--- /dev/null
+*
+* $Id$
+*
+* $Log$
+* Revision 1.1.1.1 1996/04/01 15:02:26 mclareni
+* Mathlib gen
+*
+*
+#include "gen/pilot.h"
+ FUNCTION DSPPS2(KX,KY,MX,MY,NDERX,NDERY,X,Y,TX,TY,C,NDIMC,W,NERR)
+
+#include "gen/imp64.inc"
+ DIMENSION TX(*),TY(*),C(NDIMC,*),W(*),BX(27),BY(27)
+ CHARACTER NAME*(*)
+ CHARACTER*80 ERRTXT
+ PARAMETER (NAME = 'DSPPS2')
+
+************************************************************************
+* NORBAS, VERSION: 15.03.1993
+************************************************************************
+*
+* DSPPS2 COMPUTES FUNCTION VALUES, VALUES OF DERIVATIVES, AND THE
+* VALUE OF INTEGRAL, RESPECTIVELY, OF A TWO-DIMENSIONAL POLYNOMIAL
+* SPLINE S(X,Y) IN REPRESENTATION OF NORMALIZED TWO-DIMENSIONAL
+* B-SPLINES B(I,J)(X,Y)
+*
+* S(X,Y) = SUMME(I=1,...,MX-KX-1)
+* SUMME(J=1,...,MY-KY-1) C(I,J) * B(I,J)(X,Y) .
+*
+* THE TWO-DIMENSIONAL B-SPLINES B(I,J)(X,Y) ARE THE PRODUCT OF TWO
+* ONE-DIMENSIONAL B-SPLINES BX , BY
+* B(I,J)(X,Y) = BX(I,KX)(X) * BY(J,KY)(Y)
+* OF DEGREE KX AND KY ( 0 <= KX , KY <= 25 ) WITH INDICES I , J
+* ( 1 <= I <= MX-KX-1 , 1 <= J <= MY-KY-1 ) OVER TWO SETS OF SPLINE-
+* KNOTS
+* TX(1),TX(2),...,TX(MX) ( MX >= 2*KX+2 )
+* TY(1),TY(2),...,TY(MY) ( MY >= 2*KY+2 ) ,
+* RESPECTIVELY.
+* FOR FURTHER DETAILS TO THE ONE-DIMENSIONAL NORMALIZED B-SPLINES SEE
+* THE COMMENTS TO DSPNB1.
+*
+* C(I,J) (I=1,...,MX-KX-NDERX-1 , J=1,...,MY-KY-NDERY-1) MUST CONTAIN
+* THE (I,J)-TH C COEFFICIENT OF THE POLYNOMIAL SPLINE S(X,Y) OR
+* OF ONE OF ITS PARTIAL DERIVATIVE, REPRESENTED BY NORMALIZED
+* TWO-DIMENSIONAL B-SPLINES OF DEGREE (KX-NDERX) AND (KY-NDERY),
+* RESPECTIVELY.
+*
+* FOR TRANSFORMATION THE COEFFICIENTS OF THE POLYNOMIAL SPLINE S(X,Y)
+* TO THE CORRESPONDING COEFFICIENTS OF THE NDERX-TH AND NDERY-TH
+* PARTIAL DERIVATIVE OF S(X,Y) THE ROUTINE DSPCD2 MAY BE USED.
+*
+* ESPECIALLY FOR COMPUTING THE COEFFICIENTS C(I,J) OF THE TWO-
+* DIMENSIONAL POLYNOMIAL VARIATION DIMINISHING SPLINE APPREOXIMATION
+* OF A USER SUPPLIED FUNCTION Z = F(X,Y) THE ROUTINE DSPVD2 MAY BE
+* USED.
+*
+* PARAMETERS:
+*
+* KX (INTEGER) DEGREE OF ONE-DIMENSIONAL B-SPLINES IN X-DIRECTION
+* OVER THE SET OF KNOTS TX.
+* KY (INTEGER) DEGREE OF ONE-DIMENSIONAL B-SPLINES IN Y-DIRECTION
+* OVER THE SET OF KNOTS TY.
