2010-05-02 09:43:29 +04:00
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# encoding: utf-8
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2015-12-16 08:07:31 +03:00
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# frozen_string_literal: false
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1998-01-16 15:13:05 +03:00
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#
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2004-02-01 12:27:17 +03:00
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# = matrix.rb
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1998-01-16 15:13:05 +03:00
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#
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2004-02-01 12:27:17 +03:00
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# An implementation of Matrix and Vector classes.
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1999-01-20 07:59:39 +03:00
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#
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2009-03-06 06:56:38 +03:00
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# See classes Matrix and Vector for documentation.
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1999-01-20 07:59:39 +03:00
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#
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2010-05-02 09:43:29 +04:00
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# Current Maintainer:: Marc-André Lafortune
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# Original Author:: Keiju ISHITSUKA
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# Original Documentation:: Gavin Sinclair (sourced from <i>Ruby in a Nutshell</i> (Matsumoto, O'Reilly))
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##
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2004-02-01 12:27:17 +03:00
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1998-01-16 15:13:05 +03:00
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require "e2mmap.rb"
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2004-02-01 12:27:17 +03:00
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module ExceptionForMatrix # :nodoc:
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1999-08-13 09:45:20 +04:00
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extend Exception2MessageMapper
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1998-01-16 15:13:05 +03:00
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def_e2message(TypeError, "wrong argument type %s (expected %s)")
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def_e2message(ArgumentError, "Wrong # of arguments(%d for %d)")
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1999-08-13 09:45:20 +04:00
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def_exception("ErrDimensionMismatch", "\#{self.name} dimension mismatch")
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def_exception("ErrNotRegular", "Not Regular Matrix")
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def_exception("ErrOperationNotDefined", "Operation(%s) can\\'t be defined: %s op %s")
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def_exception("ErrOperationNotImplemented", "Sorry, Operation(%s) not implemented: %s op %s")
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1998-01-16 15:13:05 +03:00
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end
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#
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# The +Matrix+ class represents a mathematical matrix. It provides methods for creating
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# matrices, operating on them arithmetically and algebraically,
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# and determining their mathematical properties (trace, rank, inverse, determinant).
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#
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# == Method Catalogue
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#
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# To create a matrix:
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# * Matrix[*rows]
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# * Matrix.[](*rows)
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# * Matrix.rows(rows, copy = true)
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# * Matrix.columns(columns)
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# * Matrix.build(row_count, column_count, &block)
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# * Matrix.diagonal(*values)
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# * Matrix.scalar(n, value)
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# * Matrix.identity(n)
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# * Matrix.unit(n)
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# * Matrix.I(n)
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# * Matrix.zero(n)
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# * Matrix.row_vector(row)
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# * Matrix.column_vector(column)
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2015-05-21 11:29:32 +03:00
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# * Matrix.empty(row_count, column_count)
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2014-10-03 07:44:20 +04:00
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# * Matrix.hstack(*matrices)
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# * Matrix.vstack(*matrices)
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#
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# To access Matrix elements/columns/rows/submatrices/properties:
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# * #[](i, j)
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# * #row_count (row_size)
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# * #column_count (column_size)
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# * #row(i)
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# * #column(j)
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# * #collect
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# * #map
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# * #each
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# * #each_with_index
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# * #find_index
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# * #minor(*param)
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# * #first_minor(row, column)
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# * #cofactor(row, column)
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# * #adjugate
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# * #laplace_expansion(row_or_column: num)
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# * #cofactor_expansion(row_or_column: num)
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#
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# Properties of a matrix:
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# * #diagonal?
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# * #empty?
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# * #hermitian?
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# * #lower_triangular?
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# * #normal?
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# * #orthogonal?
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# * #permutation?
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# * #real?
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# * #regular?
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# * #singular?
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# * #square?
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# * #symmetric?
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# * #unitary?
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# * #upper_triangular?
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# * #zero?
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#
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# Matrix arithmetic:
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# * #*(m)
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# * #+(m)
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# * #-(m)
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# * #/(m)
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# * #inverse
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# * #inv
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# * #**
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# * #+@
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# * #-@
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#
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# Matrix functions:
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# * #determinant
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# * #det
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# * #hstack(*matrices)
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# * #rank
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# * #round
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# * #trace
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# * #tr
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# * #transpose
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# * #t
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# * #vstack(*matrices)
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#
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# Matrix decompositions:
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# * #eigen
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# * #eigensystem
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# * #lup
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# * #lup_decomposition
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#
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# Complex arithmetic:
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# * conj
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# * conjugate
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# * imag
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# * imaginary
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# * real
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# * rect
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# * rectangular
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#
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# Conversion to other data types:
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# * #coerce(other)
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# * #row_vectors
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# * #column_vectors
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# * #to_a
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#
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# String representations:
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# * #to_s
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# * #inspect
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#
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class Matrix
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include Enumerable
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include ExceptionForMatrix
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autoload :EigenvalueDecomposition, "matrix/eigenvalue_decomposition"
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autoload :LUPDecomposition, "matrix/lup_decomposition"
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1998-01-16 15:13:05 +03:00
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# instance creations
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private_class_method :new
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attr_reader :rows
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protected :rows
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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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rows(rows, false)
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end
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2003-01-20 10:16:01 +03:00
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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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# of 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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#
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2000-07-10 08:49:24 +04:00
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def Matrix.rows(rows, copy = true)
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rows = convert_to_array(rows, copy)
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rows.map! do |row|
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convert_to_array(row, copy)
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end
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size = (rows[0] || []).size
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rows.each do |row|
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raise ErrDimensionMismatch, "row size differs (#{row.size} should be #{size})" unless row.size == size
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end
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new rows, size
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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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def Matrix.columns(columns)
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rows(columns, false).transpose
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end
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#
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# Creates a matrix of size +row_count+ x +column_count+.
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# It fills the values by calling the given block,
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# passing the current row and column.
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# Returns an enumerator if no block is given.
