Chimie Théorique » QMX

from math import exp, pi, sin, sqrt, cos, acos

import numpy as np

from ase.data import atomic_numbers

# Table (1) of

# D. WAASMAIER AND A. KIRFEL, Acta Cryst. (1995). A51, 416-431

waasmaier = {

    #      a1        b1         a2        b2        a3        b3          a4         b4         a5         b5        c

    'C' : [2.657506, 14.780758, 1.078079, 0.776775, 1.490909, 42.086843,  -4.241070, -0.000294, 0.713791, 0.239535, 4.297983],

    'S' : [6.372157, 1.514347, 5.154568, 22.092528, 1.473732, 0.061373,   1.635073,  55.445176, 1.209372, 0.646925, 0.154722],

    'Pd': [6.121511, 0.062549,  4.784063, 0.784031, 16.631683, 8.751391,  4.318258, 34.489983, 13.246773, 0.784031, 0.883099],

    'Ag': [6.073874, 0.055333, 17.155437, 7.896512, 4.173344, 28.443739,  0.852238, 110.376108, 17.988685, 0.716809, 0.756603],

    'Au': [16.777389, 0.122737, 19.317156, 8.621570, 32.979682, 1.256902, 5.595453, 38.008821, 10.576854, 0.000601, -6.279078],

    'P' : [1.950541, 0.908139, 4.146930, 27.044953, 1.494560, 0.071280, 1.522042, 67.520190, 5.729711, 1.981173, 0.155233],

    'Cl': [1.446071, 0.052357, 6.870609, 1.193165, 6.151801, 18.343416, 1.750347, 46.398394, 0.634168, 0.401005, 0.146773],

}

class XrDebye:

    def __init__(self, wavelength, alpha=1.01, damping=0.04, warn=True,

                 method='Iwasa'):

        """

        Obtain powder x-ray spectra.

        wavelength in Angstrom

        damping in Angstrom**2

        """

        self.wavelength = wavelength

        self.damping = damping

        self.alpha = alpha

        self.warn = warn

        self.method = method

    def set_damping(self, damping):

        self.damping = damping

    def get(self, atoms, s):

        """Get the powder x-ray (XRD) pattern using the Debye-Formula.

        After: T. Iwasa and K. Nobusada, J. Phys. Chem. C 111 (2007) 45

               s is assumed to be in 1/Angstrom

        """

        sinth = self.wavelength * s / 2.

        costh = sqrt(1. - sinth**2)

        cos2th = cos(2. * acos(costh))

        pre = exp(- self.damping * s**2 / 2)

        if self.method == 'Iwasa':

            pre *= costh / (1. + self.alpha * cos2th**2)

        f = {}

        def atomic(symbol):

            if not f.has_key(symbol):

                if self.method == 'Iwasa':

                    f[symbol] = self.get_waasmaier(symbol, s)

                else:

                    f[symbol] = atomic_numbers[symbol]

            return f[symbol]

        def sinc(x):

            if x < 1.e-6:

                x2 = x * x

                return 1 - x2 / 6. + x2 * x2 / 120.

            else:

                return sin(x) / x

        I = 0.

        for a in atoms:

            fa = atomic(a.symbol)

#            print a.symbol, fa

            for b in atoms:

                fb = atomic(b.symbol)

                if a == b:

                    twopis = 0.

                else:

                    vrij = a.position - b.position

                    rij = np.sqrt(np.dot(vrij, vrij))

                    twopisr = 2 * pi * s * rij

                I += fa * fb * sinc(twopisr)

        return pre * I

    def get_waasmaier(self, symbol, s):

        """Scattering factor for free atoms."""

        if symbol == 'H':

            # XXXX implement analytical H

            return 0

        elif waasmaier.has_key(symbol):

            abc = waasmaier[symbol]

            f = abc[10]

            s2 = s*s

            for i in range(5):

                f += abc[2 * i] * exp(-abc[2 * i + 1] * s2)

            return f

        if self.warn:

            print '<xrdebye::get_atomic> Element', symbol, 'not available'

        return 0

from math import pi, sqrt

# Constants from Konrad Hinsen's PhysicalQuantities module:

_c = 299792458.              # speed of light, m/s

_mu0 = 4.e-7 * pi            # permeability of vacuum

_eps0 = 1 / _mu0 / _c**2     # permittivity of vacuum

_Grav = 6.67259e-11          # gravitational constant

_hplanck = 6.6260755e-34     # Planck constant, J s

_hbar = _hplanck / (2 * pi)  # Planck constant / 2pi, J s

_e = 1.60217733e-19          # elementary charge

_me = 9.1093897e-31          # electron mass

_mp = 1.6726231e-27          # proton mass

_Nav = 6.0221367e23          # Avogadro number

_k = 1.380658e-23            # Boltzmann constant, J/K

_amu = 1.6605402e-27         # atomic mass unit, kg

Ang = Angstrom = 1.0

nm = 10.0

Bohr = 4e10 * pi * _eps0 * _hbar**2 / _me / _e**2  # Bohr radius

eV = 1.0

Hartree = _me * _e**3 / 16 / pi**2 / _eps0**2 / _hbar**2

kJ = 1000.0 / _e

kcal = 4.184 * kJ

mol = _Nav

Rydberg = 0.5 * Hartree

Ry = Rydberg

Ha = Hartree

second = 1e10 * sqrt(_e / _amu)

fs = 1e-15 * second

kB = _k / _e                 # Boltzmann constant, eV/K

Pascal = (1 / _e) / 1e30  # J/m^3

GPa = 1e9 * Pascal

Debye = 1e11 *_e * _c

del pi, sqrt

# Copyright (C) 2003  CAMP

# Please see the accompanying LICENSE file for further information.

from os import path

try:

    from subprocess import Popen, PIPE

except ImportError:

    from os import popen3

else:

    def popen3(cmd):

        p = Popen(cmd, shell=True, close_fds=True,

                  stdin=PIPE, stdout=PIPE, stderr=PIPE)

        return p.stdin, p.stdout, p.stderr

def write_svnversion(svnversion, dir):

    svnversionfile = path.join(dir, 'svnversion.py')

    f = open(svnversionfile,'w')

    f.write('svnversion = "%s"\n' % svnversion)

    f.close()

    print 'svnversion = ' +svnversion+' written to '+svnversionfile

    # assert svn:ignore property if the installation is under svn control

    # because svnversion.py has to be ignored by svn!

    cmd = popen3('svn propset svn:ignore svnversion.py '+dir)[1]

    output = cmd.read()

    cmd.close()

def get_svnversion_from_svn(dir):

