[ruby-matrix] Update docs (nicer rendering, undocumented method)

lib/matrix.rb

@@ -72,8 +72,8 @@ class Matrix
   #
   # Creates a matrix where each argument is a row.
   #   Matrix[ [25, 93], [-1, 66] ]
-  #      =>  25 93
+  #   #   =>  25 93
-  #          -1 66
+  #   #       -1 66
   #
   def Matrix.[](*rows)
     rows(rows, false)
@@ -84,8 +84,8 @@ class Matrix
   # 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
+  #   #   =>  25 93
-  #          -1 66
+  #   #       -1 66
   #
   def Matrix.rows(rows, copy = true)
     rows = convert_to_array(rows, copy)
@@ -102,8 +102,8 @@ class Matrix
   #
   # Creates a matrix using +columns+ as an array of column vectors.
   #   Matrix.columns([[25, 93], [-1, 66]])
-  #      =>  25 -1
+  #   #   =>  25 -1
-  #          93 66
+  #   #       93 66
   #
   def Matrix.columns(columns)
     rows(columns, false).transpose
@@ -116,9 +116,9 @@ class Matrix
   # 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]]
+  #   #  => Matrix[[0, 1, 2, 3], [-1, 0, 1, 2]]
   #   m = Matrix.build(3) { rand }
-  #     => a 3x3 matrix with random elements
+  #   #  => a 3x3 matrix with random elements
   #
   def Matrix.build(row_count, column_count = row_count)
     row_count = CoercionHelper.coerce_to_int(row_count)
@@ -136,9 +136,9 @@ class Matrix
   #
   # Creates a matrix where the diagonal elements are composed of +values+.
   #   Matrix.diagonal(9, 5, -3)
-  #     =>  9  0  0
+  #   #  =>  9  0  0
-  #         0  5  0
+  #   #      0  5  0
-  #         0  0 -3
+  #   #      0  0 -3
   #
   def Matrix.diagonal(*values)
     size = values.size
@@ -155,8 +155,8 @@ class Matrix
   # Creates an +n+ by +n+ diagonal matrix where each diagonal element is
   # +value+.
   #   Matrix.scalar(2, 5)
-  #     => 5 0
+  #   #  => 5 0
-  #        0 5
+  #   #     0 5
   #
   def Matrix.scalar(n, value)
     diagonal(*Array.new(n, value))
@@ -165,8 +165,8 @@ class Matrix
   #
   # Creates an +n+ by +n+ identity matrix.
   #   Matrix.identity(2)
-  #     => 1 0
+  #   #  => 1 0
-  #        0 1
+  #   #     0 1
   #
   def Matrix.identity(n)
     scalar(n, 1)
@@ -179,8 +179,8 @@ class Matrix
   #
   # Creates a zero matrix.
   #   Matrix.zero(2)
-  #     => 0 0
+  #   #  => 0 0
-  #        0 0
+  #   #     0 0
   #
   def Matrix.zero(row_count, column_count = row_count)
     rows = Array.new(row_count){Array.new(column_count, 0)}
@@ -191,7 +191,7 @@ class Matrix
   # 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
+  #   #  => 4 5 6
   #
   def Matrix.row_vector(row)
     row = convert_to_array(row)
@@ -202,9 +202,9 @@ class Matrix
   # Creates a single-column matrix where the values of that column are as given
   # in +column+.
   #   Matrix.column_vector([4,5,6])
-  #     => 4
+  #   #  => 4
-  #        5
+  #   #     5
-  #        6
+  #   #     6
   #
   def Matrix.column_vector(column)
     column = convert_to_array(column)
@@ -217,12 +217,12 @@ class Matrix
   #
   #   m = Matrix.empty(2, 0)
   #   m == Matrix[ [], [] ]
-  #     => true
+  #   #  => true
   #   n = Matrix.empty(0, 3)
   #   n == Matrix.columns([ [], [], [] ])
-  #     => true
+  #   #  => true
   #   m * n
-  #     => Matrix[[0, 0, 0], [0, 0, 0]]
+  #   #  => Matrix[[0, 0, 0], [0, 0, 0]]
   #
   def Matrix.empty(row_count = 0, column_count = 0)
     raise ArgumentError, "One size must be 0" if column_count != 0 && row_count != 0
@@ -276,6 +276,8 @@ class Matrix
     new result, total_column_count
   end
 
+  # :call-seq:
+  #   Matrix.combine(*matrices) { |*elements| ... }
   #
   # Create a matrix by combining matrices entrywise, using the given block
   #
@@ -301,12 +303,21 @@ class Matrix
     new rows, x.column_count
   end
 
