CSIEZ
Computes the cubic spline interpolant with the ‘not-a-knot’ condition and return values of the interpolant at specified points.
Required Arguments
XDATA — Array of length NDATA containing the data point abscissas. (Input)
The data point abscissas must be distinct.
FDATA — Array of length NDATA containing the data point ordinates. (Input)
XVEC — Array of length N containing the points at which the spline is to be evaluated. (Input)
VALUE — Array of length N containing the values of the spline at the points in XVEC. (Output)
Optional Arguments
NDATA — Number of data points. (Input)
NDATA must be at least 2.
Default: NDATA = size (XDATA,1).
N — Length of vector XVEC. (Input)
Default: N = size (XVEC,1).
FORTRAN 90 Interface
Generic: CALL CSIEZ (XDATA, FDATA, XVEC, VALUE [, …])
Specific: The specific interface names are S_CSIEZ and D_CSIEZ.
FORTRAN 77 Interface
Single: CALL CSIEZ (NDATA, XDATA, FDATA, N, XVEC, VALUE)
Double: The double precision name is DCSIEZ.
Description
This routine is designed to let the user easily compute the values of a cubic spline interpolant. The routine CSIEZ computes a spline interpolant to a set of data points (xi, fi) for i = 1, …, NDATA. The output for this routine consists of a vector of values of the computed cubic spline. Specifically, let n = N, v = XVEC, and y = VALUE, then if s is the computed spline we set
yj = s(vj ) j = 1, …, n
Additional documentation can be found by referring to the IMSL routines CSINT or SPLEZ.
Comments
Workspace may be explicitly provided, if desired, by use of C2IEZ/DC2IEZ. The reference is:
CALL C2IEZ (NDATA, XDATA, FDATA, N, XVEC, VALUE, IWK, WK1, WK2)
The additional arguments are as follows:
IWK — Integer work array of length MAX0(N, NDATA) + N.
WK1 — Real work array of length 5 * NDATA.
WK2 — Real work array of length 2 * N.
Example
In this example, a cubic spline interpolant to a function F is computed. The values of this spline are then compared with the exact function values.
USE CSIEZ_INT
USE UMACH_INT
IMPLICIT NONE
INTEGER NDATA
PARAMETER (NDATA=11)
!
INTEGER I, NOUT
REAL F, FDATA(NDATA), FLOAT, SIN, VALUE(2*NDATA-1), X,&
XDATA(NDATA), XVEC(2*NDATA-1)
INTRINSIC FLOAT, SIN
! Define function
F(X) = SIN(15.0*X)
! Set up a grid
DO 10 I=1, NDATA
XDATA(I) = FLOAT(I-1)/FLOAT(NDATA-1)
FDATA(I) = F(XDATA(I))
10 CONTINUE
DO 20 I=1, 2*NDATA - 1
XVEC(I) = FLOAT(I-1)/FLOAT(2*NDATA-2)
20 CONTINUE
! Compute cubic spline interpolant
CALL CSIEZ (XDATA, FDATA, XVEC, VALUE)
! Get output unit number
CALL UMACH (2, NOUT)
! Write heading
WRITE (NOUT,99998)
99998 FORMAT (13X, 'X', 9X, 'INTERPOLANT', 5X, 'ERROR')
! Print the interpolant and the error
! on a finer grid
DO 30 I=1, 2*NDATA - 1
WRITE (NOUT,99999) XVEC(I), VALUE(I), F(XVEC(I)) - VALUE(I)
30 CONTINUE
99999 FORMAT(' ', 2F15.3, F15.6)
END
X INTERPOLANT ERROR
0.000 0.000 0.000000
0.050 0.809 -0.127025
0.100 0.997 0.000000
0.150 0.723 0.055214
0.200 0.141 0.000000
0.250 -0.549 -0.022789
0.300 -0.978 0.000000
0.350 -0.843 -0.016246
0.400 -0.279 0.000000
0.450 0.441 0.009348
0.500 0.938 0.000000
0.550 0.903 0.019947
0.600 0.412 0.000000
0.650 -0.315 -0.004895
0.700 -0.880 0.000000
0.750 -0.938 -0.029541
0.800 -0.537 0.000000
0.850 0.148 0.034693
0.900 0.804 0.000000
0.950 1.086 -0.092559
1.000 0.650 0.000000
