! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! ! Linear Algebra Data and Routines File ! ! Generated by KPP-2.2 symbolic chemistry Kinetics PreProcessor ! (http://www.cs.vt.edu/~asandu/Software/KPP) ! KPP is distributed under GPL, the general public licence ! (http://www.gnu.org/copyleft/gpl.html) ! (C) 1995-1997, V. Damian & A. Sandu, CGRER, Univ. Iowa ! (C) 1997-2005, A. Sandu, Michigan Tech, Virginia Tech ! With important contributions from: ! M. Damian, Villanova University, USA ! R. Sander, Max-Planck Institute for Chemistry, Mainz, Germany ! ! File : gckpp_LinearAlgebra.f90 ! Time : Wed Sep 15 16:00:44 2010 ! Working directory : /mnt/lstr04/srv/home/c/ccarouge/KPP/geoschem_kppfiles/v8-03-02/SOA ! Equation file : gckpp.kpp ! Output root filename : gckpp ! ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ MODULE gckpp_LinearAlgebra USE gckpp_Parameters USE gckpp_JacobianSP IMPLICIT NONE CONTAINS ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! ! SPARSE_UTIL - SPARSE utility functions ! Arguments : ! ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SUBROUTINE KppDecomp( JVS, IER ) ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! Sparse LU factorization ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ USE gckpp_Parameters USE gckpp_JacobianSP INTEGER :: IER REAL(kind=dp) :: JVS(LU_NONZERO), W(NVAR), a INTEGER :: k, kk, j, jj a = 0. ! mz_rs_20050606 IER = 0 DO k=1,NVAR ! mz_rs_20050606: don't check if real value == 0 ! IF ( JVS( LU_DIAG(k) ) .EQ. 0. ) THEN IF ( ABS(JVS(LU_DIAG(k))) < TINY(a) ) THEN IER = k RETURN END IF DO kk = LU_CROW(k), LU_CROW(k+1)-1 W( LU_ICOL(kk) ) = JVS(kk) END DO DO kk = LU_CROW(k), LU_DIAG(k)-1 j = LU_ICOL(kk) a = -W(j) / JVS( LU_DIAG(j) ) W(j) = -a DO jj = LU_DIAG(j)+1, LU_CROW(j+1)-1 W( LU_ICOL(jj) ) = W( LU_ICOL(jj) ) + a*JVS(jj) END DO END DO DO kk = LU_CROW(k), LU_CROW(k+1)-1 JVS(kk) = W( LU_ICOL(kk) ) END DO END DO END SUBROUTINE KppDecomp ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SUBROUTINE KppDecompCmplx( JVS, IER ) ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! Sparse LU factorization, complex ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ USE gckpp_Parameters USE gckpp_JacobianSP INTEGER :: IER DOUBLE COMPLEX :: JVS(LU_NONZERO), W(NVAR), a REAL(kind=dp) :: b = 0.0 INTEGER :: k, kk, j, jj IER = 0 DO k=1,NVAR IF ( ABS(JVS(LU_DIAG(k))) < TINY(b) ) THEN IER = k RETURN END IF DO kk = LU_CROW(k), LU_CROW(k+1)-1 W( LU_ICOL(kk) ) = JVS(kk) END DO DO kk = LU_CROW(k), LU_DIAG(k)-1 j = LU_ICOL(kk) a = -W(j) / JVS( LU_DIAG(j) ) W(j) = -a DO jj = LU_DIAG(j)+1, LU_CROW(j+1)-1 W( LU_ICOL(jj) ) = W( LU_ICOL(jj) ) + a*JVS(jj) END DO END DO DO kk = LU_CROW(k), LU_CROW(k+1)-1 JVS(kk) = W( LU_ICOL(kk) ) END DO END DO END SUBROUTINE KppDecompCmplx ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SUBROUTINE KppDecompCmplxR( JVSR, JVSI, IER ) ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! Sparse LU factorization, complex ! (Real and Imaginary parts are used instead of complex data type) ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ USE gckpp_Parameters USE gckpp_JacobianSP INTEGER :: IER REAL(kind=dp) :: JVSR(LU_NONZERO), JVSI(LU_NONZERO) REAL(kind=dp) :: WR(NVAR), WI(NVAR), ar, ai, den INTEGER :: k, kk, j, jj IER = 0 ar = 0.0 DO k=1,NVAR IF ( ( ABS(JVSR(LU_DIAG(k))) < TINY(ar) ) .AND. & ( ABS(JVSI(LU_DIAG(k))) < TINY(ar) ) ) THEN IER = k RETURN END IF DO kk = LU_CROW(k), LU_CROW(k+1)-1 WR( LU_ICOL(kk) ) = JVSR(kk) WI( LU_ICOL(kk) ) = JVSI(kk) END DO DO kk = LU_CROW(k), LU_DIAG(k)-1 j = LU_ICOL(kk) den = JVSR(LU_DIAG(j))**2 + JVSI(LU_DIAG(j))**2 ar = -(WR(j)*JVSR(LU_DIAG(j)) + WI(j)*JVSI(LU_DIAG(j)))/den ai = -(WI(j)*JVSR(LU_DIAG(j)) - WR(j)*JVSI(LU_DIAG(j)))/den WR(j) = -ar WI(j) = -ai DO jj = LU_DIAG(j)+1, LU_CROW(j+1)-1 WR( LU_ICOL(jj) ) = WR( LU_ICOL(jj) ) + ar*JVSR(jj) - ai*JVSI(jj) WI( LU_ICOL(jj) ) = WI( LU_ICOL(jj) ) + ar*JVSI(jj) + ai*JVSR(jj) END DO END DO DO kk = LU_CROW(k), LU_CROW(k+1)-1 JVSR(kk) = WR( LU_ICOL(kk) ) JVSI(kk) = WI( LU_ICOL(kk) ) END DO END DO END SUBROUTINE KppDecompCmplxR ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SUBROUTINE KppSolveIndirect( JVS, X ) ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! Sparse solve subroutine using indirect addressing ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ USE gckpp_Parameters USE gckpp_JacobianSP INTEGER :: i, j REAL(kind=dp) :: JVS(LU_NONZERO), X(NVAR), sum DO i=1,NVAR DO j = LU_CROW(i), LU_DIAG(i)-1 X(i) = X(i) - JVS(j)*X(LU_ICOL(j)); END DO END DO DO i=NVAR,1,-1 sum = X(i); DO j = LU_DIAG(i)+1, LU_CROW(i+1)-1 sum = sum - JVS(j)*X(LU_ICOL(j)); END DO X(i) = sum/JVS(LU_DIAG(i)); END DO END SUBROUTINE KppSolveIndirect ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SUBROUTINE KppSolveTRIndirect( JVS, X ) ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! Complex sparse solve transpose subroutine using indirect addressing ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ USE gckpp_Parameters USE gckpp_JacobianSP INTEGER :: i, j REAL(kind=dp) :: JVS(LU_NONZERO), X(NVAR) DO i=1,NVAR X(i) = X(i)/JVS(LU_DIAG(i)) ! subtract all nonzero elements in row i of JVS from X DO j=LU_DIAG(i)+1,LU_CROW(i+1)-1 X(LU_ICOL(j)) = X(LU_ICOL(j))-JVS(j)*X(i) END DO END DO DO i=NVAR, 1, -1 ! subtract all nonzero elements in row i of JVS from X DO j=LU_CROW(i),LU_DIAG(i)-1 X(LU_ICOL(j)) = X(LU_ICOL(j))-JVS(j)*X(i) END DO END DO END SUBROUTINE KppSolveTRIndirect ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SUBROUTINE KppSolveCmplx( JVS, X ) ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! Complex sparse solve subroutine using indirect addressing ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ USE gckpp_Parameters USE gckpp_JacobianSP INTEGER :: i, j DOUBLE COMPLEX :: JVS(LU_NONZERO), X(NVAR), sum DO i=1,NVAR DO j = LU_CROW(i), LU_DIAG(i)-1 X(i) = X(i) - JVS(j)*X(LU_ICOL(j)); END DO END DO DO i=NVAR,1,-1 sum = X(i); DO j = LU_DIAG(i)+1, LU_CROW(i+1)-1 sum = sum - JVS(j)*X(LU_ICOL(j)); END DO X(i) = sum/JVS(LU_DIAG(i)); END DO END SUBROUTINE KppSolveCmplx ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SUBROUTINE KppSolveCmplxR( JVSR, JVSI, XR, XI ) ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! Complex sparse solve subroutine using indirect addressing ! (Real and Imaginary parts are used instead of complex data type) ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ USE gckpp_Parameters USE gckpp_JacobianSP INTEGER :: i, j REAL(kind=dp) :: JVSR(LU_NONZERO), JVSI(LU_NONZERO), XR(NVAR), XI(NVAR), sumr, sumi, den DO i=1,NVAR DO j = LU_CROW(i), LU_DIAG(i)-1 XR(i) = XR(i) - (JVSR(j)*XR(LU_ICOL(j)) - JVSI(j)*XI(LU_ICOL(j))) XI(i) = XI(i) - (JVSR(j)*XI(LU_ICOL(j)) + JVSI(j)*XR(LU_ICOL(j))) END DO END DO DO i=NVAR,1,-1 sumr = XR(i); sumi = XI(i) DO j = LU_DIAG(i)+1, LU_CROW(i+1)-1 sumr = sumr - (JVSR(j)*XR(LU_ICOL(j)) - JVSI(j)*XI(LU_ICOL(j))) sumi = sumi - (JVSR(j)*XI(LU_ICOL(j)) + JVSI(j)*XR(LU_ICOL(j))) END DO den = JVSR(LU_DIAG(i))**2 + JVSI(LU_DIAG(i))**2 XR(i) = (sumr*JVSR(LU_DIAG(i)) + sumi*JVSI(LU_DIAG(i)))/den XI(i) = (sumi*JVSR(LU_DIAG(i)) - sumr*JVSI(LU_DIAG(i)))/den END DO END SUBROUTINE KppSolveCmplxR ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SUBROUTINE KppSolveTRCmplx( JVS, X ) ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! Complex sparse solve transpose subroutine using indirect addressing ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ USE gckpp_Parameters USE gckpp_JacobianSP INTEGER :: i, j DOUBLE COMPLEX :: JVS(LU_NONZERO), X(NVAR) DO i=1,NVAR X(i) = X(i)/JVS(LU_DIAG(i)) ! subtract all nonzero elements in row i of JVS from X DO j=LU_DIAG(i)+1,LU_CROW(i+1)-1 X(LU_ICOL(j)) = X(LU_ICOL(j))-JVS(j)*X(i) END DO END DO DO i=NVAR, 1, -1 ! subtract all nonzero elements in row i of JVS from X DO j=LU_CROW(i),LU_DIAG(i)-1 X(LU_ICOL(j)) = X(LU_ICOL(j))-JVS(j)*X(i) END DO END DO END SUBROUTINE KppSolveTRCmplx ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SUBROUTINE KppSolveTRCmplxR( JVSR, JVSI, XR, XI ) ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! Complex sparse solve transpose subroutine using indirect addressing ! (Real and Imaginary parts are used instead of complex data type) ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ USE gckpp_Parameters USE gckpp_JacobianSP INTEGER :: i, j REAL(kind=dp) :: JVSR(LU_NONZERO), JVSI(LU_NONZERO), XR(NVAR), XI(NVAR), den DO i=1,NVAR den = JVSR(LU_DIAG(i))**2 + JVSI(LU_DIAG(i))**2 XR(i) = (XR(i)*JVSR(LU_DIAG(i)) + XI(i)*JVSI(LU_DIAG(i)))/den XI(i) = (XI(i)*JVSR(LU_DIAG(i)) - XR(i)*JVSI(LU_DIAG(i)))/den ! subtract all nonzero elements in row i of JVS from X DO j=LU_DIAG(i)+1,LU_CROW(i+1)-1 XR(LU_ICOL(j)) = XR(LU_ICOL(j))-(JVSR(j)*XR(i) - JVSI(j)*XI(i)) XI(LU_ICOL(j)) = XI(LU_ICOL(j))-(JVSI(j)*XR(i) + JVSR(j)*XI(i)) END DO END DO DO i=NVAR, 1, -1 ! subtract all nonzero elements in row i of JVS from X DO j=LU_CROW(i),LU_DIAG(i)-1 XR(LU_ICOL(j)) = XR(LU_ICOL(j))-(JVSR(j)*XR(i) - JVSI(j)*XI(i)) XI(LU_ICOL(j)) = XI(LU_ICOL(j))-(JVSI(j)*XR(i) + JVSR(j)*XI(i)) END DO END DO END SUBROUTINE KppSolveTRCmplxR ! ! Next few commented subroutines perform sparse big linear algebra ! !