def init_ao_log_gpaw(self, **kw):
""" Reads radial orbitals from a previous GPAW calculation. """
from pyscf.nao.m_log_interp import log_interp_c
#self.setups = setups if setup is saved in ao_log, we get the following error
# while performing copy
# File "/home/marc/anaconda2/lib/python2.7/copy.py", line 182, in deepcopy
# rv = reductor(2)
# TypeError: can't pickle Spline objects
self.interp_rr,self.interp_pp = log_interp_c(self.rr), log_interp_c(self.pp)
setups = kw['setups']
sdic = setups.setups
self.sp2key = sdic.keys()
#key0 = sdic.keys()[0]
#print(key0, sdic[key0].Z, dir(sdic[key0]))
self.sp_mu2j = [np.array(sdic[key].l_orb_j, np.int64) for key in sdic.keys()]
self.sp2nmult = np.array([len(mu2j) for mu2j in self.sp_mu2j], dtype=np.int64)
self.sp2charge = np.array([sdic[key].Z for key in sdic.keys()], dtype=np.int64)
self.nspecies = len(self.sp_mu2j)
self.jmx = max([max(mu2j) for mu2j in self.sp_mu2j])
self.sp2norbs = np.array([sum(2*mu2j+1) for mu2j in self.sp_mu2j], dtype=np.int64)
self.sp_mu2rcut = []
self.psi_log_rl = []
self.psi_log = []
for sp,[key,nmu,mu2j] in enumerate(zip(sdic.keys(), self.sp2nmult, self.sp_mu2j)):
self.sp_mu2rcut.append(np.array([phit.get_cutoff() for phit in sdic[key].phit_j]))
mu2ff = np.zeros([nmu, self.nr])
for mu,phit in enumerate(sdic[key].phit_j):
for ir, r in enumerate(self.rr):
mu2ff[mu,ir],deriv = phit.get_value_and_derivative(r)
self.psi_log_rl.append(mu2ff)
self.psi_log.append(mu2ff* (self.rr**mu2j[mu]))
self.sp2rcut = np.array([np.amax(rcuts) for rcuts in self.sp_mu2rcut], dtype='float64') # derived from sp_mu2rcut
self.sp_mu2s = [] # derived from sp_mu2j
for mu2j in self.sp_mu2j:
mu2s = np.zeros(len(mu2j)+1, dtype=np.int64)
for mu,j in enumerate(mu2j): mu2s[mu+1] = mu2s[mu]+2*j+1
self.sp_mu2s.append(mu2s)
#self._add_sp2info()
#self._add_psi_log_mom()
#print(self.sp_mu2j)
#print(self.sp2nmult)
#print(self.nspecies)
#print(self.jmx)
#print(self.sp2norbs)
#print(self.sp_mu2rcut)
#print(self.psi_log)
#print(self.sp2charge)
#print(self.sp2rcut)
#print(self.sp_mu2s)
return self
def init_ao_log_ion(self, sp2ion, **kw):
"""
Reads data from a previous SIESTA calculation,
interpolates the orbitals on a single log mesh.
"""
from pyscf.nao.m_log_interp import log_interp_c
from pyscf.nao.m_siesta_ion_interp import siesta_ion_interp
from pyscf.nao.m_siesta_ion_add_sp2 import _siesta_ion_add_sp2
from pyscf.nao.m_spline_diff2 import spline_diff2
from pyscf.nao.m_spline_interp import spline_interp
import numpy as np
self.init_log_mesh_ion(sp2ion, **kw)
#print(__name__, self.nr)
#print(__name__, self.rr)
#print(__name__, self.rmax)
#print(__name__, self.rmin)
#print(__name__, self.kmax)
self.interp_rr,self.interp_pp = log_interp_c(self.rr), log_interp_c(self.pp)
_siesta_ion_add_sp2(self, sp2ion) # adds the fields for counting, .nspecies etc.
self.jmx = max([mu2j.max() for mu2j in self.sp_mu2j])
self.sp2norbs = np.array([mu2s[self.sp2nmult[sp]] for sp,mu2s in enumerate(self.sp_mu2s)], dtype='int64')
self.sp2ion = sp2ion
rr = self.rr
nr = len(rr)
#print(__name__, 'self.jmx', self.jmx)
#print(__name__, 'self.sp2norbs', self.sp2norbs)
#print(__name__, 'self.sp2norbs', dir(self))
#print(__name__, 'self.sp_mu2j', self.sp_mu2j)
#print(__name__, 'self.sp_mu2rcut', self.sp_mu2rcut)
#print(__name__, 'self.sp_mu2s', self.sp_mu2s)
self.psi_log = siesta_ion_interp(rr, sp2ion, 1)
self.psi_log_rl = siesta_ion_interp(rr, sp2ion, 0)
self.sp2vna = [] # Interpolate a Neutral-atom potential V_NA(r) for each specie
for ion in sp2ion:
vna = np.zeros(nr)
if ion["vna"] is not None:
h,dat = ion["vna"]["delta"], ion["vna"]["data"][0][:, 1]
yy_diff2 = spline_diff2(h, dat, 0.0, 1.0e301)
for ir,r in enumerate(rr):
vna[ir] = spline_interp(h, dat, yy_diff2, r)
self.sp2vna.append(vna*0.5) # given in Rydberg?
