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

bsplvn() void bsplvn ( double  t[], int  jhigh, int  k, int  index, double  x, int  ileft, double  vnikx[], double  work[], int *  iwork, int *  info  ) Compute the value of B-spline basis functions Purpose This routine computes the value of all (possibly) nonzero basis functions at x of order max(jhigh, (j+1)*(index-1)), where t[k-1] <= x <= t[n] and j = iwork is set to 1 inside the routine on the first call when index = 1. ileft is input such that t[ileft-1] <= x <= t[ileft]. The following statement produces the proper ileft. interv(t, n+1, x, &ilo, &ileft, &info); bsplvn computes using the basic algorithm needed in bsplvd. If only basis functions are desired, setting jhigh = k and index = 1 can be faster than calling bsplvd. but extra coding is required for derivatives (index = 2) and bsplvd is set up for this purpose. Left limiting values are set up as described in bsplvd. Parameters [in] t[] Array t[lt] (lt >= n + k) Knot vector of length n + k, where n is number of B-spline basis functions (= sum of knot multiplicities - k). [in] jhigh Order of B-spline to be computed. (1 <= jhigh <= k) [in] k Highest possible order. (k >= 1) [in] index = 1: The computation starts from scratch and the entire B-spline values of orders 1, 2, ..., jhigh is generated order by order. = 2: Only the B-spline values of order j+1, j+2, ..., jhigh are generated. The previous entry with work[] and iwork values for order j have to be saved. [in] x Argument of basis functions. (t[k-1] <= x <= t[n]) [in] ileft Integer such that t[ileft-1] <= x <= t[ileft]. [out] vnikx[] Array vnikx[lvnikx] (lvnikx >= k) Values of basis functions. [out] work[] Array work[lwork] (lwork >= 2*k) Work array. Both work[] and iwork contain information necessary to continue for index = 2. When index = 1 exclusively, these are scratch variables and can be used for other purposes. [out] iwork Work variable. [out] info = 0: Successful exit = -2: The argument jhigh had an illegal value (jhigh < 1 or jhigh > k) = -3: The argument k had an illegal value (k < 1) = -4: The argument index had an illegal value (index != 1 and index != 2) = 1: ileft is not properly set (x < t[ileft-1] or x > t[ileft]) Reference SLATEC