| 1 | |
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| 2 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 3 | SUBROUTINE KppDecomp( JVS, IER ) |
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| 4 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 5 | ! Sparse LU factorization |
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| 6 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 7 | |
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| 8 | USE KPP_ROOT_Parameters |
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| 9 | USE KPP_ROOT_JacobianSP |
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| 10 | |
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| 11 | INTEGER :: IER |
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| 12 | KPP_REAL :: JVS(LU_NONZERO), W(NVAR), a |
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| 13 | INTEGER :: k, kk, j, jj |
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| 14 | |
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| 15 | a = 0. ! mz_rs_20050606 |
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| 16 | IER = 0 |
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| 17 | DO k=1,NVAR |
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| 18 | ! mz_rs_20050606: don't check if real value == 0 |
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| 19 | ! IF ( JVS( LU_DIAG(k) ) .EQ. 0. ) THEN |
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| 20 | IF ( ABS(JVS(LU_DIAG(k))) < TINY(a) ) THEN |
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| 21 | IER = k |
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| 22 | RETURN |
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| 23 | END IF |
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| 24 | DO kk = LU_CROW(k), LU_CROW(k+1)-1 |
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| 25 | W( LU_ICOL(kk) ) = JVS(kk) |
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| 26 | END DO |
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| 27 | DO kk = LU_CROW(k), LU_DIAG(k)-1 |
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| 28 | j = LU_ICOL(kk) |
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| 29 | a = -W(j) / JVS( LU_DIAG(j) ) |
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| 30 | W(j) = -a |
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| 31 | DO jj = LU_DIAG(j)+1, LU_CROW(j+1)-1 |
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| 32 | W( LU_ICOL(jj) ) = W( LU_ICOL(jj) ) + a*JVS(jj) |
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| 33 | END DO |
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| 34 | END DO |
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| 35 | DO kk = LU_CROW(k), LU_CROW(k+1)-1 |
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| 36 | JVS(kk) = W( LU_ICOL(kk) ) |
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| 37 | END DO |
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| 38 | END DO |
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| 39 | |
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| 40 | END SUBROUTINE KppDecomp |
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| 41 | |
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| 42 | |
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| 43 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 44 | SUBROUTINE KppDecompCmplx( JVS, IER ) |
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| 45 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 46 | ! Sparse LU factorization, complex |
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| 47 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 48 | |
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| 49 | USE KPP_ROOT_Parameters |
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| 50 | USE KPP_ROOT_JacobianSP |
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| 51 | |
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| 52 | INTEGER :: IER |
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| 53 | DOUBLE COMPLEX :: JVS(LU_NONZERO), W(NVAR), a |
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| 54 | KPP_REAL :: b = 0.0 |
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| 55 | INTEGER :: k, kk, j, jj |
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| 56 | |
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| 57 | IER = 0 |
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| 58 | DO k=1,NVAR |
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| 59 | IF ( ABS(JVS(LU_DIAG(k))) < TINY(b) ) THEN |
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| 60 | IER = k |
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| 61 | RETURN |
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| 62 | END IF |
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| 63 | DO kk = LU_CROW(k), LU_CROW(k+1)-1 |
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| 64 | W( LU_ICOL(kk) ) = JVS(kk) |
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| 65 | END DO |
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| 66 | DO kk = LU_CROW(k), LU_DIAG(k)-1 |
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| 67 | j = LU_ICOL(kk) |
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| 68 | a = -W(j) / JVS( LU_DIAG(j) ) |
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| 69 | W(j) = -a |
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| 70 | DO jj = LU_DIAG(j)+1, LU_CROW(j+1)-1 |
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| 71 | W( LU_ICOL(jj) ) = W( LU_ICOL(jj) ) + a*JVS(jj) |
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| 72 | END DO |
