def oimp_matrix_form(oimp,ops_configs,cocc,vocc):
# matrix elements of
# sum < | oimp | > where oimp acts only on the imp+bath space
# cocc, vocc: lists of core, virtual labels
assert not oimp.fermion # operator should have an even number of c/d operators
start={}
end={}
nconfigs=[len(configs) for (ops, configs) in ops_configs]
ops=[opi for (opi, configi) in ops_configs]
for i, opi in enumerate(ops):
start[opi]=sum(nconfigs[:i])
end[opi]=start[opi]+nconfigs[i]
full_mat=utils.zeros([sum(nconfigs),sum(nconfigs)])
for i, (opi, configsi) in enumerate(ops_configs):
opit=opi.t()
mat=qoperator.matrix_form(oimp,configsi,configsi)
for j, (opj, configj) in enumerate(ops_configs):
if isinstance(opit,models.Unit) and isinstance(opj,models.Unit):
norm=1.
full_mat[start[opi]:end[opi],start[opj]:end[opj]]=norm*mat
elif isinstance(opi,models.ContractedC) and isinstance(opj,models.ContractedC):
norm=norm_c(opit,opj,cocc,vocc)
full_mat[start[opi]:end[opi],start[opj]:end[opj]]=norm*mat
elif isinstance(opi,models.ContractedD) and isinstance(opj,models.ContractedD):
norm=norm_d(opit,opj,cocc,vocc)
full_mat[start[opi]:end[opi],start[opj]:end[opj]]=norm*mat
elif isinstance(opi,models.ContractedCD) and isinstance(opj,models.ContractedCD):
norm=norm_cd(opit,opj,cocc,vocc)
full_mat[start[opi]:end[opi],start[opj]:end[opj]]=norm*mat
return full_mat
def oimp_matrix_form(oimp, ops_configs, cocc, vocc):
# matrix elements of
# sum < | oimp | > where oimp acts only on the imp+bath space
# cocc, vocc: lists of core, virtual labels
assert not oimp.fermion # operator should have an even number of c/d operators
start = {}
end = {}
nconfigs = [len(configs) for (ops, configs) in ops_configs]
ops = [opi for (opi, configi) in ops_configs]
for i, opi in enumerate(ops):
start[opi] = sum(nconfigs[:i])
end[opi] = start[opi] + nconfigs[i]
full_mat = utils.zeros([sum(nconfigs), sum(nconfigs)])
for i, (opi, configsi) in enumerate(ops_configs):
opit = opi.t()
mat = qoperator.matrix_form(oimp, configsi, configsi)
for j, (opj, configj) in enumerate(ops_configs):
if isinstance(opit, models.Unit) and isinstance(opj, models.Unit):
norm = 1.
full_mat[start[opi]:end[opi], start[opj]:end[opj]] = norm * mat
elif isinstance(opi, models.ContractedC) and isinstance(
opj, models.ContractedC):
norm = norm_c(opit, opj, cocc, vocc)
full_mat[start[opi]:end[opi], start[opj]:end[opj]] = norm * mat
elif isinstance(opi, models.ContractedD) and isinstance(
opj, models.ContractedD):
norm = norm_d(opit, opj, cocc, vocc)
full_mat[start[opi]:end[opi], start[opj]:end[opj]] = norm * mat
elif isinstance(opi, models.ContractedCD) and isinstance(
opj, models.ContractedCD):
norm = norm_cd(opit, opj, cocc, vocc)
full_mat[start[opi]:end[opi], start[opj]:end[opj]] = norm * mat
return full_mat
def oimp_matrix_bra_ket_form(oimp, ops_bra_configs, ops_ket_configs, cocc,
vocc):
