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

bsplvd() void bsplvd ( double  t[], int  k, int  nderiv, double  x, int  ileft, int  ldvnikx, double  vnikx[], double  work[], int *  info  ) Compute the value and the derivatives of B-spline basis functions Purpose This routine computes the value and all derivatives of order less than nderiv of all basis functions which do not (possibly) vanish at x. 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); The output of bsplvd is an array vnikx[j][i] of dimension at least k x nderiv whose columns contain the k nonzero basis functions and their nderiv-1 right derivatives at x, i = 0 to k-1, j = 0 to nderiv-1. These basis functions have indices ileft-k+i, i = 1 to k, k <= ileft <= n. The nonzero part of the i-th basis function lies in (t[i], t[i+k]), i = 0 to n-1). If x = t[ileft] then vnikx contains left limiting values (left derivatives) at t[ileft]. In particular, ileft = n produces left limiting values at the right end point x = t[n]. To obtain left limiting values at t[i], i = k to n, set x = next lower distinct knot, call interv to get ileft, set x = t[i], and then call 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] k Order of B-spline. (k >= 1) [in] nderiv Number of derivatives + 1. (1 <= nderiv <= k) [in] x Argument of basis functions. (t[k-1] <= x <= t[n]) [in] ileft Integer such that t[ileft-1] <= x <= t[ileft]. [in] ldvnikx Leading dimension of the two dimensional array vnikx[][]. (ldvnikx >= k) [out] vnikx[][] Array vnikx[lvnikx][ldvnikx] (lvnikx >= nderiv) Matrix containing the nonzero basis functions at x and their derivatives columnwise [out] work[] Array work[lwork] (lwork >= (k + 1)*(k + 2)/2) Work array. [out] info = 0: Successful exit = -2: The argument k had an illegal value (k < 1) = -3: The argument nderiv had an illegal value (nderiv < 1 or nderiv > k) = -6: The argument ldvnikx had an illegal value (ldvnikx < k) = 1: ileft is not properly set (x < t[ileft-1] or x > t[ileft]) Reference SLATEC