SUBROUTINE NSPIV (N,IA,JA,A,B,MAX,R,C,IC,X,ITEMP,RTEMP,IERR) 1 C C C NSPIV CALLS NSPIV1 WHICH USES SPARSE GAUSSIAN ELIMINATION WITH C COLUMN INTERCHANGES TO SOLVE THE LINEAR SYSTEM A X = B. THE C ELIMINATION PHASE PERFORMS ROW OPERATIONS ON A AND B TO OBTAIN C A UNIT UPPER TRIANGULAR MATRIX U AND A VECTOR Y. THE SOLUTION C PHASE SOLVES U X = Y. C C C INPUT ARGUMENTS--- C C N INTEGER NUMBER OF EQUATIONS AND UNKNOWNS C C IA INTEGER ARRAY OF N+1 ENTRIES CONTAINING ROW POINTERS TO A C (SEE MATRIX STORAGE DESCRIPTION BELOW) C C JA INTEGER ARRAY WITH ONE ENTRY PER NONZERO IN A, CONTAINING C COLUMN NUMBERS OF THE NONZEROES OF A. (SEE MATRIX STORAGE C DESCRIPTION BELOW) C C A REAL ARRAY WITH ONE ENTRY PER NONZERO IN A, CONTAINING THE C ACTUAL NONZEROES. (SEE MATRIX STORAGE DESCRIPTION BELOW) C C B REAL ARRAY OF N ENTRIES CONTAINING RIGHT HAND SIDE DATA C C MAX INTEGER NUMBER SPECIFYING MAXIMUM NUMBER OF OFF-DIAGONAL C NONZERO ENTRIES OF U WHICH MAY BE STORED C C R INTEGER ARRAY OF N ENTRIES SPECIFYING THE ORDER OF THE C ROWS OF A (I.E., THE ELIMINATION ORDER FOR THE EQUATIONS) C C C INTEGER ARRAY OF N ENTRIES SPECIFYING THE ORDER OF THE C COLUMNS OF A. C IS ALSO AN OUTPUT ARGUMENT C C IC INTEGER ARRAY OF N ENTRIES WHICH IS THE INVERSE OF C C (I.E., IC(C(I)) = I). IC IS ALSO AN OUTPUT ARGUMENT C C ITEMP INTEGER ARRAY OF 2*N + MAX + 2 ENTRIES, FOR INTERNAL USE C C RTEMP REAL ARRAY OF N + MAX ENTRIES FOR INTERNAL USE C C C OUTPUT ARGUMENTS--- C C C INTEGER ARRAY OF N ENTRIES SPECIFYING THE ORDER OF THE C COLUMNS OF U. C IS ALSO AN INPUT ARGUMENT C C IC INTEGER ARRAY OF N ENTRIES WHICH IS THE INVERSE OF C C (I.E., IC(C(I)) = I). IC IS ALSO AN INPUT ARGUMENT C C X REAL ARRAY OF N ENTRIES CONTAINING THE SOLUTION VECTOR C C IERR INTEGER NUMBER WHICH INDICATES ERROR CONDITIONS OR C THE ACTUAL NUMBER OF OFF-DIAGONAL ENTRIES IN U (FOR C SUCCESSFUL COMPLETION) C C IERR VALUES ARE--- C C 0 LT IERR SUCCESSFUL COMPLETION. U HAS IERR C OFF-DIAGONAL NONZERO ENTRIES C C IERR = 0 ERROR. N = 0 C C -N LE IERR LT 0 ERROR. ROW NUMBER IABS(IERR) OF A IS C IS NULL C C -2*N LE IERR LT -N ERROR. ROW NUMBER IABS(IERR+N) HAS A C DUPLICATE ENTRY C C -3*N LE IERR LT -2*N ERROR. ROW NUMBER IABS(IERR+2*N) C HAS A ZERO PIVOT C C -4*N LE IERR LT -3*N ERROR. ROW