# imp is an operator that acts only on the imp and bath orbitals.
# (e.g. himp)
bra_start = {}
bra_end = {}
ket_start = {}
ket_end = {}
bra_nconfigs = [len(bra_configs) for (ops, bra_configs) in ops_bra_configs]
ket_nconfigs = [len(ket_configs) for (ops, ket_configs) in ops_ket_configs]
bra_ops = [opi for (opi, bra_configs) in ops_bra_configs]
ket_ops = [opi for (opi, ket_configs) in ops_ket_configs]
for i, opi in enumerate(bra_ops):
bra_start[opi] = sum(bra_nconfigs[:i])
bra_end[opi] = bra_start[opi] + bra_nconfigs[i]
for i, opi in enumerate(ket_ops):
ket_start[opi] = sum(ket_nconfigs[:i])
ket_end[opi] = ket_start[opi] + ket_nconfigs[i]
full_mat = utils.zeros([sum(bra_nconfigs), sum(ket_nconfigs)])
for i, (opi, bra_configsi) in enumerate(ops_bra_configs):
opit = opi.t()
for j, (opj, ket_configsj) in enumerate(ops_ket_configs):
# <imp1.core|opi oimp opj|core.imp2>:
# parity is opi.parity*oimp.parity*core.parity
# but assume core is even
mat = qoperator.matrix_form(oimp, bra_configsi, ket_configsj)
parity = 1.
if oimp.fermion and opi.fermion:
parity = -1.
if isinstance(opit, models.Unit) and isinstance(opj, models.Unit):
norm = 1.
full_mat[bra_start[opi]:bra_end[opi],
ket_start[opj]:ket_end[opj]] = norm * mat * parity
elif isinstance(opi, models.ContractedC) and isinstance(
opj, models.ContractedC):
norm = norm_c(opit, opj, cocc, vocc)
full_mat[bra_start[opi]:bra_end[opi],
ket_start[opj]:ket_end[opj]] = norm * mat * parity
elif isinstance(opi, models.ContractedD) and isinstance(
opj, models.ContractedD):
norm = norm_d(opit, opj, cocc, vocc)
full_mat[bra_start[opi]:bra_end[opi],
ket_start[opj]:ket_end[opj]] = norm * mat * parity
elif isinstance(opi, models.ContractedCD) and isinstance(
opj, models.ContractedCD):
norm = norm_cd(opit, opj, cocc, vocc)
full_mat[bra_start[opi]:bra_end[opi],
ket_start[opj]:ket_end[opj]] = norm * mat * parity
return full_mat
def matrix_form(qop, ops_configs):
"""
< bra opi | qop | opj ket >
where <bra opi| and |opj ket> are the same set
"""
nconfigs = [len(configs) for (ops, configs) in ops_configs]
full_mat = utils.zeros([sum(nconfigs), sum(nconfigs)])
for i, (opi, bra_configsi) in enumerate(ops_configs):
iptr = sum(nconfigs[:i])
for j, (opj, ket_configsj) in enumerate(ops_configs):
jptr = sum(nconfigs[:j])
prod_op = qoperator.ProductQOp([opi.t(), qop, opj])
mat = qoperator.matrix_form(prod_op, bra_configsi, ket_configsj)
full_mat[iptr:iptr + nconfigs[i], jptr:jptr + nconfigs[j]] = mat
return full_mat
def matrix_form(qop,ops_configs):
"""
< bra opi | qop | opj ket >
where <bra opi| and |opj ket> are the same set
"""
nconfigs=[len(configs) for (ops, configs) in ops_configs]
full_mat=utils.zeros([sum(nconfigs),sum(nconfigs)])
for i, (opi, bra_configsi) in enumerate(ops_configs):
iptr=sum(nconfigs[:i])
for j, (opj, ket_configsj) in enumerate(ops_configs):
jptr=sum(nconfigs[:j])
prod_op=qoperator.ProductQOp([opi.t(),qop,opj])
mat=qoperator.matrix_form(prod_op,bra_configsi,ket_configsj)
full_mat[iptr:iptr+nconfigs[i],jptr:jptr+nconfigs[j]]=mat
return full_mat
def oimp_matrix_bra_ket_form(oimp,ops_bra_configs,ops_ket_configs,cocc,vocc):
