rdoc/poly.rdoc in gsl-1.15.3 vs rdoc/poly.rdoc in gsl-1.16.0.6
- old
+ new
@@ -1,28 +1,28 @@
#
# = Polynomials
# Contents:
-# 1. {Polynomial Evaluation}[link:files/rdoc/poly_rdoc.html#1]
-# 1. {Solving polynomial equations}[link:files/rdoc/poly_rdoc.html#2]
-# 1. {Quadratic Equations}[link:files/rdoc/poly_rdoc.html#2.1]
-# 1. {Cubic Equations}[link:files/rdoc/poly_rdoc.html#2.2]
-# 1. {General Polynomial Equations}[link:files/rdoc/poly_rdoc.html#2.3]
-# 1. {GSL::Poly Class}[link:files/rdoc/poly_rdoc.html#3]
-# 1. {Constructors}[link:files/rdoc/poly_rdoc.html#3.1]
-# 1. {Methods}[link:files/rdoc/poly_rdoc.html#3.2]
-# 1. {Polynomial Fitting}[link:files/rdoc/poly_rdoc.html#4]
-# 1. {Divided-difference representations}[link:files/rdoc/poly_rdoc.html#5]
-# 1. {Extensions}[link:files/rdoc/poly_rdoc.html#6]
-# 1. {Special Polynomials}[link:files/rdoc/poly_rdoc.html#6.1]
-# 1. {Polynomial Operations}[link:files/rdoc/poly_rdoc.html#6.2]
+# 1. {Polynomial Evaluation}[link:rdoc/poly_rdoc.html#label-Polynomial+Evaluation]
+# 1. {Solving polynomial equations}[link:rdoc/poly_rdoc.html#label-Solving+polynomial+equations]
+# 1. {Quadratic Equations}[link:rdoc/poly_rdoc.html#label-Quadratic+Equations]
+# 1. {Cubic Equations}[link:rdoc/poly_rdoc.html#label-Cubic+Equations]
+# 1. {General Polynomial Equations}[link:rdoc/poly_rdoc.html#label-General+Polynomial+Equations]
+# 1. {GSL::Poly class}[link:rdoc/poly_rdoc.html#label-Poly+class]
+# 1. {Constructors}[link:rdoc/poly_rdoc.html#label-Constructors]
+# 1. {Methods}[link:rdoc/poly_rdoc.html#label-Instance+Methods]
+# 1. {Polynomial Fitting}[link:rdoc/poly_rdoc.html#label-Polynomial+fitting]
+# 1. {Divided-difference representations}[link:rdoc/poly_rdoc.html#label-Divided-difference+representations]
+# 1. {Extensions}[link:rdoc/poly_rdoc.html#label-Extensions]
+# 1. {Special Polynomials}[link:rdoc/poly_rdoc.html#label-Special+Polynomials]
+# 1. {Polynomial Operations}[link:rdoc/poly_rdoc.html#label-Polynomial+Operations]
#
-# == {}[link:index.html"name="1] Polynomial Evaluation
+# == Polynomial Evaluation
# ---
# * GSL::Poly.eval(c, x)
#
-# Evaluates the polynomial <tt>c[0] + c[1]x + c[2]x^2 + ...</tt>.
-# The polynomial coefficients <tt>c</tt> can be an <tt>Array</tt>,
+# Evaluates the polynomial <tt>c[0] + c[1]x + c[2]x^2 + ...</tt>.
+# The polynomial coefficients <tt>c</tt> can be an <tt>Array</tt>,
# a <tt>GSL::Vector</tt>, or an <tt>NArray</tt>. The evaluation point <tt>x</tt>
# is a <tt>Numeric</tt>, <tt>Array</tt>, <tt>GSL::Vector</tt> or <tt>NArray</tt>.
# From GSL 1.11, <tt>x</tt> can be a complex number, and <tt>c</tt> can be a complex polynomial given by a <tt>GSL::Vector::Complex</tt> or an <tt>Array</tt>.
