mpower: Compute the Power of a Real Symmetric Matrix
In corpcor: Efficient Estimation of Covariance and (Partial) Correlation
Description
Usage
Arguments
Details
Value
Author(s)
See Also
Examples
Description
mpower computes m^alpha, i.e.
the alpha-th power of the real symmetric
matrix m.
Usage
1
Arguments
m
a real-valued symmetric matrix.
alpha
exponent.
pseudo
if pseudo=TRUE then all zero eigenvalues are dropped
(e.g. for computing the pseudoinverse). The default is
to use all eigenvalues.
tol
tolerance - eigenvalues with absolute value smaller or equal
to tol are considered identically zero (default:
tol = max(dim(m))*max(abs(eval))*.Machine$double.eps).
Details
The matrix power of m is obtained by first computing the spectral
decomposition of m, and subsequent modification of the resulting eigenvalues.
Note that m is assumed to by symmetric, and only
its lower triangle (diagonal included) is used in eigen.
For computing the matrix power of cor.shrink use
the vastly more efficient function powcor.shrink.
Value
mpower returns
a matrix of the same dimensions as m.
Author(s)
Korbinian Strimmer (https://strimmerlab.github.io).
See Also
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Example output
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1.40352992 0.9932183 -0.2656967 -0.36188771 -0.6488742 -0.31097499
[2,] 0.99321828 1.8093366 -0.6693219 -0.60294304 -0.6099213 -0.54080690
[3,] -0.26569666 -0.6693219 1.6183805 1.23991928 -0.4199607 -0.12644279
[4,] -0.36188771 -0.6029430 1.2399193 1.49405920 -0.1272488 0.09793054
[5,] -0.64887424 -0.6099213 -0.4199607 -0.12724878 1.3514692 -0.19440061
[6,] -0.31097499 -0.5408069 -0.1264428 0.09793054 -0.1944006 1.34477836
[7,] 0.02265809 0.9978720 -0.8292401 -0.78687673 -0.3972817 0.23814360
[8,] 0.04404609 0.5836150 0.1312320 -0.37071764 -0.3960206 -0.63898830
[9,] -0.11542231 0.4742612 -0.1574868 -0.03130882 -0.2243596 -0.55105859
[10,] -0.32047972 -1.1396375 -0.1290195 0.09604356 0.4253231 0.54058729
[,7] [,8] [,9] [,10]
[1,] 0.02265809 0.04404609 -0.11542231 -0.32047972
[2,] 0.99787197 0.58361496 0.47426116 -1.13963748
[3,] -0.82924012 0.13123201 -0.15748678 -0.12901950
[4,] -0.78687673 -0.37071764 -0.03130882 0.09604356
[5,] -0.39728165 -0.39602061 -0.22435961 0.42532314
[6,] 0.23814360 -0.63898830 -0.55105859 0.54058729
[7,] 1.53523567 0.32666012 0.45381655 -0.67778368
[8,] 0.32666012 1.28767604 0.46516620 -0.66846279
[9,] 0.45381655 0.46516620 1.20454996 -0.27887359
[10,] -0.67778368 -0.66846279 -0.27887359 1.43231473
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1.40352992 0.9932183 -0.2656967 -0.36188771 -0.6488742 -0.31097499
[2,] 0.99321828 1.8093366 -0.6693219 -0.60294304 -0.6099213 -0.54080690
[3,] -0.26569666 -0.6693219 1.6183805 1.23991928 -0.4199607 -0.12644279
[4,] -0.36188771 -0.6029430 1.2399193 1.49405920 -0.1272488 0.09793054
[5,] -0.64887424 -0.6099213 -0.4199607 -0.12724878 1.3514692 -0.19440061
[6,] -0.31097499 -0.5408069 -0.1264428 0.09793054 -0.1944006 1.34477836
[7,] 0.02265809 0.9978720 -0.8292401 -0.78687673 -0.3972817 0.23814360
[8,] 0.04404609 0.5836150 0.1312320 -0.37071764 -0.3960206 -0.63898830
