From 002ddfda9f7dd612f60f72cc767373c0d0aaf0ec Mon Sep 17 00:00:00 2001 From: Norbert Preining Date: Mon, 9 Apr 2018 16:31:54 +0000 Subject: ketcindy 20180409 git-svn-id: svn://tug.org/texlive/trunk@47395 c570f23f-e606-0410-a88d-b1316a301751 --- .../ketcindy/ketlib/maximaL/fourier_sec.max | 260 +++++++++++++++++++++ .../ketcindy/ketlib/maximaL/matoperation.max | 47 ++++ .../scripts/ketcindy/ketlib/maximaL/poincare.mac | 71 ++++++ .../scripts/ketcindy/ketlib/maximaL/rkfun.lisp | 99 ++++++++ 4 files changed, 477 insertions(+) create mode 100644 Master/texmf-dist/scripts/ketcindy/ketlib/maximaL/fourier_sec.max create mode 100644 Master/texmf-dist/scripts/ketcindy/ketlib/maximaL/matoperation.max create mode 100644 Master/texmf-dist/scripts/ketcindy/ketlib/maximaL/poincare.mac create mode 100644 Master/texmf-dist/scripts/ketcindy/ketlib/maximaL/rkfun.lisp (limited to 'Master/texmf-dist/scripts/ketcindy/ketlib/maximaL') diff --git a/Master/texmf-dist/scripts/ketcindy/ketlib/maximaL/fourier_sec.max b/Master/texmf-dist/scripts/ketcindy/ketlib/maximaL/fourier_sec.max new file mode 100644 index 00000000000..c70f7f465de --- /dev/null +++ b/Master/texmf-dist/scripts/ketcindy/ketlib/maximaL/fourier_sec.max @@ -0,0 +1,260 @@ +/* +Package fourier_sec, to study piecewise defined functions +(sectionally defined, hence the name). + +Author: Jose A. Vallejo + Faculty of Sciences + Universidad Autonoma de San Luis Potosi (Mexico) + http://galia.fc.uaslp.mx/~jvallejo + +It is assumed that the functions are defined using the format + if ... then ... else ... +as, for example, +(%i1) absolute(x):=if (x<=0) then -x elseif (x>0) then x$ +(it will not work with 'abs'). +It provides three functions: +1. 'paritycheck', to check if a given piecewise defined + function is even or odd (or none). For instance, + (%i2) paritycheck(absolute(x),x); + (%o2) 0 + A '0' means 'even', '1' is 'odd', and '-1' is 'none' +2. 'fourier_sec_coeff', to compute the Fourier sine and cosine + coefficients. The function must have compact support.For + instance, for the unit step we have: + (%i3) h(x):=if (-%pi<=x and x<0) then 0 elseif (0<=x and x<=%pi) then 1$ + (%i4) fourier_sec_coeff(h(x),x); + (%o4) [1/2,0,-((-1)^n-1)/(%pi*n)] +3. 'fourier_sec_series', to compute the Fourier series, truncated + or not. The series for the unit step to the 10th order: + (%i5) fourier_sec_series(h(x),x,10); + (%o5) (2*sin(9*x))/(9*%pi)+(2*sin(7*x))/(7*%pi)+(2*sin(5*x))/(5*%pi)+(2*sin(3*x))/(3*%pi)+(2*sin(x))/%pi+1/2 + and the whole Fourier series + (%i6) fourier_sec_series(h(x),x,inf); + (%o6) (sum(((1/n-(-1)^n/n)*sin(n*x))/%pi,n,1,inf))+1/2 +*/ + + +load(fourie)$ + +load(simplify_sum)$ + +paritycheck(funvar,x):=block([subintervals,subvalues,tmp1,tmp2,token1,token0,tmp3, + subvalues_list,subintervals_list,icentral:0,middle,minusmiddle,token2, + side_subintervals_list,L,side_subvalues_list, + zero_subintervals,tmp4,tmp5,non_zero_side_subvalues_list, + non_zero_side_subintervals_list,LL,token3,expr1,expr2], + local(M,N,P,Q,count1,count2,count3,count4), + subintervals:makelist(part(funvar,i),i,makelist(2*k-1,k,1,(length(funvar)-2)/2)), + subvalues:makelist(part(funvar,i),i,makelist(2*k,k,1,(length(funvar)-2)/2)), + for j:1 thru length(subintervals) do (if operatorp(subintervals[j],["<",">","<=",">="]) then tmp1[j]:1 else tmp1[j]:0), + tmp1:makelist(tmp1[j],j,1,length(subintervals)), + tmp2:sublist_indices(tmp1,lambda([x],x=1)), + + /* if length(tmp2)=0 all the subintervals in the domain of funvar are bounded! */ + + if is(equal(length(tmp2),0)) then + ( + subvalues_list:copylist(subvalues), + tmp3:copylist(subintervals), + for j:1 thru length(tmp3) do + ( + M[j]:makelist(part(tmp3[j],k),k,1,length(tmp3[j])), + for m:1 thru 2 do N[j,m]:makelist(part(M[j],m,n),n,1,length(M[j])), + P[j]:append(N[j,1],N[j,2]),Q[j]:sort(delete(x,P[j]),"<") + ), + subintervals_list:makelist(Q[j],j,1,length(tmp3)), + for i:1 thru length(subintervals_list) do (if is(lmin(subintervals_list[i])*lmax(subintervals_list[i])<0) then icentral:i), + if is(icentral>0) then middle:subvalues_list[icentral], + if is(icentral>0) then + (if evenfunp(middle,x) then token2:0 elseif oddfunp(middle,x) then token2:1 else return(-1)) + else + + /* now we analyze what happens if icentral=0, so there are only side intervals */ + + ( + /* as before, there must be an even number of symmetric intervals, otherwise -1 */ + side_subintervals_list:copylist(subintervals_list), + if not(evenp(length(side_subintervals_list))) then return(-1), + L:length(side_subintervals_list)/2, + for k:1 thru L do count1[k]:charfun(is(equal(side_subintervals_list[k],reverse(map("-",side_subintervals_list[2*L+1-k]))))), + if sum(count1[j],j,1,L)#L then return(-1), + side_subvalues_list:copylist(subvalues_list), + for k:1 thru L do count2[k]:charfun(is(equalp(side_subvalues_list[k],ratsubst(-x,x,side_subvalues_list[2*L+1-k])))), + if is(equal(sum(count2[j],j,1,L),L)) then token3:0, + for k:1 thru L do count3[k]:charfun(is(equalp(side_subvalues_list[k],-ratsubst(-x,x,side_subvalues_list[2*L+1-k])))), + if is(equal(sum(count3[j],j,1,L),L)) then token3:1, + if is(not(equalp(token3,0)) and not(equalp(token3,1))) then return(-1) , + return(token3) + ), + + /* and what happens if icentral#0 */ + + side_subintervals_list:delete(subintervals_list[icentral],subintervals_list), + if is(equal(length(side_subintervals_list),0)) then (if is(equal(token1,token2)) then return(token1*token2) else return(-1)), + if not(evenp(length(side_subintervals_list))) then return(-1), + L:length(side_subintervals_list)/2, + for k:1 thru L do count1[k]:charfun(is(equal(side_subintervals_list[k],reverse(map("-",side_subintervals_list[2*L+1-k]))))), + if sum(count1[j],j,1,L)#L then return(-1), + side_subvalues_list:delete(subvalues_list[icentral],subvalues_list), + + /* remove those subintervals in which funvar vanishes */ + + zero_subintervals:sublist_indices(side_subvalues_list,lambda([x],x=0)), + tmp4:copylist(side_subintervals_list), + for j:1 thru length(zero_subintervals) do + (tmp4:delete(side_subintervals_list[zero_subintervals[j]],tmp4)), + non_zero_side_subintervals_list:tmp4, + tmp5:copylist(side_subvalues_list), + for j:1 thru length(zero_subintervals) do + (tmp5:delete(side_subvalues_list[zero_subintervals[j]],tmp5)), + non_zero_side_subvalues_list:tmp5, + + /* if length(non_zero_side_subintervals_list)=0 then we are done just with token2 */ + + if is(equal(length(non_zero_side_subintervals_list),0)) then