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Add updated Rosenbrock coeffs by Mike Long (17 Jul 2025)
int/rosenbrock.c int/rosenbrock.f90 int/rosenbrock.m int/rosenbrock_adj.f90 int/rosenbrock_autoreduce.f90 int/rosenbrock_h211b_qssa.f90 int/rosenbrock_tlm.f90 - Update the Rodas3.1 coefficients to the set provided by Mike Long on 17 July 2025 - Update comments accordingly Signed-off-by: Bob Yantosca <[email protected]>
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‎int/rosenbrock.c‎

Lines changed: 29 additions & 29 deletions
Original file line numberDiff line numberDiff line change
@@ -1051,7 +1051,7 @@ void Rodas3_1 ( int *ros_S, KPP_REAL ros_A[], KPP_REAL ros_C[],
10511051
char ros_NewF[], KPP_REAL *ros_ELO, char* ros_Name )
10521052
/*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
10531053
--- A STIFFLY-STABLE METHOD, 4 stages, order 3
1054-
--- Updated coefficients by Mike Long (22 May 2025)
1054+
--- Updated coefficients by Mike Long (17 Jul 2025)
10551055
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/
10561056
{
10571057
/*~~~> Name of the method */
@@ -1065,20 +1065,20 @@ void Rodas3_1 ( int *ros_S, KPP_REAL ros_A[], KPP_REAL ros_C[],
10651065
A(2,1) = ros_A[0], A(3,1)=ros_A[1], A(3,2)=ros_A[2], etc.
10661066
The general mapping formula is:
10671067
A_{i,j} = ros_A[ (i-1)*(i-2)/2 + j -1 ] */
1068-
ros_A[0] = (KPP_REAL)0.00000000000000000;
1069-
ros_A[1] = (KPP_REAL)1.5382237953138116;
1070-
ros_A[2] = (KPP_REAL)(-0.36440683885434433);
1071-
ros_A[3] = (KPP_REAL)1.538223795313811;
1072-
ros_A[4] = (KPP_REAL)(-0.36440683885434433);
1073-
ros_A[5] = (KPP_REAL)1.0000000000000000;
1068+
ros_A[0] = (KPP_REAL)0.000000000000000;
1069+
ros_A[1] = (KPP_REAL)0.646601929740551;
1070+
ros_A[2] = (KPP_REAL)0.409567801987914;
1071+
ros_A[3] = (KPP_REAL)0.646601929740551;
1072+
ros_A[4] = (KPP_REAL)0.409567801987914;
1073+
ros_A[5] = (KPP_REAL)1.000000000000000;
10741074

10751075
/*~~~> C_{i,j} = ros_C[ (i-1)*(i-2)/2 + j -1] */
1076-
ros_C[0] = (KPP_REAL)(-4.0919303685081028);
1077-
ros_C[1] = (KPP_REAL)(-3.0551174378039538e-002);
1078-
ros_C[2] = (KPP_REAL)1.7259281281917580;
1079-
ros_C[3] = (KPP_REAL)0.19561160936073679;
1080-
ros_C[4] = (KPP_REAL)1.9301670595355112;
1081-
ros_C[5] = (KPP_REAL)(-2.6267006001193960);
1076+
ros_C[0] = (KPP_REAL)4.198495621784201;
1077+
ros_C[1] = (KPP_REAL)3.711590161613010;
1078+
ros_C[2] = (KPP_REAL)(-1.787771994729384);
1079+
ros_C[3] = (KPP_REAL)4.458898153216104;
1080+
ros_C[4] = (KPP_REAL)(-2.024095448516552);
1081+
ros_C[5] = (KPP_REAL)(-2.626700600119396);
10821082

10831083
/*~~~> does the stage i require a new function evaluation (ros_NewF(i)=TRUE)
10841084
or does it re-use the function evaluation from stage i-1 (ros_NewF(i)=FALSE) */
@@ -1088,32 +1088,32 @@ void Rodas3_1 ( int *ros_S, KPP_REAL ros_A[], KPP_REAL ros_C[],
10881088
ros_NewF[3] = 1;
10891089

