10#ifndef EIGEN_AUTODIFF_SCALAR_H
11#define EIGEN_AUTODIFF_SCALAR_H
17template<
typename A,
typename B>
18struct make_coherent_impl {
19 static void run(A&, B&) {}
23template<
typename A,
typename B>
24void make_coherent(
const A& a,
const B&b)
26 make_coherent_impl<A,B>::run(a.const_cast_derived(), b.const_cast_derived());
29template<
typename DerivativeType,
bool Enable>
struct auto_diff_special_op;
33template<
typename DerivativeType>
class AutoDiffScalar;
35template<
typename NewDerType>
36inline AutoDiffScalar<NewDerType> MakeAutoDiffScalar(
const typename NewDerType::Scalar& value,
const NewDerType &der) {
37 return AutoDiffScalar<NewDerType>(value,der);
66template<
typename DerivativeType>
68 :
public internal::auto_diff_special_op
69 <DerivativeType, !internal::is_same<typename internal::traits<typename internal::remove_all<DerivativeType>::type>::Scalar,
70 typename NumTraits<typename internal::traits<typename internal::remove_all<DerivativeType>::type>::Scalar>::Real>::value>
73 typedef internal::auto_diff_special_op
74 <DerivativeType, !internal::is_same<typename internal::traits<typename internal::remove_all<DerivativeType>::type>::Scalar,
76 typedef typename internal::remove_all<DerivativeType>::type DerType;
77 typedef typename internal::traits<DerType>::Scalar Scalar;
80 using Base::operator+;
81 using Base::operator*;
89 : m_value(value), m_derivatives(DerType::Zero(nbDer))
91 m_derivatives.coeffRef(derNumber) = Scalar(1);
99 if(m_derivatives.size()>0)
100 m_derivatives.setZero();
105 : m_value(value), m_derivatives(der)
108 template<
typename OtherDerType>
110#ifndef EIGEN_PARSED_BY_DOXYGEN
111 ,
typename internal::enable_if<
112 internal::is_same<Scalar,
typename internal::traits<
typename internal::remove_all<OtherDerType>::type>::Scalar>::value
113 && internal::is_convertible<OtherDerType,DerType>::value ,
void*>::type = 0
116 : m_value(other.value()), m_derivatives(other.derivatives())
119 friend std::ostream & operator << (std::ostream & s,
const AutoDiffScalar& a)
121 return s << a.value();
125 : m_value(other.value()), m_derivatives(other.derivatives())
128 template<
typename OtherDerType>
129 inline AutoDiffScalar& operator=(
const AutoDiffScalar<OtherDerType>& other)
131 m_value = other.value();
132 m_derivatives = other.derivatives();
138 m_value = other.value();
139 m_derivatives = other.derivatives();
146 if(m_derivatives.size()>0)
147 m_derivatives.setZero();
154 inline const Scalar& value()
const {
return m_value; }
155 inline Scalar& value() {
return m_value; }
157 inline const DerType& derivatives()
const {
return m_derivatives; }
158 inline DerType& derivatives() {
return m_derivatives; }
160 inline bool operator< (
const Scalar& other)
const {
return m_value < other; }
161 inline bool operator<=(
const Scalar& other)
const {
return m_value <= other; }
162 inline bool operator> (
const Scalar& other)
const {
return m_value > other; }
163 inline bool operator>=(
const Scalar& other)
const {
return m_value >= other; }
164 inline bool operator==(
const Scalar& other)
const {
return m_value == other; }
165 inline bool operator!=(
const Scalar& other)
const {
return m_value != other; }
167 friend inline bool operator< (
const Scalar& a,
const AutoDiffScalar& b) {
return a < b.value(); }
168 friend inline bool operator<=(
const Scalar& a,
const AutoDiffScalar& b) {
return a <= b.value(); }
169 friend inline bool operator> (
const Scalar& a,
const AutoDiffScalar& b) {
return a > b.value(); }
170 friend inline bool operator>=(
const Scalar& a,
const AutoDiffScalar& b) {
return a >= b.value(); }
171 friend inline bool operator==(
const Scalar& a,
const AutoDiffScalar& b) {
return a == b.value(); }
172 friend inline bool operator!=(
const Scalar& a,
const AutoDiffScalar& b) {
return a != b.value(); }
174 template<
typename OtherDerType>
inline bool operator< (
const AutoDiffScalar<OtherDerType>& b)
const {
return m_value < b.value(); }
175 template<
typename OtherDerType>
inline bool operator<=(
const AutoDiffScalar<OtherDerType>& b)
const {
return m_value <= b.value(); }
176 template<
typename OtherDerType>
inline bool operator> (
const AutoDiffScalar<OtherDerType>& b)
const {
return m_value > b.value(); }
177 template<
typename OtherDerType>
inline bool operator>=(
const AutoDiffScalar<OtherDerType>& b)
const {
return m_value >= b.value(); }
178 template<
