9267239762

Committed 28 May 2024 09:53AM UTC coverage: 80.215% (-2.1%) from 82.348%

Build # 9267239762

Build Type

Pull #67

github

Committed by

APN-Pucky

Commit Message

fix: PREFACTOR

Pull Request Pull Request #67: add: spin correlation

Run Details

13 of 43 new or added lines in 5 files covered. (30.23%)

31 existing lines in 3 files now uncovered.

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84.21

/feynamp/form/color.py

from typing import List

from feynamp.form.form import get_dummy_index, init, run, run_parallel, string_to_form
from feynamp.leg import (
    color_vector_to_id,
    color_vector_to_index,
    color_vector_to_operator,
    get_color_vector,
    get_leg_momentum,
    is_swapped_color_vector,
)
from feynamp.log import debug

from .colorh import colorh

colorh_init = f"""
{colorh}
AutoDeclare Index Color=NR;
AutoDeclare Index Glu=NA;
"""

color_init = """
AutoDeclare Index Color;
AutoDeclare Index Glu;
Tensors f(antisymmetric), colorcorrelation;
CFunctions T;
Symbols NA,I2R;
"""

color_ids = """
repeat;
* remove df(k,j)
   id df(k?,l?)*df(l?,j?)=df(k,j);
   id T(a?,k?,l?)*df(k?,j?)=T(a,j,l);
   id T(a?,k?,l?)*df(l?,j?)=T(a,k,j);
* remove da(a,b)
   id da(a?,b?)*da(b?,c?)=da(a,c);
   id T(a?,k?,l?)*da(a?,b?)=T(b,k,l);
   id f(a?,b?,c?)*da(a?,d?)=f(d,b,c);
* simplify traces
   id T(b?,k?,k?)=0;
   id da(a?,a?)=Nc*Cf/Tr;
   id df(a?,a?)=Nc;
endrepeat;
"""

colorh_ids = """
* https://www.nikhef.nl/~form/maindir/packages/color/color.pdf
* Appendix D
id d33(cOlpR1,cOlpR2) = I2R^3/(2*Nc)*(Nc^2-1)*(Nc^2-4);
id d44(cOlpR1,cOlpR2) = I2R^4/(6*Nc^2)*(Nc^2-1)*(Nc^4-6*Nc^2+18);
repeat;
* remove df(k,j)
   id df(k?,l?)*df(l?,j?)=df(k,j);
   id T(k?,l?,a?)*df(k?,j?)=T(j,l,a);
   id T(k?,l?,a?)*df(l?,j?)=T(k,j,a);
* remove da(a,b)
   id da(a?,b?)*da(b?,c?)=da(a,c);
   id T(k?,l?,a?)*da(a?,b?)=T(k,l,b);
   id f(b?,c?,a?)*da(a?,d?)=f(b,c,d);
* simplify traces
   id T(k?,k?,b?)=0;
   id da(a?,a?)=Nc*Cf/Tr;
   id df(a?,a?)=Nc;
endrepeat;
"""

color_simplify = """
* simplify combination of factors
*   id Nc^-2=2-Nc^2+Cf^2*Tr^-2;
*   id Nc^2=1+Nc*Cf/Tr;
   id NA=Nc*Cf/Tr;
   id cA=Nc;
   id cR=Cf;
   id I2R=1/2;
   id Tr=1/2;
   id Tr^-1=2;
"""

old_color = f"""
**********************************************************
*                  COLOUR STRUCTURE SIMPLIFY             *
**********************************************************
    
repeat;
{color_ids}
* length-three objects simplify:
   id T(b?,k?,j?)*T(a?,j?,c?)*T(b?,c?,l?)=(-Tr/Nc*T(a,k,l));
   id T(b?,j?,l?)*T(c?,l?,k?)*f(a?,b?,c?)=(i_*Nc*Tr*T(a,j,k));
* length-two objects that give out df(k,j)
   id T(a?,c?,j?)*T(a?,k?,l?)=(-1/Nc*df(c, j)*df(k, l)*Tr + df(c, l)*df(j, k)*Tr);
   id T(a?,k?,l?)*T(a?,l?,j?)=(Cf*df(k,j));
* length-two objects that give out da(a,b)
   id T(a?,k?,l?)*T(b?,l?,k?)=(Tr*da(a,b));
   id f(a?,b?,c?)*f(d?,b?,c?)=Nc*da(a,d); 
{color_simplify}
* double f(a,b,c) simplify
*  id f(a?,b?,e?)*f(c?,d?,e?)=-2 * {{ [T(a), T(b)] [T(c), T(d)]}};
   id f(a?,b?,e?)*f(c?,d?,e?)=-2 * (T(a,e,N1_?)*T(b,N1_?,N2_?) - T(b,e,N1_?)*T(a,N1_?,N2_?))*(T(c,N2_?,N3_?)*T(d,N3_?,e)-T(d,N2_?,N3_?)*T(c,N3_?,e));
endrepeat;
"""


