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FSL  February 2009

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Subject:

Re: orthogonalization question

From:

Steve Smith <[log in to unmask]>

Reply-To:

FSL - FMRIB's Software Library <[log in to unmask]>

Date:

Thu, 19 Feb 2009 08:59:27 +0000

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (786 lines)

HI - please see Saad's recent detailed email on this. I'm afraid your  
approach is (in general) wrong - you either need to orthogonalise  
against an orthogonalised set of the other regressors, as Saad  
described, or use pinv() instead.

Cheers.



On 18 Feb 2009, at 21:00, Ning Liu wrote:

> I have 4 EVs: original.txt is the 4 EVs (original.txt, one EV one  
> column)
> and I want to
> remove from EV1 the parts which is related to EV2, EV3 and EV4. That  
> is let
> EV1 reflected its unique variances. I am trying to understand how the
> orthogonalise works.
>
> First, I tried to use Matlab to do the orthogonalization, I did  
> demean for
> all of them and then, I did something
> like this
> A1 = A - B.*(A'*B)/(B'*B)
> A2 = A1 - C.*(A1'*C)/(C'*C)
> A3 = A2 - D.*(A2'*D)/(D'*D)
> I get matlab.txt
>
> Then, I used FEAT -> States -> Full model setup to do the
> orthogonalise. Under the first EV, I clicked orthogonalise (see  
> FEAT.txt,
> the first column is wrt 2, the second is wrt 2 and 3, the third  
> column is
> wrt 2, 3 and 4).
> If i just orthogonalise EV1 wrt 2, the reults from matlab and FSL are
> exactly same.
> If I orthogonalise EV1 wrt 2 and 3,  the reults from matlab and FSL  
> are
> almost same.
> But when I  I orthogonalise EV1 wrt 2, 3 and 4  the reults from  
> matlab and
> FSL are not that same. I don't why.
>
> Can anyone help me figure that out?
>
>
> Thanks,
>
> Ning
>  -3.4324290e+00  -3.3128000e+00  -1.5990000e+00
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>
>
>  -3.8274479e+00  -1.4747000e+00  -2.0440000e-01  -7.7090000e-01
>  -2.2495828e+00  -1.6507000e+00  -6.2970000e-01  -8.0000000e-01
>  -9.8065892e-01  -1.7888000e+00  -1.2222000e+00  -8.1130000e-01
>  -8.2683795e-01  -1.7572000e+00  -1.4441000e+00  -8.0780000e-01
>  -1.1838109e+00  -5.1110000e-01  -1.0558000e+00  -6.9340000e-01
>  -1.5337866e+00   8.2120000e-01  -6.8710000e-01  -5.2130000e-01
>  -1.2348818e+00   8.1020000e-01  -7.3160000e-01  -4.3430000e-01
>  -6.1540543e-01   3.7040000e-01  -9.8330000e-01  -4.5510000e-01
>  -7.4771639e-02   6.3810000e-01  -9.2310000e-01  -4.1470000e-01
>  -6.2809340e-01   1.2822000e+00  -4.9780000e-01  -2.6060000e-01
>  -1.7404480e+00   1.1545000e+00  -1.9110000e-01  -1.3640000e-01
>  -1.6993261e+00   3.9990000e-01  -4.4680000e-01  -9.4300000e-02
>  -7.1451840e-01   1.3710000e-01  -1.0469000e+00  -3.0700000e-02
>   3.2592722e-01   9.2010000e-01  -1.1065000e+00   6.0900000e-02
>   4.7007657e-01   9.6550000e-01  -4.5350000e-01   1.1790000e-01
>  -1.4650574e-01   2.2760000e-01  -6.5500000e-02   1.4610000e-01
>  -4.4088123e-01   8.3600000e-02  -3.2740000e-01   6.4700000e-02
>  -5.9420416e-01  -7.5000000e-02  -4.8380000e-01  -9.2200000e-02
>  -6.7669447e-01  -3.3770000e-01  -1.2220000e-01  -1.2170000e-01
>  -1.1260053e-02  -4.0760000e-01   3.7970000e-01  -3.2000000e-02
>   1.0113381e+00   2.4500000e-02   6.1560000e-01   2.2200000e-02
>   1.1172799e+00   7.9460000e-01   3.6470000e-01   4.3800000e-02
>   5.1980377e-01   9.1250000e-01   9.4400000e-02   9.0700000e-02
>  -2.0650054e-01   6.7990000e-01   9.7800000e-02   1.4950000e-01
>  -9.9200006e-01   7.7900000e-01   2.3950000e-01   2.1290000e-01
>  -9.9544226e-01   4.2490000e-01   6.3480000e-01   2.7230000e-01
>  -5.5197660e-01  -6.1840000e-01   5.9800000e-01   2.8060000e-01
>  -9.4689767e-01  -1.6082000e+00  -8.4800000e-02   2.1110000e-01
>  -9.1036416e-01  -2.1113000e+00  -2.8330000e-01   1.4650000e-01
>   3.4046671e-01  -2.3070000e+00   1.1210000e-01   1.6890000e-01
>   1.0382489e+00  -2.0619000e+00   3.7930000e-01   2.3240000e-01
>   9.5711015e-01  -1.0493000e+00   6.4630000e-01   2.5540000e-01
>   1.4173654e+00  -2.5130000e-01   8.4140000e-01   2.3640000e-01
>   2.2170031e+00   9.6600000e-02   8.5870000e-01   2.2350000e-01
>   1.5015335e+00   4.8610000e-01   9.1650000e-01   2.2370000e-01
>  -5.8507080e-03   7.9950000e-01   7.9380000e-01   2.4540000e-01