self.sp_mu2rcut = [ np.array(ion["paos"]["cutoff"]) for ion in sp2ion]
self.sp2rcut = np.array([np.amax(rcuts) for rcuts in self.sp_mu2rcut])
self.sp2charge = [int(ion['z']) for ion in self.sp2ion]
self.sp2valence = [int(ion['valence']) for ion in self.sp2ion]
#call sp2ion_to_psi_log(sv%sp2ion, sv%rr, sv%psi_log)
#call init_psi_log_rl(sv%psi_log, sv%rr, sv%uc%mu_sp2j, sv%uc%sp2nmult, sv%psi_log_rl)
#call sp2ion_to_core(sv%sp2ion, sv%rr, sv%core_log, sv%sp2has_core, sv%sp2rcut_core)
return self
def __init__(self, rr, pp, sv=None, dm=None):
""" Basic """
from pyscf.nao.m_init_dm_libnao import init_dm_libnao
from pyscf.nao.m_init_dens_libnao import init_dens_libnao
self.interp_rr = log_interp_c(rr)
self.interp_pp = log_interp_c(pp)
self.rr3_dr = rr**3 * np.log(rr[1] / rr[0])
self.four_pi = 4 * np.pi
self.const = np.sqrt(np.pi / 2.0)
self.sv = None if sv is None else sv.init_libnao()
self.dm = None if dm is None else init_dm_libnao(dm)
if dm is not None and sv is not None: init_dens_libnao()
def __init__(self, rr, pp, sv=None, dm=None): """ Basic """ from pyscf.nao.m_init_dm_libnao import init_dm_libnao from pyscf.nao.m_init_dens_libnao import init_dens_libnao self.interp_rr = log_interp_c(rr) self.interp_pp = log_interp_c(pp) self.rr3_dr = rr**3 * np.log(rr[1]/rr[0]) self.dr_jt = np.log(rr[1]/rr[0]) self.four_pi = 4*np.pi self.const = np.sqrt(np.pi/2.0) self.pp2 = pp**2 self.sv = None if sv is None else sv.init_libnao() self.dm = None if dm is None else init_dm_libnao(dm) if dm is not None and sv is not None : init_dens_libnao()
def __init__(self, log_mesh, jmx=7, ngl=96, lbdmx=14):
"""
Expansion of the products of two atomic orbitals placed at given locations and around a center between these locations
[1] Talman JD. Multipole Expansions for Numerical Orbital Products, Int. J. Quant. Chem. 107, 1578--1584 (2007)
ngl : order of Gauss-Legendre quadrature
log_mesh : instance of log_mesh_c defining the logarithmic mesh (rr and pp arrays)
jmx : maximal angular momentum quantum number of each atomic orbital in a product
lbdmx : maximal angular momentum quantum number used for the expansion of the product phia*phib
"""
from numpy.polynomial.legendre import leggauss
from pyscf.nao.m_log_interp import log_interp_c
from pyscf.nao.m_csphar_talman_libnao import csphar_talman_libnao as csphar_jt
assert ngl>2
assert jmx>-1
assert hasattr(log_mesh, 'rr')
assert hasattr(log_mesh, 'pp')
self.ngl = ngl
self.lbdmx = lbdmx
self.xx,self.ww = leggauss(ngl)
log_mesh_c.__init__(self)
self.init_log_mesh(log_mesh.rr, log_mesh.pp)
self.plval=np.zeros([2*(self.lbdmx+jmx+1), ngl])
self.plval[0,:] = 1.0
self.plval[1,:] = self.xx
for kappa in range(1,2*(self.lbdmx+jmx)+1):
self.plval[kappa+1, :]= ((2*kappa+1)*self.xx*self.plval[kappa, :]-kappa*self.plval[kappa-1, :])/(kappa+1)
self.log_interp = log_interp_c(self.rr)
self.ylm_cr = csphar_jt([0.0,0.0,1.0], self.lbdmx+2*jmx)
return
def __init__(self, log_mesh, jmx=7, ngl=96, lbdmx=14):
"""
Expansion of the products of two atomic orbitals placed at given locations and around a center between these locations
[1] Talman JD. Multipole Expansions for Numerical Orbital Products, Int. J. Quant. Chem. 107, 1578--1584 (2007)
ngl : order of Gauss-Legendre quadrature
log_mesh : instance of log_mesh_c defining the logarithmic mesh (rr and pp arrays)
jmx : maximal angular momentum quantum number of each atomic orbital in a product
lbdmx : maximal angular momentum quantum number used for the expansion of the product phia*phib
"""
from numpy.polynomial.legendre import leggauss
from pyscf.nao.m_log_interp import log_interp_c
from pyscf.nao.m_csphar_talman_libnao import csphar_talman_libnao as csphar_jt
assert ngl > 2
assert jmx > -1
