gusucode.com > symbolic工具箱matlab源码程序 > symbolic/@sym/ilaplace.m
function F = ilaplace(L,varargin) %ILAPLACE Inverse Laplace transform. % F = ILAPLACE(L) is the inverse Laplace transform of the sym L % with default independent variable s. The default return is a % function of t. If L = L(t), then ILAPLACE returns a function of x: % F = F(x). % By definition, F(t) = int(L(s)*exp(s*t),s,c-i*inf,c+i*inf) % where c is a real number selected so that all singularities % of L(s) are to the left of the line s = c, i = sqrt(-1), and % the integration is taken with respect to s. % % F = ILAPLACE(L,y) makes F a function of y instead of the default t: % ILAPLACE(L,y) <=> F(y) = int(L(y)*exp(s*y),s,c-i*inf,c+i*inf). % % F = ILAPLACE(L,y,x) makes F a function of x instead of the default t: % ILAPLACE(L,y,x) <=> F(y) = int(L(y)*exp(x*y),y,c-i*inf,c+i*inf), % integration is taken with respect to y. % % Examples: % syms s t w x y f(x) % ilaplace(1/(s-1)) returns exp(t) % ilaplace(1/(t^2+1)) returns sin(x) % ilaplace(t^(-5/2),x) returns (4*x^(3/2))/(3*pi^(1/2)) % ilaplace(y/(y^2 + w^2),y,x) returns cos(w*x) % ilaplace(laplace(f(x),x,s),s,x) returns f(x) % % See also SYM/LAPLACE, SYM/IFOURIER, SYM/IZTRANS, SUBS. % Copyright 2011 The MathWorks, Inc. F = transform('ilaplace', 's', 't', 'x', L, varargin{:}); end