def Simulate(self, T):
        self.T = T
        x = np.zeros((self.N, self.T), dtype=int)
        v = np.zeros((self.N, self.T), dtype=int)
        Q = np.zeros((self.N, self.T), dtype=int)
        
        x[:,0] = self.x0
        v[:,0] = self.v0
        
        for t in range(1,self.T):
            X  = np.argwhere(x[:,t-1]==1)[:,0]
            dX = (np.roll(X, -1)-X)%self.N
            V  = v[X, t-1] 
            
            #Rule 1: Accelerate if possible
            V += np.logical_and(V<np.ones(len(V))*self.vmax,V<(dX+1))
            #Rule 2: Slow down if needed
            ind = np.argwhere(dX<=V)[:,0]
            V[ind] = dX[ind]-1
            #Rule 3: Slow down with chance p
            V -= np.logical_and(np.random.rand(len(V))<0.5, 0<V)
            #Rule 4: Take next time step
            x[(X+V)%self.N, t] = 1
            v[(X+V)%self.N, t] = V
            
            #Obtain the flow at each position
            for i, xi in enumerate(X):
                Q[xi:(xi+V[i])%self.N,t] +=1

        self.X = x
        self.V = v
        self.Q = Q

def gain_ratio(examples, attribute):
    "Returns the gain function for one attribute."
    ent = h(examples)

    remainder = 0
    values = examples[:, attribute]
    for v in value_attrs[attribute]:
        exs_idx = np.argwhere(values == v).flatten()
        count_v = len(exs_idx)
        exs = examples[exs_idx]
        if count_v != 0:
            remainder += float(count_v)/len(examples) * h(exs)
    ig = ent - remainder

    iv = 0
    for v in value_attrs[attribute]:
        exs_idx = np.argwhere(values == v).flatten()
        count_v = len(exs_idx)
        exs = examples[exs_idx]
        if count_v != 0:
            iv -= float(count_v)/len(examples) * np.log2(float(count_v)/len(examples))
    if iv > 1e-6:
        return ig/iv
    else:
        return ig/1e-6

def crop_data(bg, overlay):
    '''
    Crop the data to get ride of large amounts of black space surrounding the
    background image.
    '''
    #---------------------------------------------------------------
    # First find all the slices that contain data you want
    slices_list_x = list(np.argwhere(np.sum(bg, (1,2)) != 0)[:,0])
    slices_list_y = list(np.argwhere(np.sum(bg, (0,2)) != 0)[:,0])
    slices_list_z = list(np.argwhere(np.sum(bg, (0,1)) != 0)[:,0])

    slices_list = [slices_list_x, slices_list_y, slices_list_z]
    
    #---------------------------------------------------------------
    # Make a copy of the data
    bg_cropped = np.copy(bg)
    overlay_cropped = np.copy(overlay)
    
    #---------------------------------------------------------------
    # Remove all slices that have no data in the background image
    bg_cropped = bg_cropped[ slices_list_x, :, : ]
    overlay_cropped = overlay_cropped[ slices_list_x, :, : ]
    
    bg_cropped = bg_cropped[ :, slices_list_y, : ]
    overlay_cropped = overlay_cropped[ :, slices_list_y, : ]
    
    bg_cropped = bg_cropped[ :, :, slices_list_z ]
    overlay_cropped = overlay_cropped[ :, :, slices_list_z ]
        
    return bg_cropped, overlay_cropped, slices_list

def sar(el2no):
    """
    extract spatial difference matrix on the neighbores of each element
    in 2D fem using triangular mesh.

    Parameters
    ----------
    el2no : NDArray
        triangle structures

    Returns
    -------
    NDArray
        SAR matrix
    """
    ne = el2no.shape[0]
    L = np.eye(ne)
    for i in range(ne):
        ei = el2no[i, :]
        #
        i0 = np.argwhere(el2no == ei[0])[:, 0]
        i1 = np.argwhere(el2no == ei[1])[:, 0]
        i2 = np.argwhere(el2no == ei[2])[:, 0]
        idx = np.unique(np.hstack([i0, i1, i2]))
        # build row-i
        for j in idx:
            L[i, j] = -1
        nn = idx.size - 1
        L[i, i] = nn
    return L

def to_js(fname,low=-3,high=3,template_file='template.js'):
    name,suffix=fname.split('.')
    im=Image.open(fname).convert('1')
    mat=np.array(get_mat(im))
    d1=np.argwhere(np.diff(mat.all(axis=1)))
    d1min=np.min(d1)
    d1max=np.max(d1)
    d2=np.argwhere(np.diff(mat.all(axis=0)))
    d2min=np.min(d2)
    d2max=np.max(d2)
    d1_scale=Scale([d1min,d1max],[low,high])
    d2_scale=Scale([d2min,d2max],[high,low])
    l=[]
    for i in range(mat.shape[0]):
        for j in range(mat.shape[1]):
            if mat[(i,j)]==0:
                l.append([d1_scale(i),d2_scale(j)])
    with open(template_file) as f:
        s=f.read()
        template=jinja2.Template(s)
    ss=template.render(name=name+'Graph',point_list=l)
    with open(name+'.js','w') as f:
        f.write(ss)
    

        
        