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !SUBROUTINE KppDecompBig( JVS, IP, IER ) !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !! Sparse LU factorization !! for the Runge Kutta (3n)x(3n) linear system !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! ! USE gckpp_Parameters ! USE gckpp_JacobianSP ! ! INTEGER :: IP3(3), IER, IP(3,NVAR) ! REAL(kind=dp) :: JVS(3,3,LU_NONZERO), W(3,3,NVAR), a(3,3), E(3,3) ! INTEGER :: k, kk, j, jj ! ! a = 0.0d0 ! IER = 0 ! DO k=1,NVAR ! DO kk = LU_CROW(k), LU_CROW(k+1)-1 ! W( 1:3,1:3,LU_ICOL(kk) ) = JVS(1:3,1:3,kk) ! END DO ! DO kk = LU_CROW(k), LU_DIAG(k)-1 ! j = LU_ICOL(kk) ! E(1:3,1:3) = JVS( 1:3,1:3,LU_DIAG(j) ) ! ! CALL DGETRF(3,3,E,3,IP3,IER) ! CALL FAC3(E,IP3,IER) ! IF ( IER /= 0 ) RETURN ! ! a = W(j) / JVS( LU_DIAG(j) ) ! a(1:3,1:3) = W( 1:3,1:3,j ) ! ! CALL DGETRS ('N',3,3,E,3,IP3,a,3,IER) ! CALL SOL3('N',E,IP3,a(1,1)) ! CALL SOL3('N',E,IP3,a(1,2)) ! CALL SOL3('N',E,IP3,a(1,3)) ! W(1:3,1:3,j) = a(1:3,1:3) ! DO jj = LU_DIAG(j)+1, LU_CROW(j+1)-1 ! W( 1:3,1:3,LU_ICOL(jj) ) = W( 1:3,1:3,LU_ICOL(jj) ) & ! - MATMUL( a(1:3,1:3) , JVS(1:3,1:3,jj) ) ! END DO ! END DO ! DO kk = LU_CROW(k), LU_CROW(k+1)-1 ! JVS(1:3,1:3,kk) = W( 1:3,1:3,LU_ICOL(kk) ) ! END DO ! END DO ! ! DO k=1,NVAR ! ! CALL WGEFA(JVS(1,1,LU_DIAG(k)),3,3,IP(1,k),IER) ! ! CALL DGETRF(3,3,JVS(1,1,LU_DIAG(k)),3,IP(1,k),IER) ! CALL FAC3(JVS(1,1,LU_DIAG(k)),IP(1,k),IER) ! IF ( IER /= 0 ) RETURN ! END DO ! !END SUBROUTINE KppDecompBig ! ! !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !SUBROUTINE KppSolveBig( JVS, IP, X ) !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !! Sparse solve subroutine using indirect addressing !! for the Runge Kutta (3n)x(3n) linear system !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! ! USE gckpp_Parameters ! USE gckpp_JacobianSP ! ! INTEGER :: i, j, k, m, IP3(3), IP(3,NVAR), IER ! REAL(kind=dp) :: JVS(3,3,LU_NONZERO), X(3,NVAR), sum(3) ! ! DO i=1,NVAR ! DO j = LU_CROW(i), LU_DIAG(i)-1 ! !X(1:3,i) = X(1:3,i) - MATMUL(JVS(1:3,1:3,j),X(1:3,LU_ICOL(j))); ! DO k=1,3 ! DO m=1,3 ! X(k,i) = X(k,i) - JVS(k,m,j)*X(m,LU_ICOL(j)) ! END DO ! END DO ! END DO ! END DO ! ! DO i=NVAR,1,-1 ! sum(1:3) = X(1:3,i); ! DO j = LU_DIAG(i)+1, LU_CROW(i+1)-1 ! !sum(1:3) = sum(1:3) - MATMUL(JVS(1:3,1:3,j),X(1:3,LU_ICOL(j))); ! DO k=1,3 ! DO m=1,3 ! sum(k) = sum(k) - JVS(k,m,j)*X(m,LU_ICOL(j)) ! END DO ! END DO ! END DO ! ! X(i) = sum/JVS(LU_DIAG(i)); ! ! CALL DGETRS ('N',3,1,JVS(1:3,1:3,LU_DIAG(i)),3,IP(1,i),sum,3,0) ! ! CALL WGESL('N',JVS(1,1,LU_DIAG(i)),3,3,IP(1,i),sum) ! CALL SOL3('N',JVS(1,1,LU_DIAG(i)),IP(1,i),sum) ! X(1:3,i) = sum(1:3) ! END DO ! !END SUBROUTINE KppSolveBig ! ! !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !SUBROUTINE KppSolveBigTR( JVS, IP, X ) !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !! Big sparse transpose solve using indirect addressing !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! ! USE gckpp_Parameters ! USE gckpp_JacobianSP ! ! INTEGER :: i, j, k, m, IP(3,NVAR) ! REAL(kind=dp) :: JVS(3,3,LU_NONZERO), X(3,NVAR) ! ! DO i=1,NVAR ! ! X(i) = X(i)/JVS(LU_DIAG(i)) ! CALL SOL3('T',JVS(1,1,LU_DIAG(i)),IP(1,i),X(1,i)) ! DO j=LU_DIAG(i)+1,LU_CROW(i+1)-1 ! !X(1:3,LU_ICOL(j)) = X(1:3,LU_ICOL(j)) & ! ! - MATMUL( TRANSPOSE(JVS(1:3,1:3,j)), X(1:3,i) ) ! DO k=1,3 ! DO m=1,3 ! X(k,LU_ICOL(j)) = X(k,LU_ICOL(j)) - JVS(m,k,j)*X(m,i) ! END DO ! END DO ! END DO ! END DO ! ! DO i=NVAR, 1, -1 ! DO j=LU_CROW(i),LU_DIAG(i)-1 ! !X(1:3,LU_ICOL(j)) = X(1:3,LU_ICOL(j)) & ! ! - MATMUL( TRANSPOSE(JVS(1:3,1:3,j)), X(1:3,i) ) ! DO k=1,3 ! DO m=1,3 ! X(k,LU_ICOL(j)) = X(k,LU_ICOL(j)) - JVS(m,k,j)*X(m,i) ! END DO ! END DO ! END DO ! END DO ! !END SUBROUTINE KppSolveBigTR ! ! ! !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !SUBROUTINE FAC3(A,IPVT,INFO) !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !! FAC3 FACTORS THE MATRIX A (3,3) BY !! GAUSS ELIMINATION WITH PARTIAL PIVOTING !! LINPACK - LIKE !! !! Remove comments to perform pivoting !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !! ! REAL(kind=dp) :: A(3,3) ! INTEGER :: IPVT(3),INFO !! INTEGER :: L !! REAL(kind=dp) :: t, dmax, da, TMP(3) ! REAL(kind=dp), PARAMETER :: ZERO = 0.0, ONE = 1.0 ! ! info = 0 !! t = TINY(da) !! !! da = ABS(A(1,1)); L = 1 !! IF ( ABS(A(2,1))>da ) THEN !! da = ABS(A(2,1)); L = 2 !! IF ( ABS(A(3,1))>da ) THEN !! L = 3 !! END IF !! END IF !! IPVT(1) = L !! IF (L /=1 ) THEN !! TMP(1:3) = A(L,1:3) !! A(L,1:3) = A(1,1:3) !! A(1,1:3) = TMP(1:3) !! END IF !! IF (ABS(A(1,1)) < t) THEN !! info = 1 !! return !! END IF !! ! A(2,1) = A(2,1)/A(1,1) ! A(2,2) = A(2,2) - A(2,1)*A(1,2) ! A(2,3) = A(2,3) - A(2,1)*A(1,3) ! A(3,1) = A(3,1)/A(1,1) ! A(3,2) = A(3,2) - A(3,1)*A(1,2) ! A(3,3) = A(3,3) - A(3,1)*A(1,3) ! !! IPVT(2) = 2 !! IF (ABS(A(3,2))>ABS(A(2,2))) THEN !! IPVT(2) = 3 !! TMP(2:3) = A(3,2:3) !! A(3,2:3) = A(2,2:3) !! A(2,2:3) = TMP(2:3) !! END IF !! IF (ABS(A(2,2)) < t) THEN !! info = 1 !! return !! END IF !! ! A(3,2) = A(3,2)/A(2,2) ! A(3,3) = A(3,3) - A(3,2)*A(2,3) ! IPVT(3) = 3 ! !END SUBROUTINE FAC3 ! ! !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !SUBROUTINE SOL3(Trans,A,IPVT,b) !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !! SOL3 solves the system 3x3 !! A * x = b or trans(a) * x = b !! using the factors computed by WGEFA. !! !! Trans = 'N' to solve A*x = b , !! = 'T' to solve transpose(A)*x = b !! LINPACK - LIKE !! !! Remove comments to use pivoting !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! ! CHARACTER :: Trans ! REAL(kind=dp) :: a(3,3),b(3) ! INTEGER :: IPVT(3) !! INTEGER :: L !! REAL(kind=dp) :: TMP ! ! SELECT CASE (Trans) ! ! CASE ('n','N') ! Solve A * x = b ! !! Solve L*y = b !! L = IPVT(1) !! IF (L /= 1) THEN !! TMP = B(1); B(1) = B(L); B(L) = TMP !! END IF ! b(2) = b(2)-A(2,1)*b(1) ! b(3) = b(3)-A(3,1)*b(1) ! !! L = IPVT(2) !! IF (L /= 2) THEN !! TMP = B(2); B(2) = B(L); B(L) = TMP !! END IF ! b(3) = b(3)-A(3,2)*b(2) ! !! Solve U*x = y ! b(3) = b(3)/A(3,3) ! b(2) = (b(2)-A(2,3)*b(3))/A(2,2) ! b(1) = (b(1)-A(1,3)*b(3)-A(1,2)*b(2))/A(1,1) ! ! ! CASE ('t','T') ! Solve transpose(A) * x = b ! !! Solve transpose(U)*y = b ! b(1) = b(1)/A(1,1) ! b(2) = (b(2)-A(1,2)*b(1))/A(2,2) ! b(3) = (b(3)-A(1,3)*b(1)-A(2,3)*b(2))/A(3,3) ! !! Solve transpose(L)*x = y ! b(2) = b(2)-A(3,2)*b(3) !! L = ipvt(2) !! IF (L /= 2) THEN !! TMP = B(2); B(2) = B(L); B(L) = TMP !! END IF ! b(1) = b(1)-A(3,1)*b(3)-A(2,1)*b(2) !! L = ipvt(1) !! IF (L /= 1) THEN !! TMP = B(1); B(1) = B(L); B(L) = TMP !! END IF ! ! END SELECT ! !END SUBROUTINE SOL3 ! End of SPARSE_UTIL function ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! ! KppSolve - sparse back substitution ! Arguments : ! JVS - sparse Jacobian of variables ! X - Vector for variables ! ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SUBROUTINE KppSolve ( JVS, X ) ! JVS - sparse Jacobian of variables REAL(kind=dp) :: JVS(LU_NONZERO) ! X - Vector for variables REAL(kind=dp) :: X(NVAR) X(31) = X(31)-JVS(89)*X(25) X(32) = X(32)-JVS(94)*X(23) X(33) = X(33)-JVS(99)*X(24) X(60) = X(60)-JVS(207)*X(53)-JVS(208)*X(54)-JVS(209)*X(59) X(61) = X(61)-JVS(230)*X(59) X(62) = X(62)-JVS(236)*X(42) X(63) = X(63)-JVS(246)*X(54)-JVS(247)*X(55) X(65) = X(65)-JVS(265)*X(26)-JVS(266)*X(41) X(66) = X(66)-JVS(275)*X(26)-JVS(276)*X(42) X(67) = X(67)-JVS(285)*X(35)-JVS(286)*X(36)-JVS(287)*X(38)-JVS(288)*X(44)-JVS(289)*X(64) X(71) = X(71)-JVS(330)*X(57)-JVS(331)*X(70) X(72) = X(72)-JVS(340)*X(53) X(74) = X(74)-JVS(356)*X(62)-JVS(357)*X(66) X(75) = X(75)-JVS(366)*X(55) X(76) = X(76)-JVS(374)*X(51)-JVS(375)*X(61) X(77) = X(77)-JVS(385)*X(53)-JVS(386)*X(54)-JVS(387)*X(58)-JVS(388)*X(71)-JVS(389)*X(72)-JVS(390)*X(74) X(78) = X(78)-JVS(407)*X(52)-JVS(408)*X(59) X(79) = X(79)-JVS(417)*X(54)-JVS(418)*X(71) X(80) = X(80)-JVS(427)*X(56)-JVS(428)*X(64)-JVS(429)*X(69) X(81) = X(81)-JVS(438)*X(40)-JVS(439)*X(41)-JVS(440)*X(51)-JVS(441)*X(52)-JVS(442)*X(55)-JVS(443)*X(56)-JVS(444)*X(64)& &-JVS(445)*X(65)-JVS(446)*X(68)-JVS(447)*X(69)-JVS(448)*X(75)-JVS(449)*X(76)-JVS(450)*X(78)-JVS(451)*X(80) X(82) = X(82)-JVS(465)*X(1)-JVS(466)*X(39)-JVS(467)*X(44)-JVS(468)*X(45)-JVS(469)*X(47)-JVS(470)*X(48)-JVS(471)*X(50)& &-JVS(472)*X(53)-JVS(473)*X(55)-JVS(474)*X(57)-JVS(475)*X(58)-JVS(476)*X(59)-JVS(477)*X(61)-JVS(478)*X(63)& &-JVS(479)*X(64)-JVS(480)*X(65)-JVS(481)*X(66)-JVS(482)*X(68)-JVS(483)*X(69)-JVS(484)*X(70)-JVS(485)*X(71)& &-JVS(486)*X(72)-JVS(487)*X(73)-JVS(488)*X(74)-JVS(489)*X(75)-JVS(490)*X(76)-JVS(491)*X(77)-JVS(492)*X(78)& &-JVS(493)*X(79)-JVS(494)*X(80) X(83) = X(83)-JVS(516)*X(50)-JVS(517)*X(61) X(84) = X(84)-JVS(527)*X(43)-JVS(528)*X(46)-JVS(529)*X(50)-JVS(530)*X(61)-JVS(531)*X(68)-JVS(532)*X(73)-JVS(533)*X(76)& &-JVS(534)*X(83) X(85) = X(85)-JVS(550)*X(35)-JVS(551)*X(40)-JVS(552)*X(68) X(86) = X(86)-JVS(561)*X(68)-JVS(562)*X(73)-JVS(563)*X(74)-JVS(564)*X(85) X(87) = X(87)-JVS(573)*X(36)-JVS(574)*X(46)-JVS(575)*X(81)-JVS(576)*X(83)-JVS(577)*X(85)-JVS(578)*X(86) X(88) = X(88)-JVS(591)*X(54)-JVS(592)*X(55)-JVS(593)*X(64)-JVS(594)*X(69)-JVS(595)*X(71)-JVS(596)*X(72)-JVS(597)*X(73)& &-JVS(598)*X(74)-JVS(599)*X(75)-JVS(600)*X(77)-JVS(601)*X(79)-JVS(602)*X(80)-JVS(603)*X(83)-JVS(604)*X(85)& &-JVS(605)*X(86) X(89) = X(89)-JVS(620)*X(70)-JVS(621)*X(72)-JVS(622)*X(73)-JVS(623)*X(74)-JVS(624)*X(75)-JVS(625)*X(79)-JVS(626)*X(85)& &-JVS(627)*X(86) X(90) = X(90)-JVS(639)*X(27)-JVS(640)*X(43)-JVS(641)*X(81)-JVS(642)*X(83)-JVS(643)*X(85)-JVS(644)*X(86)-JVS(645)*X(89) X(91) = X(91)-JVS(658)*X(57)-JVS(659)*X(59)-JVS(660)*X(70)-JVS(661)*X(78) X(92) = X(92)-JVS(671)*X(57)-JVS(672)*X(59)-JVS(673)*X(70) X(93) = X(93)-JVS(682)*X(57)-JVS(683)*X(59)-JVS(684)*X(70)-JVS(685)*X(78)-JVS(686)*X(92) X(94) = X(94)-JVS(695)*X(28)-JVS(696)*X(47)-JVS(697)*X(63)-JVS(698)*X(64)-JVS(699)*X(71)-JVS(700)*X(75)-JVS(701)*X(79)& &-JVS(702)*X(80)-JVS(703)*X(91)-JVS(704)*X(92)-JVS(705)*X(93) X(95) = X(95)-JVS(715)*X(34)-JVS(716)*X(39)-JVS(717)*X(44)-JVS(718)*X(48)-JVS(719)*X(61)-JVS(720)*X(62)-JVS(721)*X(64)& &-JVS(722)*X(65)-JVS(723)*X(66)-JVS(724)*X(68)-JVS(725)*X(69)-JVS(726)*X(70)-JVS(727)*X(72)-JVS(728)*X(73)& &-JVS(729)*X(74)-JVS(730)*X(75)-JVS(731)*X(76)-JVS(732)*X(78)-JVS(733)*X(79)-JVS(734)*X(80)-JVS(735)*X(83)& &-JVS(736)*X(84)-JVS(737)*X(85)-JVS(738)*X(86)-JVS(739)*X(87)-JVS(740)*X(88)-JVS(741)*X(89)-JVS(742)*X(90)& &-JVS(743)*X(91)-JVS(744)*X(92)-JVS(745)*X(93)-JVS(746)*X(94) X(96) = X(96)-JVS(756)*X(29)-JVS(757)*X(30)-JVS(758)*X(31)-JVS(759)*X(32)-JVS(760)*X(33)-JVS(761)*X(39)-JVS(762)*X(40)& &-JVS(763)*X(41)-JVS(764)*X(42)-JVS(765)*X(43)-JVS(766)*X(44)-JVS(767)*X(46)-JVS(768)*X(47)-JVS(769)*X(49)& &-JVS(770)*X(50)-JVS(771)*X(51)-JVS(772)*X(52)-JVS(773)*X(53)-JVS(774)*X(54)-JVS(775)*X(55)-JVS(776)*X(56)& &-JVS(777)*X(57)-JVS(778)*X(58)-JVS(779)*X(59)-JVS(780)*X(60)-JVS(781)*X(61)-JVS(782)*X(62)-JVS(783)*X(63)& &-JVS(784)*X(64)-JVS(785)*X(65)-JVS(786)*X(66)-JVS(787)*X(68)-JVS(788)*X(69)-JVS(789)*X(70)-JVS(790)*X(71)& &-JVS(791)*X(72)-JVS(792)*X(73)-JVS(793)*X(74)-JVS(794)*X(75)-JVS(795)*X(76)-JVS(796)*X(77)-JVS(797)*X(78)& &-JVS(798)*X(79)-JVS(799)*X(80)-JVS(800)*X(81)-JVS(801)*X(82)-JVS(802)*X(83)-JVS(803)*X(84)-JVS(804)*X(85)& &-JVS(805)*X(86)-JVS(806)*X(87)-JVS(807)*X(88)-JVS(808)*X(89)-JVS(809)*X(90)-JVS(810)*X(91)-JVS(811)*X(92)& &-JVS(812)*X(93)-JVS(813)*X(94)-JVS(814)*X(95) X(97) = X(97)-JVS(823)*X(45)-JVS(824)*X(58)-JVS(825)*X(71)-JVS(826)*X(91)-JVS(827)*X(92)-JVS(828)*X(93)-JVS(829)*X(95)& &-JVS(830)*X(96) X(98) = X(98)-JVS(838)*X(38)-JVS(839)*X(58)-JVS(840)*X(59)-JVS(841)*X(61)-JVS(842)*X(71)-JVS(843)*X(90)-JVS(844)*X(91)& &-JVS(845)*X(92)-JVS(846)*X(93)-JVS(847)*X(94)-JVS(848)*X(95)-JVS(849)*X(96)-JVS(850)*X(97) X(99) = X(99)-JVS(857)*X(27)-JVS(858)*X(28)-JVS(859)*X(34)-JVS(860)*X(37)-JVS(861)*X(38)-JVS(862)*X(49)-JVS(863)*X(51)& &-JVS(864)*X(52)-JVS(865)*X(56)-JVS(866)*X(58)-JVS(867)*X(64)-JVS(868)*X(65)-JVS(869)*X(66)-JVS(870)*X(67)& &-JVS(871)*X(68)-JVS(872)*X(69)-JVS(873)*X(70)-JVS(874)*X(72)-JVS(875)*X(73)-JVS(876)*X(74)-JVS(877)*X(75)& &-JVS(878)*X(76)-JVS(879)*X(78)-JVS(880)*X(79)-JVS(881)*X(80)-JVS(882)*X(81)-JVS(883)*X(82)-JVS(884)*X(83)& &-JVS(885)*X(84)-JVS(886)*X(85)-JVS(887)*X(86)-JVS(888)*X(87)-JVS(889)*X(88)-JVS(890)*X(89)-JVS(891)*X(90)& &-JVS(892)*X(91)-JVS(893)*X(92)-JVS(894)*X(93)-JVS(895)*X(94)-JVS(896)*X(95)-JVS(897)*X(96)-JVS(898)*X(97)& &-JVS(899)*X(98) X(100) = X(100)-JVS(905)*X(34)-JVS(906)*X(35)-JVS(907)*X(36)-JVS(908)*X(38)-JVS(909)*X(44)-JVS(910)*X(49)-JVS(911)& &*X(59)-JVS(912)*X(61)-JVS(913)*X(67)-JVS(914)*X(70)-JVS(915)*X(72)-JVS(916)*X(75)-JVS(917)*X(78)-JVS(918)& &*X(79)-JVS(919)*X(80)-JVS(920)*X(81)-JVS(921)*X(82)-JVS(922)*X(83)-JVS(923)*X(84)-JVS(924)*X(85)-JVS(925)& &*X(86)-JVS(926)*X(87)-JVS(927)*X(88)-JVS(928)*X(89)-JVS(929)*X(90)-JVS(930)*X(91)-JVS(931)*X(92)-JVS(932)& &*X(93)-JVS(933)*X(94)-JVS(934)*X(95)-JVS(935)*X(96)-JVS(936)*X(97)-JVS(937)*X(98)-JVS(938)*X(99) X(101) = X(101)-JVS(943)*X(34)-JVS(944)*X(45)-JVS(945)*X(48)-JVS(946)*X(55)-JVS(947)*X(62)-JVS(948)*X(64)-JVS(949)& &*X(65)-JVS(950)*X(66)-JVS(951)*X(68)-JVS(952)*X(69)-JVS(953)*X(70)-JVS(954)*X(72)-JVS(955)*X(73)-JVS(956)& &*X(74)-JVS(957)*X(75)-JVS(958)*X(76)-JVS(959)*X(77)-JVS(960)*X(78)-JVS(961)*X(79)-JVS(962)*X(80)-JVS(963)& &*X(83)-JVS(964)*X(84)-JVS(965)*X(85)-JVS(966)*X(86)-JVS(967)*X(87)-JVS(968)*X(88)-JVS(969)*X(89)-JVS(970)& &*X(90)-JVS(971)*X(91)-JVS(972)*X(92)-JVS(973)*X(93)-JVS(974)*X(94)-JVS(975)*X(95)-JVS(976)*X(96)-JVS(977)& &*X(97)-JVS(978)*X(98)-JVS(979)*X(99)-JVS(980)*X(100) X(102) = X(102)-JVS(984)*X(23)-JVS(985)*X(24)-JVS(986)*X(25)-JVS(987)*X(26)-JVS(988)*X(29)-JVS(989)*X(30)-JVS(990)& &*X(35)-JVS(991)*X(36)-JVS(992)*X(37)-JVS(993)*X(39)-JVS(994)*X(40)-JVS(995)*X(41)-JVS(996)*X(42)-JVS(997)& &*X(43)-JVS(998)*X(44)-JVS(999)*X(45)-JVS(1000)*X(46)-JVS(1001)*X(47)-JVS(1002)*X(48)-JVS(1003)*X(49)-JVS(1004)& &*X(50)-JVS(1005)*X(51)-JVS(1006)*X(52)-JVS(1007)*X(53)-JVS(1008)*X(54)-JVS(1009)*X(55)-JVS(1010)*X(56)& &-JVS(1011)*X(57)-JVS(1012)*X(58)-JVS(1013)*X(59)-JVS(1014)*X(60)-JVS(1015)*X(61)-JVS(1016)*X(62)-JVS(1017)& &*X(63)-JVS(1018)*X(64)-JVS(1019)*X(65)-JVS(1020)*X(66)-JVS(1021)*X(67)-JVS(1022)*X(69)-JVS(1023)*X(70)& &-JVS(1024)*X(71)-JVS(1025)*X(72)-JVS(1026)*X(75)-JVS(1027)*X(76)-JVS(1028)*X(77)-JVS(1029)*X(78)-JVS(1030)& &*X(79)-JVS(1031)*X(80)-JVS(1032)*X(81)-JVS(1033)*X(82)-JVS(1034)*X(83)-JVS(1035)*X(84)-JVS(1036)*X(85)& &-JVS(1037)*X(86)-JVS(1038)*X(87)-JVS(1039)*X(88)-JVS(1040)*X(89)-JVS(1041)*X(90)-JVS(1042)*X(91)-JVS(1043)& &*X(92)-JVS(1044)*X(93)-JVS(1045)*X(94)-JVS(1046)*X(95)-JVS(1047)*X(96)-JVS(1048)*X(97)-JVS(1049)*X(98)& &-JVS(1050)*X(99)-JVS(1051)*X(100)-JVS(1052)*X(101) X(103) = X(103)-JVS(1055)*X(31)-JVS(1056)*X(32)-JVS(1057)*X(33)-JVS(1058)*X(37)-JVS(1059)*X(38)-JVS(1060)*X(64)& &-JVS(1061)*X(65)-JVS(1062)*X(66)-JVS(1063)*X(68)-JVS(1064)*X(69)-JVS(1065)*X(70)-JVS(1066)*X(72)-JVS(1067)& &*X(73)-JVS(1068)*X(74)-JVS(1069)*X(75)-JVS(1070)*X(76)-JVS(1071)*X(78)-JVS(1072)*X(79)-JVS(1073)*X(80)& &-JVS(1074)*X(83)-JVS(1075)*X(85)-JVS(1076)*X(86)-JVS(1077)*X(87)-JVS(1078)*X(89)-JVS(1079)*X(90)-JVS(1080)& &*X(91)-JVS(1081)*X(92)-JVS(1082)*X(93)-JVS(1083)*X(94)-JVS(1084)*X(95)-JVS(1085)*X(96)-JVS(1086)*X(97)& &-JVS(1087)*X(98)-JVS(1088)*X(99)-JVS(1089)*X(100)-JVS(1090)*X(101)-JVS(1091)*X(102) X(103) = X(103)/JVS(1092) X(102) = (X(102)-JVS(1054)*X(103))/(JVS(1053)) X(101) = (X(101)-JVS(982)*X(102)-JVS(983)*X(103))/(JVS(981)) X(100) = (X(100)-JVS(940)*X(101)-JVS(941)*X(102)-JVS(942)*X(103))/(JVS(939)) X(99) = (X(99)-JVS(901)*X(100)-JVS(902)*X(101)-JVS(903)*X(102)-JVS(904)*X(103))/(JVS(900)) X(98) = (X(98)-JVS(852)*