bool Expr::tryMultiplyComplex(const Expr& L, const Expr& R,
Expr& rtn) const
{
TimeMonitor t(tryMultiplyComplexTimer());
TEUCHOS_TEST_FOR_EXCEPTION(L.size() != 1 || R.size() != 1, std::logic_error,
"non-scalar exprs should have been reduced before "
"call to tryMultiplyComplex(). Left=" << L << " right="
<< R);
if (L.isComplex() || R.isComplex())
{
if (Re(L).sameAs(Re(R)) && Im(L).sameAs(-Im(R)))
{
rtn = Re(R)*Re(R) + Im(R)*Im(R);
}
else
{
Expr re = Re(L)*Re(R) - Im(L)*Im(R);
Expr im = Re(L)*Im(R) + Im(L)*Re(R);
rtn = new ComplexExpr(re, im);
}
return true;
}
else
{
return false;
}
}
bool Expr::tryAddComplex(const Expr& L, const Expr& R, int sign,
Expr& rtn) const
{
TimeMonitor t(trySumComplexTimer());
TEUCHOS_TEST_FOR_EXCEPTION(L.size() != 1 || R.size() != 1, std::logic_error,
"non-scalar exprs should have been reduced before "
"call to tryAddComplex(). Left=" << L << " right="
<< R);
if (L.isComplex() || R.isComplex())
{
if (sign > 0)
{
rtn = new ComplexExpr(L.real() + R.real(),
L.imag() + R.imag());
}
else
{
rtn = new ComplexExpr(L.real() - R.real(),
L.imag() - R.imag());
}
return true;
}
else
{
return false;
}
}
Expr Expr::operator/(const Expr& other) const
{
TimeMonitor t(opTimer());
/* if the right operand is a list, this operation
* makes no sense */
TEUCHOS_TEST_FOR_EXCEPTION(other.size() != 1,
std::runtime_error,
"Expr::operator/ detected division by a non-scalar "
"expression " << toString());
TEUCHOS_TEST_FOR_EXCEPTION(other.isSpectral(), std::logic_error,
"Division by a Spectral Expr is not yet defined");
/* If other is complex, transform to make the denominator real */
if (other.isComplex())
{
Expr magSq = other.real()*other.real() + other.imag()*other.imag();
return (*this) * other.conj() / magSq;
}
/* If I'm complex and the other is not, distribute division over re and im */
if (isComplex() && !other.isComplex())
{
return new ComplexExpr(real()/other, imag()/other);
}
/* If I'm spectral and the other is not, distribute division over coefficients */
if (isSpectral() && !other.isSpectral() && !other.isComplex())
{
const SpectralExpr* se
= dynamic_cast<const SpectralExpr*>((*this)[0].ptr().get());
SpectralBasis basis = se->getSpectralBasis();
Array<Expr> coeff(basis.nterms());
for(int i=0; i<basis.nterms(); i++)
{
coeff[i] = se->getCoeff(i)/ other[0];
}
Expr rtn = new SpectralExpr( basis, coeff);
return rtn;
}
/* if we are a scalar, do simple scalar division */
if (this->size()==1)
{
return (*this)[0].divide(other[0]);
}
/* otherwise, divide each element of the left by the right operand */
Array<Expr> rtn(this->size());
for (int i=0; i<this->size(); i++)
{
rtn[i] = (*this)[i] / other;
}
return new ListExpr(rtn);
}
Expr Complex(const Expr& re, const Expr& im)
{
TEUCHOS_TEST_FOR_EXCEPTION(re.size() != im.size(), std::runtime_error,
"arguments mismatched in Complex(). Real part="
<< re << ", imaginary part=" << im);
TEUCHOS_TEST_FOR_EXCEPTION(re.isComplex() || im.isComplex(), std::runtime_error,
"recursively defined complex number. Real part="
<< re << ", imaginary part=" << im);
if (re.totalSize() > 1)
{
Array<Expr> rtn(re.size());
for (int i=0; i<re.size(); i++)
{
rtn[i] = Complex(re[i], im[i]);
}
return new ListExpr(rtn);
}
const ZeroExpr* zr = dynamic_cast<const ZeroExpr*>(re[0].ptr().get());
const ZeroExpr* zi = dynamic_cast<const ZeroExpr*>(im[0].ptr().get());
if (zr == 0) /* nonzero real part */
{
if (zi==0) /* nonzero imag part */
{
return new ComplexExpr(re, im);
}
else /* zero imag part */
{
return re;
}
}
else /* zero real part */
{
if (zi != 0) /* both are zero */
{
return Expr(0.0);
}
else /* pure imaginary */
{
return new ComplexExpr(0.0, im);
}
}
return new ComplexExpr(re, im);
}