gaussq Matlab script

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  • Version:
  • File size: 0 KB
  • File name: gaussq.zip
  • Last update:
  • Platform: Windows / Linux / Mac OS / BSD / Solaris
  • Language: Matlab
  • Price:Freeware
  • Company: Per A. Brodtkorb (View more)

gaussq script description:




Publisher review:
gaussq numerically evaluates a integral using a Gauss quadrature. CALL:[int, tol] = gaussq('Fun',A,B,[reltol wfun],[trace,gn],p1,p2,....)[int, tol] = gaussq('Fun',A,B,[reltol wfun],[trace,gn],alpha,p1,p2,....)[int, tol] = gaussq('Fun',A,B,[reltol wfun],[trace,gn],alpha,beta,p1,p2,....)int = evaluated integraltol = absolute tolerance abs(int-intold)Fun = inline object, function handle or a function string. The function may depend on the parameters alpha and beta.A,B = lower and upper integration limits, respectively.reltol = relative tolerance (default 1e-3).wfun = integer defining the weight function:1 p(x)=1 a =-1, b = 1 Legendre (default)2 p(x)=1/sqrt((x-a)*(b-x)), a =-1, b = 1 Chebyshev of the first kind3 p(x)=sqrt((x-a)*(b-x)), a =-1, b = 1 Chebyshev of the second kind4 p(x)=sqrt((x-a)/(b-x)), a = 0, b = 15 p(x)=1/sqrt(b-x), a = 0, b = 16 p(x)=sqrt(b-x), a = 0, b = 17 p(x)=(x-a)^alpha*(b-x)^beta a =-1, b = 1 Jacobi alpha, beta >-1 (default alpha=beta=0)8 p(x)=x^alpha*exp(-x) a = 0, b = inf generalized Laguerre9 p(x)=exp(-x^2) a =-inf, b = inf Hermite10 p(x)=1 a =-1, b = 1 Legendre (slower than 1)trace = for non-zero TRACE traces the function evaluations with a point plot of the integrand (default 0).gn = number of base points and weight points to start the integration with (default 2).p1,p2,...= coefficients to be passed directly to function Fun: G = Fun(x,p1,p2,...).GAUSSQ Numerically evaluates a integral using a Gauss quadrature. The Quadrature integrates a (2m-1)th order polynomial exactly and the integral is of the formb Int (p(x)* Fun(x)) dx a GAUSSQ accept integration limits A, B and coefficients P1,P2,... as matrices or scalars and the result INT is the common size of A, B and P1,P2,....Examples :a) integration of x.^2 from 0 to 2 and from 1 to 4

b) integration of x^2*exp(-x) from zero to infinity gaussq('(x.^2)',[0 1],[2 4]) % a)gaussq('(1)',0,inf,[1e-3 8],[],2) % b)gaussq('(x.^2)',0,inf,[1e-3 8],[],0) % b) Requirements: ยท MATLAB Release: R11
gaussq is a Matlab script for Mathematics scripts design by Per A. Brodtkorb. It runs on following operating system: Windows / Linux / Mac OS / BSD / Solaris.

Operating system:
Windows / Linux / Mac OS / BSD / Solaris

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