/usr/include/trilinos/Teuchos_BLAS_MP_Vector.hpp is in libtrilinos-stokhos-dev 12.10.1-3.
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// Teuchos: Common Tools Package
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#ifndef _TEUCHOS_BLAS_MP_VECTOR_HPP_
#define _TEUCHOS_BLAS_MP_VECTOR_HPP_
#include "Teuchos_BLAS.hpp"
#include "Sacado_MP_Vector.hpp"
// Specialize some things used in the default BLAS implementation that
// don't seem correct for MP::Vector scalar type
namespace Teuchos {
namespace details {
template<typename Storage>
class GivensRotator<Sacado::MP::Vector<Storage>, false> {
public:
typedef Sacado::MP::Vector<Storage> ScalarType;
typedef ScalarType c_type;
void
ROTG (ScalarType* da,
ScalarType* db,
ScalarType* c,
ScalarType* s) const {
typedef ScalarTraits<ScalarType> STS;
// This is a straightforward translation into C++ of the
// reference BLAS' implementation of DROTG. You can get
// the Fortran 77 source code of DROTG here:
//
// http://www.netlib.org/blas/drotg.f
//
// I used the following rules to translate Fortran types and
// intrinsic functions into C++:
//
// DOUBLE PRECISION -> ScalarType
// DABS -> STS::magnitude
// DSQRT -> STM::squareroot
// DSIGN -> SIGN (see below)
//
// DSIGN(x,y) (the old DOUBLE PRECISION type-specific form of
// the Fortran type-generic SIGN intrinsic) required special
// translation, which we did in a separate utility function in
// the specializaton of GivensRotator for real arithmetic.
// (ROTG for complex arithmetic doesn't require this function.)
// C99 provides a copysign() math library function, but we are
// not able to rely on the existence of C99 functions here.
ScalarType r, roe, scale, z;
roe = *db;
if (STS::magnitude (*da) > STS::magnitude (*db)) {
roe = *da;
}
scale = STS::magnitude (*da) + STS::magnitude (*db);
if (scale == STS::zero()) {
*c = STS::one();
*s = STS::zero();
r = STS::zero();
z = STS::zero();
} else {
// I introduced temporaries into the translated BLAS code in
// order to make the expression easier to read and also save
// a few floating-point operations.
const ScalarType da_scaled = *da / scale;
const ScalarType db_scaled = *db / scale;
r = scale * STS::squareroot (da_scaled*da_scaled + db_scaled*db_scaled);
r = SIGN (STS::one(), roe) * r;
*c = *da / r;
*s = *db / r;
z = STS::one();
if (STS::magnitude (*da) > STS::magnitude (*db)) {
z = *s;
}
if (STS::magnitude (*db) >= STS::magnitude (*da) && *c != STS::zero()) {
z = STS::one() / *c;
}
}
*da = r;
*db = z;
}
private:
/// Return ABS(x) if y > 0 or y is +0, else -ABS(x) (if y is -0 or < 0).
ScalarType SIGN (ScalarType x, ScalarType y) const {
typedef typename ScalarType::value_type value_type;
typedef typename ScalarType::ordinal_type ordinal_type;
GivensRotator<value_type> value_rotator;
const ordinal_type sz = x.size() > y.size() ? x.size() : y.size();
ScalarType z(sz, 0.0);
for (ordinal_type i=0; i<sz; ++i)
z.fastAccessCoeff(i) = value_rotator.SIGN(x.coeff(i), y.coeff(i));
return z;
}
};
} // namespace details
} // namespace Teuchos
#endif // _TEUCHOS_BLAS__MP_VECTOR_HPP_
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