In [1]:

    

from __future__ import division
%pylab inline
import pandas as pd
from Bio import SeqIO
import nwalign
import itertools
from scipy import signal,fftpack,stats
import mahotas
import sklearn
import seaborn as sns
from skimage.feature import match_template


    

    




Populating the interactive namespace from numpy and matplotlib






    




/Users/skasinat/anaconda/lib/python2.7/site-packages/matplotlib/__init__.py:872: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.
  warnings.warn(self.msg_depr % (key, alt_key))

In [2]:

    

matD = np.load('../test_data/subset100/matrices/trial.100.subset.npz')


    

In [333]:

    

# plt.figure(figsize=(15,15))
ctr=0
for i,j in matD.iteritems():
    if j.size>29**2:
        L=int(j.size**0.5)
        
        # Padding
        padN=512
        s=np.int_([0,0])
        s[0]=int(padN)
        s[1]=int(padN)
        
        fft=np.fft.fft2(j,s=s,axes=[0,1])
        plt.figure(1,figsize=(12,6))

        power=abs(fft).mean(axis=0)

        #Normalize the power spectrum (scale such that max is 1)
        power = np.fft.fftshift(power/np.max(power))
        
        # Get the frequency bins
        xv=np.fft.fftshift(np.fft.fftfreq(padN))

        print i
        plt.subplot(121)
        imshow(j,interpolation='none')
        plt.subplot(122)
        plot(xv,np.log10(power))
        plt.show()


    

    




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In [37]:

    

def getDFTCoeff(N, freqArr):
    """ Compute the DFT coefficients"""
    
    n = np.resize(np.arange(N),(N,1))
    E = np.dot(n,freqArr)    
    E = exp(-2j*np.pi*E)
    
    return E

def DFT2(M, minPeriod=0, maxPeriod=None, pStep=1):
    """ Compute the 2D DFT for specified frequencies
    Parameters
    ----------
    M : np.ndarray
        2D square (N x N) array of values to transform
    

    Returns
    -------
    
    dft : np.ndarray
        2D array representing the DFT
    
    """
    
    # Matrix ß
    N = M.shape[0]
    
    # Make a frequency array
    if maxPeriod == None:
        maxPeriod = int(N)
    
    freqArray = np.arange(minPeriod,maxPeriod,pStep)/(2*N)
    nF = freqArray.size
    freqArray = np.reshape(freqArray,(1,nF))
    freqArray[0][0] = 0
    freqArray.sort()
    
    # pre-compute the coefficients
    E = getDFTCoeff(N,freqArray)
    
    # DFT along rows
    dft2 = np.dot(M,E)
    
    # DFT along the columns of the row DFT matrix
    dft2 = np.dot(dft2.T,E).T
    
    return dft2

def getPowers(dft,N):
    """Return a 1D array containing the (shifted) frequencies corresponding to DFT bins"""
    
    if N%2 == 0:
        Np = (N)/2
    else:
        Np = (N-1)/2
    
    # Normalize
    dftpSum = np.abs(dft.sum(axis=1))
    dftpSum = dftpSum/dftpSum[0]
    powers = dftpSum[Np+1:]
    powers = powers[::-1]
    
    periods = np.arange(1,len(powers)+1)
    
    
    return periods, powers


    

In [7]:

    

def makeArray(periodicity,size):
    arr=np.diag(np.ones(size))
    
    for k in range(periodicity,size,periodicity):
        arr += np.diag(np.ones(size-k),k)
        arr += np.diag(np.ones(size-k),-k)
    
    return arr

print makeArray(2,5)


    

    




[[ 1.  0.  1.  0.  1.]
 [ 0.  1.  0.  1.  0.]
 [ 1.  0.  1.  0.  1.]
 [ 0.  1.  0.  1.  0.]
 [ 1.  0.  1.  0.  1.]]

In [147]:

    

M=np.array(matD['S1_476'])
size=100
blackman1D=signal.blackmanharris(size)
blackman2D=np.outer(blackman1D,blackman1D)

# M=makeArray(10,size)
N=M.shape[0]
# M=M*blackman2D
# pStep = 1

# plt.figure(figsize=(10,6))
# dft=DFT2(M,pStep=pStep)


# ax=subplot(121)
# imshow(np.fft.fftshift(np.log10(abs(dft))),interpolation='none',cmap=cm.gray)
# ax.grid(b=False)

# ax1= subplot(122)
# # pd, pw = getPowers(dft,N)
# # print pd.shape
# # print pw.shape
# pw = np.fft.fftshift(np.abs(dft).sum(axis=1))
# plot(np.fft.fftshift(np.fft.fftfreq(len(pw))),np.log10(pw))
# plt.ylim((0,4))


    

In [146]:

    

acorr = signal.correlate2d(M,M)
# imshow(acorr,interpolation='none')
pad = acorr.shape[0]
fft = np.fft.fft2(acorr,s=(pad,pad),axes=(0,1))

fftp = np.fft.fftshift(abs(fft))

subplot(121)
imshow(M,interpolation='none')

subplot(122)
plot(np.fft.fftshift(np.fft.fftfreq(fft.shape[0])),np.log10(fftp.mean(axis=0)))