return(token2), + + /* otherwise, we must also take into account token3 */ + LL:length(non_zero_side_subintervals_list)/2, + for k:1 thru LL do count2[k]:charfun(is(equalp(non_zero_side_subvalues_list[k],ratsubst(-x,x,non_zero_side_subvalues_list[2*LL+1-k])))), + if is(equal(sum(count2[j],j,1,LL),LL)) then token3:0, + for k:1 thru LL do count3[k]:charfun(is(equalp(non_zero_side_subvalues_list[k],-ratsubst(-x,x,non_zero_side_subvalues_list[2*LL+1-k])))), + if is(equal(sum(count3[j],j,1,LL),LL)) then token3:1, + if is(not(equal(token3,0) or equal(token3,1))) then return(-1) elseif + is(token2#token3) then return(-1) + elseif is(equal(token2,0)) then return(0) + elseif is(equal(token2,1)) then return(1) + + ), + + /* we continue here with unbounded intervals */ + + expr1:subvalues[tmp2[1]], + expr2:ratsubst(-x,x,subvalues[tmp2[2]]), + if is(equalp(expr1,expr2)) then token1:0 + elseif is(equalp(expr1,-expr2)) then token1:1 + else return(-1), + + /* the problem when defining token1 is that if the asymptotic value is 0, then it is always token1:0 */ + /* although the function could be odd. To cope with this, we define token0 below */ + + tmp3:makelist(subintervals[i],i,sublist_indices(tmp1,lambda([x],x=0))), + if is(equal(length(tmp3),0)) then return(token1), + subvalues_list:makelist(subvalues[i],i,sublist_indices(tmp1,lambda([x],x=0))), + token0:if member(0,makelist(subvalues[i],i,tmp2)) then 0 else 7, + for j:1 thru length(tmp3) do + ( + M[j]:makelist(part(tmp3[j],k),k,1,length(tmp3[j])), + for m:1 thru 2 do N[j,m]:makelist(part(M[j],m,n),n,1,length(M[j])), + P[j]:append(N[j,1],N[j,2]),Q[j]:sort(delete(x,P[j]),"<") + ), + subintervals_list:makelist(Q[j],j,1,length(tmp3)), + for i:1 thru length(subintervals_list) do (if is(lmin(subintervals_list[i])*lmax(subintervals_list[i])<0) then icentral:i), + if is(icentral>0) then middle:subvalues_list[icentral], + if is(icentral>0) then + (if evenfunp(middle,x) then token2:0 elseif oddfunp(middle,x) then token2:1 else return(-1)) + else + + /* now we analyze what happens if icentral=0, so there are only non-bounded intervals and side intervals */ + + ( + /* as before, there must be an even number of symmetric intervals, otherwise -1 */ + side_subintervals_list:copylist(subintervals_list), + if not(evenp(length(side_subintervals_list))) then return(-1), + L:length(side_subintervals_list)/2, + for k:1 thru L do count1[k]:charfun(is(equal(side_subintervals_list[k],reverse(map("-",side_subintervals_list[2*L+1-k]))))), + if sum(count1[j],j,1,L)#L then return(-1), + side_subvalues_list:copylist(subvalues_list), + for k:1 thru L do count2[k]:charfun(is(equalp(side_subvalues_list[k],ratsubst(-x,x,side_subvalues_list[2*L+1-k])))), + if is(equal(sum(count2[j],j,1,L),L)) then token3:0, + for k:1 thru L do count3[k]:charfun(is(equalp(side_subvalues_list[k],-ratsubst(-x,x,side_subvalues_list[2*L+1-k])))), + if is(equal(sum(count3[j],j,1,L),L)) then token3:1, + if is(not(equal(token3,0)) and not(equal(token3,1))) then return(-1) elseif + is(not(equal(token1,token3)) and not(equal(token0,0))) then return(-1) + elseif is( equal(token0,0) and equal(token3,0)) then return(0) + elseif is( equal(token0,0) and equal(token3,1)) then return(1) + elseif is(not(equal(token0,0)) and