2 from __future__ import print_function
4 from sympy.vector.vector import *
7 from sympy.utilities.lambdify import lambdify, implemented_function
10 from moedebug import *
13 if not dbg_enabled(): return
17 if not dbg_enabled(): return
19 print('\n ' + vn + '\n')
24 N = CoordSysCartesian('N')
28 def vector_symbols(vnames):
30 for vname in vnames.split(' '):
32 for cname in 'i j k'.split(' '):
33 v += getattr(N, cname) * symbols(vname + '_' + cname)
37 A, B, C, D = vector_symbols('A B C D')
38 p = vector_symbols('p')
40 E, H = vector_symbols('E H')
41 En, Hn = vector_symbols('En Hn')
43 EFl, GHl = symbols('EFl GHl')
45 def vector_component(v, ix):
46 return v.components[N.base_vectors()[ix]]
48 # x array in numerical algorithm has:
49 # N x 3 coordinates of points 0..N-3
50 # 1 EFl = length parameter |EF| for point 1
51 # 1 GHl = length parameter |GH| for point N-2
53 # fixed array in numerical algorithm has:
66 cost_ABCD = (QR & QR) / (BC & BC)
74 #cost_EFCD = subst_vect(cost_ABCD, (A,E), (B,F))
75 #cost_FBCD = subst_vect(cost_ABCD, (A,F))
76 #cost_ABCG = subst_vect(cost_ABCD, (D,G))
77 #cost_ABGH = subst_vect(cost_ABCD, (C,G), (D,H))
79 # diff_A_i = cost_ABCD.diff(vector_component(A, 0))
85 def ourccode(*a, **kw):
86 return ccode(*a, user_functions={'sinc':'sinc'}, **kw)
92 for l in s.split('\n'):
95 def cse_prep_cprint(v, tmp_prefix):
96 # => v, but also having cprint'd the common subexpression assignments
97 sym_iter = map((lambda i: symbols('%s%d' % (tmp_prefix,i))),
99 (defs, vs) = cse(v, symbols=sym_iter)
100 for defname, defval in defs:
101 cprint('double '+ourccode(defval, assign_to=defname))
104 def cassign(v, assign_to, tmp_prefix):
105 v = cse_prep_cprint(v, tmp_prefix)
106 cprint(ourccode(v, assign_to=assign_to))
108 def gen_diff(current, smalls):
111 j = zeros(len(params),0)
115 d = diff(current, paramv)
119 j = cse_prep_cprint(j, 'jtmp')
120 for ix in range(0, j.cols):
121 cprint(ourccode(j.col(ix), 'J_COL'))
122 cprint('J_END_COL(%d)' % ix)
126 cprint('if (!IS_SMALL(' + ourccode(small) + ')) {')
127 gen_diff(current, smalls)
128 cprint('} else { /* %s small */' % small)
129 gen_diff(current.replace(
131 1 - small*small/factorial(3) - small**4/factorial(5),
135 cprint('} /* %s small */' % small)
138 cprintraw('// AUTOGENERATED - DO NOT EDIT\n')
140 def gen_point_index_macro(macro_basename, c_array_name, base_index):
141 cprintraw('#define %s (&%s[%s])'
142 % (macro_basename, c_array_name, base_index))
143 ijk = 'i j k'.split(' ')
144 for ii in range(0, len(ijk)):
145 cprintraw('#define %s_%s (%s[%d])'
146 % (macro_basename, ijk[ii], macro_basename, ii))
148 def gen_abcd_ijk_macros():
149 abcd = 'A B C D'.split(' ')
150 eh = 'E En H Hn'.split(' ')
151 for ehi in range(0, len(eh)):
152 gen_point_index_macro(eh[ehi], 'FIXED', ehi * 3)
154 for ai in range(0, len(abcd)):
155 gen_point_index_macro(abcd[ai], 'X', '(P%+d) * 3' % (ai - 2))
157 cprint('#define E_CALCULATE_MID')
158 cassign(cost_ABCD,'d','dtmp_mid')
160 def gen_e_calculate():
161 cprint('#define E_CALCULATE_MID')
163 cassign(cost_ABCD,'d','dtmp_mid')
165 def gen_f_populate():
166 cprint('#define F_POPULATE')
167 cassign(cost_ABCD,'F','ftmp')
170 def gen_j_populate():
171 cprint('#define J_POPULATE')
172 gen_diff(result_dirnscaled, (sh*sh*la, th*th*la))
177 gen_abcd_ijk_macros()
181 # https://github.com/sympy/sympy/issues/13642
182 # "lambdify sinc gives wrong answer!"
184 sinc_fixed = Function('sinc_fixed')
185 implemented_function(sinc_fixed, lambda x: np.sinc(x/np.pi))
186 out = out.subs(sinc,sinc_fixed)
187 p = list(map(eval,params))
188 return lambdify(p, out)