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#
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# m = Matrix.build(2, 4) {|row, col| col - row }
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# => Matrix[[0, 1, 2, 3], [-1, 0, 1, 2]]
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# m = Matrix.build(3) { rand }
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# => a 3x3 matrix with random elements
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#
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def Matrix.build(row_count, column_count = row_count)
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row_count = CoercionHelper.coerce_to_int(row_count)
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column_count = CoercionHelper.coerce_to_int(column_count)
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raise ArgumentError if row_count < 0 || column_count < 0
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return to_enum :build, row_count, column_count unless block_given?
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rows = Array.new(row_count) do |i|
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Array.new(column_count) do |j|
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yield i, j
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end
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end
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new rows, column_count
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end
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2003-01-20 10:16:01 +03:00
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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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1998-01-16 15:13:05 +03:00
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def Matrix.diagonal(*values)
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size = values.size
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return Matrix.empty if size == 0
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rows = Array.new(size) {|j|
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row = Array.new(size, 0)
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row[j] = values[j]
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row
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}
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new rows
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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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diagonal(*Array.new(n, value))
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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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scalar(n, 1)
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end
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class << Matrix
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alias unit identity
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alias I identity
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end
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2003-01-20 10:16:01 +03:00
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#
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2011-06-29 05:13:22 +04:00
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# Creates a 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(row_count, column_count = row_count)
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rows = Array.new(row_count){Array.new(column_count, 0)}
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new rows, column_count
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end
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2003-01-20 10:16:01 +03:00
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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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1998-01-16 15:13:05 +03:00
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def Matrix.row_vector(row)
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row = convert_to_array(row)
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new [row]
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end
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2009-03-06 06:56:38 +03:00
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2003-01-20 10:16:01 +03:00
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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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column = convert_to_array(column)
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new [column].transpose, 1
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end
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#
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# Creates a empty matrix of +row_count+ x +column_count+.
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# At least one of +row_count+ or +column_count+ must be 0.
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2009-10-20 23:01:31 +04:00
|
|
|
#
|
|
|
|
# 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]]
|
2009-10-20 17:35:15 +04:00
|
|
|
#
|
2012-12-10 20:53:57 +04:00
|
|
|
def Matrix.empty(row_count = 0, column_count = 0)
|
2013-02-05 09:43:36 +04:00
|
|
|
raise ArgumentError, "One size must be 0" if column_count != 0 && row_count != 0
|
|
|
|
raise ArgumentError, "Negative size" if column_count < 0 || row_count < 0
|
2009-10-20 17:35:15 +04:00
|
|
|
|
2012-12-10 20:53:57 +04:00
|
|
|
new([[]]*row_count, column_count)
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
|
2014-10-03 07:44:20 +04:00
|
|
|
#
|
|
|
|
# Create a matrix by stacking matrices vertically
|
|
|
|
#
|
|
|
|
# x = Matrix[[1, 2], [3, 4]]
|
|
|
|
# y = Matrix[[5, 6], [7, 8]]
|
|
|
|
# Matrix.vstack(x, y) # => Matrix[[1, 2], [3, 4], [5, 6], [7, 8]]
|
|
|
|
#
|
|
|
|
def Matrix.vstack(x, *matrices)
|
|
|
|
raise TypeError, "Expected a Matrix, got a #{x.class}" unless x.is_a?(Matrix)
|
|
|
|
result = x.send(:rows).map(&:dup)
|
|
|
|
matrices.each do |m|
|
|
|
|
raise TypeError, "Expected a Matrix, got a #{m.class}" unless m.is_a?(Matrix)
|
|
|
|
if m.column_count != x.column_count
|
|
|
|
raise ErrDimensionMismatch, "The given matrices must have #{x.column_count} columns, but one has #{m.column_count}"
|
|
|
|
end
|
|
|
|
result.concat(m.send(:rows))
|
|
|
|
end
|
|
|
|
new result, x.column_count
|
|
|
|
end
|
|
|
|
|
|
|
|
|
|
|
|
#
|
|
|
|
# Create a matrix by stacking matrices horizontally
|
|
|
|
#
|
|
|
|
# x = Matrix[[1, 2], [3, 4]]
|
|
|
|
# y = Matrix[[5, 6], [7, 8]]
|
|
|
|
# Matrix.hstack(x, y) # => Matrix[[1, 2, 5, 6], [3, 4, 7, 8]]
|
|
|
|
#
|
|
|
|
def Matrix.hstack(x, *matrices)
|
|
|
|
raise TypeError, "Expected a Matrix, got a #{x.class}" unless x.is_a?(Matrix)
|
|
|
|
result = x.send(:rows).map(&:dup)
|
|
|
|
total_column_count = x.column_count
|
|
|
|
matrices.each do |m|
|
|
|
|
raise TypeError, "Expected a Matrix, got a #{m.class}" unless m.is_a?(Matrix)
|
|
|
|
if m.row_count != x.row_count
|
|
|
|
raise ErrDimensionMismatch, "The given matrices must have #{x.row_count} rows, but one has #{m.row_count}"
|
|
|
|
end
|
|
|
|
result.each_with_index do |row, i|
|
|
|
|
row.concat m.send(:rows)[i]
|
|
|
|
end
|
|
|
|
total_column_count += m.column_count
|
|
|
|
end
|
|
|
|
new result, total_column_count
|
|
|
|
end
|
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
2009-10-20 17:35:15 +04:00
|
|
|
# Matrix.new is private; use Matrix.rows, columns, [], etc... to create.
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
2012-12-10 20:53:57 +04:00
|
|
|
def initialize(rows, column_count = rows[0].size)
|
2009-10-20 17:35:15 +04:00
|
|
|
# No checking is done at this point. rows must be an Array of Arrays.
|
2012-12-10 20:53:57 +04:00
|
|
|
# column_count must be the size of the first row, if there is one,
|
2009-10-20 17:35:15 +04:00
|
|
|
# otherwise it *must* be specified and can be any integer >= 0
|
|
|
|
@rows = rows
|
2012-12-10 20:53:57 +04:00
|
|
|
@column_count = column_count
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2012-12-10 20:53:57 +04:00
|
|
|
def new_matrix(rows, column_count = rows[0].size) # :nodoc:
|
|
|
|
self.class.send(:new, rows, column_count) # bypass privacy of Matrix.new
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2009-10-20 17:35:15 +04:00
|
|
|
private :new_matrix
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Returns element (+i+,+j+) of the matrix. That is: row +i+, column +j+.
