sddpack-package: Semidiscrete Decomposition

In sddpack: Semidiscrete Decomposition

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}.

Details

Package:	sddpack
Type:	Package
Version:	1.0
Date:	2009-06-12
License:	GPL v2
LazyLoad:	yes

Author(s)

Tamara G. Kolda, Dianne P. O'Leary (Matlab code) Eric Sun <[e-mail]> (Ported to R)

References

http://www.cs.umd.edu/~oleary/SDDPACK/#authors

Examples

	A = matrix(rnorm(100), nrow=10)
	sdd(A)

Example output

$x
                                                                             
 [1,]  0  0 -1  1 -1 -1  0  0 -1  0 -1  0  0  0  1  0  0  1  0 -1 -1  1  0  1
 [2,]  0 -1  0  1 -1  0  1  0  1  0  1  0  0  1 -1  1  0  0 -1  1 -1  0  0  1
 [3,] -1  1  0  1  0 -1 -1  0  1  0  1  1  0 -1 -1  1 -1  0  1  0 -1 -1  1 -1
 [4,]  0  1  0  0 -1  0  0  0 -1 -1  0  0  0  1  1  0 -1  0  1  1  0  1 -1  0
 [5,]  0  1 -1 -1  1 -1  0  0 -1  0  1 -1  0  0  1 -1 -1  1 -1 -1  0  1  0 -1
 [6,] -1 -1  0 -1  1  0  0  0  0 -1  0 -1  0 -1  0  0  1  1  1 -1 -1 -1 -1 -1
 [7,]  1  0  0  1  1 -1  0  0 -1  0  0  0 -1  1 -1  1  0  1  1  0  1  0  1  0
 [8,]  0 -1  0  1  0  0  0 -1 -1  0 -1 -1  0  1  0  1 -1  1  0  0  0 -1 -1  0
 [9,]  0  1  0 -1 -1  1  0  0 -1  1  1  0  1  0 -1  0  0 -1  1  1  0  0  1  0
[10,]  0 -1 -1  1  1  1  0  0  0 -1  0  1  1  0  1  1  0  0 -1  0 -1 -1  1  1
                                                                              
 [1,]  0 -1  0 0  0  1 -1  1  0 0  0 -1 -1 -1  1  0  0  0  0  0 -1  0 -1 -1  1
 [2,]  1  1  1 1  0 -1  0  1  0 1  0  1  0 -1  0 -1  0 -1  1 -1  1 -1  0  0  0
 [3,] -1 -1  1 0 -1  0  0  1  0 1  0 -1  1  0  0 -1  0 -1 -1 -1 -1  0  1 -1 -1
 [4,] -1  1  1 1 -1  0 -1  1  0 0  1  0  0 -1  1  1  0 -1  0  1  1  1  1  0  0
 [5,]  0  0 -1 1  1 -1  0  1  1 0 -1  0  0  0  1  0  1  1  0  1 -1  0 -1 -1  1
 [6,]  1  0  0 0  0  1 -1  1  1 1  1 -1  1  0 -1 -1  1  1 -1  1  1 -1  1  0  0
 [7,] -1  0  0 1  1  1  1  0  0 1  0 -1 -1 -1 -1  1  1 -1  0  1 -1 -1 -1  0 -1
 [8,]  0  0 -1 0  0  0  0  1 -1 1  0  0  0  0  1  1  1  1  1 -1 -1 -1  1  1  1
 [9,]  0  0  0 1  0 -1 -1 -1  0 0 -1 -1  1  1  1  1  0 -1  1  1  0  0 -1  0 -1
[10,]  0 -1 -1 1 -1  1  1 -1  1 0  1  1 -1  1  0  0 -1  1  0  1 -1 -1  0  0  0
                                                                               
