def paddingAnswers(answerSheet1, blankSheet1):
   numRowsA, numColsA, numBandsA, dataTypeA = ipcv.dimensions(answerSheet1)
   numRowsB, numColsB, numBandsB, dataTypeB = ipcv.dimensions(blankSheet1)
   print numRowsB, numColsB
   if numBandsA == 3:
      answerSheet = cv2.cvtColor(answerSheet1, cv.CV_BGR2GRAY)
   elif numBandsA == 1:
      answerSheet = answerSheet1

   if numBandsB == 3:
      blankSheet = cv2.cvtColor(blankSheet1, cv.CV_BGR2GRAY)
   elif numBandsB == 1:
      blankSheet = blankSheet1  

   pad = numpy.absolute(numRowsA - numColsA)/2.0
   maxCount = numpy.max(blankSheet)

   if (numRowsA-numColsA) % 2 != 0:
      answerSheet = numpy.pad(answerSheet, ((0,0),(pad,pad+1)), 'constant', constant_values=((maxCount, maxCount),(maxCount,maxCount)))
   elif (numRowsA-numColsA) % 2 == 0:
      answerSheet = numpy.pad(answerSheet, ((0,0),(pad,pad)), 'constant', constant_values=((maxCount, maxCount),(maxCount,maxCount)))

   pad1 = numpy.absolute(numRowsB - numColsB)/2.0
   maxCount = numpy.max(blankSheet)

   if (numRowsB-numColsB) % 2 != 0:
      blankSheet = numpy.pad(blankSheet, ((0,0),(pad1,pad1+1)), 'constant', constant_values=((maxCount, maxCount),(maxCount,maxCount)))
   elif (numRowsA-numColsA) % 2 == 0:
      blankSheet = numpy.pad(blankSheet, ((0,0),(pad1,pad1)), 'constant', constant_values=((maxCount, maxCount),(maxCount,maxCount)))


   return answerSheet, blankSheet

 def plotall(self):
     real = self.z_data_raw.real
     imag = self.z_data_raw.imag
     real2 = self.z_data_sim.real
     imag2 = self.z_data_sim.imag
     fig = plt.figure(figsize=(15,5))
     fig.canvas.set_window_title("Resonator fit")
     plt.subplot(131)
     plt.plot(real,imag,label='rawdata')
     plt.plot(real2,imag2,label='fit')
     plt.xlabel('Re(S21)')
     plt.ylabel('Im(S21)')
     plt.legend()
     plt.subplot(132)
     plt.plot(self.f_data*1e-9,np.absolute(self.z_data_raw),label='rawdata')
     plt.plot(self.f_data*1e-9,np.absolute(self.z_data_sim),label='fit')
     plt.xlabel('f (GHz)')
     plt.ylabel('Amplitude')
     plt.legend()
     plt.subplot(133)
     plt.plot(self.f_data*1e-9,np.unwrap(np.angle(self.z_data_raw)),label='rawdata')
     plt.plot(self.f_data*1e-9,np.unwrap(np.angle(self.z_data_sim)),label='fit')
     plt.xlabel('f (GHz)')
     plt.ylabel('Phase')
     plt.legend()
     # plt.gcf().set_size_inches(15,5)
     plt.tight_layout()
     plt.show()

    def getEnergy(self, normalized=True, mask=None):
        """
        Returns the current energy.

        Parameters:
            normalized: Flag to return the normalized energy (that is, divided
            by the total density)
        """
        if self.gpu:
            psi = self.psi.get()
            V = self.Vdt.get() / self.dt
        else:
            psi = self.psi
            V = self.Vdt.get() / self.dt
        density = np.absolute(psi) ** 2
        gradx = np.gradient(psi)[0]
        normFactor = density.sum() if normalized else 1.0
        return (
            np.ma.array(
                -(
                    0.25 * np.gradient(np.gradient(density)[0])[0]
                    - 0.5 * np.absolute(gradx) ** 2
                    - (self.g_C * density + V) * density
                ),
                mask=mask,
            ).sum()
            / normFactor
        )

def mask_good(m, badval = UNSEEN, rtol = 1.e-5, atol = 1.e-8):
    """Return a mask with False where m is close to badval
    and True elsewhere
    [absolute(m - badval) > atol + rtol * absolute(badval)]"""
    atol = npy.absolute(atol)
    rtol = npy.absolute(rtol)
    return npy.absolute(m - badval) > atol + rtol * npy.absolute(badval)

def add_data(N):
    if N<=37.0:
        Ns=N
    else:
        Ns=37.0
    X=Ns*pi*(f-f0)/f0
    A=sin(X)/sin(X/Ns)
    #ans=recur_exp(N, Np=37) 
    