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| 73 | END DO |
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| 74 | DO kk = LU_CROW(k), LU_CROW(k+1)-1 |
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| 75 | JVS(kk) = W( LU_ICOL(kk) ) |
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| 76 | END DO |
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| 77 | END DO |
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| 78 | |
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| 79 | END SUBROUTINE KppDecompCmplx |
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| 80 | |
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| 81 | |
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| 82 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 83 | SUBROUTINE KppDecompCmplxR( JVSR, JVSI, IER ) |
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| 84 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 85 | ! Sparse LU factorization, complex |
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| 86 | ! (Real and Imaginary parts are used instead of complex data type) |
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| 87 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 88 | |
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| 89 | USE KPP_ROOT_Parameters |
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| 90 | USE KPP_ROOT_JacobianSP |
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| 91 | |
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| 92 | INTEGER :: IER |
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| 93 | KPP_REAL :: JVSR(LU_NONZERO), JVSI(LU_NONZERO) |
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| 94 | KPP_REAL :: WR(NVAR), WI(NVAR), ar, ai, den |
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| 95 | INTEGER :: k, kk, j, jj |
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| 96 | |
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| 97 | IER = 0 |
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| 98 | ar = 0.0 |
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| 99 | DO k=1,NVAR |
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| 100 | IF ( ( ABS(JVSR(LU_DIAG(k))) < TINY(ar) ) .AND. & |
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| 101 | ( ABS(JVSI(LU_DIAG(k))) < TINY(ar) ) ) THEN |
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| 102 | IER = k |
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| 103 | RETURN |
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| 104 | END IF |
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| 105 | DO kk = LU_CROW(k), LU_CROW(k+1)-1 |
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| 106 | WR( LU_ICOL(kk) ) = JVSR(kk) |
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| 107 | WI( LU_ICOL(kk) ) = JVSI(kk) |
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| 108 | END DO |
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| 109 | DO kk = LU_CROW(k), LU_DIAG(k)-1 |
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| 110 | j = LU_ICOL(kk) |
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| 111 | den = JVSR(LU_DIAG(j))**2 + JVSI(LU_DIAG(j))**2 |
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| 112 | ar = -(WR(j)*JVSR(LU_DIAG(j)) + WI(j)*JVSI(LU_DIAG(j)))/den |
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| 113 | ai = -(WI(j)*JVSR(LU_DIAG(j)) - WR(j)*JVSI(LU_DIAG(j)))/den |
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| 114 | WR(j) = -ar |
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| 115 | WI(j) = -ai |
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| 116 | DO jj = LU_DIAG(j)+1, LU_CROW(j+1)-1 |
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| 117 | WR( LU_ICOL(jj) ) = WR( LU_ICOL(jj) ) + ar*JVSR(jj) - ai*JVSI(jj) |
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| 118 | WI( LU_ICOL(jj) ) = WI( LU_ICOL(jj) ) + ar*JVSI(jj) + ai*JVSR(jj) |
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| 119 | END DO |
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| 120 | END DO |
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| 121 | DO kk = LU_CROW(k), LU_CROW(k+1)-1 |
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| 122 | JVSR(kk) = WR( LU_ICOL(kk) ) |
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| 123 | JVSI(kk) = WI( LU_ICOL(kk) ) |
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| 124 | END DO |
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| 125 | END DO |
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| 126 | |
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| 127 | END SUBROUTINE KppDecompCmplxR |
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| 128 | |
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| 129 | |
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| 130 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 131 | SUBROUTINE KppSolveIndirect( JVS, X ) |
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| 132 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 133 | ! Sparse solve subroutine using indirect addressing |
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| 134 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 135 | |
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| 136 | USE KPP_ROOT_Parameters |
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| 137 | USE KPP_ROOT_JacobianSP |
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| 138 | |
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| 139 | INTEGER :: i, j |
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| 140 | KPP_REAL :: JVS(LU_NONZERO), X(NVAR), sum |
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| 141 | |
