source: trunk/GSASIIpwd.py @ 1878

#/usr/bin/env python
# -*- coding: utf-8 -*-
'''
*GSASII powder calculation module*
==================================

'''
########### SVN repository information ###################
# $Date: 2015-06-04 18:49:58 +0000 (Thu, 04 Jun 2015) $
# $Author: vondreele $
# $Revision: 1878 $
# $URL: trunk/GSASIIpwd.py $
# $Id: GSASIIpwd.py 1878 2015-06-04 18:49:58Z vondreele $
########### SVN repository information ###################
import sys
import math
import time

import numpy as np
import scipy as sp
import numpy.linalg as nl
from numpy.fft import ifft, fft, fftshift
import scipy.interpolate as si
import scipy.stats as st
import scipy.optimize as so

import GSASIIpath
GSASIIpath.SetVersionNumber("$Revision: 1878 $")
import GSASIIlattice as G2lat
import GSASIIspc as G2spc
import GSASIIElem as G2elem
import GSASIIgrid as G2gd
import GSASIIIO as G2IO
import GSASIImath as G2mth
import pypowder as pyd

# trig functions in degrees
sind = lambda x: math.sin(x*math.pi/180.)
asind = lambda x: 180.*math.asin(x)/math.pi
tand = lambda x: math.tan(x*math.pi/180.)
atand = lambda x: 180.*math.atan(x)/math.pi
atan2d = lambda y,x: 180.*math.atan2(y,x)/math.pi
cosd = lambda x: math.cos(x*math.pi/180.)
acosd = lambda x: 180.*math.acos(x)/math.pi
rdsq2d = lambda x,p: round(1.0/math.sqrt(x),p)
#numpy versions
npsind = lambda x: np.sin(x*np.pi/180.)
npasind = lambda x: 180.*np.arcsin(x)/math.pi
npcosd = lambda x: np.cos(x*math.pi/180.)
npacosd = lambda x: 180.*np.arccos(x)/math.pi
nptand = lambda x: np.tan(x*math.pi/180.)
npatand = lambda x: 180.*np.arctan(x)/np.pi
npatan2d = lambda y,x: 180.*np.arctan2(y,x)/np.pi
npT2stl = lambda tth, wave: 2.0*npsind(tth/2.0)/wave
npT2q = lambda tth,wave: 2.0*np.pi*npT2stl(tth,wave)
    
#GSASII pdf calculation routines
        
def Transmission(Geometry,Abs,Diam):
    '''
    Calculate sample transmission

    :param str Geometry: one of 'Cylinder','Bragg-Brentano','Tilting flat plate in transmission','Fixed flat plate'
    :param float Abs: absorption coeff in cm-1
    :param float Diam: sample thickness/diameter in mm
    '''
    if 'Cylinder' in Geometry:      #Lobanov & Alte da Veiga for 2-theta = 0; beam fully illuminates sample
        MuR = Abs*Diam/20.0
        if MuR <= 3.0:
            T0 = 16/(3.*math.pi)
            T1 = -0.045780
            T2 = -0.02489
            T3 = 0.003045
            T = -T0*MuR-T1*MuR**2-T2*MuR**3-T3*MuR**4
            if T < -20.:
                return 2.06e-9
            else:
                return math.exp(T)
        else:
            T1 = 1.433902
            T2 = 0.013869+0.337894
            T3 = 1.933433+1.163198
            T4 = 0.044365-0.04259
            T = (T1-T4)/(1.0+T2*(MuR-3.0))**T3+T4
            return T/100.
    elif 'plate' in Geometry:
        MuR = Abs*Diam/10.
        return math.exp(-MuR)
    elif 'Bragg' in Geometry:
        return 0.0
        
def SurfaceRough(SRA,SRB,Tth):
    ''' Suortti (J. Appl. Cryst, 5,325-331, 1972) surface roughness correction
    :param float SRA: Suortti surface roughness parameter
    :param float SRB: Suortti surface roughness parameter
    :param float Tth: 2-theta(deg) - can be numpy array
    
    '''
    sth = npsind(Tth/2.)
    T1 = np.exp(-SRB/sth)
    T2 = SRA+(1.-SRA)*np.exp(-SRB)
    return (SRA+(1.-SRA)*T1)/T2
    
def SurfaceRoughDerv(SRA,SRB,Tth):
    ''' Suortti surface roughness correction derivatives
    :param float SRA: Suortti surface roughness parameter (dimensionless)
    :param float SRB: Suortti surface roughness parameter (dimensionless)
    :param float Tth: 2-theta(deg) - can be numpy array
    :return list: [dydSRA,dydSRB] derivatives to be used for intensity derivative
    '''
    sth = npsind(Tth/2.)
    T1 = np.exp(-SRB/sth)
    T2 = SRA+(1.-SRA)*np.exp(-SRB)
    Trans = (SRA+(1.-SRA)*T1)/T2
    dydSRA = ((1.-T1)*T2-(1.-np.exp(-SRB))*Trans)/T2**2
    dydSRB = ((SRA-1.)*T1*T2/sth-Trans*(SRA-T2))/T2**2
    return [dydSRA,dydSRB]

def Absorb(Geometry,MuR,Tth,Phi=0,Psi=0):
    '''Calculate sample absorption
    :param str Geometry: one of 'Cylinder','Bragg-Brentano','Tilting Flat Plate in transmission','Fixed flat plate'
    :param float MuR: absorption coeff * sample thickness/2 or radius
    :param Tth: 2-theta scattering angle - can be numpy array
    :param float Phi: flat plate tilt angle - future
    :param float Psi: flat plate tilt axis - future
    '''
    
    def muRunder3(Sth2):
        T0 = 16.0/(3.*np.pi)
        T1 = (25.99978-0.01911*Sth2**0.25)*np.exp(-0.024551*Sth2)+ \
            0.109561*np.sqrt(Sth2)-26.04556
        T2 = -0.02489-0.39499*Sth2+1.219077*Sth2**1.5- \
            1.31268*Sth2**2+0.871081*Sth2**2.5-0.2327*Sth2**3
        T3 = 0.003045+0.018167*Sth2-0.03305*Sth2**2
        Trns = -T0*MuR-T1*MuR**2-T2*MuR**3-T3*MuR**4
        return np.exp(Trns)
    
    def muRover3(Sth2):
        T1 = 1.433902+11.07504*Sth2-8.77629*Sth2*Sth2+ \
            10.02088*Sth2**3-3.36778*Sth2**4
        T2 = (0.013869-0.01249*Sth2)*np.exp(3.27094*Sth2)+ \
            (0.337894+13.77317*Sth2)/(1.0+11.53544*Sth2)**1.555039
        T3 = 1.933433/(1.0+23.12967*Sth2)**1.686715- \
            0.13576*np.sqrt(Sth2)+1.163198
        T4 = 0.044365-0.04259/(1.0+0.41051*Sth2)**148.4202
        Trns = (T1-T4)/(1.0+T2*(MuR-3.0))**T3+T4
        return Trns/100.
        
    Sth2 = npsind(Tth/2.0)**2
    Cth2 = 1.-Sth2
    if 'Cylinder' in Geometry:      #Lobanov & Alte da Veiga for 2-theta = 0; beam fully illuminates sample
        if MuR <= 3.0:
            return muRunder3(Sth2)
        else:
            return muRover3(Sth2)
    elif 'Bragg' in Geometry:
        return 1.0
    elif 'Fixed' in Geometry: #assumes sample plane is perpendicular to incident beam
        # and only defined for 2theta < 90
        MuT = 2.*MuR
        T1 = np.exp(-MuT)
        T2 = np.exp(-MuT/npcosd(Tth))
        Tb = MuT-MuT/npcosd(Tth)
        return (T2-T1)/Tb
    elif 'Tilting' in Geometry: #assumes symmetric tilt so sample plane is parallel to diffraction vector
        MuT = 2.*MuR
        cth = npcosd(Tth/2.0)
        return np.exp(-MuT/cth)/cth
        
def AbsorbDerv(Geometry,MuR,Tth,Phi=0,Psi=0):
    'needs a doc string'
    dA = 0.001
    AbsP = Absorb(Geometry,MuR+dA,Tth,Phi,Psi)
    if MuR:
        AbsM = Absorb(Geometry,MuR-dA,Tth,Phi,Psi)
        return (AbsP-AbsM)/(2.0*dA)
    else:
        return (AbsP-1.)/dA
        
def Polarization(Pola,Tth,Azm=0.0):
    """   Calculate angle dependent x-ray polarization correction (not scaled correctly!)

    :param Pola: polarization coefficient e.g 1.0 fully polarized, 0.5 unpolarized
    :param Azm: azimuthal angle e.g. 0.0 in plane of polarization
    :param Tth: 2-theta scattering angle - can be numpy array
      which (if either) of these is "right"?
    :return: (pola, dpdPola)
      * pola = ((1-Pola)*npcosd(Azm)**2+Pola*npsind(Azm)**2)*npcosd(Tth)**2+ \
        (1-Pola)*npsind(Azm)**2+Pola*npcosd(Azm)**2
      * dpdPola: derivative needed for least squares

    """
    pola = ((1.0-Pola)*npcosd(Azm)**2+Pola*npsind(Azm)**2)*npcosd(Tth)**2+   \
        (1.0-Pola)*npsind(Azm)**2+Pola*npcosd(Azm)**2
    dpdPola = -npsind(Tth)**2*(npsind(Azm)**2-npcosd(Azm)**2)
    return pola,dpdPola
    
def Oblique(ObCoeff,Tth):
    'currently assumes detector is normal to beam'
    if ObCoeff:
        return (1.-ObCoeff)/(1.0-np.exp(np.log(ObCoeff)/npcosd(Tth)))
    else:
        return 1.0
                
def Ruland(RulCoff,wave,Q,Compton):
    'needs a doc string'
    C = 2.9978e8
    D = 1.5e-3
    hmc = 0.024262734687
    sinth2 = (Q*wave/(4.0*np.pi))**2
    dlam = (wave**2)*Compton*Q/C
    dlam_c = 2.0*hmc*sinth2-D*wave**2
    return 1.0/((1.0+dlam/RulCoff)*(1.0+(np.pi*dlam_c/(dlam+RulCoff))**2))
    
def LorchWeight(Q):
    'needs a doc string'
    return np.sin(np.pi*(Q[-1]-Q)/(2.0*Q[-1]))
            
def GetAsfMean(ElList,Sthl2):
    '''Calculate various scattering factor terms for PDF calcs

