#
# = GSL::Vector class
#
# Contents:
# 1. {Class methods}[link:rdoc/vector_rdoc.html#1]
# 1. {Notes}[link:rdoc/vector_rdoc.html#2]
# 1. {Methods}[link:rdoc/vector_rdoc.html#3]
# 1. {Accessing vector elements}[link:rdoc/vector_rdoc.html#3.1]
# 1. {Initializing vector elements}[link:rdoc/vector_rdoc.html#3.2]
# 1. {Iterators}[link:rdoc/vector_rdoc.html#3.3]
# 1. {IO}[link:rdoc/vector_rdoc.html#3.4]
# 1. {Copying vectors}[link:rdoc/vector_rdoc.html#3.5]
# 1. {Vector views}[link:rdoc/vector_rdoc.html#3.6]
# 1. {Vector operations}[link:rdoc/vector_rdoc.html#3.7]
# 1. {Vector operations with size changes}[link:rdoc/vector_rdoc.html#3.8]
# 1. {Finding maximum and minimum elements of vectors}[link:rdoc/vector_rdoc.html#3.9]
# 1. {Vector properties}[link:rdoc/vector_rdoc.html#3.10]
# 1. {Element-wise vector comparison}[link:rdoc/vector_rdoc.html#3.11]
# 1. {Histogram}[link:rdoc/vector_rdoc.html#3.12]
# 1. {Sorting}[link:rdoc/vector_rdoc.html#3.13]
# 1. {BLAS methods}[link:rdoc/vector_rdoc.html#3.14]
# 1. {Data type conversions}[link:rdoc/vector_rdoc.html#3.15]
# 1. {NArray}[link:rdoc/vector_rdoc.html#3.16]
# 1. {GNU graph interface}[link:rdoc/vector_rdoc.html#3.17]
#
# See also {GSL::Vector::Complex}[link:rdoc/vector_complex_rdoc.html].
#
# == {}[link:index.html"name="1] Class methods
#
# ---
# * GSL::Vector.alloc(ary)
# * GSL::Vector.alloc(ary)
# * GSL::Vector.alloc(range)
# * GSL::Vector.alloc(size)
# * GSL::Vector.alloc(elm0, elm1, ....)
# * GSL::Vector[elm0, elm1, ....]
#
# Constructors.
#
# Ex:
# >> v1 = GSL::Vector.alloc(5)
# => GSL::Vector: [ 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 ]
# >> v2 = GSL::Vector.alloc(1, 3, 5, 2)
# => GSL::Vector: [ 1.000e+00 3.000e+00 5.000e+00 2.000e+00 ]
# >> v3 = GSL::Vector[1, 3, 5, 2]
# => GSL::Vector: [ 1.000e+00 3.000e+00 5.000e+00 2.000e+00 ]
# >> v4 = GSL::Vector.alloc([1, 3, 5, 2])
# => GSL::Vector: [ 1.000e+00 3.000e+00 5.000e+00 2.000e+00 ]
# >> v5 = GSL::Vector[1..6]
# => GSL::Vector: [ 1.000e+00 2.000e+00 3.000e+00 4.000e+00 5.000e+00 6.000e+00 ]
#
# ---
# * GSL::Vector.calloc(size)
#
# This method creates a vector object, and initializes all the elements to zero.
#
# ---
# * GSL::Vector.linspace(min, max, n = 10)
#
# Creates an <tt>GSL::Vector</tt> with <tt>n</tt> linearly spaced elements
# between <tt>min</tt> and <tt>max</tt>. If <tt>min</tt> is greater than <tt>max</tt>,
# the elements are stored in decreasing order. This mimics the <tt>linspace</tt>
# function of {GNU Octave}[http://www.octave.org/"target="_top].
#
# Ex:
# >> x = GSL::Vector.linspace(0, 10, 5)
# [ 0.000e+00 2.500e+00 5.000e+00 7.500e+00 1.000e+01 ]
# >> y = GSL::Vector.linspace(10, 0, 5)
# [ 1.000e+01 7.500e+00 5.000e+00 2.500e+00 0.000e+00 ]
#
# ---
# * GSL::Vector.logspace(min, max, n)
#
# Similar to <tt>GSL::Vector#linspace</tt> except that the values are
# logarithmically spaced from 10^<tt>min</tt> to 10^<tt>max</tt>.
#
# Ex:
# >> x = GSL::Vector.logspace(1, 3, 5)
# [ 1.000e+01 3.162e+01 1.000e+02 3.162e+02 1.000e+03 ]
# >> x = GSL::Vector.logspace(3, 1, 5)
# [ 1.000e+03 3.162e+02 1.000e+02 3.162e+01 1.000e+01 ]
#
# ---
# * GSL::Vector.logspace2(min, max, n)
#
# Similar to <tt>GSL::Vector#linspace</tt> except that the values are
# logarithmically spaced from <tt>min</tt> to <tt>max</tt>.
#
# Ex:
# >> x = GSL::Vector.logspace2(10, 1000, 5)
# [ 1.000e+01 3.162e+01 1.000e+02 3.162e+02 1.000e+03 ]
# >> x = GSL::Vector.logspace2(1000, 10, 5)
# [ 1.000e+03 3.162e+02 1.000e+02 3.162e+01 1.000e+01 ]
#
# ---
# * GSL::Vector.indgen(n, start=0, step=1)
#
# This creates a vector of length <tt>n</tt> with elements from <tt>start</tt>
# with interval <tt>step</tt> (mimics NArray#indgen).
#
# Ex:
# >> v = GSL::Vector::Int.indgen(5)
# => GSL::Vector::Int:
# [ 0 1 2 3 4 ]
# >> v = GSL::Vector::Int.indgen(5, 3)
# => GSL::Vector::Int:
# [ 3 4 5 6 7 ]
# >> v = GSL::Vector.indgen(4, 1.2, 0.3)
# => GSL::Vector
# [ 1.200e+00 1.500e+00 1.800e+00 2.100e+00 ]
#
# ---
# * GSL::Vector.filescan(filename)
#
# Reads a formatted ascii file and returns an array of vectors.
# For a data file <tt>a.dat</tt> as
# 1 5 6 5
# 3 5 6 7
# 5 6 7 9
# then <tt>a, b, c, d = Vetor.filescan("a.dat")</tt> yields
# a = [1, 3, 5]
# b = [5, 5, 6]
# c = [6, 6, 7]
# d = [5, 7, 9]
#
# === {}[link:index.html"name="1.1] NArray Extension
# If an <tt>NArray</tt> object is given, a newly allocated vector is created.
#
# Ex:
# na = NArray[1.0, 2, 3, 4, 5]
# p na <----- NArray.float(5):
# [ 1.0, 2.0, 3.0, 4.0, 5.0]
# v = GSL::Vector.alloc(na)
# p v <----- [ 1 2 3 4 5 ]
#
#
# See also {here}[link:rdoc/vector_rdoc.html#3.16].