[9,] -0.11542231 0.4742612 -0.1574868 -0.03130882 -0.2243596 -0.55105859
[10,] -0.32047972 -1.1396375 -0.1290195 0.09604356 0.4253231 0.54058729
[,7] [,8] [,9] [,10]
[1,] 0.02265809 0.04404609 -0.11542231 -0.32047972
[2,] 0.99787197 0.58361496 0.47426116 -1.13963748
[3,] -0.82924012 0.13123201 -0.15748678 -0.12901950
[4,] -0.78687673 -0.37071764 -0.03130882 0.09604356
[5,] -0.39728165 -0.39602061 -0.22435961 0.42532314
[6,] 0.23814360 -0.63898830 -0.55105859 0.54058729
[7,] 1.53523567 0.32666012 0.45381655 -0.67778368
[8,] 0.32666012 1.28767604 0.46516620 -0.66846279
[9,] 0.45381655 0.46516620 1.20454996 -0.27887359
[10,] -0.67778368 -0.66846279 -0.27887359 1.43231473
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 2.15362678 -1.26787668 -0.08445574 0.63341006 0.84636349 0.3137123
[2,] -1.26787668 2.81657406 1.23129505 -0.94286805 0.16085694 0.4380385
[3,] -0.08445574 1.23129505 2.59608459 -1.37989210 0.85334177 0.5967004
[4,] 0.63341006 -0.94286805 -1.37989210 2.16689788 -0.06715141 -0.4153257
[5,] 0.84636349 0.16085694 0.85334177 -0.06715141 1.84506308 0.7123221
[6,] 0.31371232 0.43803851 0.59670042 -0.41532565 0.71232212 1.7368730
[7,] 0.82972760 -0.89424967 0.05555347 0.73923339 0.39889118 -0.4742407
[8,] 0.59486183 -0.51564943 -0.42500556 0.68301622 0.37001742 0.2663466
[9,] 0.31572604 0.01490004 0.45786373 -0.41628070 0.43041330 0.6529230
[10,] -0.25450270 0.93011149 0.62810133 -0.12291011 0.10256346 -0.1918883
[,7] [,8] [,9] [,10]
[1,] 0.82972760 0.59486183 0.31572604 -0.25450270
[2,] -0.89424967 -0.51564943 0.01490004 0.93011149
[3,] 0.05555347 -0.42500556 0.45786373 0.62810133
[4,] 0.73923339 0.68301622 -0.41628070 -0.12291011
[5,] 0.39889118 0.37001742 0.43041330 0.10256346
[6,] -0.47424067 0.26634661 0.65292297 -0.19188830
[7,] 1.97064510 0.29924794 -0.31141671 0.30853807
[8,] 0.29924794 1.47985073 -0.11573731 0.07335763
[9,] -0.31141671 -0.11573731 1.40473365 -0.17178753
[10,] 0.30853807 0.07335763 -0.17178753 1.63485763
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 2.15362678 -1.26787668 -0.08445574 0.63341006 0.84636349 0.3137123
[2,] -1.26787668 2.81657406 1.23129505 -0.94286805 0.16085694 0.4380385
[3,] -0.08445574 1.23129505 2.59608459 -1.37989210 0.85334177 0.5967004
[4,] 0.63341006 -0.94286805 -1.37989210 2.16689788 -0.06715141 -0.4153257
[5,] 0.84636349 0.16085694 0.85334177 -0.06715141 1.84506308 0.7123221
[6,] 0.31371232 0.43803851 0.59670042 -0.41532565 0.71232212 1.7368730
[7,] 0.82972760 -0.89424967 0.05555347 0.73923339 0.39889118 -0.4742407
[8,] 0.59486183 -0.51564943 -0.42500556 0.68301622 0.37001742 0.2663466
[9,] 0.31572604 0.01490004 0.45786373 -0.41628070 0.43041330 0.6529230
[10,] -0.25450270 0.93011149 0.62810133 -0.12291011 0.10256346 -0.1918883
[,7] [,8] [,9] [,10]
[1,] 0.82972760 0.59486183 0.31572604 -0.25450270
[2,] -0.89424967 -0.51564943 0.01490004 0.93011149
[3,] 0.05555347 -0.42500556 0.45786373 0.62810133
[4,] 0.73923339 0.68301622 -0.41628070 -0.12291011
[5,] 0.39889118 0.37001742 0.43041330 0.10256346
[6,] -0.47424067 0.26634661 0.65292297 -0.19188830
[7,] 1.97064510 0.29924794 -0.31141671 0.30853807
[8,] 0.29924794 1.47985073 -0.11573731 0.07335763