 [1,]  1 0 -1  1 -1  0  0 -1  0  1  1  1  0  0  1  0  0  1 -1  0 -1  1  1  1 -1
 [2,]  0 1 -1  0  0 -1  0  0 -1  1 -1  0  1  0  0  0  1 -1 -1  0  1  0 -1  0  0
 [3,]  1 1  0  0  1  1 -1  0  0 -1 -1  1  1  0  1  1  1  0  1  1  0  0  1 -1 -1
 [4,]  1 0  0  0 -1  1  1  1  0  1 -1 -1  0 -1  1  0 -1 -1 -1  1  0  1 -1  1 -1
 [5,] -1 0  1  1  1  1  0  0  1  1  0  0  1 -1 -1  0  0  1  0 -1  0 -1  1  1 -1
 [6,]  1 0 -1  0  1 -1  1  0  1  0  0  0 -1 -1  0  1  0 -1 -1  0 -1 -1  0  0  0
 [7,]  1 0  0 -1 -1  0 -1 -1  0 -1 -1  0 -1 -1  0  1  0  1  0 -1  0  0  0  1  0
 [8,]  0 0  0 -1  0  1  1  0 -1 -1 -1  1  0 -1 -1 -1  1 -1  0  0  0  1  1  1  1
 [9,] -1 0  0  1  1  0  1  0 -1 -1  1  0  1  0  0  0 -1  0  0  1  0  0  0  1  1
[10,] -1 0 -1  1 -1  0  0  1  1  0  1  1 -1  0  1  0  1  1  0  1  0  0  0  0  0
                                                                               
 [1,]  1 -1  0  1 -1  0  1  0  0  0 0  1  1  1  1  0  1  1 -1  1  0  0  0  0 -1
 [2,]  1  1 -1  0  0  0  0  0  1  0 1  0 -1 -1  0  0  0  1  1 -1 -1  0  1  0  1
 [3,]  0  1  0  1  0  0 -1  0  0  0 0 -1  1 -1  0  1 -1  1  0  1  0 -1  1 -1  1
 [4,] -1  1  0  0 -1  1 -1 -1  0  0 0 -1  0  1  0  0 -1  0  0  1  0 -1 -1  1 -1
 [5,]  1 -1  0  0  1 -1 -1  0  0 -1 0  0 -1  1  0  1  1  0  0 -1  0  0  0 -1  0
 [6,] -1 -1 -1  0 -1 -1 -1  1 -1  0 0  0  0  0 -1 -1 -1  1 -1 -1 -1 -1  1  1 -1
 [7,] -1  1  0  1  0 -1  1  0  1 -1 0 -1  0  0  1  0 -1  1  1  1 -1 -1 -1 -1  0
 [8,]  0 -1  1  1  0  0  0  1  0  0 0 -1  1  1  0  1 -1 -1  0  1  1 -1  0  0 -1
 [9,]  0  1 -1 -1  0  0  1  1  1 -1 0  1  0  0 -1  0  0  1  0  1  1 -1  0  0  1
[10,]  0 -1 -1  1  0  1  1 -1 -1 -1 0 -1  1  0  0 -1  0  0  0 -1  1  0  0  1  1
        
 [1,] -1
 [2,]  0
 [3,]  0
 [4,]  1
 [5,]  1
 [6,]  0
 [7,]  0
 [8,]  1
 [9,] -1
[10,] -1