+  # :call-seq:
+  #   combine(*other_matrices) { |*elements| ... }
+  #
+  # Creates new matrix by combining with <i>other_matrices</i> entrywise,
+  # using the given block.
+  #
+  #   x = Matrix[[6, 6], [4, 4]]
+  #   y = Matrix[[1, 2], [3, 4]]
+  #   x.combine(y) {|a, b| a - b} # => Matrix[[5, 4], [1, 0]]
   def combine(*matrices, &block)
     Matrix.combine(self, *matrices, &block)
   end
 
   #
-  # Matrix.new is private; use Matrix.rows, columns, [], etc... to create.
+  # Matrix.new is private; use ::rows, ::columns, ::[], etc... to create.
   #
   def initialize(rows, column_count = rows[0].size)
     # No checking is done at this point. rows must be an Array of Arrays.
@@ -491,8 +502,8 @@ class Matrix
   # * :strict_upper: yields only elements above the diagonal
   # * :upper: yields only elements on or above the diagonal
   #   Matrix[ [1,2], [3,4] ].collect { |e| e**2 }
-  #     => 1  4
+  #   #  => 1  4
-  #        9 16
+  #   #     9 16
   #
   def collect(which = :all, &block) # :yield: e
     return to_enum(:collect, which) unless block_given?
@@ -537,9 +548,9 @@ class Matrix
   # * :strict_upper: yields only elements above the diagonal
   # * :upper: yields only elements on or above the diagonal
   #
-  #   Matrix[ [1,2], [3,4] ].each { |e| puts e }
+  #     Matrix[ [1,2], [3,4] ].each { |e| puts e }
-  #     # => prints the numbers 1 to 4
+  #       # => prints the numbers 1 to 4
-  #   Matrix[ [1,2], [3,4] ].each(:strict_lower).to_a # => [3]
+  #     Matrix[ [1,2], [3,4] ].each(:strict_lower).to_a # => [3]
   #
   def each(which = :all, &block) # :yield: e
     return to_enum :each, which unless block_given?
@@ -688,8 +699,8 @@ class Matrix
   # *  row_range, col_range
   #
   #   Matrix.diagonal(9, 5, -3).minor(0..1, 0..2)
-  #     => 9 0 0
+  #   #  => 9 0 0
-  #        0 5 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
@@ -732,9 +743,9 @@ class Matrix
   # Returns the submatrix obtained by deleting the specified row and column.
   #
   #   Matrix.diagonal(9, 5, -3, 4).first_minor(1, 2)
-  #     => 9 0 0
+  #   #  => 9 0 0
-  #        0 0 0
+  #   #     0 0 0
-  #        0 0 4
+  #   #     0 0 4
   #
   def first_minor(row, column)
     raise RuntimeError, "first_minor of empty matrix is not defined" if empty?
@@ -761,7 +772,7 @@ class Matrix
   # the first minor by (-1)**(row + column).
   #
   #   Matrix.diagonal(9, 5, -3, 4).cofactor(1, 1)
-  #     => -108
+  #   #  => -108
   #
   def cofactor(row, column)
     raise RuntimeError, "cofactor of empty matrix is not defined" if empty?
@@ -775,8 +786,8 @@ class Matrix
   # Returns the adjugate of the matrix.
   #
   #   Matrix[ [7,6],[3,9] ].adjugate
-  #     => 9 -6
+  #   #  => 9 -6
-  #        -3 7
+  #   #     -3 7
   #
   def adjugate
     raise ErrDimensionMismatch unless square?
@@ -789,10 +800,10 @@ class Matrix
   # Returns the Laplace expansion along given row or column.
   #
   #    Matrix[[7,6], [3,9]].laplace_expansion(column: 1)
-  #     => 45
+  #    # => 45
   #
   #    Matrix[[Vector[1, 0], Vector[0, 1]], [2, 3]].laplace_expansion(row: 0)
-  #     => Vector[3, -2]
+  #    # => Vector[3, -2]
   #
   #
   def laplace_expansion(row: nil, column: nil)
@@ -1039,8 +1050,8 @@ class Matrix
   #
   # Matrix multiplication.
   #   Matrix[[2,4], [6,8]] * Matrix.identity(2)
-  #     => 2 4
+  #   #  => 2 4
-  #        6 8
+  #   #     6 8
   #
   def *(m) # m is matrix or vector or number
     case(m)
@@ -1072,8 +1083,8 @@ class Matrix
   #
   # Matrix addition.
   #   Matrix.scalar(2,5) + Matrix[[1,0], [-4,7]]
-  #     =>  6  0
+  #   #  =>  6  0
-  #        -4 12
+  #   #     -4 12
   #
   def +(m)
     case m
@@ -1099,8 +1110,8 @@ class Matrix
   #
   # Matrix subtraction.
   #   Matrix[[1,5], [4,2]] - Matrix[[9,3], [-4,1]]
-  #     => -8  2
+  #   #  => -8  2
-  #         8  1
+  #   #      8  1
   #
   def -(m)
     case m
@@ -1126,8 +1137,8 @@ class Matrix
   #
   # Matrix division (multiplication by the inverse).
   #   Matrix[[7,6], [3,9]] / Matrix[[2,9], [3,1]]
-  #     => -7  1
+  #   #  => -7  1
-  #        -3 -6
+  #   #     -3 -6
   #
   def /(other)
     case other
@@ -1146,8 +1157,8 @@ class Matrix
   #
   # Hadamard product
   #    Matrix[[1,2], [3,4]].hadamard_product(Matrix[[1,2], [3,2]])
-  #      => 1  4
+  #    #  => 1  4
-  #         9  8
+  #    #     9  8
   #
   def hadamard_product(m)
     combine(m){|a, b| a * b}
@@ -1157,8 +1168,8 @@ class Matrix
   #
   # Returns the inverse of the matrix.
   #   Matrix[[-1, -1], [0, -1]].inverse
-  #     => -1  1
+  #   #  => -1  1
-  #         0 -1
+  #   #      0 -1
   #
   def inverse
     raise ErrDimensionMismatch unless square?
@@ -1216,8 +1227,8 @@ class Matrix
   # Non integer exponents will be handled by diagonalizing the matrix.
   #
   #   Matrix[[7,6], [3,9]] ** 2
-  #     => 67 96
+  #   #  => 67 96
-  #        48 99
+  #   #     48 99
   #
   def **(other)
     case other
@@ -1246,6 +1257,11 @@ class Matrix
     self
   end
 