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def [](i, j)
|
2009-10-20 17:35:15 +04:00
|
|
|
@rows.fetch(i){return nil}[j]
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2005-12-09 19:10:45 +03:00
|
|
|
alias element []
|
|
|
|
alias component []
|
|
|
|
|
|
|
|
def []=(i, j, v)
|
|
|
|
@rows[i][j] = v
|
|
|
|
end
|
|
|
|
alias set_element []=
|
|
|
|
alias set_component []=
|
|
|
|
private :[]=, :set_element, :set_component
|
1998-01-16 15:13:05 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Returns the number of rows.
|
|
|
|
#
|
2012-12-10 20:53:57 +04:00
|
|
|
def row_count
|
1998-01-16 15:13:05 +03:00
|
|
|
@rows.size
|
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2012-12-10 20:53:57 +04:00
|
|
|
alias_method :row_size, :row_count
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
2009-10-20 17:35:15 +04:00
|
|
|
# Returns the number of columns.
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
2012-12-10 20:53:57 +04:00
|
|
|
attr_reader :column_count
|
|
|
|
alias_method :column_size, :column_count
|
1998-01-16 15:13:05 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# 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.
|
|
|
|
#
|
2009-09-16 08:36:37 +04:00
|
|
|
def row(i, &block) # :yield: e
|
2000-06-28 12:31:35 +04:00
|
|
|
if block_given?
|
2009-10-20 17:35:15 +04:00
|
|
|
@rows.fetch(i){return self}.each(&block)
|
|
|
|
self
|
1998-01-16 15:13:05 +03:00
|
|
|
else
|
2009-10-20 17:35:15 +04:00
|
|
|
Vector.elements(@rows.fetch(i){return nil})
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
end
|
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# 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.
|
|
|
|
#
|
|
|
|
def column(j) # :yield: e
|
2000-06-28 12:31:35 +04:00
|
|
|
if block_given?
|
2012-12-10 20:53:57 +04:00
|
|
|
return self if j >= column_count || j < -column_count
|
|
|
|
row_count.times do |i|
|
2004-02-01 12:27:17 +03:00
|
|
|
yield @rows[i][j]
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2009-10-20 17:35:15 +04:00
|
|
|
self
|
1998-01-16 15:13:05 +03:00
|
|
|
else
|
2012-12-10 20:53:57 +04:00
|
|
|
return nil if j >= column_count || j < -column_count
|
|
|
|
col = Array.new(row_count) {|i|
|
2004-02-01 12:27:17 +03:00
|
|
|
@rows[i][j]
|
1998-01-16 15:13:05 +03:00
|
|
|
}
|
2000-07-10 08:49:24 +04:00
|
|
|
Vector.elements(col, false)
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Returns a matrix that is the result of iteration of the given block over all
|
|
|
|
# elements of the matrix.
|
2005-12-09 19:10:45 +03:00
|
|
|
# Matrix[ [1,2], [3,4] ].collect { |e| e**2 }
|
2003-01-20 10:16:01 +03:00
|
|
|
# => 1 4
|
|
|
|
# 9 16
|
|
|
|
#
|
2009-09-17 01:02:54 +04:00
|
|
|
def collect(&block) # :yield: e
|
2009-10-20 17:35:15 +04:00
|
|
|
return to_enum(:collect) unless block_given?
|
2009-09-17 01:02:54 +04:00
|
|
|
rows = @rows.collect{|row| row.collect(&block)}
|
2012-12-10 20:53:57 +04:00
|
|
|
new_matrix rows, column_count
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
alias map collect
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2010-04-01 22:04:14 +04:00
|
|
|
#
|
|
|
|
# Yields all elements of the matrix, starting with those of the first row,
|
2014-11-27 04:03:46 +03:00
|
|
|
# or returns an Enumerator if no block given.
|
2011-06-29 05:08:02 +04:00
|
|
|
# Elements can be restricted by passing an argument:
|
|
|
|
# * :all (default): yields all elements
|
|
|
|
# * :diagonal: yields only elements on the diagonal
|
|
|
|
# * :off_diagonal: yields all elements except on the diagonal
|
|
|
|
# * :lower: yields only elements on or below the diagonal
|
|
|
|
# * :strict_lower: yields only elements below the diagonal
|
|
|
|
# * :strict_upper: yields only elements above the diagonal
|
|
|
|
# * :upper: yields only elements on or above the diagonal
|
|
|
|
#
|
2010-04-01 22:04:14 +04:00
|
|
|
# Matrix[ [1,2], [3,4] ].each { |e| puts e }
|
|
|
|
# # => prints the numbers 1 to 4
|
2011-06-29 05:08:02 +04:00
|
|
|
# Matrix[ [1,2], [3,4] ].each(:strict_lower).to_a # => [3]
|
|
|
|
#
|
|
|
|
def each(which = :all) # :yield: e
|
|
|
|
return to_enum :each, which unless block_given?
