I am a supporter of
St. Joseph's hospice.
If you find this site useful or if it helped you, consider a small donation to
St. Joseph's, please.
The intermediate matrix M (constant values to to equal Mildenhalls data:
The target correlation S:
The Cholesky decomposition C of S:
You can create similar data automatically with array formula in A1:A20:
and with the array formula =randomshuffle($A$1:$A$20) in cells B1:B20 (copy to columns C and D respectively).
Now you get the covariance matrix E:
And its Cholesky decomposition F:
The intermediate matrix T:
You can check the generated correlations:
Calculate the ranks of numbers in the columns of T:
Finally you get your result:
The random shuffle code: