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lib/matrix.rb
402
lib/matrix.rb
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@ -183,6 +183,19 @@ module ExceptionForMatrix
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def_exception("ErrOperationNotDefined", "This operation(%s) can\\'t defined")
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end
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#
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# Represents a mathematical matrix, and provides methods for creating
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# special-case matrices (zero, identity, diagonal, singular, vector), operating
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# on them arithmetically and algebraically, and determining their mathematical
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# properties (trace, rank, inverse, determinant).
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#
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# The capabilities of the class indicated in the above paragraph are probably
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# not exhaustive. Browse the methods and their documentation for more
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# information.
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#
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# Note that although matrices should theoretically be rectangular, this is not
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# enforced by the class.
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#
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class Matrix
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@RCS_ID='-$Id: matrix.rb,v 1.11 1999/10/06 11:01:53 keiju Exp keiju $-'
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@ -192,14 +205,34 @@ class Matrix
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# instance creations
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private_class_method :new
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#
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# Creates a matrix where each argument is a row.
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# Matrix[ [25, 93], [-1, 66] ]
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# => 25 93
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# -1 66
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#
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def Matrix.[](*rows)
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new(:init_rows, rows, false)
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end
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#
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# Creates a matrix where +rows+ is an array of arrays, each of which is a row
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# to the matrix. If the optional argument +copy+ is false, use the given
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# arrays as the internal structure of the matrix without copying.
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# Matrix.rows([[25, 93], [-1, 66]])
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# => 25 93
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# -1 66
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def Matrix.rows(rows, copy = true)
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new(:init_rows, rows, copy)
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end
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#
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# Creates a matrix using +columns+ as an array of column vectors.
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# Matrix.columns([[25, 93], [-1, 66]])
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# => 25 -1
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# 93 66
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#
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#
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def Matrix.columns(columns)
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rows = (0 .. columns[0].size - 1).collect {
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|i|
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@ -211,6 +244,13 @@ class Matrix
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Matrix.rows(rows, false)
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end
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#
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# Creates a matrix where the diagonal elements are composed of +values+.
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# Matrix.diagonal(9, 5, -3)
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# => 9 0 0
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# 0 5 0
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# 0 0 -3
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#
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def Matrix.diagonal(*values)
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size = values.size
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rows = (0 .. size - 1).collect {
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@ -222,10 +262,23 @@ class Matrix
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rows(rows, false)
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end
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#
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# Creates an +n+ by +n+ diagonal matrix where each diagonal element is
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# +value+.
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# Matrix.scalar(2, 5)
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# => 5 0
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# 0 5
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#
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def Matrix.scalar(n, value)
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Matrix.diagonal(*Array.new(n).fill(value, 0, n))
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end
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#
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# Creates an +n+ by +n+ identity matrix.
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# Matrix.identity(2)
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# => 1 0
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# 0 1
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#
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def Matrix.identity(n)
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Matrix.scalar(n, 1)
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end
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@ -234,10 +287,22 @@ class Matrix
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alias I identity
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end
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#
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# Creates an +n+ by +n+ zero matrix.
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# Matrix.zero(2)
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# => 0 0
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# 0 0
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#
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def Matrix.zero(n)
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Matrix.scalar(n, 0)
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end
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#
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# Creates a single-row matrix where the values of that row are as given in
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# +row+.
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# Matrix.row_vector([4,5,6])
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# => 4 5 6
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#
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def Matrix.row_vector(row)
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case row
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when Vector
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@ -249,6 +314,14 @@ class Matrix
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end
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end
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#
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# Creates a single-column matrix where the values of that column are as given
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# in +column+.
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# Matrix.column_vector([4,5,6])
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# => 4
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# 5
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# 6
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#
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def Matrix.column_vector(column)
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case column
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when Vector
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@ -260,7 +333,10 @@ class Matrix
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end
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end
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# initializing
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#
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# This method is used by the other methods that create matrices, and is of no
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# use to general users.
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#
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def initialize(init_method, *argv)
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self.send(init_method, *argv)
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end
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@ -275,31 +351,50 @@ class Matrix
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end
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private :init_rows
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#accessing
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#
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# Returns element (+i+,+j+) of the matrix. That is: row +i+, column +j+.
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#
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def [](i, j)
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@rows[i][j]
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end
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#
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# Returns the number of rows.
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#
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def row_size
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@rows.size
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end
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#
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# Returns the number of columns. Note that it is possible to construct a
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# matrix with uneven columns (e.g. Matrix[ [1,2,3], [4,5] ]), but this is
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# mathematically unsound. This method uses the first row to determine the
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# result.