X(99)-JVS(853)*X(100)-JVS(854)*X(101)-JVS(855)*X(102)-JVS(856)*X(103))/(JVS(851)) X(97) = (X(97)-JVS(832)*X(98)-JVS(833)*X(99)-JVS(834)*X(100)-JVS(835)*X(101)-JVS(836)*X(102)-JVS(837)*X(103))& &/(JVS(831)) X(96) = (X(96)-JVS(816)*X(97)-JVS(817)*X(98)-JVS(818)*X(99)-JVS(819)*X(100)-JVS(820)*X(101)-JVS(821)*X(102)-JVS(822)& &*X(103))/(JVS(815)) X(95) = (X(95)-JVS(748)*X(96)-JVS(749)*X(97)-JVS(750)*X(98)-JVS(751)*X(99)-JVS(752)*X(100)-JVS(753)*X(101)-JVS(754)& &*X(102)-JVS(755)*X(103))/(JVS(747)) X(94) = (X(94)-JVS(707)*X(95)-JVS(708)*X(96)-JVS(709)*X(98)-JVS(710)*X(99)-JVS(711)*X(100)-JVS(712)*X(101)-JVS(713)& &*X(102)-JVS(714)*X(103))/(JVS(706)) X(93) = (X(93)-JVS(688)*X(95)-JVS(689)*X(96)-JVS(690)*X(98)-JVS(691)*X(100)-JVS(692)*X(101)-JVS(693)*X(102)-JVS(694)& &*X(103))/(JVS(687)) X(92) = (X(92)-JVS(675)*X(95)-JVS(676)*X(96)-JVS(677)*X(98)-JVS(678)*X(100)-JVS(679)*X(101)-JVS(680)*X(102)-JVS(681)& &*X(103))/(JVS(674)) X(91) = (X(91)-JVS(663)*X(92)-JVS(664)*X(95)-JVS(665)*X(96)-JVS(666)*X(98)-JVS(667)*X(100)-JVS(668)*X(101)-JVS(669)& &*X(102)-JVS(670)*X(103))/(JVS(662)) X(90) = (X(90)-JVS(647)*X(91)-JVS(648)*X(92)-JVS(649)*X(93)-JVS(650)*X(95)-JVS(651)*X(96)-JVS(652)*X(98)-JVS(653)& &*X(99)-JVS(654)*X(100)-JVS(655)*X(101)-JVS(656)*X(102)-JVS(657)*X(103))/(JVS(646)) X(89) = (X(89)-JVS(629)*X(91)-JVS(630)*X(92)-JVS(631)*X(93)-JVS(632)*X(95)-JVS(633)*X(96)-JVS(634)*X(98)-JVS(635)& &*X(100)-JVS(636)*X(101)-JVS(637)*X(102)-JVS(638)*X(103))/(JVS(628)) X(88) = (X(88)-JVS(607)*X(89)-JVS(608)*X(91)-JVS(609)*X(92)-JVS(610)*X(93)-JVS(611)*X(95)-JVS(612)*X(96)-JVS(613)& &*X(97)-JVS(614)*X(98)-JVS(615)*X(99)-JVS(616)*X(100)-JVS(617)*X(101)-JVS(618)*X(102)-JVS(619)*X(103))& &/(JVS(606)) X(87) = (X(87)-JVS(580)*X(89)-JVS(581)*X(90)-JVS(582)*X(91)-JVS(583)*X(93)-JVS(584)*X(95)-JVS(585)*X(96)-JVS(586)& &*X(98)-JVS(587)*X(100)-JVS(588)*X(101)-JVS(589)*X(102)-JVS(590)*X(103))/(JVS(579)) X(86) = (X(86)-JVS(566)*X(89)-JVS(567)*X(95)-JVS(568)*X(96)-JVS(569)*X(100)-JVS(570)*X(101)-JVS(571)*X(102)-JVS(572)& &*X(103))/(JVS(565)) X(85) = (X(85)-JVS(554)*X(86)-JVS(555)*X(95)-JVS(556)*X(96)-JVS(557)*X(100)-JVS(558)*X(101)-JVS(559)*X(102)-JVS(560)& &*X(103))/(JVS(553)) X(84) = (X(84)-JVS(536)*X(85)-JVS(537)*X(86)-JVS(538)*X(87)-JVS(539)*X(88)-JVS(540)*X(89)-JVS(541)*X(90)-JVS(542)& &*X(93)-JVS(543)*X(95)-JVS(544)*X(96)-JVS(545)*X(98)-JVS(546)*X(100)-JVS(547)*X(101)-JVS(548)*X(102)-JVS(549)& &*X(103))/(JVS(535)) X(83) = (X(83)-JVS(519)*X(93)-JVS(520)*X(95)-JVS(521)*X(96)-JVS(522)*X(98)-JVS(523)*X(100)-JVS(524)*X(101)-JVS(525)& &*X(102)-JVS(526)*X(103))/(JVS(518)) X(82) = (X(82)-JVS(496)*X(83)-JVS(497)*X(84)-JVS(498)*X(85)-JVS(499)*X(86)-JVS(500)*X(87)-JVS(501)*X(89)-JVS(502)& &*X(90)-JVS(503)*X(91)-JVS(504)*X(92)-JVS(505)*X(93)-JVS(506)*X(94)-JVS(507)*X(95)-JVS(508)*X(96)-JVS(509)*X(97)& &-JVS(510)*X(98)-JVS(511)*X(99)-JVS(512)*X(100)-JVS(513)*X(101)-JVS(514)*X(102)-JVS(515)*X(103))/(JVS(495)) X(81) = (X(81)-JVS(453)*X(83)-JVS(454)*X(85)-JVS(455)*X(86)-JVS(456)*X(91)-JVS(457)*X(93)-JVS(458)*X(95)-JVS(459)& &*X(96)-JVS(460)*X(98)-JVS(461)*X(100)-JVS(462)*X(101)-JVS(463)*X(102)-JVS(464)*X(103))/(JVS(452)) X(80) = (X(80)-JVS(431)*X(91)-JVS(432)*X(95)-JVS(433)*X(96)-JVS(434)*X(100)-JVS(435)*X(101)-JVS(436)*X(102)-JVS(437)& &*X(103))/(JVS(430)) X(79) = (X(79)-JVS(420)*X(92)-JVS(421)*X(95)-JVS(422)*X(96)-JVS(423)*X(98)-JVS(424)*X(101)-JVS(425)*X(102)-JVS(426)& &*X(103))/(JVS(419)) X(78) = (X(78)-JVS(410)*X(95)-JVS(411)*X(96)-JVS(412)*X(98)-JVS(413)*X(100)-JVS(414)*X(101)-JVS(415)*X(102)-JVS(416)& &*X(103))/(JVS(409)) X(77) = (X(77)-JVS(392)*X(79)-JVS(393)*X(80)-JVS(394)*X(83)-JVS(395)*X(85)-JVS(396)*X(86)-JVS(397)*X(91)-JVS(398)& &*X(92)-JVS(399)*X(95)-JVS(400)*X(96)-JVS(401)*X(97)-JVS(402)*X(98)-JVS(403)*X(99)-JVS(404)*X(101)-JVS(405)& &*X(102)-JVS(406)*X(103))/(JVS(391)) X(76) = (X(76)-JVS(377)*X(93)-JVS(378)*X(95)-JVS(379)*X(96)-JVS(380)*X(98)-JVS(381)*X(100)-JVS(382)*X(101)-JVS(383)& &*X(102)-JVS(384)*X(103))/(JVS(376)) X(75) = (X(75)-JVS(368)*X(93)-JVS(369)*X(95)-JVS(370)*X(96)-JVS(371)*X(101)-JVS(372)*X(102)-JVS(373)*X(103))& &/(JVS(367)) X(74) = (X(74)-JVS(359)*X(85)-JVS(360)*X(86)-JVS(361)*X(95)-JVS(362)*X(96)-JVS(363)*X(101)-JVS(364)*X(102)-JVS(365)& &*X(103))/(JVS(358)) X(73) = (X(73)-JVS(349)*X(89)-JVS(350)*X(95)-JVS(351)*X(96)-JVS(352)*X(100)-JVS(353)*X(101)-JVS(354)*X(102)-JVS(355)& &*X(103))/(JVS(348)) X(72) = (X(72)-JVS(342)*X(91)-JVS(343)*X(95)-JVS(344)*X(96)-JVS(345)*X(101)-JVS(346)*X(102)-JVS(347)*X(103))& &/(JVS(341)) X(71) = (X(71)-JVS(333)*X(92)-JVS(334)*X(95)-JVS(335)*X(96)-JVS(336)*X(98)-JVS(337)*X(101)-JVS(338)*X(102)-JVS(339)& &*X(103))/(JVS(332)) X(70) = (X(70)-JVS(325)*X(92)-JVS(326)*X(95)-JVS(327)*X(96)-JVS(328)*X(101)-JVS(329)*X(103))/(JVS(324)) X(69) = (X(69)-JVS(318)*X(91)-JVS(319)*X(95)-JVS(320)*X(96)-JVS(321)*X(100)-JVS(322)*X(101)-JVS(323)*X(103))& &/(JVS(317)) X(68) = (X(68)-JVS(311)*X(86)-JVS(312)*X(95)-JVS(313)*X(96)-JVS(314)*X(101)-JVS(315)*X(102)-JVS(316)*X(103))& &/(JVS(310)) X(67) = (X(67)-JVS(291)*X(70)-JVS(292)*X(72)-JVS(293)*X(75)-JVS(294)*X(78)-JVS(295)*X(79)-JVS(296)*X(80)-JVS(297)& &*X(81)-JVS(298)*X(82)-JVS(299)*X(84)-JVS(300)*X(88)-JVS(301)*X(89)-JVS(302)*X(91)-JVS(303)*X(95)-JVS(304)*X(96)& &-JVS(305)*X(99)-JVS(306)*X(100)-JVS(307)*X(101)-JVS(308)*X(102)-JVS(309)*X(103))/(JVS(290)) X(66) = (X(66)-JVS(278)*X(85)-JVS(279)*X(86)-JVS(280)*X(95)-JVS(281)*X(96)-JVS(282)*X(101)-JVS(283)*X(102)-JVS(284)& &*X(103))/(JVS(277)) X(65) = (X(65)-JVS(268)*X(85)-JVS(269)*X(86)-JVS(270)*X(95)-JVS(271)*X(96)-JVS(272)*X(101)-JVS(273)*X(102)-JVS(274)& &*X(103))/(JVS(267)) X(64) = (X(64)-JVS(261)*X(95)-JVS(262)*X(96)-JVS(263)*X(101)-JVS(264)*X(103))/(JVS(260)) X(63) = (X(63)-JVS(249)*X(64)-JVS(250)*X(71)-JVS(251)*X(75)-JVS(252)*X(79)-JVS(253)*X(80)-JVS(254)*X(95)-JVS(255)& &*X(96)-JVS(256)*X(98)-JVS(257)*X(101)-JVS(258)*X(102)-JVS(259)*X(103))/(JVS(248)) X(62) = (X(62)-JVS(238)*X(66)-JVS(239)*X(85)-JVS(240)*X(86)-JVS(241)*X(95)-JVS(242)*X(96)-JVS(243)*X(101)-JVS(244)& &*X(102)-JVS(245)*X(103))/(JVS(237)) X(61) = (X(61)-JVS(232)*X(93)-JVS(233)*X(98)-JVS(234)*X(100)-JVS(235)*X(102))/(JVS(231)) X(60) = (X(60)-JVS(211)*X(61)-JVS(212)*X(62)-JVS(213)*X(63)-JVS(214)*X(71)-JVS(215)*X(72)-JVS(216)*X(79)-JVS(217)& &*X(81)-JVS(218)*X(82)-JVS(219)*X(84)-JVS(220)*X(88)-JVS(221)*X(91)-JVS(222)*X(93)-JVS(223)*X(95)-JVS(224)*X(96)& &-JVS(225)*X(98)-JVS(226)*X(100)-JVS(227)*X(101)-JVS(228)*X(102)-JVS(229)*X(103))/(JVS(210)) X(59) = (X(59)-JVS(204)*X(98)-JVS(205)*X(100)-JVS(206)*X(102))/(JVS(203)) X(58) = (X(58)-JVS(199)*X(97)-JVS(200)*X(98)-JVS(201)*X(99)-JVS(202)*X(102))/(JVS(198)) X(57) = (X(57)-JVS(194)*X(70)-JVS(195)*X(92)-JVS(196)*X(96)-JVS(197)*X(102))/(JVS(193)) X(56) = (X(56)-JVS(188)*X(64)-JVS(189)*X(69)-JVS(190)*X(80)-JVS(191)*X(96)-JVS(192)*X(102))/(JVS(187)) X(55) = (X(55)-JVS(184)*X(75)-JVS(185)*X(96)-JVS(186)*X(102))/(JVS(183)) X(54) = (X(54)-JVS(180)*X(79)-JVS(181)*X(96)-JVS(182)*X(102))/(JVS(179)) X(53) = (X(53)-JVS(176)*X(72)-JVS(177)*X(96)-JVS(178)*X(102))/(JVS(175)) X(52) = (X(52)-JVS(172)*X(78)-JVS(173)*X(96)-JVS(174)*X(102))/(JVS(171)) X(51) = (X(51)-JVS(168)*X(76)-JVS(169)*X(96)-JVS(170)*X(102))/(JVS(167)) X(50) = (X(50)-JVS(164)*X(83)-JVS(165)*X(96)-JVS(166)*X(102))/(JVS(163)) X(49) = (X(49)-JVS(160)*X(96)-JVS(161)*X(99)-JVS(162)*X(102))/(JVS(159)) X(48) = (X(48)-JVS(156)*X(96)-JVS(157)*X(101)-JVS(158)*X(102))/(JVS(155)) X(47) = (X(47)-JVS(152)*X(94)-JVS(153)*X(96)-JVS(154)*X(102))/(JVS(151)) X(46) = (X(46)-JVS(148)*X(87)-JVS(149)*X(96)-JVS(150)*X(102))/(JVS(147)) X(45) = (X(45)-JVS(144)*X(96)-JVS(145)*X(97)-JVS(146)*X(102))/(JVS(143)) X(44) = (X(44)-JVS(141)*X(100)-JVS(142)*X(102))/(JVS(140)) X(43) = (X(43)-JVS(137)*X(90)-JVS(138)*X(96)-JVS(139)*X(102))/(JVS(136)) X(42) = (X(42)-JVS(133)*X(66)-JVS(134)*X(96)-JVS(135)*X(102))/(JVS(132)) X(41) = (X(41)-JVS(129)*X(65)-JVS(130)*X(96)-JVS(131)*X(102))/(JVS(128)) X(40) = (X(40)-JVS(125)*X(85)-JVS(126)*X(96)-JVS(127)*X(102))/(JVS(124)) X(39) = (X(39)-JVS(121)*X(95)-JVS(122)*X(96)-JVS(123)*X(102))/(JVS(120)) X(38) = (X(38)-JVS(118)*X(99)-JVS(119)*X(100))/(JVS(117)) X(37) = (X(37)-JVS(114)*X(99)-JVS(115)*X(102)-JVS(116)*X(103))/(JVS(113)) X(36) = (X(36)-JVS(111)*X(100)-JVS(112)*X(102))/(JVS(110)) X(35) = (X(35)-JVS(108