+from __future__ import print_function
+
+from sympy.vector.vector import *
from sympy import *
import itertools
-
-from moedebug import dbg_enable
-
from sympy.utilities.lambdify import lambdify, implemented_function
+import numpy as np
-r, theta, s, la, mu, kappa = symbols('r theta s lambda mu kappa')
+from moedebug import *
-# start original formulation
-# rightvars replaces
+# When cse() is called for something containing BaseVector, it
+# produces infinite recursion.
+#def cse(x, *a, **kw): return ((), (x,))
def dprint(*args):
- if not dbg_enable: return
+ if not dbg_enabled(): return
print(*args)
def dbg(*args):
- if not dbg_enable: return
+ if not dbg_enabled(): return
for vn in args:
print('\n ' + vn + '\n')
pprint(eval(vn))
print('\n =\n')
pprint(cse(eval(vn)))
+def sqnorm(v): return v & v
+
+N = CoordSysCartesian('N')
+
calculated = False
+def vector_symbols(vnames):
+ out = []
+ for vname in vnames.split(' '):
+ v = Vector.zero
+ for cname in 'i j k'.split(' '):
+ v += getattr(N, cname) * symbols(vname + '_' + cname)
+ out.append(v)
+ return out
+
+A, B, C, D = vector_symbols('A B C D')
+p = vector_symbols('p')
+
+E, H = vector_symbols('E H')
+F0, G0 = vector_symbols('F0 G0')
+En, Hn = vector_symbols('En Hn')
+
+EFlq, HGlq = symbols('EFlq HGlq')
+
+def vector_component(v, ix):
+ return v.components[N.base_vectors()[ix]]
+
+# x array in numerical algorithm has:
+# N x 3 coordinates of points 0..N-3
+# 1 EFlq = sqrt of length parameter |EF| for point 1
+# 1 HGlq = sqrt of length parameter |HG| for point N-2
+
+# fixed array in numerical algorithm has:
+# 4 x 3 E, En, H, Hn
+
+#def subst_vect():
+
+iterations = []
+
+class SomeIteration():
+ def __init__(ar, names, size, expr):
+ ar.names_string = names
+ ar.names = names.split(' ')
+ ar.name = ar.names[0]
+ ar.size = size
+ ar.expr = expr
+ if dbg_enabled():
+ print('\n ' + ar.name + '\n')
+ print(expr)
+ iterations.append(ar)
+
+ def gen_calculate_cost(ar):
+ ar._gen_array()
+ cprint('for (P=0; P<(%s); P++) {' % ar.size)
+ ar._cassign()
+ cprint('}')
+
+class ScalarArray(SomeIteration):
+ def _gen_array(ar):
+ cprint('double A_%s[%s];' % (ar.name, ar.size))
+ def gen_references(ar):
+ for ai in range(0, len(ar.names)):
+ ar._gen_reference(ai, ar.names[ai])
+ def _gen_reference(ar, ai, an):
+ cprintraw('#define %s A_%s[P%+d]' % (an, ar.name, ai))
+ def _cassign(ar):
+ cassign(ar.expr, ar.name, 'tmp_'+ar.name)
+ def s(ar):
+ return symbols(ar.names_string)
+
+class CoordArray(ScalarArray):
+ def _gen_array(ar):
+ cprint('double A_%s[%s][3];' % (ar.name, ar.size))
+ def _gen_reference(ar, ai, an):
+ ScalarArray._gen_reference(ar, ai, an)
