{"id":4462,"date":"2012-08-13T17:59:46","date_gmt":"2012-08-13T16:59:46","guid":{"rendered":"http:\/\/www.walkingrandomly.com\/?p=4462"},"modified":"2012-08-13T17:59:46","modified_gmt":"2012-08-13T16:59:46","slug":"variable-precision-qr-decomposition-in-matlab","status":"publish","type":"post","link":"https:\/\/walkingrandomly.com\/?p=4462","title":{"rendered":"Variable precision QR decomposition in MATLAB"},"content":{"rendered":"

Someone recently contacted me complaining that MATLAB could not do a QR factorisation<\/a> of a variable precision arithmetic<\/a> matrix.\u00a0 Double precision matrices work fine of course:<\/p>\n

>> A=[2 1 3;-1 0 7; 0 -1 -1];\r\n>> [Q R]=qr(A)\r\n\r\nQ =\r\n   -0.8944   -0.1826    0.4082\r\n    0.4472   -0.3651    0.8165\r\n         0    0.9129    0.4082\r\n\r\nR =\r\n   -2.2361   -0.8944    0.4472\r\n         0   -1.0954   -4.0166\r\n         0         0    6.5320<\/pre>\n
Variable precision matrices do not (I’m using MATLAB 2012a and the symbolic toolbox here).<\/p>\n
>> a=vpa([2 1 3;-1 0 7; 0 -1 -1]);\r\n>> [Q R]=qr(a)\r\nUndefined function 'qr' for input arguments of type 'sym'.<\/pre>\n
It turns out that MATLAB and the symbolic toolbox CAN do variable precision QR factorisation….it’s just hidden a bit.  The following very simple function, vpa_qr.m<\/a>, shows how to get at it<\/p>\n
function [ q,r ] = vpa_qr( x )\r\nresult = feval(symengine,'linalg::factorQR',x);\r\nq=result(1);\r\nr=result(2);\r\nend<\/pre>\n
Let’s see how that does<\/p>\n
>> a=vpa([2 1 3;-1 0 7; 0 -1 -1]);\r\n>> [Q R]=vpa_qr(a);<\/pre>\n
I’ve suppressed the output because it’s so large but it has definitely worked.  Let’s take a look at the first element of Q for example<\/p>\n
>> Q(1)\r\n\r\nans =\r\n0.89442719099991587856366946749251<\/pre>\n
Which is correct to the default number of variable precision digits, 32.\u00a0 Of course we could change this to anything we like using the digits<\/a> function.<\/p>\n