    #A=sum([el[0]*exp(1j*2*pi*f/f0*el[1])/1.0 for el in ans])
    #A=sum([1.0*exp(1j*2*pi*f/f0*el[1])/1.0 for el in ans])

    #A=comb_A(N)
    Asq=absolute(A)**2
    #return Asq
    Ga0=2*mu**2*Y0*Ns**2
    Ga=Ga0*Asq/Ns**2
    Ba=Ga0*(sin(2*X)-2*X)/(2*X**2)
    w=2*pi*f
    S13=1j*sqrt(2*Ga*GL)/(Ga+1j*Ba+1j*w*C+GL)
#
#    if N>5:
#        Ns=N-5
#    else: 
#        Ns=1
#    X=Ns*pi*(f-f0)/f0
#    A=1*sin(X)/sin(X/Ns)
#    Asq=A**2
#    Ga0=2*mu**2*Y0*(Ns)**2
#    Ga=Ga0*Asq/Ns**2
#    Ba=Ga0*(sin(2*X)-2*X)/(2*X**2)
#    w=2*pi*f
#    S31=1j*sqrt(2*Ga*GL)/(Ga+1j*Ba+1j*w*C+GL)
#        
    return absolute(S13**2)

def mask_good(m, badval=UNSEEN, rtol=1.0e-5, atol=1.0e-8):
    """Returns a bool array with ``False`` where m is close to badval.

    Parameters
    ----------
    m : a map (may be a sequence of maps)
    badval : float, optional
        The value of the pixel considered as bad (:const:`UNSEEN` by default)
    rtol : float, optional
        The relative tolerance
    atol : float, optional
        The absolute tolerance

    Returns
    -------
    a bool array with the same shape as the input map, ``False`` where input map is
    close to badval, and ``True`` elsewhere.

    See Also
    --------
    mask_bad, ma

    Examples
    --------
    >>> import healpy as hp
    >>> m = np.arange(12.)
    >>> m[3] = hp.UNSEEN
    >>> hp.mask_good(m)
    array([ True,  True,  True, False,  True,  True,  True,  True,  True,
            True,  True,  True], dtype=bool)
    """
    m = np.asarray(m)
    atol = np.absolute(atol)
    rtol = np.absolute(rtol)
    return np.absolute(m - badval) > atol + rtol * np.absolute(badval)

def calculateMie(data):
    # Extract data
    (p, w, n_p, n_medium, th, n_theta, x_rv) = data
    # Size parameter
    # x      - size parameter = k*radius = 2pi/lambda * radius
    #          (lambda is the wavelength in the medium around the scatterers)
    x = np.pi * p / (w / n_medium)
    # Mie parameters
    (S1, S2, Qext, Qsca, Qback, gsca) = bhmie(x, n_p / n_medium, n_theta)
    # Phase function
    P = (np.absolute(S1) ** 2.0 + np.absolute(S2) ** 2.0) / \
        (Qsca * x ** 2.0)
    # Cumulative distribution
    cP = st.cumulativeDistributionTheta(P, th)
    # Normalize
    cP /= cP[-1]

    # Inverse cumulative distribution for random variable picking
    cPinv = st.invertNiceFunction(np.degrees(th), cP, x_rv)

    pD = {}
    pD['particleDiameter'] = p
    pD['sizeParameter'] = x
    pD['wavelength'] = w
    pD['crossSections'] = Qext * np.pi * (p / 2.0) ** 2.0
    pD['inverseCDF'] = cPinv
    pD['phaseFunction'] = P
    pD['cumulativePhaseFunction'] = cP

    # Return generated data
    return pD

def curvature_optimisation_func_lensmaker(curv_1 = 0.002, focal_length = 100.,
                                diameter = 5., thickness = 5., ref_index = 1.5):
    """
    This function is used to minimise the RMS spread of a beam of given
    diameter, propagated through a lens of given thickness, by changing
    the curvatures of the two sides of the lens. It is meant to be used
    in conjunction with an optimisation function.
    
