"""
Create PDF for material model.
"""
import numpy as np
import sympy as sp
from multipie.util.util import to_latex
from multipie.core.group import Group
# ==================================================
[docs]
class ModelPDF:
# ==================================================
[docs]
def fmt_number(self, nums, int_digits=2, frac_digits=5):
if frac_digits != 0:
width = int_digits + 1 + frac_digits
if isinstance(nums, (list, np.ndarray, tuple)):
return r"\texttt{[" + ",".join([f"{x:{width}.{frac_digits}f}" for x in nums]) + "]}"
else:
return r"\texttt{" + f"{nums:{width}.{frac_digits}f}" + "}"
else:
if isinstance(nums, (list, np.ndarray, tuple)):
return r"\texttt{[" + ",".join([f"{x}" for x in nums]) + "]}"
else:
return r"\texttt{" + f"{nums}" + "}"
# ==================================================
[docs]
def fmt_site_bond(self, site_bond):
if ";" not in site_bond:
s = f"'{site_bond}'"
else:
tail, head = site_bond.split(";")
head, n, m = head.split("_")
s = r"\texttt{" f"'{head}'" + r"}-\texttt{" + f"'{tail}'({int(n)}th,{m})" + "}"
return s
# ==================================================
[docs]
def text(self, txt=""):
self.pdf.text(txt)
# ==================================================
[docs]
def vspace(self, sp="5mm"):
self.text(r"\vspace{" + sp + "}" + "\n")
# ==================================================
[docs]
def hr(self, text="", width="0.5mm", space="3mm", pos="5mm"):
s = r"\vspace{5mm}" + "\n"
if text != "":
s += r"\noindent \rule[" + width + "]{" + pos + "}{" + width + "}"
s += r"\hspace{" + space + r"}\textbf{" + text + r"}\hspace{" + space + "}"
s += r"\leaders\hrule height " + width + r"\hfill\kern0pt"
else:
s += r"\noindent\leaders\hrule height " + width + r"\hfill\kern0pt"
s += "\n" + r"\vspace{3mm}"
self.text(s + "\n")
# ==================================================
[docs]
def number_tag(self, no):
d = r"\fbox{" + no + r"}\quad "
return d
# ==================================================
# ==================================================
[docs]
def general_info(self):
tp = self.mm["toroidal_priority"]
mn = self.mm["max_neighbor"]
scr = self.mm["search_cell_range"]
scr = str(scr[0:2]) + ", " + str(scr[2:4]) + ", " + str(scr[4:6])
basis_type = self.mm["basis_type"]
select = self.mm["SAMB_select"]
a_select = self.mm["atomic_select"]
s_select = self.mm["site_select"]
b_select = self.mm["bond_select"]
irrep = ["$" + self.mm.group.tag_irrep(i, latex=True) + "$" for i in select["Gamma"]]
a_irrep = ["$" + self.mm.group.tag_irrep(i, latex=True) + "$" for i in a_select["Gamma"]]
s_irrep = ["$" + self.mm.group.tag_irrep(i, latex=True) + "$" for i in s_select["Gamma"]]
b_irrep = ["$" + self.mm.group.tag_irrep(i, latex=True) + "$" for i in b_select["Gamma"]]
self.hr("General Condition")
self.text(r"\begin{itemize}")
self.text(r"\item Basis type: \texttt{" + basis_type + "}\n")
self.text(r"\item SAMB selection:" + "\n")
self.text(r"\, - Type: \texttt{" + str(select["X"]).replace("'", "") + "}\n")
self.text(r"\, - Rank: \texttt{" + str(select["l"]) + "}\n")
self.text(r"\, - Irrep.: [" + ", ".join(irrep) + "]\n")