#
# == {}[link:index.html"name="2] NOTE:
# In Ruby/GSL, vector length is limited within the range of Fixnum.
# For 32-bit CPU, the maximum of vector length is 2^30 ~ 1e9.
#
# == {}[link:index.html"name="3] Methods
#
# === {}[link:index.html"name="3.1] Accessing vector elements
# ---
# * GSL::Vector#get(args)
# * GSL::Vector#[args]
#
# Returns elements(s) of the vector <tt>self</tt> if <tt>args</tt> is a single
# <tt>Fixnum</tt>, a single <tt>Array</tt> of <tt>Fixnums</tt>, or a single
# <tt>GSL::Permutation</tt> (or <tt>GSL::Index</tt>). For all other <tt>args</tt>,
# the arguments are treated as with <tt>Vector#subvector</tt> and a
# <tt>Vector::View</tt> is returned.
#
# ---
# * GSL::Vector#set(args, val)
# * GSL::Vector#[args] = val
#
# If <tt>args</tt> is empty, behaves as <tt>#set_all</tt> and <tt>val</tt> must be a
# <tt>Numeric</tt>.
#
# If <tt>args</tt> is a single <tt>Fixnum</tt>, <tt>i</tt>, sets the <tt>i</tt>-th
# element of the vector <tt>self</tt> to <tt>val</tt>, which must be a
# <tt>Numeric</tt>.
#
# All other <tt>args</tt> specify a subvector (as with <tt>#subvector</tt>) whose
# elements are assigned from <tt>val</tt>. In this case, <tt>val</tt> can be an
# <tt>Array</tt>, <tt>Range</tt>, <tt>GSL::Vector</tt>, or <tt>Numeric</tt>.
#
# NOTE: GSL does not provide a vector copy function that properly copies data
# across overlapping memory regions, so watch out if assigning to part of a
# Vector from another part of itself (see example below).
#
# Ex:
# >> require 'gsl'
# => true
# >> v = GSL::Vector[0..5]
# => GSL::Vector
# [ 0.000e+00 1.000e+00 2.000e+00 3.000e+00 4.000e+00 5.000e+00 ]
# >> v[2]
# => 2.0
# >> v[1,2,3]
# => GSL::Vector::View
# [ 1.000e+00 3.000e+00 5.000e+00 ]
# >> v[[1,2,3]]
# => GSL::Vector
# [ 1.000e+00 2.000e+00 3.000e+00 ]
# >> v[3] = 9
# => 9
# >> v[-1] = 123
# => 123
# >> v
# => GSL::Vector
# [ 0.000e+00 1.000e+00 2.000e+00 9.000e+00 4.000e+00 1.230e+02 ]
# >> v[2,3] = 0
# => 0
# >> v
# => GSL::Vector
# [ 0.000e+00 1.000e+00 0.000e+00 0.000e+00 0.000e+00 1.230e+02 ]
# >> v[2,3] = [4,5,6]
# => [4, 5, 6]
# >> v
# => GSL::Vector
# [ 0.000e+00 1.000e+00 4.000e+00 5.000e+00 6.000e+00 1.230e+02 ]
# >> v[1,4] = v[0,4] # !!! Overlapping !!!
# => GSL::Vector::View
# [ 0.000e+00 0.000e+00 0.000e+00 0.000e+00 ]
# >> v
# => GSL::Vector
# [ 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 1.230e+02 ]
#
#
# === {}[link:index.html"name="3.2] Initializing vector elements
# ---
# * GSL::Vector#set_all(x)
#
# This method sets all the elements of the vector to the value <tt>x</tt>.
#
# ---
# * GSL::Vector#set_zero
#
# This method sets all the elements of the vector to zero.
#
# ---
# * GSL::Vector#set_basis!(i)
#
# This method makes a basis vector by setting all the elements of the vector
# to zero except for the <tt>i</tt>-th element, which is set to one.
# For a vector <tt>v</tt> of size 10, the method
# v.set_basis!(4)
# sets the vector <tt>v</tt> to a basis vector <tt>[0, 0, 0, 0, 1, 0, 0, 0, 0, 0]</tt>.
#
# ---
# * GSL::Vector#set_basis(i)
#
# This method returns a new basis vector by setting all the elements of the
# vector to zero except for the i-th element which is set to one.
# For a vector <tt>v</tt> of size 10, the method
# vb = v.set_basis(4)
# creates a new vector <tt>vb</tt> with elements <tt>[0, 0, 0, 0, 1, 0, 0, 0, 0, 0]</tt>.
# The vector <tt>v</tt> is not changed.
#
# ---
# * GSL::Vector#indgen!(start=0, step=1)
# * GSL::Vector#indgen(start=0, step=1)
#
# Mimics NArray#indgen!.
#
# === {}[link:index.html"name="3.3] Iterators
# ---
# * GSL::Vector#each
# * GSL::Vector#reverse_each
#
# An iterator for each of the vector elements, used as
#
# v.each do |x| # Show all the elements
# p x
# end
#
# ---
# * GSL::Vector#each_index
# * GSL::Vector#reverse_each_index
#
# Iterators
#
# ---
# * GSL::Vector#collect { |item| .. }
# * GSL::Vector#map { |item| .. }
#
# Creates a new vector by collecting the vector elements modified with some
# operations.
#
# Ex:
# >> a = GSL::Vector::Int[0..5]
# => GSL::Vector::Int
# [ 0 1 2 3 4 5 ]
# >> b = a.collect {|v| v*v}
# => GSL::Vector::Int
# [ 0 1 4 9 16 25 ]
# >> a
# => GSL::Vector::Int
# [ 0 1 2 3 4 5 ]
#
# ---
# * GSL::Vector#collect! { |item| .. }
# * GSL::Vector#map! { |item| .. }
#
# Ex:
# >> a = GSL::Vector::Int[0..5]
# => GSL::Vector::Int
# [ 0 1 2 3 4 5 ]
# >> a.collect! {|v| v*v}
# => GSL::Vector::Int
# [ 0 1 4 9 16 25 ]
# >> a
# => GSL::Vector::Int
# [ 0 1 4 9 16 25 ]
#
# === {}[link:index.html"name="3.4] IO
# ---
# * GSL::Vector#print
# * GSL::Vector#fprintf(io, format = "%e")
# * GSL::Vector#fprintf(filename, format = "%e")
# * GSL::Vector#fscanf(io)
# * GSL::Vector#fscanf(filename)
# * GSL::Vector#fwrite(io)
# * GSL::Vector#fwrite(filename)
# * GSL::Vector#fread(io)
# * GSL::Vector#fread(filename)
#
# Methods for writing or reading the vector.
