Example #1
0
def loadtxt(title, verbose=True):
    import re
    from SimpleQmap import State, ScaleInfo
    with open(title, "r") as file:
        for i, line in enumerate(file):
            if re.search('DIM', line):
                dim = int(line.split(" ")[2])
            if re.search('QMIN', line):
                qmin = float(line.split(" ")[2])
            if re.search('QMAX', line):
                qmax = float(line.split(" ")[2])
            if re.search('PMIN', line):
                pmin = float(line.split(" ")[2])
            if re.search('PMAX', line):
                pmax = float(line.split(" ")[2])
            if re.search('REP', line):
                rep = line.split(" ")[2].replace("\n", "")

    if rep not in ["q", "p"]:
        raise TypeError("must be q-rep or p-rep text file")

    data = numpy.loadtxt(title).transpose()
    vec = data[2] + 1.j * data[3]
    scl = ScaleInfo(dim, [[qmin, qmax], [pmin, pmax]])
    state = State(scl, vec)
    if rep == "p":
        state = state.p2q()
    if verbose:
        t = "load:%s\n" % title
        t += "dim:%d\n" % dim
        t += "domain:[%f,%f]x[%f,%f]\n" % (qmin, qmax, pmin, pmax)
        t += "representation:q" if rep == "q" else "!!Warning!!\nconvert original data (p-rep.) to q-rep.\n"
        print(t)
    return state
Example #2
0
    def coherent(self, q_c, p_c, x):
        """ 
        
        minimum-uncertainty Gaussian wave packet centered at (q_c,p_c, x)
        
        .. math:: 
        
            \langle x | \psi \\rangle = \exp[-(x-q_c)^2/2\hbar + p_c(x-q_c)/\hbar]
            
        .. warning::
        
            周期的境界条件を課してないので特別な理由がない限り使わないで下さい.
        
        Parameters
        ----------
        
        q_c, p_c : float
            Centroid (q_c,p_c,x) of the wave packet
        x : array
        """

        re = -(x - q_c) * (x - q_c) * numpy.pi / (self.scaleinfo.h)
        im = (x - q_c) * p_c * twopi / self.scaleinfo.h
        res = State(self.scaleinfo, data=numpy.exp(re + 1.j * im))
        norm2 = numpy.abs(res.inner(res))
        return res / numpy.sqrt(norm2)
Example #3
0
 def coherent(self, q_c, p_c, x):
     """ 
     
     minimum-uncertainty Gaussian wave packet centered at (q_c,p_c, x)
     
     .. math:: 
     
         \langle x | \psi \\rangle = \exp[-(x-q_c)^2/2\hbar + p_c(x-q_c)/\hbar]
         
     .. warning::
     
         周期的境界条件を課してないので特別な理由がない限り使わないで下さい.
     
     Parameters
     ----------
     
     q_c, p_c : float
         Centroid (q_c,p_c,x) of the wave packet
     x : array
     """ 
     
     re = -(x - q_c)*(x - q_c)*numpy.pi/(self.scaleinfo.h)
     im = (x - q_c)*p_c*twopi/self.scaleinfo.h
     res = State(self.scaleinfo, data = numpy.exp(re+ 1.j*im))
     norm2 = numpy.abs(res.inner(res)) 
     return res/numpy.sqrt(norm2)
Example #4
0
def loadtxt(title,verbose=True):
    import re
    from SimpleQmap import State,ScaleInfo
    with open(title, "r") as file:
        for i, line in enumerate(file):
            if re.search('DIM', line):
                dim = int(line.split(" ")[2])        
            if re.search('QMIN', line):
                qmin = float(line.split(" ")[2])
            if re.search('QMAX', line):
                qmax = float(line.split(" ")[2])
            if re.search('PMIN', line):
                pmin = float(line.split(" ")[2])                
            if re.search('PMAX', line):
                pmax = float(line.split(" ")[2])
            if re.search('REP', line):
                rep = line.split(" ")[2].replace("\n","")

    if rep not in ["q","p"]:
        raise TypeError("must be q-rep or p-rep text file")
    
    data = numpy.loadtxt(title).transpose()
    vec = data[2] + 1.j*data[3]
    scl = ScaleInfo(dim, [[qmin,qmax], [pmin, pmax]])
    state = State(scl, vec)
    if rep == "p":
        state = state.p2q()
    if verbose:
        t = "load:%s\n" % title
        t += "dim:%d\n" % dim
        t += "domain:[%f,%f]x[%f,%f]\n" % (qmin,qmax, pmin, pmax)
        t += "representation:q" if rep =="q" else "!!Warning!!\nconvert original data (p-rep.) to q-rep.\n"
        print(t)
    return state
Example #5
0
 def eig(self):
     data = numpy.squeeze(numpy.asarray(self))
     (evals, V) = numpy.linalg.eig(data)
     evecs = []
     for i in range(len(evals)):
         evecs.append(State(self.scaleinfo, V[:, i]))
     return evals, evecs
Example #6
0
    def p2q(self):
        """
        Fourier (inverse) transformation from
        the momentum :math:`(p)` representation to the position :math:`(q)` representation.