    :param dict ElList: element dictionary contains scattering factor coefficients, etc.
    :param np.array Sthl2: numpy array of sin theta/lambda squared values
    :returns: mean(f^2), mean(f)^2, mean(compton)
    '''
    sumNoAtoms = 0.0
    FF = np.zeros_like(Sthl2)
    FF2 = np.zeros_like(Sthl2)
    CF = np.zeros_like(Sthl2)
    for El in ElList:
        sumNoAtoms += ElList[El]['FormulaNo']
    for El in ElList:
        el = ElList[El]
        ff2 = (G2elem.ScatFac(el,Sthl2)+el['fp'])**2+el['fpp']**2
        cf = G2elem.ComptonFac(el,Sthl2)
        FF += np.sqrt(ff2)*el['FormulaNo']/sumNoAtoms
        FF2 += ff2*el['FormulaNo']/sumNoAtoms
        CF += cf*el['FormulaNo']/sumNoAtoms
    return FF2,FF**2,CF
    
def GetNumDensity(ElList,Vol):
    'needs a doc string'
    sumNoAtoms = 0.0
    for El in ElList:
        sumNoAtoms += ElList[El]['FormulaNo']
    return sumNoAtoms/Vol
           
def CalcPDF(data,inst,xydata):
    'needs a doc string'
    auxPlot = []
    import copy
    import scipy.fftpack as ft
    #subtract backgrounds - if any
    xydata['IofQ'] = copy.deepcopy(xydata['Sample'])
    if data['Sample Bkg.']['Name']:
        xydata['IofQ'][1][1] += (xydata['Sample Bkg.'][1][1]+
            data['Sample Bkg.']['Add'])*data['Sample Bkg.']['Mult']
    if data['Container']['Name']:
        xycontainer = (xydata['Container'][1][1]+data['Container']['Add'])*data['Container']['Mult']
        if data['Container Bkg.']['Name']:
            xycontainer += (xydata['Container Bkg.'][1][1]+
                data['Container Bkg.']['Add'])*data['Container Bkg.']['Mult']
        xydata['IofQ'][1][1] += xycontainer
    #get element data & absorption coeff.
    ElList = data['ElList']
    Abs = G2lat.CellAbsorption(ElList,data['Form Vol'])
    #Apply angle dependent corrections
    Tth = xydata['Sample'][1][0]
    dt = (Tth[1]-Tth[0])
    MuR = Abs*data['Diam']/20.0
    xydata['IofQ'][1][1] /= Absorb(data['Geometry'],MuR,Tth)
    if 'X' in inst['Type'][0]:
        xydata['IofQ'][1][1] /= Polarization(inst['Polariz.'][1],Tth,Azm=inst['Azimuth'][1])[0]
    if data['DetType'] == 'Image plate':
        xydata['IofQ'][1][1] *= Oblique(data['ObliqCoeff'],Tth)
    XY = xydata['IofQ'][1]    
    #convert to Q
    hc = 12.397639
    wave = G2mth.getWave(inst)
    keV = hc/wave
    minQ = npT2q(Tth[0],wave)
    maxQ = npT2q(Tth[-1],wave)    
    Qpoints = np.linspace(0.,maxQ,len(XY[0]),endpoint=True)
    dq = Qpoints[1]-Qpoints[0]
    XY[0] = npT2q(XY[0],wave)    
#    Qdata = np.nan_to_num(si.griddata(XY[0],XY[1],Qpoints,method='linear')) #only OK for scipy 0.9!
    T = si.interp1d(XY[0],XY[1],bounds_error=False,fill_value=0.0)      #OK for scipy 0.8
    Qdata = T(Qpoints)
    
    qLimits = data['QScaleLim']
    minQ = np.searchsorted(Qpoints,qLimits[0])
    maxQ = np.searchsorted(Qpoints,qLimits[1])
    newdata = []
    xydata['IofQ'][1][0] = Qpoints
    xydata['IofQ'][1][1] = Qdata
    for item in xydata['IofQ'][1]:
        newdata.append(item[:maxQ])
    xydata['IofQ'][1] = newdata
    

    xydata['SofQ'] = copy.deepcopy(xydata['IofQ'])
    FFSq,SqFF,CF = GetAsfMean(ElList,(xydata['SofQ'][1][0]/(4.0*np.pi))**2)  #these are <f^2>,<f>^2,Cf
    Q = xydata['SofQ'][1][0]
    ruland = Ruland(data['Ruland'],wave,Q,CF)
#    auxPlot.append([Q,ruland,'Ruland'])      
    CF *= ruland
#    auxPlot.append([Q,CF,'CF-Corr'])
    scale = np.sum((FFSq+CF)[minQ:maxQ])/np.sum(xydata['SofQ'][1][1][minQ:maxQ])
    xydata['SofQ'][1][1] *= scale
    xydata['SofQ'][1][1] -= CF
    xydata['SofQ'][1][1] = xydata['SofQ'][1][1]/SqFF
    scale = len(xydata['SofQ'][1][1][minQ:maxQ])/np.sum(xydata['SofQ'][1][1][minQ:maxQ])
    xydata['SofQ'][1][1] *= scale
    
    xydata['FofQ'] = copy.deepcopy(xydata['SofQ'])
    xydata['FofQ'][1][1] = xydata['FofQ'][1][0]*(xydata['SofQ'][1][1]-1.0)
    if data['Lorch']:
        xydata['FofQ'][1][1] *= LorchWeight(Q)
    
    xydata['GofR'] = copy.deepcopy(xydata['FofQ'])
    nR = len(xydata['GofR'][1][1])
    xydata['GofR'][1][1] = -dq*np.imag(ft.fft(xydata['FofQ'][1][1],4*nR)[:nR])
    xydata['GofR'][1][0] = 0.5*np.pi*np.linspace(0,nR,nR)/qLimits[1]
    
        
    return auxPlot
        
#GSASII peak fitting routines: Finger, Cox & Jephcoat model        

def factorize(num):
    ''' Provide prime number factors for integer num
    :returns: dictionary of prime factors (keys) & power for each (data)
    '''
    factors = {}
    orig = num

    # we take advantage of the fact that (i +1)**2 = i**2 + 2*i +1
    i, sqi = 2, 4
    while sqi <= num:
        while not num%i:
            num /= i
            factors[i] = factors.get(i, 0) + 1

        sqi += 2*i + 1
        i += 1

    if num != 1 and num != orig:
        factors[num] = factors.get(num, 0) + 1

    if factors:
        return factors
    else:
        return {num:1}          #a prime number!
            
def makeFFTsizeList(nmin=1,nmax=1023,thresh=15):
    ''' Provide list of optimal data sizes for FFT calculations

    :param int nmin: minimum data size >= 1
    :param int nmax: maximum data size > nmin
    :param int thresh: maximum prime factor allowed
    :Returns: list of data sizes where the maximum prime factor is < thresh
    ''' 
    plist = []
    nmin = max(1,nmin)
    nmax = max(nmin+1,nmax)
    for p in range(nmin,nmax):
        if max(factorize(p).keys()) < thresh:
            plist.append(p)
    return plist

np.seterr(divide='ignore')

# Normal distribution

# loc = mu, scale = std
_norm_pdf_C = 1./math.sqrt(2*math.pi)
class norm_gen(st.rv_continuous):
    'needs a doc string'
      
    def pdf(self,x,*args,**kwds):
        loc,scale=kwds['loc'],kwds['scale']
        x = (x-loc)/scale
        return np.exp(-x**2/2.0) * _norm_pdf_C / scale
        
norm = norm_gen(name='norm',longname='A normal',extradoc="""

Normal distribution

The location (loc) keyword specifies the mean.
The scale (scale) keyword specifies the standard deviation.

normal.pdf(x) = exp(-x**2/2)/sqrt(2*pi)
""")

## Cauchy

# median = loc

class cauchy_gen(st.rv_continuous):
    'needs a doc string'

    def pdf(self,x,*args,**kwds):
        loc,scale=kwds['loc'],kwds['scale']
        x = (x-loc)/scale
        return 1.0/np.pi/(1.0+x*x) / scale
        
cauchy = cauchy_gen(name='cauchy',longname='Cauchy',extradoc="""

Cauchy distribution

cauchy.pdf(x) = 1/(pi*(1+x**2))

This is the t distribution with one degree of freedom.
""")
    
    
#GSASII peak fitting routine: Finger, Cox & Jephcoat model        


class fcjde_gen(st.rv_continuous):
    """
    Finger-Cox-Jephcoat D(2phi,2th) function for S/L = H/L
    Ref: J. Appl. Cryst. (1994) 27, 892-900.

    :param x: array -1 to 1
    :param t: 2-theta position of peak
    :param s: sum(S/L,H/L); S: sample height, H: detector opening, 
      L: sample to detector opening distance
    :param dx: 2-theta step size in deg

