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

bintk() void bintk ( double  x[], double  y[], double  t[], int  n, int  k, double  bcoef[], double  q[], double  work[], int *  info  ) B-representation of the spline interpolation of order k Purpose This routine computes the B-representation (t[], bcoef[], n, k) of the spline of order k which interpolates given data. The spline or any of its derivatives can be evaluated by calls to bvalu. Parameters [in] x[] Array x[lx] (lx >= n) X vector of abscissae, distinct and in increasing order. [in] y[] Array y[ly] (ly >= n) Y vector of ordinates. [in] t[] Array t[lt] (lt >= n + k) Knot vector. Since t[0], ..., t[k-1] <= x[0] and t[n], ..., t[n+k-1] >= x[n-1], this leaves only n-k knots (not necessarily x[i] values) interior to [x[0], x[n-1]]. [in] n Number of data points. (n >= k) [in] k Order of the spline. (k >= 1) [out] bcoef[] Array bcoef[lbcoef] (lbcoef >= n) B-spline coefficients. [out] q[] Array q[lq] (lq >= (2*k - 1)*n) Work array, containing the triangular factorization of the coefficient matrix of the linear system being solved. The coefficients for the interpolant of an additional data set (x[i], yy[i]) (i = 1 to n) with the same abscissa can be obtained by loading yy into bcoef and then executing   banslv(n, k-1, k-1, 2*k-1, (double (*)[2*k-1])q, bcoef, &info); [out] work[] Array work[lwork] (lwork >= 2*k) Work array. [out] info = 0: Successful exit = -1: The argument x[] had an illegal value (not distinct or not in increasing order) = -4: The argument n had an illegal value (n < k) = -5: The argument k had an illegal value (k < 1) = 1: Some abscissa was not in the support of the corresponding basis function and the system is singular = 2: The system of solver detects a singular system although the theoretical conditions for a solution were satisfied Reference SLATEC