Class: Vector

Inherits:
Object
  • Object
show all
Includes:
Enumerable
Defined in:
lib/extendmatrix.rb

Defined Under Namespace

Modules: Norm

Class Method Summary collapse

Instance Method Summary collapse

Class Method Details

.concat(*args) ⇒ Object

Returns a concatenated Vector

Vector.concat(Vector[1,2,3], Vector[4,5,6])
=> Vector[1, 2, 3, 4, 5, 6]



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# File 'lib/extendmatrix.rb', line 61

def concat(*args)
  Vector.elements(args.inject([]){|ac,v| ac+v.to_a}, false)
end

.gram_schmidt(*vectors) ⇒ Object

Stabilized Gram-Schmidt process (en.wikipedia.org/wiki/Gram-Schmidt_process#Algorithm)



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# File 'lib/extendmatrix.rb', line 200

def self.gram_schmidt(*vectors)
  v = vectors.clone
  for j in 0...v.size
    for i in 0..j-1
      v[j] -= v[i] * v[j].inner_product(v[i])
    end
    v[j] /= v[j].norm
  end
  v
end

Instance Method Details

#/(c) ⇒ Object Also known as: quo

Return the vector divided by a scalar



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# File 'lib/extendmatrix.rb', line 143

def / (c)
  map {|e| e.quo(c)}
end

#[](i) ⇒ Object

Returns the value of an index vector or a Vector with the values of a range v = Vector[1, 2, 3, 4] v => 1 v => Vector[1, 2, 3]



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# File 'lib/extendmatrix.rb', line 22

def [](i)
  case i
  when Range
    Vector[*to_a.slice(i)]
  else
    index(i)
  end
end

#[]=(i, v) ⇒ Object

Sets a vector value/(range of values) with a new value/(values from a vector) v = Vector[1, 2, 3] v = 9 => Vector[1, 2, 9] v = Vector[9, 9, 9, 9, 9] => v: Vector[1, 9, 9]



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# File 'lib/extendmatrix.rb', line 43

def []=(i, v)
  case i
  when Range
    (self.size..i.begin - 1).each{|e| self[e] = 0} # self.size must be in the first place because the size of self can be modified
    [v.size, i.entries.size].min.times {|e| self[e + i.begin] = v[e]}
    (v.size + i.begin .. i.end).each {|e| self[e] = 0}
  else
    @elements[i]=v
  end
end

#collect! ⇒ Object

Changes the elements of vector and returns a Vector



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# File 'lib/extendmatrix.rb', line 69

def collect!
  els = @elements.collect! {|v| yield(v)}
  Vector.elements(els, false)
end

#each ⇒ Object

Iterates the elements of a vector



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# File 'lib/extendmatrix.rb', line 77

def each
  (0...size).each {|i| yield(self[i])}
  nil
end

#house ⇒ Object

Computes the Householder vector (MC, Golub, p. 210, algorithm 5.1.1)



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# File 'lib/extendmatrix.rb', line 159

def house
  s = self[1..length-1]
  sigma = s.inner_product(s)
  v = clone; v[0] = 1
  if sigma == 0
    beta = 0
  else
    mu = Math.sqrt(self[0] ** 2 + sigma)
    if self[0] <= 0
      v[0] = self[0] - mu
    else
      v[0] = - sigma.quo(self[0] + mu)
    end
    v2 = v[0] ** 2
    beta = 2 * v2.quo(sigma + v2)
    v /= v[0]
  end
  return v, beta
end

#index ⇒ Object 



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# File 'lib/extendmatrix.rb', line 14

alias :index :[]

#magnitude ⇒ Object

Magnitude or length of the vector Equal to sqrt(sum(x_i^2))



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# File 'lib/extendmatrix.rb', line 33

def magnitude
  Math::sqrt(to_a.inject(0) {|ac, v| ac+(v**2)})
end

#max ⇒ Object

Returns the maximum element of a vector



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# File 'lib/extendmatrix.rb', line 85

def max
  to_a.max
end

#min ⇒ Object

Returns the minimum element of a vector



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# File 'lib/extendmatrix.rb', line 92

def min
  to_a.min
end

#norm(p = 2) ⇒ Object

Returns the p-norm of a vector



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# File 'lib/extendmatrix.rb', line 104

def norm(p = 2)
  Norm.sqnorm(self, p) ** (1.quo(p))
end

#norm_inf ⇒ Object

Returns the infinite-norm



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# File 'lib/extendmatrix.rb', line 111

def norm_inf
  [min.abs, max.abs].max
end

#normalize ⇒ Object

Return the vector normalized



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# File 'lib/extendmatrix.rb', line 192

def normalize
  self.quo(self.norm)
end

#proj(v) ⇒ Object

Projection operator (en.wikipedia.org/wiki/Gram-Schmidt_process#The_Gram.E2.80.93Schmidt_process)



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# File 'lib/extendmatrix.rb', line 183

def proj(v)
  vp = v.inner_product(self)
  vp = Float vp if vp.is_a?(Integer)
  self * (vp / inner_product(self))
end

#slice(*args) ⇒ Object

Returns a slice of vector



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# File 'lib/extendmatrix.rb', line 118

def slice(*args)
  Vector[*to_a.slice(*args)]
end

#slice=(args) ⇒ Object

Sets a slice of vector



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# File 'lib/extendmatrix.rb', line 131

def slice=(args)
  case args[1]
  when Range
    slice_set(args[0], args[1].begin, args[1].last)
  else
    slice_set(args[0], args[1], args[2])
  end
end

#slice_set(v, b, e) ⇒ Object 



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# File 'lib/extendmatrix.rb', line 122

def slice_set(v, b, e)
  for i in b..e
    self[i] = v[i-b]
  end
end

#sum ⇒ Object

Returns the sum of values of the vector



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# File 'lib/extendmatrix.rb', line 98

def sum
  to_a.inject(&:+)
end

#transpose ⇒ Object Also known as: t

Return the matrix column coresponding to the vector transpose



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# File 'lib/extendmatrix.rb', line 150

def transpose
  Matrix[self.to_a]
end