# The first argument is an <tt>IO</tt> or a <tt>String</tt> object.
#
# === {}[link:index.html"name="3.5] Copying vectors
# ---
# * GSL::Vector#clone
# * GSL::Vector#duplicate
#
# Create a new vector of the same elements.
#
# === {}[link:index.html"name="3.6] Vector views
# The <tt>GSL::Vector::View</tt> class is defined to be used as "references" to
# vectors. Since the <tt>Vector::View</tt> class is a subclass of <tt>Vector</tt>,
# an instance of the <tt>View</tt> class created by slicing a <tt>Vector</tt> object
# can be used same as the original vector. A
# <tt>View</tt> object shares the data with the original vector, i.e. any changes
# in the elements of the <tt>View</tt> object affect to the original vector.
#
# ---
# * GSL::Vector#subvector
# * GSL::Vector#subvector(n)
# * GSL::Vector#subvector(offset, n)
# * GSL::Vector#subvector(offset, stride, n)
# * GSL::Vector#subvector(range, stride=1)
#
# Create a <tt>Vector::View</tt> object slicing <tt>n</tt> elements
# of the vector <tt>self</tt> from the offset <tt>offset</tt>. If called with one
# argument <tt>n</tt>, <tt>offset</tt> is set to 0. With no arguments, a view is
# created with the same length of the original vector. If called with a
# <tt>range</tt> parameter (and optional <tt>stride</tt>), a view is created for
# that range (and stride). Note the <tt>n</tt>, if given, is the length of the
# returned View.
#
# * Example:
# #!/usr/bin/env ruby
# require("gsl")
#
# v = GSL::Vector[1, 2, 3, 4, 5, 6]
# view = v.subvector(1, 4)
# p view.class <----- GSL::Vector::View
# view.print <----- [ 2 3 4 5 ]
#
# view[2] = 99
# view.print <----- [ 2 3 99 5 ]
# v.print <----- [ 1 2 3 99 5 6 ]
#
# ---
# * GSL::Vector#subvector_with_stride(stride)
# * GSL::Vector#subvector_with_stride(offset, stride)
# * GSL::Vector#subvector_with_stride(offset, stride, n)
#
# Return a <tt>Vector::View</tt> object of a subvector of another vector
# <tt>self</tt> with an additional stride argument. The subvector is formed in
# the same way as for <tt>Vector#subvector</tt> but the new vector view has
# <tt>n</tt> elements with a step-size of <tt>stride</tt> from one element to the
# next in the original vector. Note that <tt>n</tt>, if given, is the length of
# the returned View.
#
# ---
# * GSL::Vector#matrix_view(n1, n2)
#
# This creates a <tt>Matrix::View</tt> object from the vector <tt>self</tt>.
# It enables to use the vector as a {Matrix}[link:rdoc/matrix_rdoc.html] object.
#
# * Ex:
#
# >> v = GSL::Vector::Int.alloc(1..9)
# => GSL::Vector::Int:
# [ 1 2 3 4 5 6 7 8 9 ]
# >> m = v.matrix_view(3, 3)
# => GSL::Matrix::Int::View:
# [ 1 2 3
# 4 5 6
# 7 8 9 ]
# >> m[1][2] = 99
# => 99
# >> v
# => GSL::Vector::Int:
# [ 1 2 3 4 5 99 7 8 9 ]
#
# === {}[link:index.html"name="3.7] Vector operations
#
# ---
# * GSL::Vector#swap_elements(i, j)
#
# This method exchanges the i-th and j-th elements of the vector <tt>in-place</tt>.
#
# ---
# * GSL::Vector#reverse
#
# Reverses the order of the elements of the vector.
#
# >> v = GSL::Vector::Int[1..5]
# => GSL::Vector::Int:
# [ 1 2 3 4 5 ]
# >> v.reverse
# => GSL::Vector::Int:
# [ 5 4 3 2 1 ]
#
# ---
# * GSL::Vector#trans
# * GSL::Vector#transpose
# * GSL::Vector#col
# * GSL::Vector#row
#
# Transpose the vector from a row vector into a column vector and vice versa.
#
# >> v = GSL::Vector::Int[1..5]
# => GSL::Vector::Int:
# [ 1 2 3 4 5 ]
# >> v.col
# => GSL::Vector::Int::Col:
# [ 1
# 2
# 3
# 4
# 5 ]
#
# ---
# * GSL::Vector#add(b)
#
# Adds the elements of vector <tt>b</tt> to the elements
# of the vector <tt>self</tt>. A new vector is created, and the vector
# <tt>self</tt> is not changed.
#
# ---
# * GSL::Vector#sub(b)
#
# Subtracts the element of vector <tt>b</tt> from the elements of <tt>self</tt>.
# A new vector is created, and the vector <tt>self</tt> is not changed.
#
# ---
# * GSL::Vector#mul(b)
#
# Multiplies the elements of vector <tt>self</tt> by the elements of vector <tt>b</tt>.
# ---
# * GSL::Vector#div(b)
#
# Divides the elements of vector <tt>self</tt> by the elements of vector <tt>b</tt>.
#
# ---
# * GSL::Vector#scale(x)
# * GSL::Vector#scale!(x)
#
# This method multiplies the elements of vector <tt>self</tt> by
# the constant factor <tt>x</tt>.