+ gen_point_coords_macro(an)
+ def _cassign(ar):
+ cassign_vector(ar.expr, ar.name, 'tmp_'+ar.name)
+ def s(ar):
+ return vector_symbols(ar.names_string)
+
+class CostComponent(SomeIteration):
+ def __init__(cc, size, expr):
+ cc.size = size
+ cc.expr = expr
+ iterations.append(cc)
+ def gen_references(cc): pass
+ def _gen_array(cc): pass
+ def _cassign(cc):
+ cassign(cc.expr, 'P_cost', 'tmp_cost')
+ cprint('cost += P_cost;')
+
def calculate():
global calculated
if calculated: return
- p_start = Matrix([
- r * (1 - cos(theta)),
- r * sin(theta),
- mu * s,
- ])
-
- p_rightvars = p_start.subs( theta, s/r ).subs( r, 1/la )
-
- dbg('p_rightvars')
-
- p_dirn_rightvars = diff(p_rightvars, s)
-
- dbg('p_dirn_rightvars')
-
- zeta = Wild('zeta')
-
- p_nosing = (p_rightvars
- .replace( 1-cos(zeta) , 2*sin(zeta/2)**2 )
- .replace( sin(zeta)**2 , zeta*sinc(zeta)*sin(zeta) )
- )
- p_nosing[1] = (p_nosing[1]
- .replace( sin(zeta) , zeta * sinc(zeta) )
- )
-
- dbg('p_nosing')
-
- t = symbols('t')
-
- q_owncoords = p_nosing.replace(s,t).replace(la,-la)
- q_dirn_owncoords = p_dirn_rightvars.replace(s,t).replace(la,-la)
-
- dbg('q_owncoords','q_dirn_owncoords')
- dbg('q_owncoords.replace(t,0)','q_dirn_owncoords.replace(t,0)')
-
- p2q_translate = p_nosing
- #p2q_rotate_2d = Matrix([ p_dirn_rightvars[0:2],
-
- #p2q_rotate = eye(3)
- #p2q_rotate[0:2, 0] = Matrix([ p_dirn_rightvars[1], -p_dirn_rightvars[0] ])
- #p2q_rotate[0:2, 1] = p_dirn_rightvars[0:2]
-
- p2q_rotate = Matrix([[ cos(theta), sin(theta), 0 ],
- [ -sin(theta), cos(theta), 0 ],
- [ 0 , 0, 1 ]]).subs(theta,la*s)
- #p2q_rotate.add_col([0,0])
- #p2q_rotate.add_row([0,0,1])
-
- dbg('p2q_rotate')
-
- q_dirn_maincoords = p2q_rotate * q_dirn_owncoords;
- q_maincoords = p2q_rotate * q_owncoords + p2q_translate
-
- dbg('diff(p_dirn_rightvars,s)')
- dbg('diff(q_dirn_maincoords,t)')
- dbg('diff(q_dirn_maincoords,t).replace(t,0)')
+ # ---------- actual cost computation formulae ----------
- assert(Eq(p2q_rotate * Matrix([0,1,mu]), p_dirn_rightvars))
+ global F, G
+ F = E + En * pow(EFlq, 2)
+ G = H + Hn * pow(HGlq, 2)
- #for v in 's','t','la','mu':
- # dbg('diff(q_maincoords,%s)' % v)
+ global a,b, al,bl, au,bu
+ a, b = CoordArray ('a_ b_', 'NP-1', B-A ).s() # [mm]
+ al, bl = ScalarArray('al bl', 'NP-1', a.magnitude() ).s() # [mm]
+ au, bu = CoordArray ('au bu', 'NP-1', a / al ).s() # [1]
- #print('\n eye3 subs etc.\n')
- #dbg('''Eq(eye(3) * Matrix([1,0,mu]),
- # p_dirn_rightvars .cross(Matrix([0,0,1]) .subs(s,0)))''')
+ tan_theta = (au ^ bu) / (au & bu) # [1] bending
- #dbg('''Eq(p2q_rotate * Matrix([1,0,mu]),
- # p_dirn_rightvars .cross(Matrix([0,0,1])))''')
+ global mu, nu
