def test_prdred_eval(self):
from pyscf.nao.m_prod_talman import prod_talman_c
from pyscf.nao.m_ao_eval_libnao import ao_eval_libnao as ao_eval
from pyscf.nao.m_csphar_talman_libnao import csphar_talman_libnao as csphar_jt
from pyscf.nao.m_siesta_ion_xml import siesta_ion_xml
from pyscf.nao import ao_log_c
from numpy import sqrt, zeros, array
import os
dname = os.path.dirname(os.path.abspath(__file__))
sp2ion = []
sp2ion.append(siesta_ion_xml(dname + '/O.ion.xml'))
aos = ao_log_c().init_ao_log_ion(sp2ion)
jmx = aos.jmx
pt = prod_talman_c(aos)
spa, spb = 0, 0
rav, rbv, rcv = array([0.0, 0.0, -1.0]), array([0.0, 0.0,
1.0]), zeros(3)
coord = np.array(
[0.4, 0.1, 0.22]
) # Point at which we will compute the expansion and the original product
ylma, ylmb, ylmc = csphar_jt(coord - rav, jmx), csphar_jt(
coord - rbv, jmx), csphar_jt(coord + rcv, pt.lbdmx)
rcs = sqrt(sum((coord + rcv)**2))
serr = 0.0
merr = 0.0
nval = 0
for la, phia in zip(aos.sp_mu2j[spa], aos.psi_log[spa]):
fa = pt.log_interp(phia, sqrt(sum((coord - rav)**2)))
for lb, phib in zip(aos.sp_mu2j[spb], aos.psi_log[spb]):
fb = pt.log_interp(phib, sqrt(sum((coord - rbv)**2)))
jtb, clbdtb, lbdtb = pt.prdred_terms(la, lb)
jtb, clbdtb, lbdtb, rhotb = pt.prdred_libnao(
phib, lb, rbv, phia, la, rav, rcv)
rhointerp = pt.log_interp(rhotb, rcs)
for ma in range(-la, la + 1):
aovala = ylma[la * (la + 1) + ma] * fa
for mb in range(-lb, lb + 1):
aovalb = ylmb[lb * (lb + 1) + mb] * fb
ffr, m = pt.prdred_further_scalar(
la, ma, lb, mb, rcv, jtb, clbdtb, lbdtb, rhointerp)
prdval = 0.0j
for j, fr in enumerate(ffr):
prdval = prdval + fr * ylmc[j * (j + 1) + m]
derr = abs(aovala * aovalb - prdval)
nval = nval + 1
serr = serr + derr
merr = max(merr, derr)
self.assertTrue(merr < 1.0e-05)
self.assertTrue(serr / nval < 1.0e-06)
def test_prdred_eval(self):
from pyscf.nao.m_prod_talman import prod_talman_c
from pyscf.nao.m_ao_eval_libnao import ao_eval_libnao as ao_eval
from pyscf.nao.m_csphar_talman_libnao import csphar_talman_libnao as csphar_jt
from pyscf.nao.m_siesta_ion_xml import siesta_ion_xml
from pyscf.nao import ao_log_c
from numpy import sqrt, zeros, array
import os
dname = os.path.dirname(os.path.abspath(__file__))
sp2ion = []
sp2ion.append(siesta_ion_xml(dname+'/O.ion.xml'))
aos = ao_log_c().init_ao_log_ion(sp2ion)
jmx = aos.jmx
pt = prod_talman_c(aos)
spa,spb=0,0
rav,rbv,rcv = array([0.0,0.0,-1.0]),array([0.0,0.0,1.0]), zeros(3)
coord = np.array([0.4, 0.1, 0.22]) # Point at which we will compute the expansion and the original product
ylma,ylmb,ylmc = csphar_jt(coord-rav, jmx), csphar_jt(coord-rbv, jmx),csphar_jt(coord+rcv, pt.lbdmx)