    :returns: for fcj.pdf

     * T = x*dx+t
     * s = S/L+H/L
     * if x < 0::

        fcj.pdf = [1/sqrt({cos(T)**2/cos(t)**2}-1) - 1/s]/|cos(T)| 

     * if x >= 0: fcj.pdf = 0    
    """
    def _pdf(self,x,t,s,dx):
        T = dx*x+t
        ax2 = abs(npcosd(T))
        ax = ax2**2
        bx = npcosd(t)**2
        bx = np.where(ax>bx,bx,ax)
        fx = np.where(ax>bx,(np.sqrt(bx/(ax-bx))-1./s)/ax2,0.0)
        fx = np.where(fx > 0.,fx,0.0)
        return fx
             
    def pdf(self,x,*args,**kwds):
        loc=kwds['loc']
        return self._pdf(x-loc,*args)
        
fcjde = fcjde_gen(name='fcjde',shapes='t,s,dx')
                
def getWidthsCW(pos,sig,gam,shl):
    '''Compute the peak widths used for computing the range of a peak
    for constant wavelength data.
    On low-angle side, 10 FWHM are used, on high-angle side 15 are used
    (for peaks above 90 deg, these are reversed.)
    '''
    widths = [np.sqrt(sig)/100.,gam/200.]
    fwhm = 2.355*widths[0]+2.*widths[1]
    fmin = 10.*(fwhm+shl*abs(npcosd(pos)))
    fmax = 15.0*fwhm
    if pos > 90:
        fmin,fmax = [fmax,fmin]          
    return widths,fmin,fmax
    
def getWidthsTOF(pos,alp,bet,sig,gam):
    'needs a doc string'
    lnf = 3.3      # =log(0.001/2)
    widths = [np.sqrt(sig),gam]
    fwhm = 2.355*widths[0]+2.*widths[1]
    fmin = 10.*fwhm*(1.+1./alp)    
    fmax = 10.*fwhm*(1.+1./bet)
    return widths,fmin,fmax
    
def getFWHM(pos,Inst):
    'needs a doc string'
    sig = lambda Th,U,V,W: 1.17741*math.sqrt(max(0.001,U*tand(Th)**2+V*tand(Th)+W))*math.pi/180.
    sigTOF = lambda dsp,S0,S1,S2,Sq:  S0+S1*dsp**2+S2*dsp**4+Sq/dsp**2
    gam = lambda Th,X,Y: (X/cosd(Th)+Y*tand(Th))*math.pi/180.
    gamTOF = lambda dsp,X,Y: X*dsp+Y*dsp**2
    if 'C' in Inst['Type'][0]:
        s = sig(pos/2.,Inst['U'][1],Inst['V'][1],Inst['W'][1])*100.
        g = gam(pos/2.,Inst['X'][1],Inst['Y'][1])*100.
    else:
        dsp = pos/Inst['difC'][0]
        s = sigTOF(dsp,Inst['sig-0'][1],Inst['sig-1'][1],Inst['sig-2'][1],Inst['sig-q'][1])
        g = gamTOF(dsp,Inst['X'][1],Inst['Y'][1])
    return getgamFW(g,s)
    
def getgamFW(g,s):
    'needs a doc string'
    gamFW = lambda s,g: np.exp(np.log(s**5+2.69269*s**4*g+2.42843*s**3*g**2+4.47163*s**2*g**3+0.07842*s*g**4+g**5)/5.)
    return gamFW(g,s)
                
def getFCJVoigt(pos,intens,sig,gam,shl,xdata):    
    'needs a doc string'
    DX = xdata[1]-xdata[0]
    widths,fmin,fmax = getWidthsCW(pos,sig,gam,shl)
    x = np.linspace(pos-fmin,pos+fmin,256)
    dx = x[1]-x[0]
    Norm = norm.pdf(x,loc=pos,scale=widths[0])
    Cauchy = cauchy.pdf(x,loc=pos,scale=widths[1])
    arg = [pos,shl/57.2958,dx,]
    FCJ = fcjde.pdf(x,*arg,loc=pos)
    if len(np.nonzero(FCJ)[0])>5:
        z = np.column_stack([Norm,Cauchy,FCJ]).T
        Z = fft(z)
        Df = ifft(Z.prod(axis=0)).real
    else:
        z = np.column_stack([Norm,Cauchy]).T
        Z = fft(z)
        Df = fftshift(ifft(Z.prod(axis=0))).real
    Df /= np.sum(Df)
    Df = si.interp1d(x,Df,bounds_error=False,fill_value=0.0)
    return intens*Df(xdata)*DX/dx

def getBackground(pfx,parmDict,bakType,dataType,xdata):
    'needs a doc string'
    if 'T' in dataType:
        q = 2.*np.pi*parmDict[pfx+'difC']/xdata
    elif 'C' in dataType:
        wave = parmDict.get(pfx+'Lam',parmDict.get(pfx+'Lam1',1.0))
        q = 2.*np.pi*npsind(xdata/2.)/wave
    yb = np.zeros_like(xdata)
    nBak = 0
    cw = np.diff(xdata)
    cw = np.append(cw,cw[-1])
    sumBk = [0.,0.,0]
    while True:
        key = pfx+'Back;'+str(nBak)
        if key in parmDict:
            nBak += 1
        else:
            break
#empirical functions
    if bakType in ['chebyschev','cosine']:
        dt = xdata[-1]-xdata[0]    
        for iBak in range(nBak):
            key = pfx+'Back;'+str(iBak)
            if bakType == 'chebyschev':
                ybi = parmDict[key]*(2.*(xdata-xdata[0])/dt-1.)**iBak
            elif bakType == 'cosine':
                ybi = parmDict[key]*npcosd(xdata*iBak)
            yb += ybi
        sumBk[0] = np.sum(yb)
    elif bakType in ['Q^2 power series','Q^-2 powder series']:
        QT = 1.
        yb += np.ones_like(yb)*parmDict[pfx+'Back;0']
        for iBak in range(nBak-1):
            key = pfx+'Back;'+str(iBak+1)
            if '-2' in bakType:
                QT *= (iBak+1)*q**-2
            else:
                QT *= q**2/(iBak+1)
            yb += QT*parmDict[key]
        sumBk[0] = np.sum(yb)
    elif bakType in ['lin interpolate','inv interpolate','log interpolate',]:
        if nBak == 1:
            yb = np.ones_like(xdata)*parmDict[pfx+'Back;0']
        elif nBak == 2:
            dX = xdata[-1]-xdata[0]
            T2 = (xdata-xdata[0])/dX
            T1 = 1.0-T2
            yb = parmDict[pfx+'Back;0']*T1+parmDict[pfx+'Back;1']*T2
        else:
            if bakType == 'lin interpolate':
                bakPos = np.linspace(xdata[0],xdata[-1],nBak,True)
            elif bakType == 'inv interpolate':
                bakPos = 1./np.linspace(1./xdata[-1],1./xdata[0],nBak,True)
            elif bakType == 'log interpolate':
                bakPos = np.exp(np.linspace(np.log(xdata[0]),np.log(xdata[-1]),nBak,True))
            bakPos[0] = xdata[0]
            bakPos[-1] = xdata[-1]
            bakVals = np.zeros(nBak)
            for i in range(nBak):
                bakVals[i] = parmDict[pfx+'Back;'+str(i)]
            bakInt = si.interp1d(bakPos,bakVals,'linear')
            yb = bakInt(xdata)
        sumBk[0] = np.sum(yb)
#Debye function        
    if pfx+'difC' in parmDict:
        ff = 1.
    else:        
        try:
            wave = parmDict[pfx+'Lam']
        except KeyError:
            wave = parmDict[pfx+'Lam1']
        SQ = (q/(4.*np.pi))**2
        FF = G2elem.GetFormFactorCoeff('Si')[0]
        ff = np.array(G2elem.ScatFac(FF,SQ)[0])**2
    iD = 0        
    while True:
        try:
            dbA = parmDict[pfx+'DebyeA;'+str(iD)]
            dbR = parmDict[pfx+'DebyeR;'+str(iD)]
            dbU = parmDict[pfx+'DebyeU;'+str(iD)]
            ybi = ff*dbA*np.sin(q*dbR)*np.exp(-dbU*q**2)/(q*dbR)
            yb += ybi
            sumBk[1] += np.sum(ybi)
            iD += 1       
        except KeyError:
            break
#peaks
    iD = 0
    while True:
        try:
            pkP = parmDict[pfx+'BkPkpos;'+str(iD)]
            pkI = parmDict[pfx+'BkPkint;'+str(iD)]
            pkS = parmDict[pfx+'BkPksig;'+str(iD)]
            pkG = parmDict[pfx+'BkPkgam;'+str(iD)]
            if 'C' in dataType:
                Wd,fmin,fmax = getWidthsCW(pkP,pkS,pkG,.002)
            else: #'T'OF
                Wd,fmin,fmax = getWidthsTOF(pkP,1.,1.,pkS,pkG)
            iBeg = np.searchsorted(xdata,pkP-fmin)
            iFin = np.searchsorted(xdata,pkP+fmax)
            lenX = len(xdata)
            if not iBeg:
                iFin = np.searchsorted(xdata,pkP+fmax)
            elif iBeg == lenX:
                iFin = iBeg
            else:
                iFin = np.searchsorted(xdata,pkP+fmax)
            if 'C' in dataType:
                ybi = pkI*getFCJVoigt3(pkP,pkS,pkG,0.002,xdata[iBeg:iFin])
                yb[iBeg:iFin] += ybi
            else:   #'T'OF
                ybi = pkI*getEpsVoigt(pkP,1.,1.,pkS,pkG,xdata[iBeg:iFin])
                yb[iBeg:iFin] += ybi
            sumBk[2] += np.sum(ybi)
            iD += 1       
        except KeyError:
            break
        except ValueError:
            print '**** WARNING - backround peak '+str(iD)+' sigma is negative; fix & try again ****'
            break        
    return yb,sumBk
    
def getBackgroundDerv(hfx,parmDict,bakType,dataType,xdata):
    'needs a doc string'
    if 'T' in dataType:
        q = 2.*np.pi*parmDict[hfx+'difC']/xdata
    elif 'C' in dataType:
        wave = parmDict.get(hfx+'Lam',parmDict.get(hfx+'Lam1',1.0))
        q = 2.*np.pi*npsind(xdata/2.)/wave
    nBak = 0
    while True:
        key = hfx+'Back;'+str(nBak)
        if key in parmDict:
            nBak += 1
        else:
            break
    dydb = np.zeros(shape=(nBak,len(xdata)))
    dyddb = np.zeros(shape=(3*parmDict[hfx+'nDebye'],len(xdata)))
    dydpk = np.zeros(shape=(4*parmDict[hfx+'nPeaks'],len(xdata)))
    cw = np.diff(xdata)
    cw = np.append(cw,cw[-1])

