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Matrix

The Matrix class represents a mathematical matrix. It provides methods for creating matrices, operating on them arithmetically and algebraically, and determining their mathematical properties (trace, rank, inverse, determinant).

Method Catalogue

To create a matrix:

  • Matrix[*rows]

  • Matrix.[](*rows)

  • Matrix.rows(rows, copy = true)

  • Matrix.columns(columns)

  • Matrix.build(row_size, column_size, &block)

  • Matrix.diagonal(*values)

  • Matrix.scalar(n, value)

  • Matrix.identity(n)

  • Matrix.unit(n)

  • Matrix.I(n)

  • Matrix.zero(n)

  • Matrix.row_vector(row)

  • Matrix.column_vector(column)

To access Matrix elements/columns/rows/submatrices/properties:

  • [](i, j)

  • #row_size

  • #column_size

  • #row(i)

  • #column(j)

  • #collect

  • #map

  • #each

  • #each_with_index

  • #minor(*param)

Properties of a matrix:

  • #empty?

  • #real?

  • #regular?

  • #singular?

  • #square?

Matrix arithmetic:

  • *(m)

  • +(m)

  • -(m)

  • #/(m)

  • #inverse

  • #inv

  • **

Matrix functions:

  • #determinant

  • #det

  • #rank

  • #trace

  • #tr

  • #transpose

  • #t

Complex arithmetic:

  • conj

  • conjugate

  • imag

  • imaginary

  • real

  • rect

  • rectangular

Conversion to other data types:

  • #coerce(other)

  • #row_vectors

  • #column_vectors

  • #to_a

String representations:

  • #to_s

  • #inspect

Attributes

column_size[R]

Returns the number of columns.

rows[R]

instance creations

Public Class Methods

I(n) click to toggle source
Alias for: identity
[](*rows) click to toggle source

Creates a matrix where each argument is a row.

Matrix[ [25, 93], [-1, 66] ]
   =>  25 93
       -1 66
 
               # File matrix.rb, line 119
def Matrix.[](*rows)
  Matrix.rows(rows, false)
end
            
build(row_size, column_size = row_size) click to toggle source

Creates a matrix of size row_size x column_size. It fills the values by calling the given block, passing the current row and column. Returns an enumerator if no block is given.

m = Matrix.build(2, 4) {|row, col| col - row }
  => Matrix[[0, 1, 2, 3], [-1, 0, 1, 2]]
m = Matrix.build(3) { rand }
  => a 3x3 matrix with random elements
 
               # File matrix.rb, line 164
def Matrix.build(row_size, column_size = row_size)
  row_size = CoercionHelper.coerce_to_int(row_size)
  column_size = CoercionHelper.coerce_to_int(column_size)
  raise ArgumentError if row_size < 0 || column_size < 0
  return to_enum :build, row_size, column_size unless block_given?
  rows = Array.new(row_size) do |i|
    Array.new(column_size) do |j|
      yield i, j
    end
  end
  new rows, column_size
end
            
column_vector(column) click to toggle source

Creates a single-column matrix where the values of that column are as given in column.

Matrix.column_vector([4,5,6])
  => 4
     5
     6
 
               # File matrix.rb, line 248
def Matrix.column_vector(column)
  column = convert_to_array(column)
  new [column].transpose, 1
end
            
columns(columns) click to toggle source

Creates a matrix using columns as an array of column vectors.

Matrix.columns([[25, 93], [-1, 66]])
   =>  25 -1
       93 66
 
               # File matrix.rb, line 149
def Matrix.columns(columns)
  Matrix.rows(columns, false).transpose
end
            
diagonal(*values) click to toggle source

Creates a matrix where the diagonal elements are composed of values.

Matrix.diagonal(9, 5, -3)
  =>  9  0  0
      0  5  0
      0  0 -3
 
               # File matrix.rb, line 184
def Matrix.diagonal(*values)
  size = values.size
  rows = Array.new(size) {|j|
    row = Array.new(size, 0)
    row[j] = values[j]
    row
  }
  new rows
end
            
empty(row_size = 0, column_size = 0) click to toggle source

Creates a empty matrix of row_size x column_size. At least one of row_size or column_size must be 0.

m = Matrix.empty(2, 0)
m == Matrix[ [], [] ]
  => true
n = Matrix.empty(0, 3)
n == Matrix.columns([ [], [], [] ])
  => true
m * n
  => Matrix[[0, 0, 0], [0, 0, 0]]
 
               # File matrix.rb, line 266
def Matrix.empty(row_size = 0, column_size = 0)
  Matrix.Raise ArgumentError, "One size must be 0" if column_size != 0 && row_size != 0
  Matrix.Raise ArgumentError, "Negative size" if column_size < 0 || row_size < 0

  new([[]]*row_size, column_size)
end
            
identity(n) click to toggle source

Creates an n by n identity matrix.

