! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ! ! 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 15:20:39 2010 ! Working directory : /mnt/lstr04/srv/home/c/ccarouge/KPP/geoschem_kppfiles/v8-03-02/standard ! 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(47) = X(47)-JVS(167)*X(40)-JVS(168)*X(41)-JVS(169)*X(46) X(48) = X(48)-JVS(190)*X(46) X(49) = X(49)-JVS(196)*X(32) X(50) = X(50)-JVS(206)*X(41)-JVS(207)*X(42) X(52) = X(52)-JVS(225)*X(16)-JVS(226)*X(31) X(53) = X(53)-JVS(235)*X(16)-JVS(236)*X(32) X(54) = X(54)-JVS(245)*X(22)-JVS(246)*X(23)-JVS(247)*X(25)-JVS(248)*X(34)-JVS(249)*X(51) X(58) = X(58)-JVS(290)*X(45)-JVS(291)*X(57) X(59) = X(59)-JVS(300)*X(40) X(61) = X(61)-JVS(316)*X(40)-JVS(317)*X(41)-JVS(318)*X(44)-JVS(319)*X(58)-JVS(320)*X(59) X(62) = X(62)-JVS(336)*X(49)-JVS(337)*X(53) X(63) = X(63)-JVS(346)*X(38)-JVS(347)*X(48) X(64) = X(64)-JVS(357)*X(42) X(65) = X(65)-JVS(365)*X(43)-JVS(366)*X(51)-JVS(367)*X(56) X(66) = X(66)-JVS(376)*X(41)-JVS(377)*X(58) X(67) = X(67)-JVS(386)*X(39)-JVS(387)*X(46) X(68) = X(68)-JVS(396)*X(30)-JVS(397)*X(31)-JVS(398)*X(38)-JVS(399)*X(39)-JVS(400)*X(42)-JVS(401)*X(43)-JVS(402)*X(51)& &-JVS(403)*X(52)-JVS(404)*X(55)-JVS(405)*X(56)-JVS(406)*X(63)-JVS(407)*X(64)-JVS(408)*X(65)-JVS(409)*X(67) X(69) = X(69)-JVS(423)*X(26)-JVS(424)*X(27)-JVS(425)*X(28)-JVS(426)*X(34)-JVS(427)*X(36)-JVS(428)*X(37)-JVS(429)*X(40)& &-JVS(430)*X(42)-JVS(431)*X(44)-JVS(432)*X(45)-JVS(433)*X(46)-JVS(434)*X(48)-JVS(435)*X(50)-JVS(436)*X(51)& &-JVS(437)*X(52)-JVS(438)*X(53)-JVS(439)*X(55)-JVS(440)*X(56)-JVS(441)*X(57)-JVS(442)*X(58)-JVS(443)*X(59)& &-JVS(444)*X(60)-JVS(445)*X(61)-JVS(446)*X(62)-JVS(447)*X(63)-JVS(448)*X(64)-JVS(449)*X(65)-JVS(450)*X(66)& &-JVS(451)*X(67) X(70) = X(70)-JVS(473)*X(37)-JVS(474)*X(48) X(71) = X(71)-JVS(484)*X(33)-JVS(485)*X(35)-JVS(486)*X(37)-JVS(487)*X(48)-JVS(488)*X(55)-JVS(489)*X(60)-JVS(490)*X(63)& &-JVS(491)*X(70) X(72) = X(72)-JVS(507)*X(22)-JVS(508)*X(30)-JVS(509)*X(55) X(73) = X(73)-JVS(518)*X(55)-JVS(519)*X(60)-JVS(520)*X(62)-JVS(521)*X(72) X(74) = X(74)-JVS(530)*X(23)-JVS(531)*X(35)-JVS(532)*X(68)-JVS(533)*X(70)-JVS(534)*X(72)-JVS(535)*X(73) X(75) = X(75)-JVS(548)*X(41)-JVS(549)*X(42)-JVS(550)*X(51)-JVS(551)*X(56)-JVS(552)*X(58)-JVS(553)*X(59)-JVS(554)*X(60)& &-JVS(555)*X(61)-JVS(556)*X(62)-JVS(557)*X(64)-JVS(558)*X(65)-JVS(559)*X(66)-JVS(560)*X(70)-JVS(561)*X(72)& &-JVS(562)*X(73) X(76) = X(76)-JVS(577)*X(57)-JVS(578)*X(59)-JVS(579)*X(60)-JVS(580)*X(62)-JVS(581)*X(64)-JVS(582)*X(66)-JVS(583)*X(72)& &-JVS(584)*X(73) X(77) = X(77)-JVS(596)*X(45)-JVS(597)*X(46)-JVS(598)*X(57)-JVS(599)*X(67) X(78) = X(78)-JVS(609)*X(26)-JVS(610)*X(44)-JVS(611)*X(58)-JVS(612)*X(77) X(79) = X(79)-JVS(624)*X(45)-JVS(625)*X(46)-JVS(626)*X(57) X(80) = X(80)-JVS(635)*X(45)-JVS(636)*X(46)-JVS(637)*X(57)-JVS(638)*X(67)-JVS(639)*X(79) X(81) = X(81)-JVS(648)*X(18)-JVS(649)*X(33)-JVS(650)*X(68)-JVS(651)*X(70)-JVS(652)*X(72)-JVS(653)*X(73)-JVS(654)*X(76)& &-JVS(655)*X(77)-JVS(656)*X(79)-JVS(657)*X(80) X(82) = X(82)-JVS(667)*X(18)-JVS(668)*X(19)-JVS(669)*X(21)-JVS(670)*X(24)-JVS(671)*X(25)-JVS(672)*X(29)-JVS(673)*X(38)& &-JVS(674)*X(39)-JVS(675)*X(43)-JVS(676)*X(44)-JVS(677)*X(51)-JVS(678)*X(52)-JVS(679)*X(53)-JVS(680)*X(54)& &-JVS(681)*X(55)-JVS(682)*X(56)-JVS(683)*X(57)-JVS(684)*X(59)-JVS(685)*X(60)-JVS(686)*X(62)-JVS(687)*X(63)& &-JVS(688)*X(64)-JVS(689)*X(65)-JVS(690)*X(66)-JVS(691)*X(67)-JVS(692)*X(68)-JVS(693)*X(69)-JVS(694)*X(70)& &-JVS(695)*X(71)-JVS(696)*X(72)-JVS(697)*X(73)-JVS(698)*X(74)-JVS(699)*X(75)-JVS(700)*X(76)-JVS(701)*X(77)& &-JVS(702)*X(78)-JVS(703)*X(79)-JVS(704)*X(80)-JVS(705)*X(81) X(83) = X(83)-JVS(715)*X(21)-JVS(716)*X(26)-JVS(717)*X(27)-JVS(718)*X(42)-JVS(719)*X(49)-JVS(720)*X(51)-JVS(721)*X(52)& &-JVS(722)*X(53)-JVS(723)*X(55)-JVS(724)*X(56)-JVS(725)*X(57)-JVS(726)*X(59)-JVS(727)*X(60)-JVS(728)*X(61)& &-JVS(729)*X(62)-JVS(730)*X(63)-JVS(731)*X(64)-JVS(732)*X(65)-JVS(733)*X(66)-JVS(734)*X(67)-JVS(735)*X(70)& &-JVS(736)*X(71)-JVS(737)*X(72)-JVS(738)*X(73)-JVS(739)*X(74)-JVS(740)*X(75)-JVS(741)*X(76)-JVS(742)*X(77)& &-JVS(743)*X(78)-JVS(744)*X(79)-JVS(745)*X(80)-JVS(746)*X(81)-JVS(747)*X(82) X(84) = X(84)-JVS(756)*X(17)-JVS(757)*X(20)-JVS(758)*X(28)-JVS(759)*X(29)-JVS(760)*X(30)-JVS(761)*X(31)-JVS(762)*X(32)& &-JVS(763)*X(33)-JVS(764)*X(34)-JVS(765)*X(35)-JVS(766)*X(36)-JVS(767)*X(37)-JVS(768)*X(38)-JVS(769)*X(39)& &-JVS(770)*X(40)-JVS(771)*X(41)-JVS(772)*X(42)-JVS(773)*X(43)-JVS(774)*X(44)-JVS(775)*X(45)-JVS(776)*X(46)& &-JVS(777)*X(47)-JVS(778)*X(48)-JVS(779)*X(49)-JVS(780)*X(50)-JVS(781)*X(51)-JVS(782)*X(52)-JVS(783)*X(53)& &-JVS(784)*X(55)-JVS(785)*X(56)-JVS(786)*X(57)-JVS(787)*X(58)-JVS(788)*X(59)-JVS(789)*X(60)-JVS(790)*X(61)& &-JVS(791)*X(62)-JVS(792)*X(63)-JVS(793)*X(64)-JVS(794)*X(65)-JVS(795)*X(66)-JVS(796)*X(67)-JVS(797)*X(68)& &-JVS(798)*X(69)-JVS(799)*X(70)-JVS(800)*X(71)-JVS(801)*X(72)-JVS(802)*X(73)-JVS(803)*X(74)-JVS(804)*X(75)& &-JVS(805)*X(76)-JVS(806)*X(77)-JVS(807)*X(78)-JVS(808)*X(79)-JVS(809)*X(80)-JVS(810)*X(81)-JVS(811)*X(82)& &-JVS(812)*X(83) X(85) = X(85)-JVS(820)*X(24)-JVS(821)*X(25)-JVS(822)*X(51)-JVS(823)*X(52)-JVS(824)*X(53)-JVS(825)*X(55)-JVS(826)*X(56)& &-JVS(827)*X(57)-JVS(828)*X(59)-JVS(829)*X(60)-JVS(830)*X(62)-JVS(831)*X(63)-JVS(832)*X(64)-JVS(833)*X(65)& &-JVS(834)*X(66)-JVS(835)*X(67)-JVS(836)*X(70)-JVS(837)*X(72)-JVS(838)*X(73)-JVS(839)*X(74)-JVS(840)*X(76)& &-JVS(841)*X(77)-JVS(842)*X(78)-JVS(843)*X(79)-JVS(844)*X(80)-JVS(845)*X(81)-JVS(846)*X(82)-JVS(847)*X(83)& &-JVS(848)*X(84) X(86) = X(86)-JVS(855)*X(21)-JVS(856)*X(27)-JVS(857)*X(28)-JVS(858)*X(34)-JVS(859)*X(48)-JVS(860)*X(49)-JVS(861)*X(51)& &-JVS(862)*X(52)-JVS(863)*X(53)-JVS(864)*X(55)-JVS(865)*X(56)-JVS(866)*X(57)-JVS(867)*X(59)-JVS(868)*X(60)& &-JVS(869)*X(62)-JVS(870)*X(63)-JVS(871)*X(64)-JVS(872)*X(65)-JVS(873)*X(66)-JVS(874)*X(67)-JVS(875)*X(70)& &-JVS(876)*X(71)-JVS(877)*X(72)-JVS(878)*X(73)-JVS(879)*X(74)-JVS(880)*X(75)-JVS(881)*X(76)-JVS(882)*X(77)& &-JVS(883)*X(78)-JVS(884)*X(79)-JVS(885)*X(80)-JVS(886)*X(81)-JVS(887)*X(82)-JVS(888)*X(83)-JVS(889)*X(84)& &-JVS(890)*X(85) X(87) = X(87)-JVS(896)*X(21)-JVS(897)*X(22)-JVS(898)*X(23)-JVS(899)*X(25)-JVS(900)*X(29)-JVS(901)*X(34)-JVS(902)*X(46)& &-JVS(903)*X(48)-JVS(904)*X(54)-JVS(905)*X(57)-JVS(906)*X(59)-JVS(907)*X(64)-JVS(908)*X(65)-JVS(909)*X(66)& &-JVS(910)*X(67)-JVS(911)*X(68)-JVS(912)*X(69)-JVS(913)*X(70)-JVS(914)*X(71)-JVS(915)*X(72)-JVS(916)*X(73)& &-JVS(917)*X(74)-JVS(918)*X(75)-JVS(919)*X(76)-JVS(920)*X(77)-JVS(921)*X(78)-JVS(922)*X(79)-JVS(923)*X(80)& &-JVS(924)*X(81)-JVS(925)*X(82)-JVS(926)*X(83)-JVS(927)*X(84)-JVS(928)*X(85)-JVS(929)*X(86) X(88) = X(88)-JVS(934)*X(19)-JVS(935)*X(36)-JVS(936)*X(50)-JVS(937)*X(51)-JVS(938)*X(58)-JVS(939)*X(64)-JVS(940)*X(65)& &-JVS(941)*X(66)-JVS(942)*X(77)-JVS(943)*X(79)-JVS(944)*X(80)-JVS(945)*X(82)-JVS(946)*X(83)-JVS(947)*X(84)& &-JVS(948)*X(85)-JVS(949)*X(86)-JVS(950)*X(87) X(89) = X(89)-JVS(954)*X(25)-JVS(955)*X(44)-JVS(956)*X(46)-JVS(957)*X(48)-JVS(958)*X(58)-JVS(959)*X(77)-JVS(960)*X(78)& &-JVS(961)*X(79)-JVS(962)*X(80)-JVS(963)*X(81)-JVS(964)*X(82)-JVS(965)*X(83)-JVS(966)*X(84)-JVS(967)*X(85)& &-JVS(968)*X(86)-JVS(969)*X(87)-JVS(970)*X(88) X(90) = X(90)-JVS(973)*X(16)-JVS(974)*X(17)-JVS(975)*X(20)-JVS(976)*X(22)-JVS(977)*X(23)-JVS(978)*X(24)-JVS(979)*X(26)& &-JVS(980)*X(27)-JVS(981)*X(28)-JVS(982)*X(29)-JVS(983)*X(30)-JVS(984)*X(31)-JVS(985)*X(32)-JVS(986)*X(33)& &-JVS(987)*X(34)-JVS(988)*X(35)-JVS(989)*X(36)-JVS(990)*X(37)-JVS(991)*X(38)-JVS(992)*X(39)-JVS(993)*X(40)& &-JVS(994)*X(41)-JVS(995)*X(42)-JVS(996)*X(43)-JVS(997)*X(44)-JVS(998)*X(45)-JVS(999)*X(46)-JVS(1000)*X(47)& &-JVS(1001)*X(48)-JVS(1002)*X(49)-JVS(1003)*X(50)-JVS(1004)*X(51)-JVS(1005)*X(52)-JVS(1006)*X(53)-JVS(1007)& &*X(54)-JVS(1008)*X(56)-JVS(1009)*X(57)-JVS(1010)*X(58)-JVS(1011)*X(59)-JVS(1012)*X(61)-JVS(1013)*X(62)& &-JVS(1014)*X(63)-JVS(1015)*X(64)-JVS(1016)*X(65)-JVS(1017)*X(66)-JVS(1018)*X(67)-JVS(1019)*X(68)-JVS(1020)& &*X(69)-JVS(1021)*X(70)-JVS(1022)*X(71)-JVS(1023)*X(72)-JVS(1024)*X(73)-JVS(1025)*X(74)-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) X(90) = X(90)/JVS(1041) X(89) = (X(89)-JVS(972)*X(90))/(JVS(971)) X(88) = (X(88)-JVS(952)*X(89)-JVS(953)*X(90))/(JVS(951)) X(87) = (X(87)-JVS(931)*X(88)-JVS(932)*X(89)-JVS(933)*X(90))/(JVS(930)) X(86) = (X(86)-JVS(892)*X(87)-JVS(893)*X(88)-JVS(894)*X(89)-JVS(895)*X(90))/(JVS(891)) X(85) = (X(85)-JVS(850)*X(86)-JVS(851)*X(87)-JVS(852)*X(88)-JVS(853)*X(89)-JVS(854)*X(90))/(JVS(849)) X(84) = (X(84)-JVS(814)*X(85)-JVS(815)*X(86)-JVS(816)*X(87)-JVS(817)*X(88)-JVS(818)*X(89)-JVS(819)*X(90))/(JVS(813)) X(83) = (X(83)-JVS(749)*X(84)-JVS(750)*X(85)-JVS(751)*X(86)-JVS(752)*X(87)-JVS(753)*X(88)-JVS(754)*X(89)-JVS(755)& &*X(90))/(JVS(748)) X(82) = (X(82)-JVS(707)*X(83)-JVS(708)*X(84)-JVS(709)*X(85)-JVS(710)*X(86)-JVS(711)*X(87)-JVS(712)*X(88)-JVS(713)& &*X(89)-JVS(714)*X(90))/(JVS(706)) X(81) = (X(81)-JVS(659)*X(82)-JVS(660)*X(83)-JVS(661)*X(84)-JVS(662)*X(85)-JVS(663)*X(86)-JVS(664)*X(87)-JVS(665)& &*X(89)-JVS(666)*X(90))/(JVS(658)) X(80) = (X(80)-JVS(641)*X(83)-JVS(642)*X(84)-JVS(643)*X(85)-JVS(644)*X(86)-JVS(645)*X(87)-JVS(646)*X(89)-JVS(647)& &*X(90))/(JVS(640)) X(79) = (X(79)-JVS(628)*X(83