|
2012-12-10 20:53:57 +04:00
|
|
|
last = column_count - 1
|
2011-06-29 05:08:02 +04:00
|
|
|
case which
|
|
|
|
when :all
|
|
|
|
block = Proc.new
|
|
|
|
@rows.each do |row|
|
|
|
|
row.each(&block)
|
|
|
|
end
|
|
|
|
when :diagonal
|
|
|
|
@rows.each_with_index do |row, row_index|
|
|
|
|
yield row.fetch(row_index){return self}
|
|
|
|
end
|
|
|
|
when :off_diagonal
|
|
|
|
@rows.each_with_index do |row, row_index|
|
2012-12-10 20:53:57 +04:00
|
|
|
column_count.times do |col_index|
|
2011-06-29 05:08:02 +04:00
|
|
|
yield row[col_index] unless row_index == col_index
|
|
|
|
end
|
|
|
|
end
|
|
|
|
when :lower
|
|
|
|
@rows.each_with_index do |row, row_index|
|
|
|
|
0.upto([row_index, last].min) do |col_index|
|
|
|
|
yield row[col_index]
|
|
|
|
end
|
|
|
|
end
|
|
|
|
when :strict_lower
|
|
|
|
@rows.each_with_index do |row, row_index|
|
2012-12-10 20:53:57 +04:00
|
|
|
[row_index, column_count].min.times do |col_index|
|
2011-06-29 05:08:02 +04:00
|
|
|
yield row[col_index]
|
|
|
|
end
|
|
|
|
end
|
|
|
|
when :strict_upper
|
|
|
|
@rows.each_with_index do |row, row_index|
|
|
|
|
(row_index+1).upto(last) do |col_index|
|
|
|
|
yield row[col_index]
|
|
|
|
end
|
|
|
|
end
|
|
|
|
when :upper
|
|
|
|
@rows.each_with_index do |row, row_index|
|
|
|
|
row_index.upto(last) do |col_index|
|
|
|
|
yield row[col_index]
|
|
|
|
end
|
|
|
|
end
|
|
|
|
else
|
2013-02-05 09:43:36 +04:00
|
|
|
raise ArgumentError, "expected #{which.inspect} to be one of :all, :diagonal, :off_diagonal, :lower, :strict_lower, :strict_upper or :upper"
|
2010-04-01 22:04:14 +04:00
|
|
|
end
|
|
|
|
self
|
|
|
|
end
|
|
|
|
|
|
|
|
#
|
2011-06-29 05:08:02 +04:00
|
|
|
# Same as #each, but the row index and column index in addition to the element
|
|
|
|
#
|
2010-04-01 22:04:14 +04:00
|
|
|
# Matrix[ [1,2], [3,4] ].each_with_index do |e, row, col|
|
|
|
|
# puts "#{e} at #{row}, #{col}"
|
|
|
|
# end
|
2011-06-29 05:08:02 +04:00
|
|
|
# # => Prints:
|
|
|
|
# # 1 at 0, 0
|
|
|
|
# # 2 at 0, 1
|
|
|
|
# # 3 at 1, 0
|
|
|
|
# # 4 at 1, 1
|
|
|
|
#
|
|
|
|
def each_with_index(which = :all) # :yield: e, row, column
|
|
|
|
return to_enum :each_with_index, which unless block_given?
|
2012-12-10 20:53:57 +04:00
|
|
|
last = column_count - 1
|
2011-06-29 05:08:02 +04:00
|
|
|
case which
|
|
|
|
when :all
|
|
|
|
@rows.each_with_index do |row, row_index|
|
|
|
|
row.each_with_index do |e, col_index|
|
|
|
|
yield e, row_index, col_index
|
|
|
|
end
|
|
|
|
end
|
|
|
|
when :diagonal
|
|
|
|
@rows.each_with_index do |row, row_index|
|
|
|
|
yield row.fetch(row_index){return self}, row_index, row_index
|
|
|
|
end
|
|
|
|
when :off_diagonal
|
|
|
|
@rows.each_with_index do |row, row_index|
|
2012-12-10 20:53:57 +04:00
|
|
|
column_count.times do |col_index|
|
2011-06-29 05:08:02 +04:00
|
|
|
yield row[col_index], row_index, col_index unless row_index == col_index
|
|
|
|
end
|
|
|
|
end
|
|
|
|
when :lower
|
|
|
|
@rows.each_with_index do |row, row_index|
|
|
|
|
0.upto([row_index, last].min) do |col_index|
|
|
|
|
yield row[col_index], row_index, col_index
|
|
|
|
end
|
2010-04-01 22:04:14 +04:00
|
|
|
end
|
2011-06-29 05:08:02 +04:00
|
|
|
when :strict_lower
|
|
|
|
@rows.each_with_index do |row, row_index|
|
2012-12-10 20:53:57 +04:00
|
|
|
[row_index, column_count].min.times do |col_index|
|
2011-06-29 05:08:02 +04:00
|
|
|
yield row[col_index], row_index, col_index
|
|
|
|
end
|
|
|
|
end
|
|
|
|
when :strict_upper
|
|
|
|
@rows.each_with_index do |row, row_index|
|
|
|
|
(row_index+1).upto(last) do |col_index|
|
|
|
|
yield row[col_index], row_index, col_index
|
|
|
|
end
|
|
|
|
end
|
|
|
|
when :upper
|
|
|
|
@rows.each_with_index do |row, row_index|
|
|
|
|
row_index.upto(last) do |col_index|
|
|
|
|
yield row[col_index], row_index, col_index
|
|
|
|
end
|
|
|
|
end
|
|
|
|
else
|
2013-02-05 09:43:36 +04:00
|
|
|
raise ArgumentError, "expected #{which.inspect} to be one of :all, :diagonal, :off_diagonal, :lower, :strict_lower, :strict_upper or :upper"
|
2010-04-01 22:04:14 +04:00
|
|
|
end
|
|
|
|
self
|
|
|
|
end
|
|
|
|
|
2011-06-29 05:09:46 +04:00
|
|
|
SELECTORS = {all: true, diagonal: true, off_diagonal: true, lower: true, strict_lower: true, strict_upper: true, upper: true}.freeze
