5 * Revision 1.1.1.1 1996/04/01 15:02:26 mclareni
10 FUNCTION DSPPS2(KX,KY,MX,MY,NDERX,NDERY,X,Y,TX,TY,C,NDIMC,W,NERR)
12 #include "gen/imp64.inc"
13 DIMENSION TX(*),TY(*),C(NDIMC,*),W(*),BX(27),BY(27)
16 PARAMETER (NAME = 'DSPPS2')
18 ************************************************************************
19 * NORBAS, VERSION: 15.03.1993
20 ************************************************************************
22 * DSPPS2 COMPUTES FUNCTION VALUES, VALUES OF DERIVATIVES, AND THE
23 * VALUE OF INTEGRAL, RESPECTIVELY, OF A TWO-DIMENSIONAL POLYNOMIAL
24 * SPLINE S(X,Y) IN REPRESENTATION OF NORMALIZED TWO-DIMENSIONAL
25 * B-SPLINES B(I,J)(X,Y)
27 * S(X,Y) = SUMME(I=1,...,MX-KX-1)
28 * SUMME(J=1,...,MY-KY-1) C(I,J) * B(I,J)(X,Y) .
30 * THE TWO-DIMENSIONAL B-SPLINES B(I,J)(X,Y) ARE THE PRODUCT OF TWO
31 * ONE-DIMENSIONAL B-SPLINES BX , BY
32 * B(I,J)(X,Y) = BX(I,KX)(X) * BY(J,KY)(Y)
33 * OF DEGREE KX AND KY ( 0 <= KX , KY <= 25 ) WITH INDICES I , J
34 * ( 1 <= I <= MX-KX-1 , 1 <= J <= MY-KY-1 ) OVER TWO SETS OF SPLINE-
36 * TX(1),TX(2),...,TX(MX) ( MX >= 2*KX+2 )
37 * TY(1),TY(2),...,TY(MY) ( MY >= 2*KY+2 ) ,
39 * FOR FURTHER DETAILS TO THE ONE-DIMENSIONAL NORMALIZED B-SPLINES SEE
40 * THE COMMENTS TO DSPNB1.
42 * C(I,J) (I=1,...,MX-KX-NDERX-1 , J=1,...,MY-KY-NDERY-1) MUST CONTAIN
43 * THE (I,J)-TH C COEFFICIENT OF THE POLYNOMIAL SPLINE S(X,Y) OR
44 * OF ONE OF ITS PARTIAL DERIVATIVE, REPRESENTED BY NORMALIZED
45 * TWO-DIMENSIONAL B-SPLINES OF DEGREE (KX-NDERX) AND (KY-NDERY),
48 * FOR TRANSFORMATION THE COEFFICIENTS OF THE POLYNOMIAL SPLINE S(X,Y)
49 * TO THE CORRESPONDING COEFFICIENTS OF THE NDERX-TH AND NDERY-TH
50 * PARTIAL DERIVATIVE OF S(X,Y) THE ROUTINE DSPCD2 MAY BE USED.
52 * ESPECIALLY FOR COMPUTING THE COEFFICIENTS C(I,J) OF THE TWO-
53 * DIMENSIONAL POLYNOMIAL VARIATION DIMINISHING SPLINE APPREOXIMATION
54 * OF A USER SUPPLIED FUNCTION Z = F(X,Y) THE ROUTINE DSPVD2 MAY BE
59 * KX (INTEGER) DEGREE OF ONE-DIMENSIONAL B-SPLINES IN X-DIRECTION
60 * OVER THE SET OF KNOTS TX.
61 * KY (INTEGER) DEGREE OF ONE-DIMENSIONAL B-SPLINES IN Y-DIRECTION
62 * OVER THE SET OF KNOTS TY.
63 * MX (INTEGER) NUMBER OF KNOTS FOR THE B-SPLINES IN X-DIRECTION.
64 * MY (INTEGER) NUMBER OF KNOTS FOR THE B-SPLINES IN Y-DIRECTION.
65 * NDERX (INTEGER) ON ENTRY, NDERX MUST CONTAIN AN INTEGER VALUE >= -1.
66 * = -1: DSPPS2 COMPUTES THE INTEGRAL OF S(TAU,Y) OVER THE
68 * = 0: DSPPS2 COMPUTES THE FUNCTION VALUE S(X,Y) FOR
69 * FOR THE SPECIFIED VALUES OF X,Y.
70 * >= 1: DSPNB2 COMPUTES THE VALUE OF THE NDERX-TH PARTIAL
71 * DERIVATIVE OF S(X,Y) WITH RESPECT TO X
72 * FOR THE SPECIFIED VALUES OF X,Y.