)*X(100)-JVS(109)*X(102))/(JVS(107)) X(34) = (X(34)-JVS(105)*X(99)-JVS(106)*X(101))/(JVS(104)) X(33) = (X(33)-JVS(101)*X(96)-JVS(102)*X(102)-JVS(103)*X(103))/(JVS(100)) X(32) = (X(32)-JVS(96)*X(96)-JVS(97)*X(102)-JVS(98)*X(103))/(JVS(95)) X(31) = (X(31)-JVS(91)*X(96)-JVS(92)*X(102)-JVS(93)*X(103))/(JVS(90)) X(30) = (X(30)-JVS(86)*X(44)-JVS(87)*X(100)-JVS(88)*X(102))/(JVS(85)) X(29) = (X(29)-JVS(83)*X(96)-JVS(84)*X(102))/(JVS(82)) X(28) = (X(28)-JVS(80)*X(94)-JVS(81)*X(99))/(JVS(79)) X(27) = (X(27)-JVS(77)*X(90)-JVS(78)*X(99))/(JVS(76)) X(26) = (X(26)-JVS(75)*X(102))/(JVS(74)) X(25) = (X(25)-JVS(73)*X(102))/(JVS(72)) X(24) = (X(24)-JVS(71)*X(102))/(JVS(70)) X(23) = (X(23)-JVS(69)*X(102))/(JVS(68)) X(22) = (X(22)-JVS(58)*X(27)-JVS(59)*X(29)-JVS(60)*X(34)-JVS(61)*X(38)-JVS(62)*X(58)-JVS(63)*X(67)-JVS(64)*X(82)& &-JVS(65)*X(86)-JVS(66)*X(98)-JVS(67)*X(99))/(JVS(57)) X(21) = (X(21)-JVS(50)*X(59)-JVS(51)*X(60)-JVS(52)*X(91)-JVS(53)*X(98)-JVS(54)*X(101)-JVS(55)*X(102)-JVS(56)*X(103))& &/(JVS(49)) X(20) = (X(20)-JVS(47)*X(33)-JVS(48)*X(103))/(JVS(46)) X(19) = (X(19)-JVS(44)*X(33)-JVS(45)*X(96))/(JVS(43)) X(18) = (X(18)-JVS(41)*X(32)-JVS(42)*X(103))/(JVS(40)) X(17) = (X(17)-JVS(38)*X(32)-JVS(39)*X(96))/(JVS(37)) X(16) = (X(16)-JVS(35)*X(31)-JVS(36)*X(103))/(JVS(34)) X(15) = (X(15)-JVS(32)*X(31)-JVS(33)*X(96))/(JVS(31)) X(14) = (X(14)-JVS(29)*X(59)-JVS(30)*X(102))/(JVS(28)) X(13) = (X(13)-JVS(26)*X(44)-JVS(27)*X(102))/(JVS(25)) X(12) = (X(12)-JVS(23)*X(30)-JVS(24)*X(102))/(JVS(22)) X(11) = (X(11)-JVS(21)*X(86))/(JVS(20)) X(10) = (X(10)-JVS(19)*X(27))/(JVS(18)) X(9) = (X(9)-JVS(17)*X(58))/(JVS(16)) X(8) = (X(8)-JVS(15)*X(34))/(JVS(14)) X(7) = (X(7)-JVS(13)*X(98))/(JVS(12)) X(6) = (X(6)-JVS(11)*X(99))/(JVS(10)) X(5) = (X(5)-JVS(9)*X(38))/(JVS(8)) X(4) = (X(4)-JVS(7)*X(67))/(JVS(6)) X(3) = (X(3)-JVS(5)*X(29))/(JVS(4)) X(2) = (X(2)-JVS(3)*X(82))/(JVS(2)) X(1) = X(1)/JVS(1) END SUBROUTINE KppSolve ! End of KppSolve function ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! ! KppSolveTR - sparse, transposed back substitution ! Arguments : ! JVS - sparse Jacobian of variables ! X - Vector for variables ! XX - Vector for output variables ! ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ SUBROUTINE KppSolveTR ( JVS, X, XX ) ! JVS - sparse Jacobian of variables REAL(kind=dp) :: JVS(LU_NONZERO) ! X - Vector for variables REAL(kind=dp) :: X(NVAR) ! XX - Vector for output variables REAL(kind=dp) :: XX(NVAR) XX(1) = X(1)/JVS(1) XX(2) = X(2)/JVS(2) XX(3) = X(3)/JVS(4) XX(4) = X(4)/JVS(6) XX(5) = X(5)/JVS(8) XX(6) = X(6)/JVS(10) XX(7) = X(7)/JVS(12) XX(8) = X(8)/JVS(14) XX(9) = X(9)/JVS(16) XX(10) = X(10)/JVS(18) XX(11) = X(11)/JVS(20) XX(12) = X(12)/JVS(22) XX(13) = X(13)/JVS(25) XX(14) = X(14)/JVS(28) XX(15) = X(15)/JVS(31) XX(16) = X(16)/JVS(34) XX(17) = X(17)/JVS(37) XX(18) = X(18)/JVS(40) XX(19) = X(19)/JVS(43) XX(20) = X(20)/JVS(46) XX(21) = X(21)/JVS(49) XX(22) = X(22)/JVS(57) XX(23) = X(23)/JVS(68) XX(24) = X(24)/JVS(70) XX(25) = X(25)/JVS(72) XX(26) = X(26)/JVS(74) XX(27) = (X(27)-JVS(19)*XX(10)-JVS(58)*XX(22))/(JVS(76)) XX(28) = X(28)/JVS(79) XX(29) = (X(29)-JVS(5)*XX(3)-JVS(59)*XX(22))/(JVS(82)) XX(30) = (X(30)-JVS(23)*XX(12))/(JVS(85)) XX(31) = (X(31)-JVS(32)*XX(15)-JVS(35)*XX(16))/(JVS(90)) XX(32) = (X(32)-JVS(38)*XX(17)-JVS(41)*XX(18))/(JVS(95)) XX(33) = (X(33)-JVS(44)*XX(19)-JVS(47)*XX(20))/(JVS(100)) XX(34) = (X(34)-JVS(15)*XX(8)-JVS(60)*XX(22))/(JVS(104)) XX(35) = X(35)/JVS(107) XX(36) = X(36)/JVS(110) XX(37) = X(37)/JVS(113) XX(38) = (X(38)-JVS(9)*XX(5)-JVS(61)*XX(22))/(JVS(117)) XX(39) = X(39)/JVS(120) XX(40) = X(40)/JVS(124) XX(41) = X(41)/JVS(128) XX(42) = X(42)/JVS(132) XX(43) = X(43)/JVS(136) XX(44) = (X(44)-JVS(26)*XX(13)-JVS(86)*XX(30))/(JVS(140)) XX(45) = X(45)/JVS(143) XX(46) = X(46)/JVS(147) XX(47) = X(47)/JVS(151) XX(48) = X(48)/JVS(155) XX(49) = X(49)/JVS(159) XX(50) = X(50)/JVS(163) XX(51) = X(51)/JVS(167) XX(52) = X(52)/JVS(171) XX(53) = X(53)/JVS(175) XX(54) = X(54)/JVS(179) XX(55) = X(55)/JVS(183) XX(56) = X(56)/JVS(187) XX(57) = X(57)/JVS(193) XX(58) = (X(58)-JVS(17)*XX(9)-JVS(62)*XX(22))/(JVS(198)) XX(59) = (X(59)-JVS(29)*XX(14)-JVS(50)*XX(21))/(JVS(203)) XX(60) = (X(60)-JVS(51)*XX(21))/(JVS(210)) XX(61) = (X(61)-JVS(211)*XX(60))/(JVS(231)) XX(62) = (X(62)-JVS(212)*XX(60))/(JVS(237)) XX(63) = (X(63)-JVS(213)*XX(60))/(JVS(248)) XX(64) = (X(64)-JVS(188)*XX(56)-JVS(249)*XX(63))/(JVS(260)) XX(65) = (X(65)-JVS(129)*XX(41))/(JVS(267)) XX(66) = (X(66)-JVS(133)*XX(42)-JVS(238)*XX(62))/(JVS(277)) XX(67) = (X(67)-JVS(7)*XX(4)-JVS(63)*XX(22))/(JVS(290)) XX(68) = X(68)/JVS(310) XX(69) = (X(69)-JVS(189)*XX(56))/(JVS(317)) XX(70) = (X(70)-JVS(194)*XX(57)-JVS(291)*XX(67))/(JVS(324)) XX(71) = (X(71)-JVS(214)*XX(60)-JVS(250)*XX(63))/(JVS(332)) XX(72) = (X(72)-JVS(176)*XX(53)-JVS(215)*XX(60)-JVS(292)*XX(67))/(JVS(341)) XX(73) = X(73)/JVS(348) XX(74) = X(74)/JVS(358) XX(75) = (X(75)-JVS(184)*XX(55)-JVS(251)*XX(63)-JVS(293)*XX(67))/(JVS(367)) XX(76) = (X(76)-JVS(168)*XX(51))/(JVS(376)) XX(77) = X(77)/JVS(391) XX(78) = (X(78)-JVS(172)*XX(52)-JVS(294)*XX(67))/(JVS(409)) XX(79) = (X(79)-JVS(180)*XX(54)-JVS(216)*XX(60)-JVS(252)*XX(63)-JVS(295)*XX(67)-JVS(392)*XX(77))/(JVS(419)) XX(80) = (X(80)-JVS(190)*XX(56)-JVS(253)*XX(63)-JVS(296)*XX(67)-JVS(393)*XX(77))/(JVS(430)) XX(81) = (X(81)-JVS(217)*XX(60)-JVS(297)*XX(67))/(JVS(452)) XX(82) = (X(82)-JVS(3)*XX(2)-JVS(64)*XX(22)-JVS(218)*XX(60)-JVS(298)*XX(67))/(JVS(495)) XX(83) = (X(83)-JVS(164)*XX(50)-JVS(394)*XX(77)-JVS(453)*XX(81)-JVS(496)*XX(82))/(JVS(518)) XX(84) = (X(84)-JVS(219)*XX(60)-JVS(299)*XX(67)-JVS(497)*XX(82))/(JVS(535)) XX(85) = (X(85)-JVS(125)*XX(40)-JVS(239)*XX(62)-JVS(268)*XX(65)-JVS(278)*XX(66)-JVS(359)*XX(74)-JVS(395)*XX(77)& &-JVS(454)*XX(81)-JVS(498)*XX(82)-JVS(536)*XX(84))/(JVS(553)) XX(86) = (X(86)-JVS(21)*XX(11)-JVS(65)*XX(22)-JVS(240)*XX(62)-JVS(269)*XX(65)-JVS(279)*XX(66)-JVS(311)*XX(68)-JVS(360)& &*XX(74)-JVS(396)*XX(77)-JVS(455)*XX(81)-JVS(499)*XX(82)-JVS(537)*XX(84)-JVS(554)*XX(85))/(JVS(565)) XX(87) = (X(87)-JVS(148)*XX(46)-JVS(500)*XX(82)-JVS(538)*XX(84))/(JVS(579)) XX(88) = (X(88)-JVS(220)*XX(60)-JVS(300)*XX(67)-JVS(539)*XX(84))/(JVS(606)) XX(89) = (X(89)-JVS(301)*XX(67)-JVS(349)*XX(73)-JVS(501)*XX(82)-JVS(540)*XX(84)-JVS(566)*XX(86)-JVS(580)*XX(87)& &-JVS(607)*XX(88))/(JVS(628)) XX(90) = (X(90)-JVS(77)*XX(27)-JVS(137)*XX(43)-JVS(502)*XX(82)-JVS(541)*XX(84)-JVS(581)*XX(87))/(JVS(646)) XX(91) = (X(91)-JVS(52)*XX(21)-JVS(221)*XX(60)-JVS(302)*XX(67)-JVS(318)*XX(69)-JVS(342)*XX(72)-JVS(397)*XX(77)& &-JVS(431)*XX(80)-JVS(456)*XX(81)-JVS(503)*XX(82)-JVS(582)*XX(87)-JVS(608)*XX(88)-JVS(629)*XX(89)-JVS(647)& &*XX(90))/(JVS(662)) XX(92) = (X(92)-JVS(195)*XX(57)-JVS(325)*XX(70)-JVS(333)*XX(71)-JVS(398)*XX(77)-JVS(420)*XX(79)-JVS(504)*XX(82)& &-JVS(609)*XX(88)-JVS(630)*XX(89)-JVS(648)*XX(90)-JVS(663)*XX(91))/(JVS(674)) XX(93) = (X(93)-JVS(222)*XX(60)-JVS(232)*XX(61)-JVS(368)*XX(75)-JVS(377)*XX(76)-JVS(457)*XX(81)-JVS(505)*XX(82)& &-JVS(519)*XX(83)-JVS(542)*XX(84)-JVS(583)*XX(87)-JVS(610)*XX(88)-JVS(631)*XX(89)-JVS(649)*XX(90))/(JVS(687)) XX(94) = (X(94)-JVS(80)*XX(28)-JVS(152)*XX(47)-JVS(506)*XX(82))/(JVS(706)) XX(95) = (X(95)-JVS(121)*XX(39)-JVS(223)*XX(60)-JVS(241)*XX(62)-JVS(254)*XX(63)-JVS(261)*XX(64)-JVS(270)*XX(65)& &-JVS(280)*XX(66)-JVS(303)*XX(67)-JVS(312)*XX(68)-JVS(319)*XX(69)-JVS(326)*XX(70)-JVS(334)*XX(71)-JVS(343)& &*XX(72)-JVS(350)*XX(73)-JVS(361)*XX(74)-JVS(369)*XX(75)-JVS(378)*XX(76)-JVS(399)*XX(77)-JVS(410)*XX(78)& &-JVS(421)*XX(79)-JVS(432)*XX(80)-JVS(458)*XX(81)-JVS(507)*XX(82)-JVS(520)*XX(83)-JVS(543)*XX(84)-JVS(555)& &*XX(85)-JVS(567)*XX(86)-JVS(584)*XX(87)-JVS(611)*XX(88)-JVS(632)*XX(89)-JVS(650)*XX(90)-JVS(664)*XX(91)& &-JVS(675)*XX(92)-JVS(688)*XX(93)-JVS(707)*XX(94))/(JVS(747)) XX(96) = (X(96)-JVS(33)*XX(15)-JVS(39)*XX(17)-JVS(45)*XX(19)-JVS(83)*XX(29)-JVS(91)*XX(31)-JVS(96)*XX(32)-JVS(101)& &*XX(33)-JVS(122)*XX(39)-JVS(126)*XX(40)-JVS(130)*XX(41)-JVS(134)*XX(42)-JVS(138)*XX(43)-JVS(144)*XX(45)& &-JVS(149)*XX(46)-JVS(153)*XX(47)-JVS(156)*XX(48)-JVS(160)*XX(49)-JVS(165)*XX(50)-JVS(169)*XX(51)-JVS(173)& &*XX(52)-JVS(177)*XX(53)-JVS(181)*XX(54)-JVS(185)*XX(55)-JVS(191)*XX(56)-JVS(196)*XX(57)-JVS(224)*XX(60)& &-JVS(242)*XX(62)-JVS(255)*XX(63)-JVS(262)*XX(64)-JVS(271)*XX(65)-