Tempus: Adjustments to the AppAction Interface

 * Moved the RK Tableau in to RKBase, along with related
   accessors, to allow access from the base class.
    - IMEX steppers return the explicit tableau from getTableau().
 * Moved getStageNumber() to RKBase.
 * Add stageNumber to the StepperRKModifierXBase interface.
 * Added RK stepper unit tests for stageNumber and stageX.
   The stageX tests were a little difficult to develop, because
   in explicit RK steppers stageX and workingState->getX are the
   same.  So there is no stageX to test outside the stepper.
   Therefore direct comparisons against numerical values was used.
 * Added accessors to the IMEX and IMEX Partition tableaus,
   to both the explicit and implicit tableaus.
 * Added comparison operators for RKButcherTableau.
 * Added unit tests for these accessors.
 * Fix and add unit tests for StepperRKAppActionComposite.
 * Add a const version of StepperRKBase::getStageX().
 * Switch StepperRKModifierXBase::XDOT_END_STAGE to
   StepperRKModifierXBase::X_END_STAGE as that is what
   EMPIRE is using.

All tests pass on a Mac/GCC.

packages/tempus/src/Tempus_RKButcherTableau.hpp

@@ -171,6 +171,39 @@ class RKButcherTableau :
       }
     //@}
 
+    bool operator == (const RKButcherTableau & t) const {
+      const Scalar relTol = 1.0e-15;
+      if ( A_->numRows() != t.A_->numRows() ||
+           A_->numCols() != t.A_->numCols()    ) {
+        return false;
+      } else {
+        int i, j;
+        for(i = 0; i < A_->numRows(); i++) {
+          for(j = 0; j < A_->numCols(); j++) {
+            if(std::abs((t.A_(i,j) - A_(i,j))/A_(i,j)) > relTol) return false;
+          }
+        }
+      }
+
+      if ( b_->length() != t.b_->length() ||
+           b_->length() != t.c_->length() ||
+           b_->length() != t.bstar_->length() ) {
+        return false;
+      } else {
+        int i;
+        for(i = 0; i < A_->numRows(); i++) {
+          if(std::abs((t.b_(i) - b_(i))/b_(i)) > relTol) return false;
+          if(std::abs((t.c_(i) - c_(i))/c_(i)) > relTol) return false;
+          if(std::abs((t.bstar_(i) - bstar_(i))/bstar_(i)) > relTol) return false;
+        }
+      }
+      return true;
+    }
+
+    bool operator != (const RKButcherTableau & t) const {
+      return !((*this) == t);
+    }
+
   private:
 
     RKButcherTableau();

packages/tempus/src/Tempus_StepperDIRK_decl.hpp

@@ -11,7 +11,6 @@
 
 #include "Tempus_config.hpp"
 #include "Tempus_StepperRKBase.hpp"
-#include "Tempus_RKButcherTableau.hpp"
 #include "Tempus_StepperImplicit.hpp"
 #include "Tempus_WrapperModelEvaluator.hpp"
 #ifndef TEMPUS_HIDE_DEPRECATED_CODE
@@ -165,9 +164,6 @@ class StepperDIRK : virtual public Tempus::StepperImplicit<Scalar>,
     virtual Teuchos::RCP<StepperObserver<Scalar> > getObserver() const
     { return this->stepperObserver_; }
 #endif
-    virtual Teuchos::RCP<const RKButcherTableau<Scalar> > getTableau()
-    { return tableau_; }
-
     /// Initialize after construction and changing input parameters.
     virtual void initialize();
 
@@ -187,14 +183,11 @@ class StepperDIRK : virtual public Tempus::StepperImplicit<Scalar>,
 