[9,] -0.31141671 -0.11573731 1.40473365 -0.17178753
[10,] 0.30853807 0.07335763 -0.17178753 1.63485763
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1.00000000 0.4486604 -0.09686933 -0.15800400 -0.33070739 -0.14807855
[2,] 0.44866041 1.0000000 -0.29611204 -0.11528113 -0.20834267 -0.20804491
[3,] -0.09686933 -0.2961120 1.00000000 0.55513930 -0.26292910 -0.09444219
[4,] -0.15800400 -0.1152811 0.55513930 1.00000000 -0.06522868 0.05670680
[5,] -0.33070739 -0.2083427 -0.26292910 -0.06522868 1.00000000 -0.18861338
[6,] -0.14807855 -0.2080449 -0.09444219 0.05670680 -0.18861338 1.00000000
[7,] -0.12237467 0.3781663 -0.30860331 -0.30715549 -0.17939375 0.19214896
[8,] -0.07260952 0.1845497 0.11189448 -0.20528156 -0.17939276 -0.27015689
[9,] -0.11463995 0.1531420 -0.08834331 0.05916911 -0.11718240 -0.27770084
[10,] -0.05657012 -0.4688904 -0.13972443 -0.01296606 0.10787963 0.21174203
[,7] [,8] [,9] [,10]
[1,] -0.12237467 -0.07260952 -0.11463995 -0.05657012
[2,] 0.37816629 0.18454970 0.15314196 -0.46889039
[3,] -0.30860331 0.11189448 -0.08834331 -0.13972443
[4,] -0.30715549 -0.20528156 0.05916911 -0.01296606
[5,] -0.17939375 -0.17939276 -0.11718240 0.10787963
[6,] 0.19214896 -0.27015689 -0.27770084 0.21174203
[7,] 1.00000000 0.07091623 0.19242019 -0.27660781
[8,] 0.07091623 1.00000000 0.16685729 -0.23589709
[9,] 0.19242019 0.16685729 1.00000000 -0.03054996
[10,] -0.27660781 -0.23589709 -0.03054996 1.00000000
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1.00000000 0.4486604 -0.09686933 -0.15800400 -0.33070739 -0.14807855
[2,] 0.44866041 1.0000000 -0.29611204 -0.11528113 -0.20834267 -0.20804491
[3,] -0.09686933 -0.2961120 1.00000000 0.55513930 -0.26292910 -0.09444219
[4,] -0.15800400 -0.1152811 0.55513930 1.00000000 -0.06522868 0.05670680
[5,] -0.33070739 -0.2083427 -0.26292910 -0.06522868 1.00000000 -0.18861338
[6,] -0.14807855 -0.2080449 -0.09444219 0.05670680 -0.18861338 1.00000000
[7,] -0.12237467 0.3781663 -0.30860331 -0.30715549 -0.17939375 0.19214896
[8,] -0.07260952 0.1845497 0.11189448 -0.20528156 -0.17939276 -0.27015689
[9,] -0.11463995 0.1531420 -0.08834331 0.05916911 -0.11718240 -0.27770084
[10,] -0.05657012 -0.4688904 -0.13972443 -0.01296606 0.10787963 0.21174203
[,7] [,8] [,9] [,10]
[1,] -0.12237467 -0.07260952 -0.11463995 -0.05657012
[2,] 0.37816629 0.18454970 0.15314196 -0.46889039
[3,] -0.30860331 0.11189448 -0.08834331 -0.13972443
[4,] -0.30715549 -0.20528156 0.05916911 -0.01296606
[5,] -0.17939375 -0.17939276 -0.11718240 0.10787963
[6,] 0.19214896 -0.27015689 -0.27770084 0.21174203
[7,] 1.00000000 0.07091623 0.19242019 -0.27660781
[8,] 0.07091623 1.00000000 0.16685729 -0.23589709
[9,] 0.19242019 0.16685729 1.00000000 -0.03054996
[10,] -0.27660781 -0.23589709 -0.03054996 1.00000000
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1.06431917 0.5509593 -0.1270353 -0.193329903 -0.39632452 -0.1796502
[2,] 0.55095930 1.1154684 -0.3605890 -0.195101046 -0.27857182 -0.2668626
[3,] -0.12703530 -0.3605890 1.0945737 0.687109000 -0.30308941 -0.1034272
[4,] -0.19332990 -0.1951010 0.6871090 1.073006073 -0.08250179 0.0628060
