dht.rdoc in rb-gsl-1.16.0.3.rc1

- old
+ new

@@ -1,78 +1,78 @@
 #
 # = Discrete Hankel Transforms
-# This chapter describes functions for performing Discrete Hankel Transforms 
-# (DHTs). 
+# This chapter describes functions for performing Discrete Hankel Transforms
+# (DHTs).
 #
-# 1. {Definitions}[link:rdoc/dht_rdoc.html#1]
-# 1. {Initialization}[link:rdoc/dht_rdoc.html#2]
-# 1. {Methods}[link:rdoc/dht_rdoc.html#3]
+# 1. {Definitions}[link:dht_rdoc.html#label-Definitions]
+# 1. {Initialization}[link:dht_rdoc.html#label-Initialization]
+# 1. {Methods}[link:dht_rdoc.html#label-Methods]
 #
-# == {}[link:index.html"name="1] Definitions
-# The discrete Hankel transform acts on a vector of sampled data, where the 
-# samples are assumed to have been taken at points related to the zeroes of a 
-# Bessel function of fixed order; compare this to the case of the discrete 
-# Fourier transform, where samples are taken at points related to the zeroes 
-# of the sine or cosine function. 
+# == Definitions
+# The discrete Hankel transform acts on a vector of sampled data, where the
+# samples are assumed to have been taken at points related to the zeroes of a
+# Bessel function of fixed order; compare this to the case of the discrete
+# Fourier transform, where samples are taken at points related to the zeroes
+# of the sine or cosine function.
 #
-# Specifically, let f(t) be a function on the unit interval. Then the finite 
-# \nu-Hankel transform of f(t) is defined to be the set of numbers g_m given by, 
+# Specifically, let f(t) be a function on the unit interval. Then the finite
+# \nu-Hankel transform of f(t) is defined to be the set of numbers g_m given by,
 # so that, Suppose that f is band-limited in the sense that g_m=0 for m > M.
-# Then we have the following fundamental sampling theorem. It is this discrete 
-# expression which defines the discrete Hankel transform. The kernel in the 
-# summation above defines the matrix of the \nu-Hankel transform of size M-1. 
-# The coefficients of this matrix, being dependent on \nu and M, must be 
-# precomputed and stored; the <tt>GSL::Dht</tt> object encapsulates this data. 
-# The constructor <tt>GSL::Dht.alloc</tt> returns a <tt>GSL::Dht</tt> object 
-# which must be properly initialized with <tt>GSL::Dht#init</tt> before 
-# it can be used to perform transforms on data sample vectors, 
-# for fixed \nu and M, using the <tt>GSL::Dht#apply</tt> method. 
-# The implementation allows a scaling of the fundamental 
-# interval, for convenience, so that one can assume the function is defined on 
-# the interval [0,X], rather than the unit interval. 
+# Then we have the following fundamental sampling theorem. It is this discrete
+# expression which defines the discrete Hankel transform. The kernel in the
+# summation above defines the matrix of the \nu-Hankel transform of size M-1.
+# The coefficients of this matrix, being dependent on \nu and M, must be
+# precomputed and stored; the <tt>GSL::Dht</tt> object encapsulates this data.
+# The constructor <tt>GSL::Dht.alloc</tt> returns a <tt>GSL::Dht</tt> object
+# which must be properly initialized with <tt>GSL::Dht#init</tt> before
+# it can be used to perform transforms on data sample vectors,
+# for fixed \nu and M, using the <tt>GSL::Dht#apply</tt> method.
+# The implementation allows a scaling of the fundamental
+# interval, for convenience, so that one can assume the function is defined on
+# the interval [0,X], rather than the unit interval.
 #
-# Notice that by assumption f(t) vanishes at the endpoints of the interval, 
-# consistent with the inversion formula and the sampling formula given above. 
-# Therefore, this transform corresponds to an orthogonal expansion in 
-# eigenfunctions of the Dirichlet problem for the Bessel differential equation. 
+# Notice that by assumption f(t) vanishes at the endpoints of the interval,
+# consistent with the inversion formula and the sampling formula given above.
+# Therefore, this transform corresponds to an orthogonal expansion in
+# eigenfunctions of the Dirichlet problem for the Bessel differential equation.
 #
 #
-# == {}[link:index.html"name="2] Initialization
+# == Initialization
 #
 # ---
 # * GSL::Dht.alloc(size)
 # * GSL::Dht.alloc(size, nu, xmax)
 #
-#   These methods allocate a Discrete Hankel transform object <tt>GSL::Dht</tt> 
+#   These methods allocate a Discrete Hankel transform object <tt>GSL::Dht</tt>
 #   of size <tt>size</tt>.
 #   If three arguments are given, the object is initialized with the values of
 #   <tt>nu, xmax</tt>.
 #
 # ---
 # * GSL::Dht#init(nu, xmax)
 #
 #   This initializes the transform <tt>self</tt> for the given values of <tt>nu</tt> and <tt>xmax</tt>.
 #
-# == {}[link:index.html"name="3] Methods
+# == Methods
 # ---
 # * GSL::Dht#apply(vin, vout)
 # * GSL::Dht#apply(vin)
 #
-#   This applies the transform <tt>self</tt> to the vector <tt>vin</tt> whose size is 
+#   This applies the transform <tt>self</tt> to the vector <tt>vin</tt> whose size is
 #   equal to the size of the transform.
 #
 # ---
 # * GSL::Dht#x_sample(n)
 #
-#   This method returns the value of the n'th sample point in the unit interval, 
-#   (j_{nu,n+1}/j_{nu,M}) X. These are the points where the function f(t) is 
+#   This method returns the value of the n'th sample point in the unit interval,
+#   (j_{nu,n+1}/j_{nu,M}) X. These are the points where the function f(t) is
 #   assumed to be sampled.
 #
 # ---
 # * GSL::Dht#k_sample(n)
 #
-#   This method returns the value of the n'th sample point in "k-space", 
+#   This method returns the value of the n'th sample point in "k-space",
 #   j_{nu,n+1}/X.
 #
 # ---
 # * GSL::Dht#size
 #
@@ -82,20 +82,20 @@
 #
 #   Returns the Bessel function order
 # ---
 # * GSL::Dht#xmax
 #
-#   Returns the upper limit to the x-sampling domain 
+#   Returns the upper limit to the x-sampling domain
 # ---
 # * GSL::Dht#kmax
 #
-#   Returns the upper limit to the k-sampling domain 
+#   Returns the upper limit to the k-sampling domain
 #
 # ---
 # * GSL::Dht#j
 #
-#   Returns an array of computed J_nu zeros, j_{nu,s} = j[s] 
+#   Returns an array of computed J_nu zeros, j_{nu,s} = \j[s]
 #   as a <tt>GSL::Vector::View</tt>.
 #
 # ---
 # * GSL::Dht#Jjj
 #
@@ -111,12 +111,12 @@
 # * GSL::Dht#coef
 # * GSL::Dht#coef(n, m)
 #
 #   Return the (n,m)-th transform coefficient.
 #
-# {prev}[link:rdoc/sum_rdoc.html]
-# {next}[link:rdoc/roots_rdoc.html]
+# {prev}[link:sum_rdoc.html]
+# {next}[link:roots_rdoc.html]
 #
-# {Reference index}[link:rdoc/ref_rdoc.html]
+# {Reference index}[link:ref_rdoc.html]
 # {top}[link:index.html]
 #
 #