assert hasattr(log_mesh, 'rr')
assert hasattr(log_mesh, 'pp')
self.ngl = ngl
self.lbdmx = lbdmx
self.xx, self.ww = leggauss(ngl)
log_mesh_c.__init__(self)
self.init_log_mesh(log_mesh.rr, log_mesh.pp)
self.plval = np.zeros([2 * (self.lbdmx + jmx + 1), ngl])
self.plval[0, :] = 1.0
self.plval[1, :] = self.xx
for kappa in range(1, 2 * (self.lbdmx + jmx) + 1):
self.plval[kappa + 1, :] = (
(2 * kappa + 1) * self.xx * self.plval[kappa, :] -
kappa * self.plval[kappa - 1, :]) / (kappa + 1)
self.log_interp = log_interp_c(self.rr)
self.ylm_cr = csphar_jt([0.0, 0.0, 1.0], self.lbdmx + 2 * jmx)
return
def __init__(self, ao_log, sp):
self.ion = ao_log.sp2ion[sp]
self.rr,self.pp,self.nr = ao_log.rr,ao_log.pp,ao_log.nr
self.interp_rr = log_interp_c(self.rr)
self.interp_pp = log_interp_c(self.pp)
self.mu2j = ao_log.sp_mu2j[sp]
self.nmult= len(self.mu2j)
self.mu2s = ao_log.sp_mu2s[sp]
self.norbs= self.mu2s[-1]
self.mu2ff = ao_log.psi_log[sp]
self.mu2ff_rl = ao_log.psi_log_rl[sp]
self.mu2rcut = ao_log.sp_mu2rcut[sp]
self.rcut = np.amax(self.mu2rcut)
self.charge = ao_log.sp2charge[sp]
def __init__(self, ao_log, sp):
self.ion = ao_log.sp2ion[sp]
self.rr, self.pp, self.nr = ao_log.rr, ao_log.pp, ao_log.nr
self.interp_rr = log_interp_c(self.rr)
self.interp_pp = log_interp_c(self.pp)
self.mu2j = ao_log.sp_mu2j[sp]
self.nmult = len(self.mu2j)
self.mu2s = ao_log.sp_mu2s[sp]
self.norbs = self.mu2s[-1]
self.mu2ff = ao_log.psi_log[sp]
self.mu2ff_rl = ao_log.psi_log_rl[sp]
self.mu2rcut = ao_log.sp_mu2rcut[sp]
self.rcut = np.amax(self.mu2rcut)
self.charge = ao_log.sp2charge[sp]
def test_log_interp_vec(self):
""" Test the interpolation facility for an array arguments from the class log_interp_c """
rr,pp = log_mesh(1024, 0.01, 20.0)
log_interp = log_interp_c(rr)
gcs = np.array([1.2030, 3.2030, 0.7, 10.0])
ff = np.array([[np.exp(-gc*r**2) for r in rr] for gc in gcs])
for r in np.linspace(0.009, 25.0, 100):
yyref, yy = np.exp(-gcs*r**2), log_interp(ff, r)
for y,yref in zip(yy, yyref): self.assertAlmostEqual(y,yref)
def test_log_interp_vec(self):
""" Test the interpolation facility for an array arguments from the class log_interp_c """
rr,pp = log_mesh(1024, 0.01, 20.0)
log_interp = log_interp_c(rr)
gcs = np.array([1.2030, 3.2030, 0.7, 10.0])
ff = np.array([[np.exp(-gc*r**2) for r in rr] for gc in gcs])
for r in np.linspace(0.009, 25.0, 100):
yyref, yy = np.exp(-gcs*r**2), log_interp(ff, r)
for y,yref in zip(yy, yyref): self.assertAlmostEqual(y,yref)
def test_log_interp_sca(self):
""" Test the interpolation facility from the class log_interp_c """
rr, pp = log_mesh(1024, 0.01, 20.0)
log_interp = log_interp_c(rr)
gc = 1.2030
ff = np.array([np.exp(-gc * r**2) for r in rr])
for r in np.linspace(0.009, 25.0, 100):
y = log_interp(ff, r)
yrefa = np.exp(-gc * r**2)
self.assertAlmostEqual(y, yrefa)
def test_log_interp_sca(self):
""" Test the interpolation facility from the class log_interp_c """
rr,pp = log_mesh(1024, 0.01, 20.0)
log_interp = log_interp_c(rr)
gc = 1.2030
ff = np.array([np.exp(-gc*r**2) for r in rr])
for r in np.linspace(0.009, 25.0, 100):
y = log_interp(ff, r)
yrefa = np.exp(-gc*r**2)
self.assertAlmostEqual(y, yrefa)
def test_log_interp_sparse_coeffs(self):
""" Test the computation of interpolation coefficients """
rr,pp = funct_log_mesh(512, 0.01, 200.0)
lgi = log_interp_c(rr)
rrs = np.linspace(0.05, 250.0, 20000)
kr2c_csr,j2r = lgi.coeffs_csr(rrs, rcut=10.0)
j2r,j2k,ij2c = lgi.coeffs_rcut(rrs, rcut=10.0)
for r,k,cc in zip(j2r[0], j2k, ij2c.T):
for i in range(6):
self.assertEqual(cc[i], kr2c_csr[k+i,r])
def init_ao_log_ion(self, **kw):
"""
Reads data from a previous SIESTA calculation,
interpolates the Pseudo-Atomic Orbitals on a single log mesh.
