{"id":696,"date":"2017-06-03T10:51:26","date_gmt":"2017-06-03T02:51:26","guid":{"rendered":"https:\/\/www.techcoil.com\/blog\/?p=696"},"modified":"2023-01-28T11:41:41","modified_gmt":"2023-01-28T03:41:41","slug":"examples-on-using-the-sum-function-in-octave","status":"publish","type":"post","link":"https:\/\/www.techcoil.com\/blog\/examples-on-using-the-sum-function-in-octave\/","title":{"rendered":"Examples on using the sum function in Octave"},"content":{"rendered":"

If you are taking Andrew Ng's Machine Learning course on Coursera<\/a>, the sum<\/code> function is one of the functions that you will probably need to use to complete your assignments. Since the sum<\/code> function can be counter intuitive in some cases, I document some of the examples that I had created while trying to get a better understanding of the sum<\/a> function in Octave.<\/p>\n

Using sum on a row vector in Octave<\/h2>\n

When the sum<\/code> function encounters a row vector, it basically sums all the elements in the row vector and returns the total:<\/p>\n

\r\n>> rowVector = [1 2 3]\r\nrowVector =\r\n\r\n   1   2   3\r\n\r\n>> sum(rowVector)\r\nans =  6\r\n\r\n<\/pre>\n
Using sum on a column vector in Octave<\/h2>\n
As with the case of using the sum<\/code> function on a row vector, when the sum<\/code> function encounters a column vector, it will add all the elements in the column vector and returns the total:<\/p>\n
\r\ncolVector = [1; 2; 3]\r\ncolVector =\r\n\r\n   1\r\n   2\r\n   3\r\n\r\n>> sum(colVector)\r\nans =  6\r\n\r\n<\/pre>\n
Using sum<\/code> on a matrix in Octave<\/h2>\n
When a matrix is given to sum<\/code> as a parameter, the behaviour can be counter intuitive at first. Although you may expect that the sum<\/code> function returns a single value that is the total of adding all the elements in the matrix together, this is not the case.<\/p>\n
To see how the sum<\/code> function handles matrix as an input, let's first define a 2 by 3 matrix:<\/p>\n
\r\n>> x = [1 2 3; 1 2 3]\r\nx =\r\n\r\n   1   2   3\r\n   1   2   3\r\n<\/pre>\n
How to sum a matrix by column<\/h3>\n
Without any additional parameters to the matrix, the sum function collapses the matrix into a row vector by adding elements in the same column together:<\/p>\n
\r\n>> sum(x)\r\nans =\r\n\r\n   2   4   6\r\n<\/pre>\n
This behaviour is similar to supplying a '1' as an additional parameter to the matrix:<\/p>\n
\r\n>> sum(x, 1)\r\nans =\r\n\r\n   2   4   6\r\n\r\n<\/pre>\n
How to sum a matrix by row<\/h3>\n
If a '2' is supplied with the matrix to the sum<\/code> function, the sum<\/code> function will take return a column vector that contains the subtotal of all items in each row added together: <\/p>\n
\r\n>> sum(x, 2)\r\nans =\r\n\r\n   6\r\n   6\r\n\r\n<\/pre>\n
How to sum all elements in the matrix<\/h3>\n
Summing all the elements in the matrix was what I had required in computing the cost function of my learning algorithm. There are three ways which I had tried: <\/p>\n
    \n
  1. \nSumming the matrix by column and then summing the resultant row vector:<\/p>\n
    \r\n>> sum(sum(x , 1))\r\nans =  12\r\n<\/pre>\n<\/li>\n
  2. \nSumming the matrix by row and then summing the resultant column vector:<\/p>\n
    \r\n>> sum(sum(x , 2))\r\nans =  12\r\n<\/pre>\n<\/li>\n
  3. \nConverting the matrix to a column vector and then summing the resultant column vector:<\/p>\n
    \r\n>> sum(x(:))\r\nans =  12\r\n<\/pre>\n<\/li>\n<\/ol>\n\n