color = """
#call docolor
"""
# TODO do the color stuff manually (cf. MG) since the simplifications here are very expensive

color_sum = """
**********************************************************
*                  COLOUR SUM SIMPLIFY                   *
**********************************************************
repeat;
  id VA(Glua?,Momb?)*VA(Gluc?,Momb?) = da(Glua,Gluc);
  id VC(Colora?,Momb?)*VC(Colorc?,Momb?) = df(Colora,Colorc);
endrepeat;
"""


def rep(s: str):
    return f"""
repeat;
   {s}
endrepeat;
"""


repeat = rep


def get_color(fds=None, legs=None, model=None, colorcorrelation=False, s2=None):
    assert not colorcorrelation or (
        fds is not None and legs is not None and model is not None
    )
    # return get_color_v1()
    return get_color_v3(fds, legs, model, colorcorrelation=colorcorrelation, s2=s2)


def get_full_color_correlation_matrix(fds, legs, model, s2):

    left = ""
    right = ""
    vec = []
    ops = []
    ind = []
    ind1 = []
    ind2 = []
    mom = []
    swap = []
    ids = []
    for i in range(len(legs)):
        swap += [is_swapped_color_vector(fds[0], legs[i], model, s2)]
        vec += [get_color_vector(fds[0], legs[i], model)]
        ids += [color_vector_to_id(vec[i])]
        mom += [get_leg_momentum(legs[i])]
        ops += [("(-1)*" if swap[i] else "") + str(color_vector_to_operator(vec[i]))]
        ind += [color_vector_to_index(vec[i])]
        ind1 += [str(ind[i]) + legs[i].id]
        ind2 += [str(ind[i]) + get_dummy_index(underscore=False, questionmark=False)]
    dummy = "Glu" + get_dummy_index(underscore=False, questionmark=False)
    for i in range(len(legs)):
        if vec[i] is not None:
            i1 = ind1[i] + " "
            i2 = ind2[i] + "?"
            if swap[i]:
                i1, i2 = i2, i1
            left += f"{vec[i]}({i1},{mom[i]})*{vec[i]}({i2},{mom[i]})*"
            i1, i2 = i1[:-1], i2[:-1]
            for j in range(i + 1, len(legs)):
                if vec[j] is not None:

                    j1 = ind1[j]
                    j2 = ind2[j]
                    if swap[j]:
                        j1, j2 = j2, j1
                    deltas = "*"
                    for k in range(len(legs)):
                        if vec[k] is not None and i != k and j != k:
                            deltas += f"{ids[k]}({ind1[k]},{ind2[k]})*"
                    right += f"\ncolorcorrelation({mom[i]},{mom[j]})*{ops[i]}({i1},{i2},{dummy})*{ops[j]}({j1},{j2},{dummy}){deltas[:-1]}+"
                    # right += f"\n{ops[i]}({i1},{i2},{dummy})*{ops[j]}({j1},{j2},{dummy}){deltas[:-1]}+"
                    # right += f"\ncolorcorrelation({mom[i]},{mom[j]})*d_({i1},{i2})*d_({j1},{j2}){deltas[:-1]}+"
    if left == "" or right == "":
        # Nothing to color correlate => abort/return 0
        return "id PREFACTOR = 0;"
    # The minus sign below is from https://arxiv.org/pdf/1002.2581 Eq. 2.6
    ret = f"""
    id {left[:-1]} = -({right[:-1]});
    """
    # print(ret)
    return ret


def get_color_sum_v1(mom1=None, mom2=None):
    ret = ""
    if mom1 is not None and mom2 is not None:
        # new index that is summed over
        dummy = "Glu" + get_dummy_index()
        ret += repeat(
            f"""
         id VA(Glua?,{mom1})*VA(Gluc?,{mom1}) = f(Glua,Gluc,{dummy});
         id VA(Glua?,{mom2})*VA(Gluc?,{mom2}) = f(Glua,Gluc,{dummy});
         id VC(Colora?,{mom1})*VC(Colorc?,{mom1}) = T(Colora,Colorc,{dummy});
         id VC(Colora?,{mom2})*VC(Colorc?,{mom2}) = T(Colora,Colorc,{dummy});
"""
        )
    return ret + color_sum