    if bakType in ['chebyschev','cosine']:
        dt = xdata[-1]-xdata[0]    
        for iBak in range(nBak):    
            if bakType == 'chebyschev':
                dydb[iBak] = (2.*(xdata-xdata[0])/dt-1.)**iBak
            elif bakType == 'cosine':
                dydb[iBak] = npcosd(xdata*iBak)
    elif bakType in ['Q^2 power series','Q^-2 powder series']:
        QT = 1.
        dydb[0] = np.ones_like(xdata)
        for iBak in range(nBak-1):
            if '-2' in bakType:
                QT *= (iBak+1)*q**-2
            else:
                QT *= q**2/(iBak+1)
            dydb[iBak+1] = QT
    elif bakType in ['lin interpolate','inv interpolate','log interpolate',]:
        if nBak == 1:
            dydb[0] = np.ones_like(xdata)
        elif nBak == 2:
            dX = xdata[-1]-xdata[0]
            T2 = (xdata-xdata[0])/dX
            T1 = 1.0-T2
            dydb = [T1,T2]
        else:
            if bakType == 'lin interpolate':
                bakPos = np.linspace(xdata[0],xdata[-1],nBak,True)
            elif bakType == 'inv interpolate':
                bakPos = 1./np.linspace(1./xdata[-1],1./xdata[0],nBak,True)
            elif bakType == 'log interpolate':
                bakPos = np.exp(np.linspace(np.log(xdata[0]),np.log(xdata[-1]),nBak,True))
            bakPos[0] = xdata[0]
            bakPos[-1] = xdata[-1]
            for i,pos in enumerate(bakPos):
                if i == 0:
                    dydb[0] = np.where(xdata<bakPos[1],(bakPos[1]-xdata)/(bakPos[1]-bakPos[0]),0.)
                elif i == len(bakPos)-1:
                    dydb[i] = np.where(xdata>bakPos[-2],(bakPos[-1]-xdata)/(bakPos[-1]-bakPos[-2]),0.)
                else:
                    dydb[i] = np.where(xdata>bakPos[i],
                        np.where(xdata<bakPos[i+1],(bakPos[i+1]-xdata)/(bakPos[i+1]-bakPos[i]),0.),
                        np.where(xdata>bakPos[i-1],(xdata-bakPos[i-1])/(bakPos[i]-bakPos[i-1]),0.))
    if hfx+'difC' in parmDict:
        ff = 1.
    else:
        try:
            wave = parmDict[hfx+'Lam']
        except KeyError:
            wave = parmDict[hfx+'Lam1']
        q = 4.0*np.pi*npsind(xdata/2.0)/wave
        SQ = (q/(4*np.pi))**2
        FF = G2elem.GetFormFactorCoeff('Si')[0]
        ff = np.array(G2elem.ScatFac(FF,SQ)[0])
    iD = 0        
    while True:
        try:
            if hfx+'difC' in parmDict:
                q = 2*np.pi*parmDict[hfx+'difC']/xdata
            dbA = parmDict[hfx+'DebyeA;'+str(iD)]
            dbR = parmDict[hfx+'DebyeR;'+str(iD)]
            dbU = parmDict[hfx+'DebyeU;'+str(iD)]
            sqr = np.sin(q*dbR)/(q*dbR)
            cqr = np.cos(q*dbR)
            temp = np.exp(-dbU*q**2)
            dyddb[3*iD] = ff*sqr*temp/(np.pi*cw)
            dyddb[3*iD+1] = ff*dbA*temp*(cqr-sqr)/(np.pi*dbR*cw)
            dyddb[3*iD+2] = -ff*dbA*sqr*temp*q**2/(np.pi*cw)
            iD += 1       #ff*dbA*np.sin(q*dbR)*np.exp(-dbU*q**2)/(q*dbR)
        except KeyError:
            break
    iD = 0
    while True:
        try:
            pkP = parmDict[hfx+'BkPkpos;'+str(iD)]
            pkI = parmDict[hfx+'BkPkint;'+str(iD)]
            pkS = parmDict[hfx+'BkPksig;'+str(iD)]
            pkG = parmDict[hfx+'BkPkgam;'+str(iD)]
            if 'C' in dataType:
                Wd,fmin,fmax = getWidthsCW(pkP,pkS,pkG,.002)
            else: #'T'OF
                Wd,fmin,fmax = getWidthsTOF(pkP,1.,1.,pkS,pkG)
            iBeg = np.searchsorted(xdata,pkP-fmin)
            iFin = np.searchsorted(xdata,pkP+fmax)
            lenX = len(xdata)
            if not iBeg:
                iFin = np.searchsorted(xdata,pkP+fmax)
            elif iBeg == lenX:
                iFin = iBeg
            else:
                iFin = np.searchsorted(xdata,pkP+fmax)
            if 'C' in dataType:
                Df,dFdp,dFds,dFdg,x = getdFCJVoigt3(pkP,pkS,pkG,.002,xdata[iBeg:iFin])
                dydpk[4*iD][iBeg:iFin] += 100.*cw[iBeg:iFin]*pkI*dFdp
                dydpk[4*iD+1][iBeg:iFin] += 100.*cw[iBeg:iFin]*Df
                dydpk[4*iD+2][iBeg:iFin] += 100.*cw[iBeg:iFin]*pkI*dFds
                dydpk[4*iD+3][iBeg:iFin] += 100.*cw[iBeg:iFin]*pkI*dFdg
            else:   #'T'OF
                Df,dFdp,x,x,dFds,dFdg = getdEpsVoigt(pkP,1.,1.,pkS,pkG,xdata[iBeg:iFin])
                dydpk[4*iD][iBeg:iFin] += pkI*dFdp
                dydpk[4*iD+1][iBeg:iFin] += Df
                dydpk[4*iD+2][iBeg:iFin] += pkI*dFds
                dydpk[4*iD+3][iBeg:iFin] += pkI*dFdg
            iD += 1       
        except KeyError:
            break
        except ValueError:
            print '**** WARNING - backround peak '+str(iD)+' sigma is negative; fix & try again ****'
            break        
    return dydb,dyddb,dydpk

#use old fortran routine
def getFCJVoigt3(pos,sig,gam,shl,xdata):
    'needs a doc string'
    
    Df = pyd.pypsvfcj(len(xdata),xdata-pos,pos,sig,gam,shl)
#    Df = pyd.pypsvfcjo(len(xdata),xdata-pos,pos,sig,gam,shl)
    Df /= np.sum(Df)
    return Df

def getdFCJVoigt3(pos,sig,gam,shl,xdata):
    'needs a doc string'
    
    Df,dFdp,dFds,dFdg,dFdsh = pyd.pydpsvfcj(len(xdata),xdata-pos,pos,sig,gam,shl)
#    Df,dFdp,dFds,dFdg,dFdsh = pyd.pydpsvfcjo(len(xdata),xdata-pos,pos,sig,gam,shl)
    sumDf = np.sum(Df)
    return Df,dFdp,dFds,dFdg,dFdsh

def getPsVoigt(pos,sig,gam,xdata):
    'needs a doc string'
    
    Df = pyd.pypsvoigt(len(xdata),xdata-pos,sig,gam)
    Df /= np.sum(Df)
    return Df

def getdPsVoigt(pos,sig,gam,xdata):
    'needs a doc string'
    
    Df,dFdp,dFds,dFdg = pyd.pydpsvoigt(len(xdata),xdata-pos,sig,gam)
    sumDf = np.sum(Df)
    return Df,dFdp,dFds,dFdg

def getEpsVoigt(pos,alp,bet,sig,gam,xdata):
    'needs a doc string'
    Df = pyd.pyepsvoigt(len(xdata),xdata-pos,alp,bet,sig,gam)
    Df /= np.sum(Df)
    return Df  
    
def getdEpsVoigt(pos,alp,bet,sig,gam,xdata):
    'needs a doc string'
    Df,dFdp,dFda,dFdb,dFds,dFdg = pyd.pydepsvoigt(len(xdata),xdata-pos,alp,bet,sig,gam)
    sumDf = np.sum(Df)
    return Df,dFdp,dFda,dFdb,dFds,dFdg   

def ellipseSize(H,Sij,GB):
    'needs a doc string'
    HX = np.inner(H.T,GB)
    lenHX = np.sqrt(np.sum(HX**2))
    Esize,Rsize = nl.eigh(G2lat.U6toUij(Sij))            
    R = np.inner(HX/lenHX,Rsize)*Esize         #want column length for hkl in crystal
    lenR = np.sqrt(np.sum(R**2))
    return lenR

def ellipseSizeDerv(H,Sij,GB):
    'needs a doc string'
    lenR = ellipseSize(H,Sij,GB)
    delt = 0.001
    dRdS = np.zeros(6)
    for i in range(6):
        Sij[i] -= delt
        lenM = ellipseSize(H,Sij,GB)
        Sij[i] += 2.*delt
        lenP = ellipseSize(H,Sij,GB)
        Sij[i] -= delt
        dRdS[i] = (lenP-lenM)/(2.*delt)
    return lenR,dRdS

def getHKLpeak(dmin,SGData,A,Inst=None):
    'needs a doc string'
    HKL = G2lat.GenHLaue(dmin,SGData,A)        
    HKLs = []
    for h,k,l,d in HKL:
        ext = G2spc.GenHKLf([h,k,l],SGData)[0]
        if not ext:
            if Inst == None:
                HKLs.append([h,k,l,d,0,-1])
            else:
                HKLs.append([h,k,l,d,G2lat.Dsp2pos(Inst,d),-1])
    return HKLs

def getHKLMpeak(dmin,Inst,SGData,SSGData,Vec,maxH,A):
    'needs a doc string'
    HKLs = []
    vec = np.array(Vec)
    vstar = np.sqrt(G2lat.calc_rDsq(vec,A))     #find extra needed for -n SS reflections
    dvec = 1./(maxH*vstar+1./dmin)
    HKL = G2lat.GenHLaue(dvec,SGData,A)        
    SSdH = [vec*h for h in range(-maxH,maxH+1)]
    SSdH = dict(zip(range(-maxH,maxH+1),SSdH))
    for h,k,l,d in HKL:
        ext = G2spc.GenHKLf([h,k,l],SGData)[0]
        if not ext and d >= dmin:
            HKLs.append([h,k,l,0,d,G2lat.Dsp2pos(Inst,d),-1])
        for dH in SSdH:
            if dH:
                DH = SSdH[dH]
                H = [h+DH[0],k+DH[1],l+DH[2]]
                d = 1/np.sqrt(G2lat.calc_rDsq(H,A))
                if d >= dmin:
                    HKLM = np.array([h,k,l,dH])
                    if G2spc.checkSSextc(HKLM,SSGData):
                        HKLs.append([h,k,l,dH,d,G2lat.Dsp2pos(Inst,d),-1])    
    return G2lat.sortHKLd(HKLs,True,True,True)

def getPeakProfile(dataType,parmDict,xdata,varyList,bakType):
    'needs a doc string'
    