NUMBER IABS(IERR+3*N) C EXCEEDS STORAGE C C C STORAGE OF SPARSE MATRICES--- C C THE SPARSE MATRIX A IS STORED USING THREE ARRAYS IA, JA, AND A. C THE ARRAY A CONTAINS THE NONZEROES OF THE MATRIX ROW-BY-ROW, NOT C NECESSARILY IN ORDER OF INCREASING COLUMN NUMBER. THE ARRAY JA C CONTAINS THE COLUMN NUMBERS CORRESPONDING TO THE NONZEROES STORED C IN THE ARRAY A (I.E., IF THE NONZERO STORED IN A(K) IS IN C COLUMN J, THEN JA(K) = J). THE ARRAY IA CONTAINS POINTERS TO THE C ROWS OF NONZEROES/COLUMN INDICES IN THE ARRAY A/JA (I.E., C A(IA(I))/JA(IA(I)) IS THE FIRST ENTRY FOR ROW I IN THE ARRAY A/JA). C IA(N+1) IS SET SO THAT IA(N+1) - IA(1) = THE NUMBER OF NONZEROES IN A C C REAL A(1),B(1),X(1),RTEMP(1) INTEGER IA(1),JA(1),R(1),C(1),IC(1),ITEMP(1) INTEGER IU,JU,U,Y,P C C SET INDICES TO DIVIDE TEMPORARY STORAGE FOR NSPIV1 C Y = 1 U = Y + N P = 1 IU = P + N + 1 JU = IU + N + 1 C C CALL NSPIV1 TO PERFORM COMPUTATIONS C CALL NSPIV1 (N,IA,JA,A,B,MAX,R,C,IC,X,RTEMP(Y),ITEMP(P), C ITEMP(IU),ITEMP(JU),RTEMP(U),IERR) RETURN END SUBROUTINE NSPIV1 (N,IA,JA,A,B,MAX,R,C,IC,X,Y,P,IU,JU,U,IERR) 109 C C C NSPIV1 USES SPARSE GAUSSIAN ELIMINATION WITH C COLUMN INTERCHANGES TO SOLVE THE LINEAR SYSTEM A X = B. THE C ELIMINATION PHASE PERFORMS ROW OPERATIONS ON A AND B TO OBTAIN C A UNIT UPPER TRIANGULAR MATRIX U AND A VECTOR Y. THE SOLUTION C PHASE SOLVES U X = Y. C C C SEE NSPIV FOR DESCRIPTIONS OF ALL INPUT AND OUTPUT ARGUMENTS C OTHER THAN THOSE DESCRIBED BELOW C C INPUT ARGUMENTS (USED INTERNALLY ONLY)--- C C Y REAL ARRAY OF N ENTRIES USED TO COMPUTE THE UPDATED C RIGHT HAND SIDE C C P INTEGER ARRAY OF N+1 ENTRIES USED FOR A LINKED LIST. C P(N+1) IS THE LIST HEADER, AND THE ENTRY FOLLOWING C P(K) IS IN P(P(K)). THUS, P(N+1) IS THE FIRST DATA C ITEM, P(P(N+1)) IS THE SECOND, ETC. A POINTER OF C N+1 MARKS THE END OF THE LIST C C IU INTEGER ARRAY OF N+1 ENTRIES USED FOR ROW POINTERS TO U C (SEE MATRIX STORAGE DESCRIPTION BELOW) C C JU INTEGER ARRAY OF MAX ENTRIES USED FOR COLUMN NUMBERS OF C THE NONZEROES IN THE STRICT UPPER TRIANGLE OF U. (SEE C MATRIX STORAGE DESCRIPTION BELOW) C C U REAL ARRAY OF MAX ENTRIES USED FOR THE ACTUAL NONZEROES IN C THE STRICT UPPER TRIANGLE OF U. (SEE MATRIX STORAGE C DESCRIPTION BELOW) C C C STORAGE OF SPARSE MATRICES--- C