#xScale=scale([0,206],[-5,5])
#yScale=scale([0,195],[-5,5])

def rmNanAndOutliers():
    """Plot without NAN and outliers from selected pen.
    """
    if len(ds.EpmDatasetAnalysisPens.SelectedPens) < 1:
        sr.msgBox('EPM Python Plugin - Demo Tools', 'Please select a single pen before applying this function!', 'Warning')
        return 0
    sd = 6
    epmData = ds.EpmDatasetAnalysisPens.SelectedPens[0].values
    y = epmData['Value']
    t = epmData['Timestamp']
    nanPos = np.argwhere(np.isnan(y))
    y = np.delete(y,nanPos)
    t = np.delete(t,nanPos)
    s3 = np.floor(sd * np.sqrt(y.std()))
    smin = y.mean() - s3
    smax = y.mean() + s3
    outPos = np.argwhere(y<smin)
    y = np.delete(y,outPos)
    t = np.delete(t,outPos)
    outPos = np.argwhere(y>smax)
    y = np.delete(y,outPos)
    t = np.delete(t,outPos)
    res = vec2epm(t,y)
    penName = ds.EpmDatasetAnalysisPens.SelectedPens[0].name + '_NoOutliers'
    sr.plot(penName, res)
    return res

 def integralsChanged(self):
     self.integralLimits = []
     for row in range(self.integralTable.rowCount()-1):
         if self.integralTable.item(row, 0) \
                 and self.integralTable.item(row, 1):
             try:
                 limit_1 = float(self.integralTable.item(row, 0).text())
                 limit_2 = float(self.integralTable.item(row, 1).text())
                 self.integralLimits.append(
                     [row, min([limit_1, limit_2]), max([limit_1, limit_2])])
             except ValueError:
                 pass
     if not self.integralLimits or not self.qvals:
         return
     self.integralPlotWindow.clearCurves()
     for limit in self.integralLimits:
         yint = []
         xint = []
         for i, qval in enumerate(self.qvals):
             xint.append(qval)
             if self.integralMethodIntegral.isChecked():
                 yint.append(self.yvals[i][
                     np.argwhere(self.xvals[i]>=limit[1])[0][0]: \
                     np.argwhere(self.xvals[i]<=limit[2])[-1][0]].sum())
             else:
                 yint.append(self.yvals[i][
                     np.argwhere(self.xvals[i]>=limit[1])[0][0]: \
                     np.argwhere(self.xvals[i]<=limit[2])[-1][0]].mean())
             int2plot = np.vstack([xint, yint]).T
             int2plot = int2plot[int2plot[:,0].argsort()]
         self.integralPlotWindow.addCurve(int2plot[:,0], int2plot[:,1], 
             legend='Region %d' % (limit[0]+1), ylabel=' ',
             symbol='o')
     return

def dfsi(bitmap):
    #startpixel = [bitmapnonzero.item(0, 0), bitmapnonzero.item(0, 1)]

    startrow = 0
    while True:
        scanline = bitmap[startrow, :]
        if np.any(scanline):
            startcol = np.argwhere(scanline)[0, 0]
            break
        startrow += 1

    startpixel = [startrow, startcol]
    #print startpixel
    
    stack = [startpixel]
    objpix = [startpixel]

    bound = False
    while stack:
        row, col = stack.pop()
        if row == 0 or col == 0: bound = True
        edges = np.argwhere(bitmap[row-1:row+2, col-1:col+2]) - [1, 1]

        for edge in edges:
            nextpixel = [row+edge[0], col+edge[1]]
            if nextpixel not in objpix:
                stack += [nextpixel]
                objpix += [nextpixel]

    [bitmap.itemset((pix[0], pix[1]), False) for pix in objpix]

    if bound: return [], bitmap
    else: return objpix, bitmap

def multivariate_initialize_seed(CAC, from_gt=True):
    image = CAC.image_obj.image
    if from_gt:
        print 'Seed from ground truth...'
        inside_mask_seed = CAC.ground_truth_obj
        outside_mask_seed = CAC.ground_truth_obj
    else:
        center = CAC.mask_obj.center
        radius_point = CAC.mask_obj.radius_point
        print 'CENTER:', center
        print 'RADIUS POINT:', radius_point
        print 'RADIUS:', np.linalg.norm(np.array(radius_point) - np.array(center))
        radius = np.linalg.norm(np.array(radius_point) - np.array(center))

        inside_seed_omega = [center[0] + radius * 0.2, center[1]]
        outside_seed_omega = [center[0] + radius * 1.8, center[1]]

        inside_mask_seed = MaskClass()
        outside_mask_seed = MaskClass()

        inside_mask_seed.from_points_and_image(center, inside_seed_omega, image)
        outside_mask_seed.from_points_and_image(center, outside_seed_omega, image)

    inside_seed = inside_mask_seed.mask
    outside_seed = 255. - outside_mask_seed.mask
    # inside_mask_seed.plot_image()
    # CAC.mask_obj.plot_image()
    # utils.printNpArray(outside_seed)
    inside_coordinates = np.argwhere(inside_seed == 255.)
    outside_coordinates = np.argwhere(outside_seed == 255.)

    inside_gmm = get_values_in_region(inside_coordinates, image)
    outside_gmm = get_values_in_region(outside_coordinates, image)
    return inside_gmm, outside_gmm

    def psf(self,emin,emax,cthmin,cthmax):
        """Return energy- and livetime-weighted PSF density vector as
        a function of angular offset for a bin in energy and
        inclination angle."""
        
