def s2n(N, tmpdir='/tmp', Sg=1, Sv=1):
"""
S[2]*N linear transformation:
<[q,k]> = <[E(Sg)_{ij}, k_{kl}, E(Sv)_{kl}]> =
= k_{kl} [E_{il}d(kj) - E(kj)d(il)]
= k(jl)E(SgSv)(il) - k(ki)E(SgSv)(kj)
= D(SgSv)k.T(ij) - k.TD(SgSv)(ij)
= [D(SgSv), k.T](ij)
"""
SIRIFC = os.path.join(tmpdir, 'SIRIFC')
AOONEINT = os.path.join(tmpdir, 'AOONEINT')
AOTWOINT = os.path.join(tmpdir, 'AOTWOINT')
LUINDF = os.path.join(tmpdir, 'LUINDF')
ifc = sirifc.sirifc(SIRIFC)
cmo = ifc.cmo.unblock()
S = one.read('OVERLAP', filename=AOONEINT).unblock().unpack()
da, db = dens.Dab(SIRIFC)
kN = rspvec.tomat(N, ifc, tmpdir=tmpdir).T
kn = cmo*kN*cmo.T
dak = (kn.T*S*da - da*S*kn.T)
dbk = (kn.T*S*db - db*S*kn.T)*Sv
gv = -rspvec.tovec(cmo.T*S*(dak+Sg*dbk)*S*cmo, ifc)
return gv
def test_tovec(self):
Nx = rspvec.read("XDIPLEN", propfile=self.RSPVEC)["XDIPLEN"]
kx = rspvec.tomat(Nx, self.ifc, tmpdir=self.tmpdir)
Nx = rspvec.tovec(kx, self.ifc, tmpdir=self.tmpdir)
this = Nx[44]
ref = 0.75732690
assert this == approx(ref)
def e2n(N, tmpdir='/tmp', hfx=1, Sg=1, Sv=1):
"""
E[2]*N linear transformation:
[k,F] = [k(pq)E(Sv)(pq), F(rs)E(rs)]
= k(pq)F(rs) (E(ps)d(rq) - E(rq)d(ps))
= k(pq)F(ps)E(ps) - k(pq)F(rp)E(rq)
= [k,F](pq)E(pq)
= kF
<[q,kF]> = <[E_{pq}, kF(rs)E(rs)]>
= kF(rs) <E(ps)d(rq) - E(rq)d(ps)>
= kF(qs)D(ps) - kF(rp)D(rq)
= [D, kF.T](pq)
kD = <[k, E(pq)]>
= <[k(rs) E(rs), E(pq)]>
= k(rs) (E(rq)d(ps) - E(ps)d(rq))
= k(rp)D(rq) - k(qs)D(ps)
= [k.T, D](p,q)
Fk = F[kD]
"""
SIRIFC = os.path.join(tmpdir, 'SIRIFC')
AOONEINT = os.path.join(tmpdir, 'AOONEINT')
AOTWOINT = os.path.join(tmpdir, 'AOTWOINT')
LUINDF = os.path.join(tmpdir, 'LUINDF')
ifc = sirifc.sirifc(SIRIFC)
cmo = get_cmo(AOONEINT, SIRIFC)
h = one.read('ONEHAMIL', filename=AOONEINT).unblock().unpack()
S = one.read('OVERLAP', filename=AOONEINT).unblock().unpack().view(util.full.matrix)
da, db = get_densities(SIRIFC)
kN = rspvec.tomat(N, ifc, tmpdir=tmpdir).view(util.full.matrix).T
kn = (cmo*kN*cmo.T).view(util.full.matrix)
dak = (kn.T*S*da - da*S*kn.T)
dbk = (kn.T*S*db - db*S*kn.T)*Sv
(fa, fb), = two.fockab((da, db), filename=AOTWOINT, hfx=hfx)
fa += h; fb += h
(fak, fbk), = two.fockab((dak, dbk), filename=AOTWOINT, hfx=hfx)
kfa = (S*kn*fa - fa*kn*S)
kfb = (S*kn*fb - fb*kn*S)*Sv
fa = fak + kfa
fb = fbk + kfb
gao = S*(da*fa.T + Sg*db*fb.T) - (fa.T*da + Sg*fb.T*db)*S
gm = cmo.T*gao*cmo
# sign convention <[q,[k,F]]> = -E[2]*N
gv = - rspvec.tovec(gm, ifc)
return gv
def setUp(self):
n, e = os.path.splitext(__file__)
self.suppdir = n + ".d"
self.A = "XDIPLEN"
self.B = "YDIPLEN"
self.C = "XDIPLEN"
AOONEINT = os.path.join(self.suppdir, 'AOONEINT')
S = one.read(label="OVERLAP", filename=AOONEINT).unblock().unpack()
SIRIFC = os.path.join(self.suppdir, 'SIRIFC')
self.ifc = sirifc.sirifc(SIRIFC)
cmo = self.ifc.cmo.unblock()
da, db = dens.Dab(ifc_=self.ifc)
self.D = cmo.T * S * (da + db) * S * cmo
RSPVEC = os.path.join(self.suppdir, 'RSPVEC')
rspvecs = rspvec.read(self.A, self.B, self.C, propfile=RSPVEC)