     /// Get a default (initial) StepperState
     virtual Teuchos::RCP<Tempus::StepperState<Scalar> >getDefaultStepperState();
-    virtual Scalar getOrder()    const{return tableau_->order();}
-    virtual Scalar getOrderMin() const{return tableau_->orderMin();}
-    virtual Scalar getOrderMax() const{return tableau_->orderMax();}
 
     virtual bool isExplicit() const
     {
-      const int numStages = tableau_->numStages();
-      Teuchos::SerialDenseMatrix<int,Scalar> A = tableau_->A();
+      const int numStages = this->tableau_->numStages();
+      Teuchos::SerialDenseMatrix<int,Scalar> A = this->tableau_->A();
       bool isExplicit = false;
       for (int i=0; i<numStages; ++i) if (A(i,i) == 0.0) isExplicit = true;
       return isExplicit;
@@ -219,7 +212,7 @@ class StepperDIRK : virtual public Tempus::StepperImplicit<Scalar>,
   /// Return alpha = d(xDot)/dx.
   virtual Scalar getAlpha(const Scalar dt) const
   {
-    const Teuchos::SerialDenseMatrix<int,Scalar> & A=tableau_->A();
+    const Teuchos::SerialDenseMatrix<int,Scalar> & A=this->tableau_->A();
     return Scalar(1.0)/(dt*A(0,0));  // Getting the first diagonal coeff!
   }
   /// Return beta  = d(x)/dx.
@@ -273,8 +266,6 @@ class StepperDIRK : virtual public Tempus::StepperImplicit<Scalar>,
 
   virtual void setupTableau() = 0;
 
-  Teuchos::RCP<RKButcherTableau<Scalar> >                tableau_;
-
   std::vector<Teuchos::RCP<Thyra::VectorBase<Scalar> > > stageXDot_;
   Teuchos::RCP<Thyra::VectorBase<Scalar> >               xTilde_;
 

packages/tempus/src/Tempus_StepperDIRK_impl.hpp

@@ -160,7 +160,7 @@ template<class Scalar>
 void StepperDIRK<Scalar>::initialize()
 {
   // Initialize the stage vectors
-  const int numStages = tableau_->numStages();
+  const int numStages = this->tableau_->numStages();
   this->stageX_    = this->wrapperModel_->getNominalValues().get_x()->clone_v();
   stageXDot_.resize(numStages);
   for (int i=0; i<numStages; ++i) {
@@ -170,7 +170,7 @@ void StepperDIRK<Scalar>::initialize()
   xTilde_    = Thyra::createMember(this->wrapperModel_->get_x_space());
   assign(xTilde_.ptr(),    Teuchos::ScalarTraits<Scalar>::zero());
 
-  if (tableau_->isEmbedded() and this->getUseEmbedded()) {
+  if (this->tableau_->isEmbedded() and this->getUseEmbedded()) {
     ee_    = Thyra::createMember(this->wrapperModel_->get_f_space());
     abs_u0 = Thyra::createMember(this->wrapperModel_->get_f_space());
     abs_u  = Thyra::createMember(this->wrapperModel_->get_f_space());
@@ -227,10 +227,10 @@ void StepperDIRK<Scalar>::takeStep(
     const Scalar dt = workingState->getTimeStep();
     const Scalar time = currentState->getTime();
 
-    const int numStages = tableau_->numStages();
-    Teuchos::SerialDenseMatrix<int,Scalar> A = tableau_->A();
-    Teuchos::SerialDenseVector<int,Scalar> b = tableau_->b();
-    Teuchos::SerialDenseVector<int,Scalar> c = tableau_->c();
+    const int numStages = this->tableau_->numStages();
+    Teuchos::SerialDenseMatrix<int,Scalar> A = this->tableau_->A();
+    Teuchos::SerialDenseVector<int,Scalar> b = this->tableau_->b();
+    Teuchos::SerialDenseVector<int,Scalar> c = this->tableau_->c();
 
     // Reset non-zero initial guess.
     if ( this->getResetInitialGuess() && (!this->getZeroInitialGuess()) )
@@ -253,8 +253,8 @@ void StepperDIRK<Scalar>::takeStep(
       bool isNeeded = false;
       for (int k=i+1; k<numStages; ++k) if (A(k,i) != 0.0) isNeeded = true;
       if (b(i) != 0.0) isNeeded = true;
-      if (tableau_->isEmbedded() && this->getUseEmbedded() &&
-          tableau_->bstar()(i) != 0.0)
+      if (this->tableau_->isEmbedded() && this->getUseEmbedded() &&
+          this->tableau_->bstar()(i) != 0.0)
         isNeeded = true;
       if (isNeeded == false) {
         assign(stageXDot_[i].ptr(), Teuchos::ScalarTraits<Scalar>::zero());
@@ -344,14 +344,14 @@ void StepperDIRK<Scalar>::takeStep(
       }
     }
 