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#
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def column_size
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@rows[0].size
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end
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def row(i)
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#
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# Returns row vector number +i+ of the matrix as a Vector (starting at 0 like
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# an array). When a block is given, the elements of that vector are iterated.
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#
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def row(i) # :yield: e
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if block_given?
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for e in @rows[i]
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yield e
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end
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else
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Vector.elements(@rows[i])
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end
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end
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def column(j)
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#
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# Returns column vector number +j+ of the matrix as a Vector (starting at 0
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# like an array). When a block is given, the elements of that vector are
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# iterated.
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#
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def column(j) # :yield: e
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if block_given?
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0.upto(row_size - 1) do
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|i|
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@ -314,15 +409,27 @@ class Matrix
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end
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end
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def collect
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#
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# Returns a matrix that is the result of iteration of the given block over all
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# elements of the matrix.
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# Matrix[ [1,2], [3,4] ].collect { |i| i**2 }
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# => 1 4
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# 9 16
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#
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def collect # :yield: e
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rows = @rows.collect{|row| row.collect{|e| yield e}}
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Matrix.rows(rows, false)
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end
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alias map collect
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#
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# param: (from_row, row_size, from_col, size_col)
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# (from_row..to_row, from_col..to_col)
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# Returns a section of the matrix. The parameters are either:
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# * start_row, nrows, start_col, ncols; OR
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# * col_range, row_range
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#
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# Matrix.diagonal(9, 5, -3).minor(0..1, 0..2)
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# => 9 0 0
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# 0 5 0
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#
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def minor(*param)
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case param.size
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@ -346,21 +453,40 @@ class Matrix
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}
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Matrix.rows(rows, false)
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end
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# TESTING
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#--
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# TESTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
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#++
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#
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# Returns +true+ if this is a regular matrix.
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#
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def regular?
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square? and rank == column_size
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end
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#
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# Returns +true+ is this is a singular (i.e. non-regular) matrix.
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#
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def singular?
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not regular?
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end
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#
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# Returns +true+ is this is a square matrix. See note in column_size about this
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# being unreliable, though.
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#
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def square?
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column_size == row_size
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end
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# COMPARING
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#--
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# OBJECT METHODS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
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#++
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#
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# Returns +true+ if and only if the two matrices contain equal elements.
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#
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def ==(other)
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return false unless Matrix === other
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@ -368,6 +494,9 @@ class Matrix
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end
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alias eql? ==
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#
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# Not really intended for general consumption.
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#
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def compare_by_row_vectors(rows)
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return false unless @rows.size == rows.size
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|
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@ -378,10 +507,17 @@ class Matrix
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true
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end
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#
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# Returns a clone of the matrix, so that the contents of each do not reference
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# identical objects.
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#
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def clone
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Matrix.rows(@rows)
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end
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#
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# Returns a hash-code for the matrix.
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#
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def hash
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value = 0
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for row in @rows
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@ -392,8 +528,16 @@ class Matrix
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return value
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end
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# ARITHMETIC
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#--
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# ARITHMETIC -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
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#++
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#
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# Matrix multiplication.
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# Matrix[[2,4], [6,8]] * Matrix.identity(2)
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# => 2 4
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# 6 8
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#
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def *(m) # m is matrix or vector or number
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case(m)
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when Numeric
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@ -431,6 +575,12 @@ class Matrix
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end
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end
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#
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# Matrix addition.
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# Matrix.scalar(2,5) + Matrix[[1,0], [-4,7]]
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# => 6 0
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# -4 12
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#
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def +(m)
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case m
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when Numeric
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@ -455,6 +605,12 @@ class Matrix
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Matrix.rows(rows, false)
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end
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#
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# Matrix subtraction.
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# Matrix[[1,5], [4,2]] - Matrix[[9,3], [-4,1]]
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# => -8 2
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# 8 1
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#
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def -(m)
|
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case m
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when Numeric
|
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|
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@ -479,6 +635,12 @@ class Matrix
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Matrix.rows(rows, false)
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end
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#
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# Matrix division (multiplication by the inverse).
|
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# Matrix[[7,6], [3,9]] / Matrix[[2,9], [3,1]]
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# => -7 1
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# -3 -6
|
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#
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def /(other)
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case other
|
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when Numeric
|
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|
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@ -498,12 +660,21 @@ class Matrix
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end
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end
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|
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#
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# Returns the inverse of the matrix.
|
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# Matrix[[1, 2], [2, 1]].inverse
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# => -1 1
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# 0 -1
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#
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def inverse
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Matrix.Raise ErrDimensionMismatch unless square?
|
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Matrix.I(row_size).inverse_from(self)
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end
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alias inv inverse
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#
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# Not for public consumption?