#
# Ex)
@@ -52,21 +52,21 @@
# ---
# * GSL::Poly#eval_derivs(x)
# * GSL::Poly#eval_derivs(x, lenres)
#
# (GSL-1.13) Evaluate and return a polynomial and its derivatives. The output contains the values of d^k P/d x^k for the specified value of x starting with k = 0. If <tt>lenres</tt> is not given, <tt>lenres = LENGTH(self) + 1</tt> is used, therefore the last element of the output is 0.
-#
+#
# Ex.)
# >> ary = [1, 2, 3]
# => [1, 2, 3]
# >> GSL::Poly.eval_derivs(ary, 1)
# => [6.0, 8.0, 6.0, 0.0]
# >> na = NArray[1.0, 2, 3]
-# => NArray.float(3):
+# => NArray.float(3):
# [ 1.0, 2.0, 3.0 ]
# >> GSL::Poly.eval_derivs(na, 1)
-# => NArray.float(4):
+# => NArray.float(4):
# [ 6.0, 8.0, 6.0, 0.0 ]
# >> poly = GSL::Poly[1.0, 2, 3]
# => GSL::Poly
# [ 1.000e+00 2.000e+00 3.000e+00 ]
# >> GSL::Poly.eval_derivs(poly, 1)
@@ -77,48 +77,48 @@
# [ 6.000e+00 8.000e+00 6.000e+00 0.000e+00 ]
# >> poly.eval_derivs(1, 3)
# => GSL::Poly
# [ 6.000e+00 8.000e+00 6.000e+00 ]
#
-# == {}[link:index.html"name="2] Solving polynomial equations
-# === {}[link:index.html"name="2.1] Quadratic Equations
+# == Solving polynomial equations
+# === Quadratic Equations
# ---
# * GSL::Poly::solve_quadratic(a, b, c)
# * GSL::Poly::solve_quadratic([a, b, c])
#
# Find the real roots of the quadratic equation,
# a x^2 + b x + c = 0
-# The coefficients are given by 3 numbers, or a Ruby array,
+# The coefficients are given by 3 numbers, or a Ruby array,
# or a <tt>GSL::Vector</tt> object. The roots are returned as a <tt>GSL::Vector</tt>.
#
# * Ex: z^2 - 3z + 2 = 0
# >> GSL::Poly::solve_quadratic(1, -3, 2)
-# => GSL::Vector:
+# => GSL::Vector:
# [ 1.000e+00 2.000e+00 ]
#
#
# ---
# * GSL::Poly::complex_solve_quadratic(a, b, c)
# * GSL::Poly::complex_solve_quadratic([a, b, c])
#
# Find the complex roots of the quadratic equation,
# a z^2 + b z + z = 0
-# The coefficients are given by 3 numbers or a Ruby array, or a
+# The coefficients are given by 3 numbers or a Ruby array, or a
# <tt>GSL::Vector</tt>.
# The roots are returned as a <tt>GSL::Vector::Complex</tt> of two elements.
-#
+#
# * Ex: z^2 - 3z + 2 = 0
# >> require("gsl")
# => true
# >> GSL::Poly::complex_solve_quadratic(1, -3, 2)
-# [ [1.000e+00 0.000e+00] [2.000e+00 0.000e+00] ]
+# [ [1.000e+00 0.000e+00] [2.000e+00 0.000e+00] ]
# => #<GSL::Vector::Complex:0x764014>
# >> GSL::Poly::complex_solve_quadratic(1, -3, 2).real <--- Real part
-# => GSL::Vector::View:
+# => GSL::Vector::View:
# [ 1.000e+00 2.000e+00 ]
#
-# === {}[link:index.html"name="2.2] Cubic Equations
+# === Cubic Equations
# ---
# * GSL::Poly::solve_cubic(same as solve_quadratic)
#
# This method finds the real roots of the cubic equation,
# x^3 + a x^2 + b x + c = 0
@@ -127,60 +127,60 @@
# * GSL::Poly::complex_solve_cubic(same as solve_cubic)
#
# This method finds the complex roots of the cubic equation,
# z^3 + a z^2 + b z + c = 0
#
-# === {}[link:index.html"name="2.3] General Polynomial Equations
+# === General Polynomial Equations
# ---
# * GSL::Poly::complex_solve(c0, c1, c2,,, )
# * GSL::Poly::solve(c0, c1, c2,,, )
#
-# Find the complex roots of the polynomial equation. Note that
+# Find the complex roots of the polynomial equation. Note that
# the coefficients are given by "ascending" order.
#
-# * Ex: x^2 - 3 x + 2 == 0
+# * Ex: x^2 - 3 x + 2 == 0
# >> GSL::Poly::complex_solve(2, -3, 1) <--- different from Poly::quadratic_solve
# [ [1.000e+00 0.000e+00] [2.000e+00 0.000e+00] ]
# => #<GSL::Vector::Complex:0x75e614>
#
-# == {}[link:index.html"name="3] GSL::Poly Class
+# == Poly class
# This class expresses polynomials of arbitrary orders.
#
-# === {}[link:index.html"name="3.1] Constructors
+# === Constructors
# ---
# * GSL::Poly.alloc(c0, c1, c2, ....)
# * GSL::Poly[c0, c1, c2, ....]
#
-# This creates an instance of the <tt>GSL::Poly</tt> class,
+# This creates an instance of the <tt>GSL::Poly</tt> class,
# which represents a polynomial
# c0 + c1 x + c2 x^2 + ....
# This class is derived from <tt>GSL::Vector</tt>.
#
# * Ex: x^2 - 3 x + 2
# poly = GSL::Poly.alloc([2, -3, 1])
#
-# === {}[link:index.html"name="3.2] Instance Methods
+# === Instance Methods
# ---
# * GSL::Poly#eval(x)
# * GSL::Poly#at(x)
#
-# Evaluates the polynomial
-# c[0] + c[1] x + c[2] x^2 + ... + c[len-1] x^{len-1}
+# Evaluates the polynomial
+# <tt>c[0] + c[1] x + c[2] x^2 + ... + c[len-1] x^{len-1}</tt>
# using Horner's method for stability. The argument <tt>x</tt> is a
# <tt>Numeric</tt>, <tt>GSL::Vector, Matrix</tt> or an <tt>Array</tt>.
#
# ---
# * GSL::Poly#solve_quadratic
#
# Solve the quadratic equation.
#
# * Ex: z^2 - 3 z + 2 = 0:
# >> a = GSL::Poly[2, -3, 1]
-# => GSL::Poly:
+# => GSL::Poly:
# [ 2.000e+00 -3.000e+00 1.000e+00 ]
# >> a.solve_quadratic
-# => GSL::Vector:
+# => GSL::Vector:
# [ 1.000e+00 2.000e+00 ]
#
# ---
# * GSL::Poly#solve_cubic
#
@@ -194,76 +194,76 @@
# These methods find the complex roots of the quadratic equation,
# c0 + c1 z + c2 z^2 + .... = 0
#
# * Ex: z^2 - 3 z + 2 = 0:
# >> a = GSL::Poly[2, -3, 1]
-# => GSL::Poly:
+# => GSL::Poly:
# [ 2.000e+00 -3.000e+00 1.000e+00 ]
# >> a.solve
# [ [1.000e+00 0.000e+00] [2.000e+00 0.000e+00] ]
# => #<GSL::Vector::Complex:0x35db28>
#
-# == {}[link:index.html"name="4] Polynomial fitting
+# == Polynomial fitting
# ---
# * GSL::Poly.fit(x, y, order)
# * GSL::Poly.wfit(x, w, y, order)
#
-# Finds the coefficient of a polynomial of order <tt>order</tt>
+# Finds the coefficient of a polynomial of order <tt>order</tt>
# that fits the vector data (<tt>x, y</tt>) in a least-square sense.
# This provides a higher-level interface to the method
-# {GSL::Multifit#linear}[link:files/rdoc/fit_rdoc.html] in a case of polynomial fitting.
+# {GSL::Multifit#linear}[link:rdoc/fit_rdoc.html] in a case of polynomial fitting.
