| | |
| //Copyright © 2009 Jose Antonio De Santiago-Castillo | |
| //E-mail:JAntonioDeSantiago@gmail.com | |
| //Web: www.DotNumerics.com | |
| // | |
| using System; | |
| using System.Collections.Generic; | |
| using System.Text; | |
| using System.ComponentModel; | |
| using DotNumerics.ODE.Dopri5; | |
| using DotNumerics.ODE.Radau5; | |
| using DotNumerics.FortranLibrary; | |
| namespace DotNumerics.ODE | |
| { | |
| /// <summary> | |
| /// Solves an initial-value problem for stiff ordinary differential equations using | |
| /// the implicit Runge-Kutta method of order 5. | |
| /// dy(i)/dt = f(i,t,y(1),y(2),...,y(N)). | |
| /// </summary> | |
| public sealed class OdeImplicitRungeKutta5 : xBaseOdeRungeKutta | |
| { | |
| //internal SOLOUTR solout; | |
| internal FVPOL fvpol; internal JVPOL jvpol; | |
| internal BBAMPL bbampl; internal DECOMR decomr; internal DECOMC decomc; internal SLVRAR slvrar; internal SLVRAI slvrai; | |
| internal SLVRAD slvrad; internal ESTRAD estrad; internal ESTRAV estrav; internal SLVROD slvrod; internal SLVSEU slvseu; | |
| internal DEC dec; internal SOL sol; internal DECH dech; internal SOLH solh; internal DECC decc; internal SOLC solc; | |
| internal DECHC dechc; internal SOLHC solhc; internal DECB decb; internal SOLB solb; internal DECBC decbc; | |
| internal SOLBC solbc; internal ELMHES elmhes; internal RADAU5 radau5; internal RADCOR radcor; internal CONTR5 contr5; | |
| CommonBlock INTERN = new CommonBlock(1, 0, 0, 0); | |
| CommonBlock LINAL = new CommonBlock(0, 7, 0, 0); | |
| CommonBlock CONRA5 = new CommonBlock(4, 4, 0, 0); | |
| /// <summary> | |
| /// INITIAL STEP SIZE GUESS; | |
| /// FOR STIFF EQUATIONS WITH INITIAL TRANSIENT, | |
| /// H=1.D0/(NORM OF F'), USUALLY 1.D-3 OR 1.D-5, IS GOOD. | |
| /// THIS CHOICE IS NOT VERY IMPORTANT, THE STEP SIZE IS | |
| /// QUICKLY ADAPTED. (IF H=0.D0, THE CODE PUTS H=1.D-6). | |
| /// </summary> | |
| private double MeH = 1E-5; | |
| /// <summary> | |
| /// SWITCH FOR THE COMPUTATION OF THE JACOBIAN: | |
| /// IJAC=0: JACOBIAN IS COMPUTED INTERNALLY BY FINITE | |
| /// DIFFERENCES, SUBROUTINE "JAC" IS NEVER CALLED. | |
| /// IJAC=1: JACOBIAN IS SUPPLIED BY SUBROUTINE JAC. | |
| /// </summary> | |
| private int MeIJAC = 1; | |
| //private bool MeUserJacobian = true; | |
| /// <summary> | |
| /// SWITCH FOR THE BANDED STRUCTURE OF THE JACOBIAN: | |
| /// MLJAC=N: JACOBIAN IS A FULL MATRIX. THE LINEAR | |
| /// ALGEBRA IS DONE BY FULL-MATRIX GAUSS-ELIMINATION. | |
| /// 0.LE.MLJAC.LT.N: MLJAC IS THE LOWER BANDWITH OF JACOBIAN | |
| /// MATRIX (.GE. NUMBER OF NON-ZERO DIAGONALS BELOW | |
| /// THE MAIN DIAGONAL). | |
| /// </summary> | |
| private int MeMLJAC; | |
| /// <summary> | |
| /// UPPER BANDWITH OF JACOBIAN MATRIX (.GE. NUMBER OF NON- | |
| /// ZERO DIAGONALS ABOVE THE MAIN DIAGONAL). | |
| /// NEED NOT BE DEFINED IF MLJAC=N. | |
| /// </summary> | |
| private int MeMUJAC = 0; | |
| /// <summary> | |
| /// GIVES INFORMATION ON THE MASS-MATRIX: | |
| /// IMAS=0: M IS SUPPOSED TO BE THE IDENTITY | |
| /// MATRIX, MAS IS NEVER CALLED. | |
| /// IMAS=1: MASS-MATRIX IS SUPPLIED. | |
| /// </summary> | |
| private int MeIMAS = 0; | |
| /// <summary> | |
| /// SWITCH FOR THE BANDED STRUCTURE OF THE MASS-MATRIX: | |
| /// MLMAS=N: THE FULL MATRIX CASE. THE LINEAR | |
| /// ALGEBRA IS DONE BY FULL-MATRIX GAUSS-ELIMINATION. | |
| /// 0.LE.MLMAS.LT.N: MLMAS IS THE LOWER BANDWITH OF THE | |