    # try to get the last svn version number from svnversion

    cmd = popen3('svnversion -n '+dir)[1] # assert we are in the project dir

    output = cmd.read().strip()

    cmd.close()

    if output.startswith('exported'):

        # we build from exported source (e.g. rpmbuild)

        output = None

    return output

svnversion = get_svnversion_from_svn(dir='ase')

if svnversion:

    write_svnversion(svnversion, dir='ase')

from math import sqrt

import numpy as np

from ase.parallel import world, rank, size

from ase.calculators.singlepoint import SinglePointCalculator

from ase.io import read

class NEB:

    def __init__(self, images, k=0.1, climb=False, parallel=False):

        self.images = images

        self.k = k

        self.climb = climb

        self.parallel = parallel

        self.natoms = len(images[0])

        self.nimages = len(images)

        self.emax = np.nan

    def interpolate(self):

        pos1 = self.images[0].get_positions()

        pos2 = self.images[-1].get_positions()

        d = (pos2 - pos1) / (self.nimages - 1.0)

        for i in range(1, self.nimages - 1):

            self.images[i].set_positions(pos1 + i * d)

    def get_positions(self):

        positions = np.empty(((self.nimages - 2) * self.natoms, 3))

        n1 = 0

        for image in self.images[1:-1]:

            n2 = n1 + self.natoms

            positions[n1:n2] = image.get_positions()

            n1 = n2

        return positions

    def set_positions(self, positions):

        n1 = 0

        for image in self.images[1:-1]:

            n2 = n1 + self.natoms

            image.set_positions(positions[n1:n2])

            n1 = n2

    def get_forces(self):

        """Evaluate and return the forces."""

        images = self.images

        forces = np.empty(((self.nimages - 2), self.natoms, 3))

        energies = np.empty(self.nimages - 2)

        if not self.parallel:

            # Do all images - one at a time:

            for i in range(1, self.nimages - 1):

                energies[i - 1] = images[i].get_potential_energy()

                forces[i - 1] = images[i].get_forces()

        else:

            # Parallelize over images:

            i = rank * (self.nimages - 2) // size + 1

            try:

                energies[i - 1] = images[i].get_potential_energy()

                forces[i - 1] = images[i].get_forces()

            except:

                # Make sure other images also fail:

                error = world.sum(1.0)

                raise

            else:

                error = world.sum(0.0)

                if error:

                    raise RuntimeError('Parallel NEB failed!')

            for i in range(1, self.nimages - 1):

                root = (i - 1) * size // (self.nimages - 2)

                world.broadcast(energies[i - 1:i], root)

                world.broadcast(forces[i - 1], root)

        imax = 1 + np.argsort(energies)[-1]

        self.emax = energies[imax - 1]

        tangent1 = images[1].get_positions() - images[0].get_positions()

        for i in range(1, self.nimages - 1):

            tangent2 = (images[i + 1].get_positions() -

                        images[i].get_positions())

            if i < imax:

                tangent = tangent2

            elif i > imax:

                tangent = tangent1

            else:

                tangent = tangent1 + tangent2

            tt = np.vdot(tangent, tangent)

            f = forces[i - 1]

            ft = np.vdot(f, tangent)

            if i == imax and self.climb:

                f -= 2 * ft / tt * tangent

            else:

                f -= ft / tt * tangent

                f -= (np.vdot(tangent1 - tangent2, tangent) *

                      self.k / tt * tangent)

            tangent1 = tangent2

        return forces.reshape((-1, 3))

    def get_potential_energy(self):

        return self.emax

    def __len__(self):

        return (self.nimages - 2) * self.natoms

class SingleCalculatorNEB(NEB):

    def __init__(self, images, k=0.1, climb=False):

        if isinstance(images, str):

            # this is a filename

            traj = read(images, '0:')

            images = []

            for atoms in traj:

                images.append(atoms)

        NEB.__init__(self, images, k, climb, False)

        self.calculators = [None] * self.nimages

        self.energies_ok = False

    def interpolate(self, initial=0, final=-1):

        """Interpolate linearly between initial and final images."""

        if final < 0:

            final = self.nimages + final

        n = final - initial

        pos1 = self.images[initial].get_positions()

        pos2 = self.images[final].get_positions()

        d = (pos2 - pos1) / n

        for i in range(1, n):

            self.images[initial + i].set_positions(pos1 + i * d)

    def refine(self, steps=1, begin=0, end=-1):

        """Refine the NEB trajectory."""

        if end < 0:

            end = self.nimages + end

        j = begin

        n = end - begin

        for i in range(n):

            for k in range(steps):

                self.images.insert(j + 1, self.images[j].copy())

                self.calculators.insert(j + 1, None)

            self.nimages = len(self.images)

            self.interpolate(j, j + steps + 1)

            j += steps + 1

    def set_positions(self, positions):

        # new positions -> new forces

        if self.energies_ok:

            # restore calculators

            self.set_calculators(self.calculators[1:-1])

        NEB.set_positions(self, positions)

    def get_calculators(self):

        """Return the original calculators."""

        calculators = []

        for i, image in enumerate(self.images):

            if self.calculators[i] is None:

                calculators.append(image.get_calculator())

            else:

                calculators.append(self.calculators[i])

        return calculators

    def set_calculators(self, calculators):

        """Set new calculators to the images."""

        self.energies_ok = False

        if not isinstance(calculators, list):

            calculators = [calculators] * self.nimages

        n = len(calculators)

        if n == self.nimages:

            for i in range(self.nimages):

                self.images[i].set_calculator(calculators[i])   

        elif n == self.nimages - 2:

            for i in range(1, self.nimages -1):

                self.images[i].set_calculator(calculators[i-1])   

        else:

            raise RuntimeError(

                'len(calculators)=%d does not fit to len(images)=%d'

                % (n, self.nimages))

    def get_energies_and_forces(self, all=False):