JVS(281)*XX(66)-JVS(304)*XX(67)-JVS(313)& &*XX(68)-JVS(320)*XX(69)-JVS(327)*XX(70)-JVS(335)*XX(71)-JVS(344)*XX(72)-JVS(351)*XX(73)-JVS(362)*XX(74)& &-JVS(370)*XX(75)-JVS(379)*XX(76)-JVS(400)*XX(77)-JVS(411)*XX(78)-JVS(422)*XX(79)-JVS(433)*XX(80)-JVS(459)& &*XX(81)-JVS(508)*XX(82)-JVS(521)*XX(83)-JVS(544)*XX(84)-JVS(556)*XX(85)-JVS(568)*XX(86)-JVS(585)*XX(87)& &-JVS(612)*XX(88)-JVS(633)*XX(89)-JVS(651)*XX(90)-JVS(665)*XX(91)-JVS(676)*XX(92)-JVS(689)*XX(93)-JVS(708)& &*XX(94)-JVS(748)*XX(95))/(JVS(815)) XX(97) = (X(97)-JVS(145)*XX(45)-JVS(199)*XX(58)-JVS(401)*XX(77)-JVS(509)*XX(82)-JVS(613)*XX(88)-JVS(749)*XX(95)& &-JVS(816)*XX(96))/(JVS(831)) XX(98) = (X(98)-JVS(13)*XX(7)-JVS(53)*XX(21)-JVS(66)*XX(22)-JVS(200)*XX(58)-JVS(204)*XX(59)-JVS(225)*XX(60)-JVS(233)& &*XX(61)-JVS(256)*XX(63)-JVS(336)*XX(71)-JVS(380)*XX(76)-JVS(402)*XX(77)-JVS(412)*XX(78)-JVS(423)*XX(79)& &-JVS(460)*XX(81)-JVS(510)*XX(82)-JVS(522)*XX(83)-JVS(545)*XX(84)-JVS(586)*XX(87)-JVS(614)*XX(88)-JVS(634)& &*XX(89)-JVS(652)*XX(90)-JVS(666)*XX(91)-JVS(677)*XX(92)-JVS(690)*XX(93)-JVS(709)*XX(94)-JVS(750)*XX(95)& &-JVS(817)*XX(96)-JVS(832)*XX(97))/(JVS(851)) XX(99) = (X(99)-JVS(11)*XX(6)-JVS(67)*XX(22)-JVS(78)*XX(27)-JVS(81)*XX(28)-JVS(105)*XX(34)-JVS(114)*XX(37)-JVS(118)& &*XX(38)-JVS(161)*XX(49)-JVS(201)*XX(58)-JVS(305)*XX(67)-JVS(403)*XX(77)-JVS(511)*XX(82)-JVS(615)*XX(88)& &-JVS(653)*XX(90)-JVS(710)*XX(94)-JVS(751)*XX(95)-JVS(818)*XX(96)-JVS(833)*XX(97)-JVS(852)*XX(98))/(JVS(900)) XX(100) = (X(100)-JVS(87)*XX(30)-JVS(108)*XX(35)-JVS(111)*XX(36)-JVS(119)*XX(38)-JVS(141)*XX(44)-JVS(205)*XX(59)& &-JVS(226)*XX(60)-JVS(234)*XX(61)-JVS(306)*XX(67)-JVS(321)*XX(69)-JVS(352)*XX(73)-JVS(381)*XX(76)-JVS(413)& &*XX(78)-JVS(434)*XX(80)-JVS(461)*XX(81)-JVS(512)*XX(82)-JVS(523)*XX(83)-JVS(546)*XX(84)-JVS(557)*XX(85)& &-JVS(569)*XX(86)-JVS(587)*XX(87)-JVS(616)*XX(88)-JVS(635)*XX(89)-JVS(654)*XX(90)-JVS(667)*XX(91)-JVS(678)& &*XX(92)-JVS(691)*XX(93)-JVS(711)*XX(94)-JVS(752)*XX(95)-JVS(819)*XX(96)-JVS(834)*XX(97)-JVS(853)*XX(98)& &-JVS(901)*XX(99))/(JVS(939)) XX(101) = (X(101)-JVS(54)*XX(21)-JVS(106)*XX(34)-JVS(157)*XX(48)-JVS(227)*XX(60)-JVS(243)*XX(62)-JVS(257)*XX(63)& &-JVS(263)*XX(64)-JVS(272)*XX(65)-JVS(282)*XX(66)-JVS(307)*XX(67)-JVS(314)*XX(68)-JVS(322)*XX(69)-JVS(328)& &*XX(70)-JVS(337)*XX(71)-JVS(345)*XX(72)-JVS(353)*XX(73)-JVS(363)*XX(74)-JVS(371)*XX(75)-JVS(382)*XX(76)& &-JVS(404)*XX(77)-JVS(414)*XX(78)-JVS(424)*XX(79)-JVS(435)*XX(80)-JVS(462)*XX(81)-JVS(513)*XX(82)-JVS(524)& &*XX(83)-JVS(547)*XX(84)-JVS(558)*XX(85)-JVS(570)*XX(86)-JVS(588)*XX(87)-JVS(617)*XX(88)-JVS(636)*XX(89)& &-JVS(655)*XX(90)-JVS(668)*XX(91)-JVS(679)*XX(92)-JVS(692)*XX(93)-JVS(712)*XX(94)-JVS(753)*XX(95)-JVS(820)& &*XX(96)-JVS(835)*XX(97)-JVS(854)*XX(98)-JVS(902)*XX(99)-JVS(940)*XX(100))/(JVS(981)) XX(102) = (X(102)-JVS(24)*XX(12)-JVS(27)*XX(13)-JVS(30)*XX(14)-JVS(55)*XX(21)-JVS(69)*XX(23)-JVS(71)*XX(24)-JVS(73)& &*XX(25)-JVS(75)*XX(26)-JVS(84)*XX(29)-JVS(88)*XX(30)-JVS(92)*XX(31)-JVS(97)*XX(32)-JVS(102)*XX(33)-JVS(109)& &*XX(35)-JVS(112)*XX(36)-JVS(115)*XX(37)-JVS(123)*XX(39)-JVS(127)*XX(40)-JVS(131)*XX(41)-JVS(135)*XX(42)& &-JVS(139)*XX(43)-JVS(142)*XX(44)-JVS(146)*XX(45)-JVS(150)*XX(46)-JVS(154)*XX(47)-JVS(158)*XX(48)-JVS(162)& &*XX(49)-JVS(166)*XX(50)-JVS(170)*XX(51)-JVS(174)*XX(52)-JVS(178)*XX(53)-JVS(182)*XX(54)-JVS(186)*XX(55)& &-JVS(192)*XX(56)-JVS(197)*XX(57)-JVS(202)*XX(58)-JVS(206)*XX(59)-JVS(228)*XX(60)-JVS(235)*XX(61)-JVS(244)& &*XX(62)-JVS(258)*XX(63)-JVS(273)*XX(65)-JVS(283)*XX(66)-JVS(308)*XX(67)-JVS(315)*XX(68)-JVS(338)*XX(71)& &-JVS(346)*XX(72)-JVS(354)*XX(73)-JVS(364)*XX(74)-JVS(372)*XX(75)-JVS(383)*XX(76)-JVS(405)*XX(77)-JVS(415)& &*XX(78)-JVS(425)*XX(79)-JVS(436)*XX(80)-JVS(463)*XX(81)-JVS(514)*XX(82)-JVS(525)*XX(83)-JVS(548)*XX(84)& &-JVS(559)*XX(85)-JVS(571)*XX(86)-JVS(589)*XX(87)-JVS(618)*XX(88)-JVS(637)*XX(89)-JVS(656)*XX(90)-JVS(669)& &*XX(91)-JVS(680)*XX(92)-JVS(693)*XX(93)-JVS(713)*XX(94)-JVS(754)*XX(95)-JVS(821)*XX(96)-JVS(836)*XX(97)& &-JVS(855)*XX(98)-JVS(903)*XX(99)-JVS(941)*XX(100)-JVS(982)*XX(101))/(JVS(1053)) XX(103) = (X(103)-JVS(36)*XX(16)-JVS(42)*XX(18)-JVS(48)*XX(20)-JVS(56)*XX(21)-JVS(93)*XX(31)-JVS(98)*XX(32)-JVS(103)& &*XX(33)-JVS(116)*XX(37)-JVS(229)*XX(60)-JVS(245)*XX(62)-JVS(259)*XX(63)-JVS(264)*XX(64)-JVS(274)*XX(65)& &-JVS(284)*XX(66)-JVS(309)*XX(67)-JVS(316)*XX(68)-JVS(323)*XX(69)-JVS(329)*XX(70)-JVS(339)*XX(71)-JVS(347)& &*XX(72)-JVS(355)*XX(73)-JVS(365)*XX(74)-JVS(373)*XX(75)-JVS(384)*XX(76)-JVS(406)*XX(77)-JVS(416)*XX(78)& &-JVS(426)*XX(79)-JVS(437)*XX(80)-JVS(464)*XX(81)-JVS(515)*XX(82)-JVS(526)*XX(83)-JVS(549)*XX(84)-JVS(560)& &*XX(85)-JVS(572)*XX(86)-JVS(590)*XX(87)-JVS(619)*XX(88)-JVS(638)*XX(89)-JVS(657)*XX(90)-JVS(670)*XX(91)& &-JVS(681)*XX(92)-JVS(694)*XX(93)-JVS(714)*XX(94)-JVS(755)*XX(95)-JVS(822)*XX(96)-JVS(837)*XX(97)-JVS(856)& &*XX(98)-JVS(904)*XX(99)-JVS(942)*XX(100)-JVS(983)*XX(101)-JVS(1054)*XX(102))/(JVS(1092)) XX(103) = XX(103) XX(102) = XX(102)-JVS(1091)*XX(103) XX(101) = XX(101)-JVS(1052)*XX(102)-JVS(1090)*XX(103) XX(100) = XX(100)-JVS(980)*XX(101)-JVS(1051)*XX(102)-JVS(1089)*XX(103) XX(99) = XX(99)-JVS(938)*XX(100)-JVS(979)*XX(101)-JVS(1050)*XX(102)-JVS(1088)*XX(103) XX(98) = XX(98)-JVS(899)*XX(99)-JVS(937)*XX(100)-JVS(978)*XX(101)-JVS(1049)*XX(102)-JVS(1087)*XX(103) XX(97) = XX(97)-JVS(850)*XX(98)-JVS(898)*XX(99)-JVS(936)*XX(100)-JVS(977)*XX(101)-JVS(1048)*XX(102)-JVS(1086)*XX(103) XX(96) = XX(96)-JVS(830)*XX(97)-JVS(849)*XX(98)-JVS(897)*XX(99)-JVS(935)*XX(100)-JVS(976)*XX(101)-JVS(1047)*XX(102)& &-JVS(1085)*XX(103) XX(95) = XX(95)-JVS(814)*XX(96)-JVS(829)*XX(97)-JVS(848)*XX(98)-JVS(896)*XX(99)-JVS(934)*XX(100)-JVS(975)*XX(101)& &-JVS(1046)*XX(102)-JVS(1084)*XX(103) XX(94) = XX(94)-JVS(746)*XX(95)-JVS(813)*XX(96)-JVS(847)*XX(98)-JVS(895)*XX(99)-JVS(933)*XX(100)-JVS(974)*XX(101)& &-JVS(1045)*XX(102)-JVS(1083)*XX(103) XX(93) = XX(93)-JVS(705)*XX(94)-JVS(745)*XX(95)-JVS(812)*XX(96)-JVS(828)*XX(97)-JVS(846)*XX(98)-JVS(894)*XX(99)& &-JVS(932)*XX(100)-JVS(973)*XX(101)-JVS(1044)*XX(102)-JVS(1082)*XX(103) XX(92) = XX(92)-JVS(686)*XX(93)-JVS(704)*XX(94)-JVS(744)*XX(95)-JVS(811)*XX(96)-JVS(827)*XX(97)-JVS(845)*XX(98)& &-JVS(893)*XX(99)-JVS(931)*XX(100)-JVS(972)*XX(101)-JVS(1043)*XX(102)-JVS(1081)*XX(103) XX(91) = XX(91)-JVS(703)*XX(94)-JVS(743)*XX(95)-JVS(810)*XX(96)-JVS(826)*XX(97)-JVS(844)*XX(98)-JVS(892)*XX(99)& &-JVS(930)*XX(100)-JVS(971)*XX(101)-JVS(1042)*XX(102)-JVS(1080)*XX(103) XX(90) = XX(90)-JVS(742)*XX(95)-JVS(809)*XX(96)-JVS(843)*XX(98)-JVS(891)*XX(99)-JVS(929)*XX(100)-JVS(970)*XX(101)& &-JVS(1041)*XX(102)-JVS(1079)*XX(103) XX(89) = XX(89)-JVS(645)*XX(90)-JVS(741)*XX(95)-JVS(808)*XX(96)-JVS(890)*XX(99)-JVS(928)*XX(100)-JVS(969)*XX(101)& &-JVS(1040)*XX(102)-JVS(1078)*XX(103) XX(88) = XX(88)-JVS(740)*XX(95)-JVS(807)*XX(96)-JVS(889)*XX(99)-JVS(927)*XX(100)-JVS(968)*XX(101)-JVS(1039)*XX(102) XX(87) = XX(87)-JVS(739)*XX(95)-JVS(806)*XX(96)-JVS(888)*XX(99)-JVS(926)*XX(100)-JVS(967)*XX(101)-JVS(1038)*XX(102)& &-JVS(1077)*XX(103) XX(86) = XX(86)-JVS(578)*XX(87)-JVS(605)*XX(88)-JVS(627)*XX(89)-JVS(644)*XX(90)-JVS(738)*XX(95)-JVS(805)*XX(96)& &-JVS(887)*XX(99)-JVS(925)*XX(100)-JVS(966)*XX(101)-JVS(1037)*XX(102)-JVS(1076)*XX(103) XX(85) = XX(85)-JVS(564)*XX(86)-JVS(577)*XX(87)-JVS(604)*XX(88)-JVS(626)*XX(89)-JVS(643)*XX(90)-JVS(737)*XX(95)& &-JVS(804)*XX(96)-JVS(886)*XX(99)-JVS(924)*XX(100)-JVS(965)*XX(101)-JVS(1036)*XX(102)-JVS(1075)*XX(103) XX(84) = XX(84)-JVS(736)*XX(95)-JVS(803)*XX(96)-JVS(885)*XX(99)-JVS(923)*XX(100)-JVS(964)*XX(101)-JVS(1035)*XX(102) XX(83) = XX(83)-JVS(534)*XX(84)-JVS(576)*XX(87)-JVS(603)*XX(88)-JVS(642)*XX(90)-JVS(735)*XX(95)-JVS(802)*XX(96)& &-JVS(884)*XX(99)-JVS(922)*XX(100)-JVS(963)*XX(101)-JVS(1034)*XX(102)-JVS(1074)*XX(103) XX(82) = XX(82)-JVS(801)*XX(96)-JVS(883)*XX(99)-JVS(921)*XX(100)-JVS(1033)*XX(102) XX(81) = XX(81)-JVS(575)*XX(87)-JVS(641)*XX(90)-JVS(800)*XX(96)-JVS(882)*XX(99)-JVS(920)*XX(100)-JVS(1032)*XX(102) XX(80) = XX(80)-JVS(451)*XX(81)-JVS(494)*XX(82)-JVS(602)*XX(88)-JVS(702)*XX(94)-JVS(734)*XX(95)-JVS(799)*XX(96)& &-JVS(881)*XX(99)-JVS(919)*XX(100)-JVS(962)*XX(101)-JVS(1031)*XX(102)-JVS(1073)*XX(103) XX(79) = XX(79)-JVS(493)*XX(82)-JVS(601)*XX(88)-JVS(625)*XX(89)-JVS(701)*XX(94)-JVS(733)*XX(95)-JVS(798)*XX(96)& &-JVS(880)*XX