|
|
|
|
#
|
|
|
|
# :call-seq:
|
|
|
|
# index(value, selector = :all) -> [row, column]
|
|
|
|
# index(selector = :all){ block } -> [row, column]
|
|
|
|
# index(selector = :all) -> an_enumerator
|
|
|
|
#
|
|
|
|
# The index method is specialized to return the index as [row, column]
|
|
|
|
# It also accepts an optional +selector+ argument, see #each for details.
|
|
|
|
#
|
|
|
|
# Matrix[ [1,2], [3,4] ].index(&:even?) # => [0, 1]
|
|
|
|
# Matrix[ [1,1], [1,1] ].index(1, :strict_lower) # => [1, 0]
|
|
|
|
#
|
|
|
|
def index(*args)
|
|
|
|
raise ArgumentError, "wrong number of arguments(#{args.size} for 0-2)" if args.size > 2
|
|
|
|
which = (args.size == 2 || SELECTORS.include?(args.last)) ? args.pop : :all
|
|
|
|
return to_enum :find_index, which, *args unless block_given? || args.size == 1
|
|
|
|
if args.size == 1
|
|
|
|
value = args.first
|
|
|
|
each_with_index(which) do |e, row_index, col_index|
|
|
|
|
return row_index, col_index if e == value
|
|
|
|
end
|
|
|
|
else
|
|
|
|
each_with_index(which) do |e, row_index, col_index|
|
|
|
|
return row_index, col_index if yield e
|
|
|
|
end
|
|
|
|
end
|
|
|
|
nil
|
|
|
|
end
|
|
|
|
alias_method :find_index, :index
|
2014-04-06 21:46:16 +04:00
|
|
|
|
1998-01-16 15:13:05 +03:00
|
|
|
#
|
2003-01-20 10:16:01 +03:00
|
|
|
# Returns a section of the matrix. The parameters are either:
|
|
|
|
# * start_row, nrows, start_col, ncols; OR
|
2010-05-02 09:43:29 +04:00
|
|
|
# * row_range, col_range
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Matrix.diagonal(9, 5, -3).minor(0..1, 0..2)
|
|
|
|
# => 9 0 0
|
|
|
|
# 0 5 0
|
1998-01-16 15:13:05 +03:00
|
|
|
#
|
2009-10-24 10:04:41 +04:00
|
|
|
# Like Array#[], negative indices count backward from the end of the
|
|
|
|
# row or column (-1 is the last element). Returns nil if the starting
|
2012-12-10 20:53:57 +04:00
|
|
|
# row or column is greater than row_count or column_count respectively.
|
2009-10-24 10:04:41 +04:00
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def minor(*param)
|
|
|
|
case param.size
|
|
|
|
when 2
|
2010-05-02 09:43:29 +04:00
|
|
|
row_range, col_range = param
|
|
|
|
from_row = row_range.first
|
2012-12-10 20:53:57 +04:00
|
|
|
from_row += row_count if from_row < 0
|
2010-05-02 09:43:29 +04:00
|
|
|
to_row = row_range.end
|
2012-12-10 20:53:57 +04:00
|
|
|
to_row += row_count if to_row < 0
|
2010-05-02 09:43:29 +04:00
|
|
|
to_row += 1 unless row_range.exclude_end?
|
2009-10-24 10:04:41 +04:00
|
|
|
size_row = to_row - from_row
|
2010-05-02 09:43:29 +04:00
|
|
|
|
|
|
|
from_col = col_range.first
|
2012-12-10 20:53:57 +04:00
|
|
|
from_col += column_count if from_col < 0
|
2010-05-02 09:43:29 +04:00
|
|
|
to_col = col_range.end
|
2012-12-10 20:53:57 +04:00
|
|
|
to_col += column_count if to_col < 0
|
2010-05-02 09:43:29 +04:00
|
|
|
to_col += 1 unless col_range.exclude_end?
|
2009-10-24 10:04:41 +04:00
|
|
|
size_col = to_col - from_col
|
1998-01-16 15:13:05 +03:00
|
|
|
when 4
|
2009-09-16 08:36:37 +04:00
|
|
|
from_row, size_row, from_col, size_col = param
|
2009-10-24 10:04:41 +04:00
|
|
|
return nil if size_row < 0 || size_col < 0
|
2012-12-10 20:53:57 +04:00
|
|
|
from_row += row_count if from_row < 0
|
|
|
|
from_col += column_count if from_col < 0
|
1998-01-16 15:13:05 +03:00
|
|
|
else
|
2013-02-05 09:43:36 +04:00
|
|
|
raise ArgumentError, param.inspect
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2012-12-10 20:53:57 +04:00
|
|
|
return nil if from_row > row_count || from_col > column_count || from_row < 0 || from_col < 0
|
2008-12-18 10:54:50 +03:00
|
|
|
rows = @rows[from_row, size_row].collect{|row|
|
1998-01-16 15:13:05 +03:00
|
|
|
row[from_col, size_col]
|
|
|
|
}
|
2012-12-10 20:53:57 +04:00
|
|
|
new_matrix rows, [column_count - from_col, size_col].min
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2014-04-06 21:45:54 +04:00
|
|
|
#
|
|
|
|
# Returns the submatrix obtained by deleting the specified row and column.
|
|
|
|
#
|
|
|
|
# Matrix.diagonal(9, 5, -3, 4).first_minor(1, 2)
|
|
|
|
# => 9 0 0
|
|
|
|
# 0 0 0
|
|
|
|
# 0 0 4
|
|
|
|
#
|
|
|
|
def first_minor(row, column)
|
|
|
|
raise RuntimeError, "first_minor of empty matrix is not defined" if empty?
