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gckpp_LinearAlgebra.F90
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gckpp_LinearAlgebra.F90
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! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
!
! Linear Algebra Data and Routines File
!
! Generated by KPP-3.1.1 symbolic chemistry Kinetics PreProcessor
! (https:/github.com/KineticPreProcessor/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) 1997-2022, A. Sandu, Michigan Tech, Virginia Tech
! With important contributions from:
! M. Damian, Villanova University, Philadelphia, PA, USA
! R. Sander, Max-Planck Institute for Chemistry, Mainz, Germany
! M. Long, Renaissance Fiber, LLC, North Carolina, USA
! H. Lin, Harvard University, Cambridge, MA, USA
! R. Yantosca, Harvard University, Cambridge, MA, USA
!
! File : gckpp_LinearAlgebra.F90
! Equation file : gckpp.kpp
! Output root filename : gckpp
!
! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
MODULE gckpp_LinearAlgebra
USE gckpp_Global, ONLY: DO_SLV
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
COMPLEX(kind=dp) :: 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
COMPLEX(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 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
COMPLEX(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 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)
IF (DO_SLV(96)) &
X(96) = X(96)-JVS(722)*X(42)-JVS(723)*X(44)-JVS(724)*X(55)
IF (DO_SLV(110)) &
X(110) = X(110)-JVS(794)*X(76)
IF (DO_SLV(117)) &
X(117) = X(117)-JVS(827)*X(90)
IF (DO_SLV(121)) &
X(121) = X(121)-JVS(849)*X(58)
IF (DO_SLV(129)) &
X(129) = X(129)-JVS(885)*X(112)
IF (DO_SLV(134)) &
X(134) = X(134)-JVS(918)*X(89)
IF (DO_SLV(146)) &
X(146) = X(146)-JVS(982)*X(121)
IF (DO_SLV(158)) &
X(158) = X(158)-JVS(1059)*X(82)-JVS(1060)*X(101)-JVS(1061)*X(149)
IF (DO_SLV(162)) &
X(162) = X(162)-JVS(1080)*X(138)
IF (DO_SLV(170)) &
X(170) = X(170)-JVS(1123)*X(62)
IF (DO_SLV(173)) &
X(173) = X(173)-JVS(1143)*X(101)
IF (DO_SLV(176)) &
X(176) = X(176)-JVS(1165)*X(137)
IF (DO_SLV(178)) &
X(178) = X(178)-JVS(1180)*X(69)-JVS(1181)*X(98)
IF (DO_SLV(185)) &
X(185) = X(185)-JVS(1217)*X(119)-JVS(1218)*X(147)
IF (DO_SLV(189)) &
X(189) = X(189)-JVS(1247)*X(149)
IF (DO_SLV(190)) &
X(190) = X(190)-JVS(1255)*X(168)
IF (DO_SLV(195)) &
X(195) = X(195)-JVS(1281)*X(143)
IF (DO_SLV(196)) &
X(196) = X(196)-JVS(1287)*X(165)-JVS(1288)*X(178)
IF (DO_SLV(197)) &
X(197) = X(197)-JVS(1294)*X(126)
IF (DO_SLV(198)) &
X(198) = X(198)-JVS(1301)*X(174)
IF (DO_SLV(201)) &
X(201) = X(201)-JVS(1315)*X(82)-JVS(1316)*X(101)-JVS(1317)*X(149)-JVS(1318)*X(158)-JVS(1319)*X(200)
IF (DO_SLV(202)) &
X(202) = X(202)-JVS(1324)*X(158)-JVS(1325)*X(195)-JVS(1326)*X(200)
IF (DO_SLV(203)) &
X(203) = X(203)-JVS(1332)*X(117)-JVS(1333)*X(158)-JVS(1334)*X(195)-JVS(1335)*X(200)-JVS(1336)*X(202)