typename OtherDerType>
inline bool operator==(
const AutoDiffScalar<OtherDerType>& b)
const {
return m_value == b.value(); }
179 template<
typename OtherDerType>
inline bool operator!=(
const AutoDiffScalar<OtherDerType>& b)
const {
return m_value != b.value(); }
181 inline const AutoDiffScalar<DerType&> operator+(
const Scalar& other)
const
183 return AutoDiffScalar<DerType&>(m_value + other, m_derivatives);
186 friend inline const AutoDiffScalar<DerType&> operator+(
const Scalar& a,
const AutoDiffScalar& b)
188 return AutoDiffScalar<DerType&>(a + b.value(), b.derivatives());
207 template<
typename OtherDerType>
208 inline const AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,
const DerType,
const typename internal::remove_all<OtherDerType>::type> >
209 operator+(
const AutoDiffScalar<OtherDerType>& other)
const
211 internal::make_coherent(m_derivatives, other.derivatives());
212 return AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,
const DerType,
const typename internal::remove_all<OtherDerType>::type> >(
213 m_value + other.value(),
214 m_derivatives + other.derivatives());
217 template<
typename OtherDerType>
219 operator+=(
const AutoDiffScalar<OtherDerType>& other)
221 (*this) = (*this) + other;
225 inline const AutoDiffScalar<DerType&> operator-(
const Scalar& b)
const
227 return AutoDiffScalar<DerType&>(m_value - b, m_derivatives);
230 friend inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>,
const DerType> >
233 return AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>,
const DerType> >
234 (a - b.value(), -b.derivatives());
243 template<
typename OtherDerType>
244 inline const AutoDiffScalar<CwiseBinaryOp<internal::scalar_difference_op<Scalar>,
const DerType,
const typename internal::remove_all<OtherDerType>::type> >
245 operator-(
const AutoDiffScalar<OtherDerType>& other)
const
247 internal::make_coherent(m_derivatives, other.derivatives());
248 return AutoDiffScalar<CwiseBinaryOp<internal::scalar_difference_op<Scalar>,
const DerType,
const typename internal::remove_all<OtherDerType>::type> >(
249 m_value - other.value(),
250 m_derivatives - other.derivatives());
253 template<
typename OtherDerType>
255 operator-=(
const AutoDiffScalar<OtherDerType>& other)
257 *
this = *
this - other;
261 inline const AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>,
const DerType> >
264 return AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>,
const DerType> >(
269 inline const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) >
270 operator*(
const Scalar& other)
const
272 return MakeAutoDiffScalar(m_value * other, m_derivatives * other);
275 friend inline const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) >
278 return MakeAutoDiffScalar(a.value() * other, a.derivatives() * other);
297 inline const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) >
298 operator/(
const Scalar& other)
const
300 return MakeAutoDiffScalar(m_value / other, (m_derivatives * (Scalar(1)/other)));
303 friend inline const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) >
306 return MakeAutoDiffScalar(other / a.value(), a.derivatives() * (Scalar(-other) / (a.value()*a.value())));
325 template<
typename OtherDerType>
326 inline const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(
327 CwiseBinaryOp<internal::scalar_difference_op<Scalar> EIGEN_COMMA
328 const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) EIGEN_COMMA
329 const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(
typename internal::remove_all<OtherDerType>::type,Scalar,product) >,Scalar,product) >
330 operator/(
const AutoDiffScalar<OtherDerType>& other)
const
332 internal::make_coherent(m_derivatives, other.derivatives());
333 return MakeAutoDiffScalar(
334 m_value / other.value(),
335 ((m_derivatives * other.value()) - (other.derivatives() * m_value))
336 * (Scalar(1)/(other.value()*other.value())));
339 template<
typename OtherDerType>
340 inline const AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,
341 const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product),
342 const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(
typename internal::remove_all<OtherDerType>::type,Scalar,product) > >
343 operator*(
const AutoDiffScalar<OtherDerType>& other)
const
345 internal::make_coherent(m_derivatives, other.derivatives());
346 return MakeAutoDiffScalar(
