Uso do calculo simbólico na Matlab
Revisão de 17h36min de 27 de setembro de 2016 por Moecke (discussão | contribs) (→Algumas dicas sobre o cálculo simbólico)
Funções importantes para o uso do cálculo simbólico
- vpa(x) Variable-precision arithmetic: evaluate each element of the symbolic input x to at least d significant digits, where d is the value of the digits function. The default value of digits is 32.
- digits(d) Change variable precision used: sets the precision used by vpa to d significant decimal digits. The default is 32 digits.
- double(s) Convert symbolic values to MATLAB double precision: converts the symbolic value s to double precision. Converting symbolic values to double precision is useful when a MATLAB® function does not accept symbolic values.
- x = sym('x') creates symbolic variable x
- syms x Create symbolic variables and functions: Create symbolic variable x.
- p = poly2sym(c) Create symbolic polynomial from vector of coefficients: creates the symbolic polynomial expression p from the vector of coefficients c.
- S = solve(eqn,var) Equations and systems solver.
- subs(s,new) Symbolic substitution.
- g = matlabFunction(f) Convert symbolic expression to function handle or file.
- simplify(S) Algebraic simplification
- expand(S) Symbolic expansion of polynomials and elementary functions
- F = factor(x) Factorization
- numden(A) Extract numerator and denominator
- partfrac(expr,var) Partial fraction decomposition
- latex(S) LaTeX form of symbolic expression
Algumas dicas sobre o cálculo simbólico
- Choose Symbolic or Numeric Arithmetic
- Perform Symbolic Computations
- Create Symbolic Numbers, Variables, and Expressions
- Create Symbolic Functions
syms x y
f = sin(x)^2 + cos(y)^2;
diff(f)
ans = 2*cos(x)*sin(x)
- Extract Numerators and Denominators of Rational Expressions
- Generate MATLAB Functions from Symbolic Expressions
- Use subs to Evaluate Expressions and Functions
- Formula Rearrangement and Rewriting
Exemplo aplicado a substituição de variáveis
Definindo uma função de transferência como uma função simbólica
syms s
H(s) = (s^2 + 1)/(3*s^2 + 4*s + 6)
H(s) = (s^2 + 1)/(3*s^2 + 4*s + 6)
Imprimindo H(s) em formato LaTeX.
latex(H(s))
ans = \frac{s^2 + 1}{3\, s^2 + 4\, s + 6}
Substituindo a variável s pela f(z) = 2*(z-1)/(z+1);
syms z
Hz(z) = subs(H,2*(z-1)/(z+1))
Hz(z) = ((2*z - 2)^2/(z + 1)^2 + 1)/((3*(2*z - 2)^2)/(z + 1)^2 + (4*(2*z - 2))/(z + 1) + 6)
Agrupando os termos comuns em potencias de z
Hz2 = collect(Hz)
Hz2 = (5*z^2 - 6*z + 5)/(26*z^2 - 12*z + 10)