IF (DO_SLV(204)) &
X(204) = X(204)-JVS(1348)*X(82)-JVS(1349)*X(101)-JVS(1350)*X(116)-JVS(1351)*X(149)-JVS(1352)*X(189)-JVS(1353)*X(200)
IF (DO_SLV(205)) &
X(205) = X(205)-JVS(1361)*X(175)
IF (DO_SLV(208)) &
X(208) = X(208)-JVS(1377)*X(131)-JVS(1378)*X(147)
IF (DO_SLV(210)) &
X(210) = X(210)-JVS(1393)*X(209)
IF (DO_SLV(212)) &
X(212) = X(212)-JVS(1410)*X(140)
IF (DO_SLV(213)) &
X(213) = X(213)-JVS(1417)*X(114)
IF (DO_SLV(215)) &
X(215) = X(215)-JVS(1432)*X(128)-JVS(1433)*X(144)-JVS(1434)*X(150)-JVS(1435)*X(151)-JVS(1436)*X(152)-JVS(1437)*X(168)&
&-JVS(1438)*X(175)-JVS(1439)*X(186)-JVS(1440)*X(187)-JVS(1441)*X(192)-JVS(1442)*X(199)-JVS(1443)*X(209)
IF (DO_SLV(216)) &
X(216) = X(216)-JVS(1457)*X(206)
IF (DO_SLV(217)) &
X(217) = X(217)-JVS(1469)*X(181)
IF (DO_SLV(221)) &
X(221) = X(221)-JVS(1495)*X(82)-JVS(1496)*X(101)-JVS(1497)*X(143)-JVS(1498)*X(149)-JVS(1499)*X(195)-JVS(1500)*X(200)&
&-JVS(1501)*X(202)-JVS(1502)*X(220)
IF (DO_SLV(223)) &
X(223) = X(223)-JVS(1514)*X(187)-JVS(1515)*X(209)
IF (DO_SLV(224)) &
X(224) = X(224)-JVS(1521)*X(192)-JVS(1522)*X(199)
IF (DO_SLV(225)) &
X(225) = X(225)-JVS(1528)*X(111)-JVS(1529)*X(137)-JVS(1530)*X(191)
IF (DO_SLV(226)) &
X(226) = X(226)-JVS(1540)*X(186)
IF (DO_SLV(227)) &
X(227) = X(227)-JVS(1546)*X(131)-JVS(1547)*X(147)-JVS(1548)*X(153)-JVS(1549)*X(194)
IF (DO_SLV(230)) &
X(230) = X(230)-JVS(1576)*X(209)
IF (DO_SLV(231)) &
X(231) = X(231)-JVS(1582)*X(199)
IF (DO_SLV(232)) &
X(232) = X(232)-JVS(1588)*X(187)-JVS(1589)*X(192)
IF (DO_SLV(233)) &
X(233) = X(233)-JVS(1596)*X(140)-JVS(1597)*X(212)
IF (DO_SLV(234)) &
X(234) = X(234)-JVS(1604)*X(109)-JVS(1605)*X(136)-JVS(1606)*X(233)
IF (DO_SLV(235)) &
X(235) = X(235)-JVS(1615)*X(71)-JVS(1616)*X(90)-JVS(1617)*X(204)-JVS(1618)*X(220)
IF (DO_SLV(236)) &
X(236) = X(236)-JVS(1627)*X(71)-JVS(1628)*X(117)-JVS(1629)*X(203)-JVS(1630)*X(204)-JVS(1631)*X(220)-JVS(1632)*X(235)
IF (DO_SLV(238)) &
X(238) = X(238)-JVS(1650)*X(199)-JVS(1651)*X(209)
IF (DO_SLV(239)) &
X(239) = X(239)-JVS(1661)*X(64)-JVS(1662)*X(65)-JVS(1663)*X(166)-JVS(1664)*X(179)
IF (DO_SLV(240)) &
X(240) = X(240)-JVS(1682)*X(122)-JVS(1683)*X(146)-JVS(1684)*X(200)
IF (DO_SLV(242)) &
X(242) = X(242)-JVS(1699)*X(193)
IF (DO_SLV(243)) &
X(243) = X(243)-JVS(1711)*X(128)-JVS(1712)*X(192)-JVS(1713)*X(199)-JVS(1714)*X(209)
IF (DO_SLV(244)) &
X(244) = X(244)-JVS(1723)*X(199)-JVS(1724)*X(224)-JVS(1725)*X(226)
IF (DO_SLV(245)) &
X(245) = X(245)-JVS(1739)*X(110)
IF (DO_SLV(246)) &
X(246) = X(246)-JVS(1753)*X(113)
IF (DO_SLV(247)) &
X(247) = X(247)-JVS(1760)*X(125)-JVS(1761)*X(180)-JVS(1762)*X(182)-JVS(1763)*X(206)-JVS(1764)*X(216)-JVS(1765)*X(226)
IF (DO_SLV(248)) &
X(248) = X(248)-JVS(1782)*X(172)-JVS(1783)*X(205)-JVS(1784)*X(231)
IF (DO_SLV(250)) &
X(250) = X(250)-JVS(1804)*X(125)
IF (DO_SLV(253)) &