10901090
/*~~~> M_i = Coefficients for new step solution */
1091-
ros_M[0] = (KPP_REAL)1.5382237953138116;
1092-
ros_M[1] = (KPP_REAL)(-0.36440683885434444);
1093-
ros_M[2] = (KPP_REAL)1.0000000000000002;
1094-
ros_M[3] = (KPP_REAL)1.0000000000000000;
1091+
ros_M[0] = (KPP_REAL)0.646601929740551;
1092+
ros_M[1] = (KPP_REAL)0.409567801987914;
1093+
ros_M[2] = (KPP_REAL)1.000000000000000;
1094+
ros_M[3] = (KPP_REAL)1.000000000000000;
10951095

10961096
/*~~~> E_i = Coefficients for error estimator */
1097-
ros_E[0] = (KPP_REAL)0.0000000000000000;
1098-
ros_E[1] = (KPP_REAL)0.0000000000000000;
1099-
ros_E[2] = (KPP_REAL)0.0000000000000000;
1100-
ros_E[3] = (KPP_REAL)1.0000000000000000;
1097+
ros_E[0] = (KPP_REAL)0.000000000000000;
1098+
ros_E[1] = (KPP_REAL)0.000000000000000;
1099+
ros_E[2] = (KPP_REAL)0.000000000000000;
1100+
ros_E[3] = (KPP_REAL)1.000000000000000;
11011101

11021102
/*~~~> ros_ELO = estimator of local order - the minimum between the
11031103
! main and the embedded scheme orders plus 1 */
11041104
*ros_ELO = (KPP_REAL)3.0000000000000000;
11051105

11061106
/*~~~> Y_stage_i ~ Y( T + H*Alpha_i ) */
1107-
ros_Alpha[0] = (KPP_REAL)0.0000000000000000;
1108-
ros_Alpha[1] = (KPP_REAL)0.0000000000000000;
1109-
ros_Alpha[2] = (KPP_REAL)1.0000000000000000;
1110-
ros_Alpha[3] = (KPP_REAL)1.0000000000000000;
1107+
ros_Alpha[0] = (KPP_REAL)0.000000000000000;
1108+
ros_Alpha[1] = (KPP_REAL)0.000000000000000;
1109+
ros_Alpha[2] = (KPP_REAL)1.000000000000000;
1110+
ros_Alpha[3] = (KPP_REAL)1.000000000000000;
11111111

11121112
/*~~~> Gamma_i = \sum_j gamma_{i,j} */
1113-
ros_Gamma[0] = (KPP_REAL)0.5150000000000000;
1114-
ros_Gamma[1] = (KPP_REAL)(-0.57028223198756145);
1115-
ros_Gamma[2] = (KPP_REAL)0.0000000000000000;
1116-
ros_Gamma[3] = (KPP_REAL)0.0000000000000000;
1113+
ros_Gamma[0] = (KPP_REAL)0.515000000000000;
1114+
ros_Gamma[1] = (KPP_REAL)1.628546001287715;
1115+
ros_Gamma[2] = (KPP_REAL)0.000000000000000;
1116+
ros_Gamma[3] = (KPP_REAL)0.000000000000000;
11171117

11181118
} /* Rodas3.1 */
11191119

‎int/rosenbrock.f90‎

Lines changed: 41 additions & 39 deletions
Original file line numberDiff line numberDiff line change
@@ -1119,7 +1119,7 @@ END SUBROUTINE Rodas3
11191119
SUBROUTINE Rodas3_1
11201120
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
11211121
! --- A STIFFLY-STABLE METHOD, 4 stages, order 3
1122-
! --- Updated coefficients by Mike Long (22 May 2025)
1122+
! --- Updated coefficients by Mike Long (17 Jul 2025)
11231123
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
11241124