        logemin = np.log10(emin)
        logemax = np.log10(emax)

        ilo = np.argwhere(self._energy > emin)[0,0]
        ihi = np.argwhere(self._energy < emax)[-1,0]+1
        
        jlo = np.argwhere(self._ctheta_axis.center > cthmin)[0,0]
        jhi = np.argwhere(self._ctheta_axis.center < cthmax)[-1,0] +1
        
        weights = (self._energy[ilo:ihi,np.newaxis]*
                   self._exp[ilo:ihi,jlo:jhi]*
                   self._wfn(self._energy[ilo:ihi,np.newaxis]))
        
        wsum = np.sum(weights)
        psf = np.apply_over_axes(np.sum,
                                 self._psf[:,ilo:ihi,jlo:jhi]*
                                 weights[np.newaxis,...],
                                 [1,2])
        psf = np.squeeze(psf)                   
        psf *= (1./wsum)
        return self._dtheta, psf

	def crop(self, img, edges, orig):
		'''
		Crops an image so that it is a rectangle
		@npimg: an image to crop
		@return: the cropped image
		'''
		#find the extents in the y direction
		maxX = orig[0,...].max()
		maxY = orig[1,...].max()
		x1 = 0 - edges[0,0]
		x2 = maxX - edges[1,0]
		y1 = 0 - edges[0,1]
		y2 = -(maxY - edges [1,1])
		
		#slice the image in y direction
		img = img[y1+1:img.shape[0]-y2-1]
		
		#find the extents in the x direction
		cropTop = numpy.argwhere(img[0,:,3]!=0)
		cropBot = numpy.argwhere(img[-1,:,3]!=0)
		minT = cropTop.min()
		maxT = cropTop.max()
		minB = cropBot.min()
		maxB = cropBot.max()
		
		#grab the correct extents
		xMin = max(minT,minB)
		xMax = min(maxT,maxB)
		
		#slice the image in x direction
		img = img[:,xMin:xMax]
		
		return img

 def test_binary_classsification_should_out_row_vector_of_0_1_only(self):
     model = Model([np.random.rand(4, 6), np.random.rand(1, 5)])
     prediction = model.predict_binary_classification(np.random.rand(10, 5))
     self.assertEqual(prediction.shape, (10, 1))
     zeros = len(np.argwhere(prediction == 0))
     ones = len(np.argwhere(prediction == 1))
     self.assertEqual(zeros + ones, 10)

def np_combine_rare(Xtrain, Xtest, col_list = list(), rare_line=1):
    if Xtrain.shape[1] != Xtest.shape[1]:
        print 'Xtrain, Xtest shape not match.'
        return

    if not col_list :
        col_list = range(Xtrain.shape[1])
        check_int = True
    else:
        check_int = False

    n_train = Xtrain.shape[0]
    for col in col_list:
        col_data_train = Xtrain[:, col]
        col_data_test = Xtest[:, col]
        col_data = np.hstack((col_data_train, col_data_test))
        # print col_data[0]
        if issubclass(col_data.dtype.type, np.integer) or (not check_int):
            le = preprocessing.LabelEncoder()
            le.fit(col_data)
            col_data = le.transform(col_data)
            max_label = np.amax(col_data)
            counts = np.bincount(col_data)
            rare_cats = np.argwhere(counts <= rare_line)
            rare_cats = rare_cats.reshape(rare_cats.shape[0])
            rare_positions = [np.argwhere(col_data == rare_cat)[0,0] for rare_cat in rare_cats]
            # print len(rare_positions)
            col_data[rare_positions] = max_label+1
            Xtrain[:, col] = col_data[:n_train]
            Xtest[:, col] = col_data[n_train:]
        else:
            print 'col:{0:d} not integer'.format(col)

def findValidFFTWDim( inputDims ):
    """
    Finds a valid dimension for which FFTW can optimize its calculations. The 
    return is a shape which is forced to be square, as this gives uniform pixel
    size in x-y in Fourier space.
    
    If you want a minimum padding size, call as findValidFFTWDim( image.shape + 128 ) 
    or similar.
    """
    dim = np.max( np.round( inputDims ) )
    maxPow2 = np.int( np.ceil( math.log( dim, 2 ) ) )
    maxPow3 = np.int( np.ceil( math.log( dim, 3 ) ) )
    maxPow5 = np.int( np.ceil( math.log( dim, 5 ) ) )
    maxPow7 = np.int( np.ceil( math.log( dim, 7 ) ) )   
    
    dimList = np.zeros( [(maxPow2+1)*(maxPow3+1)*(maxPow5+1)*(maxPow7+1)] )
    count = 0
    for I in np.arange(0,maxPow7+1):
        for J in np.arange(0,maxPow5+1):
            for K in np.arange(0,maxPow3+1):
                for L in np.arange(0,maxPow2+1):
                    dimList[count] = 2**L * 3**K * 5**J * 7**I
                    count += 1
    dimList = np.sort( np.unique( dimList ) )
    dimList = dimList[ np.argwhere(dimList < 2*dim)].squeeze()
    dimList = dimList.astype('int64')
    # Throw out odd image shapes, this just causes more problems with many 
    # functions
    dimList = dimList[ np.mod(dimList,2)==0 ]
    