+  # Unary matrix negation.
+  #
+  #   -Matrix[[1,5], [4,2]]
+  #   # => -1 -5
+  #   #    -4 -2
   def -@
     collect {|e| -e }
   end
@@ -1269,7 +1285,7 @@ class Matrix
   # Consider using exact types like Rational or BigDecimal instead.
   #
   #   Matrix[[7,6], [3,9]].determinant
-  #     => 45
+  #   #  => 45
   #
   def determinant
     raise ErrDimensionMismatch unless square?
@@ -1377,7 +1393,7 @@ class Matrix
   # Consider using exact types like Rational or BigDecimal instead.
   #
   #   Matrix[[7,6], [3,9]].rank
-  #     => 2
+  #   #  => 2
   #
   def rank
     # We currently use Bareiss' multistep integer-preserving gaussian elimination
@@ -1425,7 +1441,7 @@ class Matrix
   #
   # Returns the trace (sum of diagonal elements) of the matrix.
   #   Matrix[[7,6], [3,9]].trace
-  #     => 16
+  #   #  => 16
   #
   def trace
     raise ErrDimensionMismatch unless square?
@@ -1438,12 +1454,12 @@ class Matrix
   #
   # Returns the transpose of the matrix.
   #   Matrix[[1,2], [3,4], [5,6]]
-  #     => 1 2
+  #   #  => 1 2
-  #        3 4
+  #   #     3 4
-  #        5 6
+  #   #     5 6
   #   Matrix[[1,2], [3,4], [5,6]].transpose
-  #     => 1 3 5
+  #   #  => 1 3 5
-  #        2 4 6
+  #   #     2 4 6
   #
   def transpose
     return self.class.empty(column_count, 0) if row_count.zero?
@@ -1502,11 +1518,11 @@ class Matrix
   #
   # Returns the conjugate of the matrix.
   #   Matrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]]
-  #     => 1+2i   i  0
+  #   #  => 1+2i   i  0
-  #           1   2  3
+  #   #        1   2  3
   #   Matrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]].conjugate
-  #     => 1-2i  -i  0
+  #   #  => 1-2i  -i  0
-  #           1   2  3
+  #   #        1   2  3
   #
   def conjugate
     collect(&:conjugate)
@@ -1516,11 +1532,11 @@ class Matrix
   #
   # Returns the imaginary part of the matrix.
   #   Matrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]]
-  #     => 1+2i  i  0
+  #   #  => 1+2i  i  0
-  #           1  2  3
+  #   #        1  2  3
   #   Matrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]].imaginary
-  #     =>   2i  i  0
+  #   #  =>   2i  i  0
-  #           0  0  0
+  #   #        0  0  0
   #
   def imaginary
     collect(&:imaginary)
@@ -1530,11 +1546,11 @@ class Matrix
   #
   # Returns the real part of the matrix.
   #   Matrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]]
-  #     => 1+2i  i  0
+  #   #  => 1+2i  i  0
-  #           1  2  3
+  #   #        1  2  3
   #   Matrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]].real
-  #     =>    1  0  0
+  #   #  =>    1  0  0
-  #           1  2  3
+  #   #        1  2  3
   #
   def real
     collect(&:real)
@@ -1544,7 +1560,7 @@ class Matrix
   # 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
+  #   m.rect == [m.real, m.imag]  # ==> true for all matrices m
   #
   def rect
     [real, imag]
@@ -1605,7 +1621,7 @@ class Matrix
 