self.text(r"\, - Spin (s): \texttt{" + str(select["s"]) + "}\n")
self.text(r"\item Atomic selection:" + "\n")
self.text(r"\, - Type: \texttt{" + str(a_select["X"]).replace("'", "") + "}\n")
self.text(r"\, - Rank: \texttt{" + str(a_select["l"]) + "}\n")
self.text(r"\, - Irrep.: [" + ", ".join(a_irrep) + "]\n")
self.text(r"\, - Spin (s): \texttt{" + str(a_select["s"]) + "}\n")
self.text(r"\item Site-cluster selection:" + "\n")
self.text(r"\, - Rank: \texttt{" + str(s_select["l"]) + "}\n")
self.text(r"\, - Irrep.: [" + ", ".join(s_irrep) + "]\n")
self.text(r"\item Bond-cluster selection:" + "\n")
self.text(r"\, - Type: \texttt{" + str(b_select["X"]).replace("'", "") + "}\n")
self.text(r"\, - Rank: \texttt{" + str(b_select["l"]) + "}\n")
self.text(r"\, - Irrep.: [" + ", ".join(b_irrep) + "]\n")
self.text(r"\item Max. neighbor: \texttt{" + str(mn) + "}\n")
self.text(r"\item Search cell range: \texttt{" + scr + "}\n")
self.text(r"\item Toroidal priority: \texttt{" + str(tp).lower() + "}\n")
self.text(r"\end{itemize}")
# ==================================================
[docs]
def group_cell_info(self):
gp = self.mm.group.latex(detail=True)
cell = self.mm["cell"]
a = self.fmt_number(cell["a"])
b = self.fmt_number(cell["b"])
c = self.fmt_number(cell["c"])
alpha = self.fmt_number(cell["alpha"], frac_digits=1)
beta = self.fmt_number(cell["beta"], frac_digits=1)
gamma = self.fmt_number(cell["gamma"], frac_digits=1)
a1, a2, a3 = self.mm["unit_vector"]
a1 = self.fmt_number(a1)
a2 = self.fmt_number(a2)
a3 = self.fmt_number(a3)
self.hr("Group and Unit Cell")
self.text(r"\begin{itemize}")
self.text(r"\item Group: " + gp)
if not self.mm.group.is_point_group:
ch_gp = self.mm.group.latex(detail=True, tp="PG")
self.text(r"\item Associated point group: " + ch_gp)
self.text(r"\end{itemize}")
self.text(r"\begin{itemize}")
self.text(r"\item Unit cell:" + "\n")
txt = f"\\quad $a={a},\\,\\, b={b},\\,\\, c={c},\\,\\, \\alpha={alpha},\\,\\, \\beta={beta},\\,\\, \\gamma={gamma}$\n"
self.text(txt)
self.text(r"\item Lattice vectors (conventional cell):" + "\n")
self.text(r"\quad $\bm{a}_1=" + a1 + "$\n")
self.text(r"\quad $\bm{a}_2=" + a2 + "$\n")
self.text(r"\quad $\bm{a}_3=" + a3 + "$\n")
if not self.mm.group.is_point_group:
ps = self.mm.group.symmetry_operation.get("plus_set", None)
if len(ps) > 1:
self.text(r"\item Plus sets:" + "\n")
ps = "$+" + r"$,\,\,\, $+".join(to_latex(ps, "vector")) + "$"
self.text(r"\quad " + ps + "\n")
self.text(r"\end{itemize}")
# ==================================================
[docs]
def cluster_samb_info(self):
c_samb = self.mm["cluster_samb"]
self.hr("Cluster SAMB")
self.text(r"\noindent\textbullet\, Site cluster" + "\n")
no = 1
for wp, samb in c_samb.items():
if "@" in wp:
continue
self.vspace("5mm")
self.text(r"\noindent ** Wyckoff: \texttt{" + wp + "}\n")
for idx, (mat, ex) in samb.items():
tag = self.mm.group.tag_multipole(idx, latex=True, superscript="s")
for e, m in zip(tag, mat):
d = self.number_tag("y" + str(no)) + sp.latex(sp.Symbol(e)) + "=" + to_latex(m, "vector")
self.pdf.equation(d, long=True)
no += 1
self.vspace("5mm")