>  -5.2360802e-01   5.0380000e-01   5.2570000e-01   2.9130000e-01
>  -3.6562885e-01   2.8820000e-01   5.1830000e-01   3.1580000e-01
>  -5.5586432e-02   3.1410000e-01   3.3780000e-01   3.1280000e-01
>   6.6218629e-01   1.5880000e-01   9.4000000e-02   4.0040000e-01
>   1.9828014e+00   6.6470000e-01   3.8370000e-01   5.4040000e-01
>   2.7591073e+00   1.6784000e+00   9.2580000e-01   5.8910000e-01
>   2.2230691e+00   2.1358000e+00   1.2978000e+00   5.3630000e-01
>   1.8881831e+00   1.6753000e+00   1.0874000e+00   4.2040000e-01
>   2.4540529e+00   8.0730000e-01   6.8400000e-01   3.3750000e-01
>   2.6474758e+00   6.1810000e-01   8.1110000e-01   3.5680000e-01
>   1.4668023e+00   4.6160000e-01   1.2250000e+00   4.2620000e-01
>   8.3459315e-01  -5.1660000e-01   1.3226000e+00   4.8530000e-01
>   1.6359247e+00  -1.2773000e+00   1.3023000e+00   5.2310000e-01
>   2.2095817e+00  -1.1314000e+00   1.3916000e+00   5.3740000e-01
>   2.2338588e+00  -9.7160000e-01   1.2751000e+00   5.9130000e-01
>   1.8294923e+00  -1.5656000e+00   1.1736000e+00   6.9980000e-01
>   1.8918257e+00  -1.8725000e+00   1.6721000e+00   7.7080000e-01
>   2.6914674e+00  -6.9700000e-01   2.0329000e+00   7.2010000e-01
>   3.6568326e+00   1.4417000e+00   1.3477000e+00   6.5620000e-01
>   4.8299304e+00   2.8793000e+00   4.9480000e-01   6.8190000e-01
>   5.0612105e+00   2.6514000e+00   7.7330000e-01   6.9780000e-01
>   3.2751695e+00   1.6054000e+00   1.4481000e+00   7.0580000e-01
>   1.1304210e+00   6.3120000e-01   1.3882000e+00   7.3670000e-01
>   3.1770540e-01   1.1550000e-01   9.9880000e-01   6.1720000e-01
>  -8.4770802e-04   5.8180000e-01   9.8550000e-01   5.0170000e-01
>   2.9118223e-02   1.1498000e+00   1.2567000e+00   6.4570000e-01
>   1.7531519e+00   3.9900000e-01   1.5931000e+00   8.3860000e-01
>   4.3103919e+00  -9.4390000e-01   2.3541000e+00   8.9930000e-01
>   5.5694785e+00  -1.0523000e+00   2.8889000e+00   8.4820000e-01
>   5.0943534e+00  -6.6930000e-01   2.5045000e+00   7.7850000e-01
>   4.2129884e+00  -5.3350000e-01   1.8823000e+00   7.3290000e-01
>   3.8509373e+00   8.2670000e-01   1.7214000e+00   7.0710000e-01
>   3.4303356e+00   2.4219000e+00   1.7396000e+00   6.5630000e-01
>   1.3799679e+00   2.1119000e+00   1.1164000e+00   2.1390000e-01
>  -1.7039545e+00   1.1411000e+00  -7.7700000e-02  -7.8980000e-01
>  -1.9109589e+00   1.5380000e-01  -7.9650000e-01  -1.5414000e+00
>  -1.7059757e-01  -1.0947000e+00  -8.9500000e-01  -1.5872000e+00
>  -3.9749888e-01  -1.2232000e+00  -9.0060000e-01  -1.4289000e+00
>  -2.4995121e+00  -2.9370000e-01  -1.1257000e+00  -1.3523000e+00
>  -4.6194534e+00  -1.6500000e-01  -1.4694000e+00  -1.2702000e+00
>  -5.6903620e+00  -1.3959000e+00  -1.5632000e+00  -1.1453000e+00
>  -4.4637390e+00  -2.5961000e+00  -1.4807000e+00  -1.0670000e+00
>  -2.7811086e+00  -1.9847000e+00  -1.5258000e+00  -1.1111000e+00
>  -3.5385017e+00  -5.6890000e-01  -1.4094000e+00  -1.2569000e+00
>  -5.1210300e+00   1.6290000e-01  -1.2247000e+00  -1.3615000e+00
>  -5.2900622e+00   4.3300000e-01  -9.8410000e-01  -1.2650000e+00
>  -3.8068022e+00  -1.5240000e-01  -5.9620000e-01  -1.0079000e+00
>  -1.4312369e+00  -1.0611000e+00  -6.2270000e-01  -8.0310000e-01
>   2.5369008e-01  -8.8560000e-01  -9.2580000e-01  -6.7200000e-01
>  -2.8102984e-02   4.5900000e-02  -1.1525000e+00  -4.6590000e-01
>  -8.1569085e-01   3.8190000e-01  -1.5736000e+00  -2.7790000e-01
>  -1.0917939e+00   4.0680000e-01  -1.7974000e+00  -2.6150000e-01
>  -1.0769446e+00   3.1570000e-01  -1.2906000e+00  -2.7790000e-01
>  -8.1535988e-01  -7.5880000e-01  -7.0680000e-01  -3.3830000e-01
>  -1.0252612e-01  -1.9928000e+00  -6.5650000e-01  -5.3660000e-01
>   4.1020771e-01  -1.7150000e+00  -7.0030000e-01  -6.1230000e-01
>  -3.6523630e-03  -1.6000000e-03  -5.1510000e-01  -5.1070000e-01
>  -5.8217543e-01   1.4907000e+00  -6.6630000e-01  -4.4930000e-01
>  -7.2967185e-01   1.1215000e+00  -1.1451000e+00  -4.1810000e-01
>  -1.0038911e+00  -9.3090000e-01  -1.2713000e+00  -3.6810000e-01
>  -1.1091132e+00  -2.1122000e+00  -1.3828000e+00  -3.8800000e-01
>  -9.1769640e-01  -1.2420000e+00  -1.8397000e+00  -4.2710000e-01
>  -1.3826367e+00  -2.2200000e-01  -1.7177000e+00  -3.5080000e-01
>  -2.3810249e+00   1.3470000e-01  -1.1057000e+00  -2.5080000e-01