+* MX (INTEGER) NUMBER OF KNOTS FOR THE B-SPLINES IN X-DIRECTION.
+* MY (INTEGER) NUMBER OF KNOTS FOR THE B-SPLINES IN Y-DIRECTION.
+* NDERX (INTEGER) ON ENTRY, NDERX MUST CONTAIN AN INTEGER VALUE >= -1.
+* = -1: DSPPS2 COMPUTES THE INTEGRAL OF S(TAU,Y) OVER THE
+* RANGE TAU <= X.
+* = 0: DSPPS2 COMPUTES THE FUNCTION VALUE S(X,Y) FOR
+* FOR THE SPECIFIED VALUES OF X,Y.
+* >= 1: DSPNB2 COMPUTES THE VALUE OF THE NDERX-TH PARTIAL
+* DERIVATIVE OF S(X,Y) WITH RESPECT TO X
+* FOR THE SPECIFIED VALUES OF X,Y.
+* (IF NDERX > KX ZERO RETURNS).
+* NDERY (INTEGER) ON ENTRY, NDERY MUST CONTAIN AN INTEGER VALUE >= -1.
+* THE MEANING OF NDERY IS THE SAME AS THAT OF THE PARAMETER
+* NDERX WITH RESPECT TO Y-DIRECTION INSTEAD OF X-DIRECTION.
+* NDIMC (INTEGER) DECLARED FIRST DIMENSION OF ARRAY C IN THE
+* CALLING PROGRAM, WITH NDIMC >= MX-KX-NDERX-1 .
+* X (DOUBLE PRECISION) ON ENTRY, X MUST CONTAIN THE VALUE OF THE
+* INDEPENDENT VARIABLE X OF S(X,Y)
+* Y (DOUBLE PRECISION) ON ENTRY, Y MUST CONTAIN THE VALUE OF THE
+* INDEPENDENT VARIABLE Y OF S(X,Y)
+* TX (DOUBLE PRECISION) ARRAY OF AT LEAST ORDER MX CONTAINING THE
+* KNOTS IN X-DIRECTION, ON ENTRY.
+* TY (DOUBLE PRECISION) ARRAY OF AT LEAST ORDER MY CONTAINING THE
+* KNOTS IN Y-DIRECTION, ON ENTRY.
+* C (DOUBLE PRECISION) ARRAY OF ORDER (NDIMC, >= MY-KY-NDERY-1),
+* CONTAINING THE COEFFICIENTS OF THE TWO-DIMENSIONAL B-SPLINE
+* REPRESENTATION OF S(X,Y) , ON ENTRY.
+* W (DOUBLE PRECISION) WORKING ARRAY OF AT LEAST ORDER MY-KY-1.
+* NERR (INTEGER) ERROR INDICATOR. ON EXIT:
+* = 0: NO ERROR DETECTED
+* = 1: AT LEAST ONE OF THE CONSTANTS KX , KY , MX , MY ,
+* NDERX , NDERY IS ILLEGAL
+*
+* USAGE:
+*
+* THE FUNCTION-CALL
+* Z = DSPPS2(KX,KY,MX,MY,NDERX,NDERY,X,Y,TX,TY,C,NDIMC,W,NERR)
+* RETURNS
+* - THE VALUE OF THE INTEGRAL (NDERX =-1 .AND. NDERY =-1) OR
+* - THE FUNCTION VALUE (NDERX = 0 .AND. NDERY = 0) OR
+* - THE VALUE OF THE NDERX-TH AND NDERY-TH PARTIAL DERIVATIVE
+* (NDERX >= 0 .AND. NDERY >= 0 .AND. NDERX + NDERY > 0)
+* OF THE POLYNOMIAL SPLINE S(X,Y) AT (X,Y).
+*
+* ERROR MESSAGES:
+*
+* IF ONE OF THE FOLLOWING RELATION IS SATISFIED BY THE CHOSEN INPUT-
+* PARAMETERS THE PROGRAM RETURNS, AND AN ERROR MESSAGE IS PRINTED:
+* KX < 0 OR KX > 25 OR KY < 0 OR KY > 25 OR
+* MX < 2*KX+2 OR MY < 2*KY+2 OR
+* NDERX < -1 OR NDERY < -1 .