    yb = getBackground('',parmDict,bakType,dataType,xdata)[0]
    yc = np.zeros_like(yb)
    cw = np.diff(xdata)
    cw = np.append(cw,cw[-1])
    if 'C' in dataType:
        shl = max(parmDict['SH/L'],0.002)
        Ka2 = False
        if 'Lam1' in parmDict.keys():
            Ka2 = True
            lamRatio = 360*(parmDict['Lam2']-parmDict['Lam1'])/(np.pi*parmDict['Lam1'])
            kRatio = parmDict['I(L2)/I(L1)']
        iPeak = 0
        while True:
            try:
                pos = parmDict['pos'+str(iPeak)]
                tth = (pos-parmDict['Zero'])
                intens = parmDict['int'+str(iPeak)]
                sigName = 'sig'+str(iPeak)
                if sigName in varyList:
                    sig = parmDict[sigName]
                else:
                    sig = G2mth.getCWsig(parmDict,tth)
                sig = max(sig,0.001)          #avoid neg sigma
                gamName = 'gam'+str(iPeak)
                if gamName in varyList:
                    gam = parmDict[gamName]
                else:
                    gam = G2mth.getCWgam(parmDict,tth)
                gam = max(gam,0.001)             #avoid neg gamma
                Wd,fmin,fmax = getWidthsCW(pos,sig,gam,shl)
                iBeg = np.searchsorted(xdata,pos-fmin)
                iFin = np.searchsorted(xdata,pos+fmin)
                if not iBeg+iFin:       #peak below low limit
                    iPeak += 1
                    continue
                elif not iBeg-iFin:     #peak above high limit
                    return yb+yc
                yc[iBeg:iFin] += intens*getFCJVoigt3(pos,sig,gam,shl,xdata[iBeg:iFin])
                if Ka2:
                    pos2 = pos+lamRatio*tand(pos/2.0)       # + 360/pi * Dlam/lam * tan(th)
                    iBeg = np.searchsorted(xdata,pos2-fmin)
                    iFin = np.searchsorted(xdata,pos2+fmin)
                    if iBeg-iFin:
                        yc[iBeg:iFin] += intens*kRatio*getFCJVoigt3(pos2,sig,gam,shl,xdata[iBeg:iFin])
                iPeak += 1
            except KeyError:        #no more peaks to process
                return yb+yc
    else:
        Pdabc = parmDict['Pdabc']
        difC = parmDict['difC']
        iPeak = 0
        while True:
            try:
                pos = parmDict['pos'+str(iPeak)]                
                tof = pos-parmDict['Zero']
                dsp = tof/difC
                intens = parmDict['int'+str(iPeak)]
                alpName = 'alp'+str(iPeak)
                if alpName in varyList:
                    alp = parmDict[alpName]
                else:
                    if len(Pdabc):
                        alp = np.interp(dsp,Pdabc[0],Pdabc[1])
                    else:
                        alp = G2mth.getTOFalpha(parmDict,dsp)
                alp = max(0.0001,alp)
                betName = 'bet'+str(iPeak)
                if betName in varyList:
                    bet = parmDict[betName]
                else:
                    if len(Pdabc):
                        bet = np.interp(dsp,Pdabc[0],Pdabc[2])
                    else:
                        bet = G2mth.getTOFbeta(parmDict,dsp)
                bet = max(0.0001,bet)
                sigName = 'sig'+str(iPeak)
                if sigName in varyList:
                    sig = parmDict[sigName]
                else:
                    sig = G2mth.getTOFsig(parmDict,dsp)
                gamName = 'gam'+str(iPeak)
                if gamName in varyList:
                    gam = parmDict[gamName]
                else:
                    gam = G2mth.getTOFgamma(parmDict,dsp)
                gam = max(gam,0.001)             #avoid neg gamma
                Wd,fmin,fmax = getWidthsTOF(pos,alp,bet,sig,gam)
                iBeg = np.searchsorted(xdata,pos-fmin)
                iFin = np.searchsorted(xdata,pos+fmax)
                lenX = len(xdata)
                if not iBeg:
                    iFin = np.searchsorted(xdata,pos+fmax)
                elif iBeg == lenX:
                    iFin = iBeg
                else:
                    iFin = np.searchsorted(xdata,pos+fmax)
                if not iBeg+iFin:       #peak below low limit
                    iPeak += 1
                    continue
                elif not iBeg-iFin:     #peak above high limit
                    return yb+yc
                yc[iBeg:iFin] += intens*getEpsVoigt(pos,alp,bet,sig,gam,xdata[iBeg:iFin])
                iPeak += 1
            except KeyError:        #no more peaks to process
                return yb+yc
            
def getPeakProfileDerv(dataType,parmDict,xdata,varyList,bakType):
    'needs a doc string'
# needs to return np.array([dMdx1,dMdx2,...]) in same order as varylist = backVary,insVary,peakVary order
    dMdv = np.zeros(shape=(len(varyList),len(xdata)))
    dMdb,dMddb,dMdpk = getBackgroundDerv('',parmDict,bakType,dataType,xdata)
    if 'Back;0' in varyList:            #background derivs are in front if present
        dMdv[0:len(dMdb)] = dMdb
    names = ['DebyeA','DebyeR','DebyeU']
    for name in varyList:
        if 'Debye' in name:
            parm,id = name.split(';')
            ip = names.index(parm)
            dMdv[varyList.index(name)] = dMddb[3*int(id)+ip]
    names = ['BkPkpos','BkPkint','BkPksig','BkPkgam']
    for name in varyList:
        if 'BkPk' in name:
            parm,id = name.split(';')
            ip = names.index(parm)
            dMdv[varyList.index(name)] = dMdpk[4*int(id)+ip]
    cw = np.diff(xdata)
    cw = np.append(cw,cw[-1])
    if 'C' in dataType:
        shl = max(parmDict['SH/L'],0.002)
        Ka2 = False
        if 'Lam1' in parmDict.keys():
            Ka2 = True
            lamRatio = 360*(parmDict['Lam2']-parmDict['Lam1'])/(np.pi*parmDict['Lam1'])
            kRatio = parmDict['I(L2)/I(L1)']
        iPeak = 0
        while True:
            try:
                pos = parmDict['pos'+str(iPeak)]
                tth = (pos-parmDict['Zero'])
                intens = parmDict['int'+str(iPeak)]
                sigName = 'sig'+str(iPeak)
                if sigName in varyList:
                    sig = parmDict[sigName]
                    dsdU = dsdV = dsdW = 0
                else:
                    sig = G2mth.getCWsig(parmDict,tth)
                    dsdU,dsdV,dsdW = G2mth.getCWsigDeriv(tth)
                sig = max(sig,0.001)          #avoid neg sigma
                gamName = 'gam'+str(iPeak)
                if gamName in varyList:
                    gam = parmDict[gamName]
                    dgdX = dgdY = 0
                else:
                    gam = G2mth.getCWgam(parmDict,tth)
                    dgdX,dgdY = G2mth.getCWgamDeriv(tth)
                gam = max(gam,0.001)             #avoid neg gamma
                Wd,fmin,fmax = getWidthsCW(pos,sig,gam,shl)
                iBeg = np.searchsorted(xdata,pos-fmin)
                iFin = np.searchsorted(xdata,pos+fmin)
                if not iBeg+iFin:       #peak below low limit
                    iPeak += 1
                    continue
                elif not iBeg-iFin:     #peak above high limit
                    break
                dMdpk = np.zeros(shape=(6,len(xdata)))
                dMdipk = getdFCJVoigt3(pos,sig,gam,shl,xdata[iBeg:iFin])
                for i in range(1,5):
                    dMdpk[i][iBeg:iFin] += 100.*cw[iBeg:iFin]*intens*dMdipk[i]
                dMdpk[0][iBeg:iFin] += 100.*cw[iBeg:iFin]*dMdipk[0]
                dervDict = {'int':dMdpk[0],'pos':dMdpk[1],'sig':dMdpk[2],'gam':dMdpk[3],'shl':dMdpk[4]}
                if Ka2:
                    pos2 = pos+lamRatio*tand(pos/2.0)       # + 360/pi * Dlam/lam * tan(th)
                    iBeg = np.searchsorted(xdata,pos2-fmin)
                    iFin = np.searchsorted(xdata,pos2+fmin)
                    if iBeg-iFin:
                        dMdipk2 = getdFCJVoigt3(pos2,sig,gam,shl,xdata[iBeg:iFin])
                        for i in range(1,5):
                            dMdpk[i][iBeg:iFin] += 100.*cw[iBeg:iFin]*intens*kRatio*dMdipk2[i]
                        dMdpk[0][iBeg:iFin] += 100.*cw[iBeg:iFin]*kRatio*dMdipk2[0]
                        dMdpk[5][iBeg:iFin] += 100.*cw[iBeg:iFin]*dMdipk2[0]
                        dervDict = {'int':dMdpk[0],'pos':dMdpk[1],'sig':dMdpk[2],'gam':dMdpk[3],'shl':dMdpk[4],'L1/L2':dMdpk[5]*intens}
                for parmName in ['pos','int','sig','gam']:
                    try:
                        idx = varyList.index(parmName+str(iPeak))
                        dMdv[idx] = dervDict[parmName]
                    except ValueError:
                        pass
                if 'U' in varyList:
                    dMdv[varyList.index('U')] += dsdU*dervDict['sig']
                if 'V' in varyList:
                    dMdv[varyList.index('V')] += dsdV*dervDict['sig']
                if 'W' in varyList:
                    dMdv[varyList.index('W')] += dsdW*dervDict['sig']
                if 'X' in varyList:
                    dMdv[varyList.index('X')] += dgdX*dervDict['gam']
                if 'Y' in varyList:
                    dMdv[varyList.index('Y')] += dgdY*dervDict['gam']
                if 'SH/L' in varyList:
                    dMdv[varyList.index('SH/L')] += dervDict['shl']         #problem here
                if 'I(L2)/I(L1)' in varyList:
                    dMdv[varyList.index('I(L2)/I(L1)')] += dervDict['L1/L2']
                iPeak += 1
            except KeyError:        #no more peaks to process
                break
    else:
        Pdabc = parmDict['Pdabc']
        difC = parmDict['difC']
        iPeak = 0
        while True:
            try:
                pos = parmDict['pos'+str(iPeak)]                
                tof = pos-parmDict['Zero']
                dsp = tof/difC
                intens = parmDict['int'+str(iPeak)]
                alpName = 'alp'+str(iPeak)
                if alpName in varyList:
                    alp = parmDict[alpName]
                else:
                    if len(Pdabc):
                        alp = np.interp(dsp,Pdabc[0],Pdabc[1])
                        dad0 = 0
                    else:
                        alp = G2mth.getTOFalpha(parmDict,dsp)
                        dada0 = G2mth.getTOFalphaDeriv(dsp)
                betName = 'bet'+str(iPeak)
                if betName in varyList:
                    bet = parmDict[betName]
                else:
                    if len(Pdabc):
                        bet = np.interp(dsp,Pdabc[0],Pdabc[2])
                        dbdb0 = dbdb1 = dbdb2 = 0
                    else:
                        bet = G2mth.getTOFbeta(parmDict,dsp)
                        dbdb0,dbdb1,dbdb2 = G2mth.getTOFbetaDeriv(dsp)
                sigName = 'sig'+str(iPeak)
                if sigName in varyList:
                    sig = parmDict[sigName]
                    dsds0 = dsds1 = dsds2 = dsds3 = 0
                else:
                    sig = G2mth.getTOFsig(parmDict,dsp)
                    dsds0,dsds1,dsds2,dsds3 = G2mth.getTOFsigDeriv(dsp)
                gamName = 'gam'+str(iPeak)
                if gamName in varyList:
                    gam = parmDict[gamName]
                    dsdX = dsdY = 0
                else:
                    gam = G2mth.getTOFgamma(parmDict,dsp)
                    dsdX,dsdY = G2mth.getTOFgammaDeriv(dsp)
                gam = max(gam,0.001)             #avoid neg gamma
                Wd,fmin,fmax = getWidthsTOF(pos,alp,bet,sig,gam)
                iBeg = np.searchsorted(xdata,pos-fmin)
                lenX = len(xdata)
                if not iBeg:
                    iFin = np.searchsorted(xdata,pos+fmax)
                elif iBeg == lenX:
                    iFin = iBeg
                else:
                    iFin = np.searchsorted(xdata,pos+fmax)
                if not iBeg+iFin:       #peak below low limit
                    iPeak += 1
                    continue
                elif not iBeg-iFin:     #peak above high limit
                    break
                dMdpk = np.zeros(shape=(7,len(xdata)))
                dMdipk = getdEpsVoigt(pos,alp,bet,sig,gam,xdata[iBeg:iFin])
                for i in range(1,6):
                    dMdpk[i][iBeg:iFin] += intens*cw[iBeg:iFin]*dMdipk[i]
                dMdpk[0][iBeg:iFin] += cw[iBeg:iFin]*dMdipk[0]
                dervDict = {'int':dMdpk[0],'pos':dMdpk[1],'alp':dMdpk[2],'bet':dMdpk[3],'sig':dMdpk[4],'gam':dMdpk[5]}
                for parmName in ['pos','int','alp','bet','sig','gam']:
                    try:
                        idx = varyList.index(parmName+str(iPeak))
                        dMdv[idx] = dervDict[parmName]
                    except ValueError:
                        pass
                if 'alpha' in varyList:
                    dMdv[varyList.index('alpha')] += dada0*dervDict['alp']
                if 'beta-0' in varyList:
                    dMdv[varyList.index('beta-0')] += dbdb0*dervDict['bet']
                if 'beta-1' in varyList:
                    dMdv[varyList.index('beta-1')] += dbdb1*dervDict['bet']
                if 'beta-q' in varyList:
                    dMdv[varyList.index('beta-q')] += dbdb2*dervDict['bet']
                if 'sig-0' in varyList:
                    dMdv[varyList.index('sig-0')] += dsds0*dervDict['sig']
                if 'sig-1' in varyList:
                    dMdv[varyList.index('sig-1')] += dsds1*dervDict['sig']
                if 'sig-2' in varyList:
                    dMdv[varyList.index('sig-2')] += dsds2*dervDict['sig']
                if 'sig-q' in varyList:
                    dMdv[varyList.index('sig-q')] += dsds3*dervDict['sig']
                if 'X' in varyList:
                    dMdv[varyList.index('X')] += dsdX*dervDict['gam']
                if 'Y' in varyList:
                    dMdv[varyList.index('Y')] += dsdY*dervDict['gam']         #problem here
                iPeak += 1
            except KeyError:        #no more peaks to process
                break
    return dMdv
        