+ mu, nu = CoordArray ('mu nu', 'NP-2', tan_theta ).s() # [1]
- #eq = Eq(qmat * q_dirn_owncoords_0, p_dirn_rightvars)
- #print
- #pprint(eq)
- #solve(eq, Q)
+ CostComponent('NP-3', sqnorm(mu - nu)) # [1]
- dbg('q_maincoords.replace(t,0)','q_dirn_maincoords.replace(t,0)')
+ dl2 = pow(al - bl, 2) # [mm^2]
+ CostComponent('NP-2', dl2 / (al*bl)) # [1]
- dbg('q_maincoords','q_dirn_maincoords')
-
- sinof_mu = sin(atan(mu))
- cosof_mu = cos(atan(mu))
-
- dbg('cosof_mu','sinof_mu')
-
- o2p_rotate1 = Matrix([[ 1, 0, 0 ],
- [ 0, cosof_mu, +sinof_mu ],
- [ 0, -sinof_mu, cosof_mu ]])
-
- check_dirn_p_s0 = o2p_rotate1 * p_dirn_rightvars.replace(s,0)
- check_dirn_p_s0.simplify()
- dbg('check_dirn_p_s0')
-
- o2p_rotate2 = Matrix([[ cos(kappa), 0, -sin(kappa) ],
- [ 0, 1, 0 ],
- [ +sin(kappa), 0, cos(kappa) ]])
-
- p_dirn_orgcoords = o2p_rotate2 * o2p_rotate1 * p_dirn_rightvars
-
- check_dirn_p_s0 = p_dirn_orgcoords.replace(s,0)
- check_dirn_p_s0.simplify()
- dbg('check_dirn_p_s0')
-
- check_accel_p_s0 = diff(p_dirn_orgcoords,s).replace(s,0)
- check_accel_p_s0.simplify()
- dbg('check_accel_p_s0')
-
- q_dirn_orgcoords = o2p_rotate2 * o2p_rotate1 * q_dirn_maincoords;
- q_orgcoords = o2p_rotate2 * o2p_rotate1 * q_maincoords;
- dbg('q_orgcoords','q_dirn_orgcoords')
-
- global sh, th
- sh, th = symbols('alpha beta')
-
- global q_sqparm
- q_dirn_sqparm = q_dirn_orgcoords.replace(s, sh**2).replace(t, th**2)
- q_sqparm = q_orgcoords .replace(s, sh**2).replace(t, th**2)
-
- dprint('----------------------------------------')
- dbg('q_sqparm', 'q_dirn_sqparm')
- dprint('----------------------------------------')
- for v in 'sh','th','la','mu':
- dbg('diff(q_sqparm,%s)' % v)
- dbg('diff(q_dirn_sqparm,%s)' % v)
- dprint('----------------------------------------')
-
- gamma = symbols('gamma')
-
- q_dirn_dirnscaled = q_dirn_sqparm * gamma
-
- global result_dirnscaled
- result_dirnscaled = q_sqparm.col_join(q_dirn_dirnscaled)
- dbg('result_dirnscaled')
+ # ---------- end of cost computation formulae ----------
calculated = True
-params = ('sh','th','la','mu','gamma','kappa')
-
def ourccode(*a, **kw):
return ccode(*a, user_functions={'sinc':'sinc'}, **kw)
v = cse_prep_cprint(v, tmp_prefix)
cprint(ourccode(v, assign_to=assign_to))
+def cassign_vector(v, assign_to, tmp_prefix):
+ ijk = 'i j k'.split(' ')
+ for ii in range(0, len(ijk)):
+ x = v & getattr(N, ijk[ii])
+ cassign(x, '%s[%d]' % (assign_to, ii), '%s_%s' % (tmp_prefix, ijk[ii]))
+
def gen_diff(current, smalls):
global j
if not smalls:
def gen_misc():
cprintraw('// AUTOGENERATED - DO NOT EDIT\n')
- cprintraw('#define N %d\n' % len(params))
-def gen_x_extract():
- cprint('#define X_EXTRACT')