equal(token1,token3)) then return(token3) + elseif is(not(equal(token0,0)) and not(equal(token1,token3))) then return(-1) + ), + + /* and what happens if icentral#0 */ + + side_subintervals_list:delete(subintervals_list[icentral],subintervals_list), + if is(equal(length(side_subintervals_list),0)) then (if is(equal(token1,token2)) then return(token1*token2) else return(-1)), + if not(evenp(length(side_subintervals_list))) then return(-1), + L:length(side_subintervals_list)/2, + for k:1 thru L do count1[k]:charfun(is(equal(side_subintervals_list[k],reverse(map("-",side_subintervals_list[2*L+1-k]))))), + if sum(count1[j],j,1,L)#L then return(-1), + side_subvalues_list:delete(subvalues_list[icentral],subvalues_list), + + /* remove those subintervals in which funvar vanishes */ + + zero_subintervals:sublist_indices(side_subvalues_list,lambda([x],x=0)), + tmp4:copylist(side_subintervals_list), + for j:1 thru length(zero_subintervals) do + (tmp4:delete(side_subintervals_list[zero_subintervals[j]],tmp4)), + non_zero_side_subintervals_list:tmp4, + tmp5:copylist(side_subvalues_list), + for j:1 thru length(zero_subintervals) do + (tmp5:delete(side_subvalues_list[zero_subintervals[j]],tmp5)), + non_zero_side_subvalues_list:tmp5, + + /* if length(non_zero_side_subintervals_list)=0 then we are done just with token1 and token2 */ + + if is(equal(length(non_zero_side_subintervals_list),0)) then (if is(equal(token1,token2)) then return(token1*token2) else return(-1)), + + /* otherwise, we must also take into account token3 */ + LL:length(non_zero_side_subintervals_list)/2, + for k:1 thru LL do count2[k]:charfun(is(equalp(non_zero_side_subvalues_list[k],ratsubst(-x,x,non_zero_side_subvalues_list[2*LL+1-k])))), + if is(equal(sum(count2[j],j,1,LL),LL)) then token3:0, + for k:1 thru LL do count3[k]:charfun(is(equalp(non_zero_side_subvalues_list[k],-ratsubst(-x,x,non_zero_side_subvalues_list[2*LL+1-k])))), + if is(equal(sum(count3[j],j,1,LL),LL)) then token3:1, + if is(not(equal(token0,0)) and is(not(equal(token1,token2)) or not(equal(token1,token3)) or not(equal(token2,token3))) ) then return(-1) + elseif is(not(equal(token0,0)) and is(equal(token1,0)) ) then return(0) + elseif is(not(equal(token0,0)) and is(equal(token1,1)) ) then return(1) + elseif is( equal(token0,0) and equal(token3,0) and equal(token2,0)) then return(0) + elseif is( equal(token0,0) and equal(token3,1) and equal(token2,1)) then return(1) + else return(-1) + +)$ + +fourier_sec_coeff(fuvar,x):= +block([pp,LL,lm,a0,coeff], + local(a,b,n,MM,NN,PP,QQ), + declare(n,integer), + pp:((length(fuvar)/2)-1), + LL:makelist(part(fuvar,i),i,makelist(2*s-1,s,1,pp)), + for j:1 thru length(LL) step 1 do + ( + MM[j]:makelist(part(LL[j],r),r,1,length(LL[j])), + for r:1 thru 2 do NN(j,r):=makelist(part(MM[j],r,k),k,1,length(MM[j])), + PP[j]:append(NN(j,1),NN(j,2)),QQ[j]:delete(x,PP[j]) + ), + for i:1 thru pp step 1 do partsums[i]:sort(QQ[i],"<"), + for i:1 thru pp step 1 do partfunc[i]:part(fuvar,2*i), + lm:lmax(unique(flatten(makelist(QQ[q],q,1,length(LL))))), + a0:(1/(2*lm))*sum(integrate(partfunc[i],x,partsums[i][1],partsums[i][2]),i,1,pp), + if is(equal(paritycheck(fuvar,x),1)) then a(n):=0 else