Matrix.identity(2)
  => 1 0
     0 1
 
               # File matrix.rb, line 211
def Matrix.identity(n)
  Matrix.scalar(n, 1)
end
            
Also aliased as: unit, I
new(rows, column_size = rows[0].size) click to toggle source

::new is private; use ::rows, columns, [], etc... to create.

 
               # File matrix.rb, line 276
def initialize(rows, column_size = rows[0].size)
  # No checking is done at this point. rows must be an Array of Arrays.
  # column_size must be the size of the first row, if there is one,
  # otherwise it *must* be specified and can be any integer >= 0
  @rows = rows
  @column_size = column_size
end
            
row_vector(row) click to toggle source

Creates a single-row matrix where the values of that row are as given in row.

Matrix.row_vector([4,5,6])
  => 4 5 6
 
               # File matrix.rb, line 235
def Matrix.row_vector(row)
  row = convert_to_array(row)
  new [row]
end
            
rows(rows, copy = true) click to toggle source

Creates a matrix where rows is an array of arrays, each of which is a row of the matrix. If the optional argument copy is false, use the given arrays as the internal structure of the matrix without copying.

Matrix.rows([[25, 93], [-1, 66]])
   =>  25 93
       -1 66
 
               # File matrix.rb, line 131
def Matrix.rows(rows, copy = true)
  rows = convert_to_array(rows)
  rows.map! do |row|
    convert_to_array(row, copy)
  end
  size = (rows[0] || []).size
  rows.each do |row|
    Matrix.Raise ErrDimensionMismatch, "row size differs (#{row.size} should be #{size})" unless row.size == size
  end
  new rows, size
end
            
scalar(n, value) click to toggle source

Creates an n by n diagonal matrix where each diagonal element is value.

Matrix.scalar(2, 5)
  => 5 0
     0 5
 
               # File matrix.rb, line 201
def Matrix.scalar(n, value)
  Matrix.diagonal(*Array.new(n, value))
end
            
unit(n) click to toggle source
Alias for: identity
zero(n) click to toggle source

Creates an n by n zero matrix.

Matrix.zero(2)
  => 0 0
     0 0
 
               # File matrix.rb, line 225
def Matrix.zero(n)
  Matrix.scalar(n, 0)
end
            

Public Instance Methods

*(m) click to toggle source

Matrix multiplication.

Matrix[[2,4], [6,8]] * Matrix.identity(2)
  => 2 4
     6 8
 
               # File matrix.rb, line 532
def *(m) # m is matrix or vector or number
  case(m)
  when Numeric
    rows = @rows.collect {|row|
      row.collect {|e| e * m }
    }
    return new_matrix rows, column_size
  when Vector
    m = Matrix.column_vector(m)
    r = self * m
    return r.column(0)
  when Matrix
    Matrix.Raise ErrDimensionMismatch if column_size != m.row_size

    rows = Array.new(row_size) {|i|
      Array.new(m.column_size) {|j|
        (0 ... column_size).inject(0) do |vij, k|
          vij + self[i, k] * m[k, j]
        end
      }
    }
    return new_matrix rows, m.column_size
  else
    return apply_through_coercion(m, __method__)
  end
end
            
**(other) click to toggle source

Matrix exponentiation. Currently implemented for integer powers only. Equivalent to multiplying the matrix by itself N times.

Matrix[[7,6], [3,9]] ** 2
  => 67 96
     48 99
 
               # File matrix.rb, line 697
def ** (other)
  case other
  when Integer
    x = self
    if other <= 0
      x = self.inverse
      return Matrix.identity(self.column_size) if other == 0
      other = -other
    end
    z = nil
    loop do
      z = z ? z * x : x if other[0] == 1
      return z if (other >>= 1).zero?
      x *= x
    end
  when Float, Rational
    Matrix.Raise ErrOperationNotImplemented, "**", self.class, other.class
  else
    Matrix.Raise ErrOperationNotDefined, "**", self.class, other.class
  end
end
            
+(m) click to toggle source

Matrix addition.