    # Find first dim that equals or exceeds dim
    nextValidDim =  dimList[np.argwhere( dimList >= dim)[0,0]]
    return np.array( [nextValidDim, nextValidDim] )    

def fwhm(array):
    """
    Computes the full width half maximum of a 1-d array
    Returns the indices of the array elements left and right closest to the
    maximum that cross below half the maximum value
    """

    assert (type(array) == type(np.ndarray([])))

    # Find the maximum in the interior of the array
    fwhm = 0.5 * array[1:-1].max()
    max_idx = array[1:-1].argmax() + 1
    # Divide the intervall in halfs at the peak and find the index of the
    # value in the left half of the intervall before it increases over max/2

    # The FWHM is between the indices closest to the maximum, whose values
    # are below 0.5 times the max
    try:
        left_idx = np.argwhere(array[1: max_idx] < fwhm)[-1] + 1
    except IndexError:
        # This can occurs if there is no value in the array smaller than
        # 0.5*max.
        # In this case, return the left limit of the array as the FWHM.
        left_idx = 0
    try:
        right_idx = np.argwhere(array[max_idx:-1] < fwhm)[0] + max_idx
    except IndexError:
        # Subtract one because the index of an array with size n is
        # within 0..n-1
        right_idx = array.size() - 1

    return np.array([int(left_idx), int(right_idx)])

def histClim( imData, cutoff = 0.01, bins_ = 512 ):
    '''Compute display range based on a confidence interval-style, from a histogram
    (i.e. ignore the 'cutoff' proportion lowest/highest value pixels)'''
    
    if( cutoff <= 0.0 ):
        return imData.min(), imData.max()
    # compute image histogram
    hh, bins_ = imHist(imData, bins_)
    hh = hh.astype( 'float' )

    # number of pixels
    Npx = np.sum(hh)
    hh_csum = np.cumsum( hh )
    
    # Find indices where hh_csum is < and > Npx*cutoff
    try:
        i_forward = np.argwhere( hh_csum < Npx*(1.0 - cutoff) )[-1][0]
        i_backward = np.argwhere( hh_csum > Npx*cutoff )[0][0]
    except IndexError:
        print( "histClim failed, returning confidence interval instead" )
        from scipy.special import erfinv
        
        sigma = np.sqrt(2) * erfinv( 1.0 - cutoff )
        return ciClim( imData, sigma )
    
    clim =  np.array( [bins_[i_backward], bins_[i_forward]] )
    if clim[0] > clim[1]:
        clim = np.array( [clim[1], clim[0]] )
    return clim

def bqp_cluster(bqp, init):
	'''
	binary quadratic programming with clustering
	:return:
	'''
	n = bqp.size()
	maxiter = 10
	q = 0.5 * bqp.q - bqp.col_sum(range(n))
	diag = bqp.diag()
	lamb = 320
	lamb_diag = lamb - diag

	# initialize cluster
	res = init
	cluster = np.argwhere(res >= 0)[:, 0]

	# find final cluster
	for i in xrange(maxiter):
		dist_to_cluster = bqp.col_sum(cluster) + 0.5 * q
		dist_to_cluster[cluster] += lamb_diag[cluster]
		# print i, dist_to_cluster
		med = np.median(dist_to_cluster)
		new_res = np.where(dist_to_cluster > med, 1, -1)
		# print np.sum(res==1), np.sum(new_res==1),np.sum(res != new_res)
		if np.sum(res != new_res) < 0.001*n:
			break
		cluster = np.argwhere(new_res >= 0)[:, 0]
		res = new_res
	res = new_res
	return res

def tg2csv_nodiff(npyfile,outname):
    data=np.load(npyfile)
    data=data[()]

    mykeys=['00065','00060','00055','00053','00046']#,'00129']
    cons=['M2  ','N2  ','S2  ','K1  ','O1  ','M4  ']
    consout=['M2 O','M2 M','M2 D','N2 O','N2 M','N2 D','S2 O','S2 M','S2 D','K1 O','K1 M','K1 D','O1 O','O1 M','O1 D','M4 O','M4 M','M4 D']
    
    tidecon=np.empty((5,18))
    for i in range(5):
        for j in range(6):
            idx=np.argwhere(data[mykeys[i]]['df'].index==cons[j])
            tidecon[i,3*j]=data[mykeys[i]]['wlevc'][idx,0]
            tidecon[i,(3*j)+1]=data[mykeys[i]]['outc'][idx,0]
            tidecon[i,(3*j)+2]=data[mykeys[i]]['df'].lookup([cons[j]],['Amp diff'])

    df=pd.DataFrame(tidecon,columns=consout,index=mykeys)
    df.to_csv(outname+'_amp.csv')


    tidecon=np.empty((5,18))
    for i in range(5):
        for j in range(6):
            idx=np.argwhere(data[mykeys[i]]['df'].index==cons[j])
            tidecon[i,3*j]=data[mykeys[i]]['wlevc'][idx,1]
            tidecon[i,(3*j)+1]=data[mykeys[i]]['outc'][idx,1]
            tidecon[i,(3*j)+2]=data[mykeys[i]]['df'].lookup([cons[j]],['Phase diff'])

    df=pd.DataFrame(tidecon,columns=consout,index=mykeys)
    df.to_csv(outname+'_phase.csv')

