banfac banslv bint4 bintk bspldr bsplev bsplpp bsplvd bsplvn bvalue interv ppvalu

bsplev() void bsplev ( double  t[], double  ad[], int  n, int  k, int  nderiv, double  x, int *  inev, double  svalue[], double  work[], int *  info  ) Evaluation of function and derivative values for B-representation of B-spline Purpose This routine computes the value of the B-spline and its derivatives at x from the B-representation (t[], a[], n, k) and returns them in svalue[i] (i = 0 to nderiv-1), where t[k-1] <= x <= t[n]. ad[i] can be the B-spline coefficients a[i] (i = 0 to n-1) if nderiv = 1. Otherwise ad[] must be computed beforehand by the following statement. bspldr(t, a, n, k, nderiv, ad); If x = t[i] (k-1 <= i <= n-1), right limiting values are obtained. To compute left derivatives or left limiting values at a knot t[i], replace n by i-1 and set x = t[i] (k <= i <= n). Parameters [in] t[] Array t[lt] (lt >= n + k) Knot vector. [in] ad[] Array ad[lad] (lad >= (2*n - nderiv + 1)*nderiv/2) Divided difference table. [in] n Number of B-spline coefficients. (n = sum of knot multiplicities - k) [in] k Order of B-spline. (k >= 1) [in] nderiv Number of the derivatives. (1 <= nderiv <= k) nderiv = 1 returns the zero-th derivative = function value. [in] x Argumrnt. (t[k-1] <= x <= t[n]) [in,out] inev An initialization parameter. [in] Must be set to 1 when the first time bslpev is called. [out] Information for efficient processing after the initial call and inev must not be changed by the user. Distinct splines require distinct inev parameters. [out] svalue[] Array svalue[lsvalue] (lsvalue >= nderiv) The spline value in svalue[0] and the nderiv-1 derivatives in the remaining components. [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 nderiv had an illegal value (nderiv < 1 or nderiv > k) = -6: The argument x had an illegal value (x < t[k-1] or x > t[n]) = 1: A left limiting value cannot be obtained at t[k-1] Reference SLATEC