bfqad bfqad_r bsqad pchia pchid pfqad pfqad_r ppqad

pfqad_r() void pfqad_r ( int  ldc, double  c[], double  xi[], int  lxi, int  k, int  id, double  x1, double  x2, double  tol, double *  quad, int *  info, double *  xx, double  yy, int *  irev  ) Integral of product of arbitrary function and PP (piecewise polynomial) form 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 PP-representation (c[][], xi[], lxi, k). [x1, x2] is normally a subinterval of [xi[0], xi[lxi]]. The integration routine using adaptive 8-point Gauss-Legendre rule integrates the product on subintervals of [x1, x2] formed by included break points. Integration outside of [xi[0], xi[lxi]] is permitted provided f is defined. Parameters [in] ldc Leading dimension of two dimensional array stored in array c[] (ldc >= k) [in] c[] Array c[lc][ldc] (lc >= lxi) Right derivatives at break points. [in] xi[] Array xi[l_xi] (l_xi >= lxi + 1) Break points. [in] lxi Number of polynomial pieces. [in] k Order of B-spline. (k >= 1) [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. (Normally xi[0] <= x1 <= xi[lxi]) [in] x2 Upper end point of quadrature interval. (Normally xi[0] <= x1 <= xi[lxi]) [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] info = 0: Successful exit = -1: The argument ldc had an illegal value (ldc < k) = -4: The argument lxi had an illegal value (lxi < 1) = -5: The argument k had an illegal value (k < 1) = -6: The argument id had an illegal value (id < 0 or id >= k) = -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 [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