    

    
Out[146]:





[<matplotlib.lines.Line2D at 0x11a981310>]






    

In [234]:

    

# M=makeArray(10,100)
M=np.array(matD['S1_735'])
bins=np.percentile(M,[20,40,60,80,100])
M=np.digitize(M,bins)
refs = [ makeArray(i,i+1) for i in range(2,40)]
acorr = np.array([ np.ptp(match_template(M,R)) for R in refs ])


# imshow(M,interpolation='none')
plot(range(2,40),acorr)
# plot(acorr)


# plot(acorr.mean(axis=0))

# fft = np.fft.fftshift(np.fft.fft(acorr.mean(axis=0)))


    

    
Out[234]:





[<matplotlib.lines.Line2D at 0x1251fa2d0>]






    

In [3]:

    

def deltaCorr(mat):
    N=mat.shape[0]
    shiftMax=int(N/2)

    
    iter_range = range(0,shiftMax)
    
    delcorr = np.zeros((shiftMax,shiftMax))
    
    for i,j in itertools.product(iter_range,iter_range):
        if (j>=i):
            delta = mat[i:,j:] - mat[:N-i,:N-j]
            
            delcorr[i][j] = np.linalg.norm(delta)/delta.shape[0]
            delcorr[j][i] = delcorr[i][j]
    
    return delcorr


    

In [158]:

    

M=np.array(matD['S1_251'])
dc=deltaCorr(M)
fft=np.fft.fft(dc.ravel())
fftp= abs(np.fft.fftshift(fft))

# imshow(dc,interpolation='none')
plot(dc.ravel()[:])


    

    
Out[158]:





[<matplotlib.lines.Line2D at 0x130b86550>]






    

In [6]:

    

def makeArray(periodicity,size):
    arr=np.ones((size,size))
    arr+=np.diag(np.ones(size))
    for k in range(periodicity,size,periodicity):
        arr += np.diag(np.ones(size-k),k)
        arr += np.diag(np.ones(size-k),-k)
    
    return arr



for i,M in matD.iteritems():
# matrices = [makeArray(i,100) for i in range(1,50)]
# for M in matrices:
#     M=np.array(matD['S1_828'])
    # M=makeArray(20,200)
    
    N=M.shape[0]

    if N>=46:
        imax=int(M.shape[0]/2)
        refs = [ makeArray(i,imax) for i in range(1,40)]
        corrs = np.array([ match_template(M,R) for R in refs])

        
        
        corrs=abs(corrs)

        sums = [ mat.max()  for mat in corrs ]

        plt.subplot(121)
        imshow(M,interpolation='none')

        plt.subplot(122)
        plot(range(1,40),np.array(sums))
        plt.show()


    

In [19]:

    

def getBEDEntry(refList,readList):
    """ Convert lists containing MAF alignments into a BED entry
    Parameters
    ----------
    refList : list
        7-entry MAF line ('s', name, align start, align length, 
                            strand, total length, alignment)
    readList : list
        7-entry MAF line
    
    Returns
    -------
    bedList : list
        6-column BED entry (ref name, align start in ref, align end in ref,
                           read name, strand, read length)
    """
    
    readName = readList[1]
    refName = refList[1]
    refMatchStart = refList[2]
    refMatchEnd = str(int(refList[2]) + int(refList[3]))
    refMatchStrand = refList[4]
    readLen = readList[3]
    
    return [refName, refMatchStart, refMatchEnd, readName, refMatchStrand, readLen]

def MAF2BED(fName):
    """ Convert a MAF file to BED format
    Parameters
    ----------
    fName : str
        Name of MAFf ile
    
    Returns
    -------
    bedList : list
        list of BED-formated entries
    """
    maf = open(fName)
    ref = []
    read = []
    bedList = []
    ctr = 0
    for line in maf:
        if line[0] == 's':
            if ctr%2 == 0:
                ref = line.split()
            else:
                read = line.split()
                outEntry = getBEDEntry(ref,read)
                bedList += [outEntry]
            ctr+=1
    maf.close()
    
    return bedList

print MAF2BED('/Users/skasinat/Downloads/ref.depth20.seed0_0001.maf')


    

    