self.NA = rspvecs[(self.A, 0)]
self.NB = rspvecs[(self.B, 0)]
self.NC = rspvecs[(self.C, 0)]
self.kA = rspvec.tomat(self.NA, self.ifc, tmpdir=self.suppdir)
self.kB = rspvec.tomat(self.NB, self.ifc, tmpdir=self.suppdir).T
self.kC = rspvec.tomat(self.NC, self.ifc, tmpdir=self.suppdir).T
AOPROPER = os.path.join(self.suppdir, 'AOPROPER')
#a, b, c = [cmo.T*x*cmo for x in prop.read(A, B, C, filename=AOPROPER, unpack=True)]
global pmat
pmat = prop.read(self.A,
self.B,
self.C,
filename=AOPROPER,
unpack=True)
self.a, self.b, self.c = [cmo.T * x * cmo for x in pmat]
def a2bc(A, B, C):
AOONEINT = os.path.join(tmp, "AOONEINT")
AOPROPER = os.path.join(tmp, "AOPROPER")
RSPVEC = os.path.join(tmp, "RSPVEC")
SIRIFC = os.path.join(tmp, "SIRIFC")
NB = rspvec.read(B, RSPVEC)
NC = rspvec.read(C, RSPVEC)
ifc = sirifc.sirifc(SIRIFC)
cmo = ifc.cmo.unblock()
dc,do = dens.ifc(ifc=ifc)
d = dc+do
a = cmo.T*prop.read(A, AOPROPER).unpack()*cmo
kB = rspvec.tomat(NB, ifc, tmpdir = tmp).T
kC = rspvec.tomat(NC, ifc, tmpdir = tmp).T
S = one.read(label = "OVERLAP", filename = AOONEINT).unblock().unpack()
D = cmo.T*S*d*S*cmo
A2B = (.5*(kC^(kB^a))&D)
A2C = (.5*(kB^(kC^a))&D)
return A2B + A2C
def main(*args, **kwargs):
labs = args
tmpdir = kwargs.get("tmpdir", ".")
ranks = kwargs.get('rank', (0, 0, 0))
pars = [ (-1)**r for r in ranks]
ifc = sirifc.sirifc(os.path.join(tmpdir, "SIRIFC"))
cmo = ifc.cmo.unblock()
AOONEINT = os.path.join(tmpdir, "AOONEINT")
AOPROPER = os.path.join(tmpdir, "AOPROPER")
RSPVEC = os.path.join(tmpdir, "RSPVEC")
vecs = rspvec.read(*labs, propfile=RSPVEC)[0]
kappa = [rspvec.tomat(vec, ifc).T for vec in vecs]
kappa[0] = kappa[0].T
a, b, c = [cmo.T*x*cmo for x in prop.read(*labs, filename=AOPROPER)]
NA = vecs[0]
kA, kB, kC = kappa
pA, pB, pC = [{ "lab":lab, "rank":rank, 'kappa':k} for lab, rank, k in zip(labs, ranks, kappa)]
da, db = dens.Dab(ifc_=ifc)
d = da + db
S = one.read(label = "OVERLAP", filename = AOONEINT).unblock().unpack()
D = cmo.T*S*d*S*cmo
E3BC = E3(pB, pC, ifc, tmpdir=tmpdir)
AE3BC = -NA&E3BC
B2C = (-(kA^(kC^b))&D)
C2B = (-(kA^(kB^c))&D)
A2B = (.5*(kC^(kB^a))&D)
A2C = (.5*(kB^(kC^a))&D)
#print "E3BC",E3BC
val = AE3BC
print("E3 %14.8f %14.8f" % (AE3BC, val))
val += B2C
print("B2C %14.8f %14.8f" % (B2C, val))
val += C2B
print("C2B %14.8f %14.8f" % (C2B, val))
val += A2B
print("A2B %14.8f %14.8f" % (A2B, val))
val += A2C
print("A2C %14.8f %14.8f" % (A2C, val))
return val
def vec2mat(self, vec):
ifc = self._sirifc()
mat = rspvec.tomat(vec, ifc)
return mat
def test_tovec(self):
ref = rspvec.read("XDIPLEN", propfile=self.RSPVEC)["XDIPLEN"]
kx = rspvec.tomat(ref, self.ifc, tmpdir=self.tmpdir)
this = rspvec.tovec(kx, self.ifc, tmpdir=self.tmpdir)
np.testing.assert_almost_equal(this, ref)
def test_tomat(self):
Nx = rspvec.read("XDIPLEN", propfile=self.RSPVEC)["XDIPLEN"]
kx = rspvec.tomat(Nx, self.ifc, tmpdir=self.tmpdir)
this = kx[5, 7]
ref = -2.34009730
assert this == approx(ref)