Set<MultipleDeriv> DiffOpEvaluator
::backedDerivs(const MultipleDeriv& mu,
const Set<MultipleDeriv>& W1, int verb) const
{
Tabs tabs;
SUNDANCE_MSG3(verb, tabs << "computing backed-out derivs for mu= " << mu
<< ", W1=" << W1);
Set<MultipleDeriv> rtn;
if (mu.order() != 0)
{
const MultiIndex& alpha = expr()->mi();
for (Set<MultipleDeriv>::const_iterator i=W1.begin(); i!=W1.end(); i++)
{
const MultipleDeriv& md = *i;
TEUCHOS_TEST_FOR_EXCEPT(md.order() != 1);
Deriv lambda = *(md.begin());
if (lambda.isCoordDeriv()) continue;
TEUCHOS_TEST_FOR_EXCEPT(!lambda.isFunctionalDeriv());
FunctionIdentifier lambda_fid = lambda.fid();
const MultiIndex& lambda_mi = lambda.opOnFunc().mi();
for (MultipleDeriv::const_iterator j=mu.begin(); j!=mu.end(); j++)
{
const Deriv& d = *j;
if (d.isCoordDeriv()) continue;
FunctionIdentifier d_fid = d.fid();
const MultiIndex& d_mi = d.opOnFunc().mi();
if (d_fid != lambda_fid) continue;
if (!(alpha + lambda_mi == d_mi)) continue;
MultipleDeriv z = mu.factorOutDeriv(d);
z.put(lambda);
rtn.put(z);
}
}
}
SUNDANCE_MSG3(verb, tabs << "backed-out derivs = " << rtn);
return rtn;
}
DiffOpEvaluator
::DiffOpEvaluator(const DiffOp* expr,
const EvalContext& context)
: UnaryEvaluator<DiffOp>(expr, context),
isConstant_(this->sparsity()->numDerivs()),
resultIndices_(this->sparsity()->numDerivs()),
constantMonomials_(this->sparsity()->numDerivs()),
vectorMonomials_(this->sparsity()->numDerivs()),
constantFuncCoeffs_(this->sparsity()->numDerivs()),
vectorFuncCoeffs_(this->sparsity()->numDerivs()),
funcEvaluators_(),
constantCoeffFuncIndices_(this->sparsity()->numDerivs()),
constantCoeffFuncMi_(this->sparsity()->numDerivs()),
vectorCoeffFuncIndices_(this->sparsity()->numDerivs()),
vectorCoeffFuncMi_(this->sparsity()->numDerivs())
{
int verb = context.setupVerbosity();
Tabs tabs;
SUNDANCE_MSG1(verb, tabs << "initializing diff op evaluator for "
<< expr->toString());
{
Tabs tab0;
SUNDANCE_MSG2(verb, tab0 << "return sparsity " << std::endl << *(this->sparsity)());
SUNDANCE_MSG2(verb, tab0 << "argument sparsity subset " << std::endl
<< *(argSparsitySuperset()));
Map<const DiscreteFuncElementEvaluator*, int> funcToIndexMap;
int vecResultIndex = 0;
int constResultIndex = 0;
for (int i=0; i<this->sparsity()->numDerivs(); i++)
{
Tabs tab1;
const MultipleDeriv& resultDeriv = this->sparsity()->deriv(i);
SUNDANCE_MSG3(verb, tab0 << "working out procedure for computing "
<< resultDeriv);
if (this->sparsity()->state(i)==ConstantDeriv)
{
Tabs tab2;
addConstantIndex(i, constResultIndex);
resultIndices_[i] = constResultIndex++;
isConstant_[i] = true;
SUNDANCE_MSG3(verb, tab2 << "deriv is constant, will be stored at index "
<< resultIndices_[i] << " in the const result array");
}
else
{
Tabs tab2;
addVectorIndex(i, vecResultIndex);
resultIndices_[i] = vecResultIndex++;
isConstant_[i] = false;
SUNDANCE_MSG3(verb, tab2 << "deriv is variable, will be stored at index "
<< resultIndices_[i] << " in the var result array");
}
int order = resultDeriv.order();
const Set<MultipleDeriv>& RArg
= argExpr()->findR(order, context);
const Set<MultipleDeriv>& RArgPlus
= argExpr()->findR(order+1, context);
const Set<MultipleDeriv>& W1Arg
= argExpr()->findW(1, context);
SUNDANCE_MSG3(verb, tab1 << "RArg = " << RArg);
SUNDANCE_MSG3(verb, tab1 << "RArgPlus = " << RArgPlus);
SUNDANCE_MSG3(verb, tab1 << "W1Arg = " << W1Arg);
Set<MultipleDeriv> funcTermCoeffs
= RArgPlus.intersection(increasedDerivs(resultDeriv, W1Arg, verb));