a(n):=(1/lm)*sum(adefint(partfunc[i]*cos(%pi*n*x/lm),x,partsums[i][1],partsums[i][2]),i,1,pp), + if is(equal(paritycheck(fuvar,x),0)) then b(n):=0 else b(n):=(1/lm)*sum(adefint(partfunc[i]*sin(%pi*n*x/lm),x,partsums[i][1],partsums[i][2]),i,1,pp), + coeff:[a0,simplify_sum(a(n)),simplify_sum(b(n))], + factor(ratsimp(coeff)) +)$ + +fourier_sec_series(fuvar,x,u):= +block([pp,LL,lm,a0,coeff], + local(a,b,n,MM,NN,PP,QQ), + declare(n,integer), + pp:((length(fuvar)/2)-1), + LL:makelist(part(fuvar,i),i,makelist(2*s-1,s,1,pp)), + for j:1 thru length(LL) step 1 do + ( + MM[j]:makelist(part(LL[j],r),r,1,length(LL[j])), + for r:1 thru 2 do NN(j,r):=makelist(part(MM[j],r,k),k,1,length(MM[j])), + PP[j]:append(NN(j,1),NN(j,2)),QQ[j]:delete(x,PP[j]) + ), + for i:1 thru pp step 1 do partsums[i]:sort(QQ[i],"<"), + for i:1 thru pp step 1 do partfunc[i]:part(fuvar,2*i), + lm:lmax(unique(flatten(makelist(QQ[q],q,1,length(LL))))), + a0:(1/(2*lm))*sum(integrate(partfunc[i],x,partsums[i][1],partsums[i][2]),i,1,pp), + if is(equal(paritycheck(fuvar,x),1)) then a(n):=0 else a(n):=(1/lm)*sum(adefint(partfunc[i]*cos(%pi*n*x/lm),x,partsums[i][1],partsums[i][2]),i,1,pp), + if is(equal(paritycheck(fuvar,x),0)) then b(n):=0 else b(n):=(1/lm)*sum(adefint(partfunc[i]*sin(%pi*n*x/lm),x,partsums[i][1],partsums[i][2]),i,1,pp), + a0+intosum(sum(a(n)*cos(%pi*n*x/lm),n,1,u))+intosum(sum(b(n)*sin(%pi*n*x/lm),n,1,u)))$ \ No newline at end of file diff --git a/Master/texmf-dist/scripts/ketcindy/ketlib/maximaL/matoperation.max b/Master/texmf-dist/scripts/ketcindy/ketlib/maximaL/matoperation.max new file mode 100644 index 00000000000..512a9ffb665 --- /dev/null +++ b/Master/texmf-dist/scripts/ketcindy/ketlib/maximaL/matoperation.max @@ -0,0 +1,47 @@ +/* Maxima tips http://www.cymric.jp/maxima/tips.html */ + +rowmult(X, n, c) := block([M], + M:matrix(), + for i:1 thru length(X) do + if i=n then M:addrow(M, c*row(X, i)) + else M:addrow(M, row(X, i)), + M +); +rowadd(X, n, m, c) := block([M], + M:matrix(), + for i:1 thru length(X) do + if i=n then M:addrow(M, c * row(X, m) + row(X, i)) + else M:addrow(M, row(X, i)), + M +); +rowch(X, m, n) := block([M], + M:matrix(), + for i:1 thru length(X) do + if i=m then M:addrow(M, row(X, n)) + else if i=n then M:addrow(M, row(X, m)) + else M:addrow(M, row(X, i)), + M +); + +colmult(X, n, c) := block([M], + M:matrix(), + for i:1 thru length(transpose(X)) do + if i=n then M:addcol(M, c*col(X, i)) + else M:addcol(M, col(X, i)), + M +); +coladd(X, n, m, c) := block([M], + M:matrix(), + for i:1 thru length(transpose(X)) do + if i=n then M:addcol(M, c * col(X, m) + col(X, i)) + else M:addcol(M, col(X, i)), + M +); +colch(X, m, n) := block([M], + M:matrix(), + for i:1 thru length(transpose(X)) do + if i=m then M:addcol(M, col(X, n)) + else if i=n then M:addcol(M, col(X, m)) + else M:addcol(M, col(X, i)), + M +); diff --git a/Master/texmf-dist/scripts/ketcindy/ketlib/maximaL/poincare.mac b/Master/texmf-dist/scripts/ketcindy/ketlib/maximaL/poincare.mac new file mode 100644 index 00000000000..aefab3a21a0 --- /dev/null +++ b/Master/texmf-dist/scripts/ketcindy/ketlib/maximaL/poincare.mac @@ -0,0 +1,71 @@ +/* Poincare.mac is a set of routines for the computation +of Poincare surfaces of sections of Hamiltonian systems */ + +/* Author: Jose A Vallejo +Universidad Autonoma de San Luis Potosi (Mexico) +josanv@gmail.com */ + +/* To avoid messages when loading draw, execute +with_stdout("/dev/null",load(draw))$ (in Linux) +with_stdout("NUL",load(draw))$ (in Windows) */ + +/* Poincare.mac requires a compiled version of +rkfun.lisp, a LISP implementation of the RK4 +algorithm due to Richard Fateman. The original +code can be downloaded from +https://people.eecs.berkeley.edu/~fateman/lisp/rkfun.lisp */ + +/*load("rkfun.fasl");*/ +/*load("rkfun.lisp");*/ + + +hameqs(H,name):=block( +[vv,t,tvv,n,Q,P,eqq,eqp,eqs], +vv:args(lhs(apply(fundef,[H]))), +tvv:cons(t,vv), +n:length(vv)/2, +Q:makelist(vv[2*j-1],j,1,n), +P:makelist(vv[2*k],k,1,n), +eqq:makelist(float(diff(apply(H,vv),P[j])),j,1,n), +eqp:makelist(float(-diff(apply(H,vv),Q[j])),j,1,n), +eqs:join(eqq,eqp), +for j:1 thru 2*n do define(funmake(concat(name,j),tvv),block([],mode_identity(float,vv),eqs[j])), +apply(compile,makelist(concat(name,j),j,1,2*n)), +[makelist(apply(concat(name,j),tvv),j,1,2*n),vv,makelist(concat(name,j),j,1,2*n)] +)$ + +lextract(ll,n):=block([l,a,b], +l:length(ll), +a:rest(ll,n), +b:rest(ll,n-l-1), +append(b,a) +)$ + +poincare3d(H,name,inicond,timestep,coord):=block( +[heq,vars,tvars,hfuns,c,sol], +heq:hameqs(H,name), +vars:heq[2], +tvars:cons(t,vars), +hfuns:heq[3], +c:first(sublist_indices(vars,lambda([x],x=coord))), +sol:rkfun(hfuns,tvars,float(inicond),timestep), +map(lambda([x],lextract(x,c)),map(lambda([x],rest(x)),sol)) +)$ + +poincare2d(H,name,inicond,timestep,scene):=block( +[heq,vars,tvars,hfuns,solu,c,soluc,sola,solb,subind,sol,e,f], +heq:hameqs(H,name), +vars:heq[2], +tvars:cons(t,vars), +hfuns:heq[3], +solu:rkfun(hfuns,tvars,float(inicond),timestep), +c:first(sublist_indices(vars,lambda([x],x=first(scene)))), +soluc:map(lambda([x],x[c+1]),solu), +sola:rest(soluc,-1)-second(scene), +solb:rest(soluc)-second(scene), +subind:sublist_indices(sola*solb,lambda([x],is(x < 0))), +sol:makelist(solu[k],k,subind), +e:first(sublist_indices(vars,lambda([x],x=third(scene))))+1, +f:first(sublist_indices(vars,lambda([x],x=fourth(scene))))+1, +makelist([j[e],j[f]],j,sol) +)$ \ No newline at end of file diff --git a/Master/texmf-dist/scripts/ketcindy/ketlib/maximaL/rkfun.lisp b/Master/texmf-dist/scripts/ketcindy/ketlib/maximaL/rkfun.lisp new file mode 100644 index 00000000000..70aafc7fffd --- /dev/null +++ b/Master/texmf-dist/scripts/ketcindy/ketlib/maximaL/rkfun.lisp @@ -0,0 +1,99 @@ +;; variation on runge-kutta (rk) routine in complex_dynamics.lisp by villate@fe.up.pt +;; this one with changed by fateman@berkeley.edu + +#| rkfun may be much faster than rk because it calls compiled programs. + rkfun (this file) should also be compiled to speed it up. + how to use: + + + first, read and understand the documentation for rk(). + next, define the ODE right hand sides as functions as shown below + +fun1(y,x,x0):= x0$ +fun2(y,x,x0):= block([], mode_declare([y, x0,x],float),(1-x^2)*x0-x); +compile(fun1)$ +compile(fun2)$ +showtime:all$ + +last(rkfun([fun1,fun2],[x,xdot],[0.0,0.6],[t,0,50,0.01])); + +/* which is, in one test, 18 times faster than */ + +last(rk([xdot,(1-x^2)*xdot -x],[x,xdot],[0.0,0.6],[t,0,50,0.01])); + +|# + +(defun $rkfun (funs vars initial domain ;; taken