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#
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def inverse_from(src)
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size = row_size - 1
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a = src.to_a
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|
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@ -547,6 +718,13 @@ class Matrix
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end
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#alias reciprocal inverse
|
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#
|
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# Matrix exponentiation. Defined for integer powers only. Equivalent to
|
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# multiplying the matrix by itself N times.
|
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# Matrix[[7,6], [3,9]] ** 2
|
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# => 67 96
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# 48 99
|
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#
|
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def ** (other)
|
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if other.kind_of?(Integer)
|
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x = self
|
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|
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@ -574,8 +752,16 @@ class Matrix
|
|||
end
|
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end
|
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|
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# Matrix functions
|
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#--
|
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# MATRIX FUNCTIONS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
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#++
|
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|
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#
|
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# Returns the determinant of the matrix. If the matrix is not square, the
|
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# result is 0.
|
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# Matrix[[7,6], [3,9]].determinant
|
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# => 63
|
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#
|
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def determinant
|
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return 0 unless square?
|
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|
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|
|
@ -608,6 +794,13 @@ class Matrix
|
|||
end
|
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alias det determinant
|
||||
|
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#
|
||||
# Returns the rank of the matrix. Beware that using Float values, with their
|
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# usual lack of precision, can affect the value returned by this method. Use
|
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# Rational values instead if this is important to you.
|
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# Matrix[[7,6], [3,9]].rank
|
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# => 2
|
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#
|
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def rank
|
||||
if column_size > row_size
|
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a = transpose.to_a
|
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|
|
@ -666,6 +859,11 @@ class Matrix
|
|||
return rank
|
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end
|
||||
|
||||
#
|
||||
# Returns the trace (sum of diagonal elements) of the matrix.
|
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# Matrix[[7,6], [3,9]].trace
|
||||
# => 16
|
||||
#
|
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def trace
|
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tr = 0
|
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0.upto(column_size - 1) do
|
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|
|
@ -676,13 +874,28 @@ class Matrix
|
|||
end
|
||||
alias tr trace
|
||||
|
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#
|
||||
# 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
|
||||
#
|
||||
def transpose
|
||||
Matrix.columns(@rows)
|
||||
end
|
||||
alias t transpose
|
||||
|
||||
# CONVERTING
|
||||
#--
|
||||
# CONVERTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
||||
#++
|
||||
|
||||
#
|
||||
# FIXME: describe #coerce.
|
||||
#
|
||||
def coerce(other)