SUNDANCE_MSG3(verb, tab1 << "function term coeffs = " << funcTermCoeffs);
if (funcTermCoeffs.size()==0)
{
SUNDANCE_MSG3(verb, tab1 << "no direct chain rule terms");
}
else
{
SUNDANCE_MSG3(verb, tab1 << "getting direct chain rule terms");
}
for (Set<MultipleDeriv>::const_iterator
j=funcTermCoeffs.begin(); j != funcTermCoeffs.end(); j++)
{
Tabs tab2;
SUNDANCE_MSG3(verb, tab2 << "getting coefficient of " << *j);
int argIndex = argSparsitySuperset()->getIndex(*j);
TEUCHOS_TEST_FOR_EXCEPTION(argIndex==-1, std::runtime_error,
"Derivative " << *j << " expected in argument "
"but not found");
Deriv lambda = remainder(*j, resultDeriv, verb);
if (lambda.isCoordDeriv())
{
Tabs tab3;
SUNDANCE_MSG3(verb, tab2 << "detected coordinate deriv");
if (lambda.coordDerivDir()!=expr->mi().firstOrderDirection())
{
SUNDANCE_MSG3(verb, tab2 << "direction mismatch, skipping");
continue;
}
const DerivState& argState = argSparsitySuperset()->state(argIndex);
if (argState==ConstantDeriv)
{
int constArgIndex = argEval()->constantIndexMap().get(argIndex);
constantMonomials_[i].append(constArgIndex);
}
else
{
int vectorArgIndex = argEval()->vectorIndexMap().get(argIndex);
vectorMonomials_[i].append(vectorArgIndex);
}
}
else if (lambda.opOnFunc().isPartial() || lambda.opOnFunc().isIdentity())
{
Tabs tab3;
SUNDANCE_MSG3(verb, tab3 << "detected functional deriv " << lambda);
const SymbolicFuncElement* f = lambda.symbFuncElem();
const MultiIndex& mi = expr->mi() + lambda.opOnFunc().mi();
SUNDANCE_MSG3(verb, tab3 << "modified multiIndex is " << mi);
const TestFuncElement* t
= dynamic_cast<const TestFuncElement*>(f);
if (t != 0) continue;
const UnknownFuncElement* u
= dynamic_cast<const UnknownFuncElement*>(f);
TEUCHOS_TEST_FOR_EXCEPTION(u==0, std::logic_error,
"Non-unknown function detected where an unknown "
"function was expected in "
"DiffOpEvaluator ctor");
const EvaluatableExpr* evalPt = u->evalPt();
const ZeroExpr* z = dynamic_cast<const ZeroExpr*>(evalPt);
if (z != 0) continue;
TEUCHOS_TEST_FOR_EXCEPTION(z != 0, std::logic_error,
"DiffOpEvaluator detected identically zero "
"function");
const DiscreteFuncElement* df
= dynamic_cast<const DiscreteFuncElement*>(evalPt);
TEUCHOS_TEST_FOR_EXCEPTION(df==0, std::logic_error,
"DiffOpEvaluator ctor: evaluation point of "
"unknown function " << u->toString()
<< " is not a discrete function");
const SymbolicFuncElementEvaluator* uEval
= dynamic_cast<const SymbolicFuncElementEvaluator*>(u->evaluator(context).get());
const DiscreteFuncElementEvaluator* dfEval = uEval->dfEval();
TEUCHOS_TEST_FOR_EXCEPTION(dfEval==0, std::logic_error,
"DiffOpEvaluator ctor: evaluator for "
"evaluation point is not a "
"DiscreteFuncElementEvaluator");
TEUCHOS_TEST_FOR_EXCEPTION(!dfEval->hasMultiIndex(mi), std::logic_error,
"DiffOpEvaluator ctor: evaluator for "
"discrete function " << df->toString()
<< " does not know about multiindex "
<< mi.toString());
int fIndex;
int miIndex = dfEval->miIndex(mi);
if (funcToIndexMap.containsKey(dfEval))
{
fIndex = funcToIndexMap.get(dfEval);
}
else
{
fIndex = funcEvaluators_.size();
funcEvaluators_.append(dfEval);
funcToIndexMap.put(dfEval, fIndex);
}
const DerivState& argState = argSparsitySuperset()->state(argIndex);
if (argState==ConstantDeriv)
{
int constArgIndex = argEval()->constantIndexMap().get(argIndex);
constantCoeffFuncIndices_[i].append(fIndex);
constantCoeffFuncMi_[i].append(miIndex);