$d
  [1] 1.333754e+00 5.923973e-01 8.027809e-01 4.776718e-01 3.519658e-01
  [6] 5.185880e-01 4.308933e-01 8.783409e-01 2.532136e-01 4.518425e-01
 [11] 3.075517e-01 3.156259e-01 3.737634e-01 3.720618e-01 1.274594e-01
 [16] 1.973997e-01 1.773824e-01 1.544997e-01 8.307704e-02 6.751287e-02
 [21] 7.278688e-02 4.660410e-02 4.129570e-02 3.646676e-02 5.816958e-02
 [26] 5.721896e-02 3.574998e-02 2.949092e-02 3.315340e-02 2.192100e-02
 [31] 2.152074e-02 2.480274e-02 2.126354e-02 1.506010e-02 1.758326e-02
 [36] 1.911937e-02 1.286397e-02 4.733646e-03 7.660728e-03 9.843922e-03
 [41] 7.795567e-03 7.732195e-03 4.132372e-03 3.701595e-03 2.787673e-03
 [46] 1.765938e-03 3.437474e-03 4.087404e-03 1.866614e-03 1.893810e-03
 [51] 3.657387e-03 1.093983e-03 1.170868e-03 6.673076e-04 1.236717e-03
 [56] 7.840004e-04 8.520031e-04 1.023818e-03 4.859900e-04 3.138012e-04
 [61] 4.774006e-04 2.595676e-04 3.063056e-04 2.338585e-04 3.272228e-04
 [66] 1.807986e-04 1.168420e-04 1.767479e-04 1.601260e-04 2.320232e-04
 [71] 1.139706e-04 8.909303e-05 1.217588e-04 6.007539e-05 5.693195e-05
 [76] 3.895866e-05 6.051746e-05 3.768976e-05 3.282583e-05 2.823740e-05
 [81] 2.785213e-05 3.894528e-05 2.342345e-05 1.904851e-05 3.064542e-05
 [86] 9.307589e-06 8.059127e-06 1.225182e-05 1.210536e-05 8.201753e-06
 [91] 1.143645e-05 1.044300e-05 5.344302e-06 2.400502e-06 4.007635e-06
 [96] 2.288425e-06 3.434242e-06 2.121975e-06 1.956015e-06 3.340614e-06

$y
                                                                             
 [1,]  1  1 1  1 -1  0  1  0 -1  0 0 1 0 0  1 0 1  0  1  0  0  1  0  0 0 0  1
 [2,] -1  1 0  0 -1  0 -1  0 -1 -1 0 0 0 0  0 0 0  0  0  1  0  1 -1  1 0 0  0
 [3,]  0 -1 1  1 -1  0 -1  0 -1  0 1 0 1 0  0 0 0  0  0  0  0  0 -1  0 0 0  0
 [4,]  1  0 1  0  1  1  0  0  0  0 0 1 0 0  0 1 0  0  0 -1  1  1  0  1 0 0  0
 [5,]  0 -1 0  0  0  0  1  0  0  0 0 0 0 1  0 0 0  0 -1  0 -1  1  1  0 0 0  1
 [6,]  0  0 0  0  0  0  0  1  1  0 1 0 0 0  1 0 0  0 -1 -1  0  1  1 -1 0 0 -1
 [7,]  1  0 0  1  0 -1 -1  0  1  0 0 0 0 0  0 1 0  0 -1  0 -1 -1  1  0 0 0  0
 [8,] -1 -1 0  1  1  0 -1  0 -1  1 0 0 0 0  0 0 1  0  0 -1  1 -1  0  1 0 0  0
 [9,]  0  1 1  0  1  0  0 -1  0  0 1 0 0 0 -1 0 0  1  1 -1 -1  1  1  0 1 0  0
[10,]  0  0 1 -1 -1  0 -1 -1  1  0 0 0 0 0 -1 0 0 -1  0 -1 -1  0 -1  0 0 1  0
                                                                               