def Dict2Values(parmdict, varylist):
    '''Use before call to leastsq to setup list of values for the parameters 
    in parmdict, as selected by key in varylist'''
    return [parmdict[key] for key in varylist] 
    
def Values2Dict(parmdict, varylist, values):
    ''' Use after call to leastsq to update the parameter dictionary with 
    values corresponding to keys in varylist'''
    parmdict.update(zip(varylist,values))
    
def SetBackgroundParms(Background):
    'needs a doc string'
    if len(Background) == 1:            # fix up old backgrounds
        BackGround.append({'nDebye':0,'debyeTerms':[]})
    bakType,bakFlag = Background[0][:2]
    backVals = Background[0][3:]
    backNames = ['Back;'+str(i) for i in range(len(backVals))]
    Debye = Background[1]           #also has background peaks stuff
    backDict = dict(zip(backNames,backVals))
    backVary = []
    if bakFlag:
        backVary = backNames

    backDict['nDebye'] = Debye['nDebye']
    debyeDict = {}
    debyeList = []
    for i in range(Debye['nDebye']):
        debyeNames = ['DebyeA;'+str(i),'DebyeR;'+str(i),'DebyeU;'+str(i)]
        debyeDict.update(dict(zip(debyeNames,Debye['debyeTerms'][i][::2])))
        debyeList += zip(debyeNames,Debye['debyeTerms'][i][1::2])
    debyeVary = []
    for item in debyeList:
        if item[1]:
            debyeVary.append(item[0])
    backDict.update(debyeDict)
    backVary += debyeVary 

    backDict['nPeaks'] = Debye['nPeaks']
    peaksDict = {}
    peaksList = []
    for i in range(Debye['nPeaks']):
        peaksNames = ['BkPkpos;'+str(i),'BkPkint;'+str(i),'BkPksig;'+str(i),'BkPkgam;'+str(i)]
        peaksDict.update(dict(zip(peaksNames,Debye['peaksList'][i][::2])))
        peaksList += zip(peaksNames,Debye['peaksList'][i][1::2])
    peaksVary = []
    for item in peaksList:
        if item[1]:
            peaksVary.append(item[0])
    backDict.update(peaksDict)
    backVary += peaksVary    
    return bakType,backDict,backVary
    
def DoCalibInst(IndexPeaks,Inst):
    
    def SetInstParms():
        dataType = Inst['Type'][0]
        insVary = []
        insNames = []
        insVals = []
        for parm in Inst:
            insNames.append(parm)
            insVals.append(Inst[parm][1])
            if parm in ['Lam','difC','difA','difB','Zero',]:
                if Inst[parm][2]:
                    insVary.append(parm)
        instDict = dict(zip(insNames,insVals))
        return dataType,instDict,insVary
        
    def GetInstParms(parmDict,Inst,varyList):
        for name in Inst:
            Inst[name][1] = parmDict[name]
        
    def InstPrint(Inst,sigDict):
        print 'Instrument Parameters:'
        if 'C' in Inst['Type'][0]:
            ptfmt = "%12.6f"
        else:
            ptfmt = "%12.3f"
        ptlbls = 'names :'
        ptstr =  'values:'
        sigstr = 'esds  :'
        for parm in Inst:
            if parm in  ['Lam','difC','difA','difB','Zero',]:
                ptlbls += "%s" % (parm.center(12))
                ptstr += ptfmt % (Inst[parm][1])
                if parm in sigDict:
                    sigstr += ptfmt % (sigDict[parm])
                else:
                    sigstr += 12*' '
        print ptlbls
        print ptstr
        print sigstr
        
    def errPeakPos(values,peakDsp,peakPos,peakWt,dataType,parmDict,varyList):
        parmDict.update(zip(varyList,values))
        return np.sqrt(peakWt)*(G2lat.getPeakPos(dataType,parmDict,peakDsp)-peakPos)

    peakPos = []
    peakDsp = []
    peakWt = []
    for peak,sig in zip(IndexPeaks[0],IndexPeaks[1]):
        if peak[2] and peak[3]:
            peakPos.append(peak[0])
            peakDsp.append(peak[-1])    #d-calc
            peakWt.append(peak[-1]**2/sig**2)   #weight by d**2
    peakPos = np.array(peakPos)
    peakDsp = np.array(peakDsp)
    peakWt = np.array(peakWt)
    dataType,insDict,insVary = SetInstParms()
    parmDict = {}
    parmDict.update(insDict)
    varyList = insVary
    if not len(varyList):
        print '**** ERROR - nothing to refine! ****'
        return False
    while True:
        begin = time.time()
        values =  np.array(Dict2Values(parmDict, varyList))
        result = so.leastsq(errPeakPos,values,full_output=True,ftol=0.000001,
            args=(peakDsp,peakPos,peakWt,dataType,parmDict,varyList))
        ncyc = int(result[2]['nfev']/2)
        runtime = time.time()-begin    
        chisq = np.sum(result[2]['fvec']**2)
        Values2Dict(parmDict, varyList, result[0])
        GOF = chisq/(len(peakPos)-len(varyList))       #reduced chi^2
        print 'Number of function calls:',result[2]['nfev'],' Number of observations: ',len(peakPos),' Number of parameters: ',len(varyList)
        print 'calib time = %8.3fs, %8.3fs/cycle'%(runtime,runtime/ncyc)
        print 'chi**2 = %12.6g, reduced chi**2 = %6.2f'%(chisq,GOF)
        try:
            sig = np.sqrt(np.diag(result[1])*GOF)
            if np.any(np.isnan(sig)):
                print '*** Least squares aborted - some invalid esds possible ***'
            break                   #refinement succeeded - finish up!
        except ValueError:          #result[1] is None on singular matrix
            print '**** Refinement failed - singular matrix ****'
        
    sigDict = dict(zip(varyList,sig))
    GetInstParms(parmDict,Inst,varyList)
    InstPrint(Inst,sigDict)
    return True
            
def DoPeakFit(FitPgm,Peaks,Background,Limits,Inst,Inst2,data,prevVaryList=[],oneCycle=False,controls=None,dlg=None):
    'needs a doc string'
        