X(253) = X(253)-JVS(1827)*X(172)-JVS(1828)*X(231)
IF (DO_SLV(254)) &
X(254) = X(254)-JVS(1838)*X(171)-JVS(1839)*X(230)
IF (DO_SLV(255)) &
X(255) = X(255)-JVS(1849)*X(167)
IF (DO_SLV(256)) &
X(256) = X(256)-JVS(1859)*X(162)-JVS(1860)*X(176)-JVS(1861)*X(177)-JVS(1862)*X(211)-JVS(1863)*X(237)-JVS(1864)*X(255)
IF (DO_SLV(257)) &
X(257) = X(257)-JVS(1881)*X(56)-JVS(1882)*X(74)-JVS(1883)*X(111)-JVS(1884)*X(225)
IF (DO_SLV(258)) &
X(258) = X(258)-JVS(1895)*X(174)-JVS(1896)*X(223)-JVS(1897)*X(224)-JVS(1898)*X(232)-JVS(1899)*X(243)
IF (DO_SLV(259)) &
X(259) = X(259)-JVS(1910)*X(159)-JVS(1911)*X(184)
IF (DO_SLV(260)) &
X(260) = X(260)-JVS(1920)*X(123)
IF (DO_SLV(261)) &
X(261) = X(261)-JVS(1930)*X(180)-JVS(1931)*X(182)-JVS(1932)*X(207)-JVS(1933)*X(226)
IF (DO_SLV(262)) &
X(262) = X(262)-JVS(1947)*X(193)-JVS(1948)*X(219)-JVS(1949)*X(229)
IF (DO_SLV(263)) &
X(263) = X(263)-JVS(1959)*X(82)-JVS(1960)*X(101)-JVS(1961)*X(137)-JVS(1962)*X(138)-JVS(1963)*X(143)-JVS(1964)*X(149)&
&-JVS(1965)*X(158)-JVS(1966)*X(160)-JVS(1967)*X(167)-JVS(1968)*X(176)-JVS(1969)*X(193)-JVS(1970)*X(195)&
&-JVS(1971)*X(200)-JVS(1972)*X(202)-JVS(1973)*X(211)-JVS(1974)*X(219)-JVS(1975)*X(220)-JVS(1976)*X(229)&
&-JVS(1977)*X(237)-JVS(1978)*X(255)-JVS(1979)*X(262)
IF (DO_SLV(264)) &
X(264) = X(264)-JVS(1993)*X(241)
IF (DO_SLV(265)) &
X(265) = X(265)-JVS(2009)*X(60)-JVS(2010)*X(88)-JVS(2011)*X(107)-JVS(2012)*X(159)-JVS(2013)*X(184)-JVS(2014)*X(194)&
&-JVS(2015)*X(201)-JVS(2016)*X(221)-JVS(2017)*X(230)-JVS(2018)*X(231)-JVS(2019)*X(259)
IF (DO_SLV(266)) &
X(266) = X(266)-JVS(2041)*X(190)-JVS(2042)*X(205)-JVS(2043)*X(206)-JVS(2044)*X(207)-JVS(2045)*X(226)-JVS(2046)*X(243)
IF (DO_SLV(269)) &
X(269) = X(269)-JVS(2073)*X(158)-JVS(2074)*X(195)-JVS(2075)*X(200)-JVS(2076)*X(202)-JVS(2077)*X(203)-JVS(2078)*X(220)&
&-JVS(2079)*X(235)-JVS(2080)*X(236)
IF (DO_SLV(270)) &
X(270) = X(270)-JVS(2089)*X(60)-JVS(2090)*X(82)-JVS(2091)*X(101)-JVS(2092)*X(143)-JVS(2093)*X(185)-JVS(2094)*X(194)&
&-JVS(2095)*X(195)-JVS(2096)*X(198)-JVS(2097)*X(200)-JVS(2098)*X(210)-JVS(2099)*X(220)-JVS(2100)*X(221)&
&-JVS(2101)*X(223)-JVS(2102)*X(224)-JVS(2103)*X(226)-JVS(2104)*X(227)-JVS(2105)*X(230)-JVS(2106)*X(231)&
&-JVS(2107)*X(232)-JVS(2108)*X(233)-JVS(2109)*X(258)-JVS(2110)*X(267)-JVS(2111)*X(268)-JVS(2112)*X(269)
IF (DO_SLV(271)) &
X(271) = X(271)-JVS(2134)*X(222)
IF (DO_SLV(272)) &
X(272) = X(272)-JVS(2142)*X(211)-JVS(2143)*X(237)
IF (DO_SLV(273)) &
X(273) = X(273)-JVS(2153)*X(129)-JVS(2154)*X(138)-JVS(2155)*X(161)-JVS(2156)*X(191)
IF (DO_SLV(274)) &
X(274) = X(274)-JVS(2166)*X(57)-JVS(2167)*X(161)-JVS(2168)*X(162)-JVS(2169)*X(163)-JVS(2170)*X(167)-JVS(2171)*X(169)&
&-JVS(2172)*X(177)-JVS(2173)*X(211)-JVS(2174)*X(237)-JVS(2175)*X(255)-JVS(2176)*X(272)-JVS(2177)*X(273)
IF (DO_SLV(275)) &
X(275) = X(275)-JVS(2189)*X(112)-JVS(2190)*X(191)-JVS(2191)*X(219)