- for ix in range(0, len(params)):
- cprint('double %s = X(%d);' % (eval(params[ix]), ix))
- cprintraw()
+def gen_point_coords_macro(macro_basename):
+ ijk = 'i j k'.split(' ')
+ for ii in range(0, len(ijk)):
+ cprintraw('#define %s_%s (%s[%d])'
+ % (macro_basename, ijk[ii], macro_basename, ii))
+
+def gen_point_index_macro(macro_basename, c_array_name, base_index):
+ cprintraw('#define %s (&%s[%s])'
+ % (macro_basename, c_array_name, base_index))
+ gen_point_coords_macro(macro_basename)
+
+def gen_point_references():
+ abcd = 'A B C D'.split(' ')
+
+ gen_point_index_macro('E', 'INPUT', '3*0')
+ gen_point_index_macro('F0', 'INPUT', '3*1')
+ gen_point_index_macro('G0', 'INPUT', '3*(NP-2)')
+ gen_point_index_macro('H', 'INPUT', '3*(NP-1)')
+ cprintraw( '#define NINPUT ( 3*(NP-0) )')
+
+ gen_point_index_macro('En', 'PREP', '3*0')
+ gen_point_index_macro('Hn', 'PREP', '3*1')
+ cprintraw( '#define NPREP (3*2)')
+
+ cprintraw('#define NX_DIRECT 3*(NP-4)')
+ cprint('#define POINT(PP) (')
+ cprint(' (PP) == 0 ? E :')
+ cprint(' (PP) == 1 ? F :')
+ cprint(' (PP) == NP-2 ? G :')
+ cprint(' (PP) == NP-1 ? H :')
+ cprint(' &X(3*((PP)-2))')
+ cprintraw(')')
+
+ cprintraw('#define EFlq X( NX_DIRECT + 0 )')
+ cprintraw('#define HGlq X( NX_DIRECT + 1 )')
+ cprintraw('#define NX ( NX_DIRECT + 2 )')
+
+ for ai in range(0, len(abcd)):
+ cprintraw('#define %s POINT(P%+d)' % (abcd[ai], ai))
+ gen_point_coords_macro(abcd[ai])
+
+ for si in iterations:
+ si.gen_references()
+
+ cprintraw('')
+
+def gen_prepare():
+ cprint('#define PREPARE')
+ cprint('memcpy(X, &INPUT[3*2], sizeof(double) * NX_DIRECT);')
+ for EH,EHs,FG0,FGs in ((E,'E', F0,'F'),
+ (H,'H', G0,'G')):
+ EFHGv = FG0 - EH
+ EFHGl = EFHGv.magnitude()
+ EFHGlq = sqrt(EFHGl)
+ cassign_vector(EFHGv/EFHGl, EHs+'n', 'tmp_'+EHs)
+ cassign(EFHGlq, EHs+FGs+'lq', 'tmp_l'+EHs)
+ cprintraw('')
-def gen_f_populate():
- cprint('#define F_POPULATE')
- cassign(result_dirnscaled,'F','ftmp')
+def gen_calculate_FG():
+ cprintraw('#define DECLARE_F_G double F[3], G[3];')
+ cprint('#define CALCULATE_F_G')
+ cassign_vector(F,'F','tmp_F')
+ cassign_vector(G,'G','tmp_G')
cprintraw('')
-def gen_j_populate():
- cprint('#define J_POPULATE')
- gen_diff(result_dirnscaled, (sh*sh*la, th*th*la))
+def gen_calculate_cost():
+ cprint('#define CALCULATE_COST')
+ cprint('double cost=0, P_cost;')
+ for si in iterations:
+ si.gen_calculate_cost()
cprintraw('')
def gen_C():
gen_misc()
- gen_x_extract()
- gen_f_populate()
- gen_j_populate()
+ gen_point_references()
+ gen_prepare()
+ gen_calculate_FG()
+ gen_calculate_cost()
def get_python():
# https://github.com/sympy/sympy/issues/13642
~ian / moebius3.git / blobdiff