(99)-JVS(918)*XX(100)-JVS(961)*XX(101)-JVS(1030)*XX(102)-JVS(1072)*XX(103) XX(78) = XX(78)-JVS(450)*XX(81)-JVS(492)*XX(82)-JVS(661)*XX(91)-JVS(685)*XX(93)-JVS(732)*XX(95)-JVS(797)*XX(96)& &-JVS(879)*XX(99)-JVS(917)*XX(100)-JVS(960)*XX(101)-JVS(1029)*XX(102)-JVS(1071)*XX(103) XX(77) = XX(77)-JVS(491)*XX(82)-JVS(600)*XX(88)-JVS(796)*XX(96)-JVS(959)*XX(101)-JVS(1028)*XX(102) XX(76) = XX(76)-JVS(449)*XX(81)-JVS(490)*XX(82)-JVS(533)*XX(84)-JVS(731)*XX(95)-JVS(795)*XX(96)-JVS(878)*XX(99)& &-JVS(958)*XX(101)-JVS(1027)*XX(102)-JVS(1070)*XX(103) XX(75) = XX(75)-JVS(448)*XX(81)-JVS(489)*XX(82)-JVS(599)*XX(88)-JVS(624)*XX(89)-JVS(700)*XX(94)-JVS(730)*XX(95)& &-JVS(794)*XX(96)-JVS(877)*XX(99)-JVS(916)*XX(100)-JVS(957)*XX(101)-JVS(1026)*XX(102)-JVS(1069)*XX(103) XX(74) = XX(74)-JVS(390)*XX(77)-JVS(488)*XX(82)-JVS(563)*XX(86)-JVS(598)*XX(88)-JVS(623)*XX(89)-JVS(729)*XX(95)& &-JVS(793)*XX(96)-JVS(876)*XX(99)-JVS(956)*XX(101)-JVS(1068)*XX(103) XX(73) = XX(73)-JVS(487)*XX(82)-JVS(532)*XX(84)-JVS(562)*XX(86)-JVS(597)*XX(88)-JVS(622)*XX(89)-JVS(728)*XX(95)& &-JVS(792)*XX(96)-JVS(875)*XX(99)-JVS(955)*XX(101)-JVS(1067)*XX(103) XX(72) = XX(72)-JVS(389)*XX(77)-JVS(486)*XX(82)-JVS(596)*XX(88)-JVS(621)*XX(89)-JVS(727)*XX(95)-JVS(791)*XX(96)& &-JVS(874)*XX(99)-JVS(915)*XX(100)-JVS(954)*XX(101)-JVS(1025)*XX(102)-JVS(1066)*XX(103) XX(71) = XX(71)-JVS(388)*XX(77)-JVS(418)*XX(79)-JVS(485)*XX(82)-JVS(595)*XX(88)-JVS(699)*XX(94)-JVS(790)*XX(96)& &-JVS(825)*XX(97)-JVS(842)*XX(98)-JVS(1024)*XX(102) XX(70) = XX(70)-JVS(331)*XX(71)-JVS(484)*XX(82)-JVS(620)*XX(89)-JVS(660)*XX(91)-JVS(673)*XX(92)-JVS(684)*XX(93)& &-JVS(726)*XX(95)-JVS(789)*XX(96)-JVS(873)*XX(99)-JVS(914)*XX(100)-JVS(953)*XX(101)-JVS(1023)*XX(102)-JVS(1065)& &*XX(103) XX(69) = XX(69)-JVS(429)*XX(80)-JVS(447)*XX(81)-JVS(483)*XX(82)-JVS(594)*XX(88)-JVS(725)*XX(95)-JVS(788)*XX(96)& &-JVS(872)*XX(99)-JVS(952)*XX(101)-JVS(1022)*XX(102)-JVS(1064)*XX(103) XX(68) = XX(68)-JVS(446)*XX(81)-JVS(482)*XX(82)-JVS(531)*XX(84)-JVS(552)*XX(85)-JVS(561)*XX(86)-JVS(724)*XX(95)& &-JVS(787)*XX(96)-JVS(871)*XX(99)-JVS(951)*XX(101)-JVS(1063)*XX(103) XX(67) = XX(67)-JVS(870)*XX(99)-JVS(913)*XX(100)-JVS(1021)*XX(102) XX(66) = XX(66)-JVS(357)*XX(74)-JVS(481)*XX(82)-JVS(723)*XX(95)-JVS(786)*XX(96)-JVS(869)*XX(99)-JVS(950)*XX(101)& &-JVS(1020)*XX(102)-JVS(1062)*XX(103) XX(65) = XX(65)-JVS(445)*XX(81)-JVS(480)*XX(82)-JVS(722)*XX(95)-JVS(785)*XX(96)-JVS(868)*XX(99)-JVS(949)*XX(101)& &-JVS(1019)*XX(102)-JVS(1061)*XX(103) XX(64) = XX(64)-JVS(289)*XX(67)-JVS(428)*XX(80)-JVS(444)*XX(81)-JVS(479)*XX(82)-JVS(593)*XX(88)-JVS(698)*XX(94)& &-JVS(721)*XX(95)-JVS(784)*XX(96)-JVS(867)*XX(99)-JVS(948)*XX(101)-JVS(1018)*XX(102)-JVS(1060)*XX(103) XX(63) = XX(63)-JVS(478)*XX(82)-JVS(697)*XX(94)-JVS(783)*XX(96)-JVS(1017)*XX(102) XX(62) = XX(62)-JVS(356)*XX(74)-JVS(720)*XX(95)-JVS(782)*XX(96)-JVS(947)*XX(101)-JVS(1016)*XX(102) XX(61) = XX(61)-JVS(375)*XX(76)-JVS(477)*XX(82)-JVS(517)*XX(83)-JVS(530)*XX(84)-JVS(719)*XX(95)-JVS(781)*XX(96)& &-JVS(841)*XX(98)-JVS(912)*XX(100)-JVS(1015)*XX(102) XX(60) = XX(60)-JVS(780)*XX(96)-JVS(1014)*XX(102) XX(59) = XX(59)-JVS(209)*XX(60)-JVS(230)*XX(61)-JVS(408)*XX(78)-JVS(476)*XX(82)-JVS(659)*XX(91)-JVS(672)*XX(92)& &-JVS(683)*XX(93)-JVS(779)*XX(96)-JVS(840)*XX(98)-JVS(911)*XX(100)-JVS(1013)*XX(102) XX(58) = XX(58)-JVS(387)*XX(77)-JVS(475)*XX(82)-JVS(778)*XX(96)-JVS(824)*XX(97)-JVS(839)*XX(98)-JVS(866)*XX(99)& &-JVS(1012)*XX(102) XX(57) = XX(57)-JVS(330)*XX(71)-JVS(474)*XX(82)-JVS(658)*XX(91)-JVS(671)*XX(92)-JVS(682)*XX(93)-JVS(777)*XX(96)& &-JVS(1011)*XX(102) XX(56) = XX(56)-JVS(427)*XX(80)-JVS(443)*XX(81)-JVS(776)*XX(96)-JVS(865)*XX(99)-JVS(1010)*XX(102) XX(55) = XX(55)-JVS(247)*XX(63)-JVS(366)*XX(75)-JVS(442)*XX(81)-JVS(473)*XX(82)-JVS(592)*XX(88)-JVS(775)*XX(96)& &-JVS(946)*XX(101)-JVS(1009)*XX(102) XX(54) = XX(54)-JVS(208)*XX(60)-JVS(246)*XX(63)-JVS(386)*XX(77)-JVS(417)*XX(79)-JVS(591)*XX(88)-JVS(774)*XX(96)& &-JVS(1008)*XX(102) XX(53) = XX(53)-JVS(207)*XX(60)-JVS(340)*XX(72)-JVS(385)*XX(77)-JVS(472)*XX(82)-JVS(773)*XX(96)-JVS(1007)*XX(102) XX(52) = XX(52)-JVS(407)*XX(78)-JVS(441)*XX(81)-JVS(772)*XX(96)-JVS(864)*XX(99)-JVS(1006)*XX(102) XX(51) = XX(51)-JVS(374)*XX(76)-JVS(440)*XX(81)-JVS(771)*XX(96)-JVS(863)*XX(99)-JVS(1005)*XX(102) XX(50) = XX(50)-JVS(471)*XX(82)-JVS(516)*XX(83)-JVS(529)*XX(84)-JVS(770)*XX(96)-JVS(1004)*XX(102) XX(49) = XX(49)-JVS(769)*XX(96)-JVS(862)*XX(99)-JVS(910)*XX(100)-JVS(1003)*XX(102) XX(48) = XX(48)-JVS(470)*XX(82)-JVS(718)*XX(95)-JVS(945)*XX(101)-JVS(1002)*XX(102) XX(47) = XX(47)-JVS(469)*XX(82)-JVS(696)*XX(94)-JVS(768)*XX(96)-JVS(1001)*XX(102) XX(46) = XX(46)-JVS(528)*XX(84)-JVS(574)*XX(87)-JVS(767)*XX(96)-JVS(1000)*XX(102) XX(45) = XX(45)-JVS(468)*XX(82)-JVS(823)*XX(97)-JVS(944)*XX(101)-JVS(999)*XX(102) XX(44) = XX(44)-JVS(288)*XX(67)-JVS(467)*XX(82)-JVS(717)*XX(95)-JVS(766)*XX(96)-JVS(909)*XX(100)-JVS(998)*XX(102) XX(43) = XX(43)-JVS(527)*XX(84)-JVS(640)*XX(90)-JVS(765)*XX(96)-JVS(997)*XX(102) XX(42) = XX(42)-JVS(236)*XX(62)-JVS(276)*XX(66)-JVS(764)*XX(96)-JVS(996)*XX(102) XX(41) = XX(41)-JVS(266)*XX(65)-JVS(439)*XX(81)-JVS(763)*XX(96)-JVS(995)*XX(102) XX(40) = XX(40)-JVS(438)*XX(81)-JVS(551)*XX(85)-JVS(762)*XX(96)-JVS(994)*XX(102) XX(39) = XX(39)-JVS(466)*XX(82)-JVS(716)*XX(95)-JVS(761)*XX(96)-JVS(993)*XX(102) XX(38) = XX(38)-JVS(287)*XX(67)-JVS(838)*XX(98)-JVS(861)*XX(99)-JVS(908)*XX(100)-JVS(1059)*XX(103) XX(37) = XX(37)-JVS(860)*XX(99)-JVS(992)*XX(102)-JVS(1058)*XX(103) XX(36) = XX(36)-JVS(286)*XX(67)-JVS(573)*XX(87)-JVS(907)*XX(100)-JVS(991)*XX(102) XX(35) = XX(35)-JVS(285)*XX(67)-JVS(550)*XX(85)-JVS(906)*XX(100)-JVS(990)*XX(102) XX(34) = XX(34)-JVS(715)*XX(95)-JVS(859)*XX(99)-JVS(905)*XX(100)-JVS(943)*XX(101) XX(33) = XX(33)-JVS(760)*XX(96)-JVS(1057)*XX(103) XX(32) = XX(32)-JVS(759)*XX(96)-JVS(1056)*XX(103) XX(31) = XX(31)-JVS(758)*XX(96)-JVS(1055)*XX(103) XX(30) = XX(30)-JVS(757)*XX(96)-JVS(989)*XX(102) XX(29) = XX(29)-JVS(756)*XX(96)-JVS(988)*XX(102) XX(28) = XX(28)-JVS(695)*XX(94)-JVS(858)*XX(99) XX(27) = XX(27)-JVS(639)*XX(90)-JVS(857)*XX(99) XX(26) = XX(26)-JVS(265)*XX(65)-JVS(275)*XX(66)-JVS(987)*XX(102) XX(25) = XX(25)-JVS(89)*XX(31)-JVS(986)*XX(102) XX(24) = XX(24)-JVS(99)*XX(33)-JVS(985)*XX(102) XX(23) = XX(23)-JVS(94)*XX(32)-JVS(984)*XX(102) XX(22) = XX(22) XX(21) = XX(21) XX(20) = XX(20) XX(19) = XX(19) XX(18) = XX(18) XX(17) = XX(17) XX(16) = XX(16) XX(15) = XX(15) XX(14) = XX(14) XX(13) = XX(13) XX(12) = XX(12) XX(11) = XX(11) XX(10) = XX(10) XX(9) = XX(9) XX(8) = XX(8) XX(7) = XX(7) XX(6) = XX(6) XX(5) = XX(5) XX(4) = XX(4) XX(3) = XX(3) XX(2) = XX(2) XX(1) = XX(1)-JVS(465)*XX(82) END SUBROUTINE KppSolveTR ! End of KppSolveTR function ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! ! BLAS_UTIL - BLAS-LIKE utility functions ! Arguments : ! ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ !-------------------------------------------------------------- ! ! BLAS/LAPACK-like subroutines used by the integration algorithms ! It is recommended to replace them by calls to the optimized ! BLAS/LAPACK library for your machine ! ! (C) Adrian Sandu, Aug. 2004 ! Virginia Polytechnic Institute and State University !-------------------------------------------------------------- !-------------------------------------------------------------- SUBROUTINE WCOPY(N,X,incX,Y,incY) !-------------------------------------------------------------- ! copies a vector, x, to a vector, y: y <- x ! only for incX=incY=1 ! after BLAS ! replace this by the function from the optimized BLAS implementation: ! CALL SCOPY(N,X,1,Y,1) or CALL DCOPY(N,X,1,Y,1) !-------------------------------------------------------------- ! USE gckpp_Precision INTEGER :: i,incX,incY,M,MP1,N REAL(kind=dp) :: X(N),Y(N) IF (N.LE.0) RETURN M = MOD(N,8) IF( M .NE. 0 ) THEN DO i = 1,M Y(i) = X(i) END DO IF( N .LT. 8 ) RETURN END IF MP1 = M+1 DO i = MP1,N,8 Y(i) = X(i) Y(i + 1) = X(i + 1) Y(i + 2) = X(i + 2) Y(i + 3) = X(i + 3) Y(i + 4) = X(i + 4) Y(i + 5) = X(i + 5) Y(i + 6) = X(i + 6) Y(i + 7) = X(i + 7) END DO END SUBROUTINE WCOPY !-------------------------------------------------------------- SUBROUTINE WAXPY(N,Alpha,X,incX,Y,incY) !