>  -2.8981660e+00   4.1370000e-01  -1.0808000e+00  -2.2180000e-01
>  -3.0585730e+00  -2.3180000e-01  -1.3317000e+00  -2.3240000e-01
>  -3.2725185e+00  -1.2972000e+00  -8.3580000e-01  -2.4150000e-01
>  -2.8847881e+00  -1.1086000e+00  -8.1600000e-02  -2.2000000e-01
>  -1.4215470e+00  -2.5540000e-01  -2.6530000e-01  -1.9020000e-01
>   2.9639981e-01   6.7400000e-02  -1.1305000e+00  -1.2940000e-01
>   1.7286394e+00   1.7500000e-02  -1.7136000e+00  -3.4300000e-02
>   2.2858276e+00  -4.2130000e-01  -1.6785000e+00   2.3400000e-02
>   7.2819405e-01  -4.7040000e-01  -1.1329000e+00   3.0300000e-02
>  -2.1361977e+00   1.2536000e+00  -5.4620000e-01   3.3000000e-03
>  -4.1772100e+00   3.4180000e+00  -3.3340000e-01  -4.4500000e-02
>  -4.2432816e+00   3.1831000e+00  -4.3070000e-01  -1.5200000e-02
>  -2.3113968e+00   1.3052000e+00  -6.6840000e-01   4.5000000e-02
>   2.4536626e-01   6.3060000e-01  -8.5990000e-01   1.6000000e-02
>   1.6351413e+00   1.2543000e+00  -8.0260000e-01  -3.2700000e-02
>   2.1140478e+00   2.1360000e+00  -6.1650000e-01  -6.9700000e-02
>   2.3787215e+00   2.1545000e+00  -5.2450000e-01  -4.4300000e-02
>   1.6956777e+00   1.3576000e+00  -2.3390000e-01   1.7070000e-01
>   2.4534977e-01   1.5611000e+00   1.8640000e-01   4.1390000e-01
>   1.4410705e-02   2.3480000e+00   9.2400000e-02   4.5870000e-01
>   1.3376429e+00   1.4567000e+00  -1.2120000e-01   4.0630000e-01
>   2.1215744e+00  -5.0930000e-01   8.6100000e-02   3.9240000e-01
>   1.0818435e+00  -1.3447000e+00   1.9790000e-01   2.1730000e-01
>  -1.5338213e+00  -1.0022000e+00   9.5000000e-02  -1.4740000e-01
>  -2.6260602e+00  -9.8340000e-01   3.2310000e-01  -2.2460000e-01
>  -1.5597784e+00  -1.9015000e+00   5.6300000e-01   6.1100000e-02
>  -5.5747429e-01  -2.9893000e+00   4.6090000e-01   2.7060000e-01
>  -3.2580378e-01  -2.8788000e+00   3.2930000e-01   2.8040000e-01
>  -3.8525023e-01  -1.7019000e+00   2.5780000e-01   2.6280000e-01
>  -3.2366457e-01  -7.4390000e-01   4.0850000e-01   2.2810000e-01
>  -6.7603640e-01  -2.3700000e-02   7.3840000e-01   1.7920000e-01
>  -1.0406265e+00   1.8330000e-01   9.0090000e-01   2.3350000e-01
>  -4.0769074e-01  -9.1560000e-01   7.3440000e-01   2.9670000e-01
>   1.3450679e+00  -2.1897000e+00   2.3990000e-01   2.9290000e-01
>   1.7691725e+00  -1.9794000e+00  -3.5170000e-01   2.9770000e-01
>   5.7996343e-01  -9.2790000e-01  -8.1900000e-01   2.9370000e-01
>  -3.2533984e-02  -4.2390000e-01  -1.0323000e+00   2.3860000e-01
>  -8.5031798e-01  -9.8290000e-01  -4.9130000e-01   1.7620000e-01
>  -2.3348412e+00  -1.2753000e+00   5.6890000e-01   1.5380000e-01
>  -2.9495631e+00  -6.4980000e-01   1.1637000e+00   1.8600000e-01
>  -2.4477165e+00  -5.8000000e-03   9.9850000e-01   2.3500000e-01
>  -1.2564016e+00   8.3900000e-02   5.3170000e-01   2.7190000e-01
>   4.2404519e-01  -5.2730000e-01   7.2400000e-02   3.0250000e-01
>   1.4034122e+00  -7.3050000e-01  -3.4300000e-01   2.5090000e-01
>   1.0624444e+00  -1.0040000e-01  -6.1280000e-01   8.0800000e-02
>   3.9528633e-01   1.2450000e-01  -4.4400000e-01   2.0500000e-02
>   5.7127660e-01  -4.4430000e-01   2.9290000e-01   1.7680000e-01
>   7.6059960e-01   1.4200000e-02   9.6180000e-01   3.6070000e-01
>   1.0548174e-01   1.5825000e+00   8.6580000e-01   4.3840000e-01
>  -2.4034150e-01   2.0861000e+00   9.5000000e-02   4.0190000e-01
>   3.1660488e-01   2.1051000e+00  -6.6530000e-01   3.2650000e-01
>   1.5548576e+00   2.2728000e+00  -9.4800000e-01   2.7980000e-01
>   2.9567642e+00   9.4860000e-01  -7.5970000e-01   2.6350000e-01
>   3.1198725e+00  -6.9940000e-01  -4.0780000e-01   2.7520000e-01
>   1.8697467e+00  -3.6400000e-01   1.0400000e-02   2.8730000e-01
>   7.1110519e-01   2.0820000e-01   4.4080000e-01   2.3360000e-01
>  -7.7615298e-01  -5.6360000e-01   4.0810000e-01  -4.3900000e-02
>  -2.1445737e+00  -1.0565000e+00   4.3400000e-02  -4.3180000e-01
>  -1.6795987e+00  -1.4040000e-01   1.1850000e-01  -4.7430000e-01
>  -2.7982740e-01   1.0812000e+00   5.5060000e-01  -2.2740000e-01
>   9.2692143e-01   1.1771000e+00   5.9040000e-01  -8.9100000e-02
>   1.9332908e+00   2.8640000e-01   1.2240000e-01  -4.4300000e-02
>   2.8920695e+00  -6.8480000e-01  -5.1750000e-01   2.4600000e-02
>   2.6934217e+00  -7.8030000e-01  -1.1040000e+00   2.4000000e-02
>   1.4287153e+00  -4.1900000e-02  -1.0210000e+00  -5.3600000e-02