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| 142 | DO i=1,NVAR |
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| 143 | DO j = LU_CROW(i), LU_DIAG(i)-1 |
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| 144 | X(i) = X(i) - JVS(j)*X(LU_ICOL(j)); |
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| 145 | END DO |
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| 146 | END DO |
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| 147 | |
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| 148 | DO i=NVAR,1,-1 |
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| 149 | sum = X(i); |
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| 150 | DO j = LU_DIAG(i)+1, LU_CROW(i+1)-1 |
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| 151 | sum = sum - JVS(j)*X(LU_ICOL(j)); |
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| 152 | END DO |
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| 153 | X(i) = sum/JVS(LU_DIAG(i)); |
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| 154 | END DO |
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| 155 | |
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| 156 | END SUBROUTINE KppSolveIndirect |
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| 157 | |
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| 158 | |
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| 159 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 160 | SUBROUTINE KppSolveTRIndirect( JVS, X ) |
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| 161 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 162 | ! Complex sparse solve transpose subroutine using indirect addressing |
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| 163 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 164 | |
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| 165 | USE KPP_ROOT_Parameters |
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| 166 | USE KPP_ROOT_JacobianSP |
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| 167 | |
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| 168 | INTEGER :: i, j |
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| 169 | KPP_REAL :: JVS(LU_NONZERO), X(NVAR) |
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| 170 | |
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| 171 | DO i=1,NVAR |
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| 172 | X(i) = X(i)/JVS(LU_DIAG(i)) |
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| 173 | ! subtract all nonzero elements in row i of JVS from X |
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| 174 | DO j=LU_DIAG(i)+1,LU_CROW(i+1)-1 |
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| 175 | X(LU_ICOL(j)) = X(LU_ICOL(j))-JVS(j)*X(i) |
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| 176 | END DO |
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| 177 | END DO |
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| 178 | |
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| 179 | DO i=NVAR, 1, -1 |
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| 180 | ! subtract all nonzero elements in row i of JVS from X |
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| 181 | DO j=LU_CROW(i),LU_DIAG(i)-1 |
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| 182 | X(LU_ICOL(j)) = X(LU_ICOL(j))-JVS(j)*X(i) |
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| 183 | END DO |
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| 184 | END DO |
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| 185 | |
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| 186 | END SUBROUTINE KppSolveTRIndirect |
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| 187 | |
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| 188 | |
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| 189 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 190 | SUBROUTINE KppSolveCmplx( JVS, X ) |
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| 191 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 192 | ! Complex sparse solve subroutine using indirect addressing |
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| 193 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 194 | |
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| 195 | USE KPP_ROOT_Parameters |
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| 196 | USE KPP_ROOT_JacobianSP |
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| 197 | |
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| 198 | INTEGER :: i, j |
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| 199 | DOUBLE COMPLEX :: JVS(LU_NONZERO), X(NVAR), sum |
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| 200 | |
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| 201 | DO i=1,NVAR |
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| 202 | DO j = LU_CROW(i), LU_DIAG(i)-1 |
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| 203 | X(i) = X(i) - JVS(j)*X(LU_ICOL(j)); |
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| 204 | END DO |
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| 205 | END DO |
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| 206 | |
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| 207 | DO i=NVAR,1,-1 |
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| 208 | sum = X(i); |
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| 209 | DO j = LU_DIAG(i)+1, LU_CROW(i+1)-1 |
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| 210 | sum = sum - JVS(j)*X(LU_ICOL(j)); |
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| 211 | END DO |