# imp is an operator that acts only on the imp and bath orbitals.
# (e.g. himp)
bra_start={}
bra_end={}
ket_start={}
ket_end={}
bra_nconfigs=[len(bra_configs) for (ops, bra_configs) in ops_bra_configs]
ket_nconfigs=[len(ket_configs) for (ops, ket_configs) in ops_ket_configs]
bra_ops=[opi for (opi, bra_configs) in ops_bra_configs]
ket_ops=[opi for (opi, ket_configs) in ops_ket_configs]
for i, opi in enumerate(bra_ops):
bra_start[opi]=sum(bra_nconfigs[:i])
bra_end[opi]=bra_start[opi]+bra_nconfigs[i]
for i, opi in enumerate(ket_ops):
ket_start[opi]=sum(ket_nconfigs[:i])
ket_end[opi]=ket_start[opi]+ket_nconfigs[i]
full_mat=utils.zeros([sum(bra_nconfigs),sum(ket_nconfigs)])
for i, (opi, bra_configsi) in enumerate(ops_bra_configs):
opit=opi.t()
for j, (opj, ket_configsj) in enumerate(ops_ket_configs):
# <imp1.core|opi oimp opj|core.imp2>:
# parity is opi.parity*oimp.parity*core.parity
# but assume core is even
mat=qoperator.matrix_form(oimp,bra_configsi,ket_configsj)
parity=1.
if oimp.fermion and opi.fermion:
parity=-1.
if isinstance(opit,models.Unit) and isinstance(opj,models.Unit):
norm=1.
full_mat[bra_start[opi]:bra_end[opi],ket_start[opj]:ket_end[opj]]=norm*mat*parity
elif isinstance(opi,models.ContractedC) and isinstance(opj,models.ContractedC):
norm=norm_c(opit,opj,cocc,vocc)
full_mat[bra_start[opi]:bra_end[opi],ket_start[opj]:ket_end[opj]]=norm*mat*parity
elif isinstance(opi,models.ContractedD) and isinstance(opj,models.ContractedD):
norm=norm_d(opit,opj,cocc,vocc)
full_mat[bra_start[opi]:bra_end[opi],ket_start[opj]:ket_end[opj]]=norm*mat*parity
elif isinstance(opi,models.ContractedCD) and isinstance(opj,models.ContractedCD):
norm=norm_cd(opit,opj,cocc,vocc)
full_mat[bra_start[opi]:bra_end[opi],ket_start[opj]:ket_end[opj]]=norm*mat*parity
return full_mat
def matrix_bra_ket_form(qop,ops_bra_configs,ops_ket_configs):
"""
< bra opi | qop | opj ket >
where <bra opi| and |opj ket> can be different sets
"""
bra_nconfigs=[len(configs) for (ops, configs) in ops_bra_configs]
ket_nconfigs=[len(configs) for (ops, configs) in ops_ket_configs]
full_mat=utils.zeros([sum(bra_nconfigs),sum(ket_nconfigs)])
for i, (opi, bra_configsi) in enumerate(ops_bra_configs):
iptr=sum(bra_nconfigs[:i])
for j, (opj, ket_configsj) in enumerate(ops_ket_configs):
jptr=sum(ket_nconfigs[:j])
prod_op=qoperator.ProductQOp([opi.t(),qop,opj])
mat=qoperator.matrix_form(prod_op,bra_configsi,ket_configsj)
full_mat[iptr:iptr+bra_nconfigs[i],jptr:jptr+ket_nconfigs[j]]=mat
return full_mat
def matrix_bra_ket_form(qop, ops_bra_configs, ops_ket_configs):
"""
< bra opi | qop | opj ket >
where <bra opi| and |opj ket> can be different sets
"""
bra_nconfigs = [len(configs) for (ops, configs) in ops_bra_configs]
ket_nconfigs = [len(configs) for (ops, configs) in ops_ket_configs]
full_mat = utils.zeros([sum(bra_nconfigs), sum(ket_nconfigs)])
for i, (opi, bra_configsi) in enumerate(ops_bra_configs):
iptr = sum(bra_nconfigs[:i])
for j, (opj, ket_configsj) in enumerate(ops_ket_configs):
jptr = sum(ket_nconfigs[:j])
prod_op = qoperator.ProductQOp([opi.t(), qop, opj])