-    if (tableau_->isEmbedded() and this->getUseEmbedded()) {
+    if (this->tableau_->isEmbedded() and this->getUseEmbedded()) {
       const Scalar tolRel = workingState->getTolRel();
       const Scalar tolAbs = workingState->getTolAbs();
 
       // just compute the error weight vector
       // (all that is needed is the error, and not the embedded solution)
       Teuchos::SerialDenseVector<int,Scalar> errWght = b ;
-      errWght -= tableau_->bstar();
+      errWght -= this->tableau_->bstar();
 
       // compute local truncation error estimate: | u^{n+1} - \hat{u}^{n+1} |
       // Sum for solution: ee_n = Sum{ (b(i) - bstar(i)) * dt*f(i) }
@@ -422,8 +422,8 @@ void StepperDIRK<Scalar>::describe(
   StepperImplicit<Scalar>::describe(out, verbLevel);
 
   out << "--- StepperDIRK ---\n";
-  out << "  tableau_            = " << tableau_ << std::endl;
-  if (tableau_ != Teuchos::null) tableau_->describe(out, verbLevel);
+  out << "  tableau_            = " << this->tableau_ << std::endl;
+  if (this->tableau_ != Teuchos::null) this->tableau_->describe(out, verbLevel);
 #ifndef TEMPUS_HIDE_DEPRECATED_CODE
   out << "  stepperObserver_    = " << stepperObserver_ << std::endl;
 #endif
@@ -452,7 +452,7 @@ bool StepperDIRK<Scalar>::isValidSetup(Teuchos::FancyOStream & out) const
   if ( !Stepper<Scalar>::isValidSetup(out) ) isValidSetup = false;
   if ( !StepperImplicit<Scalar>::isValidSetup(out) ) isValidSetup = false;
 
-  if (tableau_ == Teuchos::null) {
+  if (this->tableau_ == Teuchos::null) {
     isValidSetup = false;
     out << "The tableau is not set!\n";
   }

packages/tempus/src/Tempus_StepperExplicitRK_decl.hpp

@@ -12,7 +12,6 @@
 #include "Tempus_config.hpp"
 #include "Tempus_StepperRKBase.hpp"
 #include "Tempus_StepperExplicit.hpp"
-#include "Tempus_RKButcherTableau.hpp"
 #ifndef TEMPUS_HIDE_DEPRECATED_CODE
   #include "Tempus_StepperRKObserverComposite.hpp"
 #endif
@@ -111,9 +110,6 @@ class StepperExplicitRK : virtual public Tempus::StepperExplicit<Scalar>,
     virtual Teuchos::RCP<StepperObserver<Scalar> > getObserver() const
     { return this->stepperObserver_; }
 #endif
-    virtual Teuchos::RCP<const RKButcherTableau<Scalar> > getTableau()
-    { return tableau_; }
-
     /// Initialize during construction and after changing input parameters.
     virtual void initialize();
 
@@ -127,9 +123,6 @@ class StepperExplicitRK : virtual public Tempus::StepperExplicit<Scalar>,
 
     /// Get a default (initial) StepperState
     virtual Teuchos::RCP<Tempus::StepperState<Scalar> > getDefaultStepperState();
-    virtual Scalar getOrder() const {return tableau_->order();}
-    virtual Scalar getOrderMin() const {return tableau_->orderMin();}
-    virtual Scalar getOrderMax() const {return tableau_->orderMax();}
     virtual Scalar getInitTimeStep(
         const Teuchos::RCP<SolutionHistory<Scalar> >& solutionHistory) const;
 
@@ -191,8 +184,6 @@ class StepperExplicitRK : virtual public Tempus::StepperExplicit<Scalar>,
   virtual void setupTableau() = 0;
 
 
-  Teuchos::RCP<RKButcherTableau<Scalar> >                tableau_;
-
   std::vector<Teuchos::RCP<Thyra::VectorBase<Scalar> > > stageXDot_;
 
