sdd: Semidiscrete Decomposition
In sddpack: Semidiscrete Decomposition
Description
Usage
Arguments
Details
Value
Note
Author(s)
References
Examples
Description
The semidiscrete decomposition (SDD) approximates a matrix as a weighted sum of outer products formed by vectors with entries constrained to be in the set {-1, 0, 1}.
Usage
1
sdd(A, kmax = 100, alphamin = 0.01, lmax = 100, rhomin = 10e-20)
Arguments
A
matrix of values on which to run sdd
kmax
number of outer-loop iterations (see References)
alphamin
progress check (see References)
lmax
number of inner-loop iterations (see References)
rhomin
threshold test (See References)
Details
The semidiscrete decomposition (SDD) approximates a matrix as a weighted sum of outer products formed by vectors with entries constrained to be in the set {-1, 0, 1}.
It is useful for image compression and for latent semantic indexing (LSI) in information retrieval.
The primary advantage of the SDD over other types of matrix approximations such as the truncated singular value decomposition (SVD) is that it typically provides a more accurate approximation for far less storage.
The package has been ported from Matlab code given on http://www.cs.umd.edu/~oleary/SDDPACK/.
See the webpage for full documentation.
Value
x
matrix of X's, where A is approximately equal to X%*%diag(D)%*%Y
d
vector of D's, where A is approximately equal to X%*%diag(D)%*%Y
y
matrix of Y's, where A is approximately equal to X%*%diag(D)%*%Y
Note
Ported to R by Eric Sun <esun@cs.stanford.edu>
Author(s)
Tamara G. Kolda, Dianne P. O'Leary (Matlab code)
References
http://www.cs.umd.edu/~oleary/SDDPACK/
Examples
1
2
Example output
$x
[1,] 0 0 0 -1 -1 0 0 0 -1 0 1 1 0 -1 1 0 -1 -1 1 1 0 0 -1 1 1
[2,] 1 1 -1 0 -1 0 0 1 1 -1 0 1 1 1 0 1 0 0 0 1 -1 -1 0 -1 0
[3,] 0 0 -1 -1 1 0 -1 -1 1 -1 1 0 0 -1 1 0 1 1 -1 -1 -1 0 0 0 1
[4,] -1 0 -1 0 0 1 1 -1 -1 -1 -1 1 0 -1 -1 0 1 1 1 0 1 0 0 1 0
[5,] -1 0 1 0 0 0 -1 0 -1 -1 0 -1 0 0 1 0 0 0 -1 -1 0 -1 0 0 -1
[6,] 0 1 0 -1 1 0 1 0 0 0 1 1 -1 1 1 0 0 1 0 0 0 1 1 1 0
[7,] -1 -1 -1 1 0 0 -1 1 0 0 1 -1 1 0 1 0 -1 1 1 -1 0 0 0 1 0
[8,] 0 -1 0 -1 -1 -1 1 0 0 0 0 0 0 -1 -1 0 0 -1 0 -1 0 -1 1 0 -1
[9,] -1 1 0 -1 0 0 0 0 -1 -1 -1 1 0 -1 0 0 -1 0 -1 1 -1 1 0 0 -1
[10,] -1 1 0 -1 -1 0 -1 -1 0 1 1 1 1 1 0 0 1 0 1 -1 -1 1 0 1 -1
[1,] 0 0 -1 -1 1 1 0 -1 0 0 1 -1 -1 0 -1 1 0 -1 1 1 1 1 0 1
[2,] 1 0 -1 0 -1 -1 0 -1 -1 1 0 1 0 -1 1 1 1 0 0 0 0 -1 1 0
