rdoc/min.rdoc in gsl-1.15.3 vs rdoc/min.rdoc in gsl-1.16.0.6
- old
+ new
@@ -1,56 +1,56 @@
#
# = One dimensional Minimization
#
-# This chapter describes routines for finding minima of arbitrary
+# This chapter describes routines for finding minima of arbitrary
# one-dimensional functions.
#
#
# Contents:
-# 1. {Introduction}[link:files/rdoc/min_rdoc.html#1]
-# 1. {GSL::Min::FMinimizer class}[link:files/rdoc/min_rdoc.html#2]
-# 1. {Iteration}[link:files/rdoc/min_rdoc.html#3]
-# 1. {Stopping Parameters}[link:files/rdoc/min_rdoc.html#4]
-# 1. {Examples}[link:files/rdoc/min_rdoc.html#5]
+# 1. {Introduction}[link:rdoc/min_rdoc.html#label-Introduction]
+# 1. {GSL::Min::FMinimizer class}[link:rdoc/min_rdoc.html#label-Minimizer+class]
+# 1. {Iteration}[link:rdoc/min_rdoc.html#label-Iteration]
+# 1. {Stopping Parameters}[link:rdoc/min_rdoc.html#label-Stopping+Parameters]
+# 1. {Examples}[link:rdoc/min_rdoc.html#label-Example]
#
-# == {}[link:index.html"name="1] Introduction
+# == Introduction
#
-# The minimization algorithms begin with a bounded region known to contain
-# a minimum. The region is described by <tt>a</tt> lower bound a and an upper bound
+# The minimization algorithms begin with a bounded region known to contain
+# a minimum. The region is described by <tt>a</tt> lower bound a and an upper bound
# <tt>b</tt>, with an estimate of the location of the minimum <tt>x</tt>.
#
-# The value of the function at <tt>x</tt> must be less than the value of the
+# The value of the function at <tt>x</tt> must be less than the value of the
# function at the ends of the interval,
# f(a) > f(x) < f(b)
-# This condition guarantees that a minimum is contained somewhere within the
+# This condition guarantees that a minimum is contained somewhere within the
# interval. On each iteration a new point <tt>x'</tt> is selected using one of the
-# available algorithms. If the new point is a better estimate of the minimum,
-# <tt>f(x') < f(x)</tt>, then the current estimate of the minimum <tt>x</tt> is
-# updated. The new point also allows the size of the bounded interval to be
-# reduced, by choosing the most compact set of points which satisfies the
-# constraint <tt>f(a) > f(x) < f(b)</tt>. The interval is reduced until it
-# encloses the true minimum to a desired tolerance. This provides a best
+# available algorithms. If the new point is a better estimate of the minimum,
+# <tt>f(x') < f(x)</tt>, then the current estimate of the minimum <tt>x</tt> is
+# updated. The new point also allows the size of the bounded interval to be
+# reduced, by choosing the most compact set of points which satisfies the
+# constraint <tt>f(a) > f(x) < f(b)</tt>. The interval is reduced until it
+# encloses the true minimum to a desired tolerance. This provides a best
# estimate of the location of the minimum and a rigorous error estimate.
#
-# Several bracketing algorithms are available within a single framework.
-# The user provides a high-level driver for the algorithm, and the library
-# provides the individual functions necessary for each of the steps. There
+# Several bracketing algorithms are available within a single framework.
+# The user provides a high-level driver for the algorithm, and the library
+# provides the individual functions necessary for each of the steps. There
# are three main phases of the iteration. The steps are,
# * initialize minimizer (or <tt>solver</tt>) state, <tt>s</tt>, for algorithm <tt>T</tt>
# * update <tt>s</tt> using the iteration <tt>T</tt>
# * test <tt>s</tt> for convergence, and repeat iteration if necessary
#
-# The state of the minimizers is held in a <tt>GSL::Min::FMinimizer</tt> object.
+# The state of the minimizers is held in a <tt>GSL::Min::FMinimizer</tt> object.
# The updating procedure use only function evaluations (not derivatives).
-# The function to minimize is given as an instance of the {GSL::Function}[link:files/rdoc/function_rdoc.html] class to the minimizer.
+# The function to minimize is given as an instance of the {GSL::Function}[link:rdoc/function_rdoc.html] class to the minimizer.
#
#
-# == {}[link:index.html"name="2] GSL::Min::FMinimizer class
+# == FMinimizer class
# ---
# * GSL::Min::FMinimizer.alloc(t)
#
-# These method create an instance of the <tt>GSL::Min::FMinimizer</tt> class of
+# These method create an instance of the <tt>GSL::Min::FMinimizer</tt> class of
# type <tt>t</tt>. The type <tt>t</tt> is given by a String,
# * "goldensection"
# * "brent"
# * "quad_golden"
# or by a Ruby constant,
@@ -63,90 +63,90 @@
# s = FMinimizer.alloc(FMinimizer::BRENT)
#
# ---
# * GSL::Min::FMinimizer#set(f, xmin, xlow, xup)
#
-# This method sets, or resets, an existing minimizer <tt>self</tt> to use
+# This method sets, or resets, an existing minimizer <tt>self</tt> to use
# the function <tt>f</tt> (given by a <tt>GSL::Function</tt>
-# object) and the initial search interval [<tt>xlow, xup</tt>],
+# object) and the initial search interval [<tt>xlow, xup</tt>],
# with a guess for the location of the minimum <tt>xmin</tt>.
#
-# If the interval given does not contain a minimum, then the
+# If the interval given does not contain a minimum, then the
# method returns an error code of <tt>GSL::FAILURE</tt>.
#
# ---
# * GSL::Min::FMinimizer#set_with_values(f, xmin, fmin, xlow, flow, xup, fup)
#
-# This method is equivalent to <tt>Fminimizer#set</tt> but uses the values
-# <tt>fmin, flowe</tt> and <tt>fup</tt> instead of computing
+# This method is equivalent to <tt>Fminimizer#set</tt> but uses the values
+# <tt>fmin, flowe</tt> and <tt>fup</tt> instead of computing
# <tt>f(xmin), f(xlow)</tt> and <tt>f(xup)</tt>.
#
# ---
# * GSL::Min::FMinimizer#name
#
-# This returns the name of the minimizer.