    This function is bounded by the lensmaker equation, so it only requires
    one curvature as an argument and the other is calculated using the
    given focal length, thickness, and refractive index.
    """
    curv_2 = lensmaker_equation(curv_1, focal_length, thickness, ref_index)
    if curv_2 == 0:
        curv_2 -= 1e-13
    if curv_1 == 0:
        curv_1 += 1e-13
    aperture_radius_1 = np.absolute(1/float(curv_1))
    aperture_radius_1 -= 1e-6*aperture_radius_1
    aperture_radius_2 = np.absolute(1/float(curv_2))
    aperture_radius_2 -= 1e-6*aperture_radius_2
    lens_front = opt.SphericalRefraction(focal_length, curv_1, 
                                        aperture_radius_1, 1., ref_index)
    lens_back = opt.SphericalRefraction(focal_length + thickness, 
                                        curv_2, aperture_radius_2, 
                                        ref_index, 1.)
    max_radius = diameter/2.
    test_beam = rt.CollimatedBeam([0,0,0], [0,0,1], 6, max_radius, 2)
    rms_spread = rms_xy_spread([lens_front, lens_back], focal_length, test_beam)
    return np.log10(rms_spread)

def estimate(data):
    length=len(data)
    wave=thinkdsp.Wave(ys=data,framerate=Fs)
    spectrum=wave.make_spectrum()
    spectrum_heart=wave.make_spectrum()
    spectrum_resp=wave.make_spectrum()

    fft_mag=list(np.absolute(spectrum.hs))
    fft_length= len(fft_mag)

    spectrum_heart.high_pass(cutoff=0.8,factor=0.001)
    spectrum_heart.low_pass(cutoff=2,factor=0.001)
    fft_heart=list(np.absolute(spectrum_heart.hs))

    max_fft_heart=max(fft_heart)
    heart_sample=fft_heart.index(max_fft_heart)
    hr=heart_sample*Fs/length*60

    spectrum_resp.high_pass(cutoff=0.15,factor=0)
    spectrum_resp.low_pass(cutoff=0.4,factor=0)
    fft_resp=list(np.absolute(spectrum_resp.hs))

    max_fft_resp=max(fft_resp)
    resp_sample=fft_resp.index(max_fft_resp)
    rr=resp_sample*Fs/length*60
    
    print "Heart Rate:", hr, "BPM"
    
    if hr<10:
        print "Respiration Rate: 0 RPM"
    else:
        print "Respiration Rate:", rr, "RPM"
    
    return

def compareRecon(recon1, recon2):
    ''' compare two arrays and return 1 is they are the same within specified
        precision and 0 if not.
        function was made to accompany unit test code '''
    ## FIX: make precision a input parameter
    prec = -11   # desired precision
    if recon1.shape != recon2.shape:
        print 'shape is different!'
        print recon1.shape
        print recon2.shape
        return 0

    for i in range(recon1.shape[0]):
        for j in range(recon2.shape[1]):
            if numpy.absolute(recon1[i,j].real - recon2[i,j].real) > math.pow(10,-11):
                print "real: i=%d j=%d %.15f %.15f diff=%.15f" % (i, j, recon1[i,j].real, recon2[i,j].real, numpy.absolute(recon1[i,j].real-recon2[i,j].real))
                return 0
            ## FIX: need a better way to test
            # if we have many significant digits to the left of decimal we 
            #   need to be less stringent about digits to the right.
            # The code below works, but there must be a better way.
            if isinstance(recon1, complex):
                if int(math.log(numpy.abs(recon1[i,j].imag), 10)) > 1:
                    prec = prec + int(math.log(numpy.abs(recon1[i,j].imag), 10))
                    if prec > 0:
                        prec = -1
                print prec
                if numpy.absolute(recon1[i,j].imag - recon2[i,j].imag) > math.pow(10, prec):
                    print "imag: i=%d j=%d %.15f %.15f diff=%.15f" % (i, j, recon1[i,j].imag, recon2[i,j].imag, numpy.absolute(recon1[i,j].imag-recon2[i,j].imag))
                    return 0