constantFuncCoeffs_[i].append(constArgIndex);
}
else
{
int vectorArgIndex = argEval()->vectorIndexMap().get(argIndex);
vectorCoeffFuncIndices_[i].append(fIndex);
vectorCoeffFuncMi_[i].append(miIndex);
vectorFuncCoeffs_[i].append(vectorArgIndex);
}
}
else
{
TEUCHOS_TEST_FOR_EXCEPTION(true, std::logic_error,
"DiffOpEvaluator has been asked to preprocess a Deriv that "
"is not a simple partial derivative. The problem child is: "
<< lambda);
}
}
Set<MultipleDeriv> isolatedTerms
= RArg.intersection(backedDerivs(resultDeriv, W1Arg, verb));
if (isolatedTerms.size()==0)
{
SUNDANCE_MSG3(verb, tab1 << "no indirect chain rule terms");
}
else
{
SUNDANCE_MSG3(verb, tab1 << "getting indirect chain rule terms");
SUNDANCE_MSG3(verb, tab1 << "isolated terms = " << isolatedTerms);
}
for (Set<MultipleDeriv>::const_iterator
j=isolatedTerms.begin(); j != isolatedTerms.end(); j++)
{
int argIndex = argSparsitySuperset()->getIndex(*j);
TEUCHOS_TEST_FOR_EXCEPTION(argIndex==-1, std::runtime_error,
"Derivative " << *j << " expected in argument "
"but not found");
const DerivState& argState = argSparsitySuperset()->state(argIndex);
if (argState==ConstantDeriv)
{
int constArgIndex = argEval()->constantIndexMap().get(argIndex);
constantMonomials_[i].append(constArgIndex);
}
else
{
int vectorArgIndex = argEval()->vectorIndexMap().get(argIndex);
vectorMonomials_[i].append(vectorArgIndex);
}
}
}
}
if (verb > 2)
{
Out::os() << tabs << "instruction tables for summing spatial/functional chain rule" << std::endl;
for (int i=0; i<this->sparsity()->numDerivs(); i++)
{
Tabs tab1;
Out::os() << tab1 << "deriv " << sparsity()->deriv(i) << std::endl;
{
Tabs tab2;
Out::os() << tab2 << "constant monomials: " << constantMonomials_[i]
<< std::endl;
Out::os() << tab2 << "vector monomials: " << vectorMonomials_[i]
<< std::endl;
Out::os() << tab2 << "constant coeff functions: " << std::endl;
for (int j=0; j<constantFuncCoeffs_[i].size(); j++)
{
Tabs tab3;
Out::os() << tab3 << "func=" << constantCoeffFuncIndices_[i][j]
<< " mi=" << constantCoeffFuncMi_[i][j] << std::endl;
}
Out::os() << tab2 << "vector coeff functions: " << std::endl;
for (int j=0; j<vectorFuncCoeffs_[i].size(); j++)
{
Tabs tab3;
Out::os() << tab3 << "func=" << vectorCoeffFuncIndices_[i][j]
<< " mi=" << vectorCoeffFuncMi_[i][j] << std::endl;
}
}
}
}
}
bool testVecFunction()
{
bool pass = true;
Tabs tab;
int verb=1;
/* make a vector function */
int dim = 3;
Expr u = new UnknownFunctionStub("u", 1, 3);
Expr phi = new UnknownFunctionStub("u", 0, 1);
Expr v = new TestFunctionStub("v", 1, 3);
Expr alpha = new UnknownParameter("alpha");
TEUCHOS_TEST_EQUALITY(u.size(), dim, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(v.size(), dim, Out::os(), pass);
/* Verify that D_mi u fails for nonzero multiindex. */
// MultiIndex m1(0,1,0);
// TEST_THROW(
// funcDeriv(u, m1), pass
// );
Deriv d_du = funcDeriv(u);
Deriv d_dAlpha = funcDeriv(alpha);
Deriv d_dphi = funcDeriv(phi);
Deriv d_dphi_x = d_dphi.derivWrtMultiIndex(MultiIndex(1,0,0));
Deriv divU = divergenceDeriv(u);
Deriv divV = divergenceDeriv(v);
TEUCHOS_TEST_EQUALITY(divU.fid(), fid(u), Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dAlpha.fid(), fid(alpha), Out::os(), pass);
SUNDANCE_BANNER1(verb, tab, "checking algSpec for parameter");
TEUCHOS_TEST_EQUALITY(d_dAlpha.algSpec().isScalar(), true, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dAlpha.algSpec().isVector(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dAlpha.algSpec().isNormal(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dAlpha.algSpec().isCoordinateComponent(), false, Out::os(), pass);
