findroot expects function, not equation
try
sage: find_root(erseno(x),2,10,xtol=0.01)
does this work?
Robert
On 9 ún, 15:54, Giovanni Lanzani <ulisses...@gmail.com> wrote:
> "ma...@mendelu.cz" <ma...@mendelu.cz> writes:
> > On 9 ún, 11:22, Giovanni Lanzani <ulisses...@gmail.com> wrote:
> >> Dear all
>
> >> I have the following sage code
>
> >> sage:
> >> gamma,r,gangle,dz2,Nstep,Nrib,b=var('gamma,r,gangle,dz2,Nstep,Nrib,b')
> >> sage: a=11.5; b=6;#this is fixed
> >> sage: Nstep=2;Nrib=5;Diam=33;gangle=30*2*3.1415/360;gamma=40*0.33+20*0.33;
> >> sage: #these have all to be changed when using different structure
> >> sage: r=(Diam-2*a)/2;th=2*3.1415*Nstep/Nrib;
> >> sage: def theta(dz):
> >> ... return 2*arcsin(dz*tan(gangle)/2/r);
> >> ...
> >> sage: def dz2(dz):
> >> ... return (-(Nrib+1)/(Nrib-1)*dz+b*cos(gangle)*2/(Nrib-1));
> >> sage: def erseno(x):
> >> ... return
> >> 2*arcsin(b*sin(gangle)/2/r)-(Nrib-1)*theta(dz2(x))/2-(Nrib+1)*theta(x)/2;
> >> sage: find_root(erseno(x)==0,2,gamma,xtol=0.01)
> >> 0.0
>
> > You look for the zero on the interval which is not subset of the
> > domain of the function. Try erseno(gamma) ....
> > Do not know why Sage returns result which is not true, but you can try
> > this:
>
> > sage:
> > gamma,r,gangle,dz2,Nstep,Nrib,b=var('gamma,r,gangle,dz2,Nstep,Nrib,b')
> > sage: a=11.5; b=6;#this is fixed
> > sage:
> > Nstep=2;Nrib=5;Diam=33;gangle=30*2*3.1415/360;gamma=40*0.33+20*0.33;
> > sage: r=(Diam-2*a)/2;th=2*3.1415*Nstep/Nrib;
> > sage: def theta(dz):
> > ....: return 2*arcsin(dz*tan(gangle)/2/r);
> > ....:
> > sage: def dz2(dz):
> > ....: return (-(Nrib+1)/(Nrib-1)*dz+b*cos(gangle)*2/(Nrib-1));
> > ....:
> > sage: def erseno(x):
> > ....: return 2*arcsin(b*sin(gangle)/2/r)-(Nrib-1)*theta(dz2(x))/2-
> > (Nrib+1)*theta(x)/2;
> > ....:
> > sage: erseno(gamma)
> > NaN
> > sage: find_root(erseno(x),2,10,xtol=0.01)
> > 5.1961985254756655
>
> You are right, but this then brings me to the next problem. If I define
> theta(dz) to be
>
> sage: def theta(dz):
> ... angle=0;
> ... if 0<=dz<2*r*cot(gangle) : angle= 2*arcsin(dz*tan(gangle)/2/r);
> ... if 2*r*cot(gangle)<= dz < 2*2*r*cot(gangle) : angle=
> 2*arcsin((dz-2*r*cot(gangle))/(cot(gangle)*2*r)) - pi;
> ... if 2*2*r*cot(gangle)<= dz < 4*2*r*cot(gangle) : angle=
> 2*arcsin((dz-2*2*r*cot(gangle))/(cot(gangle)*2*r)) - 2*pi;
> ... if 0>=dz>-2*r*cot(gangle) : angle= 2*arcsin(dz*tan(gangle)/2/r);
> ... if 2*r*cot(gangle)>= dz > -2*2*r*cot(gangle) : angle=
> 2*arcsin((dz+2*r*cot(gangle))/(cot(gangle)*2*r)) - pi;
> ... if 2*2*r*cot(gangle)>= dz > -4*2*r*cot(gangle) : angle=
> 2*arcsin((dz+2*2*r*cot(gangle))/(cot(gangle)*2*r)) - 2*pi;
> ... return angle;
> ...
>
> then executing
>
> sage: find_root(erseno(x)==0,2,10,xtol=0.01)
>
> I get
>
> }} Traceback (most recent call last):
> }} File "<stdin>", line 1, in <module>
> }} File "_sage_input_69.py", line 4, in <module>
> }} open("___code___.py","w").write("# -*- coding: utf-8 -*-\n" +
> _support_.preparse_worksheet_cell(base64.b64decode("ZmluZF9yb290KGVyc2Vubyh4KT09MCwyLDEwLHh0b2w9MC4wMSk="),globals())+"\n");
> execfile(os.path.abspath("___code___.py"))
> }} File "", line 1, in <module>
> }}
> }} File
> "/private/var/folders/bc/bcpFbanYErusTUkLXieJfE+++TI/-Tmp-/tmpPx3xK6/___code___.py",
> line 3, in <module>
> }} find_root(erseno(x)==_sage_const_0 ,_sage_const_2 ,_sage_const_10
> ,xtol=_sage_const_0p01 )
> }} File "", line 1, in <module>
> }}
> }} File
> "/Applications/sage/local/lib/python2.6/site-packages/sage/numerical/optimize.py",
> line 73, in find_root
> }} left = f(a)
> }}TypeError: 'bool' object is not callable
> }}
>
> Thanks again for your kindness,
>
> Giovanni Lanzani
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