วันพุธที่ 29 กันยายน พ.ศ. 2553

QR decomposition from RQ decomposition

just reverse process here

For example,

Given,

M = [1.177 -0.0372159 -0.00193271 ;
-0.000159094 1.25581 0.0460427 ;
0.115352 0.0235739 0.993045 ;
]

If we do qr decomposition directly, we will have

>> [R,K] = qr(M)

R =

-0.9952 0.0020 -0.0975
0.0001 -0.9998 -0.0216
-0.0975 -0.0215 0.9950


K =

-1.1826 0.0349 -0.0949
0 -1.2561 -0.0674
0 0 0.9873

Anyway, we can use RQ, we reverse the cols, then transpose M

another_M = [-0.00193271 0.0460427 0.993045 ;
-0.0372159 1.25581 0.0235739 ;
1.177 -0.000159094 0.115352 ;
]

then

[another_K another_R] = rq(another_M)

another_R = [-0.097518 -0.021568 0.995 ;
-0.00196984 0.999767 0.0214782 ;
-0.995232 0.000134525 -0.0975378 ;
]

another_K = [0.987275 0.0673646 -0.0949297 ;
0 1.2561 0.034908 ;
0 0 -1.18264 ;
]

We transpose another_R, then reverse the cols. We will have R.

R =

-0.9952 -0.0020 -0.0975
0.0001 0.9998 -0.0216
-0.0975 0.0215 0.9950

We transpose another_K, then reverse the rows and cols, We will have K.

K =
-1.1826 0.0349 -0.0949
0 1.2561 0.0674
0 0 0.9873

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