def get_color_v3(fds, legs, model, colorcorrelation=False, s2=None):
    ret = ""
    if colorcorrelation:
        ret += get_full_color_correlation_matrix(fds, legs, model, s2=s2)
    else:
        ret += color_sum
    return ret + colorh_ids + color + colorh_ids + rep(color_simplify)


def get_color_v2():
    return color_sum + colorh_ids + color + colorh_ids + rep(color_simplify)


def get_color_v1():
    return color_sum + color_ids + old_color


def get_color_ids():
    return color_sum + colorh_ids


def apply_color_ids(string_expr):
    s = string_to_form(string_expr)
    return run(init + colorh_init + f"Local TMP = {s};" + get_color_ids())


def apply_color_parallel(string_exprs: List[str], **kwargs):
    return run_parallel(
        init + colorh_init,
        # we only forward one
        get_color(s2=string_exprs[0], **kwargs),
        [string_to_form(a) for a in string_exprs],
    )


def apply_color(string_expr):
    s = string_to_form(string_expr)
    return run(init + colorh_init + f"Local TMP = {s};" + get_color())


def apply_color_sum(string_expr):
    s = string_to_form(string_expr)
    return run(init + f"Local TMP = {s};" + color_sum)


def apply_color_simplify(string_expr):
    s = string_to_form(string_expr)
    return run(init + f"Local TMP = {s};" + color)