|
|
|
|
|
|
|
|
unless 0 <= row && row < row_count
|
|
|
|
raise ArgumentError, "invalid row (#{row.inspect} for 0..#{row_count - 1})"
|
|
|
|
end
|
|
|
|
|
|
|
|
unless 0 <= column && column < column_count
|
|
|
|
raise ArgumentError, "invalid column (#{column.inspect} for 0..#{column_count - 1})"
|
|
|
|
end
|
|
|
|
|
|
|
|
arrays = to_a
|
|
|
|
arrays.delete_at(row)
|
|
|
|
arrays.each do |array|
|
|
|
|
array.delete_at(column)
|
|
|
|
end
|
|
|
|
|
|
|
|
new_matrix arrays, column_count - 1
|
|
|
|
end
|
|
|
|
|
2014-04-06 21:46:16 +04:00
|
|
|
#
|
|
|
|
# Returns the (row, column) cofactor which is obtained by multiplying
|
|
|
|
# the first minor by (-1)**(row + column).
|
|
|
|
#
|
|
|
|
# Matrix.diagonal(9, 5, -3, 4).cofactor(1, 1)
|
|
|
|
# => -108
|
|
|
|
#
|
|
|
|
def cofactor(row, column)
|
|
|
|
raise RuntimeError, "cofactor of empty matrix is not defined" if empty?
|
|
|
|
Matrix.Raise ErrDimensionMismatch unless square?
|
|
|
|
|
|
|
|
det_of_minor = first_minor(row, column).determinant
|
|
|
|
det_of_minor * (-1) ** (row + column)
|
|
|
|
end
|
|
|
|
|
2014-10-29 05:43:28 +03:00
|
|
|
#
|
|
|
|
# Returns the adjugate of the matrix.
|
|
|
|
#
|
|
|
|
# Matrix[ [7,6],[3,9] ].adjugate
|
|
|
|
# => 9 -6
|
|
|
|
# -3 7
|
|
|
|
#
|
|
|
|
def adjugate
|
|
|
|
Matrix.Raise ErrDimensionMismatch unless square?
|
|
|
|
Matrix.build(row_count, column_count) do |row, column|
|
|
|
|
cofactor(column, row)
|
|
|
|
end
|
|
|
|
end
|
|
|
|
|
2014-10-07 23:30:48 +04:00
|
|
|
#
|
|
|
|
# Returns the Laplace expansion along given row or column.
|
|
|
|
#
|
|
|
|
# Matrix[[7,6], [3,9]].laplace_expansion(column: 1)
|
|
|
|
# => 45
|
|
|
|
#
|
|
|
|
# Matrix[[Vector[1, 0], Vector[0, 1]], [2, 3]].laplace_expansion(row: 0)
|
|
|
|
# => Vector[3, -2]
|
|
|
|
#
|
|
|
|
#
|
|
|
|
def laplace_expansion(row: nil, column: nil)
|
|
|
|
num = row || column
|
|
|
|
|
|
|
|
if !num || (row && column)
|
|
|
|
raise ArgumentError, "exactly one the row or column arguments must be specified"
|
|
|
|
end
|
|
|
|
|
|
|
|
Matrix.Raise ErrDimensionMismatch unless square?
|
|
|
|
raise RuntimeError, "laplace_expansion of empty matrix is not defined" if empty?
|
|
|
|
|
|
|
|
unless 0 <= num && num < row_count
|
|
|
|
raise ArgumentError, "invalid num (#{num.inspect} for 0..#{row_count - 1})"
|
|
|
|
end
|
|
|
|
|
|
|
|
send(row ? :row : :column, num).map.with_index { |e, k|
|
|
|
|
e * cofactor(*(row ? [num, k] : [k,num]))
|
|
|
|
}.inject(:+)
|
|
|
|
end
|
|
|
|
alias_method :cofactor_expansion, :laplace_expansion
|
|
|
|
|
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#--
|
|
|
|
# TESTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
|
|
|
#++
|
|
|
|
|
2011-06-29 05:11:19 +04:00
|
|
|
#
|
2014-09-25 02:54:10 +04:00
|
|
|
# Returns +true+ if this is a diagonal matrix.
|
2011-06-29 05:11:19 +04:00
|
|
|
# Raises an error if matrix is not square.
|
|
|
|
#
|
|
|
|
def diagonal?
|
|
|
|
Matrix.Raise ErrDimensionMismatch unless square?
|
|
|
|
each(:off_diagonal).all?(&:zero?)
|
|
|
|
end
|
|
|
|
|
2010-04-01 22:02:27 +04:00
|
|
|
#
|
|
|
|
# Returns +true+ if this is an empty matrix, i.e. if the number of rows
|
|
|
|
# or the number of columns is 0.
|
|
|
|
#
|
|
|
|
def empty?
|
2012-12-10 20:53:57 +04:00
|
|
|
column_count == 0 || row_count == 0
|
2010-04-01 22:02:27 +04:00
|
|
|
end
|
|
|
|
|
2011-06-29 05:11:19 +04:00
|
|
|
#
|
2014-09-25 02:54:10 +04:00
|
|
|
# Returns +true+ if this is an hermitian matrix.
|
2011-06-29 05:11:19 +04:00
|
|
|
# Raises an error if matrix is not square.
|
|
|
|
#
|
|
|
|
def hermitian?
|
|
|
|
Matrix.Raise ErrDimensionMismatch unless square?
|
2012-04-16 07:17:45 +04:00
|
|
|
each_with_index(:upper).all? do |e, row, col|
|
2011-06-29 05:11:19 +04:00
|
|
|
e == rows[col][row].conj
|
|
|
|
end
|
|
|
|
end
|
|
|
|
|
|
|
|
#
|
2014-09-25 02:54:10 +04:00
|
|
|
# Returns +true+ if this is a lower triangular matrix.
|
2011-06-29 05:11:19 +04:00
|
|
|
#
|
|
|
|
def lower_triangular?
|
|
|
|
each(:strict_upper).all?(&:zero?)
|
|
|
|
end
|
|
|
|
|
|
|
|
#
|
2014-09-25 02:54:10 +04:00
|
|
|
# Returns +true+ if this is a normal matrix.
|
2011-06-29 05:11:19 +04:00
|
|
|
# Raises an error if matrix is not square.
|
|
|
|
#
|
|
|
|
def normal?
|
|
|
|
Matrix.Raise ErrDimensionMismatch unless square?