347 m_value * other.value(),
348 (m_derivatives * other.value()) + (other.derivatives() * m_value));
353 *
this = *
this * other;
357 template<
typename OtherDerType>
358 inline AutoDiffScalar& operator*=(
const AutoDiffScalar<OtherDerType>& other)
360 *
this = *
this * other;
366 *
this = *
this / other;
370 template<
typename OtherDerType>
371 inline AutoDiffScalar& operator/=(
const AutoDiffScalar<OtherDerType>& other)
373 *
this = *
this / other;
379 DerType m_derivatives;
385template<
typename DerivativeType>
386struct auto_diff_special_op<DerivativeType, true>
390 typedef typename remove_all<DerivativeType>::type DerType;
391 typedef typename traits<DerType>::Scalar Scalar;
392 typedef typename NumTraits<Scalar>::Real Real;
404 const AutoDiffScalar<DerivativeType>& derived()
const {
return *
static_cast<const AutoDiffScalar<DerivativeType>*
>(
this); }
405 AutoDiffScalar<DerivativeType>& derived() {
return *
static_cast<AutoDiffScalar<DerivativeType>*
>(
this); }
408 inline const AutoDiffScalar<DerType&> operator+(
const Real& other)
const
410 return AutoDiffScalar<DerType&>(derived().value() + other, derived().derivatives());
413 friend inline const AutoDiffScalar<DerType&> operator+(
const Real& a,
const AutoDiffScalar<DerivativeType>& b)
415 return AutoDiffScalar<DerType&>(a + b.value(), b.derivatives());
418 inline AutoDiffScalar<DerivativeType>& operator+=(
const Real& other)
420 derived().value() += other;
425 inline const AutoDiffScalar<typename CwiseUnaryOp<bind2nd_op<scalar_product_op<Scalar,Real> >, DerType>::Type >
428 return AutoDiffScalar<typename CwiseUnaryOp<bind2nd_op<scalar_product_op<Scalar,Real> >, DerType>::Type >(
429 derived().value() * other,
430 derived().derivatives() * other);
433 friend inline const AutoDiffScalar<typename CwiseUnaryOp<bind1st_op<scalar_product_op<Real,Scalar> >, DerType>::Type >
434 operator*(
const Real& other,
const AutoDiffScalar<DerivativeType>& a)
436 return AutoDiffScalar<typename CwiseUnaryOp<bind1st_op<scalar_product_op<Real,Scalar> >, DerType>::Type >(
438 a.derivatives() * other);
441 inline AutoDiffScalar<DerivativeType>& operator*=(
const Scalar& other)
443 *
this = *
this * other;
448template<
typename DerivativeType>
449struct auto_diff_special_op<DerivativeType, false>
452 void operator-()
const;
453 void operator+()
const;
456template<
typename BinOp,
typename A,
typename B,
typename RefType>
457void make_coherent_expression(CwiseBinaryOp<BinOp,A,B> xpr,
const RefType &ref)
459 make_coherent(xpr.const_cast_derived().lhs(), ref);
460 make_coherent(xpr.const_cast_derived().rhs(), ref);
463template<
typename UnaryOp,
typename A,
typename RefType>
464void make_coherent_expression(
const CwiseUnaryOp<UnaryOp,A> &xpr,
const RefType &ref)
466 make_coherent(xpr.nestedExpression().const_cast_derived(), ref);
470template<
typename UnaryOp,
typename A,
typename RefType>
471void make_coherent_expression(
const CwiseNullaryOp<UnaryOp,A> &,
const RefType &)
474template<
typename A_Scalar,
int A_Rows,
int A_Cols,
int A_Options,
int A_MaxRows,
int A_MaxCols,
typename B>
475struct make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>, B> {
476 typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> A;
477 static void run(A& a, B& b) {
483 else if (B::SizeAtCompileTime==
Dynamic && a.size()!=0 && b.size()==0)
485 make_coherent_expression(b,a);
490template<
typename A,
typename B_Scalar,
int B_Rows,
int B_Cols,
int B_Options,
int B_MaxRows,
int B_MaxCols>
491struct make_coherent_impl<A, Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> > {
492 typedef Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> B;
493 static void run(A& a, B& b) {
499 else if (A::SizeAtCompileTime==
Dynamic && b.size()!=0 && a.size()==0)
501 make_coherent_expression(a,b);
506template<
typename A_Scalar,
int A_Rows,
int A_Cols,
int A_Options,
int A_MaxRows,
int A_MaxCols,
507 typename B_Scalar,
int B_Rows,
int B_Cols,
int B_Options,
int B_MaxRows,
int B_MaxCols>
508struct make_coherent_impl<Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols>,
509 Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> > {
510 typedef Matrix<A_Scalar, A_Rows, A_Cols, A_Options, A_MaxRows, A_MaxCols> A;
511 typedef Matrix<B_Scalar, B_Rows, B_Cols, B_Options, B_MaxRows, B_MaxCols> B;
512 static void run(A& a, B& b) {
528template<
typename DerType,
typename BinOp>