rcs = sqrt(sum((coord+rcv)**2))
serr = 0.0
merr = 0.0
nval = 0
for la,phia in zip(aos.sp_mu2j[spa], aos.psi_log[spa]):
fa = pt.log_interp(phia, sqrt(sum((coord-rav)**2)))
for lb,phib in zip(aos.sp_mu2j[spb], aos.psi_log[spb]):
fb = pt.log_interp(phib, sqrt(sum((coord-rbv)**2)))
jtb,clbdtb,lbdtb=pt.prdred_terms(la,lb)
jtb,clbdtb,lbdtb,rhotb = pt.prdred_libnao(phib,lb,rbv,phia,la,rav,rcv)
rhointerp = pt.log_interp(rhotb, rcs)
for ma in range(-la,la+1):
aovala = ylma[la*(la+1)+ma]*fa
for mb in range(-lb,lb+1):
aovalb = ylmb[lb*(lb+1)+mb]*fb
ffr,m = pt.prdred_further_scalar(la,ma,lb,mb,rcv,jtb,clbdtb,lbdtb,rhointerp)
prdval = 0.0j
for j,fr in enumerate(ffr): prdval = prdval + fr*ylmc[j*(j+1)+m]
derr = abs(aovala*aovalb-prdval)
nval = nval + 1
serr = serr + derr
merr = max(merr, derr)
self.assertTrue(merr<1.0e-05)
self.assertTrue(serr/nval<1.0e-06)
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 prdred_further(self, ja,ma,jb,mb,rcen,jtb,clbdtb,lbdtb,rhotb):
""" Evaluate the Talman's expansion at given Cartesian coordinates"""
from pyscf.nao.m_thrj import thrj
from pyscf.nao.m_fact import sgn
from pyscf.nao.m_csphar_talman_libnao import csphar_talman_libnao as csphar_jt
from numpy import zeros, sqrt, pi, array
assert all(rcen == zeros(3)) # this works only when center is at the origin
nterm = len(jtb)
assert nterm == len(clbdtb)
assert nterm == len(lbdtb)
assert nterm == rhotb.shape[0]
assert self.nr == rhotb.shape[1]
ffr = zeros([self.lbdmx+1,self.nr], np.complex128)
m = mb + ma
ylm_cr = csphar_jt([0.0,0.0,1.0], lbdtb.max())
for j,clbd,lbd,rho in zip(jtb,clbdtb,lbdtb,rhotb):
ffr[clbd,:]=ffr[clbd,:] + thrj(ja,jb,j,ma,mb,-m)*thrj(j,clbd,lbd,-m,m,0)*rho*ylm_cr[lbd*(lbd+1)]
return ffr,m
def prdred_further(self, ja, ma, jb, mb, rcen, jtb, clbdtb, lbdtb, rhotb):
""" Evaluate the Talman's expansion at given Cartesian coordinates"""
from pyscf.nao.m_thrj import thrj
from pyscf.nao.m_fact import sgn
from pyscf.nao.m_csphar_talman_libnao import csphar_talman_libnao as csphar_jt
from numpy import zeros, sqrt, pi, array
assert all(
rcen == zeros(3)) # this works only when center is at the origin
nterm = len(jtb)
assert nterm == len(clbdtb)
assert nterm == len(lbdtb)
assert nterm == rhotb.shape[0]
assert self.nr == rhotb.shape[1]
ffr = zeros([self.lbdmx + 1, self.nr], np.complex128)
m = mb + ma
ylm_cr = csphar_jt([0.0, 0.0, 1.0], lbdtb.max())
for j, clbd, lbd, rho in zip(jtb, clbdtb, lbdtb, rhotb):
ffr[clbd, :] = ffr[clbd, :] + thrj(ja, jb, j, ma, mb, -m) * thrj(
j, clbd, lbd, -m, m, 0) * rho * ylm_cr[lbd * (lbd + 1)]
return ffr, m