IF (DO_SLV(277)) &
X(277) = X(277)-JVS(2205)*X(111)-JVS(2206)*X(191)-JVS(2207)*X(219)
IF (DO_SLV(278)) &
X(278) = X(278)-JVS(2216)*X(66)-JVS(2217)*X(74)-JVS(2218)*X(160)-JVS(2219)*X(225)-JVS(2220)*X(257)-JVS(2221)*X(277)
IF (DO_SLV(279)) &
X(279) = X(279)-JVS(2231)*X(249)
IF (DO_SLV(280)) &
X(280) = X(280)-JVS(2240)*X(167)-JVS(2241)*X(191)-JVS(2242)*X(193)-JVS(2243)*X(219)-JVS(2244)*X(229)-JVS(2245)*X(262)
IF (DO_SLV(281)) &
X(281) = X(281)-JVS(2256)*X(167)-JVS(2257)*X(191)-JVS(2258)*X(219)
IF (DO_SLV(282)) &
X(282) = X(282)-JVS(2267)*X(234)-JVS(2268)*X(246)-JVS(2269)*X(249)-JVS(2270)*X(250)-JVS(2271)*X(260)-JVS(2272)*X(272)&
&-JVS(2273)*X(273)-JVS(2274)*X(275)-JVS(2275)*X(277)-JVS(2276)*X(278)-JVS(2277)*X(279)-JVS(2278)*X(281)
IF (DO_SLV(283)) &
X(283) = X(283)-JVS(2305)*X(201)-JVS(2306)*X(241)-JVS(2307)*X(249)-JVS(2308)*X(250)-JVS(2309)*X(260)-JVS(2310)*X(275)&
&-JVS(2311)*X(277)-JVS(2312)*X(279)-JVS(2313)*X(281)
IF (DO_SLV(284)) &
X(284) = X(284)-JVS(2340)*X(44)-JVS(2341)*X(55)-JVS(2342)*X(96)
IF (DO_SLV(285)) &
X(285) = X(285)-JVS(2354)*X(147)-JVS(2355)*X(151)-JVS(2356)*X(152)-JVS(2357)*X(168)-JVS(2358)*X(175)-JVS(2359)*X(187)&
&-JVS(2360)*X(192)-JVS(2361)*X(238)-JVS(2362)*X(267)-JVS(2363)*X(268)
IF (DO_SLV(286)) &
X(286) = X(286)-JVS(2374)*X(147)-JVS(2375)*X(151)-JVS(2376)*X(152)-JVS(2377)*X(168)-JVS(2378)*X(175)-JVS(2379)*X(187)&
&-JVS(2380)*X(192)-JVS(2381)*X(238)-JVS(2382)*X(267)-JVS(2383)*X(268)-JVS(2384)*X(285)
IF (DO_SLV(287)) &
X(287) = X(287)-JVS(2394)*X(144)-JVS(2395)*X(192)-JVS(2396)*X(198)-JVS(2397)*X(199)-JVS(2398)*X(223)-JVS(2399)*X(224)&
&-JVS(2400)*X(231)-JVS(2401)*X(232)-JVS(2402)*X(238)-JVS(2403)*X(253)-JVS(2404)*X(258)-JVS(2405)*X(266)&
&-JVS(2406)*X(267)-JVS(2407)*X(268)-JVS(2408)*X(271)-JVS(2409)*X(276)-JVS(2410)*X(285)-JVS(2411)*X(286)
IF (DO_SLV(288)) &
X(288) = X(288)-JVS(2428)*X(150)-JVS(2429)*X(187)-JVS(2430)*X(198)-JVS(2431)*X(209)-JVS(2432)*X(223)-JVS(2433)*X(224)&
&-JVS(2434)*X(230)-JVS(2435)*X(232)-JVS(2436)*X(238)-JVS(2437)*X(254)-JVS(2438)*X(266)-JVS(2439)*X(267)&
&-JVS(2440)*X(268)-JVS(2441)*X(271)-JVS(2442)*X(276)-JVS(2443)*X(285)-JVS(2444)*X(286)
IF (DO_SLV(289)) &
X(289) = X(289)-JVS(2461)*X(167)-JVS(2462)*X(191)-JVS(2463)*X(219)-JVS(2464)*X(280)
IF (DO_SLV(291)) &
X(291) = X(291)-JVS(2481)*X(219)
IF (DO_SLV(292)) &
X(292) = X(292)-JVS(2490)*X(160)-JVS(2491)*X(176)-JVS(2492)*X(178)-JVS(2493)*X(219)-JVS(2494)*X(251)-JVS(2495)*X(256)&
&-JVS(2496)*X(262)-JVS(2497)*X(272)-JVS(2498)*X(273)-JVS(2499)*X(275)-JVS(2500)*X(277)-JVS(2501)*X(278)&
&-JVS(2502)*X(279)-JVS(2503)*X(280)-JVS(2504)*X(281)-JVS(2505)*X(289)-JVS(2506)*X(291)
IF (DO_SLV(293)) &
X(293) = X(293)-JVS(2520)*X(145)-JVS(2521)*X(186)-JVS(2522)*X(222)
IF (DO_SLV(294)) &
X(294) = X(294)-JVS(2534)*X(82)-JVS(2535)*X(101)-JVS(2536)*X(107)-JVS(2537)*X(159)-JVS(2538)*X(184)-JVS(2539)*X(185)&