Matrix.scalar(2,5) + Matrix[[1,0], [-4,7]]
  =>  6  0
     -4 12
 
               # File matrix.rb, line 565
def +(m)
  case m
  when Numeric
    Matrix.Raise ErrOperationNotDefined, "+", self.class, m.class
  when Vector
    m = Matrix.column_vector(m)
  when Matrix
  else
    return apply_through_coercion(m, __method__)
  end

  Matrix.Raise ErrDimensionMismatch unless row_size == m.row_size and column_size == m.column_size

  rows = Array.new(row_size) {|i|
    Array.new(column_size) {|j|
      self[i, j] + m[i, j]
    }
  }
  new_matrix rows, column_size
end
            
-(m) click to toggle source

Matrix subtraction.

Matrix[[1,5], [4,2]] - Matrix[[9,3], [-4,1]]
  => -8  2
      8  1
 
               # File matrix.rb, line 592
def -(m)
  case m
  when Numeric
    Matrix.Raise ErrOperationNotDefined, "-", self.class, m.class
  when Vector
    m = Matrix.column_vector(m)
  when Matrix
  else
    return apply_through_coercion(m, __method__)
  end

  Matrix.Raise ErrDimensionMismatch unless row_size == m.row_size and column_size == m.column_size

  rows = Array.new(row_size) {|i|
    Array.new(column_size) {|j|
      self[i, j] - m[i, j]
    }
  }
  new_matrix rows, column_size
end
            
/(other) click to toggle source

Matrix division (multiplication by the inverse).

Matrix[[7,6], [3,9]] / Matrix[[2,9], [3,1]]
  => -7  1
     -3 -6
 
               # File matrix.rb, line 619
def /(other)
  case other
  when Numeric
    rows = @rows.collect {|row|
      row.collect {|e| e / other }
    }
    return new_matrix rows, column_size
  when Matrix
    return self * other.inverse
  else
    return apply_through_coercion(other, __method__)
  end
end
            
==(other) click to toggle source

Returns true if and only if the two matrices contain equal elements.

 
               # File matrix.rb, line 494
def ==(other)
  return false unless Matrix === other &&
                      column_size == other.column_size # necessary for empty matrices
  rows == other.rows
end
            
[](i, j) click to toggle source

Returns element (i,j) of the matrix. That is: row i, column j.

 
               # File matrix.rb, line 292
def [](i, j)
  @rows.fetch(i){return nil}[j]
end
            
Also aliased as: element, component
clone() click to toggle source

Returns a clone of the matrix, so that the contents of each do not reference identical objects. There should be no good reason to do this since Matrices are immutable.

 
               # File matrix.rb, line 511
def clone
  new_matrix @rows.map(&:dup), column_size
end
            
coerce(other) click to toggle source

The coerce method provides support for Ruby type coercion. This coercion mechanism is used by Ruby to handle mixed-type numeric operations: it is intended to find a compatible common type between the two operands of the operator. See also Numeric#coerce.

 
               # File matrix.rb, line 964
def coerce(other)
  case other
  when Numeric
    return Scalar.new(other), self
  else
    raise TypeError, "#{self.class} can't be coerced into #{other.class}"
  end
end
            
collect() click to toggle source

Returns a matrix that is the result of iteration of the given block over all elements of the matrix.

Matrix[ [1,2], [3,4] ].collect { |e| e**2 }
  => 1  4
     9 16
 
               # File matrix.rb, line 358
def collect(&block) # :yield: e
  return to_enum(:collect) unless block_given?
  rows = @rows.collect{|row| row.collect(&block)}
  new_matrix rows, column_size
end
            
Also aliased as: map
column(j) click to toggle source

Returns column vector number j of the matrix as a Vector (starting at 0 like an array). When a block is given, the elements of that vector are iterated.

 
               # File matrix.rb, line 335
def column(j) # :yield: e
  if block_given?
    return self if j >= column_size || j < -column_size
    row_size.times do |i|
      yield @rows[i][j]
    end
    self
  else
    return nil if j >= column_size || j < -column_size
    col = Array.new(row_size) {|i|
      @rows[i][j]
    }
    Vector.elements(col, false)
  end
end
            
column_vectors() click to toggle source

Returns an array of the column vectors of the matrix. See Vector.

 
               # File matrix.rb, line 985
def column_vectors
  Array.new(column_size) {|i|
    column(i)
  }
end
            
component(i, j) click to toggle source
Alias for: []
conj() click to toggle source
Alias for: conjugate
conjugate() click to toggle source

Returns the conjugate of the matrix.

Matrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]]
  => 1+2i   i  0
        1   2  3
Matrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]].conjugate
  => 1-2i  -i  0
        1   2  3
 
               # File matrix.rb, line 910
def conjugate
  collect(&:conjugate)
end
            
Also aliased as: conj
det() click to toggle source
Alias for: determinant
det_e() click to toggle source
Alias for: determinant_e
determinant() click to toggle source

Returns the determinant of the matrix.

Beware that using Float values can yield erroneous results because of their lack of precision. Consider using exact types like Rational or BigDecimal instead.

Matrix[[7,6], [3,9]].determinant
  => 45
 
               # File matrix.rb, line 733
def determinant
  Matrix.Raise ErrDimensionMismatch unless square?
  m = @rows
  case row_size
    # Up to 4x4, give result using Laplacian expansion by minors.
    # This will typically be faster, as well as giving good results
    # in case of Floats
  when 0
    +1
  when 1
    + m[0][0]
  when 2
    + m[0][0] * m[1][1] - m[0][1] * m[1][0]
  when 3
    m0, m1, m2 = m
    + m0[0] * m1[1] * m2[2] - m0[0] * m1[2] * m2[1]        - m0[1] * m1[0] * m2[2] + m0[1] * m1[2] * m2[0]        + m0[2] * m1[0] * m2[1] - m0[2] * m1[1] * m2[0]
  when 4
    m0, m1, m2, m3 = m
    + m0[0] * m1[1] * m2[2] * m3[3] - m0[0] * m1[1] * m2[3] * m3[2]        - m0[0] * m1[2] * m2[1] * m3[3] + m0[0] * m1[2] * m2[3] * m3[1]        + m0[0] * m1[3] * m2[1] * m3[2] - m0[0] * m1[3] * m2[2] * m3[1]        - m0[1] * m1[0] * m2[2] * m3[3] + m0[1] * m1[0] * m2[3] * m3[2]        + m0[1] * m1[2] * m2[0] * m3[3] - m0[1] * m1[2] * m2[3] * m3[0]        - m0[1] * m1[3] * m2[0] * m3[2] + m0[1] * m1[3] * m2[2] * m3[0]        + m0[2] * m1[0] * m2[1] * m3[3] - m0[2] * m1[0] * m2[3] * m3[1]        - m0[2] * m1[1] * m2[0] * m3[3] + m0[2] * m1[1] * m2[3] * m3[0]        + m0[2] * m1[3] * m2[0] * m3[1] - m0[2] * m1[3] * m2[1] * m3[0]        - m0[3] * m1[0] * m2[1] * m3[2] + m0[3] * m1[0] * m2[2] * m3[1]        + m0[3] * m1[1] * m2[0] * m3[2] - m0[3] * m1[1] * m2[2] * m3[0]        - m0[3] * m1[2] * m2[0] * m3[1] + m0[3] * m1[2] * m2[1] * m3[0]
  else
    # For bigger matrices, use an efficient and general algorithm.
    # Currently, we use the Gauss-Bareiss algorithm
    determinant_bareiss
  end
end
            
Also aliased as: det
determinant_e() click to toggle source

deprecated; use #determinant

 
               # File matrix.rb, line 815
def determinant_e
  warn "#{caller(1)[0]}: warning: Matrix#determinant_e is deprecated; use #determinant"
  rank
end
            
Also aliased as: det_e
each() click to toggle source

Yields all elements of the matrix, starting with those of the first row, or returns an Enumerator is no block given

Matrix[ [1,2], [3,4] ].each { |e| puts e }
  # => prints the numbers 1 to 4
 
               # File matrix.rb, line 371
def each(&block) # :yield: e
  return to_enum(:each) unless block_given?
  @rows.each do |row|
    row.each(&block)
  end
  self
end
            
each_with_index() click to toggle source

Yields all elements of the matrix, starting with those of the first row, along with the row index and column index, or returns an Enumerator is no block given

Matrix[ [1,2], [3,4] ].each_with_index do |e, row, col|
  puts "#{e} at #{row}, #{col}"
end
  # => 1 at 0, 0
  # => 2 at 0, 1
  # => 3 at 1, 0
  # => 4 at 1, 1
 
               # File matrix.rb, line 391
def each_with_index(&block) # :yield: e, row, column
  return to_enum(:each_with_index) unless block_given?
  @rows.each_with_index do |row, row_index|
    row.each_with_index do |e, col_index|
      yield e, row_index, col_index
    end
  end
  self
end
            
element(i, j) click to toggle source
Alias for: []
elements_to_f() click to toggle source
 
