bfqad bfqad_r bsqad pchia pchid pfqad pfqad_r ppqad

bfqad_r() void bfqad_r ( double  t[], double  bcoef[], int  n, int  k, int  id, double  x1, double  x2, double  tol, double *  quad, double  work[], int *  info, double *  xx, double  yy, int *  irev  ) Integral of product of arbitrary function and B-representation of B-spline (reverse communication version) 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] 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 = -3: The argument n had an illegal value (n < k) = -4: The argument k had an illegal value (k < 1) = -5: The argument id had an illegal value (id < 0 or id >= k) = -6: The argument x1 had an illegal value (x1 < t[k-1] or x1 > t[n]) = -7: The argument x2 had an illegal value (x2 < t[k-1] or x2 > t[n]) = -8: 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 [out] xx When returned with irev=1 to 3, xx contains the abscissa where the function value shoule be evaluated and given in the next call. [in] yy When returned with irev = 1 to 3, the function value f(xx) should be given in yy in the next call. [in,out] irev Control variable for reverse communication. [in] Before first call, irev should be initialized to zero. On succeeding calls, irev should not be altered. [out] If irev is not zero, complete the following process and call this routine again. = 0: Computation finished. See return code in info. = 1 to 3: User should set the function value at xx (f(xx)) in yy. Do not alter any variables other than yy. Reference SLATEC