1	from typing import List	1✔
2
3	from feynamp.form.form import get_dummy_index, init, run, run_parallel, string_to_form	1✔
4	from feynamp.leg import (	1✔
5	color_vector_to_id,
6	color_vector_to_index,
7	color_vector_to_operator,
8	get_color_vector,
9	get_leg_momentum,
10	is_swapped_color_vector,
11	)
12	from feynamp.log import debug	1✔
13
14	from .colorh import colorh	1✔
15
16	colorh_init = f"""	1✔
17	{colorh}
18	AutoDeclare Index Color=NR;
19	AutoDeclare Index Glu=NA;
20	"""
21
22	color_init = """	1✔
23	AutoDeclare Index Color;
24	AutoDeclare Index Glu;
25	Tensors f(antisymmetric), colorcorrelation;
26	CFunctions T;
27	Symbols NA,I2R;
28	"""
29
30	color_ids = """	1✔
31	repeat;
32	* remove df(k,j)
33	id df(k?,l?)*df(l?,j?)=df(k,j);
34	id T(a?,k?,l?)*df(k?,j?)=T(a,j,l);
35	id T(a?,k?,l?)*df(l?,j?)=T(a,k,j);
36	* remove da(a,b)
37	id da(a?,b?)*da(b?,c?)=da(a,c);
38	id T(a?,k?,l?)*da(a?,b?)=T(b,k,l);
39	id f(a?,b?,c?)*da(a?,d?)=f(d,b,c);
40	* simplify traces
41	id T(b?,k?,k?)=0;
42	id da(a?,a?)=Nc*Cf/Tr;
43	id df(a?,a?)=Nc;
44	endrepeat;
45	"""
46
47	colorh_ids = """	1✔
48	* https://www.nikhef.nl/~form/maindir/packages/color/color.pdf
49	* Appendix D
50	id d33(cOlpR1,cOlpR2) = I2R^3/(2Nc)(Nc^2-1)*(Nc^2-4);
51	id d44(cOlpR1,cOlpR2) = I2R^4/(6Nc^2)(Nc^2-1)(Nc^4-6Nc^2+18);
52	repeat;
53	* remove df(k,j)
54	id df(k?,l?)*df(l?,j?)=df(k,j);
55	id T(k?,l?,a?)*df(k?,j?)=T(j,l,a);
56	id T(k?,l?,a?)*df(l?,j?)=T(k,j,a);
57	* remove da(a,b)
58	id da(a?,b?)*da(b?,c?)=da(a,c);
59	id T(k?,l?,a?)*da(a?,b?)=T(k,l,b);
60	id f(b?,c?,a?)*da(a?,d?)=f(b,c,d);
61	* simplify traces
62	id T(k?,k?,b?)=0;
63	id da(a?,a?)=Nc*Cf/Tr;
64	id df(a?,a?)=Nc;
65	endrepeat;
66	"""
67
68	color_simplify = """	1✔
69	* simplify combination of factors
70	* id Nc^-2=2-Nc^2+Cf^2*Tr^-2;
71	* id Nc^2=1+Nc*Cf/Tr;
72	id NA=Nc*Cf/Tr;
73	id cA=Nc;
74	id cR=Cf;
75	id I2R=1/2;
76	id Tr=1/2;
77	id Tr^-1=2;
78	"""
79
80	old_color = f"""	1✔
81	**********************************************************
82	* COLOUR STRUCTURE SIMPLIFY *
83	**********************************************************
84
85	repeat;
86	{color_ids}
87	* length-three objects simplify:
88	id T(b?,k?,j?)T(a?,j?,c?)T(b?,c?,l?)=(-Tr/Nc*T(a,k,l));
89	id T(b?,j?,l?)T(c?,l?,k?)f(a?,b?,c?)=(i_NcTr*T(a,j,k));
90	* length-two objects that give out df(k,j)
91	id T(a?,c?,j?)T(a?,k?,l?)=(-1/Ncdf(c, j)df(k, l)Tr + df(c, l)df(j, k)Tr);
92	id T(a?,k?,l?)T(a?,l?,j?)=(Cfdf(k,j));
93	* length-two objects that give out da(a,b)
94	id T(a?,k?,l?)T(b?,l?,k?)=(Trda(a,b));
95	id f(a?,b?,c?)f(d?,b?,c?)=Ncda(a,d);
96	{color_simplify}
97	* double f(a,b,c) simplify
98	* id f(a?,b?,e?)f(c?,d?,e?)=-2 {{ [T(a), T(b)] [T(c), T(d)]}};
99	id f(a?,b?,e?)f(c?,d?,e?)=-2 (T(a,e,N1_?)T(b,N1_?,N2_?) - T(b,e,N1_?)T(a,N1_?,N2_?))(T(c,N2_?,N3_?)T(d,N3_?,e)-T(d,N2_?,N3_?)*T(c,N3_?,e));
100	endrepeat;
101	"""
102
103
104	color = """	1✔
105	#call docolor
106	"""
107	# TODO do the color stuff manually (cf. MG) since the simplifications here are very expensive
108
109	color_sum = """	1✔
110	**********************************************************
111	* COLOUR SUM SIMPLIFY *
112	**********************************************************
113	repeat;
114	id VA(Glua?,Momb?)*VA(Gluc?,Momb?) = da(Glua,Gluc);
115	id VC(Colora?,Momb?)*VC(Colorc?,Momb?) = df(Colora,Colorc);
116	endrepeat;
117	"""
118
119
120	def rep(s: str):	1✔
121	return f"""	1✔
122	repeat;
123	{s}
124	endrepeat;
125	"""
126
127
128	repeat = rep	1✔
129
130
131	def get_color(fds=None, legs=None, model=None, colorcorrelation=False, s2=None):	1✔
132	assert not colorcorrelation or (	1✔
133	fds is not None and legs is not None and model is not None
134	)
135	# return get_color_v1()
136	return get_color_v3(fds, legs, model, colorcorrelation=colorcorrelation, s2=s2)	1✔
137
138
139	def get_full_color_correlation_matrix(fds, legs, model, s2):	1✔
140
141	left = ""	1✔
142	right = ""	1✔
143	vec = []	1✔
144	ops = []	1✔
