Class: KXI::Math::Polynomial
- Inherits:
-
Object
- Object
- KXI::Math::Polynomial
- Defined in:
- lib/kxi/math/polynomial.rb
Overview
Represents a polynomial
Instance Method Summary collapse
-
#*(other) ⇒ Object
Multiplies polynomial.
-
#at(x) ⇒ Numeric
Returns the value of polynomial.
-
#coefficients ⇒ Array<Numeric>
Returns the coefficients of polynomial.
-
#degree ⇒ Integer
Returns the degree of polynomial.
-
#derivative(n = 1) ⇒ KXI::Math::Polynomial
Takes the derivative of polynomial.
-
#foreach {|k| ... } ⇒ Object
Iterates over every coefficient of polynomial (from higher powers to lower powers).
-
#initialize(*cfs) ⇒ Polynomial
constructor
Instantiates the Polynomial class.
-
#integral ⇒ KXI::Math::Polynomial
Takes the integral of polynomial.
-
#integrate(x1, x2) ⇒ Numeric
Integrates the polynomial.
-
#to_s ⇒ String
Converts polynomial to string.
Constructor Details
#initialize(*cfs) ⇒ Polynomial
Instantiates the KXI::Math::Polynomial class
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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
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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
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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
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# File 'lib/kxi/math/polynomial.rb', line 15 def coefficients @cfs end |
#degree ⇒ Integer
Returns the 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
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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)
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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
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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
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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
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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 |