[5,] -0.39632452 -0.2785718 -0.3030894 -0.082501793 1.05509573 -0.2032888
[6,] -0.17965023 -0.2668626 -0.1034272 0.062805998 -0.20328877 1.0533149
[7,] -0.11110048 0.4847251 -0.4042246 -0.391210784 -0.22047722 0.2157920
[8,] -0.06123765 0.2472957 0.1240850 -0.239705551 -0.22054219 -0.3426074
[9,] -0.12511833 0.2076670 -0.1006925 0.050826482 -0.13731876 -0.3345636
[10,] -0.09667476 -0.5910715 -0.1489316 -0.003598428 0.15987622 0.2724613
[,7] [,8] [,9] [,10]
[1,] -0.1111005 -0.06123765 -0.12511833 -0.096674759
[2,] 0.4847251 0.24729572 0.20766699 -0.591071459
[3,] -0.4042246 0.12408498 -0.10069254 -0.148931555
[4,] -0.3912108 -0.23970555 0.05082648 -0.003598428
[5,] -0.2204772 -0.22054219 -0.13731876 0.159876221
[6,] 0.2157920 -0.34260737 -0.33456355 0.272461252
[7,] 1.0769815 0.11219130 0.24158384 -0.350474406
[8,] 0.1121913 1.04072756 0.22127679 -0.313638544
[9,] 0.2415838 0.22127679 1.03066184 -0.066646101
[10,] -0.3504744 -0.31363854 -0.06664610 1.060220351
corpcor documentation built on Sept. 16, 2021, 5:12 p.m.
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Description Usage Arguments Details Value Author(s) See Also Examples
Description
mpower computes m^alpha, i.e.
the alpha-th power of the real symmetric
matrix m.
Usage
1 |
Arguments
m |
a real-valued symmetric matrix. |
alpha |
exponent. |
pseudo |
if |
tol |
tolerance - eigenvalues with absolute value smaller or equal
to |
Details
The matrix power of m is obtained by first computing the spectral
decomposition of m, and subsequent modification of the resulting eigenvalues.
Note that m is assumed to by symmetric, and only
its lower triangle (diagonal included) is used in eigen.
For computing the matrix power of cor.shrink use
the vastly more efficient function powcor.shrink.
Value
mpower returns
a matrix of the same dimensions as m.
Author(s)
Korbinian Strimmer (https://strimmerlab.github.io).
See Also
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 |
Example output
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1.40352992 0.9932183 -0.2656967 -0.36188771 -0.6488742 -0.31097499
[2,] 0.99321828 1.8093366 -0.6693219 -0.60294304 -0.6099213 -0.54080690
[3,] -0.26569666 -0.6693219 1.6183805 1.23991928 -0.4199607 -0.12644279
[4,] -0.36188771 -0.6029430 1.2399193 1.49405920 -0.1272488 0.09793054
[5,] -0.64887424 -0.6099213 -0.4199607 -0.12724878 1.3514692 -0.19440061
[6,] -0.31097499 -0.5408069 -0.1264428 0.09793054 -0.1944006 1.34477836
[7,] 0.02265809 0.9978720 -0.8292401 -0.78687673 -0.3972817 0.23814360
[8,] 0.04404609 0.5836150 0.1312320 -0.37071764 -0.3960206 -0.63898830
[9,] -0.11542231 0.4742612 -0.1574868 -0.03130882 -0.2243596 -0.55105859
[10,] -0.32047972 -1.1396375 -0.1290195 0.09604356 0.4253231 0.54058729
[,7] [,8] [,9] [,10]
[1,] 0.02265809 0.04404609 -0.11542231 -0.32047972
[2,] 0.99787197 0.58361496 0.47426116 -1.13963748
[3,] -0.82924012 0.13123201 -0.15748678 -0.12901950
[4,] -0.78687673 -0.37071764 -0.03130882 0.09604356
[5,] -0.39728165 -0.39602061 -0.22435961 0.42532314
[6,] 0.23814360 -0.63898830 -0.55105859 0.54058729
[7,] 1.53523567 0.32666012 0.45381655 -0.67778368
[8,] 0.32666012 1.28767604 0.46516620 -0.66846279