#
# Example:
# #!/usr/bin/env ruby
# require("gsl")
#
# x = GSL::Vector[1, 2, 3, 4, 5]
# y = GSL::Vector[5.5, 43.1, 128, 290.7, 498.4]
# # The results are stored in a polynomial "coef"
-# coef, cov, chisq, status = Poly.fit(x, y, 3)
+# coef, cov, chisq, status = Poly.fit(x, y, 3)
#
# x2 = GSL::Vector.linspace(1, 5, 20)
# graph([x, y], [x2, coef.eval(x2)], "-C -g 3 -S 4")
#
-# == {}[link:index.html"name="5] Divided-difference representations
+# == Divided-difference representations
#
# ---
# * GSL::Poly::dd_init(xa, ya)
#
-# This method computes a divided-difference representation of the
+# This method computes a divided-difference representation of the
# interpolating polynomial for the points <tt>(xa, ya)</tt>.
#
# ---
# * GSL::Poly::DividedDifference#eval(x)
#
-# This method evaluates the polynomial stored in divided-difference form
+# This method evaluates the polynomial stored in divided-difference form
# <tt>self</tt> at the point <tt>x</tt>.
#
# ---
# * GSL::Poly::DividedDifference#taylor(xp)
#
-# This method converts the divided-difference representation of a polynomial
-# to a Taylor expansion. On output the Taylor coefficients of the polynomial
+# This method converts the divided-difference representation of a polynomial
+# to a Taylor expansion. On output the Taylor coefficients of the polynomial
# expanded about the point <tt>xp</tt> are returned.
#
-# == {}[link:index.html"name="6] Extensions
-# === {}[link:index.html"name="6.1] Special Polynomials
+# == Extensions
+# === Special Polynomials
# ---
# * GSL::Poly.hermite(n)
#
# This returns coefficients of the <tt>n</tt>-th order Hermite polynomial, <tt>H(x; n)</tt>.
# For order of <tt>n</tt> >= 3, this method uses the recurrence relation
# H(x; n+1) = 2 x H(x; n) - 2 n H(x; n-1)
# * Ex:
# >> GSL::Poly.hermite(2)
-# => GSL::Poly::Int:
+# => GSL::Poly::Int:
# [ -2 0 4 ] <----- 4x^2 - 2
# >> GSL::Poly.hermite(5)
-# => GSL::Poly::Int:
+# => GSL::Poly::Int:
# [ 0 120 0 -160 0 32 ] <----- 32x^5 - 160x^3 + 120x
# >> GSL::Poly.hermite(7)
-# => GSL::Poly::Int:
+# => GSL::Poly::Int:
# [ 0 -1680 0 3360 0 -1344 0 128 ]
#
# ---
# * GSL::Poly.cheb(n)
# * GSL::Poly.chebyshev(n)
@@ -298,38 +298,38 @@
#
# Ex:
# rb(main):001:0> require("gsl")
# => true
# >> GSL::Poly.laguerre(0)
-# => GSL::Poly::Int:
+# => GSL::Poly::Int:
# [ 1 ] <--- 1
# >> GSL::Poly.laguerre(1)
-# => GSL::Poly::Int:
+# => GSL::Poly::Int:
# [ 1 -1 ] <--- -x + 1
# >> GSL::Poly.laguerre(2)
-# => GSL::Poly::Int:
+# => GSL::Poly::Int:
# [ 2 -4 1 ] <--- (x^2 - 4x + 2)/2!
# >> GSL::Poly.laguerre(3)
-# => GSL::Poly::Int:
+# => GSL::Poly::Int:
# [ 6 -18 9 -1 ] <--- (-x^3 + 9x^2 - 18x + 6)/3!
# >> GSL::Poly.laguerre(4)
-# => GSL::Poly::Int:
+# => GSL::Poly::Int:
# [ 24 -96 72 -16 1 ] <--- (x^4 - 16x^3 + 72x^2 - 96x + 24)/4!
-#
-# === {}[link:index.html"name="6.2] Polynomial Operations
+#
+# === Polynomial Operations
# ---
# * GSL::Poly#conv
# * GSL::Poly#deconv
# * GSL::Poly#reduce
# * GSL::Poly#deriv
# * GSL::Poly#integ
# * GSL::Poly#compan
#
#
-# {prev}[link:files/rdoc/complex_rdoc.html]
-# {next}[link:files/rdoc/sf_rdoc.html]
+# {prev}[link:rdoc/complex_rdoc.html]
+# {next}[link:rdoc/sf_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]
#
#
#