7 from optparse import OptionParser
9 opt_parser = OptionParser()
10 opt_parser.add_option('-q',dest='quiet',action='store_true',
11 default=False,help='suppress diagnostic output')
12 opt_parser.add_option('-7',dest='ascii',action='store_true',
13 default=False,help='use 7-bit output only')
14 opt_parser.add_option('-w',dest='width',action='store',type='int',
15 default=80,help='width for printing')
16 (options, args) = opt_parser.parse_args()
19 if (not options.ascii) and sys.stdout.encoding is None:
20 sys.stdout = codecs.open("/dev/stdout", "w", 'utf-8')
22 init_printing(use_unicode=(not options.ascii), num_columns=options.width)
24 r, theta, s, la, mu, kappa = symbols('r theta s lambda mu kappa')
26 # start original formulation
35 p_rightvars = p_start.subs( theta, s/r ).subs( r, 1/la )
38 if options.quiet: return
42 if options.quiet: return
44 print('\n ' + vn + '\n')
51 p_dirn_rightvars = diff(p_rightvars, s)
53 dbg('p_dirn_rightvars')
57 p_nosing = (p_rightvars
58 .replace( 1-cos(zeta) , 2*sin(zeta/2)**2 )
59 .replace( sin(zeta)**2 , zeta*sinc(zeta)*sin(zeta) )
61 p_nosing[1] = (p_nosing[1]
62 .replace( sin(zeta) , zeta * sinc(zeta) )
69 q_owncoords = p_nosing.replace(s,t).replace(la,-la)
70 q_dirn_owncoords = p_dirn_rightvars.replace(s,t).replace(la,-la)
72 dbg('q_owncoords','q_dirn_owncoords')
73 dbg('q_owncoords.replace(t,0)','q_dirn_owncoords.replace(t,0)')
75 p2q_translate = p_nosing
76 #p2q_rotate_2d = Matrix([ p_dirn_rightvars[0:2],
79 #p2q_rotate[0:2, 0] = Matrix([ p_dirn_rightvars[1], -p_dirn_rightvars[0] ])
80 #p2q_rotate[0:2, 1] = p_dirn_rightvars[0:2]
82 p2q_rotate = Matrix([[ cos(theta), sin(theta), 0 ],
83 [ -sin(theta), cos(theta), 0 ],
84 [ 0 , 0, 1 ]]).subs(theta,la*s)
85 #p2q_rotate.add_col([0,0])
86 #p2q_rotate.add_row([0,0,1])
90 q_dirn_maincoords = p2q_rotate * q_dirn_owncoords;
91 q_maincoords = p2q_rotate * q_owncoords + p2q_translate
93 dbg('diff(p_dirn_rightvars,s)')
94 dbg('diff(q_dirn_maincoords,t)')
95 dbg('diff(q_dirn_maincoords,t).replace(t,0)')
97 assert(Eq(p2q_rotate * Matrix([0,1,mu]), p_dirn_rightvars))
99 #for v in 's','t','la','mu':
100 # dbg('diff(q_maincoords,%s)' % v)
102 #print('\n eye3 subs etc.\n')
103 #dbg('''Eq(eye(3) * Matrix([1,0,mu]),
104 # p_dirn_rightvars .cross(Matrix([0,0,1]) .subs(s,0)))''')
106 #dbg('''Eq(p2q_rotate * Matrix([1,0,mu]),
107 # p_dirn_rightvars .cross(Matrix([0,0,1])))''')
109 #eq = Eq(qmat * q_dirn_owncoords_0, p_dirn_rightvars)
114 dbg('q_maincoords.replace(t,0)','q_dirn_maincoords.replace(t,0)')
116 dbg('q_maincoords','q_dirn_maincoords')
118 sinof_mu = sin(atan(mu))
119 cosof_mu = cos(atan(mu))
121 dbg('cosof_mu','sinof_mu')
123 o2p_rotate1 = Matrix([[ 1, 0, 0 ],
124 [ 0, cosof_mu, +sinof_mu ],
125 [ 0, -sinof_mu, cosof_mu ]])
127 check_dirn_p_s0 = o2p_rotate1 * p_dirn_rightvars.replace(s,0)