#
# ---
# * GSL::Vector#add_constant(x)
# * GSL::Vector#add_constant!(x)
#
# Adds the constant value <tt>x</tt> to the elements of the vector <tt>self</tt>.
#
# ---
# * GSL::Vector#+(b)
#
# For <tt>b</tt>,
# * a Number: ---> <tt>self.add_constanb(b)</tt>
# * a Vector: ---> <tt>self.add(b)</tt>
# ---
# * GSL::Vector#-(b)
#
# For <tt>b</tt>,
# * a Number: ---> <tt>self.add_constanb(-b)</tt>
# * a Vector: ---> <tt>self.sub(b)</tt>
# ---
# * GSL::Vector#/(b)
#
# For <tt>b</tt>,
# * a Number: ---> <tt>self.scale(1/b)</tt>
# * a Vector: ---> <tt>self.div(b)</tt>
#
# ---
# * GSL::Vector#*(b)
#
# Vector multiplication.
#
# 1. Scale
# >> v = GSL::Vector[1, 2]
# [ 1 2 ]
# >> v*2
# [ 2 4 ]
# 1. Element-by-element multiplication
# >> a = GSL::Vector[1, 2]; b = GSL::Vector[3, 4]
# [ 3 4 ]
# >> a*b
# [ 3 8 ]
# 1. Inner product
# >> a = GSL::Vector[1, 2]; b = GSL::Vector[3, 4]
# [ 3
# 4 ]
# >> a*b.col
# => 11.0
# 1. GSL::Vector::Col*Vector -> GSL::Matrix
# >> a = GSL::Vector::Col[1, 2]; b = GSL::Vector[3, 4]
# [ 3 4 ]
# >> a*b
# [ 3 4
# 6 8 ]
# 1. GSL::Matrix*Vector::Col -> GSL::Vector::Col
# >> a = GSL::Vector[1, 2]; m = GSL::Matrix[[2, 3], [4, 5]]
# [ 2 3
# 4 5 ]
# >> m*a <--- Error
# TypeError: Operation with GSL::Vector is not defined (GSL::Vector::Col expected)
# from (irb):30:in `*'
# from (irb):30
# >> m*a.col
# [ 8
# 14 ]
#
# ---
# * GSL::Vector#add!(b)
# * GSL::Vector#sub!(b)
# * GSL::Vector#mul!(b)
# * GSL::Vector#div!(b)
#
# In-place operations with a vector <tt>b</tt>.
#
# ---
# * GSL::Vector#pow(p)
# * GSL::Vector#**(p)
# * GSL::Vector#pow!(p)
#
# Element-wise calculation of power p.
#
# Ex)
# >> require("gsl")
# >> v = GSL::Vector[1, 2, 3]
# => GSL::Vector
# [ 1.000e+00 2.000e+00 3.000e+00 ]
# >> v.pow(2)
# => GSL::Vector
# [ 1.000e+00 4.000e+00 9.000e+00 ]
# >> v**2
# => GSL::Vector
# [ 1.000e+00 4.000e+00 9.000e+00 ]
# >> v
# => GSL::Vector
# [ 1.000e+00 2.000e+00 3.000e+00 ]
# >> v.pow!(2)
# => GSL::Vector
# [ 1.000e+00 4.000e+00 9.000e+00 ]
# >> v
# => GSL::Vector
# [ 1.000e+00 4.000e+00 9.000e+00 ]
#
# ---
# * GSL::Vector#swap_elements(i, j)
#
# This exchanges the <tt>i</tt>-th and <tt>j</tt>-th elements of the vector <tt>self</tt> in-place.
# ---
# * GSL::Vector#clone
# * GSL::Vector#duplicate
#
# These create a copy of the vector <tt>self</tt>.
#
# ---
# * GSL::Vector.connect(v1, v2, v3, ...)
# * GSL::Vector#connect(v2, v3, ...)
#
# Creates a new vector by connecting all the elements of the given vectors.
#
# >> v1 = GSL::Vector::Int[1, 3]
# => GSL::Vector::Int:
# [ 1 3 ]
# >> v2 = GSL::Vector::Int[4, 3, 5]
# => GSL::Vector::Int:
# [ 4 3 5 ]
# >> v1.connect(v2)
# => GSL::Vector::Int:
# [ 1 3 4 3 5 ]
#
# ---
# * GSL::Vector#sgn
# * GSL::Vector#signum
#
# Creates a new vector, with elements +1 if <tt>x_i</tt> > 0, -1 if <tt>x_i</tt> <
# 0, otherwise 0. Note that this definition gives the signum of NaN as 0
# rather than NaN.
#
# ---
# * GSL::Vector#abs
# * GSL::Vector#fabs
#
# Creates a new vector, with elements <tt>fabs(x_i)</tt>.
#
# >> v = GSL::Vector::Int[-3, 2, -5, 4]
# => GSL::Vector::Int:
# [ -3 2 -5 4 ]
# >> v.abs
# => GSL::Vector::Int:
# [ 3 2 5 4 ]
#
# ---
# * GSL::Vector#square
# * GSL::Vector#abs2
#
# Create a new vector, with elements <tt>x_i*x_i</tt>.
#
# >> v = GSL::Vector::Int[1..4]
# => GSL::Vector::Int:
# [ 1 2 3 4 ]
# >> v.square
# => GSL::Vector::Int:
# [ 1 4 9 16 ]
#
# ---
# * GSL::Vector#sqrt
#
# Creates a new vector, with elements <tt>sqrt</tt>(<tt>x_i</tt>).
#
# ---
# * GSL::Vector#floor
# * GSL::Vector#ceil
# * GSL::Vector#round
#
#
# Ex:
# >> v = GSL::Vector[1.1, 2.7, 3.5, 4.3]
# => GSL::Vector
# [ 1.100e+00 2.700e+00 3.500e+00 4.300e+00 ]
# >> v.floor
# => GSL::Vector::Int
# [ 1 2 3 4 ]
# >> v.ceil
# => GSL::Vector::Int
# [ 2 3 4 5 ]
# >> v.round
# => GSL::Vector::Int
# [ 1 3 4 4 ]
#
# ---
# * GSL::Vector#normalize(nrm = 1.0)
#
# Creates a new vector of norm <tt>nrm</tt>, by scaling the vector <tt>self</tt>.
# ---
# * GSL::Vector#normalize!(nrm = 1.0)
#
# This normalizes the vector <tt>self</tt> in-place.
#
# Ex:
# tcsh> irb
# >> require("gsl")
# => true
# >> a = GSL::Vector[-1, -2, -3, -4]
# => GSL::Vector:
# [ -1.000e+00 -2.000e+00 -3.000e+00 -4.000e+00 ]
# >> b = a.abs
# => GSL::Vector:
# [ 1.000e+00 2.000e+00 3.000e+00 4.000e+00 ]
# >> b.sqrt
# => GSL::Vector:
# [ 1.000e+00 1.414e+00 1.732e+00 2.000e+00 ]
# >> b.square
# => GSL::Vector:
# [ 1.000e+00 4.000e+00 9.000e+00 1.600e+01 ]
# >> c = b.normalize(2)
# => GSL::Vector:
# [ 2.582e-01 5.164e-01 7.746e-01 1.033e+00 ]
# >> c.square.sum
# => 2.0
#
# ---
# * GSL::Vector#decimate(n)
#
# Creates a new vector by averaring every <tt>n</tt>
# points of the vector <tt>self</tt> down to one point.