[3,] 0 -1 0 0 0 1 -1 0 1 -1 1 1 0 -1 -1 0 -1 -1 1 -1 0 1 0 0
[4,] -1 0 -1 1 1 -1 -1 -1 1 -1 -1 0 0 -1 1 0 -1 -1 -1 1 -1 1 1 0
[5,] 1 0 0 -1 -1 0 -1 0 0 1 0 -1 -1 -1 0 0 -1 0 1 0 0 0 0 0
[6,] 1 0 -1 1 0 1 0 1 0 -1 0 -1 -1 1 1 -1 -1 -1 0 0 1 0 -1 -1
[7,] -1 -1 -1 0 0 0 1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 1 0 0
[8,] -1 0 -1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 -1 1 0 0 0 1 -1
[9,] -1 0 0 -1 -1 -1 -1 0 -1 -1 -1 1 0 -1 0 1 -1 1 1 1 0 0 0 0
[10,] 0 1 0 0 0 0 0 0 1 0 1 1 -1 0 1 0 1 1 1 -1 0 1 0 -1
[1,] 1 0 -1 0 0 1 1 0 0 1 -1 0 0 0 1 1 1 -1 -1 0 1 0 -1 -1
[2,] 0 0 0 -1 0 1 0 1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 1 0 0 0 -1
[3,] 1 1 0 0 0 -1 1 0 -1 1 1 0 -1 0 0 0 0 0 -1 0 0 1 1 0
[4,] -1 0 0 0 -1 0 0 -1 -1 1 1 -1 1 0 1 1 -1 0 0 1 0 1 0 1
[5,] 0 0 -1 0 1 -1 -1 0 -1 0 1 1 0 1 1 0 1 0 -1 -1 1 1 -1 0
[6,] 0 0 -1 0 1 1 -1 0 1 1 0 0 -1 -1 -1 0 1 0 1 -1 1 0 1 1
[7,] 0 -1 -1 0 1 1 1 1 0 -1 0 -1 0 1 -1 0 1 0 0 0 1 -1 -1 0
[8,] 1 0 1 1 0 1 0 -1 -1 -1 1 0 0 -1 0 0 0 0 1 -1 1 0 -1 0
[9,] 1 -1 -1 0 -1 0 1 -1 0 0 0 0 0 -1 1 -1 1 1 0 0 0 0 0 -1
[10,] -1 0 0 1 -1 0 0 1 -1 1 0 -1 -1 1 0 0 0 1 -1 -1 -1 -1 0 1
[1,] 0 0 0 -1 1 -1 0 -1 0 1 1 -1 0 -1 0 -1 0 -1 1 0 0 0 -1 0 1
[2,] -1 -1 0 1 1 -1 -1 0 0 0 -1 0 -1 -1 0 1 1 0 1 -1 0 0 1 1 0
[3,] 1 1 0 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 -1 -1 0 -1
[4,] 0 0 1 0 -1 -1 0 0 -1 0 0 0 0 0 1 -1 1 1 0 -1 0 1 -1 1 -1
[5,] 0 -1 -1 0 0 1 -1 0 1 1 -1 -1 0 1 0 0 1 1 1 1 0 0 1 1 -1
[6,] 0 -1 0 0 0 0 0 1 1 0 0 -1 0 1 1 1 0 0 1 1 1 1 1 -1 0
[7,] 1 0 0 1 0 1 -1 -1 0 1 -1 0 0 1 -1 -1 0 1 0 0 1 1 0 0 1
[8,] 0 1 1 1 1 0 -1 0 0 -1 1 0 0 0 0 -1 1 -1 -1 1 1 0 -1 1 0
[9,] 1 -1 1 0 0 -1 1 -1 1 -1 -1 0 1 -1 0 0 1 0 -1 1 0 1 0 0 0
[10,] 0 0 0 0 1 0 0 -1 0 -1 -1 0 0 -1 0 0 -1 1 0 0 1 0 0 -1 0
[1,] 0 -1
[2,] -1 -1
[3,] -1 0
[4,] 0 0
[5,] -1 1
[6,] 0 -1
[7,] -1 0
[8,] -1 0
[9,] -1 0
[10,] -1 1
$d
[1] 7.475118e-01 7.175652e-01 8.227342e-01 3.301819e-01 5.613795e-01
[6] 6.419292e-01 4.073040e-01 2.944641e-01 4.605838e-01 2.278536e-01
[11] 1.742302e-01 1.805593e-01 2.432678e-01 1.624615e-01 2.178666e-01
[16] 2.959007e-01 1.822302e-01 1.199071e-01 1.190462e-01 5.876378e-02
[21] 7.178288e-02 5.247941e-02 7.264214e-02 4.396722e-02 3.721253e-02
[26] 3.308639e-02 3.627223e-02 2.685901e-02 1.816245e-02 3.363641e-02
[31] 2.804515e-02 2.603759e-02 1.162986e-02 1.105823e-02 7.883801e-03