&-JVS(2540)*X(194)-JVS(2541)*X(198)-JVS(2542)*X(199)-JVS(2543)*X(200)-JVS(2544)*X(201)-JVS(2545)*X(209)&
&-JVS(2546)*X(215)-JVS(2547)*X(223)-JVS(2548)*X(224)-JVS(2549)*X(227)-JVS(2550)*X(230)-JVS(2551)*X(231)&
&-JVS(2552)*X(232)-JVS(2553)*X(238)-JVS(2554)*X(244)-JVS(2555)*X(247)-JVS(2556)*X(250)-JVS(2557)*X(253)&
&-JVS(2558)*X(254)-JVS(2559)*X(258)-JVS(2560)*X(259)-JVS(2561)*X(266)-JVS(2562)*X(267)-JVS(2563)*X(268)&
&-JVS(2564)*X(271)-JVS(2565)*X(276)-JVS(2566)*X(285)-JVS(2567)*X(286)-JVS(2568)*X(287)-JVS(2569)*X(288)&
&-JVS(2570)*X(290)-JVS(2571)*X(293)
IF (DO_SLV(295)) &
X(295) = X(295)-JVS(2597)*X(91)-JVS(2598)*X(100)-JVS(2599)*X(160)-JVS(2600)*X(161)-JVS(2601)*X(162)-JVS(2602)*X(176)&
&-JVS(2603)*X(219)-JVS(2604)*X(229)-JVS(2605)*X(251)-JVS(2606)*X(262)-JVS(2607)*X(273)-JVS(2608)*X(275)&
&-JVS(2609)*X(277)-JVS(2610)*X(278)-JVS(2611)*X(279)-JVS(2612)*X(291)
IF (DO_SLV(296)) &
X(296) = X(296)-JVS(2629)*X(173)-JVS(2630)*X(183)-JVS(2631)*X(200)-JVS(2632)*X(201)-JVS(2633)*X(221)-JVS(2634)*X(240)&
&-JVS(2635)*X(246)-JVS(2636)*X(269)-JVS(2637)*X(289)-JVS(2638)*X(291)
IF (DO_SLV(297)) &
X(297) = X(297)-JVS(2652)*X(214)
IF (DO_SLV(298)) &
X(298) = X(298)-JVS(2664)*X(95)-JVS(2665)*X(97)-JVS(2666)*X(98)-JVS(2667)*X(99)-JVS(2668)*X(102)-JVS(2669)*X(125)&
&-JVS(2670)*X(130)-JVS(2671)*X(161)-JVS(2672)*X(162)-JVS(2673)*X(165)-JVS(2674)*X(169)-JVS(2675)*X(178)&
&-JVS(2676)*X(188)-JVS(2677)*X(196)-JVS(2678)*X(201)-JVS(2679)*X(212)-JVS(2680)*X(219)-JVS(2681)*X(221)&
&-JVS(2682)*X(229)-JVS(2683)*X(242)-JVS(2684)*X(249)-JVS(2685)*X(250)-JVS(2686)*X(251)-JVS(2687)*X(260)&
&-JVS(2688)*X(269)-JVS(2689)*X(272)-JVS(2690)*X(273)-JVS(2691)*X(274)-JVS(2692)*X(275)-JVS(2693)*X(279)&
&-JVS(2694)*X(280)-JVS(2695)*X(281)-JVS(2696)*X(289)-JVS(2697)*X(290)-JVS(2698)*X(291)
IF (DO_SLV(299)) &
X(299) = X(299)-JVS(2717)*X(180)-JVS(2718)*X(190)-JVS(2719)*X(205)-JVS(2720)*X(206)-JVS(2721)*X(207)-JVS(2722)*X(226)&
&-JVS(2723)*X(267)-JVS(2724)*X(268)-JVS(2725)*X(271)-JVS(2726)*X(293)
IF (DO_SLV(300)) &
X(300) = X(300)-JVS(2739)*X(102)-JVS(2740)*X(142)-JVS(2741)*X(201)
IF (DO_SLV(301)) &
X(301) = X(301)-JVS(2751)*X(145)-JVS(2752)*X(186)-JVS(2753)*X(267)-JVS(2754)*X(268)-JVS(2755)*X(299)
IF (DO_SLV(302)) &
X(302) = X(302)-JVS(2768)*X(171)-JVS(2769)*X(190)-JVS(2770)*X(207)-JVS(2771)*X(226)-JVS(2772)*X(230)-JVS(2773)*X(254)&
&-JVS(2774)*X(267)-JVS(2775)*X(271)-JVS(2776)*X(276)-JVS(2777)*X(293)-JVS(2778)*X(299)-JVS(2779)*X(301)
IF (DO_SLV(303)) &
X(303) = X(303)-JVS(2796)*X(186)-JVS(2797)*X(190)-JVS(2798)*X(205)-JVS(2799)*X(206)-JVS(2800)*X(207)-JVS(2801)*X(222)&
&-JVS(2802)*X(223)-JVS(2803)*X(224)-JVS(2804)*X(226)-JVS(2805)*X(232)-JVS(2806)*X(267)-JVS(2807)*X(268)&
&-JVS(2808)*X(271)-JVS(2809)*X(293)-JVS(2810)*X(299)
IF (DO_SLV(304)) &
X(304) = X(304)-JVS(2822)*X(186)-JVS(2823)*X(192)-JVS(2824)*X(199)-JVS(2825)*X(276)