|
||||
case other
|
||||
when Numeric
|
||||
|
|
@ -692,6 +905,9 @@ class Matrix
|
|||
end
|
||||
end
|
||||
|
||||
#
|
||||
# Returns an array of the row vectors of the matrix. See Vector.
|
||||
#
|
||||
def row_vectors
|
||||
rows = (0 .. row_size - 1).collect {
|
||||
|i|
|
||||
|
|
@ -700,6 +916,9 @@ class Matrix
|
|||
rows
|
||||
end
|
||||
|
||||
#
|
||||
# Returns an array of the column vectors of the matrix. See Vector.
|
||||
#
|
||||
def column_vectors
|
||||
columns = (0 .. column_size - 1).collect {
|
||||
|i|
|
||||
|
|
@ -708,23 +927,41 @@ class Matrix
|
|||
columns
|
||||
end
|
||||
|
||||
#
|
||||
# Returns an array of arrays that describe the rows of the matrix.
|
||||
#
|
||||
def to_a
|
||||
@rows.collect{|row| row.collect{|e| e}}
|
||||
end
|
||||
|
||||
#
|
||||
# Applies #to_f to all elements to return a new matrix.
|
||||
#
|
||||
def to_f
|
||||
collect{|e| e.to_f}
|
||||
end
|
||||
|
||||
#
|
||||
# Applies #to_i to all elements to return a new matrix.
|
||||
#
|
||||
def to_i
|
||||
collect{|e| e.to_i}
|
||||
end
|
||||
|
||||
#
|
||||
# Applies #to_r to all elements to return a new matrix.
|
||||
#
|
||||
def to_r
|
||||
collect{|e| e.to_r}
|
||||
end
|
||||
|
||||
# PRINTING
|
||||
#--
|
||||
# PRINTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
||||
#++
|
||||
|
||||
#
|
||||
# Overrides Object#to_s
|
||||
#
|
||||
def to_s
|
||||
"Matrix[" + @rows.collect{
|
||||
|row|
|
||||
|
|
@ -732,13 +969,16 @@ class Matrix
|
|||
}.join(", ")+"]"
|
||||
end
|
||||
|
||||
#
|
||||
# Overrides Object#inspect
|
||||
#
|
||||
def inspect
|
||||
"Matrix"+@rows.inspect
|
||||
end
|
||||
|
||||
# Private CLASS
|
||||
|
||||
class Scalar < Numeric
|
||||
class Scalar < Numeric # :nodoc:
|
||||
include ExceptionForMatrix
|
||||
|
||||
def initialize(value)
|
||||
|
|
@ -827,18 +1067,33 @@ class Vector
|
|||
#INSTANCE CREATION
|
||||
|
||||
private_class_method :new
|
||||
|
||||
#
|
||||
# Creates a Vector from a list of elements.
|
||||
# Vector[7, 4, ...]
|
||||
#
|
||||
def Vector.[](*array)
|
||||
new(:init_elements, array, copy = false)
|
||||
end
|
||||
|
||||
#
|
||||
# Creates a vector from an Array. The optional second argument specifies
|
||||
# whether the array itself or a copy is used internally.
|
||||
#
|
||||
def Vector.elements(array, copy = true)
|
||||
new(:init_elements, array, copy)
|
||||
end
|
||||
|
||||
#
|
||||
# For internal use.
|
||||
#
|
||||
def initialize(method, array, copy)
|
||||
self.send(method, array, copy)
|
||||
end
|
||||
|
||||
#
|
||||
# For internal use.
|
||||
#
|
||||
def init_elements(array, copy)
|
||||
if copy
|
||||
@elements = array.dup
|
||||
|
|
@ -849,16 +1104,28 @@ class Vector
|
|||
|
||||
# ACCSESSING
|
||||
|
||||
#
|
||||
# Returns element number +i+ (starting at zero) of the vector.
|
||||
#
|
||||
def [](i)
|
||||
@elements[i]
|
||||
end
|
||||
|
||||
#
|
||||
# Returns the number of elements in the vector.
|
||||
#
|
||||
def size
|
||||
@elements.size
|
||||
end
|
||||
|
||||
# ENUMRATIONS
|
||||
def each2(v)
|
||||
#--
|
||||
# ENUMRATIONS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
||||
#++
|
||||
|
||||
#
|
||||
# Iterate over the elements of this vector and +v+ in conjunction.
|
||||
#
|
||||
def each2(v) # :yield: e1, e2
|
||||
Vector.Raise ErrDimensionMismatch if size != v.size
|
||||
0.upto(size - 1) do
|
||||
|i|
|
||||
|
|
@ -866,7 +1133,11 @@ class Vector
|
|||
end
|
||||
end
|
||||
|
||||
def collect2(v)
|
||||
#
|
||||
# Collects (as in Enumerable#collect) over the elements of this vector and +v+
|
||||
# in conjunction.
|
||||
#
|
||||
def collect2(v) # :yield: e1, e2
|
||||
Vector.Raise ErrDimensionMismatch if size != v.size
|
||||
(0 .. size - 1).collect do
|
||||
|i|
|
||||
|
|
@ -874,7 +1145,13 @@ class Vector
|
|||
end
|
||||
end
|
||||
|
||||
# COMPARING
|
||||
#--
|
||||
# COMPARING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
||||
#++
|
||||
|
||||
#
|
||||
# Returns +true+ iff the two vectors have the same elements in the same order.
|
||||
#
|
||||
def ==(other)
|
||||
return false unless Vector === other
|
||||
|
||||
|
|
@ -882,21 +1159,35 @@ class Vector
|
|||
end
|
||||
alias eqn? ==
|
||||
|
||||
#
|
||||
# For internal use.
|
||||
#
|
||||
def compare_by(elements)
|
||||
@elements == elements
|
||||
end
|
||||
|
||||
#
|
||||
# Return a copy of the vector.
|
||||
#
|
||||
def clone
|
||||
Vector.elements(@elements)
