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 *
12 # When cse() is called for something containing BaseVector, it
13 # produces infinite recursion.
14 #def cse(x, *a, **kw): return ((), (x,))
17 if not dbg_enabled(): return
21 if not dbg_enabled(): return
23 print('\n ' + vn + '\n')
28 def sqnorm(v): return v & v
30 N = CoordSysCartesian('N')
34 def vector_symbols(vnames):
36 for vname in vnames.split(' '):
38 for cname in 'i j k'.split(' '):
39 v += getattr(N, cname) * symbols(vname + '_' + cname)
43 A, B, C, D = vector_symbols('A B C D')
44 p = vector_symbols('p')
46 E, H = vector_symbols('E H')
47 F0, G0 = vector_symbols('F0 G0')
48 En, Hn = vector_symbols('En Hn')
50 EFl, HGl = symbols('EFl HGl')
52 def vector_component(v, ix):
53 return v.components[N.base_vectors()[ix]]
55 # x array in numerical algorithm has:
56 # N x 3 coordinates of points 0..N-3
57 # 1 EFl = length parameter |EF| for point 1
58 # 1 HGl = length parameter |HG| for point N-2
60 # fixed array in numerical algorithm has:
67 class SomeIteration():
68 def __init__(ar, names, size, expr):
69 ar.names_string = names
70 ar.names = names.split(' ')
75 print('\n ' + ar.name + '\n')
79 def gen_calculate_cost(ar):
81 cprint('for (P=0; P<(%s); P++) {' % ar.size)
85 class ScalarArray(SomeIteration):
87 cprint('double A_%s[%s];' % (ar.name, ar.size))
88 def gen_references(ar):
89 for ai in range(0, len(ar.names)):
90 ar._gen_reference(ai, ar.names[ai])
91 def _gen_reference(ar, ai, an):
92 cprintraw('#define %s A_%s[P%+d]' % (an, ar.name, ai))
94 cassign(ar.expr, ar.name, 'tmp_'+ar.name)
96 return symbols(ar.names_string)
98 class CoordArray(ScalarArray):
100 cprint('double A_%s[%s][3];' % (ar.name, ar.size))
101 def _gen_reference(ar, ai, an):
102 ScalarArray._gen_reference(ar, ai, an)
103 gen_point_coords_macro(an)
105 cassign_vector(ar.expr, ar.name, 'tmp_'+ar.name)
107 return vector_symbols(ar.names_string)
109 class CostComponent(SomeIteration):
110 def __init__(cc, size, expr):
113 iterations.append(cc)
114 def gen_references(cc): pass
115 def _gen_array(cc): pass
117 cassign(cc.expr, 'P_cost', 'tmp_cost')
118 cprint('cost += P_cost;')
122 if calculated: return
124 # ---------- actual cost computation formulae ----------
130 global a,b, al,bl, au,bu
131 a, b = CoordArray ('a_ b_', 'NP-1', B-A ).s() # [mm]
132 al, bl = ScalarArray('al bl', 'NP-1', a.magnitude() ).s() # [mm]
133 au, bu = CoordArray ('au bu', 'NP-1', a / al ).s() # [1]
135 tan_theta = (au ^ bu) / (au & bu) # [1] bending
136 curvature = tan_theta / sqrt(al * bl) # [1/mm] bending per unit length
139 mu, nu = CoordArray ('mu nu', 'NP-2', curvature ).s() # [1/mm]
141 CostComponent('NP-3', sqnorm(mu - nu)) # [1/mm^2]
143 d_density = 1/al - 1/bl # [1/mm]
144 CostComponent('NP-2', pow(d_density, 2)) # [1/mm^2]
146 # ---------- end of cost computation formulae ----------
150 def ourccode(*a, **kw):
151 return ccode(*a, user_functions={'sinc':'sinc'}, **kw)
157 for l in s.split('\n'):
160 def cse_prep_cprint(v, tmp_prefix):
161 # => v, but also having cprint'd the common subexpression assignments
162 sym_iter = map((lambda i: symbols('%s%d' % (tmp_prefix,i))),
164 (defs, vs) = cse(v, symbols=sym_iter)
165 for defname, defval in defs:
166 cprint('double '+ourccode(defval, assign_to=defname))
169 def cassign(v, assign_to, tmp_prefix):
170 v = cse_prep_cprint(v, tmp_prefix)
171 cprint(ourccode(v, assign_to=assign_to))
173 def cassign_vector(v, assign_to, tmp_prefix):
174 ijk = 'i j k'.split(' ')
175 for ii in range(0, len(ijk)):
176 x = v & getattr(N, ijk[ii])
177 cassign(x, '%s[%d]' % (assign_to, ii), '%s_%s' % (tmp_prefix, ijk[ii]))
179 def gen_diff(current, smalls):
182 j = zeros(len(params),0)
186 d = diff(current, paramv)
190 j = cse_prep_cprint(j, 'jtmp')
191 for ix in range(0, j.cols):
192 cprint(ourccode(j.col(ix), 'J_COL'))
193 cprint('J_END_COL(%d)' % ix)
197 cprint('if (!IS_SMALL(' + ourccode(small) + ')) {')
198 gen_diff(current, smalls)
199 cprint('} else { /* %s small */' % small)
200 gen_diff(current.replace(
202 1 - small*small/factorial(3) - small**4/factorial(5),
206 cprint('} /* %s small */' % small)
209 cprintraw('// AUTOGENERATED - DO NOT EDIT\n')
211 def gen_point_coords_macro(macro_basename):
212 ijk = 'i j k'.split(' ')
213 for ii in range(0, len(ijk)):
214 cprintraw('#define %s_%s (%s[%d])'
215 % (macro_basename, ijk[ii], macro_basename, ii))
217 def gen_point_index_macro(macro_basename, c_array_name, base_index):
218 cprintraw('#define %s (&%s[%s])'
219 % (macro_basename, c_array_name, base_index))
220 gen_point_coords_macro(macro_basename)
222 def gen_point_references():
223 abcd = 'A B C D'.split(' ')
225 gen_point_index_macro('E', 'INPUT', '3*0')
226 gen_point_index_macro('F0', 'INPUT', '3*1')
227 gen_point_index_macro('G0', 'INPUT', '3*(NP-2)')
228 gen_point_index_macro('H', 'INPUT', '3*(NP-1)')
229 cprintraw( '#define NINPUT ( 3*(NP-0) )')
231 gen_point_index_macro('En', 'PREP', '3*0')
232 gen_point_index_macro('Hn', 'PREP', '3*1')
233 cprintraw( '#define NPREP (3*2)')
235 cprintraw('#define NX_DIRECT 3*(NP-4)')
236 cprint('#define POINT(PP) (')
237 cprint(' (PP) == 0 ? E :')
238 cprint(' (PP) == 1 ? F :')
239 cprint(' (PP) == NP-2 ? G :')
240 cprint(' (PP) == NP-1 ? H :')
241 cprint(' &X[3*((PP)-2)]')
244 cprintraw('#define EFl X[ NX_DIRECT + 0 ]')
245 cprintraw('#define HGl X[ NX_DIRECT + 1 ]')
246 cprintraw('#define NX ( NX_DIRECT + 2 )')
248 for ai in range(0, len(abcd)):
249 cprintraw('#define %s POINT(P%+d)' % (abcd[ai], ai))
250 gen_point_coords_macro(abcd[ai])
252 for si in iterations:
258 cprint('#define PREPARE')
259 cprint('memcpy(X, &INPUT[3*2], sizeof(double) * NX_DIRECT);')
260 for EH,EHs,FG0,FGs in ((E,'E', F0,'F'),
263 EFHGl = EFHGv.magnitude()
264 cassign_vector(EFHGv/EFHGl, EHs+'n', 'tmp_'+EHs)
265 cassign(EFHGl, EHs+FGs+'l', 'tmp_l'+EHs)
268 def gen_calculate_FG():
269 cprintraw('#define DECLARE_F_G double F[3], G[3];')
270 cprint('#define CALCULATE_F_G')
271 cassign_vector(F,'F','tmp_F')
272 cassign_vector(G,'G','tmp_G')
275 def gen_calculate_cost():
276 cprint('#define CALCULATE_COST')
277 cprint('double cost=0, P_cost;')
278 for si in iterations:
279 si.gen_calculate_cost()
284 gen_point_references()
290 # https://github.com/sympy/sympy/issues/13642
291 # "lambdify sinc gives wrong answer!"
293 sinc_fixed = Function('sinc_fixed')
294 implemented_function(sinc_fixed, lambda x: np.sinc(x/np.pi))
295 out = out.subs(sinc,sinc_fixed)
296 p = list(map(eval,params))
297 return lambdify(p, out)