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- C
- C ..................................................................
- C
- C SUBROUTINE SE13
- C
- C PURPOSE
- C TO COMPUTE A VECTOR OF SMOOTHED FUNCTION VALUES GIVEN A
- C VECTOR OF FUNCTION VALUES WHOSE ENTRIES CORRESPOND TO
- C EQUIDISTANTLY SPACED ARGUMENT VALUES.
- C
- C USAGE
- C CALL SE13(Y,Z,NDIM,IER)
- C
- C DESCRIPTION OF PARAMETERS
- C Y - GIVEN VECTOR OF FUNCTION VALUES (DIMENSION NDIM)
- C Z - RESULTING VECTOR OF SMOOTHED FUNCTION VALUES
- C (DIMENSION NDIM)
- C NDIM - DIMENSION OF VECTORS Y AND Z
- C IER - RESULTING ERROR PARAMETER
- C IER = -1 - NDIM IS LESS THAN 3
- C IER = 0 - NO ERROR
- C
- C REMARKS
- C (1) IF IER=-1 THERE HAS BEEN NO COMPUTATION.
- C (2) Z CAN HAVE THE SAME STORAGE ALLOCATION AS Y. IF Y
- C IS DISTINCT FROM Z, THEN IT IS NOT DESTROYED.
- C
- C SUBROUTINES AND SUBPROGRAMS REQUIRED
- C NONE
- C
- C METHOD
- C IF X IS THE (SUPPRESSED) VECTOR OF ARGUMENT VALUES, THEN
- C EXCEPT AT THE ENDPOINTS X(1) AND X(NDIM), EACH SMOOTHED
- C VALUE Z(I) IS OBTAINED BY EVALUATING AT X(I) THE LEAST-
- C SQUARES POLYNOMIAL OF DEGREE 1 RELEVANT TO THE 3 SUCCESSIVE
- C POINTS (X(I+K),Y(I+K)) K = -1,0,1. (SEE HILDEBRAND, F.B.,
- C INTRODUCTION TO NUMERICAL ANALYSIS, MC GRAW-HILL, NEW YORK/
- C TORONTO/LONDON, 1956, PP. 295-302.)
- C
- C ..................................................................
- C
- SUBROUTINE SE13(Y,Z,NDIM,IER)
- C
- C
- DIMENSION Y(1),Z(1)
- C
- C TEST OF DIMENSION
- IF(NDIM-3)3,1,1
- C
- C PREPARE LOOP
- 1 B=.1666667*(5.*Y(1)+Y(2)+Y(2)-Y(3))
- C=.1666667*(5.*Y(NDIM)+Y(NDIM-1)+Y(NDIM-1)-Y(NDIM-2))
- C
- C START LOOP
- DO 2 I=3,NDIM
- A=B
- B=.3333333*(Y(I-2)+Y(I-1)+Y(I))
- 2 Z(I-2)=A
- C END OF LOOP
- C
- C UPDATE LAST TWO COMPONENTS
- Z(NDIM-1)=B
- Z(NDIM)=C
- IER=0
- RETURN
- C
- C ERROR EXIT IN CASE NDIM IS LESS THAN 3
- 3 IER=-1
- RETURN
- END