>  -4.5069919e-01   2.7650000e-01  -1.2860000e-01  -1.5690000e-01
>  -2.7024871e+00  -8.4170000e-01   7.3470000e-01  -2.9230000e-01
>  -4.0196268e+00  -2.0370000e+00   9.6870000e-01  -3.3680000e-01
>  -3.6940402e+00  -1.1215000e+00   8.4950000e-01  -1.8160000e-01
>  -2.3068505e+00   6.8880000e-01   6.6630000e-01   1.6300000e-02
>  -1.4512085e+00   5.9980000e-01   8.6200000e-02   6.1100000e-02
>  -1.0061670e+00  -4.5680000e-01  -4.6240000e-01  -2.7300000e-02
>  -3.9636023e-01  -7.7800000e-01  -1.8180000e-01  -1.0100000e-01
>   2.5835998e-01  -1.3600000e-01   4.1980000e-01  -1.0570000e-01
>   6.4397677e-01   1.5187000e+00   5.1940000e-01  -8.1200000e-02
>   1.2351795e-01   1.6454000e+00   2.8020000e-01  -2.7600000e-02
>  -3.6960302e-01  -4.8690000e-01   7.2700000e-02  -3.9000000e-03
>   2.7988843e-02  -9.1870000e-01  -1.5840000e-01  -5.5300000e-02
>   3.2196581e-01   8.0540000e-01  -3.8870000e-01  -5.1000000e-02
>  -6.2851929e-01   1.6340000e+00  -3.2240000e-01   2.6600000e-02
>  -1.4112361e+00   1.6265000e+00  -1.3710000e-01   1.9600000e-02
>  -1.0211381e+00   1.1223000e+00  -5.7700000e-02  -1.0280000e-01
>   2.9692257e-01   2.9090000e-01   1.5460000e-01  -1.2710000e-01
>   1.3616603e+00   3.2090000e-01   4.1580000e-01   2.7600000e-02
>   1.2717462e+00   6.7490000e-01   4.3080000e-01   1.4150000e-01
>   2.1799826e-01   4.6650000e-01   4.2300000e-01   8.6300000e-02
>  -4.9830664e-01   3.0920000e-01   5.0390000e-01  -8.0200000e-02
>   3.6062815e-01   1.4390000e-01   8.1900000e-02  -2.8480000e-01
>   1.4713833e+00  -7.7530000e-01  -5.3810000e-01  -4.1350000e-01
>   1.5861923e+00  -1.9801000e+00  -5.7310000e-01  -2.8130000e-01
>   1.1991578e+00  -3.0681000e+00  -2.2530000e-01  -2.2400000e-02
>  -7.8170777e-02  -3.2577000e+00   1.8100000e-02   1.1020000e-01
>  -1.4558508e+00  -2.2166000e+00  -1.0710000e-01   1.5030000e-01
>  -1.6554114e+00  -1.4489000e+00  -3.4030000e-01   1.7800000e-01
>  -1.2850712e+00  -1.7974000e+00  -3.2400000e-01   1.8600000e-01
>  -1.0988559e+00  -1.8048000e+00  -7.0300000e-02   2.0780000e-01
>  -5.8293860e-01  -3.4270000e-01   4.5080000e-01   2.5200000e-01
>   7.1433260e-01   1.6097000e+00   9.3420000e-01   2.2420000e-01
>   1.9924236e+00   3.1571000e+00   1.0264000e+00   1.6520000e-01
>   2.7736598e+00   4.3708000e+00   8.6310000e-01   2.0690000e-01
>   3.1145238e+00   4.9607000e+00   4.3230000e-01   3.0580000e-01
>   2.8149025e+00   3.9671000e+00  -2.6160000e-01   2.8160000e-01
>   1.6611847e+00   1.9785000e+00  -5.9250000e-01  -2.5000000e-03
>  -9.6957670e-02   6.5750000e-01  -2.2520000e-01  -2.8950000e-01
>  -6.0575298e-01   4.7010000e-01   3.8530000e-01  -2.0060000e-01
>   3.2705681e-01   2.4800000e-02   4.2430000e-01   1.2060000e-01
>   1.1224323e+00  -8.3070000e-01  -2.0560000e-01   3.1580000e-01
>   8.4297688e-01  -1.3131000e+00  -4.5230000e-01   3.0540000e-01
>   4.5165902e-01  -1.2318000e+00   1.9100000e-02   2.1270000e-01
>   1.0680291e+00  -1.6390000e-01   3.7320000e-01   1.3460000e-01
>   2.1512422e+00   1.6781000e+00   2.8080000e-01   1.1650000e-01
>   2.7085416e+00   1.9917000e+00   1.3040000e-01   1.1770000e-01
>   1.9375904e+00   1.0377000e+00   2.7700000e-02   2.0500000e-02
>   3.8818157e-01   9.0250000e-01  -2.0170000e-01  -7.6700000e-02
>  -7.3598040e-01   1.7204000e+00  -1.1200000e-01   2.4600000e-02
>  -8.1662519e-01   2.1322000e+00   2.3290000e-01   1.6830000e-01
>   3.2032774e-02   1.3739000e+00   4.3900000e-01   2.1320000e-01
>   8.7450808e-01   6.1460000e-01   4.2200000e-01   2.5820000e-01
>   5.2614377e-01  -1.5780000e-01   3.6510000e-01   3.4670000e-01
>  -1.0368009e+00  -1.3255000e+00   5.4460000e-01   4.2200000e-01
>  -1.7233164e+00  -1.5702000e+00   5.0040000e-01   4.8920000e-01
>  -8.2649698e-01  -1.6363000e+00   1.1420000e-01   5.2340000e-01
>  -5.7308705e-01  -2.8669000e+00  -2.6750000e-01   3.9340000e-01
>  -8.2607547e-01  -3.7771000e+00  -6.1430000e-01   1.5400000e-02
>  -5.0037164e-01  -3.2397000e+00  -7.5690000e-01  -2.6030000e-01
>  -1.7202133e-01  -1.9548000e+00  -9.6600000e-02  -9.4600000e-02
>  -4.4395340e-01  -1.1647000e+00   8.3520000e-01   1.9110000e-01
>  -8.7661405e-01  -7.3440000e-01   9.5580000e-01   2.9320000e-01
>  -7.6231812e-02  -1.7460000e-01   4.5610000e-01   3.1950000e-01