def initialize_seed(CAC, from_gt=True):
    image = CAC.image_obj.hsi_image
    if from_gt:
        print 'Seed from ground truth...'
        inside_mask_seed = CAC.ground_truth_obj
        outside_mask_seed = CAC.ground_truth_obj
    else:
        center = CAC.mask_obj.center
        radius_point = CAC.mask_obj.radius_point
        radius = np.linalg.norm(np.array(radius_point) - np.array(center))

        inside_seed_omega = [center[0] + radius * 0.2, center[1]]
        outside_seed_omega = [center[0] + radius * 1.8, center[1]]

        inside_mask_seed = MaskClass()
        outside_mask_seed = MaskClass()

        inside_mask_seed.from_points_and_image(center, inside_seed_omega, image)
        outside_mask_seed.from_points_and_image(center, outside_seed_omega, image)

    inside_seed = inside_mask_seed.mask
    outside_seed = 255. - outside_mask_seed.mask
    # inside_mask_seed.plot_image()
    # CAC.mask_obj.plot_image()
    # utils.printNpArray(outside_seed)
    inside_coordinates = np.argwhere(inside_seed == 255.)
    outside_coordinates = np.argwhere(outside_seed == 255.)

    omega_in_mean = mean_color_in_region(inside_coordinates, image)
    omega_out_mean = mean_color_in_region(outside_coordinates, image)
    return omega_in_mean, omega_out_mean