from complex_dynamics.lisp + &aux d u funlist k1 k2 k3 k4 r1 r2 r3 traj r + (it (mapcar #'coerce-float (cddr domain)))) + (unless ($listp funs) (setq funs `((mlist) ,funs))) + (unless ($listp initial) (setq initial `((mlist) ,initial))) + (unless ($listp vars) (setq vars `((mlist) ,vars))) + (dolist (var (cdr vars)) + (unless (symbolp var) + (merror (intl:gettext "rk: variable name expected; found: ~M") var))) + (unless (symbolp (cadr domain)) + (merror (intl:gettext "rk: variable name expected; found: ~M") + (cadr domain))) + (setq vars (append '((mlist)) (list (cadr domain)) (cdr vars))) + (setq r (append `(,(car it)) (mapcar #'coerce-float (cdr initial)))) + (setq funlist (cdr funs)) + + (setq d (/ (- (cadr it) (car it)) (caddr it))) + (setq traj (list (cons '(mlist) r))) + (do ((m 1 (1+ m))) ((> m d)) + (progn ;;; was ignore-errors + (setq k1 (mapcar #'(lambda (x) (apply x r)) funlist)) + (setq r1 (map 'list #'+ (cdr r) (mapcar #'(lambda (x) (* 0.5d0 (caddr it) x)) k1))) + (push (+ (car r) (/ (caddr it) 2)) r1) + (setq k2 (mapcar #'(lambda (x) (apply x r1)) funlist)) + (setq r2 (map 'list #'+ (cdr r) (mapcar #'(lambda (x) (* 0.5d0(caddr it) x)) k2))) + (push (+ (car r) (/ (caddr it) 2)) r2) + (setq k3 (mapcar #'(lambda (x) (apply x r2)) funlist)) + (setq r3 (map 'list #'+ (cdr r) (mapcar #'(lambda (x) (* (caddr it) x)) k3))) + (push (+ (car r) (caddr it)) r3) + (setq k4 (mapcar #'(lambda (x) (apply x r3)) funlist)) + (setq u (map 'list #'+ + (mapcar #'(lambda (x) (* #.(/ 1.0 6.0d0) x)) k1) + (mapcar #'(lambda (x) (* #.(/ 1.0 3.0d0) x)) k2) + (mapcar #'(lambda (x) (* #.(/ 1.0 3.0d0) x)) k3) + (mapcar #'(lambda (x) (* #.(/ 1.0 6.0d0) x)) k4))) + (setq r + (append + `(,(+ (car it) (* m (caddr it)))) + (map 'list #'+ (cdr r) (mapcar #'(lambda (x) (* (caddr it) x)) u)))) + (push (cons '(mlist) r) traj))) + (when (< (car r) (cadr it)) + (let ((s (- (cadr it) (car r))) ) + (declare(double-float s)(special s)(optimize (speed 3)(safety 0))) + (progn ;; was ignore-errors + (setq k1 (mapcar #'(lambda (x) (mapply x r nil)) funlist)) + (setq r1 (map 'list #'+ (cdr r) (mapcar #'(lambda (x) + (declare(double-float x)) + (* s 0.5d0 x)) k1))) + (push (+ (car r) (* 0.5d0 s)) r1) + (setq k2 (mapcar #'(lambda (x) (mapply x r1 nil)) funlist)) + (setq r2 (map 'list #'+ (cdr r) (mapcar #'(lambda (x)(declare(double-float x)) + (* s 0.5d0 x)) k2))) + (push (+ (car r) (* 0.5d0 s)) r2) + (setq k3 (mapcar #'(lambda (x) (mapply x r2 nil)) funlist)) + (setq r3 (map 'list #'+ (cdr r) (mapcar #'(lambda (x)(declare(double-float x)) + (* s x)) k3))) + (push (+ (car r) s) r3) + (setq k4 (mapcar #'(lambda (x) (mapply x r3 nil)) funlist)) + (setq u (map 'list #'+ + (mapcar #'(lambda (x)(declare(double-float x)) + (* #.(/ 1.0d0 6.0d0) x)) k1) + (mapcar #'(lambda (x)(declare(double-float x)) + (* #.(/ 1.0d0 3.0d0) x)) k2) + (mapcar #'(lambda (x) (declare(double-float x)) + (* #.(/ 1.0d0 3.0d0) x)) k3) + (mapcar #'(lambda (x)(declare(double-float x)) + (* #.(/ 1.0d0 6.0d0) x)) k4))) + (setq r + (append + `(,(cadr it)) + (map 'list #'+ (cdr r) (mapcar #'(lambda (x)(declare(double-float x)) + (* s x)) u)))) + (push (cons '(mlist) r) traj)))) + (cons '(mlist) (nreverse traj))) \ No newline at end of file -- cgit v1.2.3