        """Evaluate energies and forces and hide the calculators"""

        if self.energies_ok:

            return

        images = self.images

        forces = np.zeros(((self.nimages - 2), self.natoms, 3))

        energies = np.zeros(self.nimages - 2)

        self.emax = -1.e32

        def calculate_and_hide(i):

            image = self.images[i]

            calc = image.get_calculator()

            if self.calculators[i] is None:

                self.calculators[i] = calc

            if calc is not None:

                if not isinstance(calc, SinglePointCalculator):

                    self.images[i].set_calculator(

                        SinglePointCalculator(image.get_potential_energy(),

                                              image.get_forces(),

                                              None,

                                              None,

                                              image))

                self.emax = min(self.emax, image.get_potential_energy())

        if all and self.calculators[0] is None:

            calculate_and_hide(0)

        # Do all images - one at a time:

        for i in range(1, self.nimages - 1):

            calculate_and_hide(i)

        if all and self.calculators[-1] is None:

            calculate_and_hide(-1)

        self.energies_ok = True

    def get_forces(self):

        self.get_energies_and_forces()

        return NEB.get_forces(self)

    def n(self):

        return self.nimages

    def write(self, filename):

        from ase.io.trajectory import PickleTrajectory

        traj = PickleTrajectory(filename, 'w', self)

        traj.write()

        traj.close()

    def __add__(self, other):

        for image in other:

            self.images.append(image)

        return self

def fit(images):

    E = [i.get_potential_energy() for i in images]

    F = [i.get_forces() for i in images]

    R = [i.get_positions() for i in images]

    return fit0(E, F, R)

def fit0(E, F, R):

    E = np.array(E) - E[0]

    n = len(E)

    Efit = np.empty((n - 1) * 20 + 1)

    Sfit = np.empty((n - 1) * 20 + 1)

    s = [0]

    for i in range(n - 1):

        s.append(s[-1] + sqrt(((R[i + 1] - R[i])**2).sum()))

    lines = []

    for i in range(n):

        if i == 0:

            d = R[1] - R[0]

            ds = 0.5 * s[1]

        elif i == n - 1:

            d = R[-1] - R[-2]

            ds = 0.5 * (s[-1] - s[-2])

        else:

            d = R[i + 1] - R[i - 1]

            ds = 0.25 * (s[i + 1] - s[i - 1])

        d = d / sqrt((d**2).sum())

        dEds = -(F[i] * d).sum()

        x = np.linspace(s[i] - ds, s[i] + ds, 3)

        y = E[i] + dEds * (x - s[i])

        lines.append((x, y))

        if i > 0:

            s0 = s[i - 1]

            s1 = s[i]

            x = np.linspace(s0, s1, 20, endpoint=False)

            c = np.linalg.solve(np.array([(1, s0,   s0**2,     s0**3),

                                          (1, s1,   s1**2,     s1**3),

                                          (0,  1,  2 * s0, 3 * s0**2),

                                          (0,  1,  2 * s1, 3 * s1**2)]),

                                np.array([E[i - 1], E[i], dEds0, dEds]))

            y = c[0] + x * (c[1] + x * (c[2] + x * c[3]))

            Sfit[(i - 1) * 20:i * 20] = x

            Efit[(i - 1) * 20:i * 20] = y

        dEds0 = dEds

    Sfit[-1] = s[-1]

    Efit[-1] = E[-1]

    return s, E, Sfit, Efit, lines

from calculators import TransportCalculator

import numpy as np

from math import sqrt, exp

def tri2full(H_nn, UL='L'):

    """Fill in values of hermitian matrix.

    Fill values in lower or upper triangle of H_nn based on the opposite

    triangle, such that the resulting matrix is symmetric/hermitian.

    UL='U' will copy (conjugated) values from upper triangle into the

    lower triangle.

    UL='L' will copy (conjugated) values from lower triangle into the

    upper triangle.

    """

    N, tmp = H_nn.shape

    assert N == tmp, 'Matrix must be square'

    #assert np.isreal(H_nn.diagonal()).all(), 'Diagonal should be real'

    if UL != 'L':

        H_nn = H_nn.T

    for n in range(N - 1):

        H_nn[n, n + 1:] = H_nn[n + 1:, n].conj()

def dagger(matrix):

    return np.conj(matrix.T)

def rotate_matrix(h, u):

    return np.dot(u.T.conj(), np.dot(h, u))

def get_subspace(matrix, index):

    """Get the subspace spanned by the basis function listed in index"""

    assert matrix.ndim == 2 and matrix.shape[0] == matrix.shape[1]

    return matrix.take(index, 0).take(index, 1)   

permute_matrix = get_subspace

def normalize(matrix, S=None):

    """Normalize column vectors.

    ::

      <matrix[:,i]| S |matrix[:,i]> = 1

    """

    for col in matrix.T:

        if S is None:

            col /= np.linalg.norm(col)

        else:

            col /= np.sqrt(np.dot(col.conj(), np.dot(S, col)))

def subdiagonalize(h_ii, s_ii, index_j):

    nb = h_ii.shape[0]

    nb_sub = len(index_j)

    h_sub_jj = get_subspace(h_ii, index_j)

    s_sub_jj = get_subspace(s_ii, index_j)

    e_j, v_jj = np.linalg.eig(np.linalg.solve(s_sub_jj, h_sub_jj))

    normalize(v_jj, s_sub_jj) # normalize: <v_j|s|v_j> = 1

    permute_list = np.argsort(e_j.real)

    e_j = np.take(e_j, permute_list)

    v_jj = np.take(v_jj, permute_list, axis=1)

    #setup transformation matrix

    c_ii = np.identity(nb, complex)

    for i in xrange(nb_sub):

        for j in xrange(nb_sub):

            c_ii[index_j[i], index_j[j]] = v_jj[i, j]

    h1_ii = rotate_matrix(h_ii, c_ii)

    s1_ii = rotate_matrix(s_ii, c_ii)

    return h1_ii, s1_ii, c_ii, e_j

def cutcoupling(h, s, index_n):

    for i in index_n:

        s[:, i] = 0.0

        s[i, :] = 0.0

        s[i, i] = 1.0

        Ei = h[i, i]

        h[:, i] = 0.0

        h[i, :] = 0.0

        h[i, i] = Ei

def fermidistribution(energy, kt):

    #fermi level is fixed to zero

    return 1.0 / (1.0 + np.exp(energy / kt) )

def fliplr(a):

    length=len(a)

    b = [0] * length

    for i in range(length):

        b[i] = a[length - i - 1]

    return b

def plot_path(energy):

    import pylab

    pylab.plot(np.real(energy), np.imag(energy), 'b--o')

    pylab.show()

def function_integral(function, calcutype):