[9,] 0.45381655 0.46516620 1.20454996 -0.27887359
[10,] -0.67778368 -0.66846279 -0.27887359 1.43231473
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1.40352992 0.9932183 -0.2656967 -0.36188771 -0.6488742 -0.31097499
[2,] 0.99321828 1.8093366 -0.6693219 -0.60294304 -0.6099213 -0.54080690
[3,] -0.26569666 -0.6693219 1.6183805 1.23991928 -0.4199607 -0.12644279
[4,] -0.36188771 -0.6029430 1.2399193 1.49405920 -0.1272488 0.09793054
[5,] -0.64887424 -0.6099213 -0.4199607 -0.12724878 1.3514692 -0.19440061
[6,] -0.31097499 -0.5408069 -0.1264428 0.09793054 -0.1944006 1.34477836
[7,] 0.02265809 0.9978720 -0.8292401 -0.78687673 -0.3972817 0.23814360
[8,] 0.04404609 0.5836150 0.1312320 -0.37071764 -0.3960206 -0.63898830
[9,] -0.11542231 0.4742612 -0.1574868 -0.03130882 -0.2243596 -0.55105859
[10,] -0.32047972 -1.1396375 -0.1290195 0.09604356 0.4253231 0.54058729
[,7] [,8] [,9] [,10]
[1,] 0.02265809 0.04404609 -0.11542231 -0.32047972
[2,] 0.99787197 0.58361496 0.47426116 -1.13963748
[3,] -0.82924012 0.13123201 -0.15748678 -0.12901950
[4,] -0.78687673 -0.37071764 -0.03130882 0.09604356
[5,] -0.39728165 -0.39602061 -0.22435961 0.42532314
[6,] 0.23814360 -0.63898830 -0.55105859 0.54058729
[7,] 1.53523567 0.32666012 0.45381655 -0.67778368
[8,] 0.32666012 1.28767604 0.46516620 -0.66846279
[9,] 0.45381655 0.46516620 1.20454996 -0.27887359
[10,] -0.67778368 -0.66846279 -0.27887359 1.43231473
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 2.15362678 -1.26787668 -0.08445574 0.63341006 0.84636349 0.3137123
[2,] -1.26787668 2.81657406 1.23129505 -0.94286805 0.16085694 0.4380385
[3,] -0.08445574 1.23129505 2.59608459 -1.37989210 0.85334177 0.5967004
[4,] 0.63341006 -0.94286805 -1.37989210 2.16689788 -0.06715141 -0.4153257
[5,] 0.84636349 0.16085694 0.85334177 -0.06715141 1.84506308 0.7123221
[6,] 0.31371232 0.43803851 0.59670042 -0.41532565 0.71232212 1.7368730
[7,] 0.82972760 -0.89424967 0.05555347 0.73923339 0.39889118 -0.4742407
[8,] 0.59486183 -0.51564943 -0.42500556 0.68301622 0.37001742 0.2663466
[9,] 0.31572604 0.01490004 0.45786373 -0.41628070 0.43041330 0.6529230
[10,] -0.25450270 0.93011149 0.62810133 -0.12291011 0.10256346 -0.1918883
[,7] [,8] [,9] [,10]
[1,] 0.82972760 0.59486183 0.31572604 -0.25450270
[2,] -0.89424967 -0.51564943 0.01490004 0.93011149
[3,] 0.05555347 -0.42500556 0.45786373 0.62810133
[4,] 0.73923339 0.68301622 -0.41628070 -0.12291011
[5,] 0.39889118 0.37001742 0.43041330 0.10256346
[6,] -0.47424067 0.26634661 0.65292297 -0.19188830
[7,] 1.97064510 0.29924794 -0.31141671 0.30853807
[8,] 0.29924794 1.47985073 -0.11573731 0.07335763
[9,] -0.31141671 -0.11573731 1.40473365 -0.17178753
[10,] 0.30853807 0.07335763 -0.17178753 1.63485763
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 2.15362678 -1.26787668 -0.08445574 0.63341006 0.84636349 0.3137123
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[5,] 0.39889118 0.37001742 0.43041330 0.10256346
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[8,] 0.29924794 1.47985073 -0.11573731 0.07335763
[9,] -0.31141671 -0.11573731 1.40473365 -0.17178753
[10,] 0.30853807 0.07335763 -0.17178753 1.63485763