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| 212 | X(i) = sum/JVS(LU_DIAG(i)); |
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| 213 | END DO |
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| 214 | |
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| 215 | END SUBROUTINE KppSolveCmplx |
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| 216 | |
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| 217 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 218 | SUBROUTINE KppSolveCmplxR( JVSR, JVSI, XR, XI ) |
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| 219 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 220 | ! Complex sparse solve subroutine using indirect addressing |
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| 221 | ! (Real and Imaginary parts are used instead of complex data type) |
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| 222 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 223 | |
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| 224 | USE KPP_ROOT_Parameters |
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| 225 | USE KPP_ROOT_JacobianSP |
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| 226 | |
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| 227 | INTEGER :: i, j |
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| 228 | KPP_REAL :: JVSR(LU_NONZERO), JVSI(LU_NONZERO), XR(NVAR), XI(NVAR), sumr, sumi, den |
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| 229 | |
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| 230 | DO i=1,NVAR |
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| 231 | DO j = LU_CROW(i), LU_DIAG(i)-1 |
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| 232 | XR(i) = XR(i) - (JVSR(j)*XR(LU_ICOL(j)) - JVSI(j)*XI(LU_ICOL(j))) |
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| 233 | XI(i) = XI(i) - (JVSR(j)*XI(LU_ICOL(j)) + JVSI(j)*XR(LU_ICOL(j))) |
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| 234 | END DO |
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| 235 | END DO |
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| 236 | |
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| 237 | DO i=NVAR,1,-1 |
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| 238 | sumr = XR(i); sumi = XI(i) |
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| 239 | DO j = LU_DIAG(i)+1, LU_CROW(i+1)-1 |
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| 240 | sumr = sumr - (JVSR(j)*XR(LU_ICOL(j)) - JVSI(j)*XI(LU_ICOL(j))) |
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| 241 | sumi = sumi - (JVSR(j)*XI(LU_ICOL(j)) + JVSI(j)*XR(LU_ICOL(j))) |
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| 242 | END DO |
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| 243 | den = JVSR(LU_DIAG(i))**2 + JVSI(LU_DIAG(i))**2 |
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| 244 | XR(i) = (sumr*JVSR(LU_DIAG(i)) + sumi*JVSI(LU_DIAG(i)))/den |
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| 245 | XI(i) = (sumi*JVSR(LU_DIAG(i)) - sumr*JVSI(LU_DIAG(i)))/den |
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| 246 | END DO |
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| 247 | |
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| 248 | END SUBROUTINE KppSolveCmplxR |
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| 249 | |
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| 250 | |
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| 251 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 252 | SUBROUTINE KppSolveTRCmplx( JVS, X ) |
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| 253 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 254 | ! Complex sparse solve transpose subroutine using indirect addressing |
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| 255 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 256 | |
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| 257 | USE KPP_ROOT_Parameters |
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| 258 | USE KPP_ROOT_JacobianSP |
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| 259 | |
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| 260 | INTEGER :: i, j |
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| 261 | DOUBLE COMPLEX :: JVS(LU_NONZERO), X(NVAR) |
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| 262 | |
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| 263 | DO i=1,NVAR |
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| 264 | X(i) = X(i)/JVS(LU_DIAG(i)) |
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| 265 | ! subtract all nonzero elements in row i of JVS from X |
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| 266 | DO j=LU_DIAG(i)+1,LU_CROW(i+1)-1 |
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| 267 | X(LU_ICOL(j)) = X(LU_ICOL(j))-JVS(j)*X(i) |
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| 268 | END DO |
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| 269 | END DO |
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| 270 | |
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| 271 | DO i=NVAR, 1, -1 |
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| 272 | ! subtract all nonzero elements in row i of JVS from X |
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| 273 | DO j=LU_CROW(i),LU_DIAG(i)-1 |
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| 274 | X(LU_ICOL(j)) = X(LU_ICOL(j))-JVS(j)*X(i) |
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| 275 | END DO |
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| 276 | END DO |
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| 277 | |