    def GetBackgroundParms(parmList,Background):
        iBak = 0
        while True:
            try:
                bakName = 'Back;'+str(iBak)
                Background[0][iBak+3] = parmList[bakName]
                iBak += 1
            except KeyError:
                break
        iDb = 0
        while True:
            names = ['DebyeA;','DebyeR;','DebyeU;']
            try:
                for i,name in enumerate(names):
                    val = parmList[name+str(iDb)]
                    Background[1]['debyeTerms'][iDb][2*i] = val
                iDb += 1
            except KeyError:
                break
        iDb = 0
        while True:
            names = ['BkPkpos;','BkPkint;','BkPksig;','BkPkgam;']
            try:
                for i,name in enumerate(names):
                    val = parmList[name+str(iDb)]
                    Background[1]['peaksList'][iDb][2*i] = val
                iDb += 1
            except KeyError:
                break
                
    def BackgroundPrint(Background,sigDict):
        if Background[0][1]:
            print 'Background coefficients for',Background[0][0],'function'
            ptfmt = "%12.5f"
            ptstr =  'values:'
            sigstr = 'esds  :'
            for i,back in enumerate(Background[0][3:]):
                ptstr += ptfmt % (back)
                sigstr += ptfmt % (sigDict['Back;'+str(i)])
            print ptstr
            print sigstr
        else:
            print 'Background not refined'
        if Background[1]['nDebye']:
            parms = ['DebyeA;','DebyeR;','DebyeU;']
            print 'Debye diffuse scattering coefficients'
            ptfmt = "%12.5f"
            print ' term       DebyeA       esd        DebyeR       esd        DebyeU        esd'
            for term in range(Background[1]['nDebye']):
                line = ' term %d'%(term)
                for ip,name in enumerate(parms):
                    line += ptfmt%(Background[1]['debyeTerms'][term][2*ip])
                    if name+str(term) in sigDict:
                        line += ptfmt%(sigDict[name+str(term)])
                print line
        if Background[1]['nPeaks']:
            parms = ['BkPkpos','BkPkint','BkPksig','BkPkgam']
            print 'Peaks in background coefficients'
            ptfmt = "%15.3f"
            names =   'names :'
            ptstr =  'values:'
            sigstr = 'esds  :'
            for item in sigDict:
                if 'BkPk' in item:
                    names += '%15s'%(item)
                    sigstr += ptfmt%(sigDict[item])
                    parm,id = item.split(';')
                    ip = parms.index(parm)
                    ptstr += ptfmt%(Background[1]['peaksList'][int(id)][2*ip])
            print names
            print ptstr
            print sigstr
                            
    def SetInstParms(Inst):
        dataType = Inst['Type'][0]
        insVary = []
        insNames = []
        insVals = []
        for parm in Inst:
            insNames.append(parm)
            insVals.append(Inst[parm][1])
            if parm in ['U','V','W','X','Y','SH/L','I(L2)/I(L1)','alpha',
                'beta-0','beta-1','beta-q','sig-0','sig-1','sig-2','sig-q',] and Inst[parm][2]:
                    insVary.append(parm)
        instDict = dict(zip(insNames,insVals))
        instDict['X'] = max(instDict['X'],0.01)
        instDict['Y'] = max(instDict['Y'],0.01)
        if 'SH/L' in instDict:
            instDict['SH/L'] = max(instDict['SH/L'],0.002)
        return dataType,instDict,insVary
        
    def GetInstParms(parmDict,Inst,varyList,Peaks):
        for name in Inst:
            Inst[name][1] = parmDict[name]
        iPeak = 0
        while True:
            try:
                sigName = 'sig'+str(iPeak)
                pos = parmDict['pos'+str(iPeak)]
                if sigName not in varyList:
                    if 'C' in Inst['Type'][0]:
                        parmDict[sigName] = G2mth.getCWsig(parmDict,pos)
                    else:
                        dsp = G2lat.Pos2dsp(Inst,pos)
                        parmDict[sigName] = G2mth.getTOFsig(parmDict,dsp)
                gamName = 'gam'+str(iPeak)
                if gamName not in varyList:
                    if 'C' in Inst['Type'][0]:
                        parmDict[gamName] = G2mth.getCWgam(parmDict,pos)
                    else:
                        dsp = G2lat.Pos2dsp(Inst,pos)
                        parmDict[gamName] = G2mth.getTOFgamma(parmDict,dsp)
                iPeak += 1
            except KeyError:
                break
        
    def InstPrint(Inst,sigDict):
        print 'Instrument Parameters:'
        ptfmt = "%12.6f"
        ptlbls = 'names :'
        ptstr =  'values:'
        sigstr = 'esds  :'
        for parm in Inst:
            if parm in  ['U','V','W','X','Y','SH/L','I(L2)/I(L1)','alpha',
                'beta-0','beta-1','beta-q','sig-0','sig-1','sig-2','sig-q',]:
                ptlbls += "%s" % (parm.center(12))
                ptstr += ptfmt % (Inst[parm][1])
                if parm in sigDict:
                    sigstr += ptfmt % (sigDict[parm])
                else:
                    sigstr += 12*' '
        print ptlbls
        print ptstr
        print sigstr

    def SetPeaksParms(dataType,Peaks):
        peakNames = []
        peakVary = []
        peakVals = []
        if 'C' in dataType:
            names = ['pos','int','sig','gam']
        else:
            names = ['pos','int','alp','bet','sig','gam']
        for i,peak in enumerate(Peaks):
            for j,name in enumerate(names):
                peakVals.append(peak[2*j])
                parName = name+str(i)
                peakNames.append(parName)
                if peak[2*j+1]:
                    peakVary.append(parName)
        return dict(zip(peakNames,peakVals)),peakVary
                
    def GetPeaksParms(Inst,parmDict,Peaks,varyList):
        if 'C' in Inst['Type'][0]:
            names = ['pos','int','sig','gam']
        else:   #'T'
            names = ['pos','int','alp','bet','sig','gam']
        for i,peak in enumerate(Peaks):
            pos = parmDict['pos'+str(i)]
            if 'difC' in Inst:
                dsp = pos/Inst['difC'][1]
            for j in range(len(names)):
                parName = names[j]+str(i)
                if parName in varyList:
                    peak[2*j] = parmDict[parName]
                elif 'alpha' in parName:
                    peak[2*j] = parmDict['alpha']/dsp
                elif 'beta' in parName:
                    peak[2*j] = G2mth.getTOFbeta(parmDict,dsp)
                elif 'sig' in parName:
                    if 'C' in Inst['Type'][0]:
                        peak[2*j] = G2mth.getCWsig(parmDict,pos)
                    else:
                        peak[2*j] = G2mth.getTOFsig(parmDict,dsp)
                elif 'gam' in parName:
                    if 'C' in Inst['Type'][0]:
                        peak[2*j] = G2mth.getCWgam(parmDict,pos)
                    else:
                        peak[2*j] = G2mth.getTOFgamma(parmDict,dsp)
                        
    def PeaksPrint(dataType,parmDict,sigDict,varyList):
        print 'Peak coefficients:'
        if 'C' in dataType:
            names = ['pos','int','sig','gam']
        else:   #'T'
            names = ['pos','int','alp','bet','sig','gam']            
        head = 13*' '
        for name in names:
            if name in ['alp','bet']:
                head += name.center(8)+'esd'.center(8)
            else:
                head += name.center(10)+'esd'.center(10)
        print head
        if 'C' in dataType:
            ptfmt = {'pos':"%10.5f",'int':"%10.1f",'sig':"%10.3f",'gam':"%10.3f"}
        else:
            ptfmt = {'pos':"%10.2f",'int':"%10.4f",'alp':"%8.3f",'bet':"%8.5f",'sig':"%10.3f",'gam':"%10.3f"}
        for i,peak in enumerate(Peaks):
            ptstr =  ':'
            for j in range(len(names)):
                name = names[j]
                parName = name+str(i)
                ptstr += ptfmt[name] % (parmDict[parName])
                if parName in varyList:
                    ptstr += ptfmt[name] % (sigDict[parName])
                else:
                    if name in ['alp','bet']:
                        ptstr += 8*' '
                    else:
                        ptstr += 10*' '
            print '%s'%(('Peak'+str(i+1)).center(8)),ptstr
                
    def devPeakProfile(values,xdata,ydata, weights,dataType,parmdict,varylist,bakType,dlg):
        parmdict.update(zip(varylist,values))
        return np.sqrt(weights)*getPeakProfileDerv(dataType,parmdict,xdata,varylist,bakType)
            
    def errPeakProfile(values,xdata,ydata, weights,dataType,parmdict,varylist,bakType,dlg):        
        parmdict.update(zip(varylist,values))
        M = np.sqrt(weights)*(getPeakProfile(dataType,parmdict,xdata,varylist,bakType)-ydata)
        Rwp = min(100.,np.sqrt(np.sum(M**2)/np.sum(weights*ydata**2))*100.)
        if dlg:
            GoOn = dlg.Update(Rwp,newmsg='%s%8.3f%s'%('Peak fit Rwp =',Rwp,'%'))[0]
            if not GoOn:
                return -M           #abort!!
        return M
        