+*
+************************************************************************
+
+ PARAMETER (Z0 = 0 , Z1 = 1)
+
+ NERR=1
+ IF(KX .LT. 0 .OR. KX .GT. 25) THEN
+ WRITE(ERRTXT,101) 'KX',KX
+ CALL MTLPRT(NAME,'E210.1',ERRTXT)
+ ELSEIF(KY .LT. 0 .OR. KY .GT. 25) THEN
+ WRITE(ERRTXT,101) 'KY',KY
+ CALL MTLPRT(NAME,'E210.1',ERRTXT)
+ ELSEIF(MX .LT. 2*KX+2) THEN
+ WRITE(ERRTXT,101) 'MX',MX
+ CALL MTLPRT(NAME,'E210.2',ERRTXT)
+ ELSEIF(MY .LT. 2*KY+2) THEN
+ WRITE(ERRTXT,101) 'MY',MY
+ CALL MTLPRT(NAME,'E210.2',ERRTXT)
+ ELSEIF(NDERX .LT. -1) THEN
+ WRITE(ERRTXT,101) 'NDERX',NDERX
+ CALL MTLPRT(NAME,'E210.5',ERRTXT)
+ ELSEIF(NDERY .LT. -1) THEN
+ WRITE(ERRTXT,101) 'NDERY',NDERY
+ CALL MTLPRT(NAME,'E210.5',ERRTXT)
+ ELSEIF(NDERX .EQ. -1 .AND. NDERY .NE. -1 .OR.
+ + NDERX .NE. -1 .AND. NDERY .EQ. -1 ) THEN
+ WRITE(ERRTXT,102) 'NDERX',NDERX,'NDERY',NDERY
+ CALL MTLPRT(NAME,'E210.6',ERRTXT)
+ ELSE
+
+ NERR=0
+ IF(NDERX .EQ. -1 .AND. NDERY .EQ. -1) THEN
+ DO 60 JJ=1,MY-KY-1
+ IF(X .GE. TX(MX-KX)) THEN
+ R=Z0
+ DO 10 I=1,MX-KX-1
+ 10 R=R+C(I,JJ)*(TX(I+KX+1)-TX(I))
+ R=R/(KX+1)
+ ELSE
+ KK=LKKSPL(X,TX(KX+1),MX-2*KX-1)+KX
+ R=Z0
+ DO 20 I=1,KK-KX-2
+ 20 R=R+C(I,JJ)*(TX(I+KX+1)-TX(I))
+ R=R/(KX+1)
+ IF(KX .EQ. 0) THEN
+ K1=MAX(1,KK-1)
+ R=R+(X-TX(K1))*C(K1,JJ)
+ ELSE
+ DO 50 I=MAX(1,KK-KX-1),KK-1
+ CALL DVSET(KX+1,Z0,BX(1),BX(2))
+ BX(KK-I)=1/(TX(KK)-TX(KK-1))
+ DO 30 L=1,KX
+ DO 30 J=MAX(1,KK-I-L),MIN(KX+1-L,KK-I)
+ DIF=TX(I+J+L)-TX(I+J-1)
+ B0=Z0
+ IF(DIF .NE. 0)
+ + B0=((X-TX(I+J-1))*BX(J)+(TX(I+J+L)-X)*BX(J+1))/DIF
+ 30 BX(J)=B0
+ S=Z0
+ DO 40 L=1,KK-I
+ 40 S=S+(X-TX(I+L-1))*BX(L)
+ S=S*(TX(I+KX+1)-TX(I))/(KX+1)
+ 50 R=R+C(I,JJ)*S
+ ENDIF
+ ENDIF
+ 60 W(JJ)=R
+ IF(Y .GE. TY(MY-KY)) THEN
+ R=Z0
+ DO 70 I=1,MY-KY-1
+ 70 R=R+W(I)*(TY(I+KY+1)-TY(I))
+ R=R/(KY+1)
