Each technique can be applied to either the whole matrix or just the rows or columns. In addition an iterative facility is provided to Normalize both rows and columns simultaneously. These operate on the matrix as follows:

Marginal: normalizes the sum to be 100. This is achieved by dividing by the current sum of the rows, columns or matrix and multiplying by 100.

Mean: normalizes the mean to be zero. This is achieved by subtracting from every row, column, or matrix element the current mean.

Standard Deviation: normalizes the standard deviation to be one. This is achieved by dividing the rows, columns or matrix by the current standard deviation.

Z-Score: standardizes the mean to be zero and the standard deviation to be one. This is achieved by subtracting from every row, column or matrix element the current mean and then dividing the rows, columns or matrix by the current standard deviation.

Euclidean: standardizes the Euclidean norm to be one. This is achieved by dividing the rows, columns or matrix by the current Euclidean norm.

Maximum: standardizes the rows, columns or matrix to each have a maximum value of 100. This is achieved by dividing the matrix or each row or column by the current maximum and multiplying by 100.

The routine also allows each of these options to be applied to the rows and columns simultaneously. This involves an iterative procedure in which the technique is first applied to the rows and then the columns and then the rows etc. It is terminated when (and if) there is convergence.

Choices are:

Choices are:

Zeros can cause this procedure to crash and this can be overcome by replacing them with a relatively small value.

When both is selected the routine iterates to convergence the tolerance specifies a point at which when the values change by less than the tolerance the routine has converged.

When both is selected the routine iterates to convergence. Convergence will be deemed to have failed if the tolerance has not been achieved before the maximum number of iterations has taken place.

Name of file which contains normalized matrix.