bfqad bfqad_r bsqad pchia pchid pfqad pfqad_r ppqad

bfqad() void bfqad ( double(*)(double)  f, double  t[], double  bcoef[], int  n, int  k, int  id, double  x1, double  x2, double  tol, double *  quad, double  work[], int *  info  ) Integral of product of arbitrary function and B-representation of B-spline Purpose This routine computes the integral on [x1, x2] of a product of a function f(x) and the id-th derivative of a k-th order B-spline, using the B-representation (t[], bcoef[], n, k). [x1, x2] must be a subinterval of [t[k-1], t[k]]. Then integration routine using adaptive 8-point Gauss-Legendre rule integrates the product on subintervals of [x1, x2] formed by included (distinct) knots. Parameters [in] f User supplied subroutine which calculates the integrand function f(x) defined as follows. double f(double x) { return the value of f(x); } [in] t[] Array t[lt] (lt >= n + k) Knot vector. [in] bcoef() Array bcoef[lbcoef] (lbcoef >= n) B-spline coefficients. [in] n Number of B-spline coefficients. (n = sum of knot multiplicities - k) [in] k Order of B-spline. (1 <= k) [in] id Order of the spline derivative. (0 <= id <= k - 1) id = 0 gives the spline function. [in] x1 Lower end point of quadrature interval. (t[k] <= x1 <= t[n+1]) [in] x2 Upper end point of quadrature interval. (t[k] <= x2 <= t[n+1]) [in] tol Desired accuracy for the quadrature. (dtol < tol <= 0.1 where dtol is max(1.0e-18, double precision unit roundoff for the machine (= d1mach(4))). [out] quad Integral of f(x)*(id-th derivative of a k-th order B-spline) on [x1, x2]. [out] work[] Array work[lwork] (lwork >= 3*k) Work array. [out] info = 0: Successful exit = -4: The argument n had an illegal value (n < k) = -5: The argument k had an illegal value (k < 1) = -6: The argument id had an illegal value (id < 0 or id >= k) = -7: The argument x1 had an illegal value (x1 < t[k-1] or x1 > t[n]) = -8: The argument x2 had an illegal value (x2 < t[k-1] or x2 > t[n]) = -9: The argument tol had an illegal value (tol < dtol or tol > 0.1) = 1: Some quadrature on [x1, x2] does not meet the requested tolerance Reference SLATEC