11251125
IMPLICIT NONE
@@ -1131,52 +1131,54 @@ SUBROUTINE Rodas3_1
11311131
ros_S = 4
11321132

11331133
!~~~> The coefficient matrices A and C are strictly lower triangular.
1134-
! The lower triangular (subdiagonal) elements are stored in row-wise order:
1135-
! A(2,1) = ros_A(1), A(3,1)=ros_A(2), A(3,2)=ros_A(3), etc.
1136-
! The general mapping formula is:
1134+
! The lower triangular (subdiagonal) elements are stored
1135+
! in row-wise order:
1136+
! A(2,1) = ros_A(1), A(3,1)=ros_A(2), A(3,2)=ros_A(3), etc.
1137+
! The general mapping formula is:
11371138
! A(i,j) = ros_A( (i-1)*(i-2)/2 + j )
11381139
! C(i,j) = ros_C( (i-1)*(i-2)/2 + j )
1139-
ros_A(1) = 0.0000000000000000_dp
1140-
ros_A(2) = 1.5382237953138116_dp
1141-
ros_A(3) = -0.36440683885434433_dp
1142-
ros_A(4) = 1.5382237953138118_dp
1143-
ros_A(5) = -0.36440683885434433_dp
1144-
ros_A(6) = 1.0000000000000000_dp
1145-
ros_C(1) = -4.0919303685081028_dp
1146-
ros_C(2) = -3.0551174378039538E-002_dp
1147-
ros_C(3) = 1.7259281281917580_dp
1148-
ros_C(4) = 0.19561160936073679_dp
1149-
ros_C(5) = 1.9301670595355112_dp
1150-
ros_C(6) = -2.6267006001193960_dp
1140+
ros_A(1) = 0.000000000000000_dp
1141+
ros_A(2) = 0.646601929740551_dp
1142+
ros_A(3) = 0.409567801987914_dp
1143+
ros_A(4) = 0.646601929740551_dp
1144+
ros_A(5) = 0.409567801987914_dp
1145+
ros_A(6) = 1.000000000000000_dp
1146+
ros_C(1) = 4.198495621784201_dp
1147+
ros_C(2) = 3.711590161613010_dp
1148+
ros_C(3) = -1.787771994729384_dp
1149+
ros_C(4) = 4.458898153216104_dp
1150+
ros_C(5) = -2.024095448516552_dp
1151+
ros_C(6) = -2.626700600119396_dp
11511152
!~~~> Does the stage i require a new function evaluation (ros_NewF(i)=TRUE)
1152-
! or does it re-use the function evaluation from stage i-1 (ros_NewF(i)=FALSE)
1153-
ros_NewF(1) = .TRUE.
1154-
ros_NewF(2) = .FALSE.
1155-
ros_NewF(3) = .TRUE.
1156-
ros_NewF(4) = .TRUE.
1153+
! or does it re-use the function evaluation from stage i-1
1154+
! (ros_NewF(i)=FALSE)
1155+
ros_NewF(1) = .TRUE.
1156+
ros_NewF(2) = .FALSE.
1157+
ros_NewF(3) = .TRUE.
1158+
ros_NewF(4) = .TRUE.
11571159
!~~~> M_i = Coefficients for new step solution
1158-
ros_M(1) = 1.5382237953138116_dp
1159-
ros_M(2) = -0.36440683885434444_dp
1160-
ros_M(3) = 1.0000000000000002_dp
1161-
ros_M(4) = 1.0000000000000000_dp
1160+
ros_M(1) = 0.646601929740551_dp
1161+
ros_M(2) = 0.409567801987914_dp
1162+
ros_M(3) = 1.000000000000000_dp
1163+
ros_M(4) = 1.000000000000000_dp
11621164
!~~~> E_i = Coefficients for error estimator
1163-
ros_E(1) = 0.0000000000000000_dp
1164-
ros_E(2) = 0.0000000000000000_dp
1165-
ros_E(3) = 0.0000000000000000_dp
1166-
ros_E(4) = 1.0000000000000000_dp
1165+
ros_E(1) = 0.000000000000000_dp
1166+
ros_E(2) = 0.000000000000000_dp
1167+
ros_E(3) = 0.000000000000000_dp
1168+
ros_E(4) = 1.000000000000000_dp
11671169
!~~~> ros_ELO = estimator of local order - the minimum between the
1168-
! main and the embedded scheme orders plus 1
1169-
ros_ELO = 3.0000000000000000_dp
1170+
! main and the embedded scheme orders plus 1
1171+
ros_ELO = 3.000000000000000_dp
11701172
! ~~~> Y_stage_i ~ Y( T + H*Alpha_i )
1171-
ros_Alpha(1) = 0.0000000000000000_dp
1172-
ros_Alpha(2) = 0.0000000000000000_dp
1173-
ros_Alpha(3) = 1.0000000000000000_dp
1174-
ros_Alpha(4) = 1.0000000000000000_dp
1173+
ros_Alpha(1) = 0.000000000000000_dp
1174+
ros_Alpha(2) = 0.000000000000000_dp
1175+
ros_Alpha(3) = 1.000000000000000_dp
1176+
ros_Alpha(4) = 1.000000000000000_dp
11751177
!~~~> Gamma_i = \sum_j gamma_{i,j}
1176-
ros_Gamma(1) = 0.51500000000000001_dp
1177-
ros_Gamma(2) = -0.57028223198756145_dp
1178-
ros_Gamma(3) = 0.0000000000000000_dp
1179-
ros_Gamma(4) = 0.0000000000000000_dp
1178+
ros_Gamma(1) = 0.515000000000000_dp
1179+
ros_Gamma(2) = 1.628546001287715_dp
1180+
ros_Gamma(3) = 0.000000000000000_dp
1181+
ros_Gamma(4) = 0.000000000000000_dp
11801182