73 * (IF NDERX > KX ZERO RETURNS).
74 * NDERY (INTEGER) ON ENTRY, NDERY MUST CONTAIN AN INTEGER VALUE >= -1.
75 * THE MEANING OF NDERY IS THE SAME AS THAT OF THE PARAMETER
76 * NDERX WITH RESPECT TO Y-DIRECTION INSTEAD OF X-DIRECTION.
77 * NDIMC (INTEGER) DECLARED FIRST DIMENSION OF ARRAY C IN THE
78 * CALLING PROGRAM, WITH NDIMC >= MX-KX-NDERX-1 .
79 * X (DOUBLE PRECISION) ON ENTRY, X MUST CONTAIN THE VALUE OF THE
80 * INDEPENDENT VARIABLE X OF S(X,Y)
81 * Y (DOUBLE PRECISION) ON ENTRY, Y MUST CONTAIN THE VALUE OF THE
82 * INDEPENDENT VARIABLE Y OF S(X,Y)
83 * TX (DOUBLE PRECISION) ARRAY OF AT LEAST ORDER MX CONTAINING THE
84 * KNOTS IN X-DIRECTION, ON ENTRY.
85 * TY (DOUBLE PRECISION) ARRAY OF AT LEAST ORDER MY CONTAINING THE
86 * KNOTS IN Y-DIRECTION, ON ENTRY.
87 * C (DOUBLE PRECISION) ARRAY OF ORDER (NDIMC, >= MY-KY-NDERY-1),
88 * CONTAINING THE COEFFICIENTS OF THE TWO-DIMENSIONAL B-SPLINE
89 * REPRESENTATION OF S(X,Y) , ON ENTRY.
90 * W (DOUBLE PRECISION) WORKING ARRAY OF AT LEAST ORDER MY-KY-1.
91 * NERR (INTEGER) ERROR INDICATOR. ON EXIT:
92 * = 0: NO ERROR DETECTED
93 * = 1: AT LEAST ONE OF THE CONSTANTS KX , KY , MX , MY ,
94 * NDERX , NDERY IS ILLEGAL
99 * Z = DSPPS2(KX,KY,MX,MY,NDERX,NDERY,X,Y,TX,TY,C,NDIMC,W,NERR)
101 * - THE VALUE OF THE INTEGRAL (NDERX =-1 .AND. NDERY =-1) OR
102 * - THE FUNCTION VALUE (NDERX = 0 .AND. NDERY = 0) OR
103 * - THE VALUE OF THE NDERX-TH AND NDERY-TH PARTIAL DERIVATIVE
104 * (NDERX >= 0 .AND. NDERY >= 0 .AND. NDERX + NDERY > 0)
105 * OF THE POLYNOMIAL SPLINE S(X,Y) AT (X,Y).
109 * IF ONE OF THE FOLLOWING RELATION IS SATISFIED BY THE CHOSEN INPUT-
110 * PARAMETERS THE PROGRAM RETURNS, AND AN ERROR MESSAGE IS PRINTED:
111 * KX < 0 OR KX > 25 OR KY < 0 OR KY > 25 OR
112 * MX < 2*KX+2 OR MY < 2*KY+2 OR
113 * NDERX < -1 OR NDERY < -1 .