    return 1

def isEqual(left, right, eps=None, masked_equal=True):
  ''' This function checks if two numpy arrays or scalars are equal within machine precision, and returns a scalar logical. '''
  diff_type = "Both arguments to function 'isEqual' must be of the same class!"
  if isinstance(left,np.ndarray):
    # ndarray
    if not isinstance(right,np.ndarray): raise TypeError(diff_type)
    if not left.dtype==right.dtype:
      right = right.astype(left.dtype) # casting='same_kind' doesn't work...
    if np.issubdtype(left.dtype, np.inexact): # also catch float32 etc
      if eps is None: return ma.allclose(left, right, masked_equal=masked_equal)
      else: return ma.allclose(left, right, masked_equal=masked_equal, atol=eps)
    elif np.issubdtype(left.dtype, np.integer) or np.issubdtype(left.dtype, np.bool):
      return np.all( left == right ) # need to use numpy's all()
  elif isinstance(left,(float,np.inexact)):
    # numbers
    if not isinstance(right,(float,np.inexact)): raise TypeError(diff_type)
    if eps is None: eps = 100.*floateps # default
    if ( isinstance(right,float) or isinstance(right,float) ) or left.dtype.itemsize == right.dtype.itemsize: 
      return np.absolute(left-right) <= eps
    else:
      if left.dtype.itemsize < right.dtype.itemsize: right = left.dtype.type(right)
      else: left = right.dtype.type(left)
      return np.absolute(left-right) <= eps  
  elif isinstance(left,(int,bool,np.integer,np.bool)):
    # logicals
    if not isinstance(right,(int,bool,np.integer,np.bool)): raise TypeError(diff_type)
    return left == right
  else: raise TypeError(left)

    def _exec_loop_moving_window(self, a_all, bd_all, mask, bd_idx):
        """Solves the kriging system by looping over all specified points.
        Less memory-intensive, but involves a Python-level loop."""
        import scipy.linalg.lapack

        npt = bd_all.shape[0]
        n = bd_idx.shape[1]
        zvalues = np.zeros(npt)
        sigmasq = np.zeros(npt)

        for i in np.nonzero(~mask)[0]:   # Note that this is the same thing as range(npt) if mask is not defined,
            b_selector = bd_idx[i]       # otherwise it takes the non-masked elements.
            bd = bd_all[i]

            a_selector = np.concatenate((b_selector, np.array([a_all.shape[0] - 1])))
            a = a_all[a_selector[:, None], a_selector]

            if np.any(np.absolute(bd) <= self.eps):
                zero_value = True
                zero_index = np.where(np.absolute(bd) <= self.eps)
            else:
                zero_index = None
                zero_value = False
            b = np.zeros((n+1, 1))
            b[:n, 0] = - self.variogram_function(self.variogram_model_parameters, bd)
            if zero_value:
                b[zero_index[0], 0] = 0.0
            b[n, 0] = 1.0

            x = scipy.linalg.solve(a, b)

            zvalues[i] = x[:n, 0].dot(self.Z[b_selector])
            sigmasq[i] = - x[:, 0].dot(b[:, 0])

        return zvalues, sigmasq

    def _exec_loop(self, a, bd_all, mask):
        """Solves the kriging system by looping over all specified points.
        Less memory-intensive, but involves a Python-level loop."""