 #ifndef TEMPUS_HIDE_DEPRECATED_CODE

packages/tempus/src/Tempus_StepperExplicitRK_impl.hpp

@@ -222,7 +222,7 @@ void StepperExplicitRK<Scalar>::setObserver(
 template<class Scalar>
 void StepperExplicitRK<Scalar>::initialize()
 {
-  TEUCHOS_TEST_FOR_EXCEPTION( tableau_ == Teuchos::null, std::logic_error,
+  TEUCHOS_TEST_FOR_EXCEPTION( this->tableau_ == Teuchos::null, std::logic_error,
     "Error - Need to set the tableau, before calling "
     "StepperExplicitRK::initialize()\n");
 
@@ -231,14 +231,14 @@ void StepperExplicitRK<Scalar>::initialize()
     "StepperExplicitRK::initialize()\n");
 
   // Initialize the stage vectors
-  int numStages = tableau_->numStages();
+  int numStages = this->tableau_->numStages();
   stageXDot_.resize(numStages);
   for (int i=0; i<numStages; ++i) {
     stageXDot_[i] = Thyra::createMember(this->appModel_->get_f_space());
     assign(stageXDot_[i].ptr(), Teuchos::ScalarTraits<Scalar>::zero());
   }
 
-  if ( tableau_->isEmbedded() and this->getUseEmbedded() ){
+  if ( this->tableau_->isEmbedded() and this->getUseEmbedded() ){
      ee_ = Thyra::createMember(this->appModel_->get_f_space());
      abs_u0 = Thyra::createMember(this->appModel_->get_f_space());
      abs_u = Thyra::createMember(this->appModel_->get_f_space());
@@ -295,10 +295,10 @@ void StepperExplicitRK<Scalar>::takeStep(
     const Scalar dt = workingState->getTimeStep();
     const Scalar time = currentState->getTime();
 
-    const int numStages = tableau_->numStages();
-    Teuchos::SerialDenseMatrix<int,Scalar> A = tableau_->A();
-    Teuchos::SerialDenseVector<int,Scalar> b = tableau_->b();
-    Teuchos::SerialDenseVector<int,Scalar> c = tableau_->c();
+    const int numStages = this->tableau_->numStages();
+    Teuchos::SerialDenseMatrix<int,Scalar> A = this->tableau_->A();
+    Teuchos::SerialDenseVector<int,Scalar> b = this->tableau_->b();
+    Teuchos::SerialDenseVector<int,Scalar> c = this->tableau_->c();
 
     this->stageX_ = workingState->getX();
     Thyra::assign(this->stageX_.ptr(), *(currentState->getX()));
@@ -376,15 +376,15 @@ void StepperExplicitRK<Scalar>::takeStep(
     // can change the step status
     workingState->setSolutionStatus(Status::PASSED);
 
-    if (tableau_->isEmbedded() and this->getUseEmbedded()) {
+    if (this->tableau_->isEmbedded() and this->getUseEmbedded()) {
 
       const Scalar tolRel = workingState->getTolRel();
       const Scalar tolAbs = workingState->getTolAbs();
 
       // just compute the error weight vector
       // (all that is needed is the error, and not the embedded solution)
       Teuchos::SerialDenseVector<int,Scalar> errWght = b ;
-      errWght -= tableau_->bstar();
+      errWght -= this->tableau_->bstar();
 
       //compute local truncation error estimate: | u^{n+1} - \hat{u}^{n+1} |
       // Sum for solution: ee_n = Sum{ (b(i) - bstar(i)) * dt*f(i) }
@@ -452,8 +452,8 @@ void StepperExplicitRK<Scalar>::describe(
   StepperExplicit<Scalar>::describe(out, verbLevel);
 
   out << "--- StepperExplicitRK ---\n";
-  if (tableau_ != Teuchos::null) tableau_->describe(out, verbLevel);
-  out << "  tableau_           = " << tableau_ << std::endl;
+  if (this->tableau_ != Teuchos::null) this->tableau_->describe(out, verbLevel);
+  out << "  tableau_           = " << this->tableau_ << std::endl;
 #ifndef TEMPUS_HIDE_DEPRECATED_CODE
   out << "  stepperObserver_   = " << stepperObserver_ << std::endl;
 #endif
@@ -481,7 +481,7 @@ bool StepperExplicitRK<Scalar>::isValidSetup(Teuchos::FancyOStream & out) const
   if ( !Stepper<Scalar>::isValidSetup(out) ) isValidSetup = false;
   if ( !StepperExplicit<Scalar>::isValidSetup(out) ) isValidSetup = false;
 