|
|
|
|
rows.each_with_index do |row_i, i|
|
|
|
|
rows.each_with_index do |row_j, j|
|
|
|
|
s = 0
|
|
|
|
rows.each_with_index do |row_k, k|
|
|
|
|
s += row_i[k] * row_j[k].conj - row_k[i].conj * row_k[j]
|
|
|
|
end
|
|
|
|
return false unless s == 0
|
|
|
|
end
|
|
|
|
end
|
|
|
|
true
|
|
|
|
end
|
|
|
|
|
|
|
|
#
|
2014-09-25 02:54:10 +04:00
|
|
|
# Returns +true+ if this is an orthogonal matrix
|
2011-06-29 05:11:19 +04:00
|
|
|
# Raises an error if matrix is not square.
|
|
|
|
#
|
|
|
|
def orthogonal?
|
|
|
|
Matrix.Raise ErrDimensionMismatch unless square?
|
|
|
|
rows.each_with_index do |row, i|
|
2012-12-10 20:53:57 +04:00
|
|
|
column_count.times do |j|
|
2011-06-29 05:11:19 +04:00
|
|
|
s = 0
|
2012-12-10 20:53:57 +04:00
|
|
|
row_count.times do |k|
|
2011-06-29 05:11:19 +04:00
|
|
|
s += row[k] * rows[k][j]
|
|
|
|
end
|
|
|
|
return false unless s == (i == j ? 1 : 0)
|
|
|
|
end
|
|
|
|
end
|
|
|
|
true
|
|
|
|
end
|
|
|
|
|
|
|
|
#
|
2014-09-25 02:54:10 +04:00
|
|
|
# Returns +true+ if this is a permutation matrix
|
2011-06-29 05:11:19 +04:00
|
|
|
# Raises an error if matrix is not square.
|
|
|
|
#
|
|
|
|
def permutation?
|
|
|
|
Matrix.Raise ErrDimensionMismatch unless square?
|
2012-12-10 20:53:57 +04:00
|
|
|
cols = Array.new(column_count)
|
2011-06-29 05:11:19 +04:00
|
|
|
rows.each_with_index do |row, i|
|
|
|
|
found = false
|
|
|
|
row.each_with_index do |e, j|
|
|
|
|
if e == 1
|
|
|
|
return false if found || cols[j]
|
|
|
|
found = cols[j] = true
|
|
|
|
elsif e != 0
|
|
|
|
return false
|
|
|
|
end
|
|
|
|
end
|
|
|
|
return false unless found
|
|
|
|
end
|
|
|
|
true
|
|
|
|
end
|
|
|
|
|
2010-04-01 22:05:11 +04:00
|
|
|
#
|
|
|
|
# Returns +true+ if all entries of the matrix are real.
|
|
|
|
#
|
|
|
|
def real?
|
|
|
|
all?(&:real?)
|
|
|
|
end
|
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
2010-04-29 22:18:58 +04:00
|
|
|
# Returns +true+ if this is a regular (i.e. non-singular) matrix.
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def regular?
|
2010-04-29 22:18:58 +04:00
|
|
|
not singular?
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
2014-09-25 02:54:10 +04:00
|
|
|
# Returns +true+ if this is a singular matrix.
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def singular?
|
2010-04-29 22:18:58 +04:00
|
|
|
determinant == 0
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
2014-09-25 02:54:10 +04:00
|
|
|
# Returns +true+ if this is a square matrix.
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def square?
|
2012-12-10 20:53:57 +04:00
|
|
|
column_count == row_count
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2011-06-29 05:11:19 +04:00
|
|
|
#
|
2014-09-25 02:54:10 +04:00
|
|
|
# Returns +true+ if this is a symmetric matrix.
|
2011-06-29 05:11:19 +04:00
|
|
|
# Raises an error if matrix is not square.
|
|
|
|
#
|
|
|
|
def symmetric?
|
|
|
|
Matrix.Raise ErrDimensionMismatch unless square?
|
2011-12-30 10:04:04 +04:00
|
|
|
each_with_index(:strict_upper) do |e, row, col|
|
|
|
|
return false if e != rows[col][row]
|
2011-06-29 05:11:19 +04:00
|
|
|
end
|
2011-12-30 10:04:04 +04:00
|
|
|
true
|
2011-06-29 05:11:19 +04:00
|
|
|
end
|
|
|
|
|
|
|
|
#
|
2014-09-25 02:54:10 +04:00
|
|
|
# Returns +true+ if this is a unitary matrix
|
2011-06-29 05:11:19 +04:00
|
|
|
# Raises an error if matrix is not square.
|
|
|
|
#
|
|
|
|
def unitary?
|
|
|
|
Matrix.Raise ErrDimensionMismatch unless square?
|
|
|
|
rows.each_with_index do |row, i|
|
2012-12-10 20:53:57 +04:00
|
|
|
column_count.times do |j|
|
2011-06-29 05:11:19 +04:00
|
|
|
s = 0
|
2012-12-10 20:53:57 +04:00
|
|
|
row_count.times do |k|
|
2011-06-29 05:11:19 +04:00
|
|
|
s += row[k].conj * rows[k][j]
|
|
|
|
end
|
|
|
|
return false unless s == (i == j ? 1 : 0)
|
|
|
|
end
|
|
|
|
end
|
|
|
|
true
|
|
|
|
end
|
|
|
|
|
|
|
|
#
|
2014-09-25 02:54:10 +04:00
|
|
|
# Returns +true+ if this is an upper triangular matrix.
|
2011-06-29 05:11:19 +04:00
|
|
|
#
|
|
|
|
def upper_triangular?
|
|
|
|
each(:strict_lower).all?(&:zero?)
|
|
|
|
end
|
|
|
|
|
|
|
|
#
|
2014-09-25 02:54:10 +04:00
|
|
|
# Returns +true+ if this is a matrix with only zero elements
|
2011-06-29 05:11:19 +04:00
|
|
|
#
|
|
|
|
def zero?
|
|
|
|
all?(&:zero?)
