chfdv chfev pchbs pchcm pchfd pchfe pchic pchim pchse pchsp

pchbs() void pchbs ( int  n, double  x[], double  f[], double  d[], int  incfd, int  knotyp, int *  nknots, double  t[], double  bcoef[], int *  ndim, int *  kord, int *  info  ) Piecewise cubic Hermite to B-spline conversion Purpose This routine computes the B-spline representation of the piecewise cubic Hermite function determined by n, x[], f[] and d[]. The output is the B-representation for the function: nknots, t[], bcoef[], ndim and kord. Since it is assumed that the input piecewise cubic Hermite function has been computed by one of the other routines in the package, input arguments n, x[], incfd are not checked for validity. Restrictions and assumptions are: n >= 2 (not checked) x[i] < x[i+1], i=0 to n-1 (not checked) incfd > 0 (not checked) knotyp <= 2 (error return if not) (*) nknots = ndim + 4 = 2*n + 4 (error return if not) (*) t[2*k + 1] = t[2*k] = x[k], k=0 to n-1 (not checked) (*): indicates this applies only if knotyp < 0. Parameters [in] n Number of data points. (n >= 2) [in] x[] Array x[lx] (lx >= n) Independent variable values. The elements of x[] must be strictly increasing. [in] f[] Array f[lf] (lf >= incfd*(n - 1) + 1) Function values. f[i*incfd] is the value corresponding to x[i] (i = 0 to n - 1). [in] d[] Array d[ld] (ld >= incfd*(n - 1) + 1) Derivative values. d[i*incfd] is the value corresponding to x[i] (i = 0 to n - 1). [in] incfd Increment between successive values in f[] and d[]. (incfd >= 1) [in] knotyp Flag to control the knot sequence. The knot sequence t[] is normally computed from x by putting a double knot at each x and setting the end knot pairs according to the value of knotyp. = 0: Quadruple knots at x[0] and x[n-1] = 1: Replicate lengths of extreme subintervals:   t[0] = t[1] = x[0] - (x[1] - x[0])   t[m + 3] = t[m + 2] = x[n - 1] + (x[n - 1] - x[n - 2]) = 2: Periodic placement of boundary knots:   t[0] = t[1] = x[0] - (x[n - 1] - x[n - 2])   t[m + 3] = t[m + 2] = x[n - 1] + (x[1] - x[0]) Here m = ndim = 2*n. If the input value of knotyp is negative, however, it is assumed that nknots and t[] were set in a previous call. This option is provided for improved efficiency when used in a parametric setting. [in,out] nknots Number of knots. [in] When knotyp < 0: nknots is an input variable, and an error return will be taken if it is not equal to ndim + 4. [out] When knotyp >= 0: nknots will be set to ndim + 4. [in,out] t[] Array t[lt] (lt >= 2*n + 4) Knots for the B-representation. [in] When knotyp < 0: It is assumed that t[] was set by a previous call to pchbs (This routine does not verify that t[] forms a legitimate knot sequence). [out] When knotyp >= 0: t[] will be returned by pchbs with the interior double knots equal to the x values and the boundary knots set as indicated above. [out] bcoef[] Array bcoef[lbcoef] (lbcoef >= 2*n) B-spline coeficients. [out] ndim Dimension of the B-spline space (set to 2*n). [out] kord Order of the B-spline (set to 4). [out] info = 0: Successful exit = -6: The argument knotyp had an illegal value (knotyp > 2) = -7: The argument nknots had an illegal value (nknots != 2*N+4 when knotyp < 0) Reference SLATEC (PCHIP)