115 ************************************************************************
117 PARAMETER (Z0 = 0 , Z1 = 1)
120 IF(KX .LT. 0 .OR. KX .GT. 25) THEN
121 WRITE(ERRTXT,101) 'KX',KX
122 CALL MTLPRT(NAME,'E210.1',ERRTXT)
123 ELSEIF(KY .LT. 0 .OR. KY .GT. 25) THEN
124 WRITE(ERRTXT,101) 'KY',KY
125 CALL MTLPRT(NAME,'E210.1',ERRTXT)
126 ELSEIF(MX .LT. 2*KX+2) THEN
127 WRITE(ERRTXT,101) 'MX',MX
128 CALL MTLPRT(NAME,'E210.2',ERRTXT)
129 ELSEIF(MY .LT. 2*KY+2) THEN
130 WRITE(ERRTXT,101) 'MY',MY
131 CALL MTLPRT(NAME,'E210.2',ERRTXT)
132 ELSEIF(NDERX .LT. -1) THEN
133 WRITE(ERRTXT,101) 'NDERX',NDERX
134 CALL MTLPRT(NAME,'E210.5',ERRTXT)
135 ELSEIF(NDERY .LT. -1) THEN
136 WRITE(ERRTXT,101) 'NDERY',NDERY
137 CALL MTLPRT(NAME,'E210.5',ERRTXT)
138 ELSEIF(NDERX .EQ. -1 .AND. NDERY .NE. -1 .OR.
139 + NDERX .NE. -1 .AND. NDERY .EQ. -1 ) THEN
140 WRITE(ERRTXT,102) 'NDERX',NDERX,'NDERY',NDERY
141 CALL MTLPRT(NAME,'E210.6',ERRTXT)
145 IF(NDERX .EQ. -1 .AND. NDERY .EQ. -1) THEN
147 IF(X .GE. TX(MX-KX)) THEN
150 10 R=R+C(I,JJ)*(TX(I+KX+1)-TX(I))
153 KK=LKKSPL(X,TX(KX+1),MX-2*KX-1)+KX
156 20 R=R+C(I,JJ)*(TX(I+KX+1)-TX(I))
160 R=R+(X-TX(K1))*C(K1,JJ)
162 DO 50 I=MAX(1,KK-KX-1),KK-1
163 CALL DVSET(KX+1,Z0,BX(1),BX(2))
164 BX(KK-I)=1/(TX(KK)-TX(KK-1))
166 DO 30 J=MAX(1,KK-I-L),MIN(KX+1-L,KK-I)
167 DIF=TX(I+J+L)-TX(I+J-1)
170 + B0=((X-TX(I+J-1))*BX(J)+(TX(I+J+L)-X)*BX(J+1))/DIF
174 40 S=S+(X-TX(I+L-1))*BX(L)
175 S=S*(TX(I+KX+1)-TX(I))/(KX+1)
180 IF(Y .GE. TY(MY-KY)) THEN
183 70 R=R+W(I)*(TY(I+KY+1)-TY(I))
186 KK=LKKSPL(Y,TY(KY+1),MY-2*KY-1)+KY
189 80 R=R+W(I)*(TY(I+KY+1)-TY(I))
195 DO 110 I=MAX(1,KK-KY-1),KK-1
196 CALL DVSET(KY+1,Z0,BY(1),BY(2))
197 BY(KK-I)=1/(TY(KK)-TY(KK-1))
199 DO 90 J=MAX(1,KK-I-L),MIN(KY+1-L,KK-I)
200 DIF=TY(I+J+L)-TY(I+J-1)
203 + B0=((Y-TY(I+J-1))*BY(J)+(TY(I+J+L)-Y)*BY(J+1))/DIF
207 100 S=S+(Y-TY(I+L-1))*BY(L)
208 S=S*(TY(I+KY+1)-TY(I))/(KY+1)
217 IF(X .LT. TX(KX+1) .OR. X .GT. TX(MX-KX) .OR.
218 + Y .LT. TY(KY+1) .OR. Y .GT. TY(MY-KY) .OR.
219 + KX .LT. NDERX .OR. KY .LT. NDERY ) RETURN
221 KKX=LKKSPL(X,TX(KX+1),MX-2*KX-1)+KX
222 KKY=LKKSPL(Y,TY(KY+1),MY-2*KY-1)+KY
225 DO 120 J=2,KX-NDERX+1
226 120 BX(J)=E1*BX(J-1)/(TX(KKX-2+J)-TX(KKX-1))
230 BX(1)=E2*BX(1)/(TX(KKX)-TX(KKX-J))
231 DO 130 L=2,KX-NDERX+1-J
232 130 BX(L)=E3*BX(L-1)/(TX(KKX-2+L)-TX(KKX-1-J))+
233 + (TX(KKX-1+L)-X)*BX(L)/(TX(KKX-1+L)-TX(KKX-J))
236 DO 140 J=2,KY-NDERY+1
237 140 BY(J)=E1*BY(J-1)/(TY(KKY-2+J)-TY(KKY-1))
241 BY(1)=E2*BY(1)/(TY(KKY)-TY(KKY-J))
242 DO 150 L=2,KY-NDERY+1-J
243 150 BY(L)=E3*BY(L-1)/(TY(KKY-2+L)-TY(KKY-1-J))+
244 + (TY(KKY-1+L)-Y)*BY(L)/(TY(KKY-1+L)-TY(KKY-J))
246 DO 160 I=1,KX-NDERX+1
247 DO 160 J=1,KY-NDERY+1
248 160 R=R+C(KKX-2-KX+I,KKY-2-KY+J)*BX(I)*BY(J)
253 101 FORMAT(1X,A5,' =',I6,' NOT IN RANGE')
254 102 FORMAT(1X,A5,' =',I6,A7,' =',I6,' INCONSISTENT')