[36] 1.670424e-02 5.164284e-03 6.763550e-03 7.542194e-03 7.037015e-03
[41] 1.006001e-02 5.784963e-03 5.679659e-03 3.786845e-03 5.465679e-03
[46] 2.985631e-03 1.965327e-03 4.235258e-03 2.278530e-03 1.476986e-03
[51] 1.847830e-03 1.755129e-03 1.993064e-03 1.609652e-03 9.784657e-04
[56] 8.015648e-04 9.801410e-04 7.060937e-04 5.244912e-04 4.570337e-04
[61] 4.401964e-04 9.070386e-04 3.321407e-04 4.077167e-04 2.672027e-04
[66] 4.581664e-04 2.774248e-04 1.544031e-04 1.670289e-04 9.834834e-05
[71] 1.845007e-04 1.553917e-04 7.812729e-05 7.302220e-05 7.205621e-05
[76] 7.245066e-05 5.248978e-05 7.804247e-05 5.845325e-05 4.868747e-05
[81] 4.319304e-05 2.814451e-05 2.123464e-05 3.557497e-05 2.426180e-05
[86] 3.817365e-05 1.220277e-05 2.039952e-05 1.174712e-05 8.466911e-06
[91] 7.469365e-06 8.110438e-06 5.671511e-06 6.136449e-06 5.216119e-06
[96] 4.389743e-06 9.564996e-06 2.955949e-06 2.377918e-06 2.179884e-06
$y
[1,] 1 0 -1 1 -1 0 0 1 0 -1 -1 0 1 1 0 0 0 -1 0 0 0 0 -1 0 0 -1
[2,] -1 1 0 0 0 1 1 1 0 0 0 0 -1 0 0 0 0 -1 0 1 0 0 0 0 1 1
[3,] 1 1 0 -1 0 0 -1 -1 1 -1 1 0 0 0 0 0 0 0 0 1 1 1 0 -1 1 -1
[4,] 0 -1 1 -1 0 0 1 0 0 0 -1 -1 0 0 0 -1 0 1 0 1 -1 1 0 0 -1 0
[5,] 1 1 1 1 0 1 -1 1 0 1 0 0 -1 1 0 0 0 0 0 0 -1 1 1 0 -1 0
[6,] -1 1 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0
[7,] 1 0 0 0 1 0 0 1 0 -1 1 1 0 0 0 1 0 1 0 1 0 -1 1 -1 0 -1
[8,] 0 -1 1 -1 -1 1 0 1 0 -1 1 -1 0 0 0 0 1 0 0 0 -1 0 0 1 1 0
[9,] 1 0 0 1 0 1 0 -1 0 -1 -1 1 0 0 0 1 0 1 0 0 1 1 0 0 1 1
[10,] 1 0 0 -1 0 -1 1 1 0 -1 0 -1 -1 0 0 0 0 0 1 0 0 0 0 0 0 0
[1,] 0 0 0 0 0 1 1 0 0 0 -1 1 0 -1 0 0 0 -1 0 -1 -1 0 0 0 1 0 0 0
[2,] 1 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 -1 0 -1 0 0 0
[3,] 0 0 0 0 0 -1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 -1 0 1 1 0 0
[4,] 0 1 -1 0 0 0 1 0 0 0 -1 -1 0 0 0 0 0 -1 1 1 1 0 0 1 0 0 1 0
[5,] 0 0 1 0 0 0 0 1 0 0 -1 0 0 1 0 0 0 -1 0 -1 1 1 0 0 0 0 0 1
[6,] 0 -1 -1 1 0 0 0 0 1 0 -1 0 0 0 1 0 0 0 0 1 1 0 1 -1 1 0 0 0
[7,] 1 0 0 0 0 0 -1 0 0 1 1 0 0 0 0 0 0 0 0 -1 1 -1 0 -1 0 0 0 0
[8,] -1 0 -1 0 0 0 1 1 -1 0 1 0 -1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0
[9,] 0 -1 0 0 1 0 0 0 0 0 -1 -1 0 0 0 0 1 0 0 -1 0 0 -1 1 0 0 0 0
[10,] 0 1 1 0 0 0 -1 1 -1 0 -1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0
[1,] 0 1 1 0 1 -1 -1 0 1 0 -1 0 0 0 -1 -1 1 0 0 -1 0 0 0 0 1 0 0 1
[2,] 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 -1 0 1 0 1 0 -1 1 0 0 0 0 -1