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| 278 | END SUBROUTINE KppSolveTRCmplx |
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| 279 | |
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| 280 | |
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| 281 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 282 | SUBROUTINE KppSolveTRCmplxR( JVSR, JVSI, XR, XI ) |
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| 283 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 284 | ! Complex sparse solve transpose subroutine using indirect addressing |
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| 285 | ! (Real and Imaginary parts are used instead of complex data type) |
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| 286 | ! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 287 | |
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| 288 | USE KPP_ROOT_Parameters |
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| 289 | USE KPP_ROOT_JacobianSP |
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| 290 | |
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| 291 | INTEGER :: i, j |
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| 292 | KPP_REAL :: JVSR(LU_NONZERO), JVSI(LU_NONZERO), XR(NVAR), XI(NVAR), den |
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| 293 | |
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| 294 | DO i=1,NVAR |
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| 295 | den = JVSR(LU_DIAG(i))**2 + JVSI(LU_DIAG(i))**2 |
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| 296 | XR(i) = (XR(i)*JVSR(LU_DIAG(i)) + XI(i)*JVSI(LU_DIAG(i)))/den |
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| 297 | XI(i) = (XI(i)*JVSR(LU_DIAG(i)) - XR(i)*JVSI(LU_DIAG(i)))/den |
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| 298 | ! subtract all nonzero elements in row i of JVS from X |
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| 299 | DO j=LU_DIAG(i)+1,LU_CROW(i+1)-1 |
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| 300 | XR(LU_ICOL(j)) = XR(LU_ICOL(j))-(JVSR(j)*XR(i) - JVSI(j)*XI(i)) |
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| 301 | XI(LU_ICOL(j)) = XI(LU_ICOL(j))-(JVSI(j)*XR(i) + JVSR(j)*XI(i)) |
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| 302 | END DO |
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| 303 | END DO |
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| 304 | |
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| 305 | DO i=NVAR, 1, -1 |
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| 306 | ! subtract all nonzero elements in row i of JVS from X |
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| 307 | DO j=LU_CROW(i),LU_DIAG(i)-1 |
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| 308 | XR(LU_ICOL(j)) = XR(LU_ICOL(j))-(JVSR(j)*XR(i) - JVSI(j)*XI(i)) |
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| 309 | XI(LU_ICOL(j)) = XI(LU_ICOL(j))-(JVSI(j)*XR(i) + JVSR(j)*XI(i)) |
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| 310 | END DO |
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| 311 | END DO |
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| 312 | |
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| 313 | END SUBROUTINE KppSolveTRCmplxR |
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| 314 | |
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| 315 | |
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| 316 | ! |
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| 317 | ! Next few commented subroutines perform sparse big linear algebra |
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| 318 | ! |
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| 319 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 320 | !SUBROUTINE KppDecompBig( JVS, IP, IER ) |
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| 321 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 322 | !! Sparse LU factorization |
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| 323 | !! for the Runge Kutta (3n)x(3n) linear system |
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| 324 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 325 | ! |
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| 326 | ! USE KPP_ROOT_Parameters |
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| 327 | ! USE KPP_ROOT_JacobianSP |
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| 328 | ! |
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| 329 | ! INTEGER :: IP3(3), IER, IP(3,NVAR) |
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| 330 | ! KPP_REAL :: JVS(3,3,LU_NONZERO), W(3,3,NVAR), a(3,3), E(3,3) |
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| 331 | ! INTEGER :: k, kk, j, jj |
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| 332 | ! |
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| 333 | ! a = 0.0d0 |
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| 334 | ! IER = 0 |
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| 335 | ! DO k=1,NVAR |
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| 336 | ! DO kk = LU_CROW(k), LU_CROW(k+1)-1 |
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| 337 | ! W( 1:3,1:3,LU_ICOL(kk) ) = JVS(1:3,1:3,kk) |
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| 338 | ! END DO |
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| 339 | ! DO kk = LU_CROW(k), LU_DIAG(k)-1 |
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| 340 | ! j = LU_ICOL(kk) |
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| 341 | ! E(1:3,1:3) = JVS( 1:3,1:3,LU_DIAG(j) ) |
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| 342 | ! ! CALL DGETRF(3,3,E,3,IP3,IER) |