529struct ScalarBinaryOpTraits<AutoDiffScalar<DerType>,typename DerType::Scalar,BinOp>
531 typedef AutoDiffScalar<DerType> ReturnType;
534template<
typename DerType,
typename BinOp>
535struct ScalarBinaryOpTraits<typename DerType::Scalar,AutoDiffScalar<DerType>, BinOp>
537 typedef AutoDiffScalar<DerType> ReturnType;
557#define EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(FUNC,CODE) \
558 template<typename DerType> \
559 inline const Eigen::AutoDiffScalar< \
560 EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(typename Eigen::internal::remove_all<DerType>::type, typename Eigen::internal::traits<typename Eigen::internal::remove_all<DerType>::type>::Scalar, product) > \
561 FUNC(const Eigen::AutoDiffScalar<DerType>& x) { \
562 using namespace Eigen; \
563 typedef typename Eigen::internal::traits<typename Eigen::internal::remove_all<DerType>::type>::Scalar Scalar; \
564 EIGEN_UNUSED_VARIABLE(sizeof(Scalar)); \
568template<
typename DerType>
569struct CleanedUpDerType {
570 typedef AutoDiffScalar<typename Eigen::internal::remove_all<DerType>::type::PlainObject> type;
573template<
typename DerType>
574inline const AutoDiffScalar<DerType>&
conj(
const AutoDiffScalar<DerType>& x) {
return x; }
575template<
typename DerType>
576inline const AutoDiffScalar<DerType>&
real(
const AutoDiffScalar<DerType>& x) {
return x; }
577template<
typename DerType>
578inline typename DerType::Scalar
imag(
const AutoDiffScalar<DerType>&) {
return 0.; }
579template<
typename DerType,
typename T>
580inline typename CleanedUpDerType<DerType>::type (min)(
const AutoDiffScalar<DerType>& x,
const T& y) {
581 typedef typename CleanedUpDerType<DerType>::type ADS;
582 return (x <= y ? ADS(x) : ADS(y));
584template<
typename DerType,
typename T>
585inline typename CleanedUpDerType<DerType>::type (max)(
const AutoDiffScalar<DerType>& x,
const T& y) {
586 typedef typename CleanedUpDerType<DerType>::type ADS;
587 return (x >= y ? ADS(x) : ADS(y));
589template<
typename DerType,
typename T>
590inline typename CleanedUpDerType<DerType>::type (min)(
const T& x,
const AutoDiffScalar<DerType>& y) {
591 typedef typename CleanedUpDerType<DerType>::type ADS;
592 return (x < y ? ADS(x) : ADS(y));
594template<
typename DerType,
typename T>
595inline typename CleanedUpDerType<DerType>::type (max)(
const T& x,
const AutoDiffScalar<DerType>& y) {
596 typedef typename CleanedUpDerType<DerType>::type ADS;
597 return (x > y ? ADS(x) : ADS(y));
599template<
typename DerType>
600inline typename CleanedUpDerType<DerType>::type (min)(
const AutoDiffScalar<DerType>& x,
const AutoDiffScalar<DerType>& y) {
601 return (x.value() < y.value() ? x : y);
603template<
typename DerType>
604inline typename CleanedUpDerType<DerType>::type (max)(
const AutoDiffScalar<DerType>& x,
const AutoDiffScalar<DerType>& y) {
605 return (x.value() >= y.value() ? x : y);
609EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(
abs,
611 return Eigen::MakeAutoDiffScalar(
abs(x.value()), x.derivatives() * (x.value()<0 ? -1 : 1) );)
613EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(
abs2,
615 return Eigen::MakeAutoDiffScalar(
abs2(x.value()), x.derivatives() * (Scalar(2)*x.value()));)
617EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(
sqrt,
619 Scalar sqrtx =
sqrt(x.value());
620 return Eigen::MakeAutoDiffScalar(sqrtx,x.derivatives() * (Scalar(0.5) / sqrtx));)
622EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(
cos,
625 return Eigen::MakeAutoDiffScalar(
cos(x.value()), x.derivatives() * (-
sin(x.value())));)
627EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(
sin,
630 return Eigen::MakeAutoDiffScalar(
sin(x.value()),x.derivatives() *
cos(x.value()));)
632EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(
exp,
634 Scalar expx =
exp(x.value());
635 return Eigen::MakeAutoDiffScalar(expx,x.derivatives() * expx);)
637EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(
log,
639 return Eigen::MakeAutoDiffScalar(
log(x.value()),x.derivatives() * (Scalar(1)/x.value()));)
641template<typename DerType>
643EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(
typename internal::remove_all<DerType>::type,
typename internal::traits<
typename internal::remove_all<DerType>::type>::Scalar,product) >
646 using namespace Eigen;
648 return Eigen::MakeAutoDiffScalar(pow(x.value(),y), x.derivatives() * (y * pow(x.value(),y-1)));
652template<