    #return the integral of the 'function' on 'intrange'    

    #the function can be a value or a matrix, arg1,arg2 are the possible

    #parameters of the function

    intctrl = function.intctrl

    if calcutype == 'eqInt':

        intrange = intctrl.eqintpath

        tol = intctrl.eqinttol

        if hasattr(function.intctrl, 'eqpath_radius'):

            radius = function.intctrl.eqpath_radius

        else:

            radius = -1

        if hasattr(function.intctrl, 'eqpath_origin'):

            origin = function.intctrl.eqpath_origin

        else:

            origin = 1000

    elif calcutype == 'neInt':

        intrange = intctrl.neintpath

        tol = intctrl.neinttol

        radius = -1

        origin = 1000

    elif calcutype == 'locInt':

        intrange = intctrl.locintpath

        tol = intctrl.locinttol

        if hasattr(function.intctrl, 'locpath_radius'):

            radius = function.intctrl.locpath_radius

        else:

            radius = -1

        if hasattr(function.intctrl, 'locpath_origin'):

            origin = function.intctrl.locpath_origin

        else:

            origin = 1000

    trace = 0    

    a = 0.

    b = 1.

    #Initialize with 13 function evaluations.

    c = (a + b) / 2

    h = (b - a) / 2

    realmin = 2e-17

    s = [.942882415695480, sqrt(2.0/3),

         .641853342345781, 1/sqrt(5.0), .236383199662150]

    s1 = [0] * len(s)

    s2 = [0] * len(s)

    for i in range(len(s)):

        s1[i] = c - s[i] * h

        s2[i] = c + fliplr(s)[i] * h

    x0 = [a] + s1 + [c] + s2 + [b]

    s0 = [.0158271919734802, .094273840218850, .155071987336585,

          .188821573960182,  .199773405226859, .224926465333340]

    w0 = s0 + [.242611071901408] + fliplr(s0)

    w1 = [1, 0, 0, 0, 5, 0, 0, 0, 5, 0, 0, 0, 1]

    w2 = [77, 0, 432, 0, 625, 0, 672, 0, 625, 0, 432, 0, 77]

    for i in range(len(w1)):

        w1[i] = w1[i] / 6.0

        w2[i] = w2[i] / 1470.0

    dZ = [intrange[:len(intrange) - 1], intrange[1:]]

    hmin = [0] * len(dZ[1])

    path_type = []

    for i in range(len(intrange) - 1):

        rs = np.abs(dZ[0][i] - origin)

        re = np.abs(dZ[1][i] - origin)

        if abs(rs - radius) < 1.0e-8 and abs(re - radius) < 1.0e-8:

            path_type.append('half_circle')

        else:

            path_type.append('line')

    for i in range(len(dZ[1])):

        if path_type[i] == 'half_circle':

            dZ[0][i] = 0

            dZ[1][i] = np.pi

    for i in range(len(dZ[1])):

        dZ[1][i] = dZ[1][i] - dZ[0][i]

        hmin[i] = realmin / 1024 * abs(dZ[1][i])

    temp = np.array([[1] * 13, x0]).transpose()

    Zx = np.dot(temp, np.array(dZ))

    Zxx = []

    for i in range(len(intrange) - 1):

        for j in range(13):

            Zxx.append(Zx[j][i])

    ns = 0

    ne = 12

    if path_type[0] == 'line':

        yns = function.calgfunc(Zxx[ns], calcutype)

    elif path_type[0] == 'half_circle':

        energy = origin + radius * np.exp((np.pi - Zxx[ns + i]) * 1.j)

        yns = -1.j * radius * np.exp(-1.j* Zxx[ns +i])* function.calgfunc(energy, calcutype)        

    fcnt = 0

    for n in range(len(intrange)-1):

        # below evaluate the integral and adjust the tolerance

        Q1pQ0 = yns * (w1[0] - w0[0])

        Q2pQ0 = yns * (w2[0] - w0[0])

        fcnt = fcnt + 12

        for i in range(1,12):

            if path_type[n] == 'line':

                yne = function.calgfunc(Zxx[ns + i], calcutype)

            elif path_type[n] == 'half_circle':

                energy = origin + radius * np.exp((np.pi -Zxx[ns + i]) * 1.j)

                yne = -1.j * radius * np.exp(-1.j * Zxx[ns + i])* function.calgfunc(energy, calcutype)

            Q1pQ0 += yne * (w1[i] - w0[i])

            Q2pQ0 += yne * (w2[i] - w0[i])

        # Increase the tolerance if refinement appears to be effective

        r = np.abs(Q2pQ0) / (np.abs(Q1pQ0) + np.abs(realmin))

        dim = np.product(r.shape)

        r = np.sum(r) / dim

        if r > 0 and r < 1:

            thistol = tol / r

        else:

            thistol = tol

        if path_type[n] == 'line':

            yne = function.calgfunc(Zxx[ne], calcutype)

        elif path_type[n] == 'half_circle':

            energy = origin + radius * np.exp((np.pi -Zxx[ne]) * 1.j)

            yne = -1.j * radius * np.exp(-1.j * Zxx[ne])* function.calgfunc(energy, calcutype)

        #Call the recursive core integrator

        Qk, xpk, wpk, fcnt, warn = quadlstep(function, Zxx[ns],

                                            Zxx[ne], yns, yne,

                                            thistol, trace, fcnt,

                                            hmin[n], calcutype, path_type[n],

                                            origin, radius)

        if n == 0:

            Q = np.copy(Qk)

            Xp = xpk[:]

            Wp = wpk[:]

        else:

            Q += Qk

            Xp = Xp[:-1] + xpk

            Wp = Wp[:-1] + [Wp[-1] + wpk[0]] + wpk[1:]

        if warn == 1:

            print 'warning: Minimum step size reached,singularity possible'

        elif warn == 2:

            print 'warning: Maximum function count excced; singularity likely'

        elif warn == 3:

            print 'warning: Infinite or Not-a-Number function value encountered'

        else:

            pass

        ns += 13

        ne += 13

        yns = np.copy(yne)

    return Q,Xp,Wp,fcnt

def quadlstep(f, Za, Zb, fa, fb, tol, trace, fcnt, hmin, calcutype,

                                                   path_type, origin, radius):

