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More Cholesky fixes.

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* Cholesky decs are NOT rank revealing so remove all the rank/isPositiveDefinite etc stuff.
* fix bug in LLT: s/return/continue/
* introduce machine_epsilon constants, they are actually needed for Higman's formula determining
  the cutoff in Cholesky. Btw fix the page reference to his book (chat with Keir).
* solve methods always return true, since this isn't a rank revealing dec. Actually... they already did always return true!! Now it's explicit.
* updated dox and unit-test
This commit is contained in:
Benoit Jacob
2009-04-01 00:21:16 +00:00
parent 8e2b191acf
commit 2f45eeb0c6
4 changed files with 35 additions and 99 deletions
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8
Eigen/src/Core/MathFunctions.h
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@@ -26,6 +26,7 @@
#define EIGEN_MATHFUNCTIONS_H
template<typename T> inline typename NumTraits<T>::Real precision();
template<typename T> inline typename NumTraits<T>::Real machine_epsilon();
template<typename T> inline T ei_random(T a, T b);
template<typename T> inline T ei_random();
template<typename T> inline T ei_random_amplitude()
@@ -50,6 +51,7 @@ template<typename T> inline typename NumTraits<T>::Real ei_hypot(T x, T y)
**************/
template<> inline int precision<int>() { return 0; }
template<> inline int machine_epsilon<int>() { return 0; }
inline int ei_real(int x) { return x; }
inline int ei_imag(int) { return 0; }
inline int ei_conj(int x) { return x; }
@@ -102,6 +104,7 @@ inline bool ei_isApproxOrLessThan(int a, int b, int = precision<int>())
**************/
template<> inline float precision<float>() { return 1e-5f; }
template<> inline float machine_epsilon<float>() { return 1.192e-07f; }
inline float ei_real(float x) { return x; }
inline float ei_imag(float) { return 0.f; }
inline float ei_conj(float x) { return x; }
@@ -147,6 +150,8 @@ inline bool ei_isApproxOrLessThan(float a, float b, float prec = precision<float
**************/
template<> inline double precision<double>() { return 1e-11; }
template<> inline double machine_epsilon<double>() { return 2.220e-16; }
inline double ei_real(double x) { return x; }
inline double ei_imag(double) { return 0.; }
inline double ei_conj(double x) { return x; }
@@ -192,6 +197,7 @@ inline bool ei_isApproxOrLessThan(double a, double b, double prec = precision<do
*********************/
template<> inline float precision<std::complex<float> >() { return precision<float>(); }
template<> inline float machine_epsilon<std::complex<float> >() { return machine_epsilon<float>(); }
inline float ei_real(const std::complex<float>& x) { return std::real(x); }
inline float ei_imag(const std::complex<float>& x) { return std::imag(x); }
inline std::complex<float> ei_conj(const std::complex<float>& x) { return std::conj(x); }
@@ -225,6 +231,7 @@ inline bool ei_isApprox(const std::complex<float>& a, const std::complex<float>&
**********************/
template<> inline double precision<std::complex<double> >() { return precision<double>(); }
template<> inline double machine_epsilon<std::complex<double> >() { return machine_epsilon<double>(); }
inline double ei_real(const std::complex<double>& x) { return std::real(x); }
inline double ei_imag(const std::complex<double>& x) { return std::imag(x); }
inline std::complex<double> ei_conj(const std::complex<double>& x) { return std::conj(x); }
@@ -259,6 +266,7 @@ inline bool ei_isApprox(const std::complex<double>& a, const std::complex<double
******************/
template<> inline long double precision<long double>() { return precision<double>(); }
template<> inline long double machine_epsilon<long double>() { return 1.084e-19l; }
inline long double ei_real(long double x) { return x; }
inline long double ei_imag(long double) { return 0.; }
inline long double ei_conj(long double x) { return x; }