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=================================
Test of QR factorization routines
=================================
QR of Real matrix
A = [[-0.283885 0.56497 -1.0746 -0.732016 -0.869443]
[1.36446 -0.596145 2.36476 -2.10553 -0.0504762]
[0.906001 -1.19732 2.36508 -0.923457 0.799682]
[1.24942 -1.26756 1.22804 -1.89227 1.02849]
[1.55783 -0.300385 0.234136 -0.664315 -0.900489]]
norm(A - Q*R) = 0
A = [[-0.227649 -1.48058]
[-1.83729 1.07507]
[0.0511841 -0.396638]
[1.44132 0.51065]]
norm(A - Q*R) = 0
A = [[1.10323 1.12342 -0.269572 1.87195]
[0.910165 1.46072 -1.00539 0.494639]]
norm(A - Q*R) = 0
QR of Real matrix without Q
A = [[0.721932 0.549174 -1.44775 -0.319305 0.075397]
[0.246282 -0.808968 0.303095 1.52358 -0.172018]
[0.672038 -2.29735 -1.39092 -1.25129 -1.20035]
[-1.00149 -0.453797 0.369303 0.658525 -1.82296]
[-0.179719 0.259649 1.60367 -0.859404 0.796193]]
norm(A.T()*A - R.T()*R) = 0
A = [[-0.0977113 0.393591]
[-1.16267 0.84653]
[1.34814 -0.269572]
[-0.181114 -0.184428]]
norm(A.T()*A - R.T()*R) = 0
A = [[0.109679 -0.939679 0.849141 -0.115989]
[-0.26294 0.462237 -0.309417 -0.49744]]
norm(A.T()*A - R.T()*R) = 0
QR of Real matrix with pivoting
A = [[0.312621 1.27429 -0.901661 -1.22057 -0.417785]
[0.897405 -0.32882 -1.76627 0.878319 0.954855]
[0.1234 1.36355 0.480208 -0.5088 -0.673021]
[-0.421365 1.18344 0.0332149 0.867379 0.170602]
[0.419113 -0.675009 -0.256686 0.716969 -1.21233]]
norm(A*mat(P) - Q*R) = 0
A = [[-0.0915031 -1.18677]
[0.797619 0.750496]
[0.914909 -0.330124]
[0.496313 -0.532099]]
norm(A*mat(P) - Q*R) = 0
A = [[1.35402 0.395377 -2.93901 -0.245957]
[1.35716 -0.234376 -0.609542 -0.942463]]
norm(A*mat(P) - Q*R) = 0
QR of Complex matrix
A = [[-0.180822+0.135151i 0.369685+1.30784i 0.358469-0.553286i -0.639508-0.0358186i -0.540905+0.0171929i]
[0.431443+0.735259i 0.644844-0.64014i 0.0173776+0.166865i 0.726389+0.0141512i -0.304334+0.475183i]
[0.373431-0.43385i -0.467499+0.248209i 0.139432-0.304968i -1.15327+0.878131i 0.136609-0.303096i]
[-0.288087+0.43428i -0.110927+0.289013i 1.67774+0.214558i -0.401499-0.367446i 0.899195-0.0308906i]
[-0.328699-0.497205i 0.366511+0.840226i -0.605614+0.544018i 0.689669+0.826762i -0.182278+0.540058i]]
norm(A - Q*R) = 0
A = [[-0.207293-0.6724i -0.550361+0.338276i]
[-0.329522+2.25393i -0.300265+0.559865i]
[-0.170705-0.25516i 0.00183951+0.242933i]
[1.69291+0.49826i 0.543132-0.612738i]]
norm(A - Q*R) = 0
A = [[0.588127+1.65792i 0.663596+0.89475i -0.951271-1.04226i 0.405477+0.301014i]
[-0.393007-0.293208i 0.303812-1.0207i -0.386231-0.37374i 0.506654+0.960425i]]
norm(A - Q*R) = 0
QR of Complex matrix without Q
A = [[0.975944+0.335689i -0.189326-0.618709i -0.541688-0.934058i 0.243942-0.735716i -0.162513-0.149577i]
[0.747608+0.158062i 0.491061+1.16609i 0.686608-1.25157i -0.246661-0.417594i -0.203973+1.13481i]
[0.51012+1.00245i -0.145443+0.983717i -0.584849-1.01874i 0.310173+0.476513i 0.870201+0.523148i]
[-0.229429+0.0881398i -0.213724-0.731866i 0.76928+0.000212176i -0.810911-0.131968i -0.765188-0.748296i]
[-0.58438+0.126475i 0.217072-0.253027i 0.228199-0.44241i -0.799134-1.16319i 1.57135+0.359823i]]
norm(A.H()*A - R.H()*R) = 0
A = [[0.0693729-0.753371i 0.531057-1.18005i]
[-0.612721-0.13247i -1.24755+0.926539i]
[-0.544132+0.132892i -0.38808+1.65558i]
[-0.419233+1.2231i -0.23692+1.54007i]]
norm(A.H()*A - R.H()*R) = 0
A = [[0.101457-0.125741i -0.392005-0.673579i 0.353439+0.134666i 0.81203-0.648739i]
[0.741277+0.247239i 0.184505-0.562731i -0.181077+0.0856875i -0.917434-0.26573i]]
norm(A.H()*A - R.H()*R) = 0
QR of Complex matrix with pivoting
A = [[-0.643503+1.73417i -0.748152+0.212312i -0.0270121-0.300359i -0.988922+0.249059i 0.745347+0.0900309i]
[0.456608+0.707365i -0.434625+0.238697i 0.101718+0.158826i -0.589429+0.887644i -0.997146+0.977005i]
[0.00694129-0.0307072i -0.566399+0.590754i -0.502674-0.63153i 0.582224-0.0248339i 0.114152-0.140535i]
[0.157592-0.580597i -0.835156-0.158393i -0.612888+0.460076i 0.78084+0.15159i 0.87207+0.389236i]
[0.937583+0.0732077i -0.157269+0.0125424i -0.878953+0.378644i -0.305971-0.415223i -0.558537+0.276085i]]
norm(A*mat(P) - Q*R) = 0
A = [[0.862114-1.06655i -1.48735+0.0430125i]
[0.16668+0.259354i -0.665631-0.370575i]
[-0.144917+0.117112i -0.431749-1.12362i]
[0.628333-0.659098i -1.24675+0.58196i]]
norm(A*mat(P) - Q*R) = 0
A = [[0.342779+0.461418i 1.34271-0.00076101i 0.195876+0.425358i -0.438732+0.463633i]
[0.702588+0.110563i -0.48476+1.40989i 0.748408+0.410579i 0.247649-0.737889i]]
norm(A*mat(P) - Q*R) = 0
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