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Add sinh, cosh, tanh and tan functions to automatic differentiation

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Change-Id: I6eb43fe9b340d4074ed3eed1461dda315f6e8ce8
This commit is contained in:
Johannes Schönberger
2013-05-30 00:11:44 +02:00
parent eb04dc10c5
commit a8d38d438a
2 changed files with 94 additions and 1 deletions
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include/ceres/jet.h
+62 -1
View File
@@ -405,7 +405,6 @@ CERES_DEFINE_JET_COMPARISON_OPERATOR( != ) // NOLINT
// double-valued and Jet-valued functions, but we are not allowed to put
// Jet-valued functions inside namespace std.
//
// Missing: cosh, sinh, tanh, tan
// TODO(keir): Switch to "using".
inline double abs (double x) { return std::abs(x); }
inline double log (double x) { return std::log(x); }
@@ -415,6 +414,11 @@ inline double cos (double x) { return std::cos(x); }
inline double acos (double x) { return std::acos(x); }
inline double sin (double x) { return std::sin(x); }
inline double asin (double x) { return std::asin(x); }
inline double tan (double x) { return std::tan(x); }
inline double atan (double x) { return std::atan(x); }
inline double sinh (double x) { return std::sinh(x); }
inline double cosh (double x) { return std::cosh(x); }
inline double tanh (double x) { return std::tanh(x); }
inline double pow (double x, double y) { return std::pow(x, y); }
inline double atan2(double y, double x) { return std::atan2(y, x); }
@@ -495,6 +499,58 @@ Jet<T, N> asin(const Jet<T, N>& f) {
return g;
}
// tan(a + h) ~= tan(a) + (1 + tan(a)^2) h
template <typename T, int N> inline
Jet<T, N> tan(const Jet<T, N>& f) {
Jet<T, N> g;
g.a = tan(f.a);
double tan_a = tan(f.a);
const T tmp = T(1.0) + tan_a * tan_a;
g.v = tmp * f.v;
return g;
}
// atan(a + h) ~= atan(a) + 1 / (1 + a^2) h
template <typename T, int N> inline
Jet<T, N> atan(const Jet<T, N>& f) {
Jet<T, N> g;
g.a = atan(f.a);
const T tmp = T(1.0) / (T(1.0) + f.a * f.a);
g.v = tmp * f.v;
return g;
}
// sinh(a + h) ~= sinh(a) + cosh(a) h
template <typename T, int N> inline
Jet<T, N> sinh(const Jet<T, N>& f) {
Jet<T, N> g;
g.a = sinh(f.a);
const T cosh_a = cosh(f.a);
g.v = cosh_a * f.v;
return g;
}
// cosh(a + h) ~= cosh(a) + sinh(a) h
template <typename T, int N> inline
Jet<T, N> cosh(const Jet<T, N>& f) {
Jet<T, N> g;
g.a = cosh(f.a);
const T sinh_a = sinh(f.a);
g.v = sinh_a * f.v;
return g;
}
// tanh(a + h) ~= tanh(a) + (1 - tanh(a)^2) h
template <typename T, int N> inline
Jet<T, N> tanh(const Jet<T, N>& f) {
Jet<T, N> g;
g.a = tanh(f.a);
double tanh_fa = tanh(f.a);
const T tmp = 1 - tanh_fa * tanh_fa;
g.v = tmp * f.v;
return g;
}
// Jet Classification. It is not clear what the appropriate semantics are for
// these classifications. This picks that IsFinite and isnormal are "all"
// operations, i.e. all elements of the jet must be finite for the jet itself
@@ -645,6 +701,11 @@ template<typename T, int N> inline Jet<T, N> ei_exp (const Jet<T, N>& x)
template<typename T, int N> inline Jet<T, N> ei_log (const Jet<T, N>& x) { return log(x); } // NOLINT
template<typename T, int N> inline Jet<T, N> ei_sin (const Jet<T, N>& x) { return sin(x); } // NOLINT
template<typename T, int N> inline Jet<T, N> ei_cos (const Jet<T, N>& x) { return cos(x); } // NOLINT
template<typename T, int N> inline Jet<T, N> ei_tan (const Jet<T, N>& x) { return tan(x); } // NOLINT
template<typename T, int N> inline Jet<T, N> ei_atan(const Jet<T, N>& x) { return atan(x); } // NOLINT
template<typename T, int N> inline Jet<T, N> ei_sinh(const Jet<T, N>& x) { return sinh(x); } // NOLINT
template<typename T, int N> inline Jet<T, N> ei_cosh(const Jet<T, N>& x) { return cosh(x); } // NOLINT
template<typename T, int N> inline Jet<T, N> ei_tanh(const Jet<T, N>& x) { return tanh(x); } // NOLINT
template<typename T, int N> inline Jet<T, N> ei_pow (const Jet<T, N>& x, Jet<T, N> y) { return pow(x, y); } // NOLINT
// Note: This has to be in the ceres namespace for argument dependent lookup to
internal/ceres/jet_test.cc
+32
View File
@@ -142,6 +142,38 @@ TEST(Jet, Jet) {
ExpectJetsClose(u, t);
}
{ // Check that tan(x) = sin(x) / cos(x).
J z = tan(x);
J w = sin(x) / cos(x);
VL << "z = " << z;
VL << "w = " << w;
ExpectJetsClose(z, w);
}
{ // Check that tan(atan(x)) = x.
J z = tan(atan(x));
J w = x;
VL << "z = " << z;
VL << "w = " << w;
ExpectJetsClose(z, w);
}
{ // Check that cosh(x)*cosh(x) - sinh(x)*sinh(x) = 1
J z = cosh(x) * cosh(x);
J w = sinh(x) * sinh(x);
VL << "z = " << z;
VL << "w = " << w;
ExpectJetsClose(z - w, J(1.0));
}
{ // Check that tanh(x + y) = (tanh(x) + tanh(y)) / (1 + tanh(x) tanh(y))
J z = tanh(x + y);
J w = (tanh(x) + tanh(y)) / (J(1.0) + tanh(x) * tanh(y));
VL << "z = " << z;
VL << "w = " << w;
ExpectJetsClose(z, w);
}
{ // Check that pow(x, 1) == x.
VL << "x = " << x;