    if controls:
        Ftol = controls['min dM/M']
        derivType = controls['deriv type']
    else:
        Ftol = 0.0001
        derivType = 'analytic'
    if oneCycle:
        Ftol = 1.0
    x,y,w,yc,yb,yd = data               #these are numpy arrays!
    yc *= 0.                            #set calcd ones to zero
    yb *= 0.
    yd *= 0.
    xBeg = np.searchsorted(x,Limits[0])
    xFin = np.searchsorted(x,Limits[1])
    bakType,bakDict,bakVary = SetBackgroundParms(Background)
    dataType,insDict,insVary = SetInstParms(Inst)
    peakDict,peakVary = SetPeaksParms(Inst['Type'][0],Peaks)
    parmDict = {}
    parmDict.update(bakDict)
    parmDict.update(insDict)
    parmDict.update(peakDict)
    parmDict['Pdabc'] = []      #dummy Pdabc
    parmDict.update(Inst2)      #put in real one if there
    if prevVaryList:
        varyList = prevVaryList[:]
    else:
        varyList = bakVary+insVary+peakVary
    fullvaryList = varyList[:]
    while True:
        begin = time.time()
        values =  np.array(Dict2Values(parmDict, varyList))
        Rvals = {}
        badVary = []
        if FitPgm == 'LSQ':
            try:
                result = so.leastsq(errPeakProfile,values,Dfun=devPeakProfile,full_output=True,ftol=Ftol,col_deriv=True,
                    args=(x[xBeg:xFin],y[xBeg:xFin],w[xBeg:xFin],dataType,parmDict,varyList,bakType,dlg))
                ncyc = int(result[2]['nfev']/2)
            finally:
                dlg.Destroy()
            runtime = time.time()-begin    
            chisq = np.sum(result[2]['fvec']**2)
            Values2Dict(parmDict, varyList, result[0])
            Rvals['Rwp'] = np.sqrt(chisq/np.sum(w[xBeg:xFin]*y[xBeg:xFin]**2))*100.      #to %
            Rvals['GOF'] = chisq/(xFin-xBeg-len(varyList))       #reduced chi^2
            print 'Number of function calls:',result[2]['nfev'],' Number of observations: ',xFin-xBeg,' Number of parameters: ',len(varyList)
            print 'fitpeak time = %8.3fs, %8.3fs/cycle'%(runtime,runtime/ncyc)
            print 'Rwp = %7.2f%%, chi**2 = %12.6g, reduced chi**2 = %6.2f'%(Rvals['Rwp'],chisq,Rvals['GOF'])
            try:
                sig = np.sqrt(np.diag(result[1])*Rvals['GOF'])
                if np.any(np.isnan(sig)):
                    print '*** Least squares aborted - some invalid esds possible ***'
                break                   #refinement succeeded - finish up!
            except ValueError:          #result[1] is None on singular matrix
                print '**** Refinement failed - singular matrix ****'
                Ipvt = result[2]['ipvt']
                for i,ipvt in enumerate(Ipvt):
                    if not np.sum(result[2]['fjac'],axis=1)[i]:
                        print 'Removing parameter: ',varyList[ipvt-1]
                        badVary.append(varyList[ipvt-1])
                        del(varyList[ipvt-1])
                        break
        elif FitPgm == 'BFGS':
            print 'Other program here'
            return {}
        
    sigDict = dict(zip(varyList,sig))
    yb[xBeg:xFin] = getBackground('',parmDict,bakType,dataType,x[xBeg:xFin])[0]
    yc[xBeg:xFin] = getPeakProfile(dataType,parmDict,x[xBeg:xFin],varyList,bakType)
    yd[xBeg:xFin] = y[xBeg:xFin]-yc[xBeg:xFin]
    GetBackgroundParms(parmDict,Background)
    BackgroundPrint(Background,sigDict)
    GetInstParms(parmDict,Inst,varyList,Peaks)
    InstPrint(Inst,sigDict)
    GetPeaksParms(Inst,parmDict,Peaks,varyList)    
    PeaksPrint(dataType,parmDict,sigDict,varyList)
    return sigDict,result,sig,Rvals,varyList,parmDict,fullvaryList,badVary

def calcIncident(Iparm,xdata):
    'needs a doc string'

    def IfunAdv(Iparm,xdata):
        Itype = Iparm['Itype']
        Icoef = Iparm['Icoeff']
        DYI = np.ones((12,xdata.shape[0]))
        YI = np.ones_like(xdata)*Icoef[0]
        
        x = xdata/1000.                 #expressions are in ms
        if Itype == 'Exponential':
            for i in [1,3,5,7,9]:
                Eterm = np.exp(-Icoef[i+1]*x**((i+1)/2))
                YI += Icoef[i]*Eterm
                DYI[i] *= Eterm
                DYI[i+1] *= -Icoef[i]*Eterm*x**((i+1)/2)            
        elif 'Maxwell'in Itype:
            Eterm = np.exp(-Icoef[2]/x**2)
            DYI[1] = Eterm/x**5
            DYI[2] = -Icoef[1]*DYI[1]/x**2
            YI += (Icoef[1]*Eterm/x**5)
            if 'Exponential' in Itype:
                for i in range(3,12,2):
                    Eterm = np.exp(-Icoef[i+1]*x**((i+1)/2))
                    YI += Icoef[i]*Eterm
                    DYI[i] *= Eterm
                    DYI[i+1] *= -Icoef[i]*Eterm*x**((i+1)/2)
            else:   #Chebyschev
                T = (2./x)-1.
                Ccof = np.ones((12,xdata.shape[0]))
                Ccof[1] = T
                for i in range(2,12):
                    Ccof[i] = 2*T*Ccof[i-1]-Ccof[i-2]
                for i in range(1,10):
                    YI += Ccof[i]*Icoef[i+2]
                    DYI[i+2] =Ccof[i]
        return YI,DYI
        
    Iesd = np.array(Iparm['Iesd'])
    Icovar = Iparm['Icovar']
    YI,DYI = IfunAdv(Iparm,xdata)
    YI = np.where(YI>0,YI,1.)
    WYI = np.zeros_like(xdata)
    vcov = np.zeros((12,12))
    k = 0
    for i in range(12):
        for j in range(i,12):
            vcov[i][j] = Icovar[k]*Iesd[i]*Iesd[j]
            vcov[j][i] = Icovar[k]*Iesd[i]*Iesd[j]
            k += 1
    M = np.inner(vcov,DYI.T)
    WYI = np.sum(M*DYI,axis=0)
    WYI = np.where(WYI>0.,WYI,0.)
    return YI,WYI
    
#testing data
NeedTestData = True
def TestData():
    'needs a doc string'
#    global NeedTestData
    NeedTestData = False
    global bakType
    bakType = 'chebyschev'
    global xdata
    xdata = np.linspace(4.0,40.0,36000)
    global parmDict0
    parmDict0 = {
        'pos0':5.6964,'int0':8835.8,'sig0':1.0,'gam0':1.0,
        'pos1':11.4074,'int1':3922.3,'sig1':1.0,'gam1':1.0,
        'pos2':20.6426,'int2':1573.7,'sig2':1.0,'gam2':1.0,
        'pos3':26.9568,'int3':925.1,'sig3':1.0,'gam3':1.0,
        'U':1.163,'V':-0.605,'W':0.093,'X':0.0,'Y':2.183,'SH/L':0.002,
        'Back0':5.384,'Back1':-0.015,'Back2':.004,
        }
    global parmDict1
    parmDict1 = {
        'pos0':13.4924,'int0':48697.6,'sig0':1.0,'gam0':1.0,
        'pos1':23.4360,'int1':43685.5,'sig1':1.0,'gam1':1.0,
        'pos2':27.1152,'int2':123712.6,'sig2':1.0,'gam2':1.0,
        'pos3':33.7196,'int3':65349.4,'sig3':1.0,'gam3':1.0,
        'pos4':36.1119,'int4':115829.8,'sig4':1.0,'gam4':1.0,
        'pos5':39.0122,'int5':6916.9,'sig5':1.0,'gam5':1.0,
        'U':22.75,'V':-17.596,'W':10.594,'X':1.577,'Y':5.778,'SH/L':0.002,
        'Back0':36.897,'Back1':-0.508,'Back2':.006,
        'Lam1':1.540500,'Lam2':1.544300,'I(L2)/I(L1)':0.5,
        }
    global parmDict2
    parmDict2 = {
        'pos0':5.7,'int0':1000.0,'sig0':0.5,'gam0':0.5,
        'U':2.,'V':-2.,'W':5.,'X':0.5,'Y':0.5,'SH/L':0.02,
        'Back0':5.,'Back1':-0.02,'Back2':.004,
#        'Lam1':1.540500,'Lam2':1.544300,'I(L2)/I(L1)':0.5,
        }
    global varyList
    varyList = []

def test0():
    if NeedTestData: TestData()
    msg = 'test '
    gplot = plotter.add('FCJ-Voigt, 11BM').gca()
    gplot.plot(xdata,getBackground('',parmDict0,bakType,'PXC',xdata)[0])   
    gplot.plot(xdata,getPeakProfile(parmDict0,xdata,varyList,bakType))
    fplot = plotter.add('FCJ-Voigt, Ka1+2').gca()
    fplot.plot(xdata,getBackground('',parmDict1,bakType,'PXC',xdata)[0])   
    fplot.plot(xdata,getPeakProfile(parmDict1,xdata,varyList,bakType))
    
def test1():
    if NeedTestData: TestData()
    time0 = time.time()
    for i in range(100):
        y = getPeakProfile(parmDict1,xdata,varyList,bakType)
    print '100+6*Ka1-2 peaks=1200 peaks',time.time()-time0
    
def test2(name,delt):
    if NeedTestData: TestData()
    varyList = [name,]
    xdata = np.linspace(5.6,5.8,400)
    hplot = plotter.add('derivatives test for '+name).gca()
    hplot.plot(xdata,getPeakProfileDerv(parmDict2,xdata,varyList,bakType)[0])
    y0 = getPeakProfile(parmDict2,xdata,varyList,bakType)
    parmDict2[name] += delt
    y1 = getPeakProfile(parmDict2,xdata,varyList,bakType)
    hplot.plot(xdata,(y1-y0)/delt,'r+')
    
def test3(name,delt):
    if NeedTestData: TestData()
    names = ['pos','sig','gam','shl']
    idx = names.index(name)
    myDict = {'pos':parmDict2['pos0'],'sig':parmDict2['sig0'],'gam':parmDict2['gam0'],'shl':parmDict2['SH/L']}
    xdata = np.linspace(5.6,5.8,800)
    dx = xdata[1]-xdata[0]
    hplot = plotter.add('derivatives test for '+name).gca()
    hplot.plot(xdata,100.*dx*getdFCJVoigt3(myDict['pos'],myDict['sig'],myDict['gam'],myDict['shl'],xdata)[idx+1])
    y0 = getFCJVoigt3(myDict['pos'],myDict['sig'],myDict['gam'],myDict['shl'],xdata)
    myDict[name] += delt
    y1 = getFCJVoigt3(myDict['pos'],myDict['sig'],myDict['gam'],myDict['shl'],xdata)
    hplot.plot(xdata,(y1-y0)/delt,'r+')

if __name__ == '__main__':
    import GSASIItestplot as plot
    global plotter
    plotter = plot.PlotNotebook()
#    test0()
#    for name in ['int0','pos0','sig0','gam0','U','V','W','X','Y','SH/L','I(L2)/I(L1)']:
    for name,shft in [['int0',0.1],['pos0',0.0001],['sig0',0.01],['gam0',0.00001],
        ['U',0.1],['V',0.01],['W',0.01],['X',0.0001],['Y',0.0001],['SH/L',0.00005]]:
        test2(name,shft)
    for name,shft in [['pos',0.0001],['sig',0.01],['gam',0.0001],['shl',0.00005]]:
        test3(name,shft)
    print "OK"
    plotter.StartEventLoop()