self.text(r"\noindent\textbullet\, Bond cluster" + "\n")
for wp, samb in c_samb.items():
if "@" not in wp:
continue
self.vspace("5mm")
self.text(r"\noindent ** Wyckoff: \texttt{" + wp + "}\n")
for idx, (mat, ex) in samb.items():
tag = self.mm.group.tag_multipole(idx, latex=True, superscript="s")
for e, m in zip(tag, mat):
d = self.number_tag("y" + str(no)) + sp.latex(sp.Symbol(e)) + "=" + to_latex(m, "vector")
self.pdf.equation(d, long=True)
no += 1
# ==================================================
[docs]
def atomic_samb_info(self):
atomic_samb = self.mm["atomic_samb"]
basis_type = self.mm["basis_type"]
self.hr("Atomic SAMB")
no = 1
for name, samb in atomic_samb.items():
if name.bh_rank > name.kt_rank:
continue
self.vspace("5mm")
bs1 = [
self.mm.group.tag_atomic_basis(
self.mm.group.atomic_basis(basis_type)[name.bh_rank][i], name.bh_rank, ket=False, latex=True
)
for i in name.bh_idx
]
bs2 = [
self.mm.group.tag_atomic_basis(
self.mm.group.atomic_basis(basis_type)[name.kt_rank][i], name.kt_rank, ket=True, latex=True
)
for i in name.kt_idx
]
bra = "$" + r",\, ".join(bs1) + "$"
ket = "$" + r",\, ".join(bs2) + "$"
self.text(r"\noindent\textbullet\, bra: " + bra + "\n")
self.text(r"\noindent\textbullet\, ket: " + ket + "\n")
for idx, (mat, ex) in samb.items():
tag = self.mm.group.tag_multipole(idx, latex=True, superscript="a")
for e, m in zip(tag, mat):
d = self.number_tag("x" + str(no))
d += sp.latex(sp.Symbol(e)) + "=" + to_latex(m, "matrix")
self.pdf.equation(d, long=True)
no += 1
# ==================================================
[docs]
def combined_samb_info(self):
combined_samb = self.mm["combined_samb"]
samb_num = self.mm["SAMB_number"]
samb_num_min = self.mm["SAMB_number_min"]
basis_type = self.mm["basis_type"]
common_id = self.mm["common_id"]
self.hr(f"SAMB: {samb_num_min} (all {samb_num})")
for comb, samb in combined_samb.items():
if not samb:
continue
no_tag, sb_tag = common_id[comb]
bk = comb.bk_info
wp = comb.wyckoff
clustar_str = "b" if wp.count("@") > 0 else "s"
bs1 = [
self.mm.group.tag_atomic_basis(
self.mm.group.atomic_basis(basis_type)[bk.bh_rank][i], bk.bh_rank, ket=False, latex=True
)
for i in bk.bh_idx
]
bs2 = [
self.mm.group.tag_atomic_basis(
self.mm.group.atomic_basis(basis_type)[bk.kt_rank][i], bk.kt_rank, ket=True, latex=True
)
for i in bk.kt_idx
]
bra = "$" + r",\, ".join(bs1) + "$"
ket = "$" + r",\, ".join(bs2) + "$"
cluster = (
r"'\texttt{" + comb.head + "}' site-cluster"
if clustar_str == "s"
else r"'\texttt{" + comb.head + r"}'-'\texttt{" + comb.tail + "}' bond-cluster"
)
cluster = r"\texttt{" + sb_tag[0] + "} : " + cluster
wyckoff = r"\texttt{" + wp + "}"
self.vspace("5mm")
self.text(r"\noindent\textbullet\, " + cluster + "\n")
self.text(r"\noindent\quad * bra: " + bra + "\n")
self.text(r"\noindent\quad * ket: " + ket + "\n")
self.text(r"\noindent\quad * wyckoff: " + wyckoff + "\n")
i = 0
for idx, (cl, ex) in samb.items():
tag = self.mm.group.tag_multipole(idx, latex=True, superscript="c")
for t, m in zip(tag, cl):
zi = no_tag[0][i]
i += 1
ex = 0
for cg, t1, c1, t2, c2 in m:
t1 = self.mm.group.tag_multipole(t1, c1, latex=True, superscript="a")