"""
from pyscf.nao.m_log_interp import log_interp_c
from pyscf.nao.m_spline_diff2 import spline_diff2
from pyscf.nao.m_spline_interp import spline_interp
self.interp_rr,self.interp_pp = log_interp_c(self.rr), log_interp_c(self.pp)
sp2ion = self.sp2ion = kw['sp2ion']
fname = kw['fname'] if 'fname' in kw else 'paos'
if fname in sp2ion[0]:
self.siesta_ion_interp(sp2ion, fname=fname)
self.sp2vna = [None]*len(sp2ion) # Interpolate a Neutral-Atom potential V_NA(r) for each specie
self.sp2rcut_vna = np.zeros(len(sp2ion))
for isp, ion in enumerate(sp2ion):
if "vna" not in ion.keys(): continue
if ion["vna"] is None: continue
self.sp2rcut_vna[isp] = ion["vna"]["cutoff"]
h,dat = ion["vna"]["delta"][0], ion["vna"]["data"][0][:,1]
d2 = spline_diff2(h, dat, 0.0, 1.0e301)
self.sp2vna[isp] = np.array([0.5*spline_interp(h, dat, d2, r) for r in self.rr]) # given in Rydberg in sp2ion
self.sp2chlocal = [None]*len(sp2ion) # Interpolate the atomic charges for each specie
self.sp2rcut_chlocal = np.zeros(len(sp2ion))
for isp, ion in enumerate(sp2ion):
if "chlocal" not in ion.keys(): continue
if ion["chlocal"] is None: continue
self.sp2rcut_chlocal[isp] = ion["chlocal"]["cutoff"]
h,dat = ion["chlocal"]["delta"][0], ion["chlocal"]["data"][0][:,1]
d2 = spline_diff2(h, dat, 0.0, 1.0e301)
self.sp2chlocal[isp] = np.array([spline_interp(h, dat, d2, r) for r in self.rr])
return self
def test_log_interp_coeffs_vec(self):
""" Test the interpolation facility for an array arguments from the class log_interp_c """
rr,pp = log_mesh(1024, 0.01, 20.0)
lgi = log_interp_c(rr)
rvecs = np.linspace(0.00, 25.0, 20)
kk1,cc1 = np.zeros(len(rvecs), dtype=np.int32), np.zeros((6,len(rvecs)))
for i,rv in enumerate(rvecs): kk1[i],cc1[:,i] = lgi.coeffs(rv)
kk2,cc2 = lgi.coeffs_vv(rvecs)
for k1,c1,k2,c2 in zip(kk1,cc1,kk2,cc2):
self.assertEqual(k1,k2)
for y1,y2 in zip(c1,c2):
self.assertAlmostEqual(y1,y2)
def test_log_interp_sca(self):
""" """
from pyscf.nao.m_log_mesh import log_mesh
from pyscf.nao.m_log_interp import log_interp_c
rr, pp = log_mesh(1024, 0.01, 20.0)
log_interp = log_interp_c(rr)
gc = 1.2030
ff = np.array([np.exp(-gc * r**2) for r in rr])
for r in np.linspace(0.009, 25.0, 100):
y = log_interp(ff, r)
yrefa = np.exp(-gc * r**2)
self.assertAlmostEqual(y, yrefa)
def test_log_interp_vec(self):
""" """
from pyscf.nao.m_log_mesh import log_mesh
from pyscf.nao.m_log_interp import log_interp_c
rr, pp = log_mesh(1024, 0.01, 20.0)
log_interp = log_interp_c(rr)
gcs = np.array([1.2030, 3.2030, 0.7, 10.0])
ff = np.array([[np.exp(-gc * r**2) for r in rr] for gc in gcs])
for r in np.linspace(0.009, 25.0, 100):
yyref, yy = np.exp(-gcs * r**2), log_interp(ff, r)
for y, yref in zip(yy, yyref):
self.assertAlmostEqual(y, yref)
def test_log_interp_diff(self):
""" Test the differentiation facility from the class log_interp_c """
import matplotlib.pyplot as plt
rr, pp = log_mesh(1024, 0.001, 20.0)
logi = log_interp_c(rr)
gc = 1.2030
ff = np.array([np.exp(-gc * r**2) for r in rr])
ffd_ref = np.array([np.exp(-gc * r**2) * (-2.0 * gc * r) for r in rr])
ffd = logi.diff(ff)
ffd_np = np.gradient(ff, rr)
s = 3
for r, d, dref, dnp in zip(rr[s:], ffd[s:], ffd_ref[s:], ffd_np[s:]):
self.assertAlmostEqual(d, dref)
def init_ao_log_ion(self, sp2ion, **kvargs):
"""
Reads data from a previous SIESTA calculation,
interpolates the orbitals on a single log mesh.