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| 343 | ! CALL FAC3(E,IP3,IER) |
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| 344 | ! IF ( IER /= 0 ) RETURN |
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| 345 | ! ! a = W(j) / JVS( LU_DIAG(j) ) |
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| 346 | ! a(1:3,1:3) = W( 1:3,1:3,j ) |
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| 347 | ! ! CALL DGETRS ('N',3,3,E,3,IP3,a,3,IER) |
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| 348 | ! CALL SOL3('N',E,IP3,a(1,1)) |
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| 349 | ! CALL SOL3('N',E,IP3,a(1,2)) |
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| 350 | ! CALL SOL3('N',E,IP3,a(1,3)) |
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| 351 | ! W(1:3,1:3,j) = a(1:3,1:3) |
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| 352 | ! DO jj = LU_DIAG(j)+1, LU_CROW(j+1)-1 |
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| 353 | ! W( 1:3,1:3,LU_ICOL(jj) ) = W( 1:3,1:3,LU_ICOL(jj) ) & |
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| 354 | ! - MATMUL( a(1:3,1:3) , JVS(1:3,1:3,jj) ) |
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| 355 | ! END DO |
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| 356 | ! END DO |
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| 357 | ! DO kk = LU_CROW(k), LU_CROW(k+1)-1 |
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| 358 | ! JVS(1:3,1:3,kk) = W( 1:3,1:3,LU_ICOL(kk) ) |
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| 359 | ! END DO |
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| 360 | ! END DO |
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| 361 | ! |
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| 362 | ! DO k=1,NVAR |
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| 363 | ! ! CALL WGEFA(JVS(1,1,LU_DIAG(k)),3,3,IP(1,k),IER) |
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| 364 | ! ! CALL DGETRF(3,3,JVS(1,1,LU_DIAG(k)),3,IP(1,k),IER) |
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| 365 | ! CALL FAC3(JVS(1,1,LU_DIAG(k)),IP(1,k),IER) |
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| 366 | ! IF ( IER /= 0 ) RETURN |
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| 367 | ! END DO |
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| 368 | ! |
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| 369 | !END SUBROUTINE KppDecompBig |
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| 370 | ! |
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| 371 | ! |
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| 372 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 373 | !SUBROUTINE KppSolveBig( JVS, IP, X ) |
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| 374 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 375 | !! Sparse solve subroutine using indirect addressing |
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| 376 | !! for the Runge Kutta (3n)x(3n) linear system |
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| 377 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 378 | ! |
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| 379 | ! USE KPP_ROOT_Parameters |
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| 380 | ! USE KPP_ROOT_JacobianSP |
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| 381 | ! |
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| 382 | ! INTEGER :: i, j, k, m, IP3(3), IP(3,NVAR), IER |
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| 383 | ! KPP_REAL :: JVS(3,3,LU_NONZERO), X(3,NVAR), sum(3) |
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| 384 | ! |
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| 385 | ! DO i=1,NVAR |
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| 386 | ! DO j = LU_CROW(i), LU_DIAG(i)-1 |
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| 387 | ! !X(1:3,i) = X(1:3,i) - MATMUL(JVS(1:3,1:3,j),X(1:3,LU_ICOL(j))); |
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| 388 | ! DO k=1,3 |
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| 389 | ! DO m=1,3 |
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| 390 | ! X(k,i) = X(k,i) - JVS(k,m,j)*X(m,LU_ICOL(j)) |
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| 391 | ! END DO |
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| 392 | ! END DO |
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| 393 | ! END DO |
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| 394 | ! END DO |
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| 395 | ! |
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| 396 | ! DO i=NVAR,1,-1 |
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| 397 | ! sum(1:3) = X(1:3,i); |
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| 398 | ! DO j = LU_DIAG(i)+1, LU_CROW(i+1)-1 |
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| 399 | ! !sum(1:3) = sum(1:3) - MATMUL(JVS(1:3,1:3,j),X(1:3,LU_ICOL(j))); |
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| 400 | ! DO k=1,3 |
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| 401 | ! DO m=1,3 |
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| 402 | ! sum(k) = sum(k) - JVS(k,m,j)*X(m,LU_ICOL(j)) |
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| 403 | ! END DO |
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| 404 | ! END DO |
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| 405 | ! END DO |
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| 406 | ! ! X(i) = sum/JVS(LU_DIAG(i)); |
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| 407 | ! ! CALL DGETRS ('N',3,1,JVS(1:3,1:3,LU_DIAG(i)),3,IP(1,i),sum,3,0) |