11811183
END SUBROUTINE Rodas3_1
11821184

‎int/rosenbrock.m‎

Lines changed: 25 additions & 24 deletions
Original file line numberDiff line numberDiff line change
@@ -77,6 +77,7 @@
7777
% = 3 : Ros4
7878
% = 4 : Rodas3
7979
% = 5 : Rodas4
80+
% = 7 : Rodas3.1
8081
%
8182
% ICNTRL(4) -> maximum number of integration steps
8283
% For ICNTRL(4)=0) the default value of 100000 is used
@@ -882,7 +883,7 @@
882883
function [ params ] = Rodas3_1()
883884
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
884885
% --- A STIFFLY-STABLE METHOD, 4 stages, order 3
885-
% --- Updated coefficients by Mike Long (22 May 2025)
886+
% --- Updated coefficients by Mike Long (17 Jul 2025)
886887
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
887888

888889
rosMethod = 4;
@@ -898,47 +899,47 @@
898899
% A(i,j) = ros_A( (i-1)*(i-2)/2 + j )
899900
% C(i,j) = ros_C( (i-1)*(i-2)/2 + j )
900901

901-
ros_A(1) = 0.0000000000000000;
902-
ros_A(2) = 1.5382237953138116;
903-
ros_A(3) = -0.36440683885434433;
904-
ros_A(4) = 1.5382237953138118;
905-
ros_A(5) = -0.36440683885434433;
906-
ros_A(6) = 1.0000000000000000;
902+
ros_A(1) = 0.000000000000000;
903+
ros_A(2) = 0.646601929740551;
904+
ros_A(3) = 0.409567801987914;
905+
ros_A(4) = 0.646601929740551;
906+
ros_A(5) = 0.409567801987914;
907+
ros_A(6) = 1.000000000000000;
907908

908-
ros_C(1) = -4.0919303685081028;
909-
ros_C(2) = -3.0551174378039538e-002;
910-
ros_C(3) = 1.7259281281917580;
911-
ros_C(4) = 0.19561160936073679;
912-
ros_C(5) = 1.9301670595355112;
913-
ros_C(6) = -2.6267006001193960;
909+
ros_C(1) = 4.198495621784201;
910+
ros_C(2) = 3.711590161613010;
911+
ros_C(3) = -1.787771994729384;
912+
ros_C(4) = 4.458898153216104;
913+
ros_C(5) = -2.024095448516552;
914+
ros_C(6) = -2.626700600119396;
914915