#
# ---
# * GSL::Vector#diff(k = 1)
#
# Calculate <tt>k</tt>-th differences of a vector <tt>self</tt>.
#
#
# ---
# * GSL::Vector#join(sep = " ")
#
# Converts the vector to a <tt>String</tt> by joining all the elements with a
# separator <tt>sep</tt>.
#
# ---
# * GSL::Vector#zip(vec, ...)
# * GSL::Vector.zip(vec, ...)
#
# Create an <tt>Array</tt> of vectors by merging the elements of <tt>self</tt>
# with corresponding elements from each arguments.
#
# Ex:
# >> require("gsl")
# >> a = GSL::Vector[4, 5, 6]
# >> b = GSL::Vector[7, 8, 9]
# >> GSL::Vector[1, 2, 3].zip(a, b)
# [[ 1.000e+00 4.000e+00 7.000e+00 ],
# [ 2.000e+00 5.000e+00 8.000e+00 ],
# [ 3.000e+00 6.000e+00 9.000e+00 ]]
# >> GSL::Vector[1, 2].zip(a, b)
# [[ 1.000e+00 4.000e+00 7.000e+00 ],
# [ 2.000e+00 5.000e+00 8.000e+00 ]]
# >> a.zip(GSL::Vector[1, 2], GSL::Vector[8.0])
# [[ 4.000e+00 1.000e+00 8.000e+00 ],
# [ 5.000e+00 2.000e+00 0.000e+00 ],
# [ 6.000e+00 0.000e+00 0.000e+00 ]]
#
# ---
# * GSL::Vector#concat(x)
#
# Returns a new Vector that contains the concatenation <tt>self</tt> and
# <tt>x</tt>, which must be an <tt>Array</tt>, <tt>Fixnum</tt>, <tt>Bignum</tt>,
# <tt>Float</tt>, <tt>Range</tt>, or <tt>GSL::Vector</tt>.
#
# === {}[link:index.html"name="3.8] Vector operations with size changes
# The methods below change vector length of <tt>self</tt>. A Vector's length may
# not extend past its original allocation. Use of these methods is discouraged.
# Existing Views may still refer to elements beyond the end of the shortened
# Vector. These elements remain allocated, but are effectvely unmanaged.
#
# ---
# * GSL::Vector#delete(x)
#
# Deletes items from <tt>self</tt> that are equal to <tt>x</tt>. If the item is
# not found, returns <tt>nil</tt>, otherwise returns <tt>x</tt>.
# ---
# * GSL::Vector#delete_at(i)
#
# Deletes the element at the specified index <tt>i</tt>,
# returning that element, or <tt>nil</tt> if the index is out of range.
# ---
# * GSL::Vector#delete_if { |x| ... }
#
# Deletes every element of <tt>self</tt> for which block evaluates to <tt>true</tt>
# and returns <tt>self</tt>.
#
# === {}[link:index.html"name="3.9] Finding maximum and minimum elements of vectors
#
# ---
# * GSL::Vector#max
#
# This method returns the maximum value in the vector.
#
# ---
# * GSL::Vector#min
#
# This method returns the minimum value in the vector.
#
# ---
# * GSL::Vector#minmax
#
# This method returns an array of two elements, the minimum and the maximum values
# in the vector <tt>self</tt>.
#
# ---
# * GSL::Vector#max_index
#
# This method returns the index of the maximum value in the vector. When there are
# several equal maximum elements then the lowest index is returned.
#
# ---
# * GSL::Vector#min_index
#
# This method returns the index of the minimum value in the vector. When there are
# several equal minimum elements then the lowest index is returned.
#
# ---
# * GSL::Vector#minmax_index
#
# This method returns an array of two elements which has the indices
# of the minimum and the maximum values in the vector <tt>self</tt>.
#
# === {}[link:index.html"name="3.10] Vector Properties
# ---
# * GSL::Vector#size
# * GSL::Vector#len
# * GSL::Vector#length
#
# Return the vector length.
#
# ---
# * GSL::Vector#stride
#
# Return the vector stride.
#
# ---
# * GSL::Vector#sum
#
# Returns the sum of the vector elements.
#
# ---
# * GSL::Vector#prod
#
# Returns the product of the vector elements.
#
# ---
# * GSL::Vector#cumsum
#
# Calculate the cumulative sum of elements of <tt>self</tt> and returns as a new vector.
#
# ---
# * GSL::Vector#cumprod
#
# Calculate the cumulative product of elements of <tt>self</tt> and returns as a new vector.
#
# ---
# * GSL::Vector#isnull
#
# Returns 1 if all the elements of the vector <tt>self</tt>
# are zero, and 0 otherwise.
# ---
# * GSL::Vector#isnull?
#
# Return <tt>true</tt> if all the elements of the vector <tt>self</tt>
# are zero, and <tt>false</tt> otherwise.
# ---
# * GSL::Vector#ispos
# * GSL::Vector#ispos?
# * GSL::Vector#isneg
# * GSL::Vector#isneg?
#
# (GSL-1.9 or later) Return 1 (true) if all the elements of the vector <tt>self</tt> are zero, strictly positive, strictly negative respectively, and 0 (false) otherwise.
#
# ---
# * GSL::Vector#isnonneg
# * GSL::Vector#isnonneg?
#
# (GSL-1.10 or later) Return 1 (true) if all the elements of the vector <tt>self</tt> are non-negative , and 0 (false) otherwise.
