#!/usr/bin/python

# Determines the first row that is dependent on the previous rows of S. 

# Returns the coefficients of dependence 

import pylab as pl

from makezero import makezero

def indep(S, gap=1e8):

    S = pl.atleast_2d(S)

    E = pl.finfo(float).eps

    r, c = S.shape

    ind = 1

    i = 2

    while ind and i<=r:

        shortS = S[:i,:]

        sigma = pl.svd(pl.dot(shortS,shortS.T))[1]

        if(sigma[-1]/sigma[0] < (E*max(i, c))):

            ind = 0

        else:

            shsig = sigma.copy()

            shsig[:-1] = sigma[1:]

            if pl.any(sigma/shsig > gap):

                ind = 0

            else:

                ind = 1

                i += 1

    if ind:

        b = pl.atleast_2d([])

    else:

        A, B = S[i-1,:], S[:i-1,:] 

        # c = A/B, 

        # c = (B.T\A.T).T

        c = pl.lstsq(B.T, A.T)[0].T

#        c = pl.solve(B.T, A.T).T

        c = makezero(c, gap)

        c = c.squeeze()

        b = pl.hstack((-c, 1))

        b = pl.atleast_2d(b)

    return b

if __name__== "__main__":

    pass