915916
%~~~> Does the stage i require a new function evaluation (ros_NewF(i)=TRUE)
916917
% or does it re-use the function evaluation from stage i-1 (ros_NewF(i)=FALSE)
917-
ros_NewF(1) = true;
918-
ros_NewF(2) = false;
919-
ros_NewF(3) = true;
920-
ros_NewF(4) = true;
918+
ros_NewF(1) = true;
919+
ros_NewF(2) = false;
920+
ros_NewF(3) = true;
921+
ros_NewF(4) = true;
921922
%~~~> M_i = Coefficients for new step solution
922-
ros_M(1) = 1.5382237953138116;
923-
ros_M(2) = -0.36440683885434444;
924-
ros_M(3) = 1.0000000000000002;
925-
ros_M(4) = 1.0000000000000000;
923+
ros_M(1) = 0.646601929740551;
924+
ros_M(2) = 0.409567801987914;
925+
ros_M(3) = 1.000000000000000;
926+
ros_M(4) = 1.000000000000000;
926927
%~~~> E_i = Coefficients for error estimator
927928
ros_E(1) = 0.0000000000000000;
928929
ros_E(2) = 0.0000000000000000;
929930
ros_E(3) = 0.0000000000000000;
930931
ros_E(4) = 1.0000000000000000;
931932
%~~~> ros_ELO = estimator of local order - the minimum between the
932933
% main and the embedded scheme orders plus 1
933-
ros_ELO = 3.0;
934+
ros_ELO = 3.0;
934935
%~~~> Y_stage_i ~ Y( T + H*Alpha_i )
935936
ros_Alpha(1) = 0.0000000000000000;
936937
ros_Alpha(2) = 0.0000000000000000;
937938
ros_Alpha(3) = 1.0000000000000000;
938939
ros_Alpha(4) = 1.0000000000000000;
939940
%~~~> Gamma_i = \sum_j gamma_{i,j}
940-
ros_Gamma(1) = 0.51500000000000001;
941-
ros_Gamma(2) = -0.57028223198756145;
941+
ros_Gamma(1) = 0.515000000000000;
942+
ros_Gamma(2) = 1.628546001287715;
942943
ros_Gamma(3) = 0.0000000000000000;
943944
ros_Gamma(4) = 0.0000000000000000;
944945

‎int/rosenbrock_adj.f90‎

Lines changed: 42 additions & 40 deletions
Original file line numberDiff line numberDiff line change
@@ -2394,7 +2394,7 @@ END SUBROUTINE Rodas3
23942394
SUBROUTINE Rodas3_1
23952395
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
23962396
! --- A STIFFLY-STABLE METHOD, 4 stages, order 3
2397-
! --- Updated coefficients by Mike Long (22 May 2025)
2397+
! --- Updated coefficients by Mike Long (17 Jul 2025)
23982398
!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
23992399