[3,] 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 -1 0 0 1 -1 0 -1 0 0
[4,] 0 0 0 0 0 0 -1 0 1 0 0 0 0 -1 1 -1 0 0 0 -1 1 1 -1 0 0 0 0 0
[5,] 0 0 0 0 0 0 1 0 0 1 0 0 -1 0 0 0 0 0 1 1 0 0 0 0 0 1 -1 1
[6,] 1 -1 0 1 1 -1 0 0 0 0 1 0 0 -1 0 1 0 0 1 0 1 0 0 0 0 0 1 0
[7,] -1 1 0 1 -1 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 -1 0 0 -1 -1 -1
[8,] 1 1 0 0 0 1 -1 0 0 0 1 0 -1 0 -1 0 0 0 -1 0 0 1 1 0 0 -1 0 1
[9,] -1 0 0 1 0 1 0 0 0 0 1 0 1 0 -1 -1 0 0 1 -1 0 0 1 1 0 0 0 0
[10,] 1 1 0 0 0 0 1 0 1 0 0 0 -1 1 0 1 0 0 -1 1 1 -1 0 0 1 0 0 -1
[1,] -1 0 0 0 1 1 -1 1 0 -1 1 0 1 0 0 -1 1 -1
[2,] 0 1 0 0 -1 0 0 0 0 0 1 -1 0 0 0 0 0 1
[3,] 0 0 1 0 0 1 -1 -1 1 0 -1 1 1 0 0 -1 0 0
[4,] 1 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 -1
[5,] 1 0 1 1 -1 0 -1 1 1 0 1 0 -1 1 0 1 1 0
[6,] 1 0 0 0 0 1 -1 0 -1 0 -1 0 -1 0 0 -1 1 0
[7,] 0 0 0 0 1 1 0 -1 0 0 1 1 0 1 0 -1 -1 0
[8,] 0 0 1 0 -1 1 1 1 -1 1 0 1 0 0 0 0 1 1
[9,] 1 0 -1 0 -1 1 -1 -1 -1 0 0 -1 1 0 0 1 -1 -1
[10,] 1 0 0 0 0 0 1 0 1 0 -1 -1 0 1 0 -1 1 -1
sddpack documentation built on May 2, 2019, 4:14 a.m.
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Description Usage Arguments Details Value Note Author(s) References Examples
Description
The semidiscrete decomposition (SDD) approximates a matrix as a weighted sum of outer products formed by vectors with entries constrained to be in the set {-1, 0, 1}.
Usage
1 | sdd(A, kmax = 100, alphamin = 0.01, lmax = 100, rhomin = 10e-20)
|
Arguments
A |
matrix of values on which to run sdd |
kmax |
number of outer-loop iterations (see References) |
alphamin |
progress check (see References) |
lmax |
number of inner-loop iterations (see References) |
rhomin |
threshold test (See References) |
Details
The semidiscrete decomposition (SDD) approximates a matrix as a weighted sum of outer products formed by vectors with entries constrained to be in the set {-1, 0, 1}.
It is useful for image compression and for latent semantic indexing (LSI) in information retrieval.
The primary advantage of the SDD over other types of matrix approximations such as the truncated singular value decomposition (SVD) is that it typically provides a more accurate approximation for far less storage.
The package has been ported from Matlab code given on http://www.cs.umd.edu/~oleary/SDDPACK/.
See the webpage for full documentation.