mat = qoperator.matrix_form(prod_op, bra_configsi, ket_configsj)
full_mat[iptr:iptr + bra_nconfigs[i],
jptr:jptr + ket_nconfigs[j]] = mat
return full_mat
def himp_ext_matrix_form(hcs_imp, hds_ext, hds_imp, hcs_ext, ops_configs, cocc,
vocc):
# matrix elements of cross terms
# sum < | hcs_imp otimes hds_ext | > + < | hds_imp otimes hcs_ext | >
assert not len(cocc) & 1, "parities assume even #els in core"
start = {}
end = {}
nconfigs = [len(configs) for (ops, configs) in ops_configs]
ops = [opi for (opi, configi) in ops_configs]
for i, opi in enumerate(ops):
start[opi] = sum(nconfigs[:i])
end[opi] = start[opi] + nconfigs[i]
full_mat = utils.zeros([sum(nconfigs), sum(nconfigs)])
for i, (opi, configi) in enumerate(ops_configs):
opit = opi.t()
for j, (opj, configj) in enumerate(ops_configs):
for hc_imp, hd_ext in zip(hcs_imp, hds_ext):
# <a1 b1.core|cimp dext|b2.core a2>:
# parity =-1 if fermion(b1) and core is even
if isinstance(opit, models.Unit) and isinstance(
opj, models.ContractedC):
mat_imp = qoperator.matrix_form(hc_imp, configi, configj)
val = eval_hd_cv(hd_ext, opj, cocc, vocc)
full_mat[start[opi]:end[opi],
start[opj]:end[opj]] += mat_imp * val
elif isinstance(opit, models.ContractedCD) and isinstance(
opj, models.ContractedC):
mat_imp = qoperator.matrix_form(hc_imp, configi, configj)
val = eval_codv_hd_cv(opit, hd_ext, opj, cocc, vocc)
full_mat[start[opi]:end[opi],
start[opj]:end[opj]] += mat_imp * val
# parity is -1, since b1 is fermionic
elif isinstance(opit, models.ContractedC) and isinstance(
opj, models.Unit):
mat_imp = qoperator.matrix_form(hc_imp, configi, configj)
val = -eval_co_hd(opit, hd_ext, cocc, vocc) # parity=-1
full_mat[start[opi]:end[opi],
start[opj]:end[opj]] += mat_imp * val
elif isinstance(opit, models.ContractedC) and isinstance(
opj, models.ContractedCD):
mat_imp = qoperator.matrix_form(hc_imp, configi, configj)
val = -eval_co_hd_cvdo(opit, hd_ext, opj, cocc,
vocc) #parity=-1
full_mat[start[opi]:end[opi],
start[opj]:end[opj]] += mat_imp * val
for hd_imp, hc_ext in zip(hds_imp, hcs_ext):
# <a1 b1.core|cext dimp|b2.core a2>:
# parity =-1 if fermion(b2) and core is even
if isinstance(opit, models.Unit) and isinstance(
opj, models.ContractedD):
mat_imp = qoperator.matrix_form(hd_imp, configi, configj)
val = -eval_hc_do(hc_ext, opj, cocc, vocc) # parity=-1
full_mat[start[opi]:end[opi],
start[opj]:end[opj]] += mat_imp * val
elif isinstance(opit, models.ContractedCD) and isinstance(
opj, models.ContractedD):
mat_imp = qoperator.matrix_form(hd_imp, configi, configj)
val = -eval_codv_hc_do(opit, hc_ext, opj, cocc,
vocc) # parity=-1
full_mat[start[opi]:end[opi],
start[opj]:end[opj]] += mat_imp * val
elif isinstance(opit, models.ContractedD) and isinstance(
opj, models.Unit):
mat_imp = qoperator.matrix_form(hd_imp, configi, configj)
val = eval_dv_hc(opit, hc_ext, cocc, vocc)
full_mat[start[opi]:end[opi],
start[opj]:end[opj]] += mat_imp * val
elif isinstance(opit, models.ContractedD) and isinstance(
opj, models.ContractedCD):