"""
from pyscf.nao.m_log_interp import log_interp_c
from pyscf.nao.m_siesta_ion_interp import siesta_ion_interp
from pyscf.nao.m_siesta_ion_add_sp2 import _siesta_ion_add_sp2
import numpy as np
self.init_log_mesh_ion(sp2ion, **kvargs)
self.interp_rr, self.interp_pp = log_interp_c(self.rr), log_interp_c(
self.pp)
_siesta_ion_add_sp2(
self, sp2ion) # adds the fields for counting, .nspecies etc.
self.jmx = max([mu2j.max() for mu2j in self.sp_mu2j])
self.sp2norbs = np.array(
[mu2s[self.sp2nmult[sp]] for sp, mu2s in enumerate(self.sp_mu2s)],
dtype='int64')
self.psi_log = siesta_ion_interp(self.rr, sp2ion, 1)
self.psi_log_rl = siesta_ion_interp(self.rr, sp2ion, 0)
self.sp2ion = sp2ion
self.sp_mu2rcut = [
np.array(ion["paos"]["cutoff"], dtype='float64') for ion in sp2ion
]
self.sp2rcut = np.array([np.amax(rcuts) for rcuts in self.sp_mu2rcut],
dtype='float64')
self.sp2charge = [int(ion['z']) for ion in self.sp2ion]
self.sp2valence = [int(ion['valence']) for ion in self.sp2ion]
#call sp2ion_to_psi_log(sv%sp2ion, sv%rr, sv%psi_log)
#call init_psi_log_rl(sv%psi_log, sv%rr, sv%uc%mu_sp2j, sv%uc%sp2nmult, sv%psi_log_rl)
#call sp2ion_to_core(sv%sp2ion, sv%rr, sv%core_log, sv%sp2has_core, sv%sp2rcut_core)
return self
def test_log_interp_diff(self):
""" Test the differentiation facility from the class log_interp_c """
import matplotlib.pyplot as plt
rr,pp = log_mesh(1024, 0.001, 20.0)
logi = log_interp_c(rr)
gc = 1.2030
ff = np.array([np.exp(-gc*r**2) for r in rr])
ffd_ref = np.array([np.exp(-gc*r**2)*(-2.0*gc*r) for r in rr])
ffd = logi.diff(ff)
ffd_np = np.gradient(ff, rr)
s = 3
for r,d,dref,dnp in zip(rr[s:],ffd[s:],ffd_ref[s:],ffd_np[s:]):
self.assertAlmostEqual(d,dref)
def test_log_interp_sv_call(self):
""" Test the interpolation facility for an array arguments from the class log_interp_c """
rr,pp = log_mesh(256, 0.01, 20.0)
lgi = log_interp_c(rr)
gc = 1.2030
ff = np.array([np.exp(-gc*r**2) for r in rr])
rvecs = np.linspace(0.05, 25.0, 200)
r2yy = lgi(ff, rvecs)
for ir, r in enumerate(rvecs):
yref = np.exp(-gc*r**2)
y1 = lgi(ff, r)
self.assertAlmostEqual(y1,yref)
self.assertAlmostEqual(r2yy[ir],yref)
def test_log_interp_coeffs_vec(self):
""" Test the interpolation facility for an array arguments from the class log_interp_c """
rr, pp = log_mesh(1024, 0.01, 20.0)
lgi = log_interp_c(rr)
rvecs = np.linspace(0.00, 25.0, 20)
kk1, cc1 = np.zeros(len(rvecs), dtype=np.int32), np.zeros(
(6, len(rvecs)))
for i, rv in enumerate(rvecs):
kk1[i], cc1[:, i] = lgi.coeffs(rv)
kk2, cc2 = lgi.coeffs_vv(rvecs)
for k1, c1, k2, c2 in zip(kk1, cc1, kk2, cc2):
self.assertEqual(k1, k2)
for y1, y2 in zip(c1, c2):
self.assertAlmostEqual(y1, y2)
def test_log_interp_sv_call(self):
""" Test the interpolation facility for an array arguments from the class log_interp_c """
rr, pp = log_mesh(256, 0.01, 20.0)
lgi = log_interp_c(rr)
gc = 1.2030
ff = np.array([np.exp(-gc * r**2) for r in rr])
rvecs = np.linspace(0.05, 25.0, 200)
r2yy = lgi(ff, rvecs)
for ir, r in enumerate(rvecs):
yref = np.exp(-gc * r**2)
y1 = lgi(ff, r)
self.assertAlmostEqual(y1, yref)
self.assertAlmostEqual(r2yy[ir], yref)
def test_log_interp_vv_speed(self):
""" Test the interpolation facility for an array arguments from the class log_interp_c """
rr,pp = funct_log_mesh(1024, 0.01, 200.0)
lgi = log_interp_c(rr)
gcs = np.array([1.2030, 3.2030, 0.7, 10.0, 5.3])
ff = np.array([[np.exp(-gc*r**2) for r in rr] for gc in gcs])
rr = np.linspace(0.05, 250.0, 2000000)
t1 = timer()
fr2yy = lgi.interp_rcut(ff, rr, rcut=16.0)
t2 = timer()
#print(__name__, 't2-t1: ', t2-t1)