C THE SPARSE MATRIX A IS STORED USING THREE ARRAYS IA, JA, AND A. C THE ARRAY A CONTAINS THE NONZEROES OF THE MATRIX ROW-BY-ROW, NOT C NECESSARILY IN ORDER OF INCREASING COLUMN NUMBER. THE ARRAY JA C CONTAINS THE COLUMN NUMBERS CORRESPONDING TO THE NONZEROES STORED C IN THE ARRAY A (I.E., IF THE NONZERO STORED IN A(K) IS IN C COLUMN J, THEN JA(K) = J). THE ARRAY IA CONTAINS POINTERS TO THE C ROWS OF NONZEROES/COLUMN INDICES IN THE ARRAY A/JA (I.E., C A(IA(I))/JA(IA(I)) IS THE FIRST ENTRY FOR ROW I IN THE ARRAY A/JA). C IA(N+1) IS SET SO THAT IA(N+1) - IA(1) = THE NUMBER OF NONZEROES IN C A. IU, JU, AND U ARE USED IN A SIMILAR WAY TO STORE THE STRICT UPPER C TRIANGLE OF U, EXCEPT THAT JU ACTUALLY CONTAINS C(J) INSTEAD OF J C C REAL A(1),B(1),U(1),X(1),Y(1) REAL DK,LKI,ONE,XPV,XPVMAX,YK,ZERO INTEGER C(1),IA(1),IC(1),IU(1),JA(1),JU(1),P(1),R(1) INTEGER CK,PK,PPK,PV,V,VI,VJ,VK C C IF (N .EQ. 0) GO TO 1001 C ONE = 1.0 ZERO = 0.0 C C INITIALIZE WORK STORAGE AND POINTERS TO JU C DO 10 J=1,N X(J) = ZERO 10 CONTINUE IU(1) = 1 JUPTR = 0 C C PERFORM SYMBOLIC AND NUMERIC FACTORIZATION ROW BY ROW C VK (VI,VJ) IS THE GRAPH VERTEX FOR ROW K (I,J) OF U C DO 170 K=1,N C C INITIALIZE LINKED LIST AND FREE STORAGE FOR THIS ROW C THE R(K)-TH ROW OF A BECOMES THE K-TH ROW OF U. C P(N+1) = N+1 VK = R(K) C C SET UP ADJACENCY LIST FOR VK, ORDERED IN C CURRENT COLUMN ORDER OF U. THE LOOP INDEX C GOES DOWNWARD TO EXPLOIT ANY COLUMNS C FROM A IN CORRECT RELATIVE ORDER C JMIN = IA(VK) JMAX = IA(VK+1) - 1 IF (JMIN .GT. JMAX) GO TO 1002 J = JMAX 20 JAJ = JA(J) VJ = IC(JAJ) C C STORE A(K,J) IN WORK VECTOR C X(VJ) = A(J) C THIS CODE INSERTS VJ INTO ADJACENCY LIST OF VK PPK = N+1 30 PK = PPK PPK = P(PK) IF (PPK - VJ) 30,1003,40 40 P(VJ) = PPK P(PK) = VJ J = J - 1 IF (J .GE. JMIN) GO TO 20 C C THE FOLLOWING CODE COMPUTES THE K-TH ROW OF U C VI = N+1 YK = B(VK) 50 VI = P(VI) IF (VI .GE. K) GO TO 110 C C VI LT VK -- PROCESS THE L(K,I) ELEMENT AND MERGE THE C ADJACENCY OF VI WITH THE ORDERED ADJACENCY OF VK C LKI = - X(VI) X(VI) = ZERO C C ADJUST RIGHT HAND SIDE TO REFLECT ELIMINATION C YK = YK + LKI * Y(VI) PPK = VI JMIN = IU(VI) JMAX = IU(VI+1) - 1 IF (JMIN .GT. JMAX) GO TO 50 DO 100 J=JMIN,JMAX JUJ = JU(J) VJ = IC(JUJ) C C IF VJ IS ALREADY IN THE ADJACENCY