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| 408 | ! ! CALL WGESL('N',JVS(1,1,LU_DIAG(i)),3,3,IP(1,i),sum) |
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| 409 | ! CALL SOL3('N',JVS(1,1,LU_DIAG(i)),IP(1,i),sum) |
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| 410 | ! X(1:3,i) = sum(1:3) |
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| 411 | ! END DO |
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| 412 | ! |
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| 413 | !END SUBROUTINE KppSolveBig |
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| 414 | ! |
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| 415 | ! |
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| 416 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 417 | !SUBROUTINE KppSolveBigTR( JVS, IP, X ) |
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| 418 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 419 | !! Big sparse transpose solve using indirect addressing |
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| 420 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 421 | ! |
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| 422 | ! USE KPP_ROOT_Parameters |
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| 423 | ! USE KPP_ROOT_JacobianSP |
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| 424 | ! |
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| 425 | ! INTEGER :: i, j, k, m, IP(3,NVAR) |
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| 426 | ! KPP_REAL :: JVS(3,3,LU_NONZERO), X(3,NVAR) |
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| 427 | ! |
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| 428 | ! DO i=1,NVAR |
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| 429 | ! ! X(i) = X(i)/JVS(LU_DIAG(i)) |
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| 430 | ! CALL SOL3('T',JVS(1,1,LU_DIAG(i)),IP(1,i),X(1,i)) |
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| 431 | ! DO j=LU_DIAG(i)+1,LU_CROW(i+1)-1 |
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| 432 | ! !X(1:3,LU_ICOL(j)) = X(1:3,LU_ICOL(j)) & |
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| 433 | ! ! - MATMUL( TRANSPOSE(JVS(1:3,1:3,j)), X(1:3,i) ) |
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| 434 | ! DO k=1,3 |
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| 435 | ! DO m=1,3 |
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| 436 | ! X(k,LU_ICOL(j)) = X(k,LU_ICOL(j)) - JVS(m,k,j)*X(m,i) |
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| 437 | ! END DO |
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| 438 | ! END DO |
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| 439 | ! END DO |
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| 440 | ! END DO |
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| 441 | ! |
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| 442 | ! DO i=NVAR, 1, -1 |
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| 443 | ! DO j=LU_CROW(i),LU_DIAG(i)-1 |
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| 444 | ! !X(1:3,LU_ICOL(j)) = X(1:3,LU_ICOL(j)) & |
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| 445 | ! ! - MATMUL( TRANSPOSE(JVS(1:3,1:3,j)), X(1:3,i) ) |
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| 446 | ! DO k=1,3 |
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| 447 | ! DO m=1,3 |
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| 448 | ! X(k,LU_ICOL(j)) = X(k,LU_ICOL(j)) - JVS(m,k,j)*X(m,i) |
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| 449 | ! END DO |
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| 450 | ! END DO |
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| 451 | ! END DO |
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| 452 | ! END DO |
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| 453 | ! |
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| 454 | !END SUBROUTINE KppSolveBigTR |
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| 455 | ! |
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| 456 | ! |
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| 457 | ! |
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| 458 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 459 | !SUBROUTINE FAC3(A,IPVT,INFO) |
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| 460 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 461 | !! FAC3 FACTORS THE MATRIX A (3,3) BY |
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| 462 | !! GAUSS ELIMINATION WITH PARTIAL PIVOTING |
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| 463 | !! LINPACK - LIKE |
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| 464 | !! |
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| 465 | !! Remove comments to perform pivoting |
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| 466 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 467 | !! |
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| 468 | ! KPP_REAL :: A(3,3) |
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| 469 | ! INTEGER :: IPVT(3),INFO |
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| 470 | !! INTEGER :: L |
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| 471 | !! KPP_REAL :: t, dmax, da, TMP(3) |
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| 472 | ! KPP_REAL, PARAMETER :: ZERO = 0.0, ONE = 1.0 |
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| 473 | ! |
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| 474 | ! info = 0 |
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| 475 | !! t = TINY(da) |