| /// MATRIX (.GE. NUMBER OF NON-ZERO DIAGONALS BELOW | |
| /// THE MAIN DIAGONAL). | |
| /// MLMAS IS SUPPOSED TO BE .LE. MLJAC. | |
| /// </summary> | |
| private int MeMLMAS; | |
| /// <summary> | |
| /// UPPER BANDWITH OF MASS-MATRIX (.GE. NUMBER OF NON- | |
| /// ZERO DIAGONALS ABOVE THE MAIN DIAGONAL). | |
| /// NEED NOT BE DEFINED IF MLMAS=N. | |
| /// MUMAS IS SUPPOSED TO BE .LE. MUJAC. | |
| /// </summary> | |
| private int MeMUMAS = 0; | |
| /// <summary> | |
| /// Initializes a new instance of the OdeImplicitRungeKutta5 class. | |
| /// </summary> | |
| public OdeImplicitRungeKutta5() | |
| { | |
| this.InitializeRungeKuttaClasses(); | |
| } | |
| /// <summary> | |
| /// Initializes a new instance of the OdeImplicitRungeKutta5 class. | |
| /// </summary> | |
| /// <param name="function">A function that evaluates the right side of the differential equations.</param> | |
| /// <param name="jacobian">A function that evaluates the jacobian matrix.</param> | |
| /// <param name="numEquations">The number of differential equations.</param> | |
| public OdeImplicitRungeKutta5(OdeFunction function, OdeJacobian jacobian, int numEquations) | |
| { | |
| this.InitializeRungeKuttaClasses(); | |
| // C IOUT SWITCH FOR CALLING THE SUBROUTINE SOLOUTR: | |
| // C IOUT=0: SUBROUTINE IS NEVER CALLED | |
| // C | |
| this._IOut = 1; | |
| this.MeIJAC = 1; | |
| base.InitializeRungeKutta(function, jacobian, numEquations); | |
| } | |
| /// <summary> | |
| /// Initializes a new instance of the OdeImplicitRungeKutta5 class. | |
| /// </summary> | |
| /// <param name="function">A function that evaluates the right side of the differential equations.</param> | |
| /// <param name="numEquations">The number of differential equations.</param> | |
| public OdeImplicitRungeKutta5(OdeFunction function, int numEquations) | |
| { | |
| this.InitializeRungeKuttaClasses(); | |
| // C IOUT SWITCH FOR CALLING THE SUBROUTINE SOLOUTR: | |
| // C IOUT=0: SUBROUTINE IS NEVER CALLED | |
| // C | |
| this._IOut = 1; | |
| this.MeIJAC = 0; | |
| base.InitializeRungeKutta(function, null, numEquations); | |
| } | |
| /// <summary> | |
| /// Method that initialize the ODE to solve. | |
| /// </summary> | |
| /// <param name="function">A function that evaluates the right side of the differential equations.</param> | |
| /// <param name="numEquations">The number of differential equations.</param> | |
| public override void InitializeODEs(OdeFunction function, int numEquations) | |
| { | |
| // C IOUT SWITCH FOR CALLING THE SUBROUTINE SOLOUTR: | |
| // C IOUT=0: SUBROUTINE IS NEVER CALLED | |
| // C | |
| this._IOut = 1; | |
| this.MeIJAC = 0; | |
| base.InitializeRungeKutta(function, null, numEquations); | |
| this._InvokeSetInitialValues = true; | |
| } | |
| /// <summary> | |
| /// Method that initialize the ODE to solve. | |
| /// </summary> | |
| /// <param name="function">A function that evaluates the right side of the differential equations.</param> | |
| /// <param name="numEquations">The number of differential equations.</param> | |
| /// <param name="t0">The initial value for the independent variable.</param> | |
| /// <param name="y0">A vector of size N containing the initial conditions. N is the number of differential equations.</param> | |
| public override void InitializeODEs(OdeFunction function, int numEquations, double t0, double[] y0) | |
| { | |
| // C IOUT SWITCH FOR CALLING THE SUBROUTINE SOLOUTR: | |