OF VK, C SKIP THE INSERTION C IF (X(VJ) .NE. ZERO) GO TO 90 C C INSERT VJ IN ADJACENCY LIST OF VK. C RESET PPK TO VI IF WE HAVE PASSED THE CORRECT C INSERTION SPOT. (THIS HAPPENS WHEN THE ADJACENCY OF C VI IS NOT IN CURRENT COLUMN ORDER DUE TO PIVOTING.) C IF (VJ - PPK) 60,90,70 60 PPK = VI 70 PK = PPK PPK = P(PK) IF (PPK - VJ) 70,90,80 80 P(VJ) = PPK P(PK) = VJ PPK = VJ C C COMPUTE L(K,J) = L(K,J) - L(K,I)*U(I,J) FOR L(K,I) NONZERO C COMPUTE U*(K,J) = U*(K,J) - L(K,I)*U(I,J) FOR U(K,J) NONZERO C (U*(K,J) = U(K,J)*D(K,K)) C 90 X(VJ) = X(VJ) + LKI * U(J) 100 CONTINUE GO TO 50 C C PIVOT--INTERCHANGE LARGEST ENTRY OF K-TH ROW OF U WITH C THE DIAGONAL ENTRY. C C FIND LARGEST ENTRY, COUNTING OFF-DIAGONAL NONZEROES C 110 IF (VI .GT. N) GO TO 1004 XPVMAX = ABS(X(VI)) MAXC = VI NZCNT = 0 PV = VI 120 V = PV PV = P(PV) IF (PV .GT. N) GO TO 130 NZCNT = NZCNT + 1 XPV = ABS(X(PV)) IF (XPV .LE. XPVMAX) GO TO 120 XPVMAX = XPV MAXC = PV MAXCL = V GO TO 120 130 IF (XPVMAX .EQ. ZERO) GO TO 1004 C C IF VI = K, THEN THERE IS AN ENTRY FOR DIAGONAL C WHICH MUST BE DELETED. OTHERWISE, DELETE THE C ENTRY WHICH WILL BECOME THE DIAGONAL ENTRY C IF (VI .EQ. K) GO TO 140 IF (VI .EQ. MAXC) GO TO 140 P(MAXCL) = P(MAXC) GO TO 150 140 VI = P(VI) C C COMPUTE D(K) = 1/L(K,K) AND PERFORM INTERCHANGE. C 150 DK = ONE / X(MAXC) X(MAXC) = X(K) I = C(K) C(K) = C(MAXC) C(MAXC) = I CK = C(K) IC(CK) = K IC(I) = MAXC X(K) = ZERO C C UPDATE RIGHT HAND SIDE. C Y(K) = YK * DK C C COMPUTE VALUE FOR IU(K+1) AND CHECK FOR STORAGE OVERFLOW C IU(K+1) = IU(K) + NZCNT IF (IU(K+1) .GT. MAX+1) GO TO 1005 C C MOVE COLUMN INDICES FROM LINKED LIST TO JU. C COLUMNS ARE STORED IN CURRENT ORDER WITH ORIGINAL C COLUMN NUMBER (C(J)) STORED FOR CURRENT COLUMN J C IF (VI .GT. N) GO TO 170 J = VI 160 JUPTR = JUPTR + 1 JU(JUPTR) = C(J) U(JUPTR) = X(J) * DK X(J) = ZERO J = P(J) IF (J .LE. N) GO TO 160 170 CONTINUE C C BACKSOLVE U X = Y, AND REORDER X TO CORRESPOND WITH A C K = N DO 200 I=1,N YK = Y(K) JMIN = IU(K) JMAX = IU(K+1) - 1 IF (JMIN .GT. JMAX) GO TO 190 DO 180 J=JMIN,JMAX JUJ = JU(J) JUJ = IC(JUJ) YK = YK - U(J) * Y(JUJ) 180 CONTINUE 190 Y(K) = YK CK = C(K) X(CK) = YK K = K-1 200 CONTINUE C C RETURN WITH IERR = NUMBER OF OFF-DIAGONAL NONZEROES IN U C IERR = IU(N+1) - IU(1) RETURN