X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?a=blobdiff_plain;f=symbolic.py;h=8680378ea06d906cbf58b4d230f09451e5ec281d;hb=c1001cc933c7a48935777908ba8338673cd091dc;hp=aa42d0766f58a9026420a4d5ebab1b63227b646c;hpb=549b367a7e3623a6fac0e2bd970667071a7be6d3;p=moebius3.git diff --git a/symbolic.py b/symbolic.py old mode 100755 new mode 100644 index aa42d07..8680378 --- a/symbolic.py +++ b/symbolic.py @@ -1,81 +1,297 @@ -#!/usr/bin/python +from __future__ import print_function + +from sympy.vector.vector import * from sympy import * +import itertools +from sympy.utilities.lambdify import lambdify, implemented_function +import numpy as np -import sys +from moedebug import * -import sys, codecs -if sys.stdout.encoding is None: - sys.stdout = codecs.open("/dev/stdout", "w", 'utf-8') +# When cse() is called for something containing BaseVector, it +# produces infinite recursion. +#def cse(x, *a, **kw): return ((), (x,)) -init_printing(use_unicode=True) +def dprint(*args): + if not dbg_enabled(): return + print(*args) -r, theta, s, la, mu = symbols('r theta s lambda mu') +def dbg(*args): + if not dbg_enabled(): return + for vn in args: + print('\n ' + vn + '\n') + pprint(eval(vn)) + print('\n =\n') + pprint(cse(eval(vn))) -# start original formulation -# rightvars replaces +def sqnorm(v): return v & v -p_start = Matrix([ - r * (1 - cos(theta)), - r * sin(theta), - mu * s, -]) +N = CoordSysCartesian('N') -p_rightvars = p_start.subs( theta, s/r ).subs( r, 1/la ) +calculated = False -def dbg(*args): - for vn in args: - print('\n' + vn + '\n') - pprint(eval(vn)) +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 + + # ---------- actual cost computation formulae ---------- + + global F, G + F = E + En * pow(EFlq, 2) + G = H + Hn * pow(HGlq, 2) + + 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] + + tan_theta = (au ^ bu) / (au & bu) # [1] bending + + global mu, nu + mu, nu = CoordArray ('mu nu', 'NP-2', tan_theta ).s() # [1] + + CostComponent('NP-3', sqnorm(mu - nu)) # [1] + + dl2 = pow(al - bl, 2) # [mm^2] + CostComponent('NP-2', dl2 / (al*bl)) # [1] + + # ---------- end of cost computation formulae ---------- + + calculated = True + +def ourccode(*a, **kw): + return ccode(*a, user_functions={'sinc':'sinc'}, **kw) + +def cprintraw(*s): + print(*s) + +def cprint(s): + for l in s.split('\n'): + cprintraw(l, '\\') + +def cse_prep_cprint(v, tmp_prefix): + # => v, but also having cprint'd the common subexpression assignments + sym_iter = map((lambda i: symbols('%s%d' % (tmp_prefix,i))), + itertools.count()) + (defs, vs) = cse(v, symbols=sym_iter) + for defname, defval in defs: + cprint('double '+ourccode(defval, assign_to=defname)) + return vs[0] + +def cassign(v, assign_to, tmp_prefix): + 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: + j = zeros(len(params),0) + for param in params: + global d + paramv = eval(param) + d = diff(current, paramv) + dbg('d') + j = j.row_join(d) + dbg('j') + j = cse_prep_cprint(j, 'jtmp') + for ix in range(0, j.cols): + cprint(ourccode(j.col(ix), 'J_COL')) + cprint('J_END_COL(%d)' % ix) + else: + small = smalls[0] + smalls = smalls[1:] + cprint('if (!IS_SMALL(' + ourccode(small) + ')) {') + gen_diff(current, smalls) + cprint('} else { /* %s small */' % small) + gen_diff(current.replace( + sinc(small), + 1 - small*small/factorial(3) - small**4/factorial(5), + ), + smalls + ) + cprint('} /* %s small */' % small) -dbg('p_rightvars') +def gen_misc(): + cprintraw('// AUTOGENERATED - DO NOT EDIT\n') -p_dirn_rightvars = diff(p_rightvars, s) +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)) -dbg('p_dirn_rightvars') +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) -zeta = Wild('zeta') +def gen_point_references(): + abcd = 'A B C D'.split(' ') -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) ) - ) + 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) )') -dbg('p_nosing') + gen_point_index_macro('En', 'PREP', '3*0') + gen_point_index_macro('Hn', 'PREP', '3*1') + cprintraw( '#define NPREP (3*2)') -t = symbols('t') + 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(')') -q_owncoords = p_nosing.replace(s,t).replace(la,-la) -q_dirn_owncoords = p_dirn_rightvars.replace(s,t).replace(la,-la) + cprintraw('#define EFlq X[ NX_DIRECT + 0 ]') + cprintraw('#define HGlq X[ NX_DIRECT + 1 ]') + cprintraw('#define NX ( NX_DIRECT + 2 )') -q_dirn_owncoords_0 = q_dirn_owncoords.replace(t,0) + for ai in range(0, len(abcd)): + cprintraw('#define %s POINT(P%+d)' % (abcd[ai], ai)) + gen_point_coords_macro(abcd[ai]) -dbg('q_owncoords','q_dirn_owncoords','q_dirn_owncoords_0') + for si in iterations: + si.gen_references() -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.add_col([0,0]) -#p2q_rotate.add_row([0,0,1]) + cprintraw('') -dbg('p2q_rotate') +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('') -assert(Eq(p2q_rotate * Matrix([0,1,mu]), p_dirn_rightvars)) +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('') -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)))''') +def gen_calculate_cost(): + cprint('#define CALCULATE_COST') + cprint('double cost=0, P_cost;') + for si in iterations: + si.gen_calculate_cost() + cprintraw('') -dbg('''Eq(p2q_rotate * Matrix([1,0,mu]), - p_dirn_rightvars .cross(Matrix([0,0,1])))''') +def gen_C(): + gen_misc() + gen_point_references() + gen_prepare() + gen_calculate_FG() + gen_calculate_cost() -#eq = Eq(qmat * q_dirn_owncoords_0, p_dirn_rightvars) -#print -#pprint(eq) -#solve(eq, Q) +def get_python(): + # https://github.com/sympy/sympy/issues/13642 + # "lambdify sinc gives wrong answer!" + out = q_sqparm + sinc_fixed = Function('sinc_fixed') + implemented_function(sinc_fixed, lambda x: np.sinc(x/np.pi)) + out = out.subs(sinc,sinc_fixed) + p = list(map(eval,params)) + return lambdify(p, out)