    #Gaussian-Lobatto and Kronrod method

    #QUADLSTEP Recursive core routine for integral

    #input parameters:

    #      f      ----------   function, here we just use the module calgfunc

    #                          to return the value, if wanna use it for

    #                          another one, change it

    #     Za, Zb  ----------   the start and end point of the integral

    #     fa, fb  ----------   the function value on Za and Zb

    #     fcnt    ----------   the number of the funtion recalled till now

    #output parameters:

    #      Q      ----------   integral

    #     Xp      ----------   selected points

    #     Wp      ----------   weight

    #    fcnt     ----------   the number of the function recalled till now

    maxfcnt = 10000

    # Evaluate integrand five times in interior of subintrval [a,b]

    Zh = (Zb - Za) / 2.0

    if abs(Zh) < hmin:

        # Minimun step size reached; singularity possible

        Q = Zh * (fa + fb)

        if path_type == 'line':

            Xp = [Za, Zb]

        elif path_type == 'half_circle':

            Xp = [origin + radius * np.exp((np.pi - Za) * 1.j),

                                      origin + radius * np.exp((np.pi - Zb) * 1.j)]

        Wp = [Zh, Zh]

        warn = 1

        return Q, Xp, Wp, fcnt, warn

    fcnt += 5

    if fcnt > maxfcnt:

        #Maximum function count exceed; singularity likely

        Q = Zh * (fa + fb)

        if path_type == 'line':

            Xp = [Za, Zb]

        elif path_type == 'half_circle':

            Xp = [origin + radius * np.exp((np.pi - Za) * 1.j),

                                      origin + radius * np.exp((np.pi - Zb) * 1.j)]

        Wp = [Zh, Zh]

        warn = 2

        return Q, Xp, Wp, fcnt, warn

    x = [0.18350341907227,   0.55278640450004,   1.0,

         1.44721359549996,   1.81649658092773];

    Zx = [0] * len(x)

    y = [0] * len(x)

    for i in range(len(x)):

        x[i] *= 0.5

        Zx[i] = Za + (Zb - Za) * x[i]

        if path_type == 'line':

            y[i] = f.calgfunc(Zx[i], calcutype)

        elif path_type == 'half_circle':

            energy = origin + radius * np.exp((np.pi - Zx[i]) * 1.j)

            y[i] = f.calgfunc(energy, calcutype)

    #Four point Lobatto quadrature

    s1 = [1.0, 0.0, 5.0, 0.0, 5.0, 0.0, 1.0]

    s2 = [77.0, 432.0, 625.0, 672.0, 625.0, 432.0, 77.0]

    Wk = [0] * 7

    Wp = [0] * 7

    for i in range(7):

        Wk[i] = (Zh / 6.0) * s1[i]

        Wp[i] = (Zh / 1470.0) * s2[i]

    if path_type == 'line':

        Xp = [Za] + Zx + [Zb]

    elif path_type == 'half_circle':

        Xp = [Za] + Zx + [Zb] 

        for i in range(7):

            factor = -1.j * radius * np.exp(1.j * (np.pi - Xp[i]))

            Wk[i] *= factor

            Wp[i] *= factor

            Xp[i] = origin + radius * np.exp((np.pi - Xp[i]) * 1.j)

    Qk = fa * Wk[0] + fb * Wk[6]

    Q = fa * Wp[0] + fb * Wp[6]

    for i in range(1, 6):

        Qk += y[i-1] * Wk[i]

        Q  += y[i-1] * Wp[i]

    if np.isinf(np.max(np.abs(Q))):

        Q = Zh * (fa + fb)

        if path_type == 'line':

            Xp = [Za, Zb]

        elif path_type == 'half_circle':

            Xp = [origin + radius * np.exp((np.pi - Za) * 1.j),

                                      origin + radius * np.exp((np.pi - Zb) * 1.j)]

        Wp = [Zh, Zh]

        warn = 3

        return Qk, Xp, Wp, fcnt, warn

    else:

        pass

    if trace:

        print fcnt, real(Za), imag(Za), abs(Zh)

    #Check accurancy of integral over this subinterval

    XXk = [Xp[0], Xp[2], Xp[4], Xp[6]]

    WWk = [Wk[0], Wk[2], Wk[4], Wk[6]]

    YYk = [fa, y[1], y[3], fb]

    if np.max(np.abs(Qk - Q)) <= tol:

        warn = 0

        return Q, XXk, WWk, fcnt, warn

    #Subdivide into six subintevals

    else:

        Q, Xk, Wk, fcnt, warn = quadlstep(f, Za, Zx[1], fa, YYk[1],

                                           tol, trace, fcnt, hmin,

                                               calcutype, path_type,

                                                origin, radius)

        Qk, xkk, wkk, fcnt, warnk = quadlstep(f, Zx[1],

                          Zx[3], YYk[1], YYk[2], tol, trace, fcnt, hmin,

                                             calcutype, path_type,

                                             origin, radius)

        Q += Qk

        Xk = Xk[:-1] + xkk

        Wk = Wk[:-1] + [Wk[-1] + wkk[0]] + wkk[1:]

        warn = max(warn, warnk)

        Qk, xkk, wkk, fcnt, warnk = quadlstep(f, Zx[3], Zb, YYk[2], fb,

                                           tol, trace, fcnt, hmin,

                                                   calcutype, path_type,

                                                   origin, radius)

        Q += Qk

        Xk = Xk[:-1] + xkk

        Wk = Wk[:-1] + [Wk[-1] + wkk[0]] + wkk[1:]

        warn = max(warn, warnk)

    return Q, Xk, Wk, fcnt, warn

def mytextread0(filename):

    num = 0

    df = file(filename)

    df.seek(0)

    for line in df:

        if num == 0:

            dim = line.strip().split(' ')

            row = int(dim[0])

            col = int(dim[1])

            mat = np.empty([row, col])

        else:

            data = line.strip().split(' ')

            if len(data) == 0 or len(data)== 1:

                break

            else:

                for i in range(len(data)):

                    mat[num - 1, i] = float(data[i])

        num += 1

    return mat

def mytextread1(filename):

    num = 0

    df = file(filename)

    df.seek(0)

    data = []

    for line in df:

        tmp = line.strip()

        if len(tmp) != 0: 

            data.append(float(tmp))

        else:

            break

    dim = int(sqrt(len(data)))

    mat = np.empty([dim, dim])

    for i in range(dim):

        for j in range(dim):

            mat[i, j] = data[num]

            num += 1

    return mat

def mytextwrite1(filename, mat):

    num = 0

    df = open(filename,'w')

    df.seek(0)

    dim = mat.shape[0]

    if dim != mat.shape[1]:

        print 'matwirte, matrix is not square'

    for i in range(dim):

        for j in range(dim):

            df.write('%20.20e\n'% mat[i, j])

    df.close()

from ase.transport.calculators import TransportCalculator

import numpy as np

#Aux. function to write data to a text file.