>   2.4026557e+00  -6.7040000e-01  -3.6000000e-03   3.1040000e-01
>   3.9095841e+00  -1.6693000e+00  -1.4080000e-01   3.4660000e-01
>   1.9700661e+00  -1.6707000e+00   3.0500000e-02   4.3430000e-01
>  -5.6880640e-01  -9.0490000e-01   3.0790000e-01   3.3910000e-01
>  -1.0503431e+00   2.8890000e-01   5.3730000e-01  -7.0000000e-04
>  -1.7133100e+00   1.2653000e+00   2.9750000e-01  -4.4270000e-01
>  -2.7691461e+00   1.3237000e+00  -2.4850000e-01  -7.9810000e-01
>  -1.9976224e+00   1.1232000e+00  -4.8680000e-01  -9.0690000e-01
>  -8.9042647e-01   8.7320000e-01  -6.6000000e-01  -9.2650000e-01
>  -1.0770505e+00   1.3222000e+00  -9.6230000e-01  -1.0096000e+00
>  -2.0264509e+00   3.1138000e+00  -1.2692000e+00  -1.1161000e+00
>
>
>  -3.8396986e+00  -1.4710000e+00  -2.0640000e-01  -7.7260000e-01
>  -2.2618335e+00  -1.6471000e+00  -6.3170000e-01  -8.0170000e-01
>  -9.9290966e-01  -1.7852000e+00  -1.2242000e+00  -8.1300000e-01
>  -8.3908869e-01  -1.7536000e+00  -1.4461000e+00  -8.0950000e-01
>  -1.1960616e+00  -5.0740000e-01  -1.0578000e+00  -6.9510000e-01
>  -1.5460373e+00   8.2480000e-01  -6.8910000e-01  -5.2300000e-01
>  -1.2471325e+00   8.1380000e-01  -7.3360000e-01  -4.3590000e-01
>  -6.2765617e-01   3.7410000e-01  -9.8530000e-01  -4.5680000e-01
>  -8.7022379e-02   6.4180000e-01  -9.2510000e-01  -4.1640000e-01
>  -6.4034414e-01   1.2858000e+00  -4.9980000e-01  -2.6230000e-01
>  -1.7526987e+00   1.1582000e+00  -1.9310000e-01  -1.3810000e-01
>  -1.7115768e+00   4.0350000e-01  -4.4880000e-01  -9.6000000e-02
>  -7.2676914e-01   1.4080000e-01  -1.0489000e+00  -3.2400000e-02
>   3.1367648e-01   9.2380000e-01  -1.1085000e+00   5.9200000e-02
>   4.5782583e-01   9.6920000e-01  -4.5550000e-01   1.1620000e-01
>  -1.5875648e-01   2.3130000e-01  -6.7400000e-02   1.4440000e-01
>  -4.5313197e-01   8.7300000e-02  -3.2940000e-01   6.3000000e-02
>  -6.0645490e-01  -7.1400000e-02  -4.8580000e-01  -9.3900000e-02
>  -6.8894521e-01  -3.3410000e-01  -1.2420000e-01  -1.2340000e-01
>  -2.3510793e-02  -4.0400000e-01   3.7770000e-01  -3.3700000e-02
>   9.9908738e-01   2.8200000e-02   6.1360000e-01   2.0500000e-02
>   1.1050292e+00   7.9830000e-01   3.6270000e-01   4.2100000e-02
>   5.0755303e-01   9.1620000e-01   9.2400000e-02   8.9000000e-02
>  -2.1875128e-01   6.8360000e-01   9.5800000e-02   1.4780000e-01
>  -1.0042508e+00   7.8260000e-01   2.3750000e-01   2.1130000e-01
>  -1.0076930e+00   4.2850000e-01   6.3280000e-01   2.7060000e-01
>  -5.6422734e-01  -6.1480000e-01   5.9600000e-01   2.7890000e-01
>  -9.5914841e-01  -1.6045000e+00  -8.6800000e-02   2.0950000e-01
>  -9.2261490e-01  -2.1077000e+00  -2.8530000e-01   1.4480000e-01
>   3.2821597e-01  -2.3034000e+00   1.1010000e-01   1.6720000e-01
>   1.0259982e+00  -2.0582000e+00   3.7730000e-01   2.3070000e-01
>   9.4485941e-01  -1.0456000e+00   6.4430000e-01   2.5370000e-01
>   1.4051147e+00  -2.4770000e-01   8.3940000e-01   2.3470000e-01
>   2.2047524e+00   1.0020000e-01   8.5670000e-01   2.2180000e-01
>   1.4892828e+00   4.8980000e-01   9.1450000e-01   2.2200000e-01
>  -1.8101448e-02   8.0310000e-01   7.9180000e-01   2.4370000e-01
>  -5.3585876e-01   5.0750000e-01   5.2370000e-01   2.8970000e-01
>  -3.7787959e-01   2.9190000e-01   5.1630000e-01   3.1410000e-01
>  -6.7837172e-02   3.1780000e-01   3.3590000e-01   3.1110000e-01
>   6.4993555e-01   1.6240000e-01   9.2000000e-02   3.9870000e-01
>   1.9705507e+00   6.6840000e-01   3.8170000e-01   5.3870000e-01
>   2.7468566e+00   1.6820000e+00   9.2380000e-01   5.8740000e-01
>   2.2108184e+00   2.1394000e+00   1.2958000e+00   5.3460000e-01
>   1.8759324e+00   1.6790000e+00   1.0854000e+00   4.1870000e-01
>   2.4418022e+00   8.1100000e-01   6.8200000e-01   3.3580000e-01
>   2.6352251e+00   6.2170000e-01   8.0910000e-01   3.5510000e-01
>   1.4545516e+00   4.6530000e-01   1.2230000e+00   4.2450000e-01
>   8.2234241e-01  -5.1300000e-01   1.3206000e+00   4.8360000e-01
>   1.6236740e+00  -1.2737000e+00   1.3003000e+00   5.2140000e-01
>   2.1973310e+00  -1.1278000e+00   1.3896000e+00   5.3570000e-01
>   2.2216081e+00  -9.6790000e-01   1.2731000e+00   5.8960000e-01
>   1.8172416e+00  -1.5620000e+00   1.1716000e+00   6.9820000e-01
>   1.8795750e+00  -1.8689000e+00   1.6701000e+00   7.6910000e-01
>   2.6792167e+00  -6.9340000e-01   2.0309000e+00   7.1840000e-01