typename DerTypeA,
typename DerTypeB>
657 typedef typename internal::traits<typename internal::remove_all<DerTypeA>::type>::Scalar Scalar;
660 ret.value() = atan2(a.value(), b.value());
662 Scalar squared_hypot = a.value() * a.value() + b.value() * b.value();
665 ret.derivatives() = (a.derivatives() * b.value() - a.value() * b.derivatives()) / squared_hypot;
670EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(
tan,
673 return Eigen::MakeAutoDiffScalar(
tan(x.value()),x.derivatives() * (Scalar(1)/numext::abs2(
cos(x.value()))));)
675EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(
asin,
678 return Eigen::MakeAutoDiffScalar(
asin(x.value()),x.derivatives() * (Scalar(1)/
sqrt(1-numext::abs2(x.value()))));)
680EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(
acos,
683 return Eigen::MakeAutoDiffScalar(
acos(x.value()),x.derivatives() * (Scalar(-1)/
sqrt(1-numext::abs2(x.value()))));)
685EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(
tanh,
688 return Eigen::MakeAutoDiffScalar(
tanh(x.value()),x.derivatives() * (Scalar(1)/numext::abs2(
cosh(x.value()))));)
690EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(
sinh,
693 return Eigen::MakeAutoDiffScalar(
sinh(x.value()),x.derivatives() *
cosh(x.value()));)
695EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY(
cosh,
698 return Eigen::MakeAutoDiffScalar(
cosh(x.value()),x.derivatives() *
sinh(x.value()));)
700#undef EIGEN_AUTODIFF_DECLARE_GLOBAL_UNARY
703 :
NumTraits<
typename NumTraits<
typename internal::remove_all<DerType>::type::Scalar>::Real >
705 typedef typename internal::remove_all<DerType>::type DerTypeCleaned;
707 0, DerTypeCleaned::MaxRowsAtCompileTime, DerTypeCleaned::MaxColsAtCompileTime> > Real;
712 RequireInitialization = 1
722 :
public numeric_limits<typename T::Scalar> {};
726 :
public numeric_limits<typename T::Scalar> {};
A scalar type replacement with automatic differentiation capability.
Definition: AutoDiffScalar.h:71
AutoDiffScalar()
Definition: AutoDiffScalar.h:84
AutoDiffScalar(const Scalar &value, int nbDer, int derNumber)
Definition: AutoDiffScalar.h:88
AutoDiffScalar(const Real &value)
Definition: AutoDiffScalar.h:96
AutoDiffScalar(const Scalar &value, const DerType &der)
Definition: AutoDiffScalar.h:104
Namespace containing all symbols from the Eigen library.
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_cosh_op< typename Derived::Scalar >, const Derived > cosh(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_cos_op< typename Derived::Scalar >, const Derived > cos(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sqrt_op< typename Derived::Scalar >, const Derived > sqrt(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_real_op< typename Derived::Scalar >, const Derived > real(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_exp_op< typename Derived::Scalar >, const Derived > exp(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_conjugate_op< typename Derived::Scalar >, const Derived > conj(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_abs_op< typename Derived::Scalar >, const Derived > abs(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_tan_op< typename Derived::Scalar >, const Derived > tan(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_abs2_op< typename Derived::Scalar >, const Derived > abs2(const Eigen::ArrayBase< Derived > &x)
const Product< Inverse< PermutationType >, SparseDerived, AliasFreeProduct > operator*(const InverseImpl< PermutationType, PermutationStorage > &tperm, const SparseMatrixBase< SparseDerived > &matrix)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_imag_op< typename Derived::Scalar >, const Derived > imag(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_log_op< typename Derived::Scalar >, const Derived > log(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sin_op< typename Derived::Scalar >, const Derived > sin(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_asin_op< typename Derived::Scalar >, const Derived > asin(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_tanh_op< typename Derived::Scalar >, const Derived > tanh(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_acos_op< typename Derived::Scalar >, const Derived > acos(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sinh_op< typename Derived::Scalar >, const Derived > sinh(const Eigen::ArrayBase< Derived > &x)