t2 = self.mm.group.tag_multipole(t2, c2, latex=True, superscript=clustar_str)
ex += cg * sp.Symbol(t1, commutative=False) * sp.Symbol(t2, commutative=False)
d = r"\hspace*{3mm}" + self.number_tag(zi)
d += sp.latex(sp.Symbol(t)) + "=" + sp.latex(ex)
self.pdf.equation(d, long=True)
if len(no_tag) > 1:
if self.mm["pdf_ctrl"]["common_samb"]:
sb_head = "(" + ", ".join(sb_tag) + ")"
sb_str = np.array(no_tag).T.tolist()
sb_str = ", ".join(["(" + ", ".join(i) + ")" for i in sb_str])
self.text(r"\noindent * common SAMBs" + "\n")
self.text(r"\noindent\texttt{" + sb_head + ", " + sb_str + "}")
else:
n = (len(no_tag) - 1) * len(no_tag[0])
self.text(r"\noindent\quad" + f"+ {n} common SAMBs" + "\n")
self.vspace()
# ==================================================
[docs]
def rep_site_bond_info(self):
site = self.mm["site"]["representative"]
bond = self.mm["bond"]["info"]
self.hr("Site and Bond")
cap = "Orbital of each site"
lbl = ["site", "orbital"]
row = []
tbl = []
hl = []
no = 0
for name, rep in site.items():
orb = sum([[self.mm.group.tag_atomic_basis(i, l, latex=True) for i in ol] for l, ol in enumerate(rep.orbital)], [])
if len(orb) < 17:
orb = "$" + "$, $".join(orb) + "$"
name = r"\texttt{" + name + "}"
row.append(rep.no)
tbl.append([name, orb])
hl.append(no)
no += 1
else:
orb1 = "$" + "$, $".join(orb[:16]) + "$"
name = r"\texttt{" + name + "}"
row.append(rep.no)
tbl.append([name, orb1])
orb2 = "$" + "$, $".join(orb[16:]) + "$"
row.append("")
tbl.append(["", orb2])
hl.append(no + 1)
no += 2
self.pdf.table(tbl, row, lbl, r"\#", cpos="ccl", long=True, stretch=1.6, hl=hl[:-1], caption=cap, center=False)
rank_dict = {0: "s", 1: "p", 2: "d", 3: "f"}
cap = "Neighbor and bra-ket of each bond"
lbl = ["head", "tail", "neighbor", "head (bra)", "tail (ket)"]
row = []
tbl = []
for no, rep in enumerate(bond):
tail = r"\texttt{" + rep.tail + "}"
head = r"\texttt{" + rep.head + "}"
nb = rep.neighbor
if len(nb) > 9:
nb = (r"\texttt{" + str(nb[:4])[:-1] + r",$\cdots$," + str(nb[-1]) + "]}").replace(" ", "")
else:
nb = (r"\texttt{" + str(nb) + "}").replace(" ", "")
tr = r"\texttt{[" + ",".join([rank_dict[i] for i in rep.t_rank]) + "]}"
hr = r"\texttt{[" + ",".join([rank_dict[i] for i in rep.h_rank]) + "]}"
row.append(str(no + 1))
tbl.append([head, tail, nb, hr, tr])
self.pdf.table(tbl, row, lbl, r"\#", cpos="ccclll", long=True, stretch=1.6, hl=True, caption=cap, center=False)
# ==================================================
[docs]
def site_info(self):
site = self.mm["site"]["cell"]
self.hr("Site in Unit Cell")
self.text(r"\noindent Sites in (conventional) cell (no plus set), SL = sublattice" + "\n")
lbl = ["position" + r" ($\bm{s})$", "mapping"]
for name, cell_site_name in site.items():
rep = self.mm["site"]["representative"][name]
cap = (
r"'\texttt{"
+ f"{name}"
+ r"}' (\#"
+ f"{rep.no}) site cluster "
+ r"(\texttt{"
+ f"{rep.wyckoff}"
+ r"}), \texttt{"
+ f"{rep.symmetry}"
+ "}"
)
row = []
tbl = []
for c in cell_site_name:
if c.plus_set != 1:
continue
pos = self.fmt_number(c.position)
m = c.mapping
if len(m) == 48: # in case of Oh (too long).