IF (DO_SLV(305)) &
X(305) = X(305)-JVS(2836)*X(186)-JVS(2837)*X(187)-JVS(2838)*X(209)-JVS(2839)*X(276)-JVS(2840)*X(304)
IF (DO_SLV(306)) &
X(306) = X(306)-JVS(2850)*X(70)-JVS(2851)*X(106)-JVS(2852)*X(113)-JVS(2853)*X(126)-JVS(2854)*X(127)-JVS(2855)*X(132)&
&-JVS(2856)*X(136)-JVS(2857)*X(174)-JVS(2858)*X(180)-JVS(2859)*X(197)-JVS(2860)*X(198)-JVS(2861)*X(201)&
&-JVS(2862)*X(202)-JVS(2863)*X(205)-JVS(2864)*X(206)-JVS(2865)*X(212)-JVS(2866)*X(220)-JVS(2867)*X(221)&
&-JVS(2868)*X(223)-JVS(2869)*X(224)-JVS(2870)*X(232)-JVS(2871)*X(233)-JVS(2872)*X(234)-JVS(2873)*X(246)&
&-JVS(2874)*X(254)-JVS(2875)*X(258)-JVS(2876)*X(262)-JVS(2877)*X(266)-JVS(2878)*X(267)-JVS(2879)*X(268)&
&-JVS(2880)*X(269)-JVS(2881)*X(271)-JVS(2882)*X(276)-JVS(2883)*X(285)-JVS(2884)*X(286)-JVS(2885)*X(288)&
&-JVS(2886)*X(291)-JVS(2887)*X(293)-JVS(2888)*X(299)-JVS(2889)*X(301)-JVS(2890)*X(302)-JVS(2891)*X(303)&
&-JVS(2892)*X(304)-JVS(2893)*X(305)
IF (DO_SLV(307)) &
X(307) = X(307)-JVS(2908)*X(123)-JVS(2909)*X(153)-JVS(2910)*X(154)-JVS(2911)*X(159)-JVS(2912)*X(174)-JVS(2913)*X(184)&
&-JVS(2914)*X(198)-JVS(2915)*X(205)-JVS(2916)*X(207)-JVS(2917)*X(215)-JVS(2918)*X(223)-JVS(2919)*X(224)&
&-JVS(2920)*X(230)-JVS(2921)*X(231)-JVS(2922)*X(232)-JVS(2923)*X(242)-JVS(2924)*X(243)-JVS(2925)*X(248)&
&-JVS(2926)*X(253)-JVS(2927)*X(256)-JVS(2928)*X(258)-JVS(2929)*X(259)-JVS(2930)*X(260)-JVS(2931)*X(267)&
&-JVS(2932)*X(268)-JVS(2933)*X(271)-JVS(2934)*X(272)-JVS(2935)*X(273)-JVS(2936)*X(275)-JVS(2937)*X(276)&
&-JVS(2938)*X(277)-JVS(2939)*X(278)-JVS(2940)*X(280)-JVS(2941)*X(281)-JVS(2942)*X(285)-JVS(2943)*X(286)&
&-JVS(2944)*X(287)-JVS(2945)*X(289)-JVS(2946)*X(290)-JVS(2947)*X(291)-JVS(2948)*X(293)-JVS(2949)*X(299)&
&-JVS(2950)*X(301)-JVS(2951)*X(303)-JVS(2952)*X(304)-JVS(2953)*X(305)
IF (DO_SLV(308)) &
X(308) = X(308)-JVS(2971)*X(248)-JVS(2972)*X(253)-JVS(2973)*X(276)-JVS(2974)*X(301)-JVS(2975)*X(303)-JVS(2976)*X(304)&
&-JVS(2977)*X(305)
IF (DO_SLV(309)) &
X(309) = X(309)-JVS(2991)*X(135)-JVS(2992)*X(144)-JVS(2993)*X(168)-JVS(2994)*X(192)-JVS(2995)*X(199)-JVS(2996)*X(222)&
&-JVS(2997)*X(231)-JVS(2998)*X(276)-JVS(2999)*X(299)-JVS(3000)*X(303)-JVS(3001)*X(304)-JVS(3002)*X(305)
IF (DO_SLV(310)) &
X(310) = X(310)-JVS(3014)*X(222)-JVS(3015)*X(276)
IF (DO_SLV(311)) &
X(311) = X(311)-JVS(3026)*X(186)-JVS(3027)*X(276)-JVS(3028)*X(310)
IF (DO_SLV(312)) &
X(312) = X(312)-JVS(3038)*X(109)-JVS(3039)*X(191)-JVS(3040)*X(220)-JVS(3041)*X(233)-JVS(3042)*X(255)-JVS(3043)*X(276)&
&-JVS(3044)*X(281)-JVS(3045)*X(290)-JVS(3046)*X(309)-JVS(3047)*X(310)-JVS(3048)*X(311)
IF (DO_SLV(313)) &
X(313) = X(313)-JVS(3064)*X(244)-JVS(3065)*X(271)-JVS(3066)*X(276)-JVS(3067)*X(287)-JVS(3068)*X(295)-JVS(3069)*X(300)&
&-JVS(3070)*X(301)-JVS(3071)*X(303)-JVS(3072)*X(304)-JVS(3073)*X(305)-JVS(3074)*X(309)-JVS(3075)*X(310)&
