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Viewing changes to demos/npend/Maple/Euler.map

  • Committer: Bazaar Package Importer
  • Author(s): Torsten Werner
  • Date: 2005-01-09 22:58:21 UTC
  • mfrom: (1.1.1 upstream)
  • Revision ID: james.westby@ubuntu.com-20050109225821-473xr8vhgugxxx5j
Tags: 3.0-12
http://bugs.debian.org/255869
changed configure.in to build scilab's own malloc.o, closes: #255869

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demos/npend/Maple/Euler.map
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# Copyright INRIA
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with(share):
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if SearchText(`Release 3`,interface(version))<>0 then
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        matadd:=add;
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        readshare(tex):
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        readshare(macrofor,numerics):
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elif SearchText(`Release 4`,interface(version))<>0 then
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        readshare(tex,system):
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        readshare(macrofor,numerics):
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else
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  ERROR(`Unknown Release`)
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fi;
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#----------------------------------------------------------------------------
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#     GENERAL PART
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#----------------------------------------------------------------------------
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#----------------------------------------------------------------------------
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# Notation for Tex output 
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# and TeX output routines
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# this routines generates proper derivative notations up to second derivative
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# for a set of variable. The TeX name for the variables is also given
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# Warning this function will detroy previous values of texsub 
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# Ex : addnotations( { x = `x`  , th = `\\theta`, y =`y` } );
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#-----------------------------------------------------------------------------
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addnotations:=proc(varlist)
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        global texsub;
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        local x,nots:
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        nots:={};
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        for x in varlist do
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                nots:={op(nots),x, 
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                        cat(lhs(x),`d`)=cat(`\\dot{`,rhs(x),`}`),
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                        cat(lhs(x),`dd`)=cat(`\\ddot{`,rhs(x),`}`)}
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        od;
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        texsub:=nots
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end:
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sortieinit:=proc(filename)
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        writeto(filename);
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        writeto(terminal);
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end:
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sorties:=proc(filename,comment,exp)
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        appendto(filename);
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        lprint(comment);
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        lprint(` `);
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        mtex(exp,latex);
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        writeto(terminal);
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end:
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sortiesI:=proc(filename,comment)
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        appendto(filename);
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        lprint(comment);
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        writeto(terminal);
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end:
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sortiesM:=proc(filename,comment,expr)
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        appendto(filename);
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        lprint(comment);
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        lprint(` `);
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        map(x -> mtex(x,latex),expr);
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        writeto(terminal);
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end:
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texwid:=120;
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sortieinit(`systeme.tex`);
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#---------------------------------------------------------------
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# functions for computing euler equations 
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# L : the Lagrangian,
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# q,qd,qdd are the state vector and its derivatives
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#---------------------------------------------------------------
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with(`linalg`):
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euler_equations:=proc(L,q,qd,qdd)
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        local k,m:
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        m:=nops(q);
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        v:=matrix(m,1,0);
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        for i to m  do  
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           v[i,1]:=LL(q[i])=simplify(time_diff(diff(L,qd[i]),q,qd,qdd)
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                                -diff(L,q[i]));
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        od;
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        eval(v):
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        end:
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#---------------------------------------------------------------
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# Time derivative computation of an expression 
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# depending on q,qd,qdd 
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# used to compute Euler equations 
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#---------------------------------------------------------------
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        ttvar:=proc(xx)
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                if type(xx,`indexed`) 
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                then cat(op(0,xx),`d`)[op(xx)]
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                else cat(xx,`d`) fi
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        end:
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time_diff:=proc(phi,q,qd,qdd)
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        local phi_copy,k,ttvar,diff_phi:
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        # subtitution to specify that q,qd ,qdd depends on time 
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        phi_copy:=phi:
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        phi_copy:=subs(map( xx-> xx=xx(t),[op(q),op(qd)]),phi_copy):
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        diff_phi:=diff(phi_copy,t):
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        # subtitution to come back to our variables 
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        diff_phi:=subs(map(xx->diff(xx(t),t)=ttvar(xx),[op(q),op(qd)]),
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                        diff_phi):
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        diff_phi:=subs(map(xx->xx(t)=xx,[op(q),op(qd),op(qdd)]),diff_phi):
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end:
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#-----------------------------------------------------
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# Rewritting the Euler equations to have a canonical form 
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#           ..         .
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# El= ME(q)  q + CE(q) q^2 + RE(q)
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# Computation of ME,CE,RE 
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# CEuler returns a list [ME,CE,RE];
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#-----------------------------------------------------
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CEuler:=proc(E,q,qd,qdd)
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        local Me,Ce,Re:
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        Me:=MME(E,q,qd,qdd):
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        Ce:=CCE(E,q,qd,qdd):
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        Re:=RRE(E,Me,Ce,q,qd,qdd):
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        [eval(Me),eval(Ce),eval(Re)]:
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        end:
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MME:=proc(E,q,qd,qdd)
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        local E1:
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        E1:=eval(E):
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        genmatrix([seq(E1[i,1],i=1..nops(qdd))],qdd):
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        end:
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#-----------------------------------------------------
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# extract the CE(q) matrix  El= ME(q)  qdd + CE(q) qd^2 + RE(q)
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#-----------------------------------------------------
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        ttvarp:=proc(xx)
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                if type(xx,`indexed`) 
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                then cat(op(0,xx),`2`)[op(xx)]
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                else cat(xx,`2`) fi
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        end:
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CCE:=proc(E,q,qd,qdd)
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        local E_copy,q2d:
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        E_copy:=eval(E):
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        q2d:= map(x-> ttvarp(x),qd): 
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        E_copy:=subs( map(x-> x**2=ttvarp(x),qd),eval(E_copy));
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        genmatrix([seq(E_copy[i,1],i=1..nops(qd))],q2d);
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        end:
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#-----------------------------------------------------
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# extract the RE(q) matrix  El= ME(q)  qdd + CE(q) qd^2 + RE(q)
156
 
#-----------------------------------------------------
157
 
 
158
 
RRE:=proc(E,ME,CE,q,qd,qdd)
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        local MM:
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        MM:=matadd(     E,
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                matadd(multiply(ME,matrix(nops(q),1,qdd)),
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                multiply(CE,matrix(nops(q),1,map(x->x**2,qd)))),
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                1,-1);
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        MM:=map((x)-> simplify(x),eval(MM)):
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        end:
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167
 
#
168
 
#-----------------------------------------------------
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# FORTRAN GENERATION 
170
 
#-----------------------------------------------------
171
 
 
172
 
Gener:=proc(filename,fortranlist)
173
 
        global optimized;
174
 
        init_genfor();
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        optimized:=true:
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        writeto(filename):
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        genfor(flist):
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        writeto(terminal):
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        end:
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