m = (r"\texttt{" + str(m[:4])[:-1] + r",$\cdots$," + str(m[-1]) + "]}").replace(" ", "")
else:
m = self.fmt_number(m, frac_digits=0)
row.append(str(c.no))
tbl.append([pos, m])
self.pdf.table(tbl, row, lbl, "SL", cpos="cll", long=True, stretch=1.6, hl=True, caption=cap, center=False)
# ==================================================
[docs]
def bond_info(self):
bond = self.mm["bond"]["cell"]
neighbor = self.mm["pdf_ctrl"]["max_neighbor"]
self.hr("Bond in Unit Cell")
self.text(
r"\noindent Bonds in (conventional) cell (no plus set): tail, head = (SL, plus set), (N)D = (non)directional"
+ f" (listed up to {neighbor}th neighbor at most)"
+ "\n"
)
lbl = ["vector" + r" ($\bm{v})$", "center" + r" ($\bm{c})$", "mapping", "head", "tail", r"$\bm{R}$ (primitive)"]
for name, cell_bond_name in bond.items():
rep = self.mm["bond"]["representative"][name]
if neighbor is not None and rep.neighbor > neighbor:
continue
d_str = "D" if rep.directional else "ND"
ss, cn, mul = name.split("_")
tail_atom, head_atom = ss.split(";")
dist = round(rep.distance, 5)
cap = (
f"{rep.neighbor}-th "
+ r"'\texttt{"
+ f"{head_atom}"
+ r"}'-'\texttt{"
+ f"{tail_atom}"
+ "}'"
+ f" [{mul}] ("
+ r"\#"
+ f"{rep.no}"
+ ") bond cluster ("
+ r"\texttt{"
+ f"{rep.wyckoff}"
+ "}"
+ f"), {d_str}, "
+ r"$|\bm{v}|"
+ f"={dist}$ (cartesian)"
)
row = []
tbl = []
for i in cell_bond_name:
if i.plus_set != 1:
continue
v = self.fmt_number(i.vector)
c = self.fmt_number(i.center)
m = i.mapping
if len(m) == 48: # in case of Oh (too long).
m = (r"\texttt{" + str(m[:4])[:-1] + r",$\cdots$," + str(m[-1]) + "]}").replace(" ", "")
else:
m = self.fmt_number(m, frac_digits=0)
t, h = i.t_idx, i.h_idx
t = (r"\texttt{" + str(t) + "}").replace(" ", "")
h = (r"\texttt{" + str(h) + "}").replace(" ", "")
R = self.fmt_number(i.R_primitive, frac_digits=0)
row.append(str(i.no))
tbl.append([v, c, m, h, t, R])
self.pdf.table(tbl, row, lbl, "SL", cpos="cllllll", long=True, stretch=1.6, hl=True, caption=cap, center=False)
# ==================================================
[docs]
def harmonics_info(self):
if not self.mm["pdf_ctrl"]["harmonics"]:
return
harmonics = self.mm.get_multipole_expression()
self.hr("Harmonics")
cap = "Harmonics"
lbl = ["symbol", "irrep.", "rank", "X", "multiplicity", "component", "symmetry"]
no = 0
row = []
tbl = []
hl = []
for (X, irrep, rank, n), ex_set in harmonics.items():
idx = (X, rank, irrep, n, -1, 0, 0, "q")
irrep = "$" + self.mm.group.tag_irrep(irrep, latex=True) + "$"
rank = str(rank)
XX = "$Q$, $T$" if X == "Q" else "$G$, $M$"
d = len(ex_set)
n = "-" if n == -1 else str(n)
if d == 1:
sym = "$" + self.mm.group.tag_multipole(idx, comp=-1, latex=True) + "$"
row.append(str(no + 1))
tbl.append([sym, irrep, rank, XX, n, "-", "$" + sp.latex(ex_set[0]) + "$"])