&-JVS(3076)*X(311)
IF (DO_SLV(314)) &
X(314) = X(314)-JVS(3092)*X(82)-JVS(3093)*X(101)-JVS(3094)*X(133)-JVS(3095)*X(150)-JVS(3096)*X(175)-JVS(3097)*X(187)&
&-JVS(3098)*X(209)-JVS(3099)*X(219)-JVS(3100)*X(222)-JVS(3101)*X(229)-JVS(3102)*X(230)-JVS(3103)*X(262)&
&-JVS(3104)*X(276)-JVS(3105)*X(291)-JVS(3106)*X(299)-JVS(3107)*X(303)-JVS(3108)*X(304)-JVS(3109)*X(305)&
&-JVS(3110)*X(310)-JVS(3111)*X(311)
IF (DO_SLV(315)) &
X(315) = X(315)-JVS(3121)*X(118)-JVS(3122)*X(251)-JVS(3123)*X(279)-JVS(3124)*X(292)-JVS(3125)*X(296)-JVS(3126)*X(298)&
&-JVS(3127)*X(300)-JVS(3128)*X(314)
IF (DO_SLV(316)) &
X(316) = X(316)-JVS(3146)*X(148)-JVS(3147)*X(218)
IF (DO_SLV(318)) &
X(318) = X(318)-JVS(3177)*X(251)-JVS(3178)*X(269)
IF (DO_SLV(319)) &
X(319) = X(319)-JVS(3190)*X(97)-JVS(3191)*X(130)-JVS(3192)*X(142)-JVS(3193)*X(161)-JVS(3194)*X(162)-JVS(3195)*X(169)&
&-JVS(3196)*X(178)-JVS(3197)*X(249)-JVS(3198)*X(272)-JVS(3199)*X(273)-JVS(3200)*X(274)-JVS(3201)*X(275)&
&-JVS(3202)*X(279)-JVS(3203)*X(281)-JVS(3204)*X(300)-JVS(3205)*X(318)
IF (DO_SLV(320)) &
X(320) = X(320)-JVS(3217)*X(219)-JVS(3218)*X(292)-JVS(3219)*X(300)-JVS(3220)*X(318)-JVS(3221)*X(319)
IF (DO_SLV(321)) &
X(321) = X(321)-JVS(3232)*X(99)-JVS(3233)*X(141)-JVS(3234)*X(251)-JVS(3235)*X(279)-JVS(3236)*X(292)-JVS(3237)*X(298)&
&-JVS(3238)*X(300)-JVS(3239)*X(314)-JVS(3240)*X(318)-JVS(3241)*X(319)-JVS(3242)*X(320)
IF (DO_SLV(322)) &
X(322) = X(322)-JVS(3256)*X(124)-JVS(3257)*X(155)-JVS(3258)*X(160)-JVS(3259)*X(176)-JVS(3260)*X(196)-JVS(3261)*X(201)&
&-JVS(3262)*X(221)-JVS(3263)*X(240)-JVS(3264)*X(246)-JVS(3265)*X(269)-JVS(3266)*X(277)-JVS(3267)*X(278)&
&-JVS(3268)*X(292)-JVS(3269)*X(298)-JVS(3270)*X(300)-JVS(3271)*X(314)-JVS(3272)*X(318)-JVS(3273)*X(319)&
&-JVS(3274)*X(320)-JVS(3275)*X(321)
IF (DO_SLV(323)) &
X(323) = X(323)-JVS(3288)*X(100)-JVS(3289)*X(141)-JVS(3290)*X(251)-JVS(3291)*X(279)-JVS(3292)*X(292)-JVS(3293)*X(298)&
&-JVS(3294)*X(300)-JVS(3295)*X(314)-JVS(3296)*X(318)-JVS(3297)*X(319)-JVS(3298)*X(320)-JVS(3299)*X(321)&
&-JVS(3300)*X(322)
IF (DO_SLV(324)) &
X(324) = X(324)-JVS(3312)*X(92)-JVS(3313)*X(107)-JVS(3314)*X(115)-JVS(3315)*X(122)-JVS(3316)*X(130)-JVS(3317)*X(139)&
&-JVS(3318)*X(146)-JVS(3319)*X(159)-JVS(3320)*X(169)-JVS(3321)*X(184)-JVS(3322)*X(185)-JVS(3323)*X(194)&
&-JVS(3324)*X(196)-JVS(3325)*X(200)-JVS(3326)*X(208)-JVS(3327)*X(209)-JVS(3328)*X(227)-JVS(3329)*X(230)&
&-JVS(3330)*X(231)-JVS(3331)*X(240)-JVS(3332)*X(243)-JVS(3333)*X(244)-JVS(3334)*X(247)-JVS(3335)*X(249)&
&-JVS(3336)*X(250)-JVS(3337)*X(254)-JVS(3338)*X(257)-JVS(3339)*X(258)-JVS(3340)*X(259)-JVS(3341)*X(260)&
&-JVS(3342)*X(261)-JVS(3343)*X(263)-JVS(3344)*X(267)-JVS(3345)*X(268)-JVS(3346)*X(271)-JVS(3347)*X(272)&
&-JVS(3348)*X(274)-JVS(3349)*X(275)-JVS(3350)*X(276)-JVS(3351)*X(277)-JVS(3352)*X(278)-JVS(3353)*X(279)&
