Class: SyMath::Matrix

Inherits:
Value
  • Object
show all
Defined in:
lib/symath/matrix.rb

Instance Attribute Summary collapse

Instance Method Summary collapse

Methods inherited from Value

#*, #**, #<, #<=, #<=>, #>, #>=, #^, #add, #base, compose_with_simplify, create, #deep_clone, #div, #dump, #evaluate, #exponent, #factors, #inspect, #inv, #is_divisor_factor?, #is_finite?, #is_nan?, #is_negative?, #is_negative_number?, #is_number?, #is_positive?, #is_prod_exp?, #is_sum_exp?, #is_unit_quaternion?, #is_zero?, #mul, #neg, #power, #reduce, #reduce_modulo_sign, #sign, #sub, #terms, #to_m, #wedge

Methods included from Operation::Exterior

#flat, #hodge, #sharp

Methods included from Operation::Integration

#anti_derivative, #get_linear_constants, initialize, #int_constant, #int_failure, #int_function, #int_inv, #int_pattern, #int_power, #int_product, #int_sum, #integral_bounds

Methods included from Operation::Differential

#_d_wedge, #d, #d_failure, #d_fraction, #d_function, #d_function_def, #d_power, #d_product, initialize

Methods included from Operation

#iterate, #recurse

Methods included from Operation::DistributiveLaw

#combfrac_add_term, #combfrac_sum, #combine_fractions, #expand, #expand_product, #expand_single_pass, #factorize, #factorize_integer_poly, #factorize_simple, #has_fractional_terms?

Methods included from Operation::Normalization

#combine_factors, #compare_factors_and_swap, #normalize, #normalize_matrix, #normalize_power, #normalize_product, #normalize_single_pass, #normalize_sum, #order_product, #product_on_fraction_form, #reduce_constant_factors, #replace_combined_factors, #swap_factors

Methods included from Operation::Match

#build_assoc_op, #match, #match_assoc, #match_replace

Constructor Details

#initialize(data) ⇒ Matrix

Returns a new instance of Matrix.



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# File 'lib/symath/matrix.rb', line 7

def initialize(data)
  raise 'Not an array: ' + data.to_s if !data.is_a?(Array)
  raise 'Array is empty' if data.length == 0

  if data[0].is_a?(Array) then
    # Multidimensional array
    @nrows = data.length
    raise 'Number of columns is zero' if data[0].length == 0
    @ncols = data[0].length
    # Check that all rows contain arrays of the same length
    data.each do |r|
      raise 'Row is not array' if !r.is_a?(Array)
      raise 'Row has invalid length' if r.length != @ncols
    end
    @elements = data.map { |r| r.map { |c| c.to_m } }
  else
    # Simple array. Creates a single row matrix
    @nrows = 1
    @ncols = data.length
    @elements = [data.map { |c| c.to_m }]
  end
end

Instance Attribute Details

#ncols ⇒ Object (readonly)

Returns the value of attribute ncols.



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# File 'lib/symath/matrix.rb', line 5

def ncols
  @ncols
end

#nrows ⇒ Object (readonly)

Returns the value of attribute nrows.



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# File 'lib/symath/matrix.rb', line 5

def nrows
  @nrows
end

Instance Method Details

#+(other) ⇒ Object 



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# File 'lib/symath/matrix.rb', line 112

def +(other)
  return add(other)
end

#-(other) ⇒ Object 



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# File 'lib/symath/matrix.rb', line 128

def -(other)
  return sub(other)
end

#-@ ⇒ Object 



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# File 'lib/symath/matrix.rb', line 142

def -@()
  return neg
end

#/(other) ⇒ Object 



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# File 'lib/symath/matrix.rb', line 92

def /(other)
  return div(other)
end

#==(other) ⇒ Object Also known as: eql? 



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# File 'lib/symath/matrix.rb', line 219

def ==(other)
  return false if !other.is_a?(SyMath::Matrix)

  return false if nrows != other.nrows
  return false if ncols != other.ncols

  (0..@nrows - 1).each do |r|
    (0..@ncols - 1).each do |c|
      return false if self[r, c] != other[r, c]
    end
  end

  return true
end

#[](i, j) ⇒ Object 



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# File 'lib/symath/matrix.rb', line 52

def [](i, j)
  return @elements[i][j]
end

#adjugate ⇒ Object

The adjugate of a matrix is the transpose of the cofactor matrix



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# File 'lib/symath/matrix.rb', line 157

def adjugate()
  data = (0..@ncols - 1).map do |c|
    (0..@nrows - 1).map { |r| cofactor(r, c) }
  end

  return SyMath::Matrix.new(data)
end

#cofactor(r, c) ⇒ Object

The cofactor of an element is the minor given by the rows and columns not including the element, multiplied by a sign factor which alternates for each row and column



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# File 'lib/symath/matrix.rb', line 206

def cofactor(r, c)
  sign = (-1)**(r + c)
  rows = (0..@nrows - 1).to_a - [r]
  cols = (0..@ncols - 1).to_a - [c]
  return minor(rows, cols)*sign.to_m
end

#col(i) ⇒ Object 



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# File 'lib/symath/matrix.rb', line 48

def col(i)
  return @elements.map { |r| r[i] }
end

#determinant ⇒ Object 



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# File 'lib/symath/matrix.rb', line 165

def determinant()
  raise 'Matrix is not square' if !is_square?
  