yyref = np.exp(-(gcs.reshape(gcs.size,1)) * (rr.reshape(1,rr.size)**2))
self.assertTrue(np.allclose(fr2yy, yyref) )
def test_log_interp_vv(self):
""" Test the interpolation facility for an array arguments from the class log_interp_c """
rr, pp = log_mesh(256, 0.01, 20.0)
lgi = log_interp_c(rr)
gcs = np.array([1.2030, 3.2030, 0.7, 10.0])
ff = np.array([[np.exp(-gc * r**2) for r in rr] for gc in gcs])
rvecs = np.linspace(0.05, 25.0, 200)
fr2yy = lgi.interp_vv(ff, rvecs)
yy_vv1 = np.zeros((len(ff), len(rvecs)))
for ir, r in enumerate(rvecs):
yyref = np.exp(-gcs * r**2)
yy = yy_vv1[:, ir] = lgi.interp_vv(ff, r)
for y1, yref, y2 in zip(yy, yyref, fr2yy[:, ir]):
self.assertAlmostEqual(y1, yref)
self.assertAlmostEqual(y2, yref)
def test_log_interp_vv(self):
""" Test the interpolation facility for an array arguments from the class log_interp_c """
rr,pp = log_mesh(256, 0.01, 20.0)
lgi = log_interp_c(rr)
gcs = np.array([1.2030, 3.2030, 0.7, 10.0])
ff = np.array([[np.exp(-gc*r**2) for r in rr] for gc in gcs])
rvecs = np.linspace(0.05, 25.0, 200)
fr2yy = lgi.interp_vv(ff, rvecs)
yy_vv1 = np.zeros((len(ff),len(rvecs)))
for ir, r in enumerate(rvecs):
yyref = np.exp(-gcs*r**2)
yy = yy_vv1[:,ir] = lgi.interp_vv(ff, r)
for y1,yref,y2 in zip(yy, yyref,fr2yy[:,ir]):
self.assertAlmostEqual(y1,yref)
self.assertAlmostEqual(y2,yref)
def _init_ao_log_gto(self, **kw):
""" supposed to be private """
import numpy as np
from pyscf.nao.m_log_interp import log_interp_c
self.interp_rr,self.interp_pp = log_interp_c(self.rr), log_interp_c(self.pp)
sv = nao = kw['nao']
rcut_tol = kw['rcut_tol']
gto = kw['gto'] if 'gto' in kw else nao.gto
self.sp_mu2j = [0]*sv.nspecies
self.psi_log = [0]*sv.nspecies
self.psi_log_rl = [0]*sv.nspecies
self.sp2nmult = np.zeros(sv.nspecies, dtype=np.int64)
self.nspecies = sv.nspecies
seen_species = [] # this is auxiliary to organize the loop over species
for ia,sp in enumerate(sv.atom2sp):
if sp in seen_species: continue
seen_species.append(sp)
self.sp2nmult[sp] = nmu = sum([gto.bas_nctr(sid) for sid in gto.atom_shell_ids(ia)])
mu2ff = np.zeros((nmu, self.nr))
mu2ff_rl = np.zeros((nmu, self.nr))
mu2j = np.zeros(nmu, dtype=np.int64)
mu = -1
for sid in gto.atom_shell_ids(ia):
pows, coeffss = gto.bas_exp(sid), gto.bas_ctr_coeff(sid)
for coeffs in coeffss.T:
mu=mu+1
l = mu2j[mu] = gto.bas_angular(sid)
for ir, r in enumerate(self.rr):
mu2ff_rl[mu,ir] = sum(pows[:]**((2*l+3)/4.0)*coeffs[:]*np.exp(-pows[:]*r**2))
mu2ff[mu,ir] = r**l*mu2ff_rl[mu,ir]
self.sp_mu2j[sp] = mu2j
norms = [np.sqrt(self.interp_rr.dg_jt*sum(ff**2*self.rr**3)) for ff in mu2ff]
for mu,norm in enumerate(norms):
mu2ff[mu,:] = mu2ff[mu,:]/norm
mu2ff_rl[mu,:] = mu2ff_rl[mu,:]/norm
self.psi_log[sp] = mu2ff
self.psi_log_rl[sp] = mu2ff_rl
self.jmx = max([mu2j.max() for mu2j in self.sp_mu2j])
self.sp_mu2s = []
for mu2j in self.sp_mu2j:
mu2s = np.zeros(len(mu2j)+1, dtype=np.int64)
for mu,j in enumerate(mu2j): mu2s[mu+1] = mu2s[mu]+2*j+1
self.sp_mu2s.append(mu2s)
self.sp2norbs = np.array([mu2s[-1] for mu2s in self.sp_mu2s])
self.sp2charge = sv.sp2charge
self.sp_mu2rcut = []
for sp, mu2ff in enumerate(self.psi_log):
mu2rcut = np.zeros(len(mu2ff))
for mu,ff in enumerate(mu2ff):
ffmx,irmx = abs(mu2ff[mu]).max(), abs(mu2ff[mu]).argmax()
irrp = np.argmax(abs(ff[irmx:])<ffmx*rcut_tol)
irrc = irmx+irrp if irrp>0 else -1
mu2rcut[mu] = self.rr[irrc]
self.sp_mu2rcut.append(mu2rcut)
self.sp2rcut = np.array([mu2rcut.max() for mu2rcut in self.sp_mu2rcut])
return self
def init_ao_log_ion(self, sp2ion, **kw):
"""
Reads data from a previous SIESTA calculation,
interpolates the orbitals on a single log mesh.