def write(fname,xs,ys):

    fd = open(fname,'w')

    for x,y in zip(xs,ys):

        print >> fd, x, y

    fd.close()

H_lead = np.zeros([4,4])

# On-site energies are zero

for i in range(4):

    H_lead[i,i] = 0.0

# Nearest neighbor hopping is -1.0

for i in range(3):

    H_lead[i,i+1] = -1.0

    H_lead[i+1,i] = -1.0

# Next-nearest neighbor hopping is 0.2

for i in range(2):

    H_lead[i,i+2] = 0.2

    H_lead[i+2,i] = 0.2

H_scat = np.zeros([6,6])

# Principal layers on either side of S

H_scat[:2,:2] = H_lead[:2,:2]

H_scat[-2:,-2:] = H_lead[:2,:2]

# Scattering region

H_scat[2,2] = 0.0

H_scat[3,3] = 0.0

H_scat[2,3] = -0.8

H_scat[3,2] = -0.8

# External coupling

H_scat[1,2] = 0.2

H_scat[2,1] = 0.2

H_scat[3,4] = 0.2

H_scat[4,3] = 0.2

energies = np.arange(-3,3,0.02)

tcalc = TransportCalculator(h=H_scat,

                            h1=H_lead,

                            eta=0.02,

                            energies=energies)

T = tcalc.get_transmission()

tcalc.set(pdos=[2, 3])

pdos = tcalc.get_pdos()

tcalc.set(dos=True)

dos = tcalc.get_dos()

write('T.dat',tcalc.energies,T)

write('pdos0.dat', tcalc.energies,pdos[0])

write('pdos1.dat', tcalc.energies,pdos[1])

#subdiagonalize

h_rot, s_rot, eps, u = tcalc.subdiagonalize_bfs([2, 3], apply=True)

T_rot = tcalc.get_transmission()

dos_rot = tcalc.get_dos()

pdos_rot = tcalc.get_pdos()

write('T_rot.dat', tcalc.energies,T_rot)

write('pdos0_rot.dat', tcalc.energies, pdos_rot[0])

write('pdos1_rot.dat', tcalc.energies, pdos_rot[1])

print 'Subspace eigenvalues:', eps

assert sum(abs(eps-(-0.8, 0.8))) < 2.0e-15, 'Subdiagonalization. error'

print 'Max deviation of T after the rotation:', np.abs(T-T_rot).max()

assert max(abs(T-T_rot)) < 2.0e-15, 'Subdiagonalization. error'

#remove coupling

h_cut, s_cut = tcalc.cutcoupling_bfs([2], apply=True)

T_cut = tcalc.get_transmission()

dos_cut = tcalc.get_dos()

pdos_cut = tcalc.get_pdos()

write('T_cut.dat', tcalc.energies, T_cut)

write('pdos0_cut.dat', tcalc.energies,pdos_cut[0])

write('pdos1_cut.dat', tcalc.energies,pdos_cut[1])

import numpy as np

import pylab

import ase.transport.stm as stm

#           Parameters for a simple model.

#

#                           

#                         * eps_a

#                 v_ts /   \ v_a2 

#  ... *  *  *  *            *  *  *  *  * ...

#       \/                          \/

#       t1                          t2

#

#       Tip                      Surface

# ----------------|      |-----------------------

t1 = -1.0

t2 = -2.0

eps_a = 0.4

v_ts  = 0.05

v_a2 = 1.0

#Tip

h1 = np.zeros([2, 2])

h1[0, 1] = t1

h1[1, 0] = t1

s1 = np.identity(2)

h10 = np.zeros([2,2])

h10[0, 1] = t1

h10[1, 0] = t1

s10 = np.identity(2)

#Surface with "molecule" a.

h2 = np.zeros([2,2])

h2[0, 1] = v_a2 

h2[1, 0] = v_a2

h1[0, 0] = eps_a

s2 = np.identity(2)

h20 = np.zeros([2,2])

h20[0, 1] = t2

h20[1, 0] = t2

s20 = np.identity(2)

#Tip Surface coupling

V_ts = np.zeros([2,2])

V_ts[1, 0] = v_ts

eta1 = 0.0001

eta2 = 0.0001

stm = reload(stm)

stm_calc = stm.STM(h1, s1, h2, s2, h10, s10, h20, s20, eta1, eta2)

energies = np.arange(-3.0, 3.0, 0.01)

stm_calc.initialize(energies)

T_stm = stm_calc.get_transmission(V_ts)

#Perform the full calculation and compare

from ase.transport.calculators import TransportCalculator as TC

h = np.zeros([4,4])

h[:2, :2] = h1

h[-2:, -2:] = h2

h[:2, -2:] = V_ts

h[-2:, :2] = V_ts.T

tc = TC(energies=energies,

        h=h,

        h1=h10,

        h2=h20,

        eta=eta1, eta1=eta1, eta2=eta2)

T_full = tc.get_transmission()

pylab.plot(stm_calc.energies, T_stm, 'b')

pylab.plot(tc.energies, T_full, 'r--')

pylab.show()

#bias stuff

biass = np.arange(-2.0, 2.0, 0.2)

Is = [stm_calc.get_current(bias, V_ts) for bias in biass]

pylab.plot(biass, Is, '+')

pylab.show()

import numpy as np

class LeadSelfEnergy:

    conv = 1e-8 # Convergence criteria for surface Green function

    def __init__(self, hs_dii, hs_dij, hs_dim, eta=1e-4):

        self.h_ii, self.s_ii = hs_dii # onsite principal layer

        self.h_ij, self.s_ij = hs_dij # coupling between principal layers

        self.h_im, self.s_im = hs_dim # coupling to the central region

        self.nbf = self.h_im.shape[1] # nbf for the scattering region

        self.eta = eta

        self.energy = None

        self.bias = 0

        self.sigma_mm = np.empty((self.nbf, self.nbf), complex)

    def retarded(self, energy):

        """Return self-energy (sigma) evaluated at specified energy."""

        if energy != self.energy:

            self.energy = energy

            z = energy - self.bias + self.eta * 1.j           

            tau_im = z * self.s_im - self.h_im

            a_im = np.linalg.solve(self.get_sgfinv(energy), tau_im)

            tau_mi = z * self.s_im.T.conj() - self.h_im.T.conj()

            self.sigma_mm[:] = np.dot(tau_mi, a_im)

        return self.sigma_mm

    def set_bias(self, bias):

        self.bias = bias

    def get_lambda(self, energy):

        """Return the lambda (aka Gamma) defined by i(S-S^d).