#
# ---
# * GSL::Vector#all?
#
# Returns <tt>true</tt> if all the vector elements are non-zero, and <tt>false</tt>
# otherwise. If a block is given, the method returns <tt>true</tt> if the
# tests are true for all the elements.
# ---
# * GSL::Vector#any?
#
# Returns <tt>true</tt> if any the vector elements are non-zero, and <tt>false</tt>
# otherwise. If a block is given, the method returns <tt>true</tt> if the
# tests are true for any of the elements.
# ---
# * GSL::Vector#none?
#
# Returns <tt>true</tt> if all the elements of the vector <tt>self</tt>
# are zero, and <tt>false</tt> otherwise (just as <tt>GSL::Vector#isnull?</tt>).
# If a block is given, the method returns <tt>true</tt> if the
# tests are false for all the elements.
#
# Ex:
# >> a = GSL::Vector[1, 2, 3]
# >> b = GSL::Vector[1, 2, 0]
# >> c = GSL::Vector[0, 0, 0]
# >> a.all?
# => true
# >> b.all?
# => false
# >> b.any?
# => true
# >> c.any?
# => false
# >> a.none?
# => false
# >> c.none?
# => true
#
# ---
# * GSL::Vector#all
# * GSL::Vector#any
# * GSL::Vector#none
#
# Returns 1 or 0.
#
# ---
# * GSL::Vector#equal?(other, eps = 1e-10)
# * GSL::Vector#==(other, eps = 1e-10)
#
# Returns <tt>true</tt> if the vectors have same size and elements
# equal to absolute accurary <tt>eps</tt> for all the indices,
# and <tt>false</tt> otherwise.
#
# === {}[link:index.html"name="3.11] Element-wise vector comparison
# ---
# * GSL::Vector#eq(other)
# * GSL::Vector#ne(other)
# * GSL::Vector#gt(other)
# * GSL::Vector#ge(other)
# * GSL::Vector#lt(other)
# * GSL::Vector#le(other)
#
# Return a <tt>Block::Byte</tt> object with elements 0/1 by comparing the two vectors
# <tt>self</tt> and <tt>other</tt>. Note that the values returned are 0/1,
# not <tt>true/false</tt>, thus all of the elements are "true" in Ruby.
#
# Ex:
# >> a = GSL::Vector[1, 2, 3]
# >> b = GSL::Vector[1, 2, 5]
# >> a.eq(b)
# [ 1 1 0 ]
# >> a.ne(b)
# [ 0 0 1 ]
# >> a.gt(b)
# [ 0 0 0 ]
# >> a.ge(b)
# [ 1 1 0 ]
# >> a.eq(3)
# [ 0 0 1 ]
# >> a.ne(2)
# [ 1 0 1 ]
# >> a.ge(2)
# [ 0 1 1 ]
#
# ---
# * GSL::Vector#and(other)
# * GSL::Vector#or(other)
# * GSL::Vector#xor(other)
# * GSL::Vector#not
#
#
# Ex:
# >> a = GSL::Vector[1, 0, 3, 0]
# >> b = GSL::Vector[3, 4, 0, 0]
# >> a.and(b)
# [ 1 0 0 0 ]
# >> a.or(b)
# [ 1 1 1 0 ]
# >> a.xor(b)
# [ 0 1 1 0 ]
# >> a.not
# [ 0 1 0 1 ]
# >> b.not
# [ 0 0 1 1 ]
#
# ---
# * GSL::Vector#where
# * GSL::Vector#where { |elm| ... }
#
# Returns the vector indices where the tests are true. If all the test failed
# <tt>nil</tt> is returned.
#
# Ex:
# >> v = GSL::Vector::Int[0, 3, 0, -2, 3, 5, 0, 3]
# >> v.where
# [ 1 3 4 5 7 ] # where elements are non-zero
# >> v.where { |elm| elm == -2 }
# [ 3 ]
# >> a = GSL::Vector[0, 0, 0]
# >> a.where
# => nil
#
# === {}[link:index.html"name="3.12] Histogram
# ---
# * GSL::Vector#histogram(n)
# * GSL::Vector#histogram(ranges)
# * GSL::Vector#histogram(n, min, max)
# * GSL::Vector#histogram(n, [min, max])
#
# Creates a histogram filling the vector <tt>self</tt>.
#
# Example:
# >> r = GSL::Rng.alloc # Random number generator
# => #<GSL::Rng:0x6d8594>
# >> v = r.gaussian(1, 1000) # Generate 1000 Gaussian random numbers
# => GSL::Vector
# [ 1.339e-01 -8.810e-02 1.674e+00 7.336e-01 9.975e-01 -1.278e+00 -2.397e+00 ... ]
# >> h = v.histogram(50, [-4, 4]) # Creates a histogram of size 50, range [-4, 4)
# => #<GSL::Histogram:0x6d28b0>
# >> h.graph("-T X -C -g 3") # Show the histogram
# => true
#
# This is equivalent to
# h = Histogram.alloc(50, [-4, 4])
# h.increment(v)
#
# === {}[link:index.html"name="3.13] Sorting
#
# ---
# * GSL::Vector#sort
# * GSL::Vector#sort!