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| 476 | !! |
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| 477 | !! da = ABS(A(1,1)); L = 1 |
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| 478 | !! IF ( ABS(A(2,1))>da ) THEN |
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| 479 | !! da = ABS(A(2,1)); L = 2 |
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| 480 | !! IF ( ABS(A(3,1))>da ) THEN |
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| 481 | !! L = 3 |
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| 482 | !! END IF |
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| 483 | !! END IF |
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| 484 | !! IPVT(1) = L |
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| 485 | !! IF (L /=1 ) THEN |
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| 486 | !! TMP(1:3) = A(L,1:3) |
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| 487 | !! A(L,1:3) = A(1,1:3) |
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| 488 | !! A(1,1:3) = TMP(1:3) |
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| 489 | !! END IF |
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| 490 | !! IF (ABS(A(1,1)) < t) THEN |
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| 491 | !! info = 1 |
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| 492 | !! return |
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| 493 | !! END IF |
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| 494 | !! |
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| 495 | ! A(2,1) = A(2,1)/A(1,1) |
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| 496 | ! A(2,2) = A(2,2) - A(2,1)*A(1,2) |
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| 497 | ! A(2,3) = A(2,3) - A(2,1)*A(1,3) |
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| 498 | ! A(3,1) = A(3,1)/A(1,1) |
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| 499 | ! A(3,2) = A(3,2) - A(3,1)*A(1,2) |
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| 500 | ! A(3,3) = A(3,3) - A(3,1)*A(1,3) |
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| 501 | ! |
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| 502 | !! IPVT(2) = 2 |
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| 503 | !! IF (ABS(A(3,2))>ABS(A(2,2))) THEN |
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| 504 | !! IPVT(2) = 3 |
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| 505 | !! TMP(2:3) = A(3,2:3) |
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| 506 | !! A(3,2:3) = A(2,2:3) |
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| 507 | !! A(2,2:3) = TMP(2:3) |
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| 508 | !! END IF |
|---|
| 509 | !! IF (ABS(A(2,2)) < t) THEN |
|---|
| 510 | !! info = 1 |
|---|
| 511 | !! return |
|---|
| 512 | !! END IF |
|---|
| 513 | !! |
|---|
| 514 | ! A(3,2) = A(3,2)/A(2,2) |
|---|
| 515 | ! A(3,3) = A(3,3) - A(3,2)*A(2,3) |
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| 516 | ! IPVT(3) = 3 |
|---|
| 517 | ! |
|---|
| 518 | !END SUBROUTINE FAC3 |
|---|
| 519 | ! |
|---|
| 520 | ! |
|---|
| 521 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 522 | !SUBROUTINE SOL3(Trans,A,IPVT,b) |
|---|
| 523 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 524 | !! SOL3 solves the system 3x3 |
|---|
| 525 | !! A * x = b or trans(a) * x = b |
|---|
| 526 | !! using the factors computed by WGEFA. |
|---|
| 527 | !! |
|---|
| 528 | !! Trans = 'N' to solve A*x = b , |
|---|
| 529 | !! = 'T' to solve transpose(A)*x = b |
|---|
| 530 | !! LINPACK - LIKE |
|---|
| 531 | !! |
|---|
| 532 | !! Remove comments to use pivoting |
|---|
| 533 | !! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
|---|
| 534 | ! |
|---|
| 535 | ! CHARACTER :: Trans |
|---|
| 536 | ! KPP_REAL :: a(3,3),b(3) |
|---|
| 537 | ! INTEGER :: IPVT(3) |
|---|
| 538 | !! INTEGER :: L |
|---|
| 539 | !! KPP_REAL :: TMP |
|---|
| 540 | ! |
|---|
| 541 | ! SELECT CASE (Trans) |
|---|
| 542 | ! |
|---|
| 543 | ! CASE ('n','N') ! Solve A * x = b |
|---|
| 544 | ! |
|---|
| 545 | !! Solve L*y = b |
|---|
| 546 | !! L = IPVT(1) |
|---|
| 547 | !! IF (L /= 1) THEN |
|---|
| 548 | !! TMP = B(1); B(1) = B(L); B(L) = TMP |
|---|
| 549 | !! END IF |
|---|
| 550 | ! b(2) = b(2)-A(2,1)*b(1) |
|---|
| 551 | ! b(3) = b(3)-A(3,1)*b(1) |
|---|
| 552 | ! |
|---|
| 553 | !! L = IPVT(2) |
|---|
| 554 | !! IF (L /= 2) THEN |
|---|
| 555 | !! TMP = B(2); B(2) = B(L); B(L) = TMP |
|---|
| 556 | !! END IF |
|---|
| 557 | ! b(3) = b(3)-A(3,2)*b(2) |
|---|
| 558 | ! |
|---|
| 559 | !! Solve U*x = y |
|---|
| 560 | ! b(3) = b(3)/A(3,3) |
|---|
| 561 | ! b(2) = (b(2)-A(2,3)*b(3))/A(2,2) |
|---|
| 562 | ! b(1) = (b(1)-A(1,3)*b(3)-A(1,2)*b(2))/A(1,1) |
|---|
| 563 | ! |
|---|
| 564 | ! |
|---|
| 565 | ! CASE ('t','T') ! Solve transpose(A) * x = b |
|---|
| 566 | ! |
|---|
| 567 | !! Solve transpose(U)*y = b |
|---|
| 568 | ! b(1) = b(1)/A(1,1) |
|---|
| 569 | ! b(2) = (b(2)-A(1,2)*b(1))/A(2,2) |
|---|
| 570 | ! b(3) = (b(3)-A(1,3)*b(1)-A(2,3)*b(2))/A(3,3) |
|---|
| 571 | ! |
|---|
| 572 | !! Solve transpose(L)*x = y |
|---|
| 573 | ! b(2) = b(2)-A(3,2)*b(3) |
|---|
| 574 | !! L = ipvt(2) |
|---|
| 575 | !! IF (L /= 2) THEN |
|---|
| 576 | !! TMP = B(2); B(2) = B(L); B(L) = TMP |
|---|
| 577 | !! END IF |
|---|
| 578 | ! b(1) = b(1)-A(3,1)*b(3)-A(2,1)*b(2) |
|---|
| 579 | !! L = ipvt(1) |
|---|
| 580 | !! IF (L /= 1) THEN |
|---|
| 581 | !! TMP = B(1); B(1) = B(L); B(L) = TMP |
|---|
| 582 | !! END IF |
|---|
| 583 | ! |
|---|
| 584 | ! END SELECT |
|---|
| 585 | ! |
|---|
| 586 | !END SUBROUTINE SOL3 |
|---|
| 587 | |
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