		def voigtking(v,a):
			oneonsqrtpi=0.56418958354775630
			h0 = np.array([ 1.0e0, 0.9975031223974601240368798e0, 0.9900498337491680535739060e0, 0.9777512371933363639286036e0, 0.9607894391523232094392107e0, 0.9394130628134757861197108e0, 0.9139311852712281867473535e0, 0.8847059049434835594929548e0, 0.8521437889662113384563470e0, 0.8166864825981108401538061e0, 0.7788007830714048682451703e0, 0.7389684882589442416058206e0, 0.6976763260710310572091293e0, 0.6554062543268405127576690e0, 0.6126263941844160689885800e0, 0.5697828247309230097666297e0, 0.5272924240430485572436946e0, 0.4855368951540794399916001e0, 0.4448580662229411344814454e0, 0.4055545050633205516443034e0, 0.3678794411714423215955238e0, 0.3320399453446606420249195e0, 0.2981972794298873779316010e0, 0.2664682978135241116965901e0, 0.2369277586821217567233665e0, 0.2096113871510978225241101e0, 0.1845195239929892676298138e0, 0.1616211924653392539324509e0, 0.1408584209210449961479715e0, 0.1221506695399900084151679e0, 0.1053992245618643367832177e0, 0.9049144166369591062935159e-1, 0.7730474044329974599046566e-1, 0.6571027322750286139200605e-1, 0.5557621261148306865356766e-1, 0.4677062238395898365276137e-1, 0.3916389509898707373977109e-1, 0.3263075599289603180381419e-1, 0.2705184686635041108596167e-1, 0.2231491477696640649487920e-1, 0.1831563888873418029371802e-1, 0.1495813470057748930092482e-1, 0.1215517832991493721502629e-1, 0.9828194835379685936011149e-2, 0.7907054051593440493635646e-2, 0.6329715427485746576865117e-2, 0.5041760259690979102410257e-2, 0.3995845830084632413030896e-2, 0.3151111598444440557819106e-2, 0.2472563035874193226953048e-2, 0.1930454136227709242213512e-2, 0.1499685289329846120368399e-2, 0.1159229173904591150012118e-2, 0.8915937199952195568639939e-3, 0.6823280527563766163014506e-3, 0.5195746821548384817648154e-3, 0.3936690406550782109805393e-3, 0.2967857677932108344855019e-3, 0.2226298569188890101840659e-3, 0.1661698666072774484528398e-3, 0.1234098040866795494976367e-3, 0.9119595636226606575873788e-4, 0.6705482430281108867614262e-4, 0.4905835745620769579106241e-4, 0.3571284964163521691234528e-4, 0.2586810022265412127035909e-4, 0.1864374233151683041526522e-4, 0.1336996212084380475632834e-4, 0.9540162873079234841590110e-5, 0.6773449997703748098370991e-5, 0.4785117392129009089609771e-5, 0.3363595724825637829225185e-5, 0.2352575200009772922652510e-5, 0.1637237807196195233271403e-5, 0.1133727138747965652009438e-5, 0.7811489408304490795473004e-6, 0.5355347802793106157479094e-6, 0.3653171341207511214363159e-6, 0.2479596018045029629499234e-6, 0.1674635703137489046698250e-6, 0.1125351747192591145137752e-6, 0.7524623257644829651017174e-7, 0.5006218020767042215644986e-7, 0.3314082270898834287088712e-7, 0.2182957795125479209083827e-7, 0.1430724191856768833467676e-7, 0.9330287574504991120387842e-8, 0.6054282282484886644264747e-8, 0.3908938434264861859681131e-8, 0.2511212833271291589987176e-8, 0.1605228055185611608653934e-8, 0.1020982947159334870301705e-8, 0.6461431773106108989429857e-9, 0.4068811450655793356678124e-9, 0.2549381880391968872012880e-9, 0.1589391009451636652873474e-9, 0.9859505575991508240729766e-10, 0.6085665105518337082108266e-10, 0.3737571327944262032923964e-10, 0.2284017657993705413027994e-10, 0.1388794386496402059466176e-10, 0.8402431396484308187150245e-11, 0.5058252742843793235026422e-11, 0.3029874246723653849216172e-11, 0.1805831437513215621913785e-11, 0.1070923238250807645586450e-11, 0.6319285885175366663984108e-12, 0.3710275783094727281418983e-12, 0.2167568882618961942307398e-12, 0.1259993054847742150188394e-12, 0.7287724095819692419343177e-13, 0.4194152536192217185131208e-13, 0.2401734781620959445230543e-13, 0.1368467228126496785536523e-13, 0.7758402075696070467242451e-14, 0.4376618502870849893821267e-14, 0.2456595368792144453705261e-14, 0.1372009419645128473380053e-14, 0.7624459905389739760616425e-15, 0.4215893238174252040735029e-15, 0.2319522830243569388312264e-15, 0.1269802641377875575018264e-15, 0.6916753975541448863883054e-16, 0.3748840457745443581785685e-16, 0.2021715848695342027119482e-16, 0.1084855264042937802512215e-16, 0.5792312885394857923477507e-17, 0.3077235638152508657901574e-17, 0.1626664621453244338034305e-17, 0.8555862896902856300749061e-18, 0.4477732441718301199042103e-18, 0.2331744656246116743545942e-18, 0.1208182019899973571654094e-18, 0.6228913128535643653088166e-19, 0.3195366717748344275120932e-19, 0.1631013922670185678641901e-19, 0.8283677007682876110228791e-20, 0.4186173006145967657832773e-20, 0.2104939978339734445589080e-20, 0.1053151347744013743766989e-20, 0.5242885663363463937171805e-21, 0.2597039249246848208769072e-21, 0.1280015319051641983953037e-21, 0.6277407889747195099574399e-22, 0.3063190864577440373821128e-22, 0.1487292181651270619154227e-22, 0.7185335635902193010046941e-23, 0.3454031957013868448981675e-23, 0.1652091782314268593068387e-23, 0.7862678502984538622254116e-24, 0.3723363121750510429289070e-24, 0.1754400713566556605465117e-24, 0.8225280651606668501925640e-25, 0.3837082905344536379879530e-25, 0.1781066634757091357021587e-25, 0.8225980595143903024275237e-26, 0.3780277844776084635218009e-26, 0.1728575244037268289032505e-26, 0.7864685935766448441713277e-27, 0.3560434556451067378310069e-27, 0.1603810890548637852976087e-27, 0.7188393394953158727447087e-28, 0.3205819323394999444158648e-28, 0.1422573701362478490703169e-28, 0.6281148147605989215436687e-29, 0.2759509067522042024589005e-29, 0.1206293927781149203841840e-29, 0.5246902396795390138796640e-30, 0.2270812922026396509517690e-30, 