#
# These methods sort the vector <tt>self</tt> in ascending numerical order.
#
# ---
# * GSL::Vector#sort_index
#
# This method indirectly sorts the elements of the vector <tt>self</tt> into
# ascending order, and returns the resulting permutation.
# The elements of permutation give the index of the vector element which
# would have been stored in that position if the vector had been sorted in place.
# The first element of permutation gives the index of the least element in the
# vector, and the last element of permutation gives the index of the greatest
# vector element. The vector <tt>self</tt> is not changed.
#
# ---
# * GSL::Vector#sort_smallest(n)
# * GSL::Vector#sort_largest(n)
# * GSL::Vector#sort_smallest_index(n)
# * GSL::Vector#sort_largest_index(n)
#
#
# Ex:
# >> v = GSL::Vector::Int[8, 2, 3, 7, 9, 1, 4]
# => GSL::Vector::Int:
# [ 8 2 3 7 9 1 4 ]
# >> v.sort
# => GSL::Vector::Int:
# [ 1 2 3 4 7 8 9 ]
# >> v.sort_index
# => GSL::Permutation:
# [ 5 1 2 6 3 0 4 ]
# >> v.sort_largest(3)
# => GSL::Vector::Int:
# [ 9 8 7 ]
# >> v.sort_smallest(3)
# => GSL::Vector::Int:
# [ 1 2 3 ]
#
# === {}[link:index.html"name="3.14] BLAS Methods
# ---
# * GSL::Vector#nrm2
# * GSL::Vector#dnrm2
#
# Compute the Euclidean norm ||x||_2 = sqrt {sum x_i^2} of the vector.
#
# ---
# * GSL::Vector#asum
# * GSL::Vector#dasum
#
# Compute the absolute sum \sum |x_i| of the elements of the vector.
#
# === {}[link:index.html"name="3.15] Data type conversions
# ---
# * GSL::Vector#to_a
#
# This method converts the vector into a Ruby array. A Ruby array also can be
# converted into a GSL::Vector object with the <tt>to_gv</tt> method. For example,
#
# v = GSL::Vector.alloc([1, 2, 3, 4, 5])
# a = v.to_a -> GSL::Vector to an array
# p a -> [1.0, 2.0, 3.0, 4.0, 5.0]
# a[2] = 12.0
# v2 = a.to_gv -> a new GSL::Vector object
# v2.print -> 1.0000e+00 2.0000e+00 1.2000e+01 4.0000e+00 5.0000e+00
#
# ---
# * GSL::Vector#to_m(nrow, ncol)
#
# Creates a <tt>GSL::Matrix</tt> object of <tt>nrow</tt> rows and <tt>ncol</tt> columns.
#
# >> v = GSL::Vector::Int[1..5]
# => GSL::Vector::Int:
# [ 1 2 3 4 5 ]
# >> v.to_m(2, 3)
# => GSL::Matrix::Int:
# [ 1 2 3
# 4 5 0 ]
# >> v.to_m(2, 2)
# => GSL::Matrix::Int:
# [ 1 2
# 3 4 ]
# >> v.to_m(3, 2)
# => GSL::Matrix::Int:
# [ 1 2
# 3 4
# 5 0 ]
#
# ---
# * GSL::Vector#to_m_diagonal
#
# Converts the vector into a diagonal matrix.
# See also {GSL::Matrix.diagonal(v)}[link:rdoc/matrix_rdoc.html].
#
# >> v = GSL::Vector[1..4].to_i
# => GSL::Vector::Int:
# [ 1 2 3 4 ]
# >> v.to_m_diagonal
# => GSL::Matrix::Int:
# [ 1 0 0 0
# 0 2 0 0
# 0 0 3 0
# 0 0 0 4 ]
#
# ---
# * GSL::Vector#to_m_circulant
#
# Creates a circulant matrix.
#
# >> v = GSL::Vector::Int[1..5]
# => GSL::Vector::Int:
# [ 1 2 3 4 5 ]
# >> v.to_m_circulant
# => GSL::Matrix::Int:
# [ 5 1 2 3 4
# 4 5 1 2 3
# 3 4 5 1 2
# 2 3 4 5 1
# 1 2 3 4 5 ]
#
# ---
# * GSL::Vector#to_complex
# * GSL::Vector#to_complex2
#
# Example:
#
# >> v = GSL::Vector[1..4]
# => GSL::Vector
# [ 1.000e+00 2.000e+00 3.000e+00 4.000e+00 ]
# >> v.to_complex
# [ [1.000e+00 0.000e+00] [2.000e+00 0.000e+00] [3.000e+00 0.000e+00] [4.000e+00 0.000e+00] ]
# => #<GSL::Vector::Complex:0x6d7d24>
# >> v.to_complex2
# [ [1.000e+00 2.000e+00] [3.000e+00 4.000e+00] ]
# => #<GSL::Vector::Complex:0x6d6424>
#
# ---
# * GSL::Vector#to_tensor(rank, dimension)
#
#
# === {}[link:index.html"name="3.16] GSL::Vector <---> NArray
#
# ---
# * GSL::Vector#to_na
#
# Converts a vector <tt>self</tt> into an <tt>NArray</tt> object.