[['ref', '47367', '49781', 'S1_1', '+', '2613'], ['ref', '46032', '47992', 'S1_2', '+', '2121'], ['ref', '87775', '89726', 'S1_3', '+', '2112'], ['ref', '49567', '50608', 'S1_4', '+', '1135'], ['ref', '36391', '40410', 'S1_5', '+', '4249'], ['ref', '118135', '119333', 'S1_6', '+', '1295'], ['ref', '148068', '151882', 'S1_7', '+', '4039'], ['ref', '28695', '31390', 'S1_8', '+', '2855'], ['ref', '69578', '70537', 'S1_9', '+', '1058'], ['ref', '130935', '133393', 'S1_10', '+', '2605'], ['ref', '12279', '14748', 'S1_11', '+', '2665'], ['ref', '142793', '146588', 'S1_12', '+', '4112'], ['ref', '136287', '137493', 'S1_13', '+', '1292'], ['ref', '30882', '33686', 'S1_14', '+', '3032'], ['ref', '58685', '63199', 'S1_15', '+', '4825'], ['ref', '73948', '76530', 'S1_16', '+', '2815'], ['ref', '112848', '114526', 'S1_17', '+', '1807'], ['ref', '115214', '127089', 'S1_18', '+', '12839'], ['ref', '157553', '158554', 'S1_19', '+', '1070'], ['ref', '97744', '99897', 'S1_20', '+', '2313'], ['ref', '13748', '16026', 'S1_21', '+', '2391'], ['ref', '67625', '70499', 'S1_22', '+', '3061'], ['ref', '82393', '85685', 'S1_23', '+', '3591'], ['ref', '3847', '6383', 'S1_24', '+', '2694'], ['ref', '31275', '32697', 'S1_25', '+', '1546'], ['ref', '59204', '61100', 'S1_26', '+', '2044'], ['ref', '128179', '132451', 'S1_27', '+', '4605'], ['ref', '149502', '150531', 'S1_28', '+', '1092'], ['ref', '41377', '44739', 'S1_29', '+', '3570'], ['ref', '59616', '62774', 'S1_30', '+', '3374'], ['ref', '151125', '154855', 'S1_31', '+', '3919'], ['ref', '65840', '67241', 'S1_32', '+', '1495'], ['ref', '85258', '88108', 'S1_33', '+', '3007'], ['ref', '79021', '81006', 'S1_34', '+', '2118'], ['ref', '123390', '131896', 'S1_35', '+', '9275'], ['ref', '61392', '63794', 'S1_36', '+', '2526'], ['ref', '63112', '66671', 'S1_37', '+', '3833'], ['ref', '105277', '108020', 'S1_38', '+', '2936'], ['ref', '76330', '78739', 'S1_39', '+', '2620'], ['ref', '96366', '97699', 'S1_40', '+', '1432'], ['ref', '107110', '108817', 'S1_41', '+', '1898'], ['ref', '109155', '112663', 'S1_42', '+', '3697'], ['ref', '123911', '133566', 'S1_43', '+', '10138'], ['ref', '8211', '14405', 'S1_44', '+', '6695'], ['ref', '147531', '151170', 'S1_45', '+', '3894'], ['ref', '67540', '69337', 'S1_46', '+', '1936'], ['ref', '86812', '88157', 'S1_47', '+', '1450'], ['ref', '40346', '42383', 'S1_48', '+', '2129'], ['ref', '158485', '160226', 'S1_49', '+', '1836'], ['ref', '32486', '33796', 'S1_50', '+', '1387'], ['ref', '74501', '76036', 'S1_51', '+', '1661'], ['ref', '24308', '26981', 'S1_52', '+', '2796'], ['ref', '61298', '66147', 'S1_53', '+', '5151'], ['ref', '125507', '126828', 'S1_54', '+', '1443'], ['ref', '49361', '52032', 'S1_55', '+', '2892'], ['ref', '41824', '44370', 'S1_56', '+', '2650'], ['ref', '135993', '138490', 'S1_57', '+', '2649'], ['ref', '74401', '83798', 'S1_58', '+', '10017'], ['ref', '101296', '103345', 'S1_59', '+', '2164'], ['ref', '31636', '33872', 'S1_60', '+', '2414'], ['ref', '135990', '138942', 'S1_61', '+', '3157'], ['ref', '37247', '42152', 'S1_62', '+', '5257'], ['ref', '127464', '128888', 'S1_63', '+', '1556'], ['ref', '81131', '85530', 'S1_64', '+', '4765'], ['ref', '155033', '156255', 'S1_65', '+', '1290'], ['ref', '55608', '57435', 'S1_66', '+', '1915'], ['ref', '11264', '12881', 'S1_67', '+', '1707'], ['ref', '18278', '20834', 'S1_68', '+', '2722'], ['ref', '90622', '95105', 'S1_69', '+', '4737'], ['ref', '123991', '125096', 'S1_70', '+', '1169'], ['ref', '46805', '53986', 'S1_71', '+', '7744'], ['ref', '130152', '132781', 'S1_72', '+', '2779'], ['ref', '122304', '124919', 'S1_73', '+', '2777'], ['ref', '49553', '54506', 'S1_74', '+', '5326'], ['ref', '45715', '48040', 'S1_75', '+', '2435'], ['ref', '128413', '132985', 'S1_76', '+', '4958'], ['ref', '46890', '49335', 'S1_77', '+', '2605'], ['ref', '76838', '83919', 'S1_78', '+', '7462'], ['ref', '8865', '12102', 'S1_79', '+', '3421'], ['ref', '137884', '139478', 'S1_80', '+', '1719'], ['ref', '2031', '3257', 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