               # File matrix.rb, line 998
def elements_to_f
  warn "#{caller(1)[0]}: warning: Matrix#elements_to_f is deprecated, use map(&:to_f)"
  map(&:to_f)
end
            
elements_to_i() click to toggle source
 
               # File matrix.rb, line 1003
def elements_to_i
  warn "#{caller(1)[0]}: warning: Matrix#elements_to_i is deprecated, use map(&:to_i)"
  map(&:to_i)
end
            
elements_to_r() click to toggle source
 
               # File matrix.rb, line 1008
def elements_to_r
  warn "#{caller(1)[0]}: warning: Matrix#elements_to_r is deprecated, use map(&:to_r)"
  map(&:to_r)
end
            
empty?() click to toggle source

Returns true if this is an empty matrix, i.e. if the number of rows or the number of columns is 0.

 
               # File matrix.rb, line 455
def empty?
  column_size == 0 || row_size == 0
end
            
eql?(other) click to toggle source
 
               # File matrix.rb, line 500
def eql?(other)
  return false unless Matrix === other &&
                      column_size == other.column_size # necessary for empty matrices
  rows.eql? other.rows
end
            
hash() click to toggle source

Returns a hash-code for the matrix.

 
               # File matrix.rb, line 518
def hash
  @rows.hash
end
            
imag() click to toggle source
Alias for: imaginary
imaginary() click to toggle source

Returns the imaginary part of the matrix.

Matrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]]
  => 1+2i  i  0
        1  2  3
Matrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]].imaginary
  =>   2i  i  0
        0  0  0
 
               # File matrix.rb, line 924
def imaginary
  collect(&:imaginary)
end
            
Also aliased as: imag
inspect() click to toggle source

Overrides Object#inspect

 
               # File matrix.rb, line 1033
def inspect
  if empty?
    "Matrix.empty(#{row_size}, #{column_size})"
  else
    "Matrix#{@rows.inspect}"
  end
end
            
inv() click to toggle source
Alias for: inverse
inverse() click to toggle source

Returns the inverse of the matrix.

Matrix[[-1, -1], [0, -1]].inverse
  => -1  1
      0 -1
 
               # File matrix.rb, line 639
def inverse
  Matrix.Raise ErrDimensionMismatch unless square?
  Matrix.I(row_size).send(:inverse_from, self)
end
            
Also aliased as: inv
map() click to toggle source
Alias for: collect
minor(*param) click to toggle source

Returns a section of the matrix. The parameters are either:

  • start_row, nrows, start_col, ncols; OR

  • row_range, col_range

Matrix.diagonal(9, 5, -3).minor(0..1, 0..2)
  => 9 0 0
     0 5 0

Like Array#[], negative indices count backward from the end of the row or column (-1 is the last element). Returns nil if the starting row or column is greater than #row_size or #column_size respectively.

 
               # File matrix.rb, line 414
def minor(*param)
  case param.size
  when 2
    row_range, col_range = param
    from_row = row_range.first
    from_row += row_size if from_row < 0
    to_row = row_range.end
    to_row += row_size if to_row < 0
    to_row += 1 unless row_range.exclude_end?
    size_row = to_row - from_row

    from_col = col_range.first
    from_col += column_size if from_col < 0
    to_col = col_range.end
    to_col += column_size if to_col < 0
    to_col += 1 unless col_range.exclude_end?
    size_col = to_col - from_col
  when 4
    from_row, size_row, from_col, size_col = param
    return nil if size_row < 0 || size_col < 0
    from_row += row_size if from_row < 0
    from_col += column_size if from_col < 0
  else
    Matrix.Raise ArgumentError, param.inspect
  end

  return nil if from_row > row_size || from_col > column_size || from_row < 0 || from_col < 0
  rows = @rows[from_row, size_row].collect{|row|
    row[from_col, size_col]
  }
  new_matrix rows, [column_size - from_col, size_col].min
end
            
rank() click to toggle source

Returns the rank of the matrix. Beware that using Float values can yield erroneous results because of their lack of precision. Consider using exact types like Rational or BigDecimal instead.