SUNDANCE_BANNER1(verb, tab, "checking algSpec for divergence");
TEUCHOS_TEST_EQUALITY(divU.algSpec().isScalar(), true, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(divU.algSpec().isVector(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(divU.algSpec().isNormal(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(divU.algSpec().isCoordinateComponent(), false, Out::os(), pass);
SUNDANCE_BANNER1(verb, tab, "checking algSpec for vector operative func");
TEUCHOS_TEST_EQUALITY(d_du.algSpec().isScalar(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_du.algSpec().isVector(), true, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_du.algSpec().isNormal(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_du.algSpec().isCoordinateComponent(), false, Out::os(), pass);
SUNDANCE_BANNER1(verb, tab, "checking algSpec for scalar operative func");
TEUCHOS_TEST_EQUALITY(d_dphi.algSpec().isScalar(), true, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dphi.algSpec().isVector(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dphi.algSpec().isNormal(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dphi.algSpec().isCoordinateComponent(), false, Out::os(), pass);
SUNDANCE_BANNER1(verb, tab, "checking algSpec for d/d(Dx(phi))");
TEUCHOS_TEST_EQUALITY(d_dphi_x.algSpec().isScalar(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dphi_x.algSpec().isVector(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dphi_x.algSpec().isNormal(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dphi_x.algSpec().isCoordinateComponent(), true, Out::os(), pass);
SUNDANCE_BANNER1(verb, tab, "checking distinction between functional and spatial derivs");
TEUCHOS_TEST_EQUALITY(d_dAlpha.isFunctionalDeriv(), true, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dAlpha.isCoordDeriv(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(divU.isFunctionalDeriv(), true, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(divU.isCoordDeriv(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_du.isFunctionalDeriv(), true, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_du.isCoordDeriv(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dphi.isFunctionalDeriv(), true, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dphi.isCoordDeriv(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dphi_x.isFunctionalDeriv(), true, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dphi_x.isCoordDeriv(), false, Out::os(), pass);
SUNDANCE_BANNER1(verb, tab, "checking identification of differentiation order");
TEUCHOS_TEST_EQUALITY(divU.opOnFunc().derivOrder(), 1, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_du.opOnFunc().derivOrder(), 0, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dAlpha.opOnFunc().derivOrder(), 0, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dphi.opOnFunc().derivOrder(), 0, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dphi_x.opOnFunc().derivOrder(), 1, Out::os(), pass);
SUNDANCE_BANNER1(verb, tab, "checking identification of test and unk funcs");