>   3.6445819e+00   1.4453000e+00   1.3457000e+00   6.5450000e-01
>   4.8176797e+00   2.8829000e+00   4.9280000e-01   6.8020000e-01
>   5.0489598e+00   2.6551000e+00   7.7130000e-01   6.9610000e-01
>   3.2629188e+00   1.6090000e+00   1.4461000e+00   7.0410000e-01
>   1.1181703e+00   6.3480000e-01   1.3862000e+00   7.3500000e-01
>   3.0545466e-01   1.1910000e-01   9.9690000e-01   6.1550000e-01
>  -1.3098448e-02   5.8540000e-01   9.8350000e-01   5.0000000e-01
>   1.6867483e-02   1.1534000e+00   1.2547000e+00   6.4400000e-01
>   1.7409012e+00   4.0260000e-01   1.5911000e+00   8.3690000e-01
>   4.2981412e+00  -9.4030000e-01   2.3521000e+00   8.9760000e-01
>   5.5572278e+00  -1.0487000e+00   2.8869000e+00   8.4650000e-01
>   5.0821027e+00  -6.6560000e-01   2.5025000e+00   7.7680000e-01
>   4.2007377e+00  -5.2990000e-01   1.8804000e+00   7.3120000e-01
>   3.8386866e+00   8.3030000e-01   1.7194000e+00   7.0540000e-01
>   3.4180849e+00   2.4255000e+00   1.7376000e+00   6.5460000e-01
>   1.3677172e+00   2.1156000e+00   1.1144000e+00   2.1220000e-01
>  -1.7162052e+00   1.1448000e+00  -7.9700000e-02  -7.9150000e-01
>  -1.9232096e+00   1.5740000e-01  -7.9840000e-01  -1.5431000e+00
>  -1.8284831e-01  -1.0910000e+00  -8.9700000e-01  -1.5889000e+00
>  -4.0974962e-01  -1.2196000e+00  -9.0260000e-01  -1.4306000e+00
>  -2.5117628e+00  -2.9010000e-01  -1.1277000e+00  -1.3540000e+00
>  -4.6317041e+00  -1.6130000e-01  -1.4714000e+00  -1.2719000e+00
>  -5.7026127e+00  -1.3923000e+00  -1.5652000e+00  -1.1470000e+00
>  -4.4759897e+00  -2.5924000e+00  -1.4827000e+00  -1.0687000e+00
>  -2.7933593e+00  -1.9811000e+00  -1.5278000e+00  -1.1127000e+00
>  -3.5507524e+00  -5.6530000e-01  -1.4113000e+00  -1.2586000e+00
>  -5.1332807e+00   1.6650000e-01  -1.2267000e+00  -1.3632000e+00
>  -5.3023129e+00   4.3660000e-01  -9.8610000e-01  -1.2667000e+00
>  -3.8190529e+00  -1.4880000e-01  -5.9820000e-01  -1.0096000e+00
>  -1.4434876e+00  -1.0574000e+00  -6.2470000e-01  -8.0480000e-01
>   2.4143934e-01  -8.8200000e-01  -9.2780000e-01  -6.7370000e-01
>  -4.0353724e-02   4.9500000e-02  -1.1545000e+00  -4.6760000e-01
>  -8.2794159e-01   3.8550000e-01  -1.5756000e+00  -2.7960000e-01
>  -1.1040446e+00   4.1050000e-01  -1.7994000e+00  -2.6320000e-01
>  -1.0891953e+00   3.1930000e-01  -1.2926000e+00  -2.7960000e-01
>  -8.2761062e-01  -7.5510000e-01  -7.0880000e-01  -3.4000000e-01
>  -1.1477686e-01  -1.9891000e+00  -6.5850000e-01  -5.3830000e-01
>   3.9795697e-01  -1.7114000e+00  -7.0230000e-01  -6.1390000e-01
>  -1.5903103e-02   2.0000000e-03  -5.1700000e-01  -5.1240000e-01
>  -5.9442617e-01   1.4943000e+00  -6.6830000e-01  -4.5100000e-01
>  -7.4192259e-01   1.1252000e+00  -1.1471000e+00  -4.1980000e-01
>  -1.0161418e+00  -9.2730000e-01  -1.2733000e+00  -3.6980000e-01
>  -1.1213639e+00  -2.1086000e+00  -1.3848000e+00  -3.8960000e-01
>  -9.2994714e-01  -1.2384000e+00  -1.8417000e+00  -4.2880000e-01
>  -1.3948874e+00  -2.1840000e-01  -1.7197000e+00  -3.5250000e-01
>  -2.3932756e+00   1.3830000e-01  -1.1077000e+00  -2.5250000e-01
>  -2.9104167e+00   4.1730000e-01  -1.0828000e+00  -2.2350000e-01
>  -3.0708237e+00  -2.2820000e-01  -1.3337000e+00  -2.3410000e-01
>  -3.2847692e+00  -1.2936000e+00  -8.3780000e-01  -2.4320000e-01
>  -2.8970388e+00  -1.1050000e+00  -8.3600000e-02  -2.2170000e-01
>  -1.4337977e+00  -2.5180000e-01  -2.6730000e-01  -1.9190000e-01
>   2.8414907e-01   7.1100000e-02  -1.1325000e+00  -1.3110000e-01
>   1.7163887e+00   2.1200000e-02  -1.7156000e+00  -3.6000000e-02
>   2.2735769e+00  -4.1770000e-01  -1.6805000e+00   2.1700000e-02
>   7.1594331e-01  -4.6670000e-01  -1.1349000e+00   2.8700000e-02
>  -2.1484484e+00   1.2572000e+00  -5.4820000e-01   1.6000000e-03
>  -4.1894607e+00   3.4216000e+00  -3.3540000e-01  -4.6200000e-02
>  -4.2555323e+00   3.1867000e+00  -4.3270000e-01  -1.6900000e-02
>  -2.3236475e+00   1.3088000e+00  -6.7040000e-01   4.3300000e-02
>   2.3311552e-01   6.3430000e-01  -8.6190000e-01   1.4300000e-02
>   1.6228906e+00   1.2580000e+00  -8.0460000e-01  -3.4400000e-02
>   2.1017971e+00   2.1397000e+00  -6.1850000e-01  -7.1400000e-02
>   2.3664708e+00   2.1582000e+00  -5.2650000e-01  -4.6000000e-02
>   1.6834270e+00   1.3613000e+00  -2.3590000e-01   1.6910000e-01