| // C IOUT=0: SUBROUTINE IS NEVER CALLED | |
| // C | |
| this._IOut = 1; | |
| this.MeIJAC = 0; | |
| base.InitializeRungeKutta(function, null, numEquations); | |
| this.SetInitialValues(t0, y0); | |
| } | |
| /// <summary> | |
| /// Method that initialize the ODE to solve. | |
| /// </summary> | |
| /// <param name="function">A function that evaluates the right side of the differential equations.</param> | |
| /// <param name="jacobian">A function that evaluates the jacobian matrix.</param> | |
| /// <param name="numEquations">The number of differential equations.</param> | |
| public void InitializeODEs(OdeFunction function, OdeJacobian jacobian, int numEquations) | |
| { | |
| this._IOut = 1; | |
| this.MeIJAC = 1; | |
| base.InitializeRungeKutta(function, jacobian, numEquations); | |
| this._InvokeSetInitialValues = true; | |
| } | |
| /// <summary> | |
| /// Method that initialize the ODE to solve. | |
| /// </summary> | |
| /// <param name="function">A function that evaluates the right side of the differential equations.</param> | |
| /// <param name="jacobian">A function that evaluates the jacobian matrix.</param> | |
| /// <param name="numEquations">The number of differential equations.</param> | |
| /// <param name="t0">The initial value for the independent variable.</param> | |
| /// <param name="y0">A vector of size N containing the initial conditions. N is the number of differential equations.</param> | |
| public void InitializeODEs(OdeFunction function, OdeJacobian jacobian, int numEquations, double t0, double[] y0) | |
| { | |
| this._IOut = 1; | |
| this.MeIJAC = 1; | |
| base.InitializeRungeKutta(function, jacobian, numEquations); | |
| this.SetInitialValues(t0, y0); | |
| } | |
| internal override void InitializeRungeKuttaClasses() | |
| { | |
| bbampl = new BBAMPL(); | |
| dec = new DEC(); | |
| sol = new SOL(); | |
| dech = new DECH(); | |
| solh = new SOLH(); | |
| decc = new DECC(); | |
| solc = new SOLC(); | |
| dechc = new DECHC(); | |
| solhc = new SOLHC(); | |
| decb = new DECB(); | |
| solb = new SOLB(); | |
| decbc = new DECBC(); | |
| solbc = new SOLBC(); | |
| elmhes = new ELMHES(); | |
| //solout = new SOLOUTR(INTERN); | |
| contr5 = new CONTR5(CONRA5); | |
| decomr = new DECOMR(dec, decb, elmhes, dech, LINAL); | |
| decomc = new DECOMC(decc, decbc, dechc, LINAL); | |
| slvrar = new SLVRAR(sol, solb, solh, LINAL); | |
| slvrai = new SLVRAI(solc, solbc, solhc, LINAL); | |
| slvrad = new SLVRAD(sol, solc, solb, solbc, solh, solhc, LINAL); | |
| estrad = new ESTRAD(sol, solb, solh, LINAL); | |
| estrav = new ESTRAV(sol, solb, solh, LINAL); | |
| slvrod = new SLVROD(sol, solb, LINAL); | |
| slvseu = new SLVSEU(sol, solb, solh, LINAL); | |
| radcor = new RADCOR(decomr, decomc, slvrad, estrad, CONRA5, LINAL); | |
| radau5 = new RADAU5(radcor); | |
| //dr1_radau5 = new DR1_RADAU5(fvpol, jvpol, solout, bbampl, radau5); | |
| base._RKSolOut = new RKSolOut(this.contr5); | |
| } | |
| internal override void InitializeExceptionMessages() | |
| { | |
| this._Errors = new string[5]; | |
| this._Errors[0] = ""; | |
| this._Errors[1] = "INPUT IS NOT CONSISTENT."; | |
| this._Errors[2] = "LARGER NMAX IS NEEDED."; | |
| this._Errors[3] = "STEP SIZE BECOMES TOO SMALL."; | |
| this._Errors[4] = "MATRIX IS REPEATEDLY SINGULAR."; | |
| } | |
| internal override void InitializeFunctionAndJacobian(OdeFunction fun, OdeJacobian jac) | |
| { | |
