0 

Description

Make the matrix symmetric by making all "mirrored" positions consistent. A variety of methods are provided to make the matrix symmetrical.

Usage

symmetricize(matrix, method = c("max", "min", "avg", "ld", "ud"),
  adjacencyList = FALSE)

Arguments

matrix

The matrix to make symmatric

method

The method to use to make the matrix symmetric. Default is to take the maximum.

• "max" For each position, m_{i,j}, use the maxiumum of (m_{i,j}, m_{j,i})
• "min" For each position, m_{i,j}, use the minimum of (m_{i,j}, m_{j,i})
• "avg" For each position, m_{i,j}, use the mean:
• "ld" Copy the lower triangular portion of the matrix to the upper triangular portion.
• "ud" Copy the upper triangular portion of the matrix to the lower triangular portion.

adjacencyList

Logical. If false, returns the symmetric matrix (the same format as the input). If true, returns an adjacency list representing the upper triangular portion of the adjacency matrix with addressing based on the row.names of the matrix provided.

Values

The symmetric matrix

Examples

#Create a sample 3x3 matrix
mat <- matrix(1:9, ncol=3)
 
#Copy the upper diagonal portion to the lower
symmetricize(mat, "ud")
 
#Take the average of each symmetric location
symmetricize(mat, "avg")

Author(s)

Jeffrey D. Allen Jeffrey.Allen@UTSouthwestern.edu

Documentation reproduced from package ENA, version 1.3-0. License: GPL (>= 2)

But it was possible to extract the code of this function:

symmetricize <-
  function(matrix, method=c("max", "min","avg", "ld", "ud"), adjacencyList=FALSE){
    method <- match.arg(method)
    
    if (missing(matrix)){
      stop("You must provide a matrix to symmetricize.")
    }
    
    x <- matrix
    if (method=="ld"){
      #solution from Michael Conklin, http://www.biostat.wustl.edu/archives/html/s-news/2000-03/msg00127.html
      x[matrix(c(col(x)[lower.tri(x)], row(x)[lower.tri(x)]), ncol = 2)] <-
        x[matrix(c(row(x)[lower.tri(x)], col(x)[lower.tri(x)]), ncol = 2)]
    }
    if (method=="ud"){
      x[matrix(c(col(x)[upper.tri(x)], row(x)[upper.tri(x)]), ncol = 2)] <-
        x[matrix(c(row(x)[upper.tri(x)], col(x)[upper.tri(x)]), ncol = 2)]
    }
    if (method=="max" || method=="min" || method=="avg"){
      #retrieve the (row,col) indices for the lower-diagonal entries in the matrix
      ldi <- matrix(c(row(x)[lower.tri(x)], col(x)[lower.tri(x)]), ncol = 2)
      #already column-major, so we can leave this
      
      #retrieve the (row,col) indices for the upper-diagonal entries in the matrix
      udi <- matrix(c(row(x)[upper.tri(x)], col(x)[upper.tri(x)]), ncol = 2)
      #in order for these to be in the symmetrical order as ldi, we need to sort.
      udi <- udi[order(udi[,1], udi[,2]),]
      
      #extract the upper and lower diagonal elements in a way that's symmetrical in their indexces
      ud <- x[udi]
      ld <- x[ldi]
      
      #replace with either the min, max, or mean, depending on the selection
      if (method=="max"){
        x[ldi] <- apply(rbind(ld,ud),2,max);
        x[udi] <- apply(rbind(ld,ud),2,max);
      }
      if (method=="min"){
        x[ldi] <- apply(rbind(ld,ud),2,min);
        x[udi] <- apply(rbind(ld,ud),2,min);
      }
      if (method=="avg"){
        x[ldi] <- apply(rbind(ld,ud),2,mean);
        x[udi] <- apply(rbind(ld,ud),2,mean);
      }
    }
    
    if (!adjacencyList){
      #return the adjacency matrix
      return(x)
    }
    else{
      #convert to adjacency list and add addressing
      if (is.null(rownames(matrix))){
        stop("You requested adjacency list format, but the matrix provided has no (row) names.")
      }
      names <- rownames(matrix)
      add <- getTableAddressing(names)
      toReturn <- (cbind(add, x[upper.tri(x)]))
      colnames(toReturn) <- c("Source", "Dest", "Symmetric")
      return(toReturn)
    }
  }