        npt = bd_all.shape[0]
        n = self.X_ADJUSTED.shape[0]
        zvalues = np.zeros(npt)
        sigmasq = np.zeros(npt)

        a_inv = scipy.linalg.inv(a)

        for j in np.nonzero(~mask)[0]:   # Note that this is the same thing as range(npt) if mask is not defined,
            bd = bd_all[j]               # otherwise it takes the non-masked elements.
            if np.any(np.absolute(bd) <= self.eps):
                zero_value = True
                zero_index = np.where(np.absolute(bd) <= self.eps)
            else:
                zero_index = None
                zero_value = False

            b = np.zeros((n+1, 1))
            b[:n, 0] = - self.variogram_function(self.variogram_model_parameters, bd)
            if zero_value:
                b[zero_index[0], 0] = 0.0
            b[n, 0] = 1.0
            x = np.dot(a_inv, b)
            zvalues[j] = np.sum(x[:n, 0] * self.Z)
            sigmasq[j] = np.sum(x[:, 0] * -b[:, 0])

        return zvalues, sigmasq

    def _exec_vector(self, a, bd, mask):
        """Solves the kriging system as a vectorized operation. This method
        can take a lot of memory for large grids and/or large datasets."""

        npt = bd.shape[0]
        n = self.X_ADJUSTED.shape[0]
        zero_index = None
        zero_value = False

        a_inv = scipy.linalg.inv(a)

        if np.any(np.absolute(bd) <= self.eps):
            zero_value = True
            zero_index = np.where(np.absolute(bd) <= self.eps)

        b = np.zeros((npt, n+1, 1))
        b[:, :n, 0] = - self.variogram_function(self.variogram_model_parameters, bd)
        if zero_value:
            b[zero_index[0], zero_index[1], 0] = 0.0
        b[:, n, 0] = 1.0

        if (~mask).any():
            mask_b = np.repeat(mask[:, np.newaxis, np.newaxis], n+1, axis=1)
            b = np.ma.array(b, mask=mask_b)

        x = np.dot(a_inv, b.reshape((npt, n+1)).T).reshape((1, n+1, npt)).T
        zvalues = np.sum(x[:, :n, 0] * self.Z, axis=1)
        sigmasq = np.sum(x[:, :, 0] * -b[:, :, 0], axis=1)

        return zvalues, sigmasq

def niceformat(x, l, s):
    """Get a nice formatted string of a number.

    Parameters:
        x: scalar
        l: boolean
            latex expression if True else ordinary
        s: boolean
            use '$' if True else don't

    Returns: expr
        expr: string
            string representing the number
            no measure unit
    """
    if l:
        pref = PREFIXES.copy()
        if s:
            pref[-6] = r'$\mu$'
        else:
            pref[-6] = r'\mu'
    else:
        pref = PREFIXES 
    xexp = 0
    while np.absolute(x) < 1 and xexp >= min(PREFIXES.keys()):
        xexp -= 3
        x *= 1000.
    while np.absolute(x) >= 1e3 and xexp <= max(PREFIXES.keys()):
        xexp += 3
        x /= 1000.
    s = '%.4g'%x + ' ' + pref[xexp]
    return s

def det_trace_iter(A, v, E):
    """
    :param A: input matrix
    :param v: vector used for power method
    :param E: tolerance parameter
    :return: (determinant, trace, N) ->determinant, trace, number of iterations
    """
    N = 0
    err = 0
    lamda = 0
    while np.absolute(err) >= np.absolute(lamda * E) and N <= 100:
        N += 1
        temp = matrix_multiply(A, v)
        newlamda = matrix_multiply(np.transpose(v), temp)[0, 0]
        newlamda = newlamda / matrix_multiply(np.transpose(v), v)[0, 0]

        # can we use magnitude method???
        err = np.absolute(newlamda - lamda)
        v = temp
        lamda = newlamda
    # does multiple multiplication for power method!!!
    if np.absolute(err) < np.absolute(lamda * E):
        return (determinant_for_2x2(A), trace(A), N)
    else:
        #print("Uhh, failed")
        return None

def callback(data):
    # trouble shoot - print data from subscriber
    #rospy.loginfo(rospy.get_caller_id() + "leftx: %s, rightx: %s", data.leftx, data.rightx)    
    
	# unpack values
    global m1val
    global m2val
    global xl 
    global xr
    xlnew = float(data.leftx);
    xrnew = float(data.rightx);

    if(numpy.absolute(xlnew-xl) < 0.02):
        xl = xlnew;
    #else:
    	#print('invalid x1, not updated')

    if(numpy.absolute(xrnew-xr) < 0.02):
        xr = xrnew;
    #else:
    	#print('invalid x2, not updated')




    xlcm = xl * 100;
    xrcm = xr * 100;
    #print 'leftx: {0:.3f} cm, rightx: {1:.3f} cm.'.format(xlcm, xrcm)

