Feature/changefinder1d

[myui]

Revising the PR of #305 by @L3Sota

[myui]

@L3Sota Are you expecting each C_i as a submatrix and flatting a matrix of matrix to a matrix?

R will not become a Toeplitz Matrix then and it's hard to solve A by LUDecomposition.

[L3Sota]

@myui Yes, that's expected. I didn't know non-Toeplitz makes LU decomp so difficult at the time of writing, though :(

Small points: the comments from L116-129 seem to be a little off regarding style, not too important:

• In the Yule-Walker equations, i and j are 1..k, but in the visualisation of the equation the C and A vector-of-matrices' run from 1..n
• The A vector-of-matrices should be horizontal
• Both C'_i and C_i' are used

[myui]

Is this expected behavior for combineMatrix() (i.e., flatten() )?

    @Test
    public void testFlatten2d() {
        RealMatrix[] m1 = new RealMatrix[] { new Array2DRowRealMatrix(new double[] {1, 1.1}), new Array2DRowRealMatrix(new double[] {2, 2.2}), new Array2DRowRealMatrix(new double[] {3, 3.3})}; 
        // {1.0,1.1}
        // {2.0,2.2}
        // {3.0,3.3}
        RealMatrix[][] toeplitz1 = MatrixUtils.toeplitz(m1, 3);
        // {1.0,1.1}  {2.0,2.2}' {3.0,3.3}'
        // {2.0,2.2}  {1.0,1.1}  {2.0,2.2}'
        // {3.0,3.3}  {2.0,2.2}  {1.0,1.1}
        RealMatrix flatten1 = MatrixUtils.flatten(toeplitz1, 2);
        // 1.0 0.0 2.0 2.2 3.0 3.3
        // 1.1 0.0 0.0 0.0 0.0 0.0
        // 2.0 0.0 1.0 0.0 2.0 2.2
        // 2.2 0.0 1.1 0.0 0.0 0.0
        // 3.0 0.0 2.0 0.0 1.0 0.0
        // 3.3 0.0 2.2 0.0 1.1 0.0
    }

LUDecomposition assume a squared matrix.
http://commons.apache.org/proper/commons-math/userguide/linear.html

[myui]

>>> from scipy import linalg
>>> import numpy as np
>>> x = np.array([[1.0,1.1],[2.0,2.2],[3.0,3.3]])
>>> x
array([[ 1. ,  1.1],
       [ 2. ,  2.2],
       [ 3. ,  3.3]])
>>> linalg.toeplitz(x)
array([[ 1. ,  1.1,  2. ,  2.2,  3. ,  3.3],
       [ 1.1,  1. ,  1.1,  2. ,  2.2,  3. ],
       [ 2. ,  1.1,  1. ,  1.1,  2. ,  2.2],
       [ 2.2,  2. ,  1.1,  1. ,  1.1,  2. ],
       [ 3. ,  2.2,  2. ,  1.1,  1. ,  1.1],
       [ 3.3,  3. ,  2.2,  2. ,  1.1,  1. ]])
>>> x = np.matrix([[1.0,1.1],[2.0,2.2],[3.0,3.3]])
>>> x
matrix([[ 1. ,  1.1],
        [ 2. ,  2.2],
        [ 3. ,  3.3]])
>>> linalg.toeplitz(x)
array([[ 1. ,  1.1,  2. ,  2.2,  3. ,  3.3],
       [ 1.1,  1. ,  1.1,  2. ,  2.2,  3. ],
       [ 2. ,  1.1,  1. ,  1.1,  2. ,  2.2],
       [ 2.2,  2. ,  1.1,  1. ,  1.1,  2. ],
       [ 3. ,  2.2,  2. ,  1.1,  1. ,  1.1],
       [ 3.3,  3. ,  2.2,  2. ,  1.1,  1. ]])
>>> x = np.array([np.array([[1.0,1.1],[2.0,2.2]]),np.array([[3.0,3.3],[4.0,4.4]])])
>>> x
array([[[ 1. ,  1.1],
        [ 2. ,  2.2]],

       [[ 3. ,  3.3],
        [ 4. ,  4.4]]])
>>> linalg.toeplitz(x)
array([[ 1. ,  1.1,  2. ,  2.2,  3. ,  3.3,  4. ,  4.4],
       [ 1.1,  1. ,  1.1,  2. ,  2.2,  3. ,  3.3,  4. ],
       [ 2. ,  1.1,  1. ,  1.1,  2. ,  2.2,  3. ,  3.3],
       [ 2.2,  2. ,  1.1,  1. ,  1.1,  2. ,  2.2,  3. ],
       [ 3. ,  2.2,  2. ,  1.1,  1. ,  1.1,  2. ,  2.2],
       [ 3.3,  3. ,  2.2,  2. ,  1.1,  1. ,  1.1,  2. ],
       [ 4. ,  3.3,  3. ,  2.2,  2. ,  1.1,  1. ,  1.1],
       [ 4.4,  4. ,  3.3,  3. ,  2.2,  2. ,  1.1,  1. ]])
>>> y = x.flatten()
>>> y
array([ 1. ,  1.1,  2. ,  2.2,  3. ,  3.3,  4. ,  4.4])
>>> y.shape
(8,)

Fix transpose scheme of toeplitz().
https://github.com/scipy/scipy/blob/v0.14.0/scipy/linalg/special_matrices.py#L186
http://mathworld.wolfram.com/ToeplitzMatrix.html

Before:
                if (row < col) {
                    toeplitz[row][col] = c[col - row];
                } else if (row > col) {
                    toeplitz[row][col] = c[row - col].transpose();
                }
After:
                if (row < col) {
                    toeplitz[row][col] = c[col - row].transpose();
                } else if (row > col) {
                    toeplitz[row][col] = c[row - col];
                }

[L3Sota]

Invliad -> Invalid

[myui]

@L3Sota Thanks. Fixed typos.

[myui]

@L3Sota

I think it should be flattened as follows to be solved by LU decomposition:

>>> x = np.array([[1.0,1.1],[2.0,2.2],[3.0,3.3]])
>>> x
array([[ 1. ,  1.1],
       [ 2. ,  2.2],
       [ 3. ,  3.3]])
>>> linalg.toeplitz(x)
array([[ 1. ,  1.1,  2. ,  2.2,  3. ,  3.3],
       [ 1.1,  1. ,  1.1,  2. ,  2.2,  3. ],
       [ 2. ,  1.1,  1. ,  1.1,  2. ,  2.2],
       [ 2.2,  2. ,  1.1,  1. ,  1.1,  2. ],
       [ 3. ,  2.2,  2. ,  1.1,  1. ,  1.1],
       [ 3.3,  3. ,  2.2,  2. ,  1.1,  1. ]])

[myui]

5 dimenasional input of @L3Sota 's test

Hyperparameters used: K=10, T1=10, T2=10, r1=0.01, r2=0.01, lossFunc1=logloss, lossFunc2=lossloss

set ytics nomirror
set y2tics
set y2r[-5:60]
set style fill transparent solid 0.3 noborder

plot \
  for [i=7:11:1] \
    "sota5d.dat" using 1:(sum [col=i:11] column(col)) \
    title columnheader(i) with filledcurves y1=0 axes x1y1, \
  "sota5d.dat" using 1:12 with lines title "outlier" axes x1y2, \
  "sota5d.dat" using 1:13 with lines title "change" axes x1y2

[myui]

@L3Sota @takuti merged into master. Thank you for the contributions!

[coveralls]

Changes Unknown when pulling 622a793 on feature/changefinder1d into * on master*.