)-JVS(629)*X(84)-JVS(630)*X(85)-JVS(631)*X(86)-JVS(632)*X(87)-JVS(633)*X(89)-JVS(634)& &*X(90))/(JVS(627)) X(78) = (X(78)-JVS(614)*X(79)-JVS(615)*X(80)-JVS(616)*X(82)-JVS(617)*X(83)-JVS(618)*X(84)-JVS(619)*X(85)-JVS(620)& &*X(86)-JVS(621)*X(87)-JVS(622)*X(89)-JVS(623)*X(90))/(JVS(613)) X(77) = (X(77)-JVS(601)*X(79)-JVS(602)*X(83)-JVS(603)*X(84)-JVS(604)*X(85)-JVS(605)*X(86)-JVS(606)*X(87)-JVS(607)& &*X(89)-JVS(608)*X(90))/(JVS(600)) X(76) = (X(76)-JVS(586)*X(77)-JVS(587)*X(79)-JVS(588)*X(80)-JVS(589)*X(83)-JVS(590)*X(84)-JVS(591)*X(85)-JVS(592)& &*X(86)-JVS(593)*X(87)-JVS(594)*X(89)-JVS(595)*X(90))/(JVS(585)) X(75) = (X(75)-JVS(564)*X(76)-JVS(565)*X(77)-JVS(566)*X(78)-JVS(567)*X(79)-JVS(568)*X(80)-JVS(569)*X(82)-JVS(570)& &*X(83)-JVS(571)*X(84)-JVS(572)*X(85)-JVS(573)*X(86)-JVS(574)*X(87)-JVS(575)*X(89)-JVS(576)*X(90))/(JVS(563)) X(74) = (X(74)-JVS(537)*X(76)-JVS(538)*X(77)-JVS(539)*X(80)-JVS(540)*X(81)-JVS(541)*X(83)-JVS(542)*X(84)-JVS(543)& &*X(85)-JVS(544)*X(86)-JVS(545)*X(87)-JVS(546)*X(89)-JVS(547)*X(90))/(JVS(536)) X(73) = (X(73)-JVS(523)*X(76)-JVS(524)*X(83)-JVS(525)*X(84)-JVS(526)*X(85)-JVS(527)*X(86)-JVS(528)*X(87)-JVS(529)& &*X(90))/(JVS(522)) X(72) = (X(72)-JVS(511)*X(73)-JVS(512)*X(83)-JVS(513)*X(84)-JVS(514)*X(85)-JVS(515)*X(86)-JVS(516)*X(87)-JVS(517)& &*X(90))/(JVS(510)) X(71) = (X(71)-JVS(493)*X(72)-JVS(494)*X(73)-JVS(495)*X(74)-JVS(496)*X(75)-JVS(497)*X(76)-JVS(498)*X(77)-JVS(499)& &*X(81)-JVS(500)*X(83)-JVS(501)*X(84)-JVS(502)*X(85)-JVS(503)*X(86)-JVS(504)*X(87)-JVS(505)*X(89)-JVS(506)& &*X(90))/(JVS(492)) X(70) = (X(70)-JVS(476)*X(77)-JVS(477)*X(83)-JVS(478)*X(84)-JVS(479)*X(85)-JVS(480)*X(86)-JVS(481)*X(87)-JVS(482)& &*X(89)-JVS(483)*X(90))/(JVS(475)) X(69) = (X(69)-JVS(453)*X(70)-JVS(454)*X(71)-JVS(455)*X(72)-JVS(456)*X(73)-JVS(457)*X(74)-JVS(458)*X(76)-JVS(459)& &*X(77)-JVS(460)*X(78)-JVS(461)*X(79)-JVS(462)*X(80)-JVS(463)*X(81)-JVS(464)*X(82)-JVS(465)*X(83)-JVS(466)*X(84)& &-JVS(467)*X(85)-JVS(468)*X(86)-JVS(469)*X(87)-JVS(470)*X(88)-JVS(471)*X(89)-JVS(472)*X(90))/(JVS(452)) X(68) = (X(68)-JVS(411)*X(70)-JVS(412)*X(72)-JVS(413)*X(73)-JVS(414)*X(77)-JVS(415)*X(80)-JVS(416)*X(83)-JVS(417)& &*X(84)-JVS(418)*X(85)-JVS(419)*X(86)-JVS(420)*X(87)-JVS(421)*X(89)-JVS(422)*X(90))/(JVS(410)) X(67) = (X(67)-JVS(389)*X(83)-JVS(390)*X(84)-JVS(391)*X(85)-JVS(392)*X(86)-JVS(393)*X(87)-JVS(394)*X(89)-JVS(395)& &*X(90))/(JVS(388)) X(66) = (X(66)-JVS(379)*X(79)-JVS(380)*X(83)-JVS(381)*X(84)-JVS(382)*X(85)-JVS(383)*X(86)-JVS(384)*X(89)-JVS(385)& &*X(90))/(JVS(378)) X(65) = (X(65)-JVS(369)*X(80)-JVS(370)*X(83)-JVS(371)*X(84)-JVS(372)*X(85)-JVS(373)*X(86)-JVS(374)*X(87)-JVS(375)& &*X(90))/(JVS(368)) X(64) = (X(64)-JVS(359)*X(77)-JVS(360)*X(83)-JVS(361)*X(84)-JVS(362)*X(85)-JVS(363)*X(86)-JVS(364)*X(90))/(JVS(358)) X(63) = (X(63)-JVS(349)*X(77)-JVS(350)*X(83)-JVS(351)*X(84)-JVS(352)*X(85)-JVS(353)*X(86)-JVS(354)*X(87)-JVS(355)& &*X(89)-JVS(356)*X(90))/(JVS(348)) X(62) = (X(62)-JVS(339)*X(72)-JVS(340)*X(73)-JVS(341)*X(83)-JVS(342)*X(84)-JVS(343)*X(85)-JVS(344)*X(86)-JVS(345)& &*X(90))/(JVS(338)) X(61) = (X(61)-JVS(322)*X(62)-JVS(323)*X(65)-JVS(324)*X(66)-JVS(325)*X(70)-JVS(326)*X(78)-JVS(327)*X(79)-JVS(328)& &*X(80)-JVS(329)*X(82)-JVS(330)*X(83)-JVS(331)*X(84)-JVS(332)*X(85)-JVS(333)*X(86)-JVS(334)*X(89)-JVS(335)& &*X(90))/(JVS(321)) X(60) = (X(60)-JVS(309)*X(76)-JVS(310)*X(83)-JVS(311)*X(84)-JVS(312)*X(85)-JVS(313)*X(86)-JVS(314)*X(87)-JVS(315)& &*X(90))/(JVS(308)) X(59) = (X(59)-JVS(302)*X(80)-JVS(303)*X(83)-JVS(304)*X(84)-JVS(305)*X(85)-JVS(306)*X(86)-JVS(307)*X(90))/(JVS(301)) X(58) = (X(58)-JVS(293)*X(79)-JVS(294)*X(83)-JVS(295)*X(84)-JVS(296)*X(85)-JVS(297)*X(86)-JVS(298)*X(89)-JVS(299)& &*X(90))/(JVS(292)) X(57) = (X(57)-JVS(285)*X(79)-JVS(286)*X(83)-JVS(287)*X(84)-JVS(288)*X(85)-JVS(289)*X(86))/(JVS(284)) X(56) = (X(56)-JVS(278)*X(80)-JVS(279)*X(83)-JVS(280)*X(84)-JVS(281)*X(85)-JVS(282)*X(86)-JVS(283)*X(87))/(JVS(277)) X(55) = (X(55)-JVS(271)*X(73)-JVS(272)*X(83)-JVS(273)*X(84)-JVS(274)*X(85)-JVS(275)*X(86)-JVS(276)*X(90))/(JVS(270)) X(54) = (X(54)-JVS(251)*X(57)-JVS(252)*X(59)-JVS(253)*X(64)-JVS(254)*X(65)-JVS(255)*X(66)-JVS(256)*X(67)-JVS(257)& &*X(68)-JVS(258)*X(69)-JVS(259)*X(71)-JVS(260)*X(75)-JVS(261)*X(76)-JVS(262)*X(80)-JVS(263)*X(82)-JVS(264)*X(83)& &-JVS(265)*X(84)-JVS(266)*X(85)-JVS(267)*X(86)-JVS(268)*X(87)-JVS(269)*X(90))/(JVS(250)) X(53) = (X(53)-JVS(238)*X(72)-JVS(239)*X(73)-JVS(240)*X(83)-JVS(241)*X(84)-JVS(242)*X(85)-JVS(243)*X(86)-JVS(244)& &*X(90))/(JVS(237)) X(52) = (X(52)-JVS(228)*X(72)-JVS(229)*X(73)-JVS(230)*X(83)-JVS(231)*X(84)-JVS(232)*X(85)-JVS(233)*X