Class jacobian_gsl (o2scl)

O2scl : Class List

template<class func_t = mm_funct, class vec_t = boost::numeric::ublas::vector<double>, class mat_t = boost::numeric::ublas::matrix<double>>
class jacobian_gsl : public o2scl::jacobian<mm_funct, boost::numeric::ublas::vector<double>, boost::numeric::ublas::matrix<double>>

Simple automatic Jacobian.

This class computes a numerical Jacobian by finite differencing. The stepsize is initially chosen to be \( h_j = \mathrm{max}(\mathrm{epsrel}~|x_j|,\mathrm{epsmin}) \). Then if \( h_j = 0 \), the value of \( h_j \) is set to \( \mathrm{epsrel}) \) .

Values of epsmin which are non-zero are useful, for example, in mroot_hybrids when one of the variables is either very small or zero, so that the step size doesn’t become too small.

If the function evaluation leads to a non-zero return value, then the step size is alternately flipped in sign or decreased by a fixed factor (default \( 10^2 \), set in set_shrink_fact() ) in order to obtain a valid result. This process is repeated a fixed number of times (default 10, set in set_max_shrink_iters() ).

This is equivalent to the GSL method for computing Jacobians as in multiroots/fdjac.c if one calls set_max_shrink_iters() with a parameter value of zero.

If one row of the Jacobian is all zero, or if there was no step-size found which would give a zero return value from the user-specified function, then the error handler is called depending on the value of err_nonconv.

This class does not separately check the vector and matrix sizes to ensure they are commensurate.

Default template arguments

• func_t - mm_funct

• vec_t - boost::numeric::ublas::vector<double>

• mat_t - boost::numeric::ublas::matrix<double>

Public Functions

inline jacobian_gsl()

inline virtual ~jacobian_gsl()

inline double get_epsrel()

Get the relative stepsize (default \( 10^{-4} \) )

inline double get_epsmin()

Get the minimum stepsize (default \( 10^{-15} \))

inline void set_epsrel(double l_epsrel)

Set the relative stepsize (must be \( > 0 \))

inline void set_epsmin(double l_epsmin)

Set the minimum stepsize (must be \( \geq 0 \))

inline void set_shrink_fact(double l_shrink_fact)

Set shrink factor for decreasing step size.

inline void set_max_shrink_iters(size_t it)

Set number of times to decrease step size.

inline virtual int operator()(size_t nx, vec_t &x, size_t ny, vec_t &y, mat_t &jac)

The operator()

Protected Attributes

vec_t f

Function values.

vec_t xx

Function arguments.

size_t mem_size_x

Size of allocated memory in x.

size_t mem_size_y

Size of allocated memory in y.

double epsrel

The relative stepsize for finite-differencing.

double epsmin

The minimum stepsize.

size_t max_shrink_iters

Maximum number of times to shrink the step size.

double shrink_fact

Factor to shrink stepsize by.