C C ERROR RETURNS C C N = 0 C 1001 IERR = 0 RETURN C C ROW K OF A IS NULL C 1002 IERR = -K RETURN C C ROW K OF A HAS A DUPLICATE ENTRY C 1003 IERR = -(N+K) RETURN C C ZERO PIVOT IN ROW K C 1004 IERR = -(2*N+K) RETURN C C STORAGE FOR U EXCEEDED ON ROW K C 1005 IERR = -(3*N+K) RETURN END C PROGRAM PIVCHK(OUTPUT,TAPE6=OUTPUT) 1 C 2 C THIS PROGRAM ILLUSTRATES THE USE OF NSPIV BY SOLVING THE 3 C SYSTEM OF LINEAR EQUATIONS 4 C 5 C A X = B 6 C 7 C WITH A AN NG X NG BLOCK TRIDIAGONAL MATRIX, WITH NG X NG BLOCKS. 8 C THE DIAGONAL BLOCKS OF A ARE LOWER BI-DIAGONAL (ENTRIES ARE 4.0 9 C ON THE DIAGONAL, -1.0 ON THE SUBDIAGONAL), AND THE OFF-DIAGONAL 10 C BLOCKS OF A ARE DIAGONAL (ENTRIES ARE -1.0 IN THE LOWER TRIANGLE, 11 C -1.5 IN THE UPPER TRIANGLE.) X IS CHOSEN TO BE A VECTOR 12 C OF ALL ONES, AND B IS COMPUTED ACCORDINGLY. 13 C 14 C 15 INTEGER IA(101),JA(400),R(100),C(100),IC(100),ITEMP(597) 16 REAL A(400),B(100),X(100),RTEMP(495) 17 DATA MAX/395/,NG/10/,N/100/ 18 C 19 C SET UP PROBLEM 20 C 21 K = 1 22 IA(1) = 1 23 IAPTR = 1 24 DO 5 I=1,NG 25 DO 5 J=1,NG 26 BK = 0. 27 IF (I .EQ. 1) GO TO 1 28 JA(IAPTR) = K - NG 29 A(IAPTR) = -1. 30 BK = BK - 1. 31 IAPTR = IAPTR + 1 32 1 IF (J .EQ. 1) GO TO 2 33 JA(IAPTR) = K - 1 34 A(IAPTR) = -1. 35 BK = BK - 1. 36 IAPTR = IAPTR + 1 37 2 JA(IAPTR) = K 38 A(IAPTR) = 4. 39 BK = BK + 4. 40 IAPTR = IAPTR + 1 41 IF (I .EQ. NG) GO TO 4 42 JA(IAPTR) = K + NG 43 A(IAPTR) = -1.5 44 BK = BK - 1.5 45 IAPTR = IAPTR + 1 46 4 B(K) = BK 47 K = K + 1 48 IA(K) = IAPTR 49 5 CONTINUE 50 C 51 C CALL PREORD TO ORDER ROWS OF A BY INCREASING NUMBERS OF NONZEROES 52 C 53 CALL PREORD(N,IA,R,C,IC) 54 C 55 C CALL NSPIV TO SOLVE SYSTEM 56 C 57 CALL NSPIV(N,IA,JA,A,B,MAX,R,C,IC,X,ITEMP,RTEMP,IERR) 58 WRITE (6,101) IERR 59 101 FORMAT (8H IERR = ,I10) 60 C 61 C CALL RESCHK TO COMPUTE MAX-NORM AND 2-NORM OF RESIDUAL 62 C 63 CALL RESCHK(N,IA,JA,A,B,X) 64 C 65 STOP 66 END 67 SUBROUTINE PREORD(N,IA,R,C,IC) 68 C C PREORD ORDERS THE ROWS OF A BY INCREASING NUMBER OF NONZEROES. C THE ROW PERMUTATION IS RETURNED IN R. C IS SET TO THE IDENTITY. C INTEGER IA(1),R(1),C(1),IC(1) C DO 1 I=1,N R(I) = I C(I) = I IC(I) = I 1 CONTINUE DO 5 I = 1,N 5 C(I) = 0 DO 10 K = 1,N KDEG = IA(K+1) - IA(K) IF (KDEG .EQ. 0) KDEG = KDEG + 1 IC(K) = C(KDEG) C(KDEG) = K 