145	ind = []	1✔
146	ind1 = []	1✔
147	ind2 = []	1✔
148	mom = []	1✔
149	swap = []	1✔
150	ids = []	1✔
151	for i in range(len(legs)):	1✔
152	swap += [is_swapped_color_vector(fds[0], legs[i], model, s2)]	1✔
153	vec += [get_color_vector(fds[0], legs[i], model)]	1✔
154	ids += [color_vector_to_id(vec[i])]	1✔
155	mom += [get_leg_momentum(legs[i])]	1✔
156	ops += [("(-1)*" if swap[i] else "") + str(color_vector_to_operator(vec[i]))]	1✔
157	ind += [color_vector_to_index(vec[i])]	1✔
158	ind1 += [str(ind[i]) + legs[i].id]	1✔
159	ind2 += [str(ind[i]) + get_dummy_index(underscore=False, questionmark=False)]	1✔
160	dummy = "Glu" + get_dummy_index(underscore=False, questionmark=False)	1✔
161	for i in range(len(legs)):	1✔
162	if vec[i] is not None:	1✔
163	i1 = ind1[i] + " "	1✔
164	i2 = ind2[i] + "?"	1✔
165	if swap[i]:	1✔
166	i1, i2 = i2, i1	1✔
167	left += f"{vec[i]}({i1},{mom[i]}){vec[i]}({i2},{mom[i]})"	1✔
168	i1, i2 = i1[:-1], i2[:-1]	1✔
169	for j in range(i + 1, len(legs)):	1✔
170	if vec[j] is not None:	1✔
171
172	j1 = ind1[j]	1✔
173	j2 = ind2[j]	1✔
174	if swap[j]:	1✔
175	j1, j2 = j2, j1	1✔
176	deltas = "*"	1✔
177	for k in range(len(legs)):	1✔
178	if vec[k] is not None and i != k and j != k:	1✔
179	deltas += f"{ids[k]}({ind1[k]},{ind2[k]})*"	1✔
180	right += f"\ncolorcorrelation({mom[i]},{mom[j]}){ops[i]}({i1},{i2},{dummy}){ops[j]}({j1},{j2},{dummy}){deltas[:-1]}+"	1✔
181	# right += f"\n{ops[i]}({i1},{i2},{dummy})*{ops[j]}({j1},{j2},{dummy}){deltas[:-1]}+"
182	# right += f"\ncolorcorrelation({mom[i]},{mom[j]})d_({i1},{i2})d_({j1},{j2}){deltas[:-1]}+"
183	if left == "" or right == "":	1✔
184	# Nothing to color correlate => abort/return 0
NEW 185	return "id PREFACTOR = 0;"	×
186	# The minus sign below is from https://arxiv.org/pdf/1002.2581 Eq. 2.6
187	ret = f"""	1✔
188	id {left[:-1]} = -({right[:-1]});
189	"""
190	# print(ret)
191	return ret	1✔
192
193
194	def get_color_sum_v1(mom1=None, mom2=None):	1✔
195	ret = ""	×
196	if mom1 is not None and mom2 is not None:	×
197	# new index that is summed over
198	dummy = "Glu" + get_dummy_index()	×
199	ret += repeat(	×
200	f"""
201	id VA(Glua?,{mom1})*VA(Gluc?,{mom1}) = f(Glua,Gluc,{dummy});
202	id VA(Glua?,{mom2})*VA(Gluc?,{mom2}) = f(Glua,Gluc,{dummy});
203	id VC(Colora?,{mom1})*VC(Colorc?,{mom1}) = T(Colora,Colorc,{dummy});
204	id VC(Colora?,{mom2})*VC(Colorc?,{mom2}) = T(Colora,Colorc,{dummy});
205	"""
206	)
207	return ret + color_sum	×
208
209
210	def get_color_v3(fds, legs, model, colorcorrelation=False, s2=None):	1✔
211	ret = ""	1✔
212	if colorcorrelation:	1✔
213	ret += get_full_color_correlation_matrix(fds, legs, model, s2=s2)	1✔
214	else:
215	ret += color_sum	1✔
216	return ret + colorh_ids + color + colorh_ids + rep(color_simplify)	1✔
217
218
219	def get_color_v2():	1✔
220	return color_sum + colorh_ids + color + colorh_ids + rep(color_simplify)	×
221
222
223	def get_color_v1():	1✔
224	return color_sum + color_ids + old_color	×
225
226
227	def get_color_ids():	1✔
228	return color_sum + colorh_ids	×
229
230
231	def apply_color_ids(string_expr):	1✔
232	s = string_to_form(string_expr)	×
233	return run(init + colorh_init + f"Local TMP = {s};" + get_color_ids())	×
234
235
236	def apply_color_parallel(string_exprs: List[str], **kwargs):	1✔
237	return run_parallel(	1✔
238	init + colorh_init,
239	# we only forward one
240	get_color(s2=string_exprs[0], **kwargs),
241	[string_to_form(a) for a in string_exprs],
242	)
243
244
245	def apply_color(string_expr):	1✔
246	s = string_to_form(string_expr)	1✔
247	return run(init + colorh_init + f"Local TMP = {s};" + get_color())	1✔
248
249
250	def apply_color_sum(string_expr):	1✔
251	s = string_to_form(string_expr)	×
252	return run(init + f"Local TMP = {s};" + color_sum)	×
253
254
255	def apply_color_simplify(string_expr):	1✔
256	s = string_to_form(string_expr)	×
257	return run(init + f"Local TMP = {s};" + color)	×

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