Value
x |
matrix of |
d |
vector of |
y |
matrix of |
Note
Ported to R by Eric Sun <esun@cs.stanford.edu>
Author(s)
Tamara G. Kolda, Dianne P. O'Leary (Matlab code)
References
http://www.cs.umd.edu/~oleary/SDDPACK/
Examples
1 2 |
Example output
$x
[1,] 0 0 0 -1 -1 0 0 0 -1 0 1 1 0 -1 1 0 -1 -1 1 1 0 0 -1 1 1
[2,] 1 1 -1 0 -1 0 0 1 1 -1 0 1 1 1 0 1 0 0 0 1 -1 -1 0 -1 0
[3,] 0 0 -1 -1 1 0 -1 -1 1 -1 1 0 0 -1 1 0 1 1 -1 -1 -1 0 0 0 1
[4,] -1 0 -1 0 0 1 1 -1 -1 -1 -1 1 0 -1 -1 0 1 1 1 0 1 0 0 1 0
[5,] -1 0 1 0 0 0 -1 0 -1 -1 0 -1 0 0 1 0 0 0 -1 -1 0 -1 0 0 -1
[6,] 0 1 0 -1 1 0 1 0 0 0 1 1 -1 1 1 0 0 1 0 0 0 1 1 1 0
[7,] -1 -1 -1 1 0 0 -1 1 0 0 1 -1 1 0 1 0 -1 1 1 -1 0 0 0 1 0
[8,] 0 -1 0 -1 -1 -1 1 0 0 0 0 0 0 -1 -1 0 0 -1 0 -1 0 -1 1 0 -1
[9,] -1 1 0 -1 0 0 0 0 -1 -1 -1 1 0 -1 0 0 -1 0 -1 1 -1 1 0 0 -1
[10,] -1 1 0 -1 -1 0 -1 -1 0 1 1 1 1 1 0 0 1 0 1 -1 -1 1 0 1 -1
[1,] 0 0 -1 -1 1 1 0 -1 0 0 1 -1 -1 0 -1 1 0 -1 1 1 1 1 0 1
[2,] 1 0 -1 0 -1 -1 0 -1 -1 1 0 1 0 -1 1 1 1 0 0 0 0 -1 1 0
[3,] 0 -1 0 0 0 1 -1 0 1 -1 1 1 0 -1 -1 0 -1 -1 1 -1 0 1 0 0
[4,] -1 0 -1 1 1 -1 -1 -1 1 -1 -1 0 0 -1 1 0 -1 -1 -1 1 -1 1 1 0
[5,] 1 0 0 -1 -1 0 -1 0 0 1 0 -1 -1 -1 0 0 -1 0 1 0 0 0 0 0
[6,] 1 0 -1 1 0 1 0 1 0 -1 0 -1 -1 1 1 -1 -1 -1 0 0 1 0 -1 -1
[7,] -1 -1 -1 0 0 0 1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 1 0 0
[8,] -1 0 -1 0 0 1 0 1 0 0 1 1 0 0 1 0 0 -1 1 0 0 0 1 -1
[9,] -1 0 0 -1 -1 -1 -1 0 -1 -1 -1 1 0 -1 0 1 -1 1 1 1 0 0 0 0
[10,] 0 1 0 0 0 0 0 0 1 0 1 1 -1 0 1 0 1 1 1 -1 0 1 0 -1
[1,] 1 0 -1 0 0 1 1 0 0 1 -1 0 0 0 1 1 1 -1 -1 0 1 0 -1 -1
[2,] 0 0 0 -1 0 1 0 1 -1 -1 -1 0 0 0 -1 -1 -1 -1 0 1 0 0 0 -1
[3,] 1 1 0 0 0 -1 1 0 -1 1 1 0 -1 0 0 0 0 0 -1 0 0 1 1 0
[4,] -1 0 0 0 -1 0 0 -1 -1 1 1 -1 1 0 1 1 -1 0 0 1 0 1 0 1
[5,] 0 0 -1 0 1 -1 -1 0 -1 0 1 1 0 1 1 0 1 0 -1 -1 1 1 -1 0
[6,] 0 0 -1 0 1 1 -1 0 1 1 0 0 -1 -1 -1 0 1 0 1 -1 1 0 1 1
[7,] 0 -1 -1 0 1 1 1 1 0 -1 0 -1 0 1 -1 0 1 0 0 0 1 -1 -1 0
[8,] 1 0 1 1 0 1 0 -1 -1 -1 1 0 0 -1 0 0 0 0 1 -1 1 0 -1 0
[9,] 1 -1 -1 0 -1 0 1 -1 0 0 0 0 0 -1 1 -1 1 1 0 0 0 0 0 -1
[10,] -1 0 0 1 -1 0 0 1 -1 1 0 -1 -1 1 0 0 0 1 -1 -1 -1 -1 0 1
[1,] 0 0 0 -1 1 -1 0 -1 0 1 1 -1 0 -1 0 -1 0 -1 1 0 0 0 -1 0 1
[2,] -1 -1 0 1 1 -1 -1 0 0 0 -1 0 -1 -1 0 1 1 0 1 -1 0 0 1 1 0