0.9778860615814667663870901e-31, 0.4190093194494397377123780e-31, 0.1786436718517518413888050e-31, 0.7578445267618382646037748e-32, 0.3198903416725805416294188e-32, 0.1343540197758737662452134e-32, 0.5614728092387934579799402e-33, 0.2334722783487267408869808e-33, 0.9659851300583384710233199e-34, 0.3976803097901655265751816e-34, 0.1629019426220514693169818e-34, 0.6639677199580734400702255e-35, 0.2692751000456178970430831e-35, 0.1086610640745980532852592e-35, 0.4362950029268711046345153e-36, 0.1743070896645292498913954e-36, 0.6929124938815710000577778e-37, 0.2740755284722598699701951e-37, 0.1078675105373929991550997e-37, 0.4224152406206200437573993e-38, 0.1645951484063258284098658e-38, 0.6381503448060790393554118e-39, 0.2461826907787885454919214e-39, 0.9449754976491185028813549e-40, 0.3609209642415355020302235e-40, 0.1371614910949353618952282e-40, 0.5186576811908572940413120e-41, 0.1951452380295377748121319e-41, 0.7305730197111493885868359e-42, 0.2721434140093713884466599e-42, 0.1008696596314342558322441e-42, 0.3720075976020835962959696e-43, 0.1365122395620087240477630e-43 ], dtype=np.float64)
			h1 = np.array([ -1.128379167095512573896159e0, -1.122746665023313894112994e0, -1.105961434222613497822717e0, -1.078356949458362356972974e0, -1.040477963566390226869037e0, -0.9930644092865188274925694e0, -0.9370297574325730524254160e0, -0.8734346738611667009559691e0, -0.8034569860177944012914767e0, -0.7283590897795191457635390e0, -0.6494539941944691013512214e0, -0.5680712138345335512208471e0, -0.4855236771153186839197872e0, -0.4030767281964792012404736e0, -0.3219201665209207840831093e0, -0.2431441002236951675148354e0, -0.1677191974661332963609891e0, -0.9648171389061105293546881e-1, -0.3012346558870770535102483e-1, 0.3081328457047809980986685e-1, 0.8593624458727488433391777e-1, 0.1349991935349749351748713e0, 0.1778942744880748462232135e0, 0.2146410885736963723412265e0, 0.2453732617833523433216744e0, 0.2703231847626659615037426e0, 0.2898056218155761132507312e0, 0.3042008523837261147222841e0, 0.3139379509747736418513567e0, 0.3194787353320834397089635e0, 0.3213028233267945998845488e0, 0.3198941423604233541674753e0, 0.3157291364070343763776039e0, 0.3092668200208504802085382e0, 0.3009407397271468294117335e0, 0.2911528243392948676821857e0, 0.2802690390913659378360681e0, 0.2686167052981096351368975e0, 0.2564833079412283848897372e0, 0.2441165877658165024921633e0, 0.2317257011687522312257119e0, 0.2194832289213470945135105e0, 0.2075278218310246553881156e0, 0.1959672858880207128215797e0, 0.1848819293094190730287360e0, 0.1743280173110208640535652e0, 0.1643412057011470302647273e0, 0.1549398500207542791790132e0, 0.1461281117364874603340094e0, 0.1378988059908943461128856e0, 0.1302359559637753421977543e0, 0.1231170365911391556632533e0, 0.1165149050377156668055896e0, 0.1103994269264874144398788e0, 0.1047388160423518894772002e0, 0.9950071130235648759030670e-1, 0.9465301854781620910441970e-1, 0.9016454652735125189272609e-1, 0.8600546667768981700419079e-1, 0.8214762533231104047151097e-1, 0.7856473513008974607178765e-1, 0.7523246995193424459351750e-1, 0.7212848493340500348466924e-1, 0.6923238018945846374255513e-1, 0.6652562400245432725286132e-1, 0.6399144848312167544450556e-1, 0.6161472819590847810012464e-1, 0.5938184999317344054777048e-1, 0.5728058034957269600588669e-1, 0.5529993483145627029203620e-1, 0.5343005296426139233134751e-1, 0.5166208065197234887486323e-1, 0.4998806142885727821214551e-1, 0.4840083715410895783485349e-1, 0.4689395826338997495993764e-1, 0.4546160333748704598916335e-1, 0.4409850750954268216573793e-1, 0.4279989908392569899980027e-1, 0.4156144366035708515282858e-1, 0.4037919502845779134315796e-1, 0.3924955210570969222557380e-1, 0.3816922122416471946490538e-1, 0.3713518311895684989765586e-1, 0.3614466402785612590311943e-1, 0.3519511037069617482332004e-1, 0.3428416653694949866994660e-1, 0.3340965536664229903158673e-1, 0.3256956096272257612903376e-1, 0.3176201352112533673779090e-1, 0.3098527590780517228496903e-1, 0.3023773174995156695256252e-1, 0.2951787484170619418302355e-1, 0.2882429969333463230632146e-1, 0.2815569307740452259166926e-1, 0.2751082644654734935368337e-1, 0.2688854911528297388431485e-1, 0.2628778211358937241904422e-1, 0.2570751263279204975253415e-1, 0.2514678899527364475073049e-1, 0.2460471608876676259183765e-1, 0.2408045121385331090696902e-1, 0.2357320029997478838776359e-1, 0.2308221445094914570064896e-1, 0.2260678678585010840991674e-1, 0.2214624954526743636682309e-1, 0.2169997143654264861646818e-1, 0.2126735519465680897241377e-1, 0.2084783533811200664569883e-1, 0.2044087610146017752978434e-1, 0.2004596952814515567227767e-1, 0.1966263370908071277476715e-1, 0.1929041115392591487587378e-1, 0.1892886728337045173071115e-1, 0.1857758903193275942486415e-1, 0.1823618355182474294515453e-1, 0.1790427700936730343669473e-1, 0.1758151346626646308038721e-1, 0.1726755383879409857500321e-1, 0.1696207492857163038741910e-1, 0.1666476851923932358834102e-1, 0.1637534053381661837450139e-1, 0.1609351024802744708797459e-1, 0.1581900955528515170398058e-1, 0.1555158227940989996039230e-1, 0.1529098353149220739767610e-1, 0.1503697910762349625920090e-1, 0.1478934492449222808347731e-1, 0.1454786649009525295887101e-1, 0.1431233840704145462214254e-1, 0.1408256390613103046576229e-1, 0.1385835440808103075999097e-1, 0.1363952911143803959964144e-1, 0.1342591460487383719630737e-1, 0.1321734450220107129175951e-1, 0.1301365909857474699723209e-1, 0.1281470504646293252049926e-1, 0.1262033505007755515762735e-1, 