10 CONTINUE I = 0 DO 30 J = 1,N IF (C(J) .EQ. 0) GO TO 30 K = C(J) 20 I = I + 1 R(I) = K K = IC(K) IF (K .GT. 0) GO TO 20 30 CONTINUE DO 40 I = 1,N C(I) = I IC(I) = I 40 CONTINUE RETURN END SUBROUTINE RESCHK(N,IA,JA,A,B,X) 103 C C RESCHK COMPUTES THE MAX-NORM AND 2-NORM OF THE RESIDUAL. C DOUBLE PRECISION IS USED FOR THE COMPUTATION. C INTEGER IA(1),JA(1) REAL A(1),B(1),X(1) DOUBLE PRECISION RESID,RESIDM,ROWSUM RESID = 0. RESIDM = 0. DO 20 I=1,N ROWSUM = DBLE(B(I)) JMIN = IA(I) JMAX = IA(I+1) - 1 DO 10 J=JMIN,JMAX JAJ = JA(J) ROWSUM = ROWSUM - DBLE(A(J)) * DBLE(X(JAJ)) 10 CONTINUE IF (DABS(ROWSUM) .GT. RESIDM) RESIDM = DABS(ROWSUM) RESID = RESID + ROWSUM**2 20 CONTINUE RESID = DSQRT(RESID) WRITE (6,25) RESID 25 FORMAT (22H 2-NORM OF RESIDUAL = ,D14.7) WRITE (6,30) RESIDM 30 FORMAT(24H MAX NORM OF RESIDUAL = ,D14.7) RETURN END C PROGRAM PIVCHK(INPUT,OUTPUT,TAPE6=OUTPUT,TAPE5=INPUT) 1 C 2 C THIS PROGRAM ILLUSTRATES THE USE OF NSPIV BY SOLVING THE 3 C SYSTEM OF LINEAR EQUATIONS 4 C 5 C A X = B 6 C 7 C WHERE A IS A BANDED 192 X 192 MATRIX OF BANDWIDTH 20. X IS 8 C CHOSEN TO BE A VECTOR OF ALL ONES, AND B IS COMPUTED ACCORDINGLY. 9 C 10 C 11 INTEGER IA(193),JA(3500),R(192),C(192),IC(192),ITEMP(7500) 12 REAL A(3500),B(192),X(192),RTEMP(7200) 13 DATA MAX/7000/,N/192/ 14 C 15 C CALL GENPRB TO SET UP PROBLEM 16 C 17 CALL GENPRB(N,IA,JA,A,ITEMP,B) 18 C 19 C CALL PREORD TO ORDER ROWS OF A BY INCREASING NUMBERS OF NONZEROES 20 C 21 CALL PREORD(N,IA,R,C,IC) 22 C 23 C CALL NSPIV TO SOLVE SYSTEM 24 C 25 CALL NSPIV(N,IA,JA,A,B,MAX,R,C,IC,X,ITEMP,RTEMP,IERR) 26 WRITE (6,101) IERR 27 101 FORMAT (8H IERR = ,I10) 28 C 29 C CALL RESCHK TO COMPUTE MAX-NORM AND 2-NORM OF RESIDUAL 30 C 31 CALL RESCHK(N,IA,JA,A,B,X) 32 C 33 STOP 34 END 35 SUBROUTINE GENPRB(N,IA,JA,A,B,RHS) 104 C C GENPRB SETS UP THE MATRIX AND RIGHT HAND SIDE FROM C THE DATA ON CARDS. THE PROBLEM IS ONE FROM THE USGS. C INTEGER IA(1),JA(1) REAL B(1),A(1),RHS(1) C KMIN = 1 DO 5 I=1,N KMAX = KMIN + 38 READ (5,101) (B(K),K=KMIN,KMAX) 101 FORMAT (8G10.3) KMIN = KMAX + 1 5 CONTINUE C IA(1) = 1 IAPTR = 1 IPART = 0 DO 15 I=1,N RHSI = 0. DO 10 J=1,39 K = I - 20 + J IF (K .LE. 0) GO TO 10 IF (K .GT. N) GO TO 10 IPARTJ = IPART + J IF (B(IPARTJ) .EQ. 0.) GO TO 10 