X-Git-Url: http://www.chiark.greenend.org.uk/ucgi/~ian/git?a=blobdiff_plain;f=symbolic.py;h=8680378ea06d906cbf58b4d230f09451e5ec281d;hb=c1001cc933c7a48935777908ba8338673cd091dc;hp=611bbd575fedc228c05bd14f57fe996ff025bf95;hpb=69a84b4bca382a3c177c83a8ea34259e4e00a0d9;p=moebius3.git diff --git a/symbolic.py b/symbolic.py index 611bbd5..8680378 100644 --- a/symbolic.py +++ b/symbolic.py @@ -1,169 +1,151 @@ +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) @@ -187,6 +169,12 @@ 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: @@ -218,34 +206,92 @@ def gen_diff(current, 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 # "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, q_sqparm) + return lambdify(p, out)