0.1243040757705449418533892e-1, 0.1224478658626222948827240e-1, 0.1206334127070085131071308e-1, 0.1188594581452897199141430e-1, 0.1171247916332562864755594e-1, 0.1154282480675818732553606e-1, 0.1137687057288605896976939e-1, 0.1121450843338417065773542e-1, 0.1105563431902001242285305e-1, 0.1090014794476407143162512e-1, 0.1074795264395590657657700e-1, 0.1059895521098731117021612e-1, 0.1045306575200023435008377e-1, 0.1031019754313063242129945e-1, 0.1017026689586042607609242e-1, 0.1003319302906845397201302e-1, 0.9898897947397924639729408e-2, 0.9767306325582547468180475e-2, 0.9638345398396424782187982e-2, 0.9511944855914052317394595e-2, 0.9388036743786533882143785e-2, 0.9266555368258485665416943e-2, 0.9147437205667194364984339e-2, 0.9030620816181499749829423e-2, 0.8916046761552686783940876e-2, 0.8803657526663477808232965e-2, 0.8693397444674087410976982e-2, 0.8585212625576311168220303e-2, 0.8479050887977828363904268e-2, 0.8374861693949366877024963e-2, 0.8272596086777159693185345e-2, 0.8172206631472266686907249e-2, 0.8073647357896888215194357e-2, 0.7976873706375800846399120e-2, 0.7881842475668539112571351e-2, 0.7788511773184966394916599e-2, 0.7696840967333456047851643e-2, 0.7606790641897071224649652e-2, 0.7518322552338916854888971e-2, 0.7431399583943265980411531e-2, 0.7345985711704159367477213e-2, 0.7262045961877964368036759e-2, 0.7179546375120877141317720e-2, 0.7098453971136580788416864e-2, 0.7018736714763248519923831e-2, 0.6940363483432822204243367e-2, 0.6863304035939017881037086e-2, 0.6787528982453825324020280e-2, 0.6713009755735391745310971e-2, 0.6639718583473122562606414e-2, 0.6567628461718606252976457e-2, 0.6496713129353586350126915e-2, 0.6426947043548671526978323e-2, 0.6358305356168803683625031e-2, 0.6290763891083702643557758e-2, 0.6224299122343582476647260e-2, 0.6158888153182396103862750e-2, 0.6094508695812718682782931e-2, 0.6031139051978132847456608e-2, 0.5968758094230636272231571e-2, 0.5907345247902159938278185e-2, 0.5846880473740769223255677e-2, 0.5787344251183524483318654e-2, 0.5728717562239307805652498e-2, 0.5670981875956182433959706e-2 ], dtype=np.float64)
			h2 = np.array([ 1.0e0, 0.9925156067854728234166954e0, 0.9702488370741846925024279e0, 0.9337524315196362275518164e0, 0.8839262840201373526840738e0, 0.8219864299617913128547470e0, 0.7494235719224071131328299e0, 0.6679529582323300874171809e0, 0.5794577764970237101503160e0, 0.4859284571458759498915146e0, 0.3894003915357024341225852e0, 0.2918925528622829754342991e0, 0.1953493712998886960185562e0, 0.1015879694206602794774387e0, 0.1225252788368832137977160e-1, -0.7122285309136537622082871e-1, -0.1476418787320535960282345e0, -0.2160639183435653507962620e0, -0.2758120010582235033784961e0, -0.3264713765759730440736642e0, -0.3678794411714423215955238e0, -0.4001081341403160736400280e0, -0.4234401367904400766628734e0, -0.4383403499032471637408907e0, -0.4454241863223889026399290e0, -0.4454241976960828728637340e0, -0.4391564671033144569589568e0, -0.4274880540708223266513326e0, -0.4113065890894513887520768e0, -0.3914928958756679769706131e0, -0.3688972859665251787412620e0, -0.3443199355303629399446828e0, -0.3184955306263949534807185e0, -0.2920821644962502188874669e0, -0.2656542962828890681640534e0, -0.2396994397177897912204020e0, -0.2146181451424491640939456e0, -0.1907267687784773058932939e0, -0.1682624875086995569546816e0, -0.1473900121018631148986771e0, -0.1282094722211392620560261e0, -0.1107649874577763082733483e0, -0.9505349453993480902150559e-1, -0.8103346641770551054241192e-1, -0.6863322916783106348475741e-1, -0.5775865327580743751389419e-1, -0.4830006328783957980109026e-1, -0.4013827136320013258889535e-1, -0.3314969401563551466825700e-1, -0.2721055620979549646261829e-1, -0.2220022256661865628545539e-1, -0.1800372189840480267502263e-1, -0.1451354925728548119815172e-1, -0.1163084007733763911929080e-1, -0.9266014956431594449373699e-2, -0.7338992385437093554928018e-2, -0.5779061516816548137194317e-2, -0.4524499030007499171731476e-2, -0.3522004336456824141111923e-2, -0.2726016661692386541868837e-2, -0.2097966669473552341459824e-2, -0.1605504811757694087682580e-2, -0.1221738898797218035679319e-2, -0.9245047462622340271825711e-3, -0.6956863110190540254524861e-3, -0.5205955169809141905659767e-3, -0.3874169656489197360292113e-3, -0.2867188376814953929994613e-3, -0.2110284027525126746959732e-3, -0.1544685271976339753833504e-3, -0.1124502587150317136058296e-3, -0.8141583451940456365639560e-4, -0.5862617398424354123250055e-4, -0.4198696356554642675724513e-4, -0.2990772192017133390000897e-4, -0.2118866502002593128272052e-4, -0.1493070967418717996705171e-4, -0.1046450930688891587354327e-4, -0.7294971485088477169986746e-5, -0.5058237141326785665552064e-5, -0.3488590416297032549927031e-5, -0.2393206427093938070506012e-5, -0.1633028318374209170743394e-5, -0.1108394815502115127316820e-5, -0.7483179321690142728739359e-6, -0.5025418723896900527555212e-6, -0.3357037469306895805115546e-6, -0.2230700306981556484079346e-6, -0.1474451577404705893471723e-6, -0.9694537142843821183145493e-7, -0.6340650817983165854183039e-7, -0.4125281597997292543454039e-7, -0.2669863608647444234432417e-7, -0.1718869397329539903528673e-7, -0.1100823095953252158935162e-7, -0.7013187829205346730804204e-8, -0.4444665113656971914920979e-8, -0.2802144497835918309456751e-8, -0.1757406038399392007880848e-8, -0.1096442676719878283524089e-8, -0.6805092493832370091384262e-9, -0.4201635819811978308984480e-9, -0.2580720549398903308510481e-9, -0.1576898051707325645824557e-9, -0.9585353270