[3,] 1 1 0 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 -1 -1 0 -1
[4,] 0 0 1 0 -1 -1 0 0 -1 0 0 0 0 0 1 -1 1 1 0 -1 0 1 -1 1 -1
[5,] 0 -1 -1 0 0 1 -1 0 1 1 -1 -1 0 1 0 0 1 1 1 1 0 0 1 1 -1
[6,] 0 -1 0 0 0 0 0 1 1 0 0 -1 0 1 1 1 0 0 1 1 1 1 1 -1 0
[7,] 1 0 0 1 0 1 -1 -1 0 1 -1 0 0 1 -1 -1 0 1 0 0 1 1 0 0 1
[8,] 0 1 1 1 1 0 -1 0 0 -1 1 0 0 0 0 -1 1 -1 -1 1 1 0 -1 1 0
[9,] 1 -1 1 0 0 -1 1 -1 1 -1 -1 0 1 -1 0 0 1 0 -1 1 0 1 0 0 0
[10,] 0 0 0 0 1 0 0 -1 0 -1 -1 0 0 -1 0 0 -1 1 0 0 1 0 0 -1 0
[1,] 0 -1
[2,] -1 -1
[3,] -1 0
[4,] 0 0
[5,] -1 1
[6,] 0 -1
[7,] -1 0
[8,] -1 0
[9,] -1 0
[10,] -1 1
$d
[1] 7.475118e-01 7.175652e-01 8.227342e-01 3.301819e-01 5.613795e-01
[6] 6.419292e-01 4.073040e-01 2.944641e-01 4.605838e-01 2.278536e-01
[11] 1.742302e-01 1.805593e-01 2.432678e-01 1.624615e-01 2.178666e-01
[16] 2.959007e-01 1.822302e-01 1.199071e-01 1.190462e-01 5.876378e-02
[21] 7.178288e-02 5.247941e-02 7.264214e-02 4.396722e-02 3.721253e-02
[26] 3.308639e-02 3.627223e-02 2.685901e-02 1.816245e-02 3.363641e-02
[31] 2.804515e-02 2.603759e-02 1.162986e-02 1.105823e-02 7.883801e-03
[36] 1.670424e-02 5.164284e-03 6.763550e-03 7.542194e-03 7.037015e-03
[41] 1.006001e-02 5.784963e-03 5.679659e-03 3.786845e-03 5.465679e-03
[46] 2.985631e-03 1.965327e-03 4.235258e-03 2.278530e-03 1.476986e-03
[51] 1.847830e-03 1.755129e-03 1.993064e-03 1.609652e-03 9.784657e-04
[56] 8.015648e-04 9.801410e-04 7.060937e-04 5.244912e-04 4.570337e-04
[61] 4.401964e-04 9.070386e-04 3.321407e-04 4.077167e-04 2.672027e-04
[66] 4.581664e-04 2.774248e-04 1.544031e-04 1.670289e-04 9.834834e-05
[71] 1.845007e-04 1.553917e-04 7.812729e-05 7.302220e-05 7.205621e-05
[76] 7.245066e-05 5.248978e-05 7.804247e-05 5.845325e-05 4.868747e-05
[81] 4.319304e-05 2.814451e-05 2.123464e-05 3.557497e-05 2.426180e-05
[86] 3.817365e-05 1.220277e-05 2.039952e-05 1.174712e-05 8.466911e-06
[91] 7.469365e-06 8.110438e-06 5.671511e-06 6.136449e-06 5.216119e-06
[96] 4.389743e-06 9.564996e-06 2.955949e-06 2.377918e-06 2.179884e-06
$y
[1,] 1 0 -1 1 -1 0 0 1 0 -1 -1 0 1 1 0 0 0 -1 0 0 0 0 -1 0 0 -1
[2,] -1 1 0 0 0 1 1 1 0 0 0 0 -1 0 0 0 0 -1 0 1 0 0 0 0 1 1
[3,] 1 1 0 -1 0 0 -1 -1 1 -1 1 0 0 0 0 0 0 0 0 1 1 1 0 -1 1 -1
[4,] 0 -1 1 -1 0 0 1 0 0 0 -1 -1 0 0 0 -1 0 1 0 1 -1 1 0 0 -1 0