-------------------------------------------------------------- ! constant times a vector plus a vector: y <- y + Alpha*x ! only for incX=incY=1 ! after BLAS ! replace this by the function from the optimized BLAS implementation: ! CALL SAXPY(N,Alpha,X,1,Y,1) or CALL DAXPY(N,Alpha,X,1,Y,1) !-------------------------------------------------------------- INTEGER :: i,incX,incY,M,MP1,N REAL(kind=dp) :: X(N),Y(N),Alpha REAL(kind=dp), PARAMETER :: ZERO = 0.0_dp IF (Alpha .EQ. ZERO) RETURN IF (N .LE. 0) RETURN M = MOD(N,4) IF( M .NE. 0 ) THEN DO i = 1,M Y(i) = Y(i) + Alpha*X(i) END DO IF( N .LT. 4 ) RETURN END IF MP1 = M + 1 DO i = MP1,N,4 Y(i) = Y(i) + Alpha*X(i) Y(i + 1) = Y(i + 1) + Alpha*X(i + 1) Y(i + 2) = Y(i + 2) + Alpha*X(i + 2) Y(i + 3) = Y(i + 3) + Alpha*X(i + 3) END DO END SUBROUTINE WAXPY !-------------------------------------------------------------- SUBROUTINE WSCAL(N,Alpha,X,incX) !-------------------------------------------------------------- ! constant times a vector: x(1:N) <- Alpha*x(1:N) ! only for incX=incY=1 ! after BLAS ! replace this by the function from the optimized BLAS implementation: ! CALL SSCAL(N,Alpha,X,1) or CALL DSCAL(N,Alpha,X,1) !-------------------------------------------------------------- INTEGER :: i,incX,M,MP1,N REAL(kind=dp) :: X(N),Alpha REAL(kind=dp), PARAMETER :: ZERO=0.0_dp, ONE=1.0_dp IF (Alpha .EQ. ONE) RETURN IF (N .LE. 0) RETURN M = MOD(N,5) IF( M .NE. 0 ) THEN IF (Alpha .EQ. (-ONE)) THEN DO i = 1,M X(i) = -X(i) END DO ELSEIF (Alpha .EQ. ZERO) THEN DO i = 1,M X(i) = ZERO END DO ELSE DO i = 1,M X(i) = Alpha*X(i) END DO END IF IF( N .LT. 5 ) RETURN END IF MP1 = M + 1 IF (Alpha .EQ. (-ONE)) THEN DO i = MP1,N,5 X(i) = -X(i) X(i + 1) = -X(i + 1) X(i + 2) = -X(i + 2) X(i + 3) = -X(i + 3) X(i + 4) = -X(i + 4) END DO ELSEIF (Alpha .EQ. ZERO) THEN DO i = MP1,N,5 X(i) = ZERO X(i + 1) = ZERO X(i + 2) = ZERO X(i + 3) = ZERO X(i + 4) = ZERO END DO ELSE DO i = MP1,N,5 X(i) = Alpha*X(i) X(i + 1) = Alpha*X(i + 1) X(i + 2) = Alpha*X(i + 2) X(i + 3) = Alpha*X(i + 3) X(i + 4) = Alpha*X(i + 4) END DO END IF END SUBROUTINE WSCAL !-------------------------------------------------------------- REAL(kind=dp) FUNCTION WLAMCH( C ) !-------------------------------------------------------------- ! returns epsilon machine ! after LAPACK ! replace this by the function from the optimized LAPACK implementation: ! CALL SLAMCH('E') or CALL DLAMCH('E') !-------------------------------------------------------------- ! USE gckpp_Precision CHARACTER :: C INTEGER :: i REAL(kind=dp), SAVE :: Eps REAL(kind=dp) :: Suma REAL(kind=dp), PARAMETER :: ONE=1.0_dp, HALF=0.5_dp LOGICAL, SAVE :: First=.TRUE. !$OMP THREADPRIVATE( Eps, First ) IF (First) THEN First = .FALSE. Eps = HALF**(16) DO i = 17, 80 Eps = Eps*HALF CALL WLAMCH_ADD(ONE,Eps,Suma) IF (Suma.LE.ONE) GOTO 10 END DO PRINT*,'ERROR IN WLAMCH. EPS < ',Eps RETURN 10 Eps = Eps*2 i = i-1 END IF WLAMCH = Eps END FUNCTION WLAMCH SUBROUTINE WLAMCH_ADD( A, B, Suma ) ! USE gckpp_Precision REAL(kind=dp) A, B, Suma Suma = A + B END SUBROUTINE WLAMCH_ADD !-------------------------------------------------------------- !-------------------------------------------------------------- SUBROUTINE SET2ZERO(N,Y) !-------------------------------------------------------------- ! copies zeros into the vector y: y <- 0 ! after BLAS !-------------------------------------------------------------- INTEGER :: i,M,MP1,N REAL(kind=dp) :: Y(N) REAL(kind=dp), PARAMETER :: ZERO = 0.0d0 IF (N.LE.0) RETURN M = MOD(N,8) IF( M .NE. 0 ) THEN DO i = 1,M Y(i) = ZERO END DO IF( N .LT. 8 ) RETURN END IF MP1 = M+1 DO i = MP1,N,8 Y(i) = ZERO Y(i + 1) = ZERO Y(i + 2) = ZERO Y(i + 3) = ZERO Y(i + 4) = ZERO Y(i + 5) = ZERO Y(i + 6) = ZERO Y(i + 7) = ZERO END DO END SUBROUTINE SET2ZERO !-------------------------------------------------------------- REAL(kind=dp) FUNCTION WDOT (N, DX, incX, DY, incY) !-------------------------------------------------------------- ! dot produce: wdot = x(1:N)*y(1:N) ! only for incX=incY=1 ! after BLAS ! replace this by the function from the optimized BLAS implementation: ! CALL SDOT(N,X,1,Y,1) or CALL DDOT(N,X,1,Y,1) !-------------------------------------------------------------- ! USE messy_mecca_kpp_Precision !-------------------------------------------------------------- IMPLICIT NONE INTEGER :: N, incX, incY REAL(kind=dp) :: DX(N), DY(N) INTEGER :: i, IX, IY, M, MP1, NS WDOT = 0.0D0 IF (N .LE. 0) RETURN IF (incX .EQ. incY) IF (incX-1) 5,20,60 ! ! Code for unequal or nonpositive increments. ! 5 IX = 1 IY = 1 IF (incX .LT. 0) IX = (-N+1)*incX + 1 IF (incY .LT. 0) IY = (-N+1)*incY + 1 DO i = 1,N WDOT = WDOT + DX(IX)*DY(IY) IX = IX + incX IY = IY + incY END DO RETURN ! ! Code for both increments equal to 1. ! ! Clean-up loop so remaining vector length is a multiple of 5. ! 20 M = MOD(N,5) IF (M .EQ. 0) GO TO 40 DO i = 1,M WDOT = WDOT + DX(i)*DY(i) END DO IF (N .LT. 5) RETURN 40 MP1 = M + 1 DO i = MP1,N,5 WDOT = WDOT + DX(i)*DY(i) + DX(i+1)*DY(i+1) + DX(i+2)*DY(i+2) + & DX(i+3)*DY(i+3) + DX(i+4)*DY(i+4) END DO RETURN ! ! Code for equal, positive, non-unit increments. ! 60 NS = N*incX DO i = 1,NS,incX WDOT = WDOT + DX(i)*DY(i) END DO END FUNCTION WDOT !-------------------------------------------------------------- SUBROUTINE WADD(N,X,Y,Z) !-------------------------------------------------------------- ! adds two vectors: z <- x + y ! BLAS - like !-------------------------------------------------------------- ! USE gckpp_Precision INTEGER :: i, M, MP1, N REAL(kind=dp) :: X(N),Y(N),Z(N) IF (N.LE.0) RETURN M = MOD(N,5) IF( M /= 0 ) THEN DO i = 1,M Z(i) = X(i) + Y(i) END DO IF( N < 5 ) RETURN END IF MP1 = M+1 DO i = MP1,N,5 Z(i) = X(i) + Y(i) Z(i + 1) = X(i + 1) + Y(i + 1) Z(i + 2) = X(i + 2) + Y(i + 2) Z(i + 3) = X(i + 3) + Y(i + 3) Z(i + 4) = X(i + 4) + Y(i + 4) END DO END SUBROUTINE WADD !-------------------------------------------------------------- SUBROUTINE WGEFA(N,A,Ipvt,info) !-------------------------------------------------------------- ! WGEFA FACTORS THE MATRIX A (N,N) BY ! GAUSS ELIMINATION WITH PARTIAL PIVOTING ! LINPACK - LIKE !-------------------------------------------------------------- ! INTEGER :: N,Ipvt(N),info REAL(kind=dp) :: A(N,N) REAL(kind=dp) :: t, dmax, da INTEGER :: j,k,l REAL(kind=dp), PARAMETER :: ZERO = 0.0, ONE = 1.0 info = 0 size: IF (n > 1) THEN col: DO k = 1, n-1 ! find l = pivot index ! l = idamax(n-k+1,A(k,k),1) + k - 1 l = k; dmax = abs(A(k,k)) DO j = k+1,n da = ABS(A(j,k)) IF (da > dmax) THEN l = j; dmax = da END IF END DO Ipvt(k) = l ! zero pivot implies this column already triangularized IF (ABS(A(l,k)) < TINY(ZERO)) THEN info = k return ELSE IF (l /= k) THEN t = A(l,k); A(l,k) = A(k,k); A(k,k) = t END IF t = -ONE/A(k,k) CALL WSCAL(n-k,t,A(k+1,k),1) DO j = k+1, n t = A(l,j) IF (l /= k) THEN A(l,j) = A(k,j); A(k,j) = t END IF CALL WAXPY(n-k,t,A(k+1,k),1,A(k+1,j),1) END DO END IF END DO col END IF size Ipvt(N) = N IF (ABS(A(N,N)) == ZERO) info = N END SUBROUTINE WGEFA !-------------------------------------------------------------- SUBROUTINE WGESL(Trans,N,A,Ipvt,b) !-------------------------------------------------------------- ! WGESL solves the system ! a * x = b or trans(a) * x = b ! using the factors computed by WGEFA. ! ! Trans = 'N' to solve A*x = b , ! = 'T' to solve transpose(A)*x = b ! LINPACK - LIKE !-------------------------------------------------------------- INTEGER :: N,Ipvt(N) CHARACTER :: trans REAL(kind=dp) :: A(N,N),b(N) REAL(kind=dp) :: t INTEGER :: k,kb,l SELECT CASE (Trans) CASE ('n','N') ! Solve A * x = b ! first solve L*y = b IF (n >= 2) THEN DO k = 1, n-1 l = Ipvt(k) t = b(l) IF (l /= k) THEN b(l) = b(k) b(k) = t END IF CALL WAXPY(n-k,t,a(k+1,k),1,b(k+1),1) END DO END IF ! now solve U*x = y DO kb = 1, n k = n + 1 - kb b(k) = b(k)/a(k,k) t = -b(k) CALL WAXPY(k-1,t,a(1,k),1,b(1),1) END DO CASE ('t','T') ! Solve transpose(A) * x = b ! first solve trans(U)*y = b DO k = 1, n t = WDOT(k-1,a(1,k),1,b(1),1) b(k) = (b(k) - t)/a(k,k) END DO ! now solve trans(L)*x = y IF (n >= 2) THEN DO kb = 1, n-1 k = n - kb b(k) = b(k) + WDOT(n-k,a(k+1,k),1,b(k+1),1) l = Ipvt(k) IF (l /= k) THEN t = b(l); b(l) = b(k); b(k) = t END IF END DO END IF END SELECT END SUBROUTINE WGESL ! End of BLAS_UTIL function ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ END MODULE gckpp_LinearAlgebra