        Here S is the retarded selfenergy, and d denotes the hermitian

        conjugate.

        """

        sigma_mm = self.retarded(energy)

        return 1.j * (sigma_mm - sigma_mm.T.conj())

    def get_sgfinv(self, energy):

        """The inverse of the retarded surface Green function""" 

        z = energy - self.bias + self.eta * 1.j

        v_00 = z * self.s_ii.T.conj() - self.h_ii.T.conj()

        v_11 = v_00.copy()

        v_10 = z * self.s_ij - self.h_ij

        v_01 = z * self.s_ij.T.conj() - self.h_ij.T.conj()

        delta = self.conv + 1

        while delta > self.conv:

            a = np.linalg.solve(v_11, v_01)

            b = np.linalg.solve(v_11, v_10)

            v_01_dot_b = np.dot(v_01, b)

            v_00 -= v_01_dot_b

            v_11 -= np.dot(v_10, a) 

            v_11 -= v_01_dot_b

            v_01 = -np.dot(v_01, a)

            v_10 = -np.dot(v_10, b)

            delta = abs(v_01).max()

        return v_00

class BoxProbe:

    """Box shaped Buttinger probe.

    Kramers-kroning: real = H(imag); imag = -H(real)

    """

    def __init__(self, eta, a, b, energies, S, T=0.3):

        from Transport.Hilbert import hilbert

        se = np.empty(len(energies), complex)

        se.imag = .5 * (np.tanh(.5 * (energies - a) / T) -

                        np.tanh(.5 * (energies - b) / T))

        se.real = hilbert(se.imag)

        se.imag -= 1

        self.selfenergy_e = eta * se

        self.energies = energies

        self.S = S

    def retarded(self, energy):

        return self.selfenergy_e[self.energies.searchsorted(energy)] * self.S

import numpy as np

from ase.transport.tools import dagger

from ase.transport.selfenergy import LeadSelfEnergy

from ase.transport.greenfunction import GreenFunction

import time

from gpaw.mpi import world

class STM:

    def __init__(self, h1, s1, h2, s2 ,h10, s10, h20, s20, eta1, eta2, w=0.5, pdos=[], logfile = None):

        """XXX

        1. Tip

        2. Surface

        h1: ndarray

            Hamiltonian and overlap matrix for the isolated tip

            calculation.  Note, h1 should contain (at least) one

            principal layer.

        h2: ndarray

            Same as h1 but for the surface.

        h10: ndarray

            periodic part of the tip. must include two and only

            two principal layers.

        h20: ndarray

            same as h10, but for the surface

        The s* are the corresponding overlap matrices.  eta1, and eta

        2 are (finite) infinitesimals.  """

        self.pl1 = len(h10) // 2 #principal layer size for the tip

        self.pl2 = len(h20) // 2 #principal layer size for the surface

        self.h1 = h1 

        self.s1 = s1

        self.h2 = h2

        self.s2 = s2

        self.h10 = h10 

        self.s10 = s10 

        self.h20 = h20 

        self.s20 = s20

        self.eta1 = eta1

        self.eta2 = eta2

        self.w = w #asymmetry of the applied bias (0.5=>symmetric)

        self.pdos = []

        self.log = logfile

    def initialize(self, energies, bias=0):

        """

            energies: list of energies 

            for which the transmission function should be evaluated.

            bias.

            Will precalculate the surface greenfunctions of the tip and

            surface.

        """

        self.bias = bias

        self.energies = energies

        nenergies = len(energies)

        pl1, pl2 = self.pl1, self.pl2

        nbf1, nbf2 = len(self.h1), len(self.h2)

        #periodic part of the tip

        hs1_dii = self.h10[:pl1, :pl1], self.s10[:pl1, :pl1]

        hs1_dij = self.h10[:pl1, pl1:2*pl1], self.s10[:pl1, pl1:2*pl1]

        #coupling betwen per. and non. per part of the tip

        h1_im = np.zeros((pl1, nbf1), complex) 

        s1_im = np.zeros((pl1, nbf1), complex)

        h1_im[:pl1, :pl1], s1_im[:pl1, :pl1] = hs1_dij

        hs1_dim = [h1_im, s1_im]

        #periodic part the surface 

        hs2_dii = self.h20[:pl2, :pl2], self.s20[:pl2, :pl2]

        hs2_dij = self.h20[pl2:2*pl2, :pl2], self.s20[pl2:2*pl2, :pl2]

        #coupling betwen per. and non. per part of the surface

        h2_im = np.zeros((pl2, nbf2), complex)

        s2_im = np.zeros((pl2, nbf2), complex) 

        h2_im[-pl2:, -pl2:], s2_im[-pl2:, -pl2:] = hs2_dij

        hs2_dim = [h2_im, s2_im]

        #tip and surface greenfunction 

        self.selfenergy1 = LeadSelfEnergy(hs1_dii, hs1_dij, hs1_dim, self.eta1)

        self.selfenergy2 = LeadSelfEnergy(hs2_dii, hs2_dij, hs2_dim, self.eta2)

        self.greenfunction1 = GreenFunction(self.h1-self.bias*self.w*self.s1, self.s1, 

                                            [self.selfenergy1], self.eta1)

        self.greenfunction2 = GreenFunction(self.h2-self.bias*(self.w-1)*self.s2, self.s2, 

                                            [self.selfenergy2], self.eta2)

        #Shift the bands due to the bias.