>   2.3309903e-01   1.5648000e+00   1.8450000e-01   4.1220000e-01
>   2.1599655e-03   2.3516000e+00   9.0400000e-02   4.5700000e-01
>   1.3253922e+00   1.4603000e+00  -1.2320000e-01   4.0470000e-01
>   2.1093237e+00  -5.0570000e-01   8.4100000e-02   3.9070000e-01
>   1.0695928e+00  -1.3410000e+00   1.9590000e-01   2.1560000e-01
>  -1.5460720e+00  -9.9850000e-01   9.3000000e-02  -1.4910000e-01
>  -2.6383109e+00  -9.7970000e-01   3.2110000e-01  -2.2630000e-01
>  -1.5720291e+00  -1.8979000e+00   5.6100000e-01   5.9400000e-02
>  -5.6972503e-01  -2.9857000e+00   4.5890000e-01   2.6890000e-01
>  -3.3805452e-01  -2.8752000e+00   3.2730000e-01   2.7880000e-01
>  -3.9750097e-01  -1.6983000e+00   2.5580000e-01   2.6110000e-01
>  -3.3591531e-01  -7.4020000e-01   4.0650000e-01   2.2640000e-01
>  -6.8828714e-01  -2.0100000e-02   7.3640000e-01   1.7750000e-01
>  -1.0528772e+00   1.8690000e-01   8.9890000e-01   2.3180000e-01
>  -4.1994148e-01  -9.1200000e-01   7.3240000e-01   2.9500000e-01
>   1.3328172e+00  -2.1861000e+00   2.3790000e-01   2.9120000e-01
>   1.7569218e+00  -1.9757000e+00  -3.5370000e-01   2.9600000e-01
>   5.6771269e-01  -9.2430000e-01  -8.2090000e-01   2.9200000e-01
>  -4.4784724e-02  -4.2020000e-01  -1.0343000e+00   2.3690000e-01
>  -8.6256872e-01  -9.7920000e-01  -4.9330000e-01   1.7450000e-01
>  -2.3470919e+00  -1.2717000e+00   5.6690000e-01   1.5210000e-01
>  -2.9618138e+00  -6.4620000e-01   1.1617000e+00   1.8430000e-01
>  -2.4599672e+00  -2.1000000e-03   9.9650000e-01   2.3330000e-01
>  -1.2686523e+00   8.7600000e-02   5.2970000e-01   2.7020000e-01
>   4.1179445e-01  -5.2370000e-01   7.0400000e-02   3.0080000e-01
>   1.3911615e+00  -7.2680000e-01  -3.4500000e-01   2.4920000e-01
>   1.0501937e+00  -9.6700000e-02  -6.1480000e-01   7.9100000e-02
>   3.8303559e-01   1.2810000e-01  -4.4600000e-01   1.8800000e-02
>   5.5902586e-01  -4.4070000e-01   2.9090000e-01   1.7510000e-01
>   7.4834886e-01   1.7800000e-02   9.5990000e-01   3.5900000e-01
>   9.3231000e-02   1.5861000e+00   8.6380000e-01   4.3670000e-01
>  -2.5259224e-01   2.0897000e+00   9.3000000e-02   4.0030000e-01
>   3.0435414e-01   2.1087000e+00  -6.6730000e-01   3.2480000e-01
>   1.5426069e+00   2.2765000e+00  -9.5000000e-01   2.7810000e-01
>   2.9445135e+00   9.5220000e-01  -7.6170000e-01   2.6180000e-01
>   3.1076218e+00  -6.9570000e-01  -4.0980000e-01   2.7350000e-01
>   1.8574960e+00  -3.6040000e-01   8.5000000e-03   2.8560000e-01
>   6.9885445e-01   2.1180000e-01   4.3880000e-01   2.3190000e-01
>  -7.8840372e-01  -5.6000000e-01   4.0610000e-01  -4.5600000e-02
>  -2.1568244e+00  -1.0529000e+00   4.1400000e-02  -4.3350000e-01
>  -1.6918494e+00  -1.3670000e-01   1.1650000e-01  -4.7600000e-01
>  -2.9207814e-01   1.0849000e+00   5.4860000e-01  -2.2910000e-01
>   9.1467069e-01   1.1807000e+00   5.8850000e-01  -9.0800000e-02
>   1.9210401e+00   2.9000000e-01   1.2040000e-01  -4.6000000e-02
>   2.8798188e+00  -6.8110000e-01  -5.1950000e-01   2.2900000e-02
>   2.6811710e+00  -7.7670000e-01  -1.1060000e+00   2.2300000e-02
>   1.4164646e+00  -3.8200000e-02  -1.0230000e+00  -5.5200000e-02
>  -4.6294993e-01   2.8010000e-01  -1.3060000e-01  -1.5860000e-01
>  -2.7147378e+00  -8.3800000e-01   7.3270000e-01  -2.9400000e-01
>  -4.0318775e+00  -2.0334000e+00   9.6670000e-01  -3.3850000e-01
>  -3.7062909e+00  -1.1178000e+00   8.4750000e-01  -1.8320000e-01
>  -2.3191012e+00   6.9250000e-01   6.6430000e-01   1.4600000e-02
>  -1.4634592e+00   6.0350000e-01   8.4200000e-02   5.9400000e-02
>  -1.0184177e+00  -4.5310000e-01  -4.6440000e-01  -2.9000000e-02
>  -4.0861097e-01  -7.7440000e-01  -1.8380000e-01  -1.0270000e-01
>   2.4610924e-01  -1.3240000e-01   4.1780000e-01  -1.0740000e-01
>   6.3172603e-01   1.5224000e+00   5.1740000e-01  -8.2900000e-02
>   1.1126721e-01   1.6490000e+00   2.7820000e-01  -2.9300000e-02
>  -3.8185376e-01  -4.8320000e-01   7.0700000e-02  -5.6000000e-03
>   1.5738103e-02  -9.1510000e-01  -1.6040000e-01  -5.7000000e-02
>   3.0971507e-01   8.0900000e-01  -3.9070000e-01  -5.2700000e-02
>  -6.4077003e-01   1.6376000e+00  -3.2440000e-01   2.5000000e-02
>  -1.4234868e+00   1.6302000e+00  -1.3910000e-01   1.7900000e-02
>  -1.0333888e+00   1.1260000e+00  -5.9700000e-02  -1.0450000e-01