-  if (tableau_ == Teuchos::null) {
+  if (this->tableau_ == Teuchos::null) {
     isValidSetup = false;
     out << "The tableau is not set!\n";
   }

packages/tempus/src/Tempus_StepperIMEX_RK_Partition_decl.hpp

@@ -356,15 +356,27 @@ class StepperIMEX_RK_Partition : virtual public Tempus::StepperImplicit<Scalar>,
 
   /// \name Basic stepper methods
   //@{
+    /// Returns the explicit tableau!
+    virtual Teuchos::RCP<const RKButcherTableau<Scalar> > getTableau() const
+    { return getExplicitTableau(); }
+
     /// Set both the explicit and implicit tableau from ParameterList
     virtual void setTableaus(std::string stepperType = "",
       Teuchos::RCP<const RKButcherTableau<Scalar> > explicitTableau = Teuchos::null,
       Teuchos::RCP<const RKButcherTableau<Scalar> > implicitTableau = Teuchos::null);
 
+    /// Return explicit tableau.
+    virtual Teuchos::RCP<const RKButcherTableau<Scalar> > getExplicitTableau() const
+    { return explicitTableau_; }
+
     /// Set the explicit tableau from tableau
     virtual void setExplicitTableau(
       Teuchos::RCP<const RKButcherTableau<Scalar> > explicitTableau);
 
+    /// Return implicit tableau.
+    virtual Teuchos::RCP<const RKButcherTableau<Scalar> > getImplicitTableau() const
+    { return implicitTableau_; }
+
     /// Set the implicit tableau from tableau
     virtual void setImplicitTableau(
       Teuchos::RCP<const RKButcherTableau<Scalar> > implicitTableau);
@@ -417,7 +429,10 @@ class StepperIMEX_RK_Partition : virtual public Tempus::StepperImplicit<Scalar>,
     virtual OrderODE getOrderODE()   const {return FIRST_ORDER_ODE;}
   //@}
 
-  Teuchos::RCP<Thyra::VectorBase<Scalar> >& getStageZ() {return stageZ_;};
+  /// Return the full stage solution which is Z (the concat of X and Y) for IMEX Partition.
+  Teuchos::RCP<Thyra::VectorBase<Scalar> > getStageX() {return stageZ_;}
+  /// Explicitly return the full stage solution, Z.
+  Teuchos::RCP<Thyra::VectorBase<Scalar> > getStageZ() {return stageZ_;};
   std::vector<Teuchos::RCP<Thyra::VectorBase<Scalar> > >& getStageF() {return stageF_;};
   std::vector<Teuchos::RCP<Thyra::VectorBase<Scalar> > >& getStageGx() {return stageGx_;};
   Teuchos::RCP<Thyra::VectorBase<Scalar> >& getXTilde() {return xTilde_;};

packages/tempus/src/Tempus_StepperIMEX_RK_decl.hpp

@@ -326,15 +326,27 @@ class StepperIMEX_RK : virtual public Tempus::StepperImplicit<Scalar>,
 
   /// \name Basic stepper methods
   //@{
+    /// Returns the explicit tableau!
+    virtual Teuchos::RCP<const RKButcherTableau<Scalar> > getTableau() const
+    { return getExplicitTableau(); }
+
     /// Set both the explicit and implicit tableau from ParameterList
     virtual void setTableaus( std::string stepperType = "",
       Teuchos::RCP<const RKButcherTableau<Scalar> > explicitTableau = Teuchos::null,
       Teuchos::RCP<const RKButcherTableau<Scalar> > implicitTableau = Teuchos::null);
 
+    /// Return explicit tableau.
+    virtual Teuchos::RCP<const RKButcherTableau<Scalar> > getExplicitTableau() const
+    { return explicitTableau_; }
+
     /// Set the explicit tableau from tableau
     virtual void setExplicitTableau(
       Teuchos::RCP<const RKButcherTableau<Scalar> > explicitTableau);
 
+    /// Return implicit tableau.
+    virtual Teuchos::RCP<const RKButcherTableau<Scalar> > getImplicitTableau() const
+    { return implicitTableau_; }
+
     /// Set the implicit tableau from tableau
     virtual void setImplicitTableau(
       Teuchos::RCP<const RKButcherTableau<Scalar> > implicitTableau);