Vector

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 1865
def Vector.[](*array)
  new convert_to_array(array, false)
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 1882
def Vector.basis(size:, index:)
  raise ArgumentError, "invalid size (#{size} for 1..)" if size < 1
  raise ArgumentError, "invalid index (#{index} for 0...#{size})" unless 0 <= index && index < size
  array = Array.new(size, 0)
  array[index] = 1
  new convert_to_array(array, false)
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 1873
def Vector.elements(array, copy = true)
  new convert_to_array(array, copy)
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2029
def Vector.independent?(*vs)
  vs.each do |v|
    raise TypeError, "expected Vector, got #{v.class}" unless v.is_a?(Vector)
    Vector.Raise ErrDimensionMismatch unless v.size == vs.first.size
  end
  return false if vs.count > vs.first.size
  Matrix[*vs].rank.eql?(vs.count)
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 1904
def initialize(array)
  # No checking is done at this point.
  @elements = array
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 1895
def Vector.zero(size)
  raise ArgumentError, "invalid size (#{size} for 0..)" if size < 0
  array = Array.new(size, 0)
  new convert_to_array(array, false)
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2103
def *(x)
  case x
  when Numeric
    els = @elements.collect{|e| e * x}
    self.class.elements(els, false)
  when Matrix
    Matrix.column_vector(self) * x
  when Vector
    Vector.Raise ErrOperationNotDefined, "*", self.class, x.class
  else
    apply_through_coercion(x, __method__)
  end
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2120
def +(v)
  case v
  when Vector
    Vector.Raise ErrDimensionMismatch if size != v.size
    els = collect2(v) {|v1, v2|
      v1 + v2
    }
    self.class.elements(els, false)
  when Matrix
    Matrix.column_vector(self) + v
  else
    apply_through_coercion(v, __method__)
  end
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2168
def +@
  self
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2138
def -(v)
  case v
  when Vector
    Vector.Raise ErrDimensionMismatch if size != v.size
    els = collect2(v) {|v1, v2|
      v1 - v2
    }
    self.class.elements(els, false)
  when Matrix
    Matrix.column_vector(self) - v
  else
    apply_through_coercion(v, __method__)
  end
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2172
def -@
  collect {|e| -e }
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2156
def /(x)
  case x
  when Numeric
    els = @elements.collect{|e| e / x}
    self.class.elements(els, false)
  when Matrix, Vector
    Vector.Raise ErrOperationNotDefined, "/", self.class, x.class
  else
    apply_through_coercion(x, __method__)
  end
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2079
def ==(other)
  return false unless Vector === other
  @elements == other.elements
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 1918
def [](i)
  @elements[i]
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 1933
def []=(i, v)
  raise FrozenError, "can't modify frozen Vector" if frozen?
  if i.is_a?(Range)
    range = Matrix::CoercionHelper.check_range(i, size, :vector)
    set_range(range, v)
  else
    index = Matrix::CoercionHelper.check_int(i, size, :index)
    set_value(index, v)
  end
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2288
def angle_with(v)
  raise TypeError, "Expected a Vector, got a #{v.class}" unless v.is_a?(Vector)
  Vector.Raise ErrDimensionMismatch if size != v.size
  prod = magnitude * v.magnitude
  raise ZeroVectorError, "Can't get angle of zero vector" if prod == 0
  dot = inner_product(v)
  if dot.abs >= prod
    dot.positive? ? 0 : Math::PI
  else
    Math.acos(dot / prod)
  end
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2348
def coerce(other)
  case other
  when Numeric
    return Matrix::Scalar.new(other), self
  else
    raise TypeError, "#{self.class} can't be coerced into #{other.class}"
  end
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2232
def collect(&block) # :yield: e
  return to_enum(:collect) unless block_given?
  els = @elements.collect(&block)
  self.class.elements(els, false)
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2242
def collect!(&block)
  return to_enum(:collect!) unless block_given?
  raise FrozenError, "can't modify frozen Vector" if frozen?
  @elements.collect!(&block)
  self
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2007
def collect2(v) # :yield: e1, e2
  raise TypeError, "Integer is not like Vector" if v.kind_of?(Integer)
  Vector.Raise ErrDimensionMismatch if size != v.size
  return to_enum(:collect2, v) unless block_given?
  Array.new(size) do |i|
    yield @elements[i], v[i]
  end
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2308
def covector
  Matrix.row_vector(self)
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2207
def cross_product(*vs)
  raise ErrOperationNotDefined, "cross product is not defined on vectors of dimension #{size}" unless size >= 2
  raise ArgumentError, "wrong number of arguments (#{vs.size} for #{size - 2})" unless vs.size == size - 2
  vs.each do |v|
    raise TypeError, "expected Vector, got #{v.class}" unless v.is_a? Vector
    Vector.Raise ErrDimensionMismatch unless v.size == size
  end
  case size
  when 2
    Vector[-@elements[1], @elements[0]]
  when 3
    v = vs[0]
    Vector[ v[2]*@elements[1] - v[1]*@elements[2],
      v[0]*@elements[2] - v[2]*@elements[0],
      v[1]*@elements[0] - v[0]*@elements[1] ]
  else
    rows = self, *vs, Array.new(size) {|i| Vector.basis(size: size, index: i) }
    Matrix.rows(rows).laplace_expansion(row: size - 1)
  end
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 1984
def each(&block)
  return to_enum(:each) unless block_given?
  @elements.each(&block)
  self
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 1993
def each2(v) # :yield: e1, e2
  raise TypeError, "Integer is not like Vector" if v.kind_of?(Integer)
  Vector.Raise ErrDimensionMismatch if size != v.size
  return to_enum(:each2, v) unless block_given?
  size.times do |i|
    yield @elements[i], v[i]
  end
  self
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2326
def elements_to_f
  warn "Vector#elements_to_f is deprecated", uplevel: 1
  map(&:to_f)
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2331
def elements_to_i
  warn "Vector#elements_to_i is deprecated", uplevel: 1
  map(&:to_i)
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2336
def elements_to_r
  warn "Vector#elements_to_r is deprecated", uplevel: 1
  map(&:to_r)
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2084
def eql?(other)
  return false unless Vector === other
  @elements.eql? other.elements
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2058
def freeze
  @elements.freeze
  super
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2092
def hash
  @elements.hash
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2047
def independent?(*vs)
  self.class.independent?(self, *vs)
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2066
        def initialize_copy(v)
  super
  @elements = @elements.dup unless frozen?
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2184
def inner_product(v)
  Vector.Raise ErrDimensionMismatch if size != v.size