 [1,]  0 -1  0  0 1 0  0 0 0 -1  1  0 0  1 0  0  0  0  0 1 0  0 0  0  0  0  0 0
 [2,]  1  0 -1  0 0 1  0 0 0  0  1  0 0  0 1  1  0  0  0 0 0  1 1  0  0  0  1 0
 [3,] -1  0  0 -1 0 1  0 0 0  0  1  0 0 -1 0  0  0  1 -1 0 1 -1 0  0  1  0 -1 1
 [4,] -1  1  0  0 0 0  1 0 0  0 -1 -1 0  0 0  1  1  0 -1 0 0  1 0  0 -1  1 -1 0
 [5,]  0  0 -1  1 0 0  0 0 0  0  1  0 0  0 0 -1  1 -1  0 0 0 -1 1  0 -1  0 -1 0
 [6,]  0  0 -1  0 0 0 -1 1 0  0 -1  1 0  0 0  0  1  1  1 0 0  1 0  1  1  0  1 0
 [7,]  1  0  1  0 0 1  0 1 0  0 -1  0 1  0 0 -1  0  0  1 0 1  0 0  0  0  1  0 0
 [8,]  0  0  0  1 0 0 -1 0 1  0 -1  0 0  0 0 -1 -1  0 -1 0 0  1 0  0  1 -1  0 0
 [9,]  0  0  0  0 0 0  1 0 0  0 -1 -1 0  0 0 -1  0  1  1 0 0  0 0 -1  1  0 -1 0
[10,]  0  0  0  1 0 0 -1 0 0  1  1  0 0  1 0  0  1  1 -1 0 0 -1 0  0  1  1  1 0
                                                                               
 [1,]  0  1 0 -1  1  1  0  1  0  0 -1  1  0 -1  0  1 -1  0 -1  1  0  1  0  0  1
 [2,] -1  1 0 -1  1  1  1 -1  1  0  0 -1  0  0  0  0  1  0  1  0  0  1  1  0 -1
 [3,]  0  0 0  0  0  0 -1  0  1  0  0 -1  0  0  0  1  0  1  0 -1 -1  0  0  1  1
 [4,]  1  1 0  1 -1  1  1  0  0 -1  0 -1  0  0  0  1  0 -1  1  0  0  0  1 -1  0
 [5,] -1  0 0  0  1 -1  1  1 -1  1 -1 -1  1  0 -1  0  0  0  1  0  1  0  0  1  1
 [6,]  1  1 0  0  0 -1 -1  1  1  0  1  1  1  0  0  0 -1  0  0 -1  1  0  0  1  0
 [7,]  1  0 0 -1  0  0 -1  0 -1  0  0  1  0  1  0  1  1  0  1  0  0  0 -1  1 -1
 [8,]  1  0 0  1  1  1 -1  0 -1  0  1 -1  0 -1  0 -1  0  0  1  0 -1  1  0  0  1
 [9,] -1  1 1  0  1  0  0  1  0  1  0 -1 -1  0  1  0 -1  0  0  1  0 -1  1  1 -1
[10,]  0 -1 0  1  0  0  1  1  0  0  1  0 -1  0 -1  0  1  0  0  1  1  0  0 -1  1
                                                            
 [1,]  0 0  1 1  0  1  1  0  0  0 1 0  0 -1  1 -1  1 -1  0 0
 [2,]  0 0  0 0  0 -1  1  0  0  1 0 1  0  1  0  1  0  0  0 0
 [3,]  0 0  1 0 -1 -1 -1  1  0  1 0 0  1 -1  1  1  0  1  0 0
 [4,]  0 0  1 1 -1  0 -1  0  0  0 0 0  1  1  0 -1  0  1 -1 0
 [5,] -1 0 -1 1  0  1  0  0  1  0 0 0  1  0 -1  1 -1 -1  1 0
 [6,]  1 0  0 1 -1 -1  0 -1  1 -1 0 0  0  0  0  0  1  0 -1 0
 [7,]  0 1  0 0  0  0  1  0  0  0 0 0  1  1  0  0 -1 -1  0 0
 [8,]  0 0  1 0  1  0  1 -1  0  1 0 0 -1  1  1  0  0  0  0 1
 [9,]  0 0  1 1  0 -1  0 -1 -1  0 0 0  1  1  1  1  0  1  1 0
[10,]  0 0  1 0  1  0 -1 -1  1  0 0 0  1  1  0 -1  1  0  1 0

sddpack documentation built on May 2, 2019, 4:14 a.m.