Comandos Úteis e Simples

Seção 2.8: Os Pacotes do Maple

Session 2.8.1: O link  MATLAB

>

restart;

>	with( Matlab );

>	with( LinearAlgebra ):

>	Digits := trunc( evalhf(Digits) );

>	evalM( " x=linspace(0,pi,1024) " );

>	evalM( " v=sin(50*x)+0.1*sin(200*x)+0.5*sin(500*x)+0.00001*rand(1,1024) " );

>	V := getvar( "v" );

>	p := fft( V );

>	Spectrum := map( abs, p ):

>	plot( [seq( [2*(k-1)/1024,log[10](Spectrum[k])], k=1..512 )],        style=POINT, colour=black, axes=BOXED );

>	evalM( "p = fft(v)" );

>	evalM( "semilogy( x(1:512), abs(p(1:512)) )" );

>

restart;

>	with( Matlab );

>	p := expand( (t-1.99)*(t-3.0)*(t-1) );

>	q := expand( (t+1)*(t-2.01) );

>

N := 3;

>	p1 := p + add( x(i)*t^(i-1), i=1..N );

>	q1 := q + add( x(i+N)*t^(i-1), i=1..N-1 );

>	constraint := resultant( p1, q1, t );

>	unconstrained := add( x(i)^2, i=1..2*N-1 ) + 1.0e30*constraint^2:

>	fd := fopen( "C:/books/ess/programs/unconstrained.m", WRITE ); fprintf( fd, "function y = unconstrained(x)\n" ); fprintf( fd, "y=%a;\n", unconstrained ); fprintf( fd, "end;\n" ); fclose( fd );

>	evalM( "path('C:\\books\\ess\\programs',path)" );

>	initialguess := [seq(0.,k=0..2*N-1)];

>	mstring := sprintf( "pert = fminsearch( @unconstrained, %a, optimset('TolX',1.0e-14) )", initialguess ) ;

>	evalM( mstring );

>	ans := getvar( "pert" );

>	subs( seq(x(i)=ans[i],i=1..2*N), [unconstrained,constraint] );

>	subs( seq(x(i)=initialguess[i],i=1..2*N), [unconstrained,constraint] );

>	perturbed := subs( seq(x(i)=ans[i],i=1..2*N), [p1,q1] );

>	fsolve( perturbed[1], t, complex );

>	fsolve( perturbed[2], t, complex );

>

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