A(IAPTR) = B(IPARTJ) JA(IAPTR) = K RHSI = RHSI + B(IAPTR) IAPTR = IAPTR + 1 10 CONTINUE IA(I+1) = IAPTR RHS(I) = RHSI 15 IPART = IPART + 39 RETURN END 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2.67 -.819 -.475 -.409 0 0 0 0 0 0 0 0 0 0 0 0 -.475 -.409 -1.14 -.204 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1.960E-02 .125 -7.451E-03 6.258E-02 0 0 0 0 0 0 0 0 0 0 0 0-7.451E-03 6.258E-02-1.233E-02 3.117E-02 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0-2.970E-02-2.556E-02 .333 -.102 -2.970E-02-2.556E-02 0 0 0 0 0 0 0 0 0 0-7.142E-02-1.278E-02-5.939E-02-5.120E-02-7.142E-02-1.278E-02 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -7.451E-03 6.258E-02 3.912E-02 .249 -7.451E-03 6.258E-02 0 0 0 0 0 0 0 0 0 0 -1.233E-02 3.117E-02-1.490E-02 .125 -1.233E-02 3.117E-02 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0-2.970E-02-2.556E-02 .333 -.102 -2.970E-02-2.556E-02 0 0 0 0 0 0 0 0 0 0-7.142E-02-1.278E-02-5.939E-02-5.120E-02-7.142E-02-1.278E-02 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -.119 1.00 .626 3.99 -.119 1.00 0 0 0 0 0 0 0 0 0 0 -.197 .499 -.238 1.99 -.197 .499 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0-2.970E-02-2.556E-02 .333 -.102 -2.970E-02-2.556E-02 0 0 0 0 0 0 0 0 0 0-7.142E-02-1.278E-02-5.939E-02-5.120E-02-7.142E-02-1.278E-02 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -.119 1.00 .626 3.99 -.119 1.00 0 0 0 0 0 0 0 0 0 0 -.197 .499 -.238 1.99 -.197 .499 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0-2.970E-02-2.556E-02 .333 -.102 -2.970E-02-2.556E-02 0 0 0 0 0 0 0 0 0 0-7.142E-02-1.278E-02-5.939E-02-5.120E-02-7.142E-02-1.278E-02 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -.119 1.00 .626 3.99 -.119 1.00 0 0 0 0 0 0 0 0 0 0 -.197 .499 -.238 1.99 -.197 .499 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0-2.970E-02-2.556E-02 .333 -.102 -2.970E-02-2.556E-02 0 0 0 0 0 0 0 0 0 0-7.142E-02-1.278E-02-5.939E-02-5.120E-02-7.142E-02-1.278E-02 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -.119 1.00 .626 3.99 -.119 1.00 0 0 0 0 0 0 0 0 0 0 -.197 .499 -.238 1.99 -.197 .499 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0-2.970E-02-2.556E-02 .333 -.102 -2.970E-02-2.556E-02 0 0 0 0 0 0 0 0 0 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