(86)-JVS(234)& &*X(90))/(JVS(227)) X(51) = (X(51)-JVS(221)*X(83)-JVS(222)*X(84)-JVS(223)*X(85)-JVS(224)*X(86))/(JVS(220)) X(50) = (X(50)-JVS(209)*X(51)-JVS(210)*X(58)-JVS(211)*X(64)-JVS(212)*X(65)-JVS(213)*X(66)-JVS(214)*X(83)-JVS(215)& &*X(84)-JVS(216)*X(85)-JVS(217)*X(86)-JVS(218)*X(89)-JVS(219)*X(90))/(JVS(208)) X(49) = (X(49)-JVS(198)*X(53)-JVS(199)*X(72)-JVS(200)*X(73)-JVS(201)*X(83)-JVS(202)*X(84)-JVS(203)*X(85)-JVS(204)& &*X(86)-JVS(205)*X(90))/(JVS(197)) X(48) = (X(48)-JVS(192)*X(77)-JVS(193)*X(87)-JVS(194)*X(89)-JVS(195)*X(90))/(JVS(191)) X(47) = (X(47)-JVS(171)*X(48)-JVS(172)*X(49)-JVS(173)*X(50)-JVS(174)*X(58)-JVS(175)*X(59)-JVS(176)*X(66)-JVS(177)& &*X(68)-JVS(178)*X(69)-JVS(179)*X(71)-JVS(180)*X(75)-JVS(181)*X(77)-JVS(182)*X(80)-JVS(183)*X(83)-JVS(184)*X(84)& &-JVS(185)*X(85)-JVS(186)*X(86)-JVS(187)*X(87)-JVS(188)*X(89)-JVS(189)*X(90))/(JVS(170)) X(46) = (X(46)-JVS(164)*X(87)-JVS(165)*X(89)-JVS(166)*X(90))/(JVS(163)) X(45) = (X(45)-JVS(159)*X(57)-JVS(160)*X(79)-JVS(161)*X(84)-JVS(162)*X(90))/(JVS(158)) X(44) = (X(44)-JVS(154)*X(78)-JVS(155)*X(82)-JVS(156)*X(89)-JVS(157)*X(90))/(JVS(153)) X(43) = (X(43)-JVS(148)*X(51)-JVS(149)*X(56)-JVS(150)*X(65)-JVS(151)*X(84)-JVS(152)*X(90))/(JVS(147)) X(42) = (X(42)-JVS(144)*X(64)-JVS(145)*X(84)-JVS(146)*X(90))/(JVS(143)) X(41) = (X(41)-JVS(140)*X(66)-JVS(141)*X(84)-JVS(142)*X(90))/(JVS(139)) X(40) = (X(40)-JVS(136)*X(59)-JVS(137)*X(84)-JVS(138)*X(90))/(JVS(135)) X(39) = (X(39)-JVS(132)*X(67)-JVS(133)*X(84)-JVS(134)*X(90))/(JVS(131)) X(38) = (X(38)-JVS(128)*X(63)-JVS(129)*X(84)-JVS(130)*X(90))/(JVS(127)) X(37) = (X(37)-JVS(124)*X(70)-JVS(125)*X(84)-JVS(126)*X(90))/(JVS(123)) X(36) = (X(36)-JVS(120)*X(84)-JVS(121)*X(88)-JVS(122)*X(90))/(JVS(119)) X(35) = (X(35)-JVS(116)*X(74)-JVS(117)*X(84)-JVS(118)*X(90))/(JVS(115)) X(34) = (X(34)-JVS(113)*X(87)-JVS(114)*X(90))/(JVS(112)) X(33) = (X(33)-JVS(109)*X(81)-JVS(110)*X(84)-JVS(111)*X(90))/(JVS(108)) X(32) = (X(32)-JVS(105)*X(53)-JVS(106)*X(84)-JVS(107)*X(90))/(JVS(104)) X(31) = (X(31)-JVS(101)*X(52)-JVS(102)*X(84)-JVS(103)*X(90))/(JVS(100)) X(30) = (X(30)-JVS(97)*X(72)-JVS(98)*X(84)-JVS(99)*X(90))/(JVS(96)) X(29) = (X(29)-JVS(93)*X(82)-JVS(94)*X(84)-JVS(95)*X(90))/(JVS(92)) X(28) = (X(28)-JVS(89)*X(84)-JVS(90)*X(86)-JVS(91)*X(90))/(JVS(88)) X(27) = (X(27)-JVS(85)*X(83)-JVS(86)*X(84)-JVS(87)*X(90))/(JVS(84)) X(26) = (X(26)-JVS(81)*X(78)-JVS(82)*X(84)-JVS(83)*X(90))/(JVS(80)) X(25) = (X(25)-JVS(78)*X(82)-JVS(79)*X(87))/(JVS(77)) X(24) = (X(24)-JVS(74)*X(82)-JVS(75)*X(85)-JVS(76)*X(90))/(JVS(73)) X(23) = (X(23)-JVS(71)*X(87)-JVS(72)*X(90))/(JVS(70)) X(22) = (X(22)-JVS(68)*X(87)-JVS(69)*X(90))/(JVS(67)) X(21) = (X(21)-JVS(65)*X(82)-JVS(66)*X(83))/(JVS(64)) X(20) = (X(20)-JVS(61)*X(34)-JVS(62)*X(87)-JVS(63)*X(90))/(JVS(60)) X(19) = (X(19)-JVS(58)*X(82)-JVS(59)*X(88))/(JVS(57)) X(18) = (X(18)-JVS(55)*X(81)-JVS(56)*X(82))/(JVS(54)) X(17) = (X(17)-JVS(52)*X(84)-JVS(53)*X(90))/(JVS(51)) X(16) = (X(16)-JVS(50)*X(90))/(JVS(49)) X(15) = (X(15)-JVS(47)*X(46)-JVS(48)*X(90))/(JVS(46)) X(14) = (X(14)-JVS(36)*X(17)-JVS(37)*X(18)-JVS(38)*X(21)-JVS(39)*X(25)-JVS(40)*X(44)-JVS(41)*X(54)-JVS(42)*X(69)& &-JVS(43)*X(73)-JVS(44)*X(82)-JVS(45)*X(89))/(JVS(35)) X(13) = (X(13)-JVS(28)*X(46)-JVS(29)*X(47)-JVS(30)*X(80)-JVS(31)*X(83)-JVS(32)*X(85)-JVS(33)*X(89)-JVS(34)*X(90))& &/(JVS(27)) X(12) = (X(12)-JVS(25)*X(34)-JVS(26)*X(90))/(JVS(24)) X(11) = (X(11)-JVS(22)*X(20)-JVS(23)*X(90))/(JVS(21)) X(10) = (X(10)-JVS(20)*X(73))/(JVS(19)) X(9) = (X(9)-JVS(18)*X(18))/(JVS(17)) X(8) = (X(8)-JVS(16)*X(44))/(JVS(15)) X(7) = (X(7)-JVS(14)*X(21))/(JVS(13)) X(6) = (X(6)-JVS(12)*X(89))/(JVS(11)) X(5) = (X(5)-JVS(10)*X(82))/(JVS(9)) X(4) = (X(4)-JVS(8)*X(25))/(JVS(7)) X(3) = (X(3)-JVS(6)*X(54))/(JVS(5)) X(2) = (X(2)-JVS(4)*X(17))/(JVS(3)) X(1) = (X(1)-JVS(2)*X(69))/(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(3) XX(3) = X(3)/JVS(5) XX(4) = X(4)/JVS(7) XX(5) = X(5)/JVS(9) XX(6) = X(6)/JVS(11) XX(7) = X(7)/JVS(13) XX(8) = X(8)/JVS(15) XX(9) = X(9)/JVS(17) XX(10) = X(10)/JVS(19) XX(11) = X(11)/JVS(21) XX(12) = X(12)/JVS(24) XX(13) = X(13)/JVS(27) XX(14) = X(14)/JVS(35) XX(15) = X(15)/JVS(46) XX(16) = X(16)/JVS(49) XX(17) = (X(17)-JVS(4)*XX(2)-JVS(36)*XX(14))/(JVS(51)) XX(18) = (X(18)-JVS(18)*XX(9)-JVS(37)*XX(14))/(JVS(54)) XX(19) = X(19)/JVS(57) XX(20) = (X(20)-JVS(22)*XX(11))/(JVS(60)) XX(21) = (X(21)-JVS(14)*XX(7)-JVS(38)*XX(14))/(JVS(64)) XX(22) = X(22)/JVS(67) XX(23) = X(23)/JVS(70) XX(24) = X(24)/JVS(73) XX(25) = (X(25)-JVS(8)*XX(4)-JVS(39)*XX(14))/(JVS(77)) XX(26) = X(26)/JVS(80) XX(27) = X(27)/JVS(84) XX(28) = X(28)/JVS(88