        .. math::

            \\langle q | \\psi\\rangle = \\sum_p \\langle q | p\\rangle \\!\\langle p | \\psi \\rangle

        """

        data = State(self.scaleinfo, self)
        if self.scaleinfo.domain[1][0]*self.scaleinfo.domain[1][1] < 0:
            data = numpy.fft.fftshift(data)
        data = numpy.fft.ifft(data)*numpy.sqrt(self.scaleinfo.dim)#/numpy.sqrt(self.scaleinfo.dim)
        return State(self.scaleinfo, data)
Example #7
0
 def eigh(self):
     data = numpy.squeeze(numpy.asarray(self))
     (evals, V) = numpy.linalg.eigh(data)
     index = numpy.argsort(evals)
     evecs = []
     for i in index:
         evecs.append(State(self.scaleinfo, V[:, i]))
     return evals, evecs
Example #8
0
    def cs(self, q_c, p_c):
        """ 
        create new State object which 
        minimum-uncertainty Gaussian wave packet centered at (q_c,p_c) on periodic boundary condition.
                
        Parameters
        ----------
        
        q_c, p_c : float
            Centroid (q_c,p_c) of wave packet
        
        Examples
        ----------
        
        >>> from state import State, ScaleInfo
        >>> scl = ScaleInfo(10, [[0,1],[-0.5,0.5]])
        >>> state = State(scl)
        >>> state.cs(0.5,0.1)
        State([ -5.19214101e-04 +4.91950621e-47j,
                -3.55650243e-03 -2.58395027e-03j,
                -1.22265106e-02 -3.76293303e-02j,
                 5.88151479e-02 -1.81014412e-01j,
                 3.95164004e-01 -2.87103454e-01j,
                 6.68740103e-01 -8.71513377e-71j,
                 3.95164004e-01 +2.87103454e-01j,
                 5.88151479e-02 +1.81014412e-01j,
                -1.22265106e-02 +3.76293303e-02j,  -3.55650243e-03 +2.58395027e-03j])
                
        .. seealso:: 
        
            Module :state:`coherent`
        
        """

        qrange = self.scaleinfo.domain[0]
        d = qrange[1] - qrange[0]
        lqmin, lqmax = qrange[0] - 2 * d, qrange[1] + 2 * d
        long_q = numpy.linspace(lqmin,
                                lqmax,
                                5 * self.scaleinfo.dim,
                                endpoint=False)

        coh_state = self.coherent(q_c, p_c, long_q)

        vec = numpy.zeros(self.scaleinfo.dim, dtype=numpy.complex128)
        m = int(len(coh_state) / self.scaleinfo.dim)
        coh_state = coh_state.reshape(m, self.scaleinfo.dim)

        for i in range(m):
            vec += coh_state[i][::1]
        norm2 = numpy.dot(vec, numpy.conj(vec))

        return State(self.scaleinfo, vec / numpy.sqrt(norm2))
Example #9
0
 def q2p(self):
     """
     Fourier (forward) transformation from
     the position :math:`(q)` representation to the momentum :math:`(p)` representation. 
     
     .. math::
     
         \\langle p | \\psi\\rangle = \\sum_q \\langle p | q\\rangle \\!\\langle q | \\psi \\rangle
         
     """
     data = numpy.fft.fft(self) / numpy.sqrt(self.scaleinfo.dim)
     if self.scaleinfo.domain[1][0] * self.scaleinfo.domain[1][1] < 0:
         data = numpy.fft.fftshift(data)
     return State(self.scaleinfo, data)  #*numpy.sqrt(self.scaleinfo.dim)
Example #10
0
 def copy(self):
     return State(self.scaleinfo, self.toarray())
Example #11
0
 def inner(self, phi):
     """
     return :math:`\\langle \\phi | \\psi\\rangle` as complex value constant (numpy.complex128)
     """
     res = numpy.sum(self * numpy.conj(phi))
     return State(self.scaleinfo, res)
Example #12
0
 def prep(self):
     """
     return :math:`\\langle p | \\psi\\rangle` as a State object
     """
     return State(self.scaleinfo, self.q2p())
Example #13
0
 def state(self):
     return State(self)
Example #14
0
 def state(self, data=[]):
     if len(data) == 0:
         return State(self)
     else:
         return State(self, data)