  p = 0
  each2(v) {|v1, v2|
    p += v1 * v2.conj
  }
  p
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2371
def inspect
  "Vector" + @elements.inspect
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2254
def magnitude
  Math.sqrt(@elements.inject(0) {|v, e| v + e.abs2})
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2263
def map2(v, &block) # :yield: e1, e2
  return to_enum(:map2, v) unless block_given?
  els = collect2(v, &block)
  self.class.elements(els, false)
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2277
def normalize
  n = magnitude
  raise ZeroVectorError, "Zero vectors can not be normalized" if n == 0
  self / n
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 1966
def round(ndigits=0)
  map{|e| e.round(ndigits)}
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 1951
        def set_range(range, value)
  if value.is_a?(Vector)
    raise ArgumentError, "vector to be set has wrong size" unless range.size == value.size
    @elements[range] = value.elements
  elsif value.is_a?(Matrix)
    Matrix.Raise ErrDimensionMismatch unless value.row_count == 1
    @elements[range] = value.row(0).elements
  else
    @elements[range] = Array.new(range.size, value)
  end
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 1947
        def set_value(index, value)
  @elements[index] = value
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 1973
def size
  @elements.size
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2315
def to_a
  @elements.dup
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2322
def to_matrix
  Matrix.column_vector(self)
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2364
def to_s
  "Vector[" + @elements.join(", ") + "]"
end

          
        

          
            
# File tmp/rubies/ruby-2.6.10/lib/matrix.rb, line 2054
def zero?
  all?(&:zero?)
end