Matrix[[7,6], [3,9]].rank
  => 2
 
               # File matrix.rb, line 830
def rank
  # We currently use Bareiss' multistep integer-preserving gaussian elimination
  # (see comments on determinant)
  a = to_a
  last_column = column_size - 1
  last_row = row_size - 1
  rank = 0
  pivot_row = 0
  previous_pivot = 1
  0.upto(last_column) do |k|
    switch_row = (pivot_row .. last_row).find {|row|
      a[row][k] != 0
    }
    if switch_row
      a[switch_row], a[pivot_row] = a[pivot_row], a[switch_row] unless pivot_row == switch_row
      pivot = a[pivot_row][k]
      (pivot_row+1).upto(last_row) do |i|
         ai = a[i]
         (k+1).upto(last_column) do |j|
           ai[j] =  (pivot * ai[j] - ai[k] * a[pivot_row][j]) / previous_pivot
         end
       end
      pivot_row += 1
      previous_pivot = pivot
    end
  end
  pivot_row
end
            
rank_e() click to toggle source

deprecated; use #rank

 
               # File matrix.rb, line 862
def rank_e
  warn "#{caller(1)[0]}: warning: Matrix#rank_e is deprecated; use #rank"
  rank
end
            
real() click to toggle source

Returns the real part of the matrix.

Matrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]]
  => 1+2i  i  0
        1  2  3
Matrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]].real
  =>    1  0  0
        1  2  3
 
               # File matrix.rb, line 938
def real
  collect(&:real)
end
            
real?() click to toggle source

Returns true if all entries of the matrix are real.

 
               # File matrix.rb, line 462
def real?
  all?(&:real?)
end
            
rect() click to toggle source

Returns an array containing matrices corresponding to the real and imaginary parts of the matrix

m.rect == [m.real, m.imag] # ==> true for all matrices m

 
               # File matrix.rb, line 948
def rect
  [real, imag]
end
            
Also aliased as: rectangular
rectangular() click to toggle source
Alias for: rect
regular?() click to toggle source

Returns true if this is a regular (i.e. non-singular) matrix.

 
               # File matrix.rb, line 469
def regular?
  not singular?
end
            
row(i) click to toggle source

Returns row vector number i of the matrix as a Vector (starting at 0 like an array). When a block is given, the elements of that vector are iterated.

 
               # File matrix.rb, line 321
def row(i, &block) # :yield: e
  if block_given?
    @rows.fetch(i){return self}.each(&block)
    self
  else
    Vector.elements(@rows.fetch(i){return nil})
  end
end
            
row_size() click to toggle source

Returns the number of rows.

 
               # File matrix.rb, line 308
def row_size
  @rows.size
end
            
row_vectors() click to toggle source

Returns an array of the row vectors of the matrix. See Vector.

 
               # File matrix.rb, line 976
def row_vectors
  Array.new(row_size) {|i|
    row(i)
  }
end
            
singular?() click to toggle source

Returns true is this is a singular matrix.

 
               # File matrix.rb, line 476
def singular?
  determinant == 0
end
            
square?() click to toggle source

Returns true is this is a square matrix.

 
               # File matrix.rb, line 483
def square?
  column_size == row_size
end
            
t() click to toggle source
Alias for: transpose
to_a() click to toggle source

Returns an array of arrays that describe the rows of the matrix.

 
               # File matrix.rb, line 994
def to_a
  @rows.collect(&:dup)
end
            
to_s() click to toggle source

Overrides Object#to_s

 
               # File matrix.rb, line 1020
def to_s
  if empty?
    "Matrix.empty(#{row_size}, #{column_size})"
  else
    "Matrix[" + @rows.collect{|row|
      "[" + row.collect{|e| e.to_s}.join(", ") + "]"
    }.join(", ")+"]"
  end
end
            
tr() click to toggle source
Alias for: trace
trace() click to toggle source

Returns the trace (sum of diagonal elements) of the matrix.

Matrix[[7,6], [3,9]].trace
  => 16
 
               # File matrix.rb, line 873
def trace
  Matrix.Raise ErrDimensionMismatch unless square?
  (0...column_size).inject(0) do |tr, i|
    tr + @rows[i][i]
  end
end
            
Also aliased as: tr
transpose() click to toggle source

Returns the transpose of the matrix.

Matrix[[1,2], [3,4], [5,6]]
  => 1 2
     3 4
     5 6
Matrix[[1,2], [3,4], [5,6]].transpose
  => 1 3 5
     2 4 6
 
               # File matrix.rb, line 891
def transpose
  return Matrix.empty(column_size, 0) if row_size.zero?
  new_matrix @rows.transpose, row_size
end
            
Also aliased as: t

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