+# This returns the name of the minimizer.
#
-# == {}[link:index.html"name="3] Iteration
+# == Iteration
# ---
# * GSL::Min::FMinimizer#iterate
#
-# This method performs a single iteration of the minimizer <tt>self</tt>.
-# If the iteration encounters an unexpected problem then an error code
+# This method performs a single iteration of the minimizer <tt>self</tt>.
+# If the iteration encounters an unexpected problem then an error code
# will be returned,
-# * <tt>GSL::EBADFUNC</tt>: the iteration encountered a singular point where the
+# * <tt>GSL::EBADFUNC</tt>: the iteration encountered a singular point where the
# function evaluated to <tt>Inf</tt> or <tt>NaN</tt>.
-# * <tt>GSL::FAILURE</tt>: the algorithm could not improve the current best
+# * <tt>GSL::FAILURE</tt>: the algorithm could not improve the current best
# approximation or bounding interval.
-# The minimizer maintains a current best estimate of the position of
-# the minimum at all times, and the current interval bounding the minimum.
+# The minimizer maintains a current best estimate of the position of
+# the minimum at all times, and the current interval bounding the minimum.
# This information can be accessed with the following auxiliary methods
#
# ---
# * GSL::Min::FMinimizer#x_minimum
#
-# Returns the current estimate of the position of the minimum
+# Returns the current estimate of the position of the minimum
# for the minimizer <tt>self</tt>.
#
# ---
# * GSL::Min::FMinimizer#x_upper
# * GSL::Min::FMinimizer#x_lower
#
-# Return the current upper and lower bound of the interval for the
+# Return the current upper and lower bound of the interval for the
# minimizer <tt>self</tt>.
#
# ---
# * GSL::Min::FMinimizer#f_minimum
# * GSL::Min::FMinimizer#f_upper
# * GSL::Min::FMinimizer#f_lower
#
-# Return the value of the function at the current estimate of the
-# minimum and at the upper and lower bounds of interval
+# Return the value of the function at the current estimate of the
+# minimum and at the upper and lower bounds of interval
# for the minimizer <tt>self</tt>.
#
-# == {}[link:index.html"name="4] Stopping Parameters
+# == Stopping Parameters
# ---
# * GSL::Min::FMinimizer#test_interval(epsabs, epsrel)
# * GSL::Min.test_interval(xlow, xup, epsabs, epsrel)
#
-# These methoeds test for the convergence of the interval
-# [<tt>xlow, xup</tt>] with absolute error <tt>epsabs</tt> and relative
-# error <tt>epsrel</tt>. The test returns <tt>GSL::SUCCESS</tt>
+# These methoeds test for the convergence of the interval
+# [<tt>xlow, xup</tt>] with absolute error <tt>epsabs</tt> and relative
+# error <tt>epsrel</tt>. The test returns <tt>GSL::SUCCESS</tt>
# if the following condition is achieved,
-# |a - b| < epsabs + epsrel min(|a|,|b|)
-# when the interval <tt>x = [a,b]</tt> does not include the origin.
-# If the interval includes the origin then <tt>min(|a|,|b|)</tt> is
-# replaced by zero (which is the minimum value of |x| over the interval).
-# This ensures that the relative error is accurately estimated for minima
+# |a - b| < epsabs + epsrel min(|a|,|b|)
+# when the interval <tt>x = [a,b]</tt> does not include the origin.
+# If the interval includes the origin then <tt>min(|a|,|b|)</tt> is
+# replaced by zero (which is the minimum value of |x| over the interval).
+# This ensures that the relative error is accurately estimated for minima
# close to the origin.
#
-# This condition on the interval also implies that any estimate of the
-# minimum x_m in the interval satisfies the same condition with respect
+# This condition on the interval also implies that any estimate of the
+# minimum x_m in the interval satisfies the same condition with respect
# to the true minimum x_m^*,
# |x_m - x_m^*| < epsabs + epsrel x_m^*
# assuming that the true minimum x_m^* is contained within the interval.
#
-# == {}[link:index.html"name="5] Example
+# == Example
# To find the minimum of the function f(x) = cos(x) + 1.0:
#
# #!/usr/bin/env ruby
# require("gsl")
# include GSL::Min
@@ -178,12 +178,12 @@
# m = gmf.x_minimum
# printf("%5d [%.7f, %.7f] %.7f %+.7f %.7f\n",
# iter, a, b, m, m - m_expected, b - a);
# end while status == GSL::CONTINUE and iter < max_iter
#
-# {prev}[link:files/rdoc/roots_rdoc.html]
-# {next}[link:files/rdoc/multiroot_rdoc.html]
+# {prev}[link:rdoc/roots_rdoc.html]
+# {next}[link:rdoc/multiroot_rdoc.html]
#
-# {Reference index}[link:files/rdoc/ref_rdoc.html]
-# {top}[link:files/rdoc/index_rdoc.html]
+# {Reference index}[link:rdoc/ref_rdoc.html]
+# {top}[link:index.html]
#
#