mat_imp = qoperator.matrix_form(hd_imp, configi, configj)
val = eval_dv_hc_cvdo(opit, hc_ext, opj, cocc, vocc)
full_mat[start[opi]:end[opi],
start[opj]:end[opj]] += mat_imp * val
return full_mat
def himp_ext_matrix_form(hcs_imp,hds_ext,hds_imp,hcs_ext,ops_configs,cocc,vocc):
# matrix elements of cross terms
# sum < | hcs_imp otimes hds_ext | > + < | hds_imp otimes hcs_ext | >
assert not len(cocc) & 1, "parities assume even #els in core"
start={}
end={}
nconfigs=[len(configs) for (ops, configs) in ops_configs]
ops=[opi for (opi, configi) in ops_configs]
for i, opi in enumerate(ops):
start[opi]=sum(nconfigs[:i])
end[opi]=start[opi]+nconfigs[i]
full_mat=utils.zeros([sum(nconfigs),sum(nconfigs)])
for i, (opi, configi) in enumerate(ops_configs):
opit=opi.t()
for j, (opj, configj) in enumerate(ops_configs):
for hc_imp, hd_ext in zip(hcs_imp,hds_ext):
# <a1 b1.core|cimp dext|b2.core a2>:
# parity =-1 if fermion(b1) and core is even
if isinstance(opit,models.Unit) and isinstance(opj,models.ContractedC):
mat_imp=qoperator.matrix_form(hc_imp,configi,configj)
val=eval_hd_cv(hd_ext,opj,cocc,vocc)
full_mat[start[opi]:end[opi],start[opj]:end[opj]]+=mat_imp*val
elif isinstance(opit,models.ContractedCD) and isinstance(opj,models.ContractedC):
mat_imp=qoperator.matrix_form(hc_imp,configi,configj)
val=eval_codv_hd_cv(opit,hd_ext,opj,cocc,vocc)
full_mat[start[opi]:end[opi],start[opj]:end[opj]]+=mat_imp*val
# parity is -1, since b1 is fermionic
elif isinstance(opit,models.ContractedC) and isinstance(opj,models.Unit):
mat_imp=qoperator.matrix_form(hc_imp,configi,configj)
val=-eval_co_hd(opit,hd_ext,cocc,vocc) # parity=-1
full_mat[start[opi]:end[opi],start[opj]:end[opj]]+=mat_imp*val
elif isinstance(opit,models.ContractedC) and isinstance(opj,models.ContractedCD):
mat_imp=qoperator.matrix_form(hc_imp,configi,configj)
val=-eval_co_hd_cvdo(opit,hd_ext,opj,cocc,vocc) #parity=-1
full_mat[start[opi]:end[opi],start[opj]:end[opj]]+=mat_imp*val
for hd_imp, hc_ext in zip(hds_imp,hcs_ext):
# <a1 b1.core|cext dimp|b2.core a2>:
# parity =-1 if fermion(b2) and core is even
if isinstance(opit,models.Unit) and isinstance(opj,models.ContractedD):
mat_imp=qoperator.matrix_form(hd_imp,configi,configj)
val=-eval_hc_do(hc_ext,opj,cocc,vocc) # parity=-1
full_mat[start[opi]:end[opi],start[opj]:end[opj]]+=mat_imp*val
elif isinstance(opit,models.ContractedCD) and isinstance(opj,models.ContractedD):
mat_imp=qoperator.matrix_form(hd_imp,configi,configj)
val=-eval_codv_hc_do(opit,hc_ext,opj,cocc,vocc) # parity=-1
full_mat[start[opi]:end[opi],start[opj]:end[opj]]+=mat_imp*val
elif isinstance(opit,models.ContractedD) and isinstance(opj,models.Unit):
mat_imp=qoperator.matrix_form(hd_imp,configi,configj)
val=eval_dv_hc(opit,hc_ext,cocc,vocc)
full_mat[start[opi]:end[opi],start[opj]:end[opj]]+=mat_imp*val
elif isinstance(opit,models.ContractedD) and isinstance(opj,models.ContractedCD):
mat_imp=qoperator.matrix_form(hd_imp,configi,configj)
val=eval_dv_hc_cvdo(opit,hc_ext,opj,cocc,vocc)
full_mat[start[opi]:end[opi],start[opj]:end[opj]]+=mat_imp*val
return full_mat