# gaussq 1.0

OS : Windows / Linux / Mac OS / BSD / Solaris
Script Licensing : Freeware
Created : Aug 28, 2007
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## CALL:<br />[int, tol] = gaussq('Fun',A,B,[reltol ...

CALL:
[int, tol] = gaussq by Per A. Brodtkorb('Fun', A, B, [reltol wfun], [trace, gn], p1, p2, . . . . )
[int, tol] = gaussq 1.0('Fun', A, B, [reltol wfun], [trace, gn], alpha, p1, p2, . . . . )
[int, tol] = gaussq [gaussq1.0.exe]('Fun', A, B, [reltol wfun], [trace, gn], alpha, beta, p1, p2, . . . . )
int = evaluated integral
tol = 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 kind
3 p(x)=sqrt((x-a)*(b-x)), a =-1, b = 1 Chebyshev of the second kind
4 p(x)=sqrt((x-a)/(b-x)), a = 0, b = 1
5 p(x)=1/sqrt(b-x), a = 0, b = 1
6 p(x)=sqrt(b-x), a = 0, b = 1
7 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 Laguerre
9 p(x)=exp(-x^2) a =-inf, b = inf Hermite
10 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 - 0MB Numerically evaluates a integral using a Gauss quadrature. The Quadrature integrates a (2m-1)th order polynomial exactly and the integral is of the form
b
Int (p(x)* Fun(x)) dx
a
gaussq 1.0 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)
Demands:
matlab Release: R11

gaussq 1.0 scripting tags: default, function, tol, inf, matlab, mathematics, gaussq, gaussqfunabreltol, matlab gaussq, integration, matlab mathematics, gaussq mathematics. What is new in gaussq 1.0 software script? - Unable to find gaussq 1.0 news. What is improvements are expecting? Newly-made gaussq 1.1 will be downloaded from here. You may download directly. Please write the reviews of the gaussq. License limitations are unspecified.