"""
from pyscf.nao.m_log_interp import log_interp_c
from pyscf.nao.m_siesta_ion_interp import siesta_ion_interp
from pyscf.nao.m_siesta_ion_add_sp2 import _siesta_ion_add_sp2
from pyscf.nao.m_spline_diff2 import spline_diff2
from pyscf.nao.m_spline_interp import spline_interp
import numpy as np
self.init_log_mesh_ion(sp2ion, **kw)
#print(__name__, self.nr)
#print(__name__, self.rr)
#print(__name__, self.rmax)
#print(__name__, self.rmin)
#print(__name__, self.kmax)
self.interp_rr, self.interp_pp = log_interp_c(self.rr), log_interp_c(
self.pp)
_siesta_ion_add_sp2(
self, sp2ion) # adds the fields for counting, .nspecies etc.
self.jmx = max([mu2j.max() for mu2j in self.sp_mu2j])
self.sp2norbs = np.array(
[mu2s[self.sp2nmult[sp]] for sp, mu2s in enumerate(self.sp_mu2s)],
dtype='int64')
self.sp2ion = sp2ion
rr = self.rr
nr = len(rr)
#print(__name__, 'self.jmx', self.jmx)
#print(__name__, 'self.sp2norbs', self.sp2norbs)
#print(__name__, 'self.sp2norbs', dir(self))
#print(__name__, 'self.sp_mu2j', self.sp_mu2j)
#print(__name__, 'self.sp_mu2rcut', self.sp_mu2rcut)
#print(__name__, 'self.sp_mu2s', self.sp_mu2s)
self.psi_log = siesta_ion_interp(rr, sp2ion, 1)
self.psi_log_rl = siesta_ion_interp(rr, sp2ion, 0)
self.sp2vna = [
] # Interpolate a Neutral-atom potential V_NA(r) for each specie
for ion in sp2ion:
vna = np.zeros(nr)
if ion["vna"] is not None:
h, dat = ion["vna"]["delta"], ion["vna"]["data"][0][:, 1]
yy_diff2 = spline_diff2(h, dat, 0.0, 1.0e301)
for ir, r in enumerate(rr):
vna[ir] = spline_interp(h, dat, yy_diff2, r)
self.sp2vna.append(vna * 0.5) # given in Rydberg?
self.sp_mu2rcut = [np.array(ion["paos"]["cutoff"]) for ion in sp2ion]
self.sp2rcut = np.array([np.amax(rcuts) for rcuts in self.sp_mu2rcut])
self.sp2charge = [int(ion['z']) for ion in self.sp2ion]
self.sp2valence = [int(ion['valence']) for ion in self.sp2ion]
#call sp2ion_to_psi_log(sv%sp2ion, sv%rr, sv%psi_log)
#call init_psi_log_rl(sv%psi_log, sv%rr, sv%uc%mu_sp2j, sv%uc%sp2nmult, sv%psi_log_rl)
#call sp2ion_to_core(sv%sp2ion, sv%rr, sv%core_log, sv%sp2has_core, sv%sp2rcut_core)
return self
def __init__(self, gg):
#assert(type(rr)==np.ndarray)
assert(len(gg)>2)
self.nr = len(gg)
self.gammin_jt = np.log(gg[0])
self.dg_jt = np.log(gg[1]/gg[0])
def __call__(self, ff, r):
assert ff.shape[-1]==self.nr
k,cc = comp_coeffs(self, r)
result = np.zeros(ff.shape[0:-2])
for j,c in enumerate(cc): result = result + c*ff[...,j+k]
return result
# Example:
# loginterp =log_interp_c(rr)
if __name__ == '__main__':
from pyscf.nao.m_log_interp import log_interp, log_interp_c, comp_coeffs_
from pyscf.nao.m_log_mesh import log_mesh
rr,pp = log_mesh(1024, 0.01, 20.0)
interp_c = log_interp_c(rr)
gc = 0.234450
ff = np.array([np.exp(-gc*r**2) for r in rr])
rho_min_jt, dr_jt = np.log(rr[0]), np.log(rr[1]/rr[0])
for r in np.linspace(0.01, 25.0, 100):
yref = log_interp(ff, r, rho_min_jt, dr_jt)
k,coeffs = comp_coeffs(interp_c, r)
y = sum(coeffs*ff[k:k+6])
if(abs(y-yref)>1e-15): print(r, yref, y, np.exp(-gc*r**2))
def init_ao_log_gto(self, **kw):
""" supposed to be private """
import numpy as np
from pyscf.nao.m_log_interp import log_interp_c
self.interp_rr,self.interp_pp = log_interp_c(self.rr), log_interp_c(self.pp)
gto,rcut_tol = kw['gto'],self.rcut_tol
a2s = [gto.atom_symbol(ia) for ia in range(gto.natm) ]
self.sp2symbol = sorted(list(set(a2s)))
nspecies = self.nspecies = len(self.sp2symbol)
atom2sp = np.array([self.sp2symbol.index(s) for s in a2s], dtype=np.int64)
self.sp2charge = np.array([-999]*self.nspecies, dtype=np.int64)
for ia,sp in enumerate(atom2sp): self.sp2charge[sp]=gto.atom_charge(ia)
self.sp_mu2j = [0]*nspecies
self.psi_log = [0]*nspecies
self.psi_log_rl = [0]*nspecies
self.sp2nmult = np.zeros(nspecies, dtype=np.int64)