+ ELSE
+ KK=LKKSPL(Y,TY(KY+1),MY-2*KY-1)+KY
+ R=Z0
+ DO 80 I=1,KK-KY-2
+ 80 R=R+W(I)*(TY(I+KY+1)-TY(I))
+ R=R/(KY+1)
+ IF(KY .EQ. 0) THEN
+ K1=MAX(1,KK-1)
+ R=R+(Y-TY(K1))*W(K1)
+ ELSE
+ DO 110 I=MAX(1,KK-KY-1),KK-1
+ CALL DVSET(KY+1,Z0,BY(1),BY(2))
+ BY(KK-I)=1/(TY(KK)-TY(KK-1))
+ DO 90 L=1,KY
+ DO 90 J=MAX(1,KK-I-L),MIN(KY+1-L,KK-I)
+ DIF=TY(I+J+L)-TY(I+J-1)
+ B0=Z0
+ IF(DIF .NE. 0)
+ + B0=((Y-TY(I+J-1))*BY(J)+(TY(I+J+L)-Y)*BY(J+1))/DIF
+ 90 BY(J)=B0
+ S=Z0
+ DO 100 L=1,KK-I
+ 100 S=S+(Y-TY(I+L-1))*BY(L)
+ S=S*(TY(I+KY+1)-TY(I))/(KY+1)
+ 110 R=R+W(I)*S
+ ENDIF
+ ENDIF
+ DSPPS2=R
+ RETURN
+ ENDIF
+
+ DSPPS2=Z0
+ IF(X .LT. TX(KX+1) .OR. X .GT. TX(MX-KX) .OR.
+ + Y .LT. TY(KY+1) .OR. Y .GT. TY(MY-KY) .OR.
+ + KX .LT. NDERX .OR. KY .LT. NDERY ) RETURN
+
+ KKX=LKKSPL(X,TX(KX+1),MX-2*KX-1)+KX
+ KKY=LKKSPL(Y,TY(KY+1),MY-2*KY-1)+KY
+ E1=X-TX(KKX-1)
+ BX(1)=Z1
+ DO 120 J=2,KX-NDERX+1
+ 120 BX(J)=E1*BX(J-1)/(TX(KKX-2+J)-TX(KKX-1))
+ E2=TX(KKX)-X
+ DO 130 J=1,KX-NDERX
+ E3=X-TX(KKX-1-J)
+ BX(1)=E2*BX(1)/(TX(KKX)-TX(KKX-J))
+ DO 130 L=2,KX-NDERX+1-J
+ 130 BX(L)=E3*BX(L-1)/(TX(KKX-2+L)-TX(KKX-1-J))+
+ + (TX(KKX-1+L)-X)*BX(L)/(TX(KKX-1+L)-TX(KKX-J))
+ E1=Y-TY(KKY-1)
+ BY(1)=Z1
+ DO 140 J=2,KY-NDERY+1
+ 140 BY(J)=E1*BY(J-1)/(TY(KKY-2+J)-TY(KKY-1))
+ E2=TY(KKY)-Y
+ DO 150 J=1,KY-NDERY
+ E3=Y-TY(KKY-1-J)
+ BY(1)=E2*BY(1)/(TY(KKY)-TY(KKY-J))
+ DO 150 L=2,KY-NDERY+1-J
+ 150 BY(L)=E3*BY(L-1)/(TY(KKY-2+L)-TY(KKY-1-J))+
+ + (TY(KKY-1+L)-Y)*BY(L)/(TY(KKY-1+L)-TY(KKY-J))
+ R=Z0
+ DO 160 I=1,KX-NDERX+1
+ DO 160 J=1,KY-NDERY+1
+ 160 R=R+C(KKX-2-KX+I,KKY-2-KY+J)*BX(I)*BY(J)
+ DSPPS2=R
+ ENDIF
+ RETURN
+
+ 101 FORMAT(1X,A5,' =',I6,' NOT IN RANGE')
+ 102 FORMAT(1X,A5,' =',I6,A7,' =',I6,' INCONSISTENT')
+ END
+
+
+
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