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[10,] -0.05657012 -0.4688904 -0.13972443 -0.01296606 0.10787963 0.21174203
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[1,] -0.12237467 -0.07260952 -0.11463995 -0.05657012
[2,] 0.37816629 0.18454970 0.15314196 -0.46889039
[3,] -0.30860331 0.11189448 -0.08834331 -0.13972443
[4,] -0.30715549 -0.20528156 0.05916911 -0.01296606
[5,] -0.17939375 -0.17939276 -0.11718240 0.10787963
[6,] 0.19214896 -0.27015689 -0.27770084 0.21174203
[7,] 1.00000000 0.07091623 0.19242019 -0.27660781
[8,] 0.07091623 1.00000000 0.16685729 -0.23589709
[9,] 0.19242019 0.16685729 1.00000000 -0.03054996
[10,] -0.27660781 -0.23589709 -0.03054996 1.00000000
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[1,] 1.00000000 0.4486604 -0.09686933 -0.15800400 -0.33070739 -0.14807855
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[6,] -0.14807855 -0.2080449 -0.09444219 0.05670680 -0.18861338 1.00000000
[7,] -0.12237467 0.3781663 -0.30860331 -0.30715549 -0.17939375 0.19214896
[8,] -0.07260952 0.1845497 0.11189448 -0.20528156 -0.17939276 -0.27015689
[9,] -0.11463995 0.1531420 -0.08834331 0.05916911 -0.11718240 -0.27770084
[10,] -0.05657012 -0.4688904 -0.13972443 -0.01296606 0.10787963 0.21174203
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[1,] -0.12237467 -0.07260952 -0.11463995 -0.05657012
[2,] 0.37816629 0.18454970 0.15314196 -0.46889039
[3,] -0.30860331 0.11189448 -0.08834331 -0.13972443
[4,] -0.30715549 -0.20528156 0.05916911 -0.01296606
[5,] -0.17939375 -0.17939276 -0.11718240 0.10787963
[6,] 0.19214896 -0.27015689 -0.27770084 0.21174203
[7,] 1.00000000 0.07091623 0.19242019 -0.27660781
[8,] 0.07091623 1.00000000 0.16685729 -0.23589709
[9,] 0.19242019 0.16685729 1.00000000 -0.03054996
[10,] -0.27660781 -0.23589709 -0.03054996 1.00000000
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1.06431917 0.5509593 -0.1270353 -0.193329903 -0.39632452 -0.1796502
[2,] 0.55095930 1.1154684 -0.3605890 -0.195101046 -0.27857182 -0.2668626
[3,] -0.12703530 -0.3605890 1.0945737 0.687109000 -0.30308941 -0.1034272
[4,] -0.19332990 -0.1951010 0.6871090 1.073006073 -0.08250179 0.0628060
[5,] -0.39632452 -0.2785718 -0.3030894 -0.082501793 1.05509573 -0.2032888
[6,] -0.17965023 -0.2668626 -0.1034272 0.062805998 -0.20328877 1.0533149
[7,] -0.11110048 0.4847251 -0.4042246 -0.391210784 -0.22047722 0.2157920
[8,] -0.06123765 0.2472957 0.1240850 -0.239705551 -0.22054219 -0.3426074
[9,] -0.12511833 0.2076670 -0.1006925 0.050826482 -0.13731876 -0.3345636
[10,] -0.09667476 -0.5910715 -0.1489316 -0.003598428 0.15987622 0.2724613
[,7] [,8] [,9] [,10]
[1,] -0.1111005 -0.06123765 -0.12511833 -0.096674759
[2,] 0.4847251 0.24729572 0.20766699 -0.591071459
[3,] -0.4042246 0.12408498 -0.10069254 -0.148931555
[4,] -0.3912108 -0.23970555 0.05082648 -0.003598428
[5,] -0.2204772 -0.22054219 -0.13731876 0.159876221
[6,] 0.2157920 -0.34260737 -0.33456355 0.272461252
[7,] 1.0769815 0.11219130 0.24158384 -0.350474406
[8,] 0.1121913 1.04072756 0.22127679 -0.313638544
[9,] 0.2415838 0.22127679 1.03066184 -0.066646101
[10,] -0.3504744 -0.31363854 -0.06664610 1.060220351
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