) XX(29) = X(29)/JVS(92) XX(30) = X(30)/JVS(96) XX(31) = X(31)/JVS(100) XX(32) = X(32)/JVS(104) XX(33) = X(33)/JVS(108) XX(34) = (X(34)-JVS(25)*XX(12)-JVS(61)*XX(20))/(JVS(112)) XX(35) = X(35)/JVS(115) XX(36) = X(36)/JVS(119) XX(37) = X(37)/JVS(123) XX(38) = X(38)/JVS(127) XX(39) = X(39)/JVS(131) XX(40) = X(40)/JVS(135) XX(41) = X(41)/JVS(139) XX(42) = X(42)/JVS(143) XX(43) = X(43)/JVS(147) XX(44) = (X(44)-JVS(16)*XX(8)-JVS(40)*XX(14))/(JVS(153)) XX(45) = X(45)/JVS(158) XX(46) = (X(46)-JVS(28)*XX(13)-JVS(47)*XX(15))/(JVS(163)) XX(47) = (X(47)-JVS(29)*XX(13))/(JVS(170)) XX(48) = (X(48)-JVS(171)*XX(47))/(JVS(191)) XX(49) = (X(49)-JVS(172)*XX(47))/(JVS(197)) XX(50) = (X(50)-JVS(173)*XX(47))/(JVS(208)) XX(51) = (X(51)-JVS(148)*XX(43)-JVS(209)*XX(50))/(JVS(220)) XX(52) = (X(52)-JVS(101)*XX(31))/(JVS(227)) XX(53) = (X(53)-JVS(105)*XX(32)-JVS(198)*XX(49))/(JVS(237)) XX(54) = (X(54)-JVS(6)*XX(3)-JVS(41)*XX(14))/(JVS(250)) XX(55) = X(55)/JVS(270) XX(56) = (X(56)-JVS(149)*XX(43))/(JVS(277)) XX(57) = (X(57)-JVS(159)*XX(45)-JVS(251)*XX(54))/(JVS(284)) XX(58) = (X(58)-JVS(174)*XX(47)-JVS(210)*XX(50))/(JVS(292)) XX(59) = (X(59)-JVS(136)*XX(40)-JVS(175)*XX(47)-JVS(252)*XX(54))/(JVS(301)) XX(60) = X(60)/JVS(308) XX(61) = X(61)/JVS(321) XX(62) = (X(62)-JVS(322)*XX(61))/(JVS(338)) XX(63) = (X(63)-JVS(128)*XX(38))/(JVS(348)) XX(64) = (X(64)-JVS(144)*XX(42)-JVS(211)*XX(50)-JVS(253)*XX(54))/(JVS(358)) XX(65) = (X(65)-JVS(150)*XX(43)-JVS(212)*XX(50)-JVS(254)*XX(54)-JVS(323)*XX(61))/(JVS(368)) XX(66) = (X(66)-JVS(140)*XX(41)-JVS(176)*XX(47)-JVS(213)*XX(50)-JVS(255)*XX(54)-JVS(324)*XX(61))/(JVS(378)) XX(67) = (X(67)-JVS(132)*XX(39)-JVS(256)*XX(54))/(JVS(388)) XX(68) = (X(68)-JVS(177)*XX(47)-JVS(257)*XX(54))/(JVS(410)) XX(69) = (X(69)-JVS(2)*XX(1)-JVS(42)*XX(14)-JVS(178)*XX(47)-JVS(258)*XX(54))/(JVS(452)) XX(70) = (X(70)-JVS(124)*XX(37)-JVS(325)*XX(61)-JVS(411)*XX(68)-JVS(453)*XX(69))/(JVS(475)) XX(71) = (X(71)-JVS(179)*XX(47)-JVS(259)*XX(54)-JVS(454)*XX(69))/(JVS(492)) XX(72) = (X(72)-JVS(97)*XX(30)-JVS(199)*XX(49)-JVS(228)*XX(52)-JVS(238)*XX(53)-JVS(339)*XX(62)-JVS(412)*XX(68)& &-JVS(455)*XX(69)-JVS(493)*XX(71))/(JVS(510)) XX(73) = (X(73)-JVS(20)*XX(10)-JVS(43)*XX(14)-JVS(200)*XX(49)-JVS(229)*XX(52)-JVS(239)*XX(53)-JVS(271)*XX(55)-JVS(340)& &*XX(62)-JVS(413)*XX(68)-JVS(456)*XX(69)-JVS(494)*XX(71)-JVS(511)*XX(72))/(JVS(522)) XX(74) = (X(74)-JVS(116)*XX(35)-JVS(457)*XX(69)-JVS(495)*XX(71))/(JVS(536)) XX(75) = (X(75)-JVS(180)*XX(47)-JVS(260)*XX(54)-JVS(496)*XX(71))/(JVS(563)) XX(76) = (X(76)-JVS(261)*XX(54)-JVS(309)*XX(60)-JVS(458)*XX(69)-JVS(497)*XX(71)-JVS(523)*XX(73)-JVS(537)*XX(74)& &-JVS(564)*XX(75))/(JVS(585)) XX(77) = (X(77)-JVS(181)*XX(47)-JVS(192)*XX(48)-JVS(349)*XX(63)-JVS(359)*XX(64)-JVS(414)*XX(68)-JVS(459)*XX(69)& &-JVS(476)*XX(70)-JVS(498)*XX(71)-JVS(538)*XX(74)-JVS(565)*XX(75)-JVS(586)*XX(76))/(JVS(600)) XX(78) = (X(78)-JVS(81)*XX(26)-JVS(154)*XX(44)-JVS(326)*XX(61)-JVS(460)*XX(69)-JVS(566)*XX(75))/(JVS(613)) XX(79) = (X(79)-JVS(160)*XX(45)-JVS(285)*XX(57)-JVS(293)*XX(58)-JVS(327)*XX(61)-JVS(379)*XX(66)-JVS(461)*XX(69)& &-JVS(567)*XX(75)-JVS(587)*XX(76)-JVS(601)*XX(77)-JVS(614)*XX(78))/(JVS(627)) XX(80) = (X(80)-JVS(30)*XX(13)-JVS(182)*XX(47)-JVS(262)*XX(54)-JVS(278)*XX(56)-JVS(302)*XX(59)-JVS(328)*XX(61)& &-JVS(369)*XX(65)-JVS(415)*XX(68)-JVS(462)*XX(69)-JVS(539)*XX(74)-JVS(568)*XX(75)-JVS(588)*XX(76)-JVS(615)& &*XX(78))/(JVS(640)) XX(81) = (X(81)-JVS(55)*XX(18)-JVS(109)*XX(33)-JVS(463)*XX(69)-JVS(499)*XX(71)-JVS(540)*XX(74))/(JVS(658)) XX(82) = (X(82)-JVS(10)*XX(5)-JVS(44)*XX(14)-JVS(56)*XX(18)-JVS(58)*XX(19)-JVS(65)*XX(21)-JVS(74)*XX(24)-JVS(78)& &*XX(25)-JVS(93)*XX(29)-JVS(155)*XX(44)-JVS(263)*XX(54)-JVS(329)*XX(61)-JVS(464)*XX(69)-JVS(569)*XX(75)& &-JVS(616)*XX(78)-JVS(659)*XX(81))/(JVS(706)) XX(83) = (X(83)-JVS(31)*XX(13)-JVS(66)*XX(21)-JVS(85)*XX(27)-JVS(183)*XX(47)-JVS(201)*XX(49)-JVS(214)*XX(50)-JVS(221)& &*XX(51)-JVS(230)*XX(52)-JVS(240)*XX(53)-JVS(264)*XX(54)-JVS(272)*XX(55)-JVS(279)*XX(56)-JVS(286)*XX(57)& &-JVS(294)*XX(58)-JVS(303)*XX(59)-JVS(310)*XX(60)-JVS(330)*XX(61)-JVS(341)*XX(62)-JVS(350)*XX(63)-JVS(360)& &*XX(64)-JVS(370)*XX(65)-JVS(380)*XX(66)-JVS(389)*XX(67)-JVS(416)*XX(68)-JVS(465)*XX(69)-JVS(477)*XX(70)& &-JVS(500)*XX(71)-JVS(512)*XX(72)-JVS(524)*XX(73)-JVS(541)*XX(74)-JVS(570)*XX(75)-JVS(589)*XX(76)-JVS(602)& &*XX(77)-JVS(617)*XX(78)-JVS(628)*XX(79)-JVS(641)*XX(80)-JVS(660)*XX(81)-JVS(707)*XX(82))/(JVS(748)) XX(84) = (X(84)-JVS(52)*XX(17)-JVS(82)*XX(26)-JVS(86)*XX(27)-JVS(89)*XX(28)-JVS(94)*XX(29)-JVS(98)*XX(30)-JVS(102)& &*XX(31)-JVS(106)*XX(32)-JVS(110)*XX(33)-JVS(117)*XX(35)-JVS(120)*XX(36)-JVS(125)*XX(37)-JVS(129)*XX(38)& &-JVS(133)*XX(39)-JVS(137)*XX(40)-JVS(141)*XX(41)-JVS(145)*XX(42)-JVS(151)*XX(43)-JVS(161)*XX(45)-JVS(184)& &*XX(47)-JVS(202)*XX(49)-JVS(215)*XX(50)-JVS(222)*XX(51)-JVS(231)*XX(52)-JVS(241)*XX(53)-JVS(265)*XX(54)& &-JVS(273)*XX(55)-JVS(280)*XX(56)-JVS(287)*XX(57)-JVS(295)*XX(58)-JVS(304)*XX(59)-JVS(311)*XX(60)-JVS(331)& &*XX(61)-JVS(342)*XX(62)-JVS(351)*XX(63)-JVS(361)*XX(64)-JVS(371)*XX(65)-JVS(381)*XX(66)-JVS(390)*XX(67)& &-JVS(417)*XX(68)-JVS(466)*XX(69)-JVS(478)*XX(70)-JVS(501)*XX(71)-JVS(513)*XX(72)-JVS(525)*XX(73)-JVS(542)& &*XX(74)-JVS(571)*XX(75)-JVS(590)*XX(76)-JVS(603)*XX(77)-JVS(618)*XX(78)-JVS(629)*XX(79)-JVS(642)*XX(80)& &-JVS(661)*XX(81)-JVS(708)*XX(82)-JVS(749)*XX(83))/(JVS(813)) XX(85) = (X(85)-JVS(32)*XX(13)-JVS(75)*XX(24)-JVS(185)*XX(47)-JVS(203)*XX(49)-JVS(216)*XX(50)-JVS(223)*XX(51)-JVS(232)& &*XX(52)-JVS(242)*XX(53)-JVS(266)*XX(54)-JVS(274)*XX(55)-JVS(281)*XX(56)-JVS(288)*XX(57)-JVS(296)*XX(58)& &-JVS(305)*XX(59)-JVS(312)*XX(60)-JVS(332)*XX(61)-JVS(343)*XX(62)-JVS(352)*XX(63)-JVS(362)*XX(64)-JVS(372)& &*XX(65)-JVS(382)*XX(66)-JVS(391)*XX(67)-JVS(418)*XX(68)-JVS(467)*XX(69)-JVS(479)*XX(70)-JVS(502)*XX(71)& &-JVS(514)*XX(72)-JVS(526)*XX(73)-JVS(543)*XX(74)-JVS(572)*XX(75)-JVS(591)*XX(76)-JVS(604)*XX(77)-JVS(619)& &*XX(78)-JVS(630)*XX(79)-JVS(643)*XX(80)-JVS(662)*XX(81)-JVS(709)*XX(82)-JVS(750)*XX(83)-JVS(814)*XX(84))& &/(JVS(849)) XX(86) = (X(86)-JVS(90)*XX(28)-JVS(186)*XX(47)-JVS(204)*XX(49)-JVS(217)*XX(50)-JVS(224)*XX(51)-JVS(233)*XX(52)& &-JVS(243)*XX(53)-JVS(267)*XX(54)-JVS(275)*XX(55)-JVS(282)*XX(56)-JVS(289)*XX(57)-JVS(297)*XX(58)-JVS(306)& &*XX(59)-JVS(313)*XX(60)-JVS(333)*XX(61)-JVS(344)*XX(62)-JVS(353)*XX(63)-JVS(363)*XX(64)-JVS(373)*XX(65)& &-JVS(383)*XX(66)-JVS(392)*XX(67)-JVS(419)*XX(68)-JVS(468)*XX(69)-JVS(480)*XX(70)-JVS(503)*XX(71)-JVS(515)& &*XX(72)-JVS(527)*XX(73)-JVS(544)*XX(74)-JVS(573)*XX(75)-JVS(592)*XX(76)-JVS(605)*XX(77)-JVS(620)*XX(78)& &-JVS(631)*XX(79)-JVS(644)*XX(80)-JVS(663)*XX(81)-JVS(710)*XX(82)-JVS(751)*XX(83)-JVS(815)*XX(84)-JVS(850)& &*XX(85))/(JVS(891)) XX(87) = (X(87)-JVS(62)*XX(20)-JVS(68)*XX(22)-JVS(71)*XX(23)-JVS(79)*XX(25)-JVS(113)*XX(34)-JVS(164)*XX(46)-JVS(187)& &*XX(47)-JVS(193)*XX(48)-JVS(268)*XX(54)-JVS(283)*XX(56)-JVS(314)*XX(60)-JVS(354)*XX(63)-JVS(374)*XX(65)& &-JVS(393)*XX(67)-JVS(420)*XX(68)-JVS(469)*XX(69)-JVS(481)*XX(70)-JVS(504)*XX(71)-JVS(516)*XX(72)-JVS(528)& &*XX(73)-JVS(545)*XX(74)-JVS(574)*XX(75)-JVS(593)*XX(76)-JVS(606)*XX(77)-JVS(621)*XX(78)-JVS(632)*XX(79)& &-JVS(645)*XX(80)-JVS(664)*XX(81)-JVS(711)*XX(82)-JVS(752)*XX(83)-JVS(816)*XX(84)-JVS(851)*XX(85)-JVS(892)& &*XX(86))/(JVS(930)) XX(88) = (X(88)-JVS(59)*XX(19)-JVS(121)*XX(36)-JVS(470)*XX(69)-JVS(712)*XX(82)-JVS(753)*XX(83)-JVS(817)*XX(84)& &-JVS(852)*XX(85)-JVS(893)*XX(86)-JVS(931)*XX(87))/(JVS(951)) XX(89) = (X(89)-JVS(12)*XX(6)-JVS(33)*XX(13)-JVS(45)*XX(14)-JVS(156)*XX(44)-JVS(165)*XX(46)-JVS(188)*XX(47)-JVS(194)& &*XX(48)-JVS(218)*XX(50)-JVS(298)*XX(58)-JVS(334)*XX(61)-JVS(355)*XX(63)-JVS(384)*XX(66)-JVS(394)*XX(67)& &-JVS(421)*XX(68)-JVS(471)*XX(69)-JVS(482)*XX(70)-JVS(505)*XX(71)-JVS(546)*XX(74)-JVS(575)*XX(75)-JVS(594)& &*XX(76)-JVS(607)*XX(77)-JVS(622)*XX(78)-JVS(633)*XX(79)-JVS(646)*XX(80)-JVS(665)*XX(81)-JVS(713)*XX(82)& &-JVS(754)*XX(83)-JVS(818)*XX(84)-JVS(853)*XX(85)-JVS(894)*XX(86)-JVS(932)*XX(87)-JVS(952)*XX(88))/(JVS(971)) XX(90) = (X(90)-JVS(23)*XX(11)-JVS(26)*XX(12)-JVS(34)*XX(13)-JVS(48)*XX(15)-JVS(50)*XX(16)-JVS(53)*XX(17)-JVS(63)& &*XX(20)-JVS(69)*XX(22)-JVS(72)*XX(23)-JVS(76)*XX(24)-JVS(83)*XX(26)-JVS(87)*XX(27)-JVS(91)*XX(28)-JVS(95)& &*XX(29)-JVS(99)*XX(30)-JVS(103)*XX(31)-JVS(107)*XX(32)-JVS(111)*XX(33)-JVS(114)*XX(34)-JVS(118)*XX(35)& &-JVS(122)*XX(36)-JVS(126)*XX(37)-JVS(130)*XX(38)-JVS(134)*XX(39)-JVS(138)*XX(40)-JVS(142)*XX(41)-JVS(146)& &*XX(42)-JVS(152)*XX(43)-JVS(157)*XX(44)-JVS(162)*XX(45)-JVS(166)*XX(46)-JVS(189)*XX(47)-JVS(195)*XX(48)& &-JVS(205)*XX(49)-JVS(219)*XX(50)-JVS(234)*XX(52)-JVS(244)*XX(53)-JVS(269)*XX(54)-JVS(276)*XX(55)-JVS(299)& &*XX(58)-JVS(307)*XX(59)-JVS(315)*XX(60)-JVS(335)*XX(61)-JVS(345)*XX(62)-JVS(356)*XX(63)-JVS(364)*XX(64)& &-JVS(375)*XX(65)-JVS(385)*XX(66)-JVS(395)*XX(67)-JVS(422)*XX(68)-JVS(472)*XX(69)-JVS(483)*XX(70)-JVS(506)& &*XX(71)-JVS(517)*XX(72)-JVS(529)*XX(73)-JVS(547)*XX(74)-JVS(576)*XX(75)-JVS(595)*XX(76)-JVS(608)*XX(77)& &-JVS(623)*XX(78)-JVS(634)*XX(79)-JVS(647)*XX(80)-JVS(666)*XX(81)-JVS(714)*XX(82)-JVS(755)*XX(83)-JVS(819)& &*XX(84)-JVS(854)*XX(85)-JVS(895)*XX(86)-JVS(933)*XX(87)-JVS(953)*XX(88)-JVS(972)*XX(89))/(JVS(1041)) XX(90