        bias_shift1 = -bias * self.w

        bias_shift2 = -bias * (self.w - 1)

        self.selfenergy1.set_bias(bias_shift1)

        self.selfenergy2.set_bias(bias_shift2)

        #tip and surface greenfunction matrices.

        nbf1_small = nbf1 #XXX Change this for efficiency in the future

        nbf2_small = nbf2 #XXX -||-

        coupling_list1 = range(nbf1_small)# XXX -||-

        coupling_list2 = range(nbf2_small)# XXX -||-

        self.gft1_emm = np.zeros((nenergies, nbf1_small, nbf1_small), complex) 

        self.gft2_emm = np.zeros((nenergies, nbf2_small, nbf2_small), complex)

        for e, energy in enumerate(self.energies):

            if self.log != None: # and world.rank == 0:

                    T = time.localtime()

                    self.log.write(' %d:%02d:%02d, ' % (T[3], T[4], T[5]) +

                                   '%d, %d, %02f\n' % (world.rank, e, energy))

            gft1_mm = self.greenfunction1.retarded(energy)[coupling_list1]

            gft1_mm = np.take(gft1_mm, coupling_list1, axis=1)

            gft2_mm = self.greenfunction2.retarded(energy)[coupling_list2]

            gft2_mm = np.take(gft2_mm, coupling_list2, axis=1)

            self.gft1_emm[e] = gft1_mm

            self.gft2_emm[e] = gft2_mm

            if self.log != None and world.rank == 0:

                self.log.flush()

    def get_transmission(self, v_12, v_11_2=None, v_22_1=None):

        """XXX

        v_12:

            coupling between tip and surface 

        v_11_2:

            correction to "on-site" tip elements due to the 

            surface (eq.16). Is only included to first order.

        v_22_1:

            corretion to "on-site" surface elements due to he

            tip (eq.17). Is only included to first order.

        """

        dim0 = v_12.shape[0]

        dim1 = v_12.shape[1]

        nenergies = len(self.energies)

        T_e = np.empty(nenergies,float)

        v_21 = dagger(v_12)

        for e, energy in enumerate(self.energies):

            gft1 = self.gft1_emm[e]

            if v_11_2!=None:

                gf1 = np.dot(v_11_2, np.dot(gft1, v_11_2)) 

                gf1 += gft1 #eq. 16

            else:

                gf1 = gft1

            gft2 = self.gft2_emm[e]

            if v_22_1!=None:

                gf2 = np.dot(v_22_1,np.dot(gft2, v_22_1))

                gf2 += gft2 #eq. 17

            else:

                gf2 = gft2

            a1 = (gf1 - dagger(gf1))

            a2 = (gf2 - dagger(gf2))

            self.v_12 = v_12

            self.a2 = a2

            self.v_21 = v_21

            self.a1 = a1

            v12_a2 = np.dot(v_12, a2[:dim1])

            v21_a1 = np.dot(v_21, a1[-dim0:])

            self.v12_a2 = v12_a2

            self.v21_a1 = v21_a1

            T = -np.trace(np.dot(v12_a2[:,:dim1], v21_a1[:,-dim0:])) #eq. 11

            T_e[e] = T

            self.T_e = T_e

        return T_e

    def get_current(self, bias, v_12, v_11_2=None, v_22_1=None):

        """Very simple function to calculate the current.

        Asummes zero temperature.

        bias: type? XXX

            bias voltage (V)

        v_12: XXX

            coupling between tip and surface.

        v_11_2:

            correction to onsite elements of the tip

            due to the potential of the surface.

        v_22_1:

            correction to onsite elements of the surface

            due to the potential of the tip.

        """

        energies = self.energies

        T_e = self.get_transmission(v_12, v_11_2, v_22_1)

        bias_window = -np.array([bias * self.w, bias * (self.w - 1)])

        bias_window.sort()

        self.bias_window = bias_window

        #print 'bias window', np.around(bias_window,3)

        #print 'Shift of tip lead do to the bias:', self.selfenergy1.bias

        #print 'Shift of surface lead do to the bias:', self.selfenergy2.bias

        i1 = sum(energies < bias_window[0]) 

        i2 = sum(energies < bias_window[1])

        step = 1 

        if i2 < i1:

            step = -1

        return np.sign(bias)*np.trapz(x=energies[i1:i2:step], y=T_e[i1:i2:step])

import numpy as np

class GreenFunction:

    """Equilibrium retarded Green function."""

    def __init__(self, H, S=None, selfenergies=[], eta=1e-4):

        self.H = H

        self.S = S

        self.selfenergies = selfenergies

        self.eta = eta

        self.energy = None

        self.Ginv = np.empty(H.shape, complex)

    def retarded(self, energy, inverse=False):

        """Get retarded Green function at specified energy.

        If 'inverse' is True, the inverse Green function is returned (faster).

        """

        if energy != self.energy:

            self.energy = energy

            z = energy + self.eta * 1.j

            if self.S is None:

                self.Ginv[:] = 0.0

                self.Ginv.flat[:: len(self.S) + 1] = z

            else:

                self.Ginv[:] = z

                self.Ginv *= self.S

            self.Ginv -= self.H

            for selfenergy in self.selfenergies:

                self.Ginv -= selfenergy.retarded(energy)

        if inverse:

            return self.Ginv

        else:

            return np.linalg.inv(self.Ginv)

    def calculate(self, energy, sigma):

        """XXX is this really needed"""

        ginv = energy * self.S - self.H - sigma 

        return np.linalg.inv(ginv)

    def apply_retarded(self, energy, X):

        """Apply retarded Green function to X.

        Returns the matrix product G^r(e) . X

        """

        return np.linalg.solve(self.retarded(energy, inverse=True), X)

    def dos(self, energy):

        """Total density of states -1/pi Im(Tr(GS))"""

        if self.S is None:

            return -self(energy).imag.trace() / np.pi

        else:

            GS = self.apply_retarded(energy, self.S)

            return -GS.imag.trace() / np.pi

    def pdos(self, energy):

        """Projected density of states -1/pi Im(SGS/S)"""

        if self.S is None:

            return -self.retarded(energy).imag.diagonal() / np.pi

        else:

            S = self.S

            SGS = np.dot(S, self.apply_retarded(energy, S))

            return -(SGS.diagonal() / S.diagonal()).imag / np.pi

import numpy as np

from numpy import linalg

from ase.transport.selfenergy import LeadSelfEnergy, BoxProbe