Class: KXI::Math::Polynomial

Inherits:
Object
  • Object
show all
Defined in:
lib/kxi/math/polynomial.rb

Overview

Represents a polynomial

Instance Method Summary collapse

Constructor Details

#initialize(*cfs) ⇒ Polynomial

Instantiates the KXI::Math::Polynomial class

Parameters:

  • cfs (Numeric) —

    Coefficients of polynomial



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# File 'lib/kxi/math/polynomial.rb', line 21

def initialize(*cfs)
  cfs.shift while cfs.length > 1 and cfs[0] == 0
  @cfs = cfs.collect do |i|
    raise(KXI::Exceptions::InvalidTypeException.new(i.class, Numeric)) unless i.is_a?(Numeric)
    i.to_f
  end
end

Instance Method Details

#*(other) ⇒ KXI::Math::Polynomial #*(other) ⇒ KXI::Math::Polynomial

Multiplies polynomial

Overloads:



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# File 'lib/kxi/math/polynomial.rb', line 125

def *(other)
  if other.is_a?(Polynomial)
    cfs = [0] * (degree + other.degree + 1)
    foreach do |k1, d1|
      other.foreach do |k2, d2|
        cfs[d1 + d2] += k1 * k2
      end
    end
    return Polynomial.new(*cfs)
  elsif other.is_a?(Numeric)
    return @cfs.collect { |k| k * other }
  else
    raise(KXI::Exceptions::InvalidTypeException.new(other.class, Numeric, KXI::Math::Polynomial))
  end
end

#at(x) ⇒ Numeric

Returns the value of polynomial

Parameters:

  • x (Numeric) —

    Value of x

Returns:

  • (Numeric) —

    Value of polynomial at x



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# File 'lib/kxi/math/polynomial.rb', line 97

def at(x)
  sum = 0
  foreach do |k, d|
    sum += k * (x ** d)
  end
  return sum
end

#coefficients ⇒ Array<Numeric>

Returns the coefficients of polynomial

Returns:

  • (Array<Numeric>) —

    Coefficients of polynomial



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# File 'lib/kxi/math/polynomial.rb', line 15

def coefficients
  @cfs
end

#degree ⇒ Integer

Returns the degree of polynomial

Returns:

  • (Integer) —

    Degree of polynomial



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# File 'lib/kxi/math/polynomial.rb', line 9

def degree
  @cfs.length - 1
end

#derivative(n = 1) ⇒ KXI::Math::Polynomial

Takes the derivative of polynomial

Parameters:

  • n (Integer) (defaults to: 1) —

    Order of derivation

Returns:



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# File 'lib/kxi/math/polynomial.rb', line 61

def derivative(n = 1)
  return Polynomial.new(0) if degree <= n
  cfs = []
  foreach do |k, d|
    if d >= n
      cfs.push(k * KXI::Math.pfact(d, d - n))
    end
  end
  return Polynomial.new(*cfs)
end

#foreach {|k| ... } ⇒ Object

Iterates over every coefficient of polynomial (from higher powers to lower powers)

Yields:

  • (k) —

    Iterator

Yield Parameters:

  • k (Numeric) —

    Coefficient of polynomial



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# File 'lib/kxi/math/polynomial.rb', line 108

def foreach
  d = degree
  @cfs.each do |k|
    yield(k, d)
    d -= 1
  end
end

#integral ⇒ KXI::Math::Polynomial

Takes the integral of polynomial

Returns:



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# File 'lib/kxi/math/polynomial.rb', line 74

def integral
  cfs = []
  foreach do |k, d|
    cfs.push(k / (d + 1))
  end
  cfs.push(0)
  return Polynomial.new(*cfs)
end

#integrate(x1, x2) ⇒ Numeric

Integrates the polynomial

Parameters:

  • x1 (Numeric) —

    First bound of integration

  • x2 (Numeric) —

    Second bound of integration

Returns:

  • (Numeric) —

    Result of integration



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# File 'lib/kxi/math/polynomial.rb', line 87

def integrate(x1, x2)
  min = x1 > x2 ? x2 : x1
  max = x1 > x2 ? x1 : x2
  i   = integral
  return i.at(max) - i.at(min)
end

#to_s ⇒ String

Converts polynomial to string

Returns:

  • (String) —

    String equivalent to polynomial



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# File 'lib/kxi/math/polynomial.rb', line 31

def to_s
  return (@cfs[0] == @cfs[0].to_i ? @cfs[0].to_i : @cfs[0]) if degree == 0
  ret = nil
  foreach do |k, d|
    if k != 0
      k = k.to_i if k.to_i == k
      if d > 0
        if ret == nil
          ret = k >= 0 ? '' : '-'
        else
          ret += k >= 0 ? ' + ' : ' - '
        end
        ret += (k >= 0 ? k : -k).to_s if k != 1 and k != -1
        ret += "x#{d > 1 ? "^#{d.to_s}" : ''}"
      else
        if ret == nil
          ret = k >= 0 ? '' : '-'
        else
          ret += k >= 0 ? ' + ' : ' - '
        end
        ret += (k >= 0 ? k : -k).to_s
      end
    end
  end
  return ret
end