|
||||
end
|
||||
|
||||
#
|
||||
# Return a hash-code for the vector.
|
||||
#
|
||||
def hash
|
||||
@elements.hash
|
||||
end
|
||||
|
||||
# ARITHMETIC
|
||||
#--
|
||||
# ARITHMETIC -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
||||
#++
|
||||
|
||||
def *(x) #x is matrix or number
|
||||
#
|
||||
# Multiplies the vector by +x+, where +x+ is a number or another vector.
|
||||
#
|
||||
def *(x)
|
||||
case x
|
||||
when Numeric
|
||||
els = @elements.collect{|e| e * x}
|
||||
|
|
@ -909,6 +1200,9 @@ class Vector
|
|||
end
|
||||
end
|
||||
|
||||
#
|
||||
# Vector addition.
|
||||
#
|
||||
def +(v)
|
||||
case v
|
||||
when Vector
|
||||
|
|
@ -926,6 +1220,9 @@ class Vector
|
|||
end
|
||||
end
|
||||
|
||||
#
|
||||
# Vector subtraction.
|
||||
#
|
||||
def -(v)
|
||||
case v
|
||||
when Vector
|
||||
|
|
@ -943,8 +1240,14 @@ class Vector
|
|||
end
|
||||
end
|
||||
|
||||
# VECTOR FUNCTIONS
|
||||
#--
|
||||
# VECTOR FUNCTIONS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
||||
#++
|
||||
|
||||
#
|
||||
# Returns the inner product of this vector with the other.
|
||||
# Vector[4,7].inner_product Vector[10,1] => 47
|
||||
#
|
||||
def inner_product(v)
|
||||
Vector.Raise ErrDimensionMismatch if size != v.size
|
||||
|
||||
|
|
@ -956,7 +1259,10 @@ class Vector
|
|||
p
|
||||
end
|
||||
|
||||
def collect
|
||||
#
|
||||
# Like Array#collect.
|
||||
#
|
||||
def collect # :yield: e
|
||||
els = @elements.collect {
|
||||
|v|
|
||||
yield v
|
||||
|
|
@ -965,7 +1271,10 @@ class Vector
|
|||
end
|
||||
alias map collect
|
||||
|
||||
def map2(v)
|
||||
#
|
||||
# Like Vector#collect2, but returns a Vector instead of an Array.
|
||||
#
|
||||
def map2(v) # :yield: e1, e2
|
||||
els = collect2(v) {
|
||||
|v1, v2|
|
||||
yield v1, v2
|
||||
|
|
@ -973,6 +1282,10 @@ class Vector
|
|||
Vector.elements(els, false)
|
||||
end
|
||||
|
||||
#
|
||||
# Returns the modulus (Pythagorean distance) of the vector.
|
||||
# Vector[5,8,2].r => 9.643650761
|
||||
#
|
||||
def r
|
||||
v = 0
|
||||
for e in @elements
|
||||
|
|
@ -981,27 +1294,48 @@ class Vector
|
|||
return Math.sqrt(v)
|
||||
end
|
||||
|
||||
#--
|
||||
# CONVERTING
|
||||
#++
|
||||
|
||||
#
|
||||
# Creates a single-row matrix from this vector.
|
||||
#
|
||||
def covector
|
||||
Matrix.row_vector(self)
|
||||
end
|
||||
|
||||
#
|
||||
# Returns the elements of the vector in an array.
|
||||
#
|
||||
def to_a
|
||||
@elements.dup
|
||||
end
|
||||
|
||||
#
|
||||
# Applies #to_f to each element to produce a new vector.
|
||||
#
|
||||
def to_f
|
||||
collect{|e| e.to_f}
|
||||
end
|
||||
|
||||
#
|
||||
# Applies #to_i to each element to produce a new vector.
|
||||
#
|
||||
def to_i
|
||||
collect{|e| e.to_i}
|
||||
end
|
||||
|
||||
#
|
||||
# Applies #to_f to each element to produce a new vector.
|
||||
#
|
||||
def to_r
|
||||
collect{|e| e.to_r}
|
||||
end
|
||||
|
||||
#
|
||||
# FIXME: describe Vector#coerce.
|
||||
#
|
||||
def coerce(other)
|
||||
case other
|
||||
when Numeric
|
||||
|
|
@ -1011,13 +1345,27 @@ class Vector
|
|||
end
|
||||
end
|
||||
|
||||
# PRINTING
|
||||
#--
|
||||
# PRINTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
||||
#++
|
||||
|
||||
#
|
||||
# Overrides Object#to_s
|
||||
#
|
||||
def to_s
|
||||
"Vector[" + @elements.join(", ") + "]"
|
||||
end
|
||||
|
||||
#
|
||||
# Overrides Object#inspect
|
||||
#
|
||||
def inspect
|
||||
str = "Vector"+@elements.inspect
|
||||
end
|
||||
end
|
||||
|
||||
|
||||
# Documentation comments:
|
||||
# - Matrix#coerce and Vector#coerce need to be documented
|
||||
# - Matrix class methods (aliases) unit and I don't appear in RDoc output
|
||||
# becuase of "class << Matrix". This is an RDoc issue.
|
||||
|
|
|
|||
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