24002400
IMPLICIT NONE
@@ -2406,52 +2406,54 @@ SUBROUTINE Rodas3_1
24062406
ros_S = 4
24072407

24082408
!~~~> The coefficient matrices A and C are strictly lower triangular.
2409-
! The lower triangular (subdiagonal) elements are stored in row-wise order:
2410-
! A(2,1) = ros_A(1), A(3,1)=ros_A(2), A(3,2)=ros_A(3), etc.
2411-
! The general mapping formula is:
2409+
! The lower triangular (subdiagonal) elements are stored
2410+
! in row-wise order:
2411+
! A(2,1) = ros_A(1), A(3,1)=ros_A(2), A(3,2)=ros_A(3), etc.
2412+
! The general mapping formula is:
24122413
! A(i,j) = ros_A( (i-1)*(i-2)/2 + j )
24132414
! C(i,j) = ros_C( (i-1)*(i-2)/2 + j )
2414-
ros_A(1) = 0.0000000000000000_dp
2415-
ros_A(2) = 1.5382237953138116_dp
2416-
ros_A(3) = -0.36440683885434433_dp
2417-
ros_A(4) = 1.5382237953138118_dp
2418-
ros_A(5) = -0.36440683885434433_dp
2419-
ros_A(6) = 1.0000000000000000_dp
2420-
ros_C(1) = -4.0919303685081028_dp
2421-
ros_C(2) = -3.0551174378039538E-002_dp
2422-
ros_C(3) = 1.7259281281917580_dp
2423-
ros_C(4) = 0.19561160936073679_dp
2424-
ros_C(5) = 1.9301670595355112_dp
2425-
ros_C(6) = -2.6267006001193960_dp
2415+
ros_A(1) = 0.000000000000000_dp
2416+
ros_A(2) = 0.646601929740551_dp
2417+
ros_A(3) = 0.409567801987914_dp
2418+
ros_A(4) = 0.646601929740551_dp
2419+
ros_A(5) = 0.409567801987914_dp
2420+
ros_A(6) = 1.000000000000000_dp
2421+
ros_C(1) = 4.198495621784201_dp
2422+
ros_C(2) = 3.711590161613010_dp
2423+
ros_C(3) = -1.787771994729384_dp
2424+
ros_C(4) = 4.458898153216104_dp
2425+
ros_C(5) = -2.024095448516552_dp
2426+
ros_C(6) = -2.626700600119396_dp
24262427
!~~~> Does the stage i require a new function evaluation (ros_NewF(i)=TRUE)
2427-
! or does it re-use the function evaluation from stage i-1 (ros_NewF(i)=FALSE)
2428-
ros_NewF(1) = .TRUE.
2429-
ros_NewF(2) = .FALSE.
2430-
ros_NewF(3) = .TRUE.
2431-
ros_NewF(4) = .TRUE.
2428+
! or does it re-use the function evaluation from stage i-1
2429+
! (ros_NewF(i)=FALSE)
2430+
ros_NewF(1) = .TRUE.
2431+
ros_NewF(2) = .FALSE.
2432+
ros_NewF(3) = .TRUE.
2433+
ros_NewF(4) = .TRUE.
24322434
!~~~> M_i = Coefficients for new step solution
2433-
ros_M(1) = 1.5382237953138116_dp
2434-
ros_M(2) = -0.36440683885434444_dp
2435-
ros_M(3) = 1.0000000000000002_dp
2436-
ros_M(4) = 1.0000000000000000_dp
2435+
ros_M(1) = 0.646601929740551_dp
2436+
ros_M(2) = 0.409567801987914_dp
2437+
ros_M(3) = 1.000000000000000_dp
2438+
ros_M(4) = 1.000000000000000_dp
24372439
!~~~> E_i = Coefficients for error estimator
2438-
ros_E(1) = 0.0000000000000000_dp
2439-
ros_E(2) = 0.0000000000000000_dp
2440-
ros_E(3) = 0.0000000000000000_dp
2441-
ros_E(4) = 1.0000000000000000_dp
2440+
ros_E(1) = 0.000000000000000_dp
2441+
ros_E(2) = 0.000000000000000_dp
2442+
ros_E(3) = 0.000000000000000_dp
2443+
ros_E(4) = 1.000000000000000_dp
24422444
!~~~> ros_ELO = estimator of local order - the minimum between the
2443-
! main and the embedded scheme orders plus 1
2444-
ros_ELO = 3.0000000000000000_dp
2445-
! ~~~> Y_stage_i ~ Y( T + H*Alpha_i )
2446-
ros_Alpha(1) = 0.0000000000000000_dp
2447-
ros_Alpha(2) = 0.0000000000000000_dp
2448-
ros_Alpha(3) = 1.0000000000000000_dp
2449-
ros_Alpha(4) = 1.0000000000000000_dp
2445+
! main and the embedded scheme orders plus 1
2446+
ros_ELO = 3.000000000000000_dp
2447+
! ~~~> Y_stage_i ~ Y( T + H*Alpha_i )
2448+
ros_Alpha(1) = 0.000000000000000_dp
2449+
ros_Alpha(2) = 0.000000000000000_dp
2450+
ros_Alpha(3) = 1.000000000000000_dp
2451+
ros_Alpha(4) = 1.000000000000000_dp
24502452
!~~~> Gamma_i = \sum_j gamma_{i,j}
2451-
ros_Gamma(1) = 0.51500000000000001_dp
2452-
ros_Gamma(2) = -0.57028223198756145_dp
2453-
ros_Gamma(3) = 0.0000000000000000_dp
2454-
ros_Gamma(4) = 0.0000000000000000_dp
2453+
ros_Gamma(1) = 0.515000000000000_dp
2454+
ros_Gamma(2) = 1.628546001287715_dp
2455+
ros_Gamma(3) = 0.000000000000000_dp
2456+
ros_Gamma(4) = 0.000000000000000_dp
24552457

24562458
END SUBROUTINE Rodas3_1
24572459

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