TEUCHOS_TEST_EQUALITY(d_du.isTestFunction(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_du.isUnknownFunction(), true, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_du.isParameter(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dphi.isTestFunction(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dphi.isUnknownFunction(), true, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dphi.isParameter(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dphi_x.isTestFunction(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dphi_x.isUnknownFunction(), true, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dphi.isParameter(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(divU.isTestFunction(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(divU.isUnknownFunction(), true, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(divU.isParameter(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(divV.isTestFunction(), true, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(divV.isUnknownFunction(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(divV.isParameter(), false, Out::os(), pass);
/* unknown parameters are both unknown and parameters */
TEUCHOS_TEST_EQUALITY(d_dAlpha.isTestFunction(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dAlpha.isUnknownFunction(), true, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(d_dAlpha.isParameter(), true, Out::os(), pass);
SUNDANCE_BANNER1(verb, tab, "checking identification of spatial operators acting on operative functions");
TEUCHOS_TEST_EQUALITY(divU.opOnFunc().isDivergence(), true, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(divU.opOnFunc().isNormal(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(divU.opOnFunc().isPartial(), false, Out::os(), pass);
TEUCHOS_TEST_EQUALITY(divU.opOnFunc().isIdentity(), false, Out::os(), pass);
SUNDANCE_BANNER1(verb, tab, "checking that asking for component information from a divergence throws an exception");
TEST_THROW(divU.opOnFunc().normalDerivOrder(), pass);
TEST_THROW(divU.opOnFunc().mi(), pass);
SUNDANCE_BANNER1(verb, tab, "checking that applying a partial derivative to a divergence throws an exception");
TEST_THROW(divU.opOnFunc().derivWrtMultiIndex(MultiIndex(1,0,0)), pass);
TEST_THROW(divU.opOnFunc().derivWrtMultiIndex(MultiIndex(0,1,0)), pass);
TEST_THROW(divU.opOnFunc().derivWrtMultiIndex(MultiIndex(0,0,1)), pass);
SUNDANCE_BANNER1(verb, tab, "checking that applying a zero-order partial derivative to a divergence does not throw an exception");
TEST_NOTHROW(divU.opOnFunc().derivWrtMultiIndex(MultiIndex(0,0,0)), pass);
SUNDANCE_BANNER1(verb, tab, "checking that applying a partial derivative to a divergence throws an exception");
TEST_THROW(divU.derivWrtMultiIndex(MultiIndex(1,0,0)), pass);
TEST_THROW(divU.derivWrtMultiIndex(MultiIndex(0,1,0)), pass);
TEST_THROW(divU.derivWrtMultiIndex(MultiIndex(0,0,1)), pass);
SUNDANCE_BANNER1(verb, tab, "checking that applying a zero-order partial derivative to a divergence does not throw an exception");
TEST_NOTHROW(divU.derivWrtMultiIndex(MultiIndex(0,0,0)), pass);
SUNDANCE_BANNER1(verb, tab, "checking that applying a partial derivative to a parameter throws an exception");
TEST_THROW(d_dAlpha.derivWrtMultiIndex(MultiIndex(1,0,0)), pass);
TEST_THROW(d_dAlpha.derivWrtMultiIndex(MultiIndex(0,1,0)), pass);
TEST_THROW(d_dAlpha.derivWrtMultiIndex(MultiIndex(0,0,1)), pass);
SUNDANCE_BANNER1(verb, tab, "checking that applying a zero-order partial derivative to a divergence does not throw an exception");
TEST_NOTHROW(d_dAlpha.derivWrtMultiIndex(MultiIndex(0,0,0)), pass);
SUNDANCE_BANNER1(verb, tab, "all done!");
return pass;
}