) = XX(90) XX(89) = XX(89)-JVS(1040)*XX(90) XX(88) = XX(88)-JVS(970)*XX(89)-JVS(1039)*XX(90) XX(87) = XX(87)-JVS(950)*XX(88)-JVS(969)*XX(89)-JVS(1038)*XX(90) XX(86) = XX(86)-JVS(929)*XX(87)-JVS(949)*XX(88)-JVS(968)*XX(89)-JVS(1037)*XX(90) XX(85) = XX(85)-JVS(890)*XX(86)-JVS(928)*XX(87)-JVS(948)*XX(88)-JVS(967)*XX(89)-JVS(1036)*XX(90) XX(84) = XX(84)-JVS(848)*XX(85)-JVS(889)*XX(86)-JVS(927)*XX(87)-JVS(947)*XX(88)-JVS(966)*XX(89)-JVS(1035)*XX(90) XX(83) = XX(83)-JVS(812)*XX(84)-JVS(847)*XX(85)-JVS(888)*XX(86)-JVS(926)*XX(87)-JVS(946)*XX(88)-JVS(965)*XX(89)& &-JVS(1034)*XX(90) XX(82) = XX(82)-JVS(747)*XX(83)-JVS(811)*XX(84)-JVS(846)*XX(85)-JVS(887)*XX(86)-JVS(925)*XX(87)-JVS(945)*XX(88)& &-JVS(964)*XX(89)-JVS(1033)*XX(90) XX(81) = XX(81)-JVS(705)*XX(82)-JVS(746)*XX(83)-JVS(810)*XX(84)-JVS(845)*XX(85)-JVS(886)*XX(86)-JVS(924)*XX(87)& &-JVS(963)*XX(89)-JVS(1032)*XX(90) XX(80) = XX(80)-JVS(657)*XX(81)-JVS(704)*XX(82)-JVS(745)*XX(83)-JVS(809)*XX(84)-JVS(844)*XX(85)-JVS(885)*XX(86)& &-JVS(923)*XX(87)-JVS(944)*XX(88)-JVS(962)*XX(89)-JVS(1031)*XX(90) XX(79) = XX(79)-JVS(639)*XX(80)-JVS(656)*XX(81)-JVS(703)*XX(82)-JVS(744)*XX(83)-JVS(808)*XX(84)-JVS(843)*XX(85)& &-JVS(884)*XX(86)-JVS(922)*XX(87)-JVS(943)*XX(88)-JVS(961)*XX(89)-JVS(1030)*XX(90) XX(78) = XX(78)-JVS(702)*XX(82)-JVS(743)*XX(83)-JVS(807)*XX(84)-JVS(842)*XX(85)-JVS(883)*XX(86)-JVS(921)*XX(87)& &-JVS(960)*XX(89)-JVS(1029)*XX(90) XX(77) = XX(77)-JVS(612)*XX(78)-JVS(655)*XX(81)-JVS(701)*XX(82)-JVS(742)*XX(83)-JVS(806)*XX(84)-JVS(841)*XX(85)& &-JVS(882)*XX(86)-JVS(920)*XX(87)-JVS(942)*XX(88)-JVS(959)*XX(89)-JVS(1028)*XX(90) XX(76) = XX(76)-JVS(654)*XX(81)-JVS(700)*XX(82)-JVS(741)*XX(83)-JVS(805)*XX(84)-JVS(840)*XX(85)-JVS(881)*XX(86)& &-JVS(919)*XX(87)-JVS(1027)*XX(90) XX(75) = XX(75)-JVS(699)*XX(82)-JVS(740)*XX(83)-JVS(804)*XX(84)-JVS(880)*XX(86)-JVS(918)*XX(87)-JVS(1026)*XX(90) XX(74) = XX(74)-JVS(698)*XX(82)-JVS(739)*XX(83)-JVS(803)*XX(84)-JVS(839)*XX(85)-JVS(879)*XX(86)-JVS(917)*XX(87)& &-JVS(1025)*XX(90) XX(73) = XX(73)-JVS(535)*XX(74)-JVS(562)*XX(75)-JVS(584)*XX(76)-JVS(653)*XX(81)-JVS(697)*XX(82)-JVS(738)*XX(83)& &-JVS(802)*XX(84)-JVS(838)*XX(85)-JVS(878)*XX(86)-JVS(916)*XX(87)-JVS(1024)*XX(90) XX(72) = XX(72)-JVS(521)*XX(73)-JVS(534)*XX(74)-JVS(561)*XX(75)-JVS(583)*XX(76)-JVS(652)*XX(81)-JVS(696)*XX(82)& &-JVS(737)*XX(83)-JVS(801)*XX(84)-JVS(837)*XX(85)-JVS(877)*XX(86)-JVS(915)*XX(87)-JVS(1023)*XX(90) XX(71) = XX(71)-JVS(695)*XX(82)-JVS(736)*XX(83)-JVS(800)*XX(84)-JVS(876)*XX(86)-JVS(914)*XX(87)-JVS(1022)*XX(90) XX(70) = XX(70)-JVS(491)*XX(71)-JVS(533)*XX(74)-JVS(560)*XX(75)-JVS(651)*XX(81)-JVS(694)*XX(82)-JVS(735)*XX(83)& &-JVS(799)*XX(84)-JVS(836)*XX(85)-JVS(875)*XX(86)-JVS(913)*XX(87)-JVS(1021)*XX(90) XX(69) = XX(69)-JVS(693)*XX(82)-JVS(798)*XX(84)-JVS(912)*XX(87)-JVS(1020)*XX(90) XX(68) = XX(68)-JVS(532)*XX(74)-JVS(650)*XX(81)-JVS(692)*XX(82)-JVS(797)*XX(84)-JVS(911)*XX(87)-JVS(1019)*XX(90) XX(67) = XX(67)-JVS(409)*XX(68)-JVS(451)*XX(69)-JVS(599)*XX(77)-JVS(638)*XX(80)-JVS(691)*XX(82)-JVS(734)*XX(83)& &-JVS(796)*XX(84)-JVS(835)*XX(85)-JVS(874)*XX(86)-JVS(910)*XX(87)-JVS(1018)*XX(90) XX(66) = XX(66)-JVS(450)*XX(69)-JVS(559)*XX(75)-JVS(582)*XX(76)-JVS(690)*XX(82)-JVS(733)*XX(83)-JVS(795)*XX(84)& &-JVS(834)*XX(85)-JVS(873)*XX(86)-JVS(909)*XX(87)-JVS(941)*XX(88)-JVS(1017)*XX(90) XX(65) = XX(65)-JVS(408)*XX(68)-JVS(449)*XX(69)-JVS(558)*XX(75)-JVS(689)*XX(82)-JVS(732)*XX(83)-JVS(794)*XX(84)& &-JVS(833)*XX(85)-JVS(872)*XX(86)-JVS(908)*XX(87)-JVS(940)*XX(88)-JVS(1016)*XX(90) XX(64) = XX(64)-JVS(407)*XX(68)-JVS(448)*XX(69)-JVS(557)*XX(75)-JVS(581)*XX(76)-JVS(688)*XX(82)-JVS(731)*XX(83)& &-JVS(793)*XX(84)-JVS(832)*XX(85)-JVS(871)*XX(86)-JVS(907)*XX(87)-JVS(939)*XX(88)-JVS(1015)*XX(90) XX(63) = XX(63)-JVS(406)*XX(68)-JVS(447)*XX(69)-JVS(490)*XX(71)-JVS(687)*XX(82)-JVS(730)*XX(83)-JVS(792)*XX(84)& &-JVS(831)*XX(85)-JVS(870)*XX(86)-JVS(1014)*XX(90) XX(62) = XX(62)-JVS(446)*XX(69)-JVS(520)*XX(73)-JVS(556)*XX(75)-JVS(580)*XX(76)-JVS(686)*XX(82)-JVS(729)*XX(83)& &-JVS(791)*XX(84)-JVS(830)*XX(85)-JVS(869)*XX(86)-JVS(1013)*XX(90) XX(61) = XX(61)-JVS(445)*XX(69)-JVS(555)*XX(75)-JVS(728)*XX(83)-JVS(790)*XX(84)-JVS(1012)*XX(90) XX(60) = XX(60)-JVS(444)*XX(69)-JVS(489)*XX(71)-JVS(519)*XX(73)-JVS(554)*XX(75)-JVS(579)*XX(76)-JVS(685)*XX(82)& &-JVS(727)*XX(83)-JVS(789)*XX(84)-JVS(829)*XX(85)-JVS(868)*XX(86) XX(59) = XX(59)-JVS(320)*XX(61)-JVS(443)*XX(69)-JVS(553)*XX(75)-JVS(578)*XX(76)-JVS(684)*XX(82)-JVS(726)*XX(83)& &-JVS(788)*XX(84)-JVS(828)*XX(85)-JVS(867)*XX(86)-JVS(906)*XX(87)-JVS(1011)*XX(90) XX(58) = XX(58)-JVS(319)*XX(61)-JVS(377)*XX(66)-JVS(442