| this.fvpol = new FVPOL(this._NEquations, fun); | |
| this.jvpol = new JVPOL(this._NEquations, jac); | |
| } | |
| internal override void InitializeWorkingSpace() | |
| { | |
| // C WORK ARRAY OF WORKING SPACE OF LENGTH "LWORK". | |
| // C WORK(1), WORK(2),.., WORK(20) SERVE AS PARAMETERS | |
| // C FOR THE CODE. FOR STANDARD USE OF THE CODE | |
| // C WORK(1),..,WORK(20) MUST BE SET TO ZERO BEFORE | |
| // C CALLING. SEE BELOW FOR A MORE SOPHISTICATED USE. | |
| // C WORK(21),..,WORK(LWORK) SERVE AS WORKING SPACE | |
| // C FOR ALL VECTORS AND MATRICES. | |
| // C "LWORK" MUST BE AT LEAST | |
| // C N*(LJAC+LMAS+3*LE+12)+20 | |
| // C WHERE | |
| // C LJAC=N IF MLJAC=N (FULL JACOBIAN) | |
| // C LJAC=MLJAC+MUJAC+1 IF MLJAC<N (BANDED JAC.) | |
| // C AND | |
| // C LMAS=0 IF IMAS=0 | |
| // C LMAS=N IF IMAS=1 AND MLMAS=N (FULL) | |
| // C LMAS=MLMAS+MUMAS+1 IF MLMAS<N (BANDED MASS-M.) | |
| // C AND | |
| // C LE=N IF MLJAC=N (FULL JACOBIAN) | |
| // C LE=2*MLJAC+MUJAC+1 IF MLJAC<N (BANDED JAC.) | |
| // C | |
| // C IN THE USUAL CASE WHERE THE JACOBIAN IS FULL AND THE | |
| // C MASS-MATRIX IS THE INDENTITY (IMAS=0), THE MINIMUM | |
| // C STORAGE REQUIREMENT IS | |
| // C LWORK = 4*N*N+12*N+20. | |
| // C IF IWORK(9)=M1>0 THEN "LWORK" MUST BE AT LEAST | |
| // C N*(LJAC+12)+(N-M1)*(LMAS+3*LE)+20 | |
| // C WHERE IN THE DEFINITIONS OF LJAC, LMAS AND LE THE | |
| // C NUMBER N CAN BE REPLACED BY N-M1. | |
| // C | |
| // C LWORK DECLARED LENGTH OF ARRAY "WORK". | |
| // C | |
| // C IWORK INTEGER WORKING SPACE OF LENGTH "LIWORK". | |
| // C IWORK(1),IWORK(2),...,IWORK(20) SERVE AS PARAMETERS | |
| // C FOR THE CODE. FOR STANDARD USE, SET IWORK(1),.., | |
| // C IWORK(20) TO ZERO BEFORE CALLING. | |
| // C IWORK(21),...,IWORK(LIWORK) SERVE AS WORKING AREA. | |
| // C "LIWORK" MUST BE AT LEAST 3*N+20. | |
| // C | |
| // C LIWORK DECLARED LENGTH OF ARRAY "IWORK". | |
| // C IN THE USUAL CASE WHERE THE JACOBIAN IS FULL AND THE | |
| // C MASS-MATRIX IS THE INDENTITY (IMAS=0), THE MINIMUM | |
| // C STORAGE REQUIREMENT IS | |
| // C LWORK = 4*N*N+12*N+20. | |
| this._Lrw = 4 * this._NEquations * this._NEquations + 12 * this._NEquations + 20; | |
| // C IWORK INTEGER WORKING SPACE OF LENGTH "LIWORK". | |
| // C IWORK(1),IWORK(2),...,IWORK(20) SERVE AS PARAMETERS | |
| // C FOR THE CODE. FOR STANDARD USE, SET IWORK(1),.., | |
| // C IWORK(20) TO ZERO BEFORE CALLING. | |
| // C IWORK(21),...,IWORK(LIWORK) SERVE AS WORKING AREA. | |
| // C "LIWORK" MUST BE AT LEAST 3*N+20. | |
| this._Liw = 3 * this._NEquations + 20; | |
| this._RWork = new double[this._Lrw]; | |
| this._IWork = new int[this._Liw]; | |
| } | |
| internal override void Solve() | |
| { | |
| bool WasSuccessfully = true; | |
| this.MeMLJAC = this._NEquations; | |
| this.MeMLMAS = this._NEquations; | |
| this.radau5.Run(this._NEquations, this.fvpol, ref this._T0, ref this._Y0, 0, this.MeTf, ref this.MeH, ref this._RelTolArray, 0 | |
| , ref this._AbsTolArray, 0, this._ITolRK, this.jvpol, this.MeIJAC, ref this.MeMLJAC, ref this.MeMUJAC, this.bbampl, this.MeIMAS, this.MeMLMAS, ref this.MeMUMAS, this._RKSolOut, this._IOut, ref this._RWork, 0, this._Lrw | |
| , ref this._IWork, 0, this._Liw, this._RPar, 0, this._IPar, 0, ref this._IDID); | |
| if (this._IDID < 0) WasSuccessfully = false; | |
| if (WasSuccessfully == false) | |
| { | |
| throw new Exception(this._Errors[-this._IDID]); | |
| } | |
| } | |
| } | |
| } | |