128 check_dirn_p_s0.simplify()
129 dbg('check_dirn_p_s0')
131 o2p_rotate2 = Matrix([[ cos(kappa), 0, -sin(kappa) ],
133 [ +sin(kappa), 0, cos(kappa) ]])
135 p_dirn_orgcoords = o2p_rotate2 * o2p_rotate1 * p_dirn_rightvars
137 check_dirn_p_s0 = p_dirn_orgcoords.replace(s,0)
138 check_dirn_p_s0.simplify()
139 dbg('check_dirn_p_s0')
141 check_accel_p_s0 = diff(p_dirn_orgcoords,s).replace(s,0)
142 check_accel_p_s0.simplify()
143 dbg('check_accel_p_s0')
145 q_dirn_orgcoords = o2p_rotate2 * o2p_rotate1 * q_dirn_maincoords;
146 q_orgcoords = o2p_rotate2 * o2p_rotate1 * q_maincoords;
147 dbg('q_orgcoords','q_dirn_orgcoords')
149 sh, th = symbols('alpha beta')
151 q_dirn_sqparm = q_dirn_orgcoords.replace(s, sh**2).replace(t, th**2)
152 q_sqparm = q_orgcoords .replace(s, sh**2).replace(t, th**2)
154 dprint('----------------------------------------')
155 dbg('q_sqparm', 'q_dirn_sqparm')
156 dprint('----------------------------------------')
157 for v in 'sh','th','la','mu':
158 dbg('diff(q_sqparm,%s)' % v)
159 dbg('diff(q_dirn_sqparm,%s)' % v)
160 dprint('----------------------------------------')
162 gamma = symbols('gamma')
164 q_dirn_dirnscaled = q_dirn_sqparm * gamma
166 result_dirnscaled = q_sqparm.col_join(q_dirn_dirnscaled)
167 dbg('result_dirnscaled')
169 params = ('sh','th','la','mu','gamma','kappa')
171 def ourccode(*a, **kw):
172 return ccode(*a, user_functions={'sinc':'sinc'}, **kw)
178 for l in s.split('\n'):
181 def cse_prep_cprint(v, tmp_prefix):
182 # => v, but also having cprint'd the common subexpression assignments
183 sym_iter = map((lambda i: symbols('%s%d' % (tmp_prefix,i))),
185 (defs, vs) = cse(v, symbols=sym_iter)
186 for defname, defval in defs:
187 cprint('double '+ourccode(defval, assign_to=defname))
190 def cassign(v, assign_to, tmp_prefix):
191 v = cse_prep_cprint(v, tmp_prefix)
192 cprint(ourccode(v, assign_to=assign_to))
194 def gen_diff(current, smalls):
197 j = zeros(len(params),0)
201 d = diff(current, paramv)
205 j = cse_prep_cprint(j, 'jtmp')
206 for ix in range(0, j.cols):
207 cprint(ourccode(j.col(ix), 'J_COL'))
208 cprint('J_END_COL(%d)' % ix)
212 cprint('if (!IS_SMALL(' + ourccode(small) + ')) {')
213 gen_diff(current, smalls)
214 cprint('} else { /* %s small */' % small)
215 gen_diff(current.replace(
217 1 - small*small/factorial(3) - small**4/factorial(5),
221 cprint('} /* %s small */' % small)
224 cprintraw('// AUTOGENERATED - DO NOT EDIT\n')
225 cprintraw('#define N %d\n' % len(params))
228 cprint('#define X_EXTRACT')
229 for ix in range(0, len(params)):
230 cprint('double %s = X(%d);' % (eval(params[ix]), ix))
233 def gen_f_populate():
234 cprint('#define F_POPULATE')
235 cassign(result_dirnscaled,'F','ftmp')
238 def gen_j_populate():
239 cprint('#define J_POPULATE')
240 gen_diff(result_dirnscaled, (sh*sh*la, th*th*la))