)*XX(69)-JVS(552)*XX(75)-JVS(611)*XX(78)-JVS(787)*XX(84)& &-JVS(938)*XX(88)-JVS(958)*XX(89)-JVS(1010)*XX(90) XX(57) = XX(57)-JVS(291)*XX(58)-JVS(441)*XX(69)-JVS(577)*XX(76)-JVS(598)*XX(77)-JVS(626)*XX(79)-JVS(637)*XX(80)& &-JVS(683)*XX(82)-JVS(725)*XX(83)-JVS(786)*XX(84)-JVS(827)*XX(85)-JVS(866)*XX(86)-JVS(905)*XX(87)-JVS(1009)& &*XX(90) XX(56) = XX(56)-JVS(367)*XX(65)-JVS(405)*XX(68)-JVS(440)*XX(69)-JVS(551)*XX(75)-JVS(682)*XX(82)-JVS(724)*XX(83)& &-JVS(785)*XX(84)-JVS(826)*XX(85)-JVS(865)*XX(86)-JVS(1008)*XX(90) XX(55) = XX(55)-JVS(404)*XX(68)-JVS(439)*XX(69)-JVS(488)*XX(71)-JVS(509)*XX(72)-JVS(518)*XX(73)-JVS(681)*XX(82)& &-JVS(723)*XX(83)-JVS(784)*XX(84)-JVS(825)*XX(85)-JVS(864)*XX(86) XX(54) = XX(54)-JVS(680)*XX(82)-JVS(904)*XX(87)-JVS(1007)*XX(90) XX(53) = XX(53)-JVS(337)*XX(62)-JVS(438)*XX(69)-JVS(679)*XX(82)-JVS(722)*XX(83)-JVS(783)*XX(84)-JVS(824)*XX(85)& &-JVS(863)*XX(86)-JVS(1006)*XX(90) XX(52) = XX(52)-JVS(403)*XX(68)-JVS(437)*XX(69)-JVS(678)*XX(82)-JVS(721)*XX(83)-JVS(782)*XX(84)-JVS(823)*XX(85)& &-JVS(862)*XX(86)-JVS(1005)*XX(90) XX(51) = XX(51)-JVS(249)*XX(54)-JVS(366)*XX(65)-JVS(402)*XX(68)-JVS(436)*XX(69)-JVS(550)*XX(75)-JVS(677)*XX(82)& &-JVS(720)*XX(83)-JVS(781)*XX(84)-JVS(822)*XX(85)-JVS(861)*XX(86)-JVS(937)*XX(88)-JVS(1004)*XX(90) XX(50) = XX(50)-JVS(435)*XX(69)-JVS(780)*XX(84)-JVS(936)*XX(88)-JVS(1003)*XX(90) XX(49) = XX(49)-JVS(336)*XX(62)-JVS(719)*XX(83)-JVS(779)*XX(84)-JVS(860)*XX(86)-JVS(1002)*XX(90) XX(48) = XX(48)-JVS(347)*XX(63)-JVS(434)*XX(69)-JVS(474)*XX(70)-JVS(487)*XX(71)-JVS(778)*XX(84)-JVS(859)*XX(86)& &-JVS(903)*XX(87)-JVS(957)*XX(89)-JVS(1001)*XX(90) XX(47) = XX(47)-JVS(777)*XX(84)-JVS(1000)*XX(90) XX(46) = XX(46)-JVS(169)*XX(47)-JVS(190)*XX(48)-JVS(387)*XX(67)-JVS(433)*XX(69)-JVS(597)*XX(77)-JVS(625)*XX(79)& &-JVS(636)*XX(80)-JVS(776)*XX(84)-JVS(902)*XX(87)-JVS(956)*XX(89)-JVS(999)*XX(90) XX(45) = XX(45)-JVS(290)*XX(58)-JVS(432)*XX(69)-JVS(596)*XX(77)-JVS(624)*XX(79)-JVS(635)*XX(80)-JVS(775)*XX(84)& &-JVS(998)*XX(90) XX(44) = XX(44)-JVS(318)*XX(61)-JVS(431)*XX(69)-JVS(610)*XX(78)-JVS(676)*XX(82)-JVS(774)*XX(84)-JVS(955)*XX(89)& &-JVS(997)*XX(90) XX(43) = XX(43)-JVS(365)*XX(65)-JVS(401)*XX(68)-JVS(675)*XX(82)-JVS(773)*XX(84)-JVS(996)*XX(90) XX(42) = XX(42)-JVS(207)*XX(50)-JVS(357)*XX(64)-JVS(400)*XX(68)-JVS(430)*XX(69)-JVS(549)*XX(75)-JVS(718)*XX(83)& &-JVS(772)*XX(84)-JVS(995)*XX(90) XX(41) = XX(41)-JVS(168)*XX(47)-JVS(206)*XX(50)-JVS(317)*XX(61)-JVS(376)*XX(66)-JVS(548)*XX(75)-JVS(771)*XX(84)& &-JVS(994)*XX(90) XX(40) = XX(40)-JVS(167)*XX(47)-JVS(300)*XX(59)-JVS(316)*XX(61)-JVS(429)*XX(69)-JVS(770)*XX(84)-JVS(993)*XX(90) XX(39) = XX(39)-JVS(386)*XX(67)-JVS(399)*XX(68)-JVS(674)*XX(82)-JVS(769)*XX(84)-JVS(992)*XX(90) XX(38) = XX(38)-JVS(346)*XX(63)-JVS(398)*XX(68)-JVS(673)*XX(82)-JVS(768)*XX(84)-JVS(991)*XX(90) XX(37) = XX(37)-JVS(428)*XX(69)-JVS(473)*XX(70)-JVS(486)*XX(71)-JVS(767)*XX(84)-JVS(990)*XX(90) XX(36) = XX(36)-JVS(427)*XX(69)-JVS(766)*XX(84)-JVS(935)*XX(88)-JVS(989)*XX(90) XX(35) = XX(35)-JVS(485)*XX(71)-JVS(531)*XX(74)-JVS(765)*XX(84)-JVS(988)*XX(90) XX(34) = XX(34)-JVS(248)*XX(54)-JVS(426)*XX(69)-JVS(764)*XX(84)-JVS(858)*XX(86)-JVS(901)*XX(87)-JVS(987)*XX(90) XX(33) = XX(33)-JVS(484)*XX(71)-JVS(649)*XX(81)-JVS(763)*XX(84)-JVS(986)*XX(90) XX(32) = XX(32)-JVS(196)*XX(49)-JVS(236)*XX(53)-JVS(762)*XX(84)-JVS(985)*XX(90) XX(31) = XX(31)-JVS(226)*XX(52)-JVS(397)*XX(68)-JVS(761)*XX(84)-JVS(984)*XX(90) XX(30) = XX(30)-JVS(396)*XX(68)-JVS(508)*XX(72)-JVS(760)*XX(84)-JVS(983)*XX(90) XX(29) = XX(29)-JVS(672)*XX(82)-JVS(759)*XX(84)-JVS(900)*XX(87)-JVS(982)*XX(90) XX(28) = XX(28)-JVS(425)*XX(69)-JVS(758)*XX(84)-JVS(857)*XX(86)-JVS(981)*XX(90) XX(27) = XX(27)-JVS(424)*XX(69)-JVS(717)*XX(83)-JVS(856)*XX(86)-JVS(980)*XX(90) XX(26) = XX(26)-JVS(423)*XX(69)-JVS(609)*XX(78)-JVS(716)*XX(83)-JVS(979)*XX(90) XX(25) = XX(25)-JVS(247)*XX(54)-JVS(671)*XX(82)-JVS(821)*XX(85)-JVS(899)*XX(87)-JVS(954)*XX(89) XX(24) = XX(24)-JVS(670)*XX(82)-JVS(820)*XX(85)-JVS(978)*XX(90) XX(23) = XX(23)-JVS(246)*XX(54)-JVS(530)*XX(74)-JVS(898)*XX(87)-JVS(977)*XX(90) XX(22) = XX(22)-JVS(245)*XX(54)-JVS(507)*XX(72)-JVS(897)*XX(87)-JVS(976)*XX(90) XX(21) = XX(21)-JVS(669)*XX(82)-JVS(715)*XX(83)-JVS(855)*XX(86)-JVS(896)*XX(87) XX(20) = XX(20)-JVS(757)*XX(84)-JVS(975)*XX(90) XX(19) = XX(19)-JVS(668)*XX(82)-JVS(934)*XX(88) XX(18) = XX(18)-JVS(648)*XX(81)-JVS(667)*XX(82) XX(17) = XX(17)-JVS(756)*XX(84)-JVS(974)*XX(90) XX(16) = XX(16)-JVS(225)*XX(52)-JVS(235)*XX(53)-JVS(973)*XX(90) 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) 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