seen_species = [] # this is auxiliary to organize the loop over species
for ia,sp in enumerate(atom2sp):
if sp in seen_species: continue
seen_species.append(sp)
self.sp2nmult[sp] = nmu = sum([gto.bas_nctr(sid) for sid in gto.atom_shell_ids(ia)])
mu2ff = np.zeros((nmu, self.nr))
mu2ff_rl = np.zeros((nmu, self.nr))
mu2j = np.zeros(nmu, dtype=np.int64)
mu = -1
for sid in gto.atom_shell_ids(ia):
pows, coeffss = gto.bas_exp(sid), gto.bas_ctr_coeff(sid)
for coeffs in coeffss.T:
mu=mu+1
l = mu2j[mu] = gto.bas_angular(sid)
for ir, r in enumerate(self.rr):
mu2ff_rl[mu,ir] = sum(pows[:]**((2*l+3)/4.0)*coeffs[:]*np.exp(-pows[:]*r**2))
mu2ff[mu,ir] = r**l*mu2ff_rl[mu,ir]
self.sp_mu2j[sp] = mu2j
norms = [np.sqrt(self.interp_rr.dg_jt*sum(ff**2*self.rr**3)) for ff in mu2ff]
for mu,norm in enumerate(norms):
mu2ff[mu,:] = mu2ff[mu,:]/norm
mu2ff_rl[mu,:] = mu2ff_rl[mu,:]/norm
self.psi_log[sp] = mu2ff
self.psi_log_rl[sp] = mu2ff_rl
self.jmx = max([mu2j.max() for mu2j in self.sp_mu2j])
self.sp_mu2s = []
for mu2j in self.sp_mu2j:
mu2s = np.zeros(len(mu2j)+1, dtype=np.int64)
for mu,j in enumerate(mu2j): mu2s[mu+1] = mu2s[mu]+2*j+1
self.sp_mu2s.append(mu2s)
self.sp2norbs = np.array([mu2s[-1] for mu2s in self.sp_mu2s])
self.sp_mu2rcut = []
for sp, mu2ff in enumerate(self.psi_log):
mu2rcut = np.zeros(len(mu2ff))
for mu,ff in enumerate(mu2ff):
ffmx,irmx = abs(mu2ff[mu]).max(), abs(mu2ff[mu]).argmax()
irrp = np.argmax(abs(ff[irmx:])<ffmx*rcut_tol)
irrc = irmx+irrp if irrp>0 else -1
mu2rcut[mu] = self.rr[irrc]
self.sp_mu2rcut.append(mu2rcut)
self.sp2rcut = np.array([mu2rcut.max() for mu2rcut in self.sp_mu2rcut])
return self
def init_ao_log_gpaw(self, setups, **kvargs):
""" Reads radial orbitals from a previous GPAW calculation. """
from pyscf.nao.m_log_interp import log_interp_c
from pyscf.nao.m_siesta_ion_interp import siesta_ion_interp
#self.setups = setups if setup is saved in ao_log, we grt the following error
# while performing copy
# File "/home/marc/anaconda2/lib/python2.7/copy.py", line 182, in deepcopy
# rv = reductor(2)
# TypeError: can't pickle Spline objects
self.init_log_mesh_gpaw(setups, **kvargs)
self.interp_rr,self.interp_pp = log_interp_c(self.rr), log_interp_c(self.pp)
sdic = setups.setups
self.sp2key = sdic.keys()
#key0 = sdic.keys()[0]
#print(key0, sdic[key0].Z, dir(sdic[key0]))
self.sp_mu2j = [np.array(sdic[key].l_orb_j, np.int64) for key in sdic.keys()]
self.sp2nmult = np.array([len(mu2j) for mu2j in self.sp_mu2j], dtype=np.int64)
self.sp2charge = np.array([sdic[key].Z for key in sdic.keys()], dtype=np.int64)
self.nspecies = len(self.sp_mu2j)
self.jmx = max([max(mu2j) for mu2j in self.sp_mu2j])
self.sp2norbs = np.array([sum(2*mu2j+1) for mu2j in self.sp_mu2j], dtype=np.int64)
self.sp_mu2rcut = []
self.psi_log_rl = []
self.psi_log = []
for sp,[key,nmu,mu2j] in enumerate(zip(sdic.keys(), self.sp2nmult, self.sp_mu2j)):
self.sp_mu2rcut.append(np.array([phit.get_cutoff() for phit in sdic[key].phit_j]))
mu2ff = np.zeros([nmu, self.nr])
for mu,phit in enumerate(sdic[key].phit_j):
for ir, r in enumerate(self.rr):
mu2ff[mu,ir],deriv = phit.get_value_and_derivative(r)
self.psi_log_rl.append(mu2ff)
self.psi_log.append(mu2ff* (self.rr**mu2j[mu]))
self.sp2rcut = np.array([np.amax(rcuts) for rcuts in self.sp_mu2rcut], dtype='float64') # derived from sp_mu2rcut
self.sp_mu2s = [] # derived from sp_mu2j
for mu2j in self.sp_mu2j:
mu2s = np.zeros(len(mu2j)+1, dtype=np.int64)
for mu,j in enumerate(mu2j): mu2s[mu+1] = mu2s[mu]+2*j+1
self.sp_mu2s.append(mu2s)
#self._add_sp2info()
#self._add_psi_log_mom()
#print(self.sp_mu2j)
#print(self.sp2nmult)
#print(self.nspecies)
#print(self.jmx)
#print(self.sp2norbs)
#print(self.sp_mu2rcut)
#print(self.psi_log)
#print(self.sp2charge)
#print(self.sp2rcut)
#print(self.sp_mu2s)
return self