&-JVS(3354)*X(280)-JVS(3355)*X(281)-JVS(3356)*X(285)-JVS(3357)*X(286)-JVS(3358)*X(287)-JVS(3359)*X(288)&
&-JVS(3360)*X(289)-JVS(3361)*X(290)-JVS(3362)*X(291)-JVS(3363)*X(292)-JVS(3364)*X(293)-JVS(3365)*X(294)&
&-JVS(3366)*X(295)-JVS(3367)*X(296)-JVS(3368)*X(299)-JVS(3369)*X(300)-JVS(3370)*X(301)-JVS(3371)*X(302)&
&-JVS(3372)*X(303)-JVS(3373)*X(304)-JVS(3374)*X(305)-JVS(3375)*X(307)-JVS(3376)*X(308)-JVS(3377)*X(309)&
&-JVS(3378)*X(310)-JVS(3379)*X(311)-JVS(3380)*X(313)-JVS(3381)*X(314)-JVS(3382)*X(315)-JVS(3383)*X(318)&
&-JVS(3384)*X(319)-JVS(3385)*X(320)-JVS(3386)*X(321)-JVS(3387)*X(322)-JVS(3388)*X(323)
IF (DO_SLV(325)) &
X(325) = X(325)-JVS(3400)*X(72)-JVS(3401)*X(80)-JVS(3402)*X(88)-JVS(3403)*X(89)-JVS(3404)*X(92)-JVS(3405)*X(93)&
&-JVS(3406)*X(94)-JVS(3407)*X(106)-JVS(3408)*X(109)-JVS(3409)*X(112)-JVS(3410)*X(114)-JVS(3411)*X(122)&
&-JVS(3412)*X(123)-JVS(3413)*X(127)-JVS(3414)*X(130)-JVS(3415)*X(136)-JVS(3416)*X(137)-JVS(3417)*X(138)&
&-JVS(3418)*X(139)-JVS(3419)*X(140)-JVS(3420)*X(146)-JVS(3421)*X(149)-JVS(3422)*X(159)-JVS(3423)*X(160)&
&-JVS(3424)*X(164)-JVS(3425)*X(165)-JVS(3426)*X(168)-JVS(3427)*X(169)-JVS(3428)*X(175)-JVS(3429)*X(176)&
&-JVS(3430)*X(187)-JVS(3431)*X(190)-JVS(3432)*X(191)-JVS(3433)*X(192)-JVS(3434)*X(196)-JVS(3435)*X(197)&
&-JVS(3436)*X(199)-JVS(3437)*X(200)-JVS(3438)*X(205)-JVS(3439)*X(206)-JVS(3440)*X(207)-JVS(3441)*X(208)&
&-JVS(3442)*X(209)-JVS(3443)*X(210)-JVS(3444)*X(211)-JVS(3445)*X(212)-JVS(3446)*X(213)-JVS(3447)*X(215)&
&-JVS(3448)*X(219)-JVS(3449)*X(220)-JVS(3450)*X(222)-JVS(3451)*X(223)-JVS(3452)*X(224)-JVS(3453)*X(226)&
&-JVS(3454)*X(228)-JVS(3455)*X(229)-JVS(3456)*X(230)-JVS(3457)*X(231)-JVS(3458)*X(233)-JVS(3459)*X(234)&
&-JVS(3460)*X(235)-JVS(3461)*X(236)-JVS(3462)*X(240)-JVS(3463)*X(243)-JVS(3464)*X(244)-JVS(3465)*X(246)&
&-JVS(3466)*X(247)-JVS(3467)*X(249)-JVS(3468)*X(250)-JVS(3469)*X(253)-JVS(3470)*X(254)-JVS(3471)*X(255)&
&-JVS(3472)*X(257)-JVS(3473)*X(258)-JVS(3474)*X(259)-JVS(3475)*X(260)-JVS(3476)*X(261)-JVS(3477)*X(262)&
&-JVS(3478)*X(263)-JVS(3479)*X(267)-JVS(3480)*X(268)-JVS(3481)*X(270)-JVS(3482)*X(271)-JVS(3483)*X(272)&
&-JVS(3484)*X(273)-JVS(3485)*X(274)-JVS(3486)*X(275)-JVS(3487)*X(276)-JVS(3488)*X(277)-JVS(3489)*X(278)&
&-JVS(3490)*X(279)-JVS(3491)*X(280)-JVS(3492)*X(281)-JVS(3493)*X(282)-JVS(3494)*X(285)-JVS(3495)*X(286)&
&-JVS(3496)*X(287)-JVS(3497)*X(288)-JVS(3498)*X(289)-JVS(3499)*X(290)-JVS(3500)*X(291)-JVS(3501)*X(293)&
&-JVS(3502)*X(296)-JVS(3503)*X(299)-JVS(3504)*X(300)-JVS(3505)*X(301)-JVS(3506)*X(302)-JVS(3507)*X(303)&
&-JVS(3508)*X(304)-JVS(3509)*X(305)-JVS(3510)*X(306)-JVS(3511)*X(307)-JVS(3512)*X(308)-JVS(3513)*X(309)&
&-JVS(3514)*X(310)-JVS(3515)*X(311)-JVS(3516)*X(312)-JVS(3517)*X(313)-JVS(3518)*X(314)-JVS(3519)*X(315)&
&-JVS(3520)*X(318)-JVS(3521)*X(319)-JVS(3522)*X(320)-JVS(3523)*X(321)-JVS(3524)*X(322)-JVS(3525)*X(323)&