no += 1
else:
for i, ex in enumerate(ex_set):
sym = "$" + self.mm.group.tag_multipole(idx, comp=i, latex=True) + "$"
row.append(str(no + 1))
if i == 0:
tbl.append([sym, irrep, rank, XX, n, str(i + 1), "$" + sp.latex(ex) + "$"])
else:
tbl.append([sym, "", "", "", "", str(i + 1), "$" + sp.latex(ex) + "$"])
no += 1
hl.append(no - 1)
self.pdf.table(tbl, row, lbl, r"\#", cpos="clcccccl", long=True, stretch=1.6, hl=hl[:-1], caption=cap, center=False)
# ==================================================
[docs]
def full_matrix_info(self):
# full matrix.
basis = self.mm.ket()
self.hr("Basis in full matrix")
cap = f"dimension = {len(basis)}"
tbl = []
for no, b in enumerate(basis):
b = "$" + str(b) + "$"
tbl.append([str(no), b])
tbl = sum(tbl, [])
self.pdf.table(
tbl,
[""],
col=[r"\#", "orbital@atom(SL)"] * min(len(tbl) // 2, 5),
caption=cap,
cpos="c" + "|cl" * min(len(tbl) // 2, 5),
stretch=1.6,
long=True,
center=False,
)
# atomic basis.
if self.mm["basis_type"] == "jml":
return
site = self.mm["site"]["representative"]
basis = self.mm.group.atomic_basis("lg")
basis_form = Group.global_info()["harmonics"]["basis_function"]
ranks = sorted(
list(set(sum([[rank for rank, orb in enumerate(rep.orbital) if len(orb) > 0] for rep in site.values()], [])))
)
cap = "Atomic basis (orbital part only)"
lbl = ["definition"]
row = []
tbl = []
hl = []
no = -1
for rank in ranks:
for i in basis[rank]:
form = sp.latex(basis_form[i][0])
sb = self.mm.group.tag_atomic_basis(i, rank, latex=True)
row.append(sb)
tbl.append([form])
no += 1
hl.append(no)
self.pdf.table(
tbl,
row,
lbl,
"orbital",
caption=cap,
cpos="ll",
hl=hl[:-1],
rmath=True,
tmath=True,
stretch=1.6,
long=True,
center=False,
)
# ==================================================
[docs]
def symmetry_operation_info(self):
so = self.mm.group.symmetry_operation["tag"]
self.hr("Symmetry Operation")
cap = "Symmetry operation"
# symmetry operation.
tbl = []
for no, op in enumerate(so):
op = "$" + self.mm.group.tag_symmetry_operation(op, latex=True) + "$"
tbl.append([str(no + 1), op])
tbl = sum(tbl, [])
self.pdf.table(
tbl,
[""],
col=[r"\#", "SO"] * min(len(tbl), 5),
caption=cap,
cpos="c" + "|cl" * min(len(tbl), 5),
stretch=1.6,
long=True,
center=False,
)
# ==================================================
def __init__(self, mm, pdf):
"""
create pdf file from material model.
Args:
mm (MaterialModel): material model class.
"""
self.mm = mm
self.pdf = pdf
self.header()
self.general_info()
self.group_cell_info()
self.symmetry_operation_info()
self.harmonics_info()
self.full_matrix_info()
self.combined_samb_info()
self.atomic_samb_info()
self.cluster_samb_info()
self.rep_site_bond_info()
self.site_info()
self.bond_info()
self.pdf.build()