   # Deprecated.
   #
-  # Use map(&:to_f)
+  # Use <code>map(&:to_f)</code>
   def elements_to_f
     warn "Matrix#elements_to_f is deprecated, use map(&:to_f)", uplevel: 1
     map(&:to_f)
@@ -1613,7 +1629,7 @@ class Matrix
 
   # Deprecated.
   #
-  # Use map(&:to_i)
+  # Use <code>map(&:to_i)</code>
   def elements_to_i
     warn "Matrix#elements_to_i is deprecated, use map(&:to_i)", uplevel: 1
     map(&:to_i)
@@ -1621,7 +1637,7 @@ class Matrix
 
   # Deprecated.
   #
-  # Use map(&:to_r)
+  # Use <code>map(&:to_r)</code>
   def elements_to_r
     warn "Matrix#elements_to_r is deprecated, use map(&:to_r)", uplevel: 1
     map(&:to_r)
@@ -1857,8 +1873,8 @@ end
 # * #-@
 #
 # Vector functions:
-# * #inner_product(v), dot(v)
+# * #inner_product(v), #dot(v)
-# * #cross_product(v), cross(v)
+# * #cross_product(v), #cross(v)
 # * #collect
 # * #collect!
 # * #magnitude
@@ -1923,7 +1939,7 @@ class Vector
   #
   # Return a zero vector.
   #
-  #    Vector.zero(3) => Vector[0, 0, 0]
+  #    Vector.zero(3) # => Vector[0, 0, 0]
   #
   def Vector.zero(size)
     raise ArgumentError, "invalid size (#{size} for 0..)" if size < 0
@@ -2054,10 +2070,10 @@ class Vector
   # Returns +true+ iff all of vectors are linearly independent.
   #
   #   Vector.independent?(Vector[1,0], Vector[0,1])
-  #     => true
+  #   #  => true
   #
   #   Vector.independent?(Vector[1,2], Vector[2,4])
-  #     => false
+  #   #  => false
   #
   def Vector.independent?(*vs)
     vs.each do |v|
@@ -2072,10 +2088,10 @@ class Vector
   # Returns +true+ iff all of vectors are linearly independent.
   #
   #   Vector[1,0].independent?(Vector[0,1])
-  #     => true
+  #   # => true
   #
   #   Vector[1,2].independent?(Vector[2,4])
-  #     => false
+  #   # => false
   #
   def independent?(*vs)
     self.class.independent?(self, *vs)
@@ -2212,7 +2228,7 @@ class Vector
 
   #
   # Returns the inner product of this vector with the other.
-  #   Vector[4,7].inner_product Vector[10,1]  => 47
+  #   Vector[4,7].inner_product Vector[10,1] # => 47
   #
   def inner_product(v)
     raise ErrDimensionMismatch if size != v.size
@@ -2227,7 +2243,7 @@ class Vector
 
   #
   # Returns the cross product of this vector with the others.
-  #   Vector[1, 0, 0].cross_product Vector[0, 1, 0]   => Vector[0, 0, 1]
+  #   Vector[1, 0, 0].cross_product Vector[0, 1, 0]  # => Vector[0, 0, 1]
   #
   # It is generalized to other dimensions to return a vector perpendicular
   # to the arguments.
@@ -2282,7 +2298,7 @@ class Vector
 
   #
   # Returns the modulus (Pythagorean distance) of the vector.
-  #   Vector[5,8,2].r => 9.643650761
+  #   Vector[5,8,2].r # => 9.643650761
   #
   def magnitude
     Math.sqrt(@elements.inject(0) {|v, e| v + e.abs2})
@@ -2305,7 +2321,7 @@ class Vector
   # Returns a new vector with the same direction but with norm 1.
   #   v = Vector[5,8,2].normalize
   #   # => Vector[0.5184758473652127, 0.8295613557843402, 0.20739033894608505]
-  #   v.norm => 1.0
+  #   v.norm # => 1.0
   #
   def normalize
     n = magnitude