>   2.8467183e-01   2.9450000e-01   1.5260000e-01  -1.2880000e-01
>   1.3494096e+00   3.2460000e-01   4.1380000e-01   2.5900000e-02
>   1.2594955e+00   6.7860000e-01   4.2880000e-01   1.3990000e-01
>   2.0574752e-01   4.7010000e-01   4.2100000e-01   8.4600000e-02
>  -5.1055738e-01   3.1290000e-01   5.0190000e-01  -8.1900000e-02
>   3.4837741e-01   1.4760000e-01   7.9900000e-02  -2.8650000e-01
>   1.4591326e+00  -7.7170000e-01  -5.4010000e-01  -4.1520000e-01
>   1.5739416e+00  -1.9764000e+00  -5.7510000e-01  -2.8300000e-01
>   1.1869071e+00  -3.0645000e+00  -2.2730000e-01  -2.4100000e-02
>  -9.0421517e-02  -3.2540000e+00   1.6100000e-02   1.0850000e-01
>  -1.4681015e+00  -2.2130000e+00  -1.0910000e-01   1.4860000e-01
>  -1.6676621e+00  -1.4453000e+00  -3.4230000e-01   1.7630000e-01
>  -1.2973219e+00  -1.7937000e+00  -3.2600000e-01   1.8430000e-01
>  -1.1111066e+00  -1.8012000e+00  -7.2300000e-02   2.0610000e-01
>  -5.9518934e-01  -3.3900000e-01   4.4890000e-01   2.5030000e-01
>   7.0208186e-01   1.6133000e+00   9.3220000e-01   2.2250000e-01
>   1.9801729e+00   3.1607000e+00   1.0245000e+00   1.6350000e-01
>   2.7614091e+00   4.3744000e+00   8.6110000e-01   2.0520000e-01
>   3.1022731e+00   4.9644000e+00   4.3030000e-01   3.0410000e-01
>   2.8026518e+00   3.9708000e+00  -2.6360000e-01   2.7990000e-01
>   1.6489340e+00   1.9822000e+00  -5.9440000e-01  -4.2000000e-03
>  -1.0920841e-01   6.6120000e-01  -2.2720000e-01  -2.9120000e-01
>  -6.1800372e-01   4.7380000e-01   3.8330000e-01  -2.0220000e-01
>   3.1480607e-01   2.8400000e-02   4.2230000e-01   1.1890000e-01
>   1.1101816e+00  -8.2700000e-01  -2.0760000e-01   3.1410000e-01
>   8.3072614e-01  -1.3095000e+00  -4.5430000e-01   3.0370000e-01
>   4.3940828e-01  -1.2281000e+00   1.7100000e-02   2.1100000e-01
>   1.0557784e+00  -1.6030000e-01   3.7120000e-01   1.3290000e-01
>   2.1389915e+00   1.6818000e+00   2.7880000e-01   1.1480000e-01
>   2.6962909e+00   1.9954000e+00   1.2840000e-01   1.1600000e-01
>   1.9253397e+00   1.0414000e+00   2.5700000e-02   1.8800000e-02
>   3.7593083e-01   9.0620000e-01  -2.0370000e-01  -7.8400000e-02
>  -7.4823114e-01   1.7241000e+00  -1.1400000e-01   2.2900000e-02
>  -8.2887593e-01   2.1359000e+00   2.3090000e-01   1.6660000e-01
>   1.9782034e-02   1.3776000e+00   4.3700000e-01   2.1150000e-01
>   8.6225734e-01   6.1830000e-01   4.2000000e-01   2.5650000e-01
>   5.1389303e-01  -1.5410000e-01   3.6310000e-01   3.4500000e-01
>  -1.0490516e+00  -1.3218000e+00   5.4260000e-01   4.2030000e-01
>  -1.7355671e+00  -1.5665000e+00   4.9840000e-01   4.8750000e-01
>  -8.3874772e-01  -1.6327000e+00   1.1220000e-01   5.2170000e-01
>  -5.8533779e-01  -2.8633000e+00  -2.6950000e-01   3.9180000e-01
>  -8.3832621e-01  -3.7735000e+00  -6.1630000e-01   1.3800000e-02
>  -5.1262238e-01  -3.2360000e+00  -7.5890000e-01  -2.6190000e-01
>  -1.8427207e-01  -1.9511000e+00  -9.8600000e-02  -9.6300000e-02
>  -4.5620414e-01  -1.1610000e+00   8.3320000e-01   1.8940000e-01
>  -8.8886479e-01  -7.3080000e-01   9.5380000e-01   2.9150000e-01
>  -8.8482552e-02  -1.7100000e-01   4.5410000e-01   3.1780000e-01
>   2.3904050e+00  -6.6680000e-01  -5.6000000e-03   3.0870000e-01
>   3.8973334e+00  -1.6657000e+00  -1.4280000e-01   3.4490000e-01
>   1.9578154e+00  -1.6671000e+00   2.8500000e-02   4.3260000e-01
>  -5.8105714e-01  -9.0130000e-01   3.0590000e-01   3.3740000e-01
>  -1.0625938e+00   2.9250000e-01   5.3530000e-01  -2.4000000e-03
>  -1.7255607e+00   1.2690000e+00   2.9550000e-01  -4.4440000e-01
>  -2.7813968e+00   1.3273000e+00  -2.5050000e-01  -7.9980000e-01
>  -2.0098731e+00   1.1268000e+00  -4.8870000e-01  -9.0860000e-01
>  -9.0267721e-01   8.7680000e-01  -6.6200000e-01  -9.2820000e-01
>  -1.0893012e+00   1.3258000e+00  -9.6430000e-01  -1.0113000e+00
>  -2.0387016e+00   3.1174000e+00  -1.2712000e+00  -1.1178000e+00
>
>


---------------------------------------------------------------------------
Stephen M. Smith, Professor of Biomedical Engineering
Associate Director,  Oxford University FMRIB Centre

FMRIB, JR Hospital, Headington, Oxford  OX3 9DU, UK
+44 (0) 1865 222726  (fax 222717)
[log in to unmask]    http://www.fmrib.ox.ac.uk/~steve
---------------------------------------------------------------------------

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