[5,] 1 1 1 1 0 1 -1 1 0 1 0 0 -1 1 0 0 0 0 0 0 -1 1 1 0 -1 0
[6,] -1 1 0 1 1 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0
[7,] 1 0 0 0 1 0 0 1 0 -1 1 1 0 0 0 1 0 1 0 1 0 -1 1 -1 0 -1
[8,] 0 -1 1 -1 -1 1 0 1 0 -1 1 -1 0 0 0 0 1 0 0 0 -1 0 0 1 1 0
[9,] 1 0 0 1 0 1 0 -1 0 -1 -1 1 0 0 0 1 0 1 0 0 1 1 0 0 1 1
[10,] 1 0 0 -1 0 -1 1 1 0 -1 0 -1 -1 0 0 0 0 0 1 0 0 0 0 0 0 0
[1,] 0 0 0 0 0 1 1 0 0 0 -1 1 0 -1 0 0 0 -1 0 -1 -1 0 0 0 1 0 0 0
[2,] 1 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 -1 0 -1 0 0 0
[3,] 0 0 0 0 0 -1 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 -1 0 1 1 0 0
[4,] 0 1 -1 0 0 0 1 0 0 0 -1 -1 0 0 0 0 0 -1 1 1 1 0 0 1 0 0 1 0
[5,] 0 0 1 0 0 0 0 1 0 0 -1 0 0 1 0 0 0 -1 0 -1 1 1 0 0 0 0 0 1
[6,] 0 -1 -1 1 0 0 0 0 1 0 -1 0 0 0 1 0 0 0 0 1 1 0 1 -1 1 0 0 0
[7,] 1 0 0 0 0 0 -1 0 0 1 1 0 0 0 0 0 0 0 0 -1 1 -1 0 -1 0 0 0 0
[8,] -1 0 -1 0 0 0 1 1 -1 0 1 0 -1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0
[9,] 0 -1 0 0 1 0 0 0 0 0 -1 -1 0 0 0 0 1 0 0 -1 0 0 -1 1 0 0 0 0
[10,] 0 1 1 0 0 0 -1 1 -1 0 -1 1 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0
[1,] 0 1 1 0 1 -1 -1 0 1 0 -1 0 0 0 -1 -1 1 0 0 -1 0 0 0 0 1 0 0 1
[2,] 0 0 0 1 0 0 0 1 0 0 1 0 0 1 0 -1 0 1 0 1 0 -1 1 0 0 0 0 -1
[3,] 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 -1 0 0 1 -1 0 -1 0 0
[4,] 0 0 0 0 0 0 -1 0 1 0 0 0 0 -1 1 -1 0 0 0 -1 1 1 -1 0 0 0 0 0
[5,] 0 0 0 0 0 0 1 0 0 1 0 0 -1 0 0 0 0 0 1 1 0 0 0 0 0 1 -1 1
[6,] 1 -1 0 1 1 -1 0 0 0 0 1 0 0 -1 0 1 0 0 1 0 1 0 0 0 0 0 1 0
[7,] -1 1 0 1 -1 0 0 0 1 0 0 1 0 0 0 0 0 0 1 1 1 1 -1 0 0 -1 -1 -1
[8,] 1 1 0 0 0 1 -1 0 0 0 1 0 -1 0 -1 0 0 0 -1 0 0 1 1 0 0 -1 0 1
[9,] -1 0 0 1 0 1 0 0 0 0 1 0 1 0 -1 -1 0 0 1 -1 0 0 1 1 0 0 0 0
[10,] 1 1 0 0 0 0 1 0 1 0 0 0 -1 1 0 1 0 0 -1 1 1 -1 0 0 1 0 0 -1
[1,] -1 0 0 0 1 1 -1 1 0 -1 1 0 1 0 0 -1 1 -1
[2,] 0 1 0 0 -1 0 0 0 0 0 1 -1 0 0 0 0 0 1
[3,] 0 0 1 0 0 1 -1 -1 1 0 -1 1 1 0 0 -1 0 0
[4,] 1 0 0 0 0 0 0 1 1 1 0 0 0 0 1 0 0 -1
[5,] 1 0 1 1 -1 0 -1 1 1 0 1 0 -1 1 0 1 1 0
[6,] 1 0 0 0 0 1 -1 0 -1 0 -1 0 -1 0 0 -1 1 0
[7,] 0 0 0 0 1 1 0 -1 0 0 1 1 0 1 0 -1 -1 0
[8,] 0 0 1 0 -1 1 1 1 -1 1 0 1 0 0 0 0 1 1
[9,] 1 0 -1 0 -1 1 -1 -1 -1 0 0 -1 1 0 0 1 -1 -1
[10,] 1 0 0 0 0 0 1 0 1 0 -1 -1 0 1 0 -1 1 -1
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