    # read currents
    m1cur, m2cur = readcurrents();

def crunchy2(pt_and_sigma, sec, hand=None):
    pt, sigma = pt_and_sigma
    py, px = pt

    powers = []
    powers_norm = []

    y_axis = sec.get_y_axis()
    x_axis = sec.get_x_axis()
    px_y = np.absolute(y_axis[1] - y_axis[0])
    px_x = np.absolute(x_axis[1] - x_axis[0])

    if sigma == None:
        sigma = [px_y, px_x]
    if sigma[0] < px_y:
        sigma = [px_y, sigma[1]]
    if sigma[1] < px_x:
        sigma = [sigma[0], px_x]

    for yi in range(len(y_axis)):
        y = y_axis[yi]
        for xi in range(len(x_axis)):
            x = x_axis[xi]
            this_weight = weight_function2(y, x, py, px, sigma)
            if this_weight is None:
                powers.append(None)
                powers_norm.append(None)
            else:
                variance = 1 / this_weight
                powers.append(sec.get([yi, xi]) / variance)
                powers_norm.append(1 / variance)
    p = np.nansum(list(filter(None, powers)))
    pn = np.nansum(list(filter(None, powers_norm)))
    return pt, p / pn

def plotCoeff(X, y, obj, featureNames, whichReg):
    """ Plot Regression's Coeff
    """
    clf = classifiers[whichReg]
    clf,_,_ = fitAlgo(clf, X,y, opt= True, param_dict = param_dist_dict[whichReg])
    if whichReg == "LogisticRegression":
    	coeff = np.absolute(clf.coef_[0])
    else:
    	coeff = np.absolute(clf.coef_)
    print coeff
    indices = np.argsort(coeff)[::-1]
    print indices
    print featureNames
    featureList = []
    # num_features = len(featureNames)
    print("Feature ranking:")
    for f in range(num_features):
        featureList.append(featureNames[indices[f]])
        print("%d. feature %s (%.2f)" % (f, featureNames[indices[f]], coeff[indices[f]]))
    fig = pl.figure(figsize=(8,6),dpi=150)
    pl.title("Feature importances",fontsize=30)
    # pl.bar(range(num_features), coeff[indices],
    #         yerr = std_importance[indices], color=paired[0], align="center",
    #         edgecolor=paired[0],ecolor=paired[1])
    pl.bar(range(num_features), coeff[indices], color=paired[0], align="center",
            edgecolor=paired[0],ecolor=paired[1])
    pl.xticks(range(num_features), featureList, size=15,rotation=90)
    pl.ylabel("Importance",size=30)
    pl.yticks(size=20)
    pl.xlim([-1, num_features])
    # fix_axes()
    pl.tight_layout()
    save_path = 'plots/'+obj+'/'+whichReg+'_feature_importances.pdf'
    fig.savefig(save_path)

def crunchy3(offset, eta, sec, sigma=None):
    powers = []
    powers_norm = []

    y_axis = sec.get_y_axis()
    x_axis = sec.get_x_axis()
    px_y = np.absolute(y_axis[1] - y_axis[0])
    px_x = np.absolute(x_axis[1] - x_axis[0])

    if sigma is None:
        sigma = [px_y, px_x]
    if sigma[0] < px_y:
        sigma = [px_y, sigma[1]]
    if sigma[1] < px_x:
        sigma = [sigma[0], px_x]

    for yi in range(len(y_axis)):
        y = y_axis[yi]
        for xi in range(len(x_axis)):
            x = x_axis[xi]
            y_eff = y + eta * offset ** 2
            x_eff = x - offset
            this_weight = weight_function3(eta, y, x, y_eff, x_eff, sigma)
            if this_weight is None:
                powers.append(None)
                powers_norm.append(None)
            else:
                variance = 1 / this_weight
                powers.append(sec.get([yi, xi]) / variance)
                powers_norm.append(1 / variance)
    p = np.nansum(list(filter(None, powers)))
    pn = np.nansum(list(filter(None, powers_norm)))
    return offset, p / pn