5 * Revision 1.1.1.1 1996/04/01 15:02:26 mclareni
10 FUNCTION DSPNB1(K,M,I,NDER,X,T,NERR)
12 #include "gen/imp64.inc"
13 DIMENSION T(*),B(27),D(27)
16 PARAMETER (NAME = 'DSPNB1')
18 ************************************************************************
19 * NORBAS, VERSION: 15.03.1993
20 ************************************************************************
22 * DSPNB1 COMPUTES FUNCTION VALUES, VALUES OF DERIVATIVES, AND THE
23 * VALUE OF INTEGRAL, RESPECTIVELY, OF NORMALIZED B-SPLINES
25 * OF DEGREE K ( 0<= K <= 25 ) WITH INDEX I ( 1 <= I <= M-K-1 )
26 * OVER A SET OF SPLINE-KNOTS
27 * T(1),T(2), ... ,T(M) ( M >= 2*K+2 )
28 * (KNOTS IN ASCENDING ORDER, WITH MULTIPLICITIES NOT GREATER
31 * THE FUNCTION VALUE OF THE NORMALIZED B-SPLINE B(I,K)(X) IS
32 * IDENTICALLY ZERO OUTSIDE THE INTERVAL T(I) <= X < T(I+K+1).
34 * THE NORMALIZATION OF N(X) = B(I,K)(X) IS SUCH THAT THE INTGRAL OF
35 * N(X) OVER THE WHOLE X-RANGE EQUALS
36 * ( T(I+K+1) - T(I) ) / (K+1) .
40 * K (INTEGER) DEGREE (= ORDER - 1) OF B-SPLINES.
41 * M (INTEGER) NUMBER OF KNOTS FOR THE B-SPLINES.
42 * NDER (INTEGER) ON ENTRY, NDER MUST CONTAIN AN INTEGER VALUE .GE. -1
43 * = -1: DSPNB1 COMPUTES THE INTEGRAL OF B(I,K)(TAU) OVER THE
45 * = 0: DSPNB1 COMPUTES THE FUNCTION VALUE B(I,K)(X) FOR
46 * FOR THE SPECIFIED VALUES OF I, K, AND X.
47 * >= 1: DSPNB1 COMPUTES THE VALUE OF THE NDER-TH DERIVATIVE OF
48 * B(I,K)(X) FOR THE SPECIFIED VALUES OF I, K, AND X
49 * (IF NDER > K ZERO RETURNS).
50 * X (DOUBLE PRECISION) ON ENTRY, X MUST CONTAIN THE VALUE OF THE
51 * INDEPENDENT VARIABLE X OF B(I,K)(X)
52 * T (DOUBLE PRECISION) ARRAY OF AT LEAST ORDER M CONTAINING THE
54 * I (INTEGER) INDEX OF THE B-SPLINE B(I,K)(X)
55 * NERR (INTEGER) ERROR INDICATOR. ON EXIT:
56 * = 0: NO ERROR DETECTED
57 * = 1: AT LEAST ONE OF THE CONSTANTS K , M , I , NDER IS ILLEGAL
62 * A = DSPNB1(K,M,I,NDER,X,T,NERR)
64 * - THE VALUE OF THE INTEGRAL (NDER = -1) OR
65 * - THE FUNCTION VALUE (NDER = 0 ) OR
66 * - THE VALUE OF THE NDER-TH DERIVATIVE (NDER > 0 )
67 * OF THE NORMALIZED B-SPLINE B(I,K)(X) OF DEGREE K WITH INDEX I AT X.
71 * IF ONE OF THE FOLLOWING RELATION IS SATISFIED BY THE CHOSEN INPUT-
72 * PARAMETERS THE PROGRAM RETURNS, AND AN ERROR MESSAGE IS PRINTED:
78 ************************************************************************
80 PARAMETER (Z0 = 0 , Z1 = 1)
83 IF(K .LT. 0 .OR. K .GT. 25) THEN
84 WRITE(ERRTXT,101) 'K',K
85 CALL MTLPRT(NAME,'E210.1',ERRTXT)
86 ELSEIF(M .LT. 2*K+2) THEN
87 WRITE(ERRTXT,101) 'M',M
88 CALL MTLPRT(NAME,'E210.2',ERRTXT)
89 ELSEIF(I . LT. 1 .OR. I .GT. M-K-1) THEN
90 WRITE(ERRTXT,101) 'I',I
91 CALL MTLPRT(NAME,'E210.3',ERRTXT)
92 ELSEIF(NDER .LT. -1) THEN
93 WRITE(ERRTXT,101) 'NDER',NDER
94 CALL MTLPRT(NAME,'E210.5',ERRTXT)
100 + .OR. X .GT. T(I+K+1) .AND. NDER .GE. 0
101 + .OR. K .LT. NDER ) RETURN
103 IF(NDER .EQ. -1) THEN
104 IF(X .GE. T(I+K+1)) THEN
105 R=(T(I+K+1)-T(I))/(K+1)
107 KK=LKKSPL(X,T(I),MIN(2*(K+1),M-K-I))+I-1
111 CALL DVSET(K+1,Z0,B(1),B(2))
112 B(KK-I)=1/(T(KK)-T(KK-1))
114 DO 10 J=MAX(1,KK-I-L),MIN(K+1-L,KK-I)
115 DIF=T(I+J+L)-T(I+J-1)
117 IF(DIF .NE. 0) B0=((X-T(I+J-1))*B(J)+(T(I+J+L)-X)*B(J+1))/DIF
121 20 S=S+(X-T(I+L-1))*B(L)
122 R=S*(T(I+K+1)-T(I))/(K+1)
132 KK=LKKSPL(X,T(I),MIN(2*(K+1),M-K-I))+I-1
140 30 B(J)=E1*B(J-1)/(T(KK-2+J)-T(KK-1))
141 IF(KK .NE. I+1 .OR. NDER .NE. 0) THEN
145 B(1)=E2*B(1)/(T(KK)-T(KK-J))
147 40 B(L)=E3*B(L-1)/(T(KK-2+L)-T(KK-1-J))+
148 + (T(KK-1+L)-X)*B(L)/(T(KK-1+L)-T(KK-J))
153 CALL DVSET(K+2,Z0,D(1),D(2))
158 DIF=T(L+KK-1)-T(L+KK-K-2+J)
160 IF(DIF .NE. 0) D0=A*(D(L+1)-D(L))/DIF
162 R=DVMPY(K-NDER+1,B(1),B(2),D(1),D(2))
170 101 FORMAT(1X,A5,' =',I6,' NOT IN RANGE')