# The data are copied to newly allocated memory.
#
# ---
# * GSL::Vector#to_na2
# * GSL::Vector#to_na_ref
#
# Create an <tt>NArray</tt> reference of the vector <tt>self</tt>.
#
# Example:
# >> v = GSL::Vector::Int[1, 2, 3, 4]
# => GSL::Vector::Int
# [ 1 2 3 4 ]
# >> na = v.to_na
# => NArray.int(4):
# [ 1, 2, 3, 4 ]
# >> na2 = v.to_na2
# => NArray(ref).int(4):
# [ 1, 2, 3, 4 ]
# >> na[1] = 99
# => 99
# >> v # na and v are independent
# => GSL::Vector::Int
# [ 1 2 3 4 ]
# >> na2[1] = 99 # na2 points to the data of v
# => 99
# >> v
# => GSL::Vector::Int
# [ 1 99 3 4 ]
#
# ---
# * NArray#to_gv
# * NArray#to_gslv
#
# Create <tt>GSL::Vector</tt> object from the <tt>NArray</tt> object <tt>self</tt>.
#
# ---
# * NArray#to_gv_view
# * NArray#to_gv2
# * NArray#to_gslv_view
#
# A <tt>GSL::Vector::View</tt> object is created from the NArray object <tt>self</tt>.
# This method does not allocate memory for the data: the data of <tt>self</tt>
# are not copied, but shared with the <tt>View</tt> object created, thus
# any modifications to the <tt>View</tt> object affect on the original NArray
# object. In other words, the <tt>View</tt> object can be used as a <tt>reference</tt>
# to the NArray object.
#
# Ex:
# tcsh> irb
# >> require("gsl")
# => true
# >> na = NArray[1.0, 2, 3, 4, 5]
# => NArray.float(5):
# [ 1.0, 2.0, 3.0, 4.0, 5.0 ]
# >> vv = na.to_gv_view # Create a view sharing the memory
# => GSL::Vector::View
# [ 1.000e+00 2.000e+00 3.000e+00 4.000e+00 5.000e+00 ]
# >> vv[3] = 9
# => 9
# >> na
# => NArray.float(5):
# [ 1.0, 2.0, 3.0, 9.0, 5.0 ] # The data are changed
# >> v = na.to_gv # A vector with newly allocated memory
# => GSL::Vector
# [ 1.000e+00 2.000e+00 3.000e+00 9.000e+00 5.000e+00 ]
# >> v[1] = 123
# => 123
# >> v
# => GSL::Vector
# [ 1.000e+00 1.230e+02 3.000e+00 9.000e+00 5.000e+00 ]
# >> na
# => NArray.float(5):
# [ 1.0, 2.0, 3.0, 9.0, 5.0 ] # v and na are independent
# >> na = NArray[1.0, 2, 3, 4, 5, 6]
# => NArray.float(6):
# [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ]
# >> m = na.to_gv_view.matrix_view(2, 3)
# => GSL::Matrix::View
# [ 1.000e+00 2.000e+00 3.000e+00
# 4.000e+00 5.000e+00 6.000e+00 ]
# >> m[1][2] = 9
# => 9
# >> na
# => NArray.float(6):
# [ 1.0, 2.0, 3.0, 4.0, 5.0, 9.0 ]
#
# === {}[link:index.html"name="3.17] Graphics
# ---
# * GSL::Vector.graph(y)
# * GSL::Vector.graph(y, options)
# * GSL::Vector.graph(x, y)
# * GSL::Vector.graph(x, y, options)
# * GSL::Vector#graph(options)
# * GSL::Vector#graph(x, options)
#
# These methods use the GNU plotutils <tt>graph</tt> application to plot
# a vector <tt>self</tt>. The options of <tt>graph</tt> as "-T X -C" can be given by a String.
#
# Example:
# >> x = GSL::Vector.linspace(0, 2.0*M_PI, 20)
# >> c = GSL::Sf::cos(x)
# >> s = GSL::Sf::sin(x)
# >> GSL::Vector.graph(x, c, s, "-T X -C -L 'cos(x), sin(x)'")
#
# {prev}[link:rdoc/sf_rdoc.html]
# {next}[link:rdoc/matrix_rdoc.html]
#
# {Reference index}[link:rdoc/ref_rdoc.html]
# {top}[link:index.html]
#
#