  return minor((0..@nrows - 1).to_a, (0..@ncols - 1).to_a)
end

#hash ⇒ Object

:nocov:



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# File 'lib/symath/matrix.rb', line 40

def hash()
  return [0, 0].hash
end

#inverse ⇒ Object 



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# File 'lib/symath/matrix.rb', line 150

def inverse()
  raise 'Matrix is not square' if !is_square?

  return adjugate.matrix_div(determinant)
end

#is_associative? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/symath/matrix.rb', line 35

def is_associative?()
  return true
end

#is_commutative? ⇒ Boolean

:nocov:

Returns:

  • (Boolean) 


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# File 'lib/symath/matrix.rb', line 31

def is_commutative?()
  return false
end

#is_square? ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/symath/matrix.rb', line 56

def is_square?()
  return @ncols == @nrows
end

#matrix_add(other) ⇒ Object 



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# File 'lib/symath/matrix.rb', line 96

def matrix_add(other)
  if other.is_a?(SyMath::Minus) and other.argument.is_a?(SyMath::Matrix)
    return self.matrix_sub(other.argument)
  end

  raise 'Invalid dimensions' if @ncols != other.ncols or @nrows != other.nrows

  data = (0..@nrows - 1).map do |r|
    (0..@ncols - 1).map do |c|
      self[r, c] + other[r, c]
    end
  end

  return SyMath::Matrix.new(data)
end

#matrix_div(other) ⇒ Object 



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# File 'lib/symath/matrix.rb', line 82

def matrix_div(other)
  raise 'Cannot divide matrix by matrix' if other.is_a?(SyMath::Matrix)

  data = (0..@nrows - 1).map do |r|
    (0..@ncols - 1).map { |c| self[r, c]/other }
  end

  return SyMath::Matrix.new(data)
end

#matrix_mul(other) ⇒ Object 



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# File 'lib/symath/matrix.rb', line 60

def matrix_mul(other)
  if !other.is_a?(SyMath::Matrix)
    data = (0..@nrows - 1).map do |r|
      (0..@ncols - 1).map { |c| self[r, c]*other }
    end

    return SyMath::Matrix.new(data)
  end
  
  raise 'Invalid dimensions' if @ncols != other.nrows

  data = (0..@nrows - 1).map do |r|
    (0..other.ncols - 1).map do |c|
      (0..@ncols - 1).map do |c2|
        self[r, c2]*other[c2, c]
      end.inject(:+) 
    end
  end

  return SyMath::Matrix.new(data)
end

#matrix_neg ⇒ Object 



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# File 'lib/symath/matrix.rb', line 132

def matrix_neg()
  data = @elements.map do |r|
    r.map do |e|
      - e
    end
  end

  return SyMath::Matrix.new(data)
end

#matrix_sub(other) ⇒ Object 



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# File 'lib/symath/matrix.rb', line 116

def matrix_sub(other)
  raise 'Invalid dimensions' if @ncols != other.ncols or @nrows != other.nrows

  data = (0..@nrows - 1).map do |r|
    (0..@ncols - 1).map do |c|
      self[r, c] - other[r, c]
    end
  end

  return SyMath::Matrix.new(data)
end

#minor(rows, cols) ⇒ Object

The minor is the determinant of a submatrix. The submatrix is given by the rows and cols which are arrays of indexes to the rows and columns to be included



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# File 'lib/symath/matrix.rb', line 174

def minor(rows, cols)
  raise 'Not square' if rows.length != cols.length

  # Determinant of a single element is just the element
  if rows.length == 1
    return self[rows[0], cols[0]]
  end

  ret = 0.to_m
  sign = 1
  subrows = rows - [rows[0]]

  # Loop over all elements e in first row. Calculate determinant as:
  #   sum(sign*e*det(rows + cols except the one including e))
  # The sign variable alternates between 1 and -1 for each summand 
  cols.each do |c|
    subcols = cols - [c]
    if (sign > 0)
      ret += self[rows[0], c]*minor(subrows, subcols)
    else
      ret -= self[rows[0], c]*minor(subrows, subcols)
    end

    sign *= -1
  end

  return ret
end

#row(i) ⇒ Object 



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# File 'lib/symath/matrix.rb', line 44

def row(i)
  return @elements[i]
end

#to_s ⇒ Object 



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# File 'lib/symath/matrix.rb', line 236

def to_s()
  # This will in many cases look rather messy, but we don't have the option
  # to format the matrix over multiple lines.
  return '[' + @elements.map { |r| r.map { |c| c.to_s }.join(', ') }.join('; ') + ']'
end

#trace ⇒ Object 



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# File 'lib/symath/matrix.rb', line 213

def trace()
  raise 'Matrix is not square' if !is_square?
  
  return (0..@nrows - 1).map { |i| self[i, i] }.inject(:+)
end

#transpose ⇒ Object 



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# File 'lib/symath/matrix.rb', line 146

def transpose()
  return SyMath::Matrix.new(@elements.transpose)
end

#type ⇒ Object 



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# File 'lib/symath/matrix.rb', line 242

def type()
  return SyMath::Type.new('matrix', dimn: ncols, dimm: nrows)
end