|
|
|
|
end
|
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#--
|
|
|
|
# OBJECT METHODS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
|
|
|
#++
|
|
|
|
|
|
|
|
#
|
|
|
|
# Returns +true+ if and only if the two matrices contain equal elements.
|
|
|
|
#
|
1999-01-20 07:59:39 +03:00
|
|
|
def ==(other)
|
2010-06-05 08:18:08 +04:00
|
|
|
return false unless Matrix === other &&
|
2012-12-10 20:53:57 +04:00
|
|
|
column_count == other.column_count # necessary for empty matrices
|
2009-10-20 17:35:15 +04:00
|
|
|
rows == other.rows
|
1999-01-20 07:59:39 +03:00
|
|
|
end
|
2009-10-20 17:35:15 +04:00
|
|
|
|
2008-09-15 16:02:39 +04:00
|
|
|
def eql?(other)
|
2010-06-05 08:18:08 +04:00
|
|
|
return false unless Matrix === other &&
|
2012-12-10 20:53:57 +04:00
|
|
|
column_count == other.column_count # necessary for empty matrices
|
2009-10-20 17:35:15 +04:00
|
|
|
rows.eql? other.rows
|
2008-09-15 16:02:39 +04:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Returns a clone of the matrix, so that the contents of each do not reference
|
|
|
|
# identical objects.
|
2009-10-20 17:35:15 +04:00
|
|
|
# There should be no good reason to do this since Matrices are immutable.
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
1999-01-20 07:59:39 +03:00
|
|
|
def clone
|
2012-12-10 20:53:57 +04:00
|
|
|
new_matrix @rows.map(&:dup), column_count
|
1999-01-20 07:59:39 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Returns a hash-code for the matrix.
|
|
|
|
#
|
1999-01-20 07:59:39 +03:00
|
|
|
def hash
|
2009-09-16 08:36:37 +04:00
|
|
|
@rows.hash
|
1999-01-20 07:59:39 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#--
|
|
|
|
# ARITHMETIC -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
|
|
|
#++
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Matrix multiplication.
|
|
|
|
# Matrix[[2,4], [6,8]] * Matrix.identity(2)
|
|
|
|
# => 2 4
|
|
|
|
# 6 8
|
|
|
|
#
|
2001-11-03 16:41:57 +03:00
|
|
|
def *(m) # m is matrix or vector or number
|
1998-01-16 15:13:05 +03:00
|
|
|
case(m)
|
|
|
|
when Numeric
|
2008-12-18 10:54:50 +03:00
|
|
|
rows = @rows.collect {|row|
|
2010-06-05 08:17:44 +04:00
|
|
|
row.collect {|e| e * m }
|
1998-01-16 15:13:05 +03:00
|
|
|
}
|
2012-12-10 20:53:57 +04:00
|
|
|
return new_matrix rows, column_count
|
1998-01-16 15:13:05 +03:00
|
|
|
when Vector
|
2011-09-11 00:23:36 +04:00
|
|
|
m = self.class.column_vector(m)
|
1998-01-16 15:13:05 +03:00
|
|
|
r = self * m
|
|
|
|
return r.column(0)
|
|
|
|
when Matrix
|
2012-12-10 20:53:57 +04:00
|
|
|
Matrix.Raise ErrDimensionMismatch if column_count != m.row_count
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2012-12-10 20:53:57 +04:00
|
|
|
rows = Array.new(row_count) {|i|
|
|
|
|
Array.new(m.column_count) {|j|
|
|
|
|
(0 ... column_count).inject(0) do |vij, k|
|
2009-09-17 01:02:54 +04:00
|
|
|
vij + self[i, k] * m[k, j]
|
2004-02-01 12:27:17 +03:00
|
|
|
end
|
|
|
|
}
|
1998-01-16 15:13:05 +03:00
|
|
|
}
|
2012-12-10 20:53:57 +04:00
|
|
|
return new_matrix rows, m.column_count
|
1998-01-16 15:13:05 +03:00
|
|
|
else
|
2010-04-11 22:30:58 +04:00
|
|
|
return apply_through_coercion(m, __method__)
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Matrix addition.
|
|
|
|
# Matrix.scalar(2,5) + Matrix[[1,0], [-4,7]]
|
|
|
|
# => 6 0
|
|
|
|
# -4 12
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def +(m)
|
|
|
|
case m
|
|
|
|
when Numeric
|
2010-01-27 17:28:47 +03:00
|
|
|
Matrix.Raise ErrOperationNotDefined, "+", self.class, m.class
|
1998-01-16 15:13:05 +03:00
|
|
|
when Vector
|
2011-09-11 00:23:36 +04:00
|
|
|
m = self.class.column_vector(m)
|
1998-01-16 15:13:05 +03:00
|
|
|
when Matrix
|
|
|
|
else
|
2010-04-11 22:30:58 +04:00
|
|
|
return apply_through_coercion(m, __method__)
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2014-07-18 14:04:15 +04:00
|
|
|
Matrix.Raise ErrDimensionMismatch unless row_count == m.row_count && column_count == m.column_count
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2012-12-10 20:53:57 +04:00
|
|
|
rows = Array.new(row_count) {|i|
|
|
|
|
Array.new(column_count) {|j|
|
2004-02-01 12:27:17 +03:00
|
|
|
self[i, j] + m[i, j]
|
1998-01-16 15:13:05 +03:00
|
|
|
}
|
|
|
|
}
|
2012-12-10 20:53:57 +04:00
|
|
|
new_matrix rows, column_count
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Matrix subtraction.
|
|
|
|
# Matrix[[1,5], [4,2]] - Matrix[[9,3], [-4,1]]
|
|
|
|
# => -8 2
|
|
|
|
# 8 1
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def -(m)
|
|
|
|
case m
|
|
|
|
when Numeric
|
2010-01-27 17:28:47 +03:00
|
|
|
Matrix.Raise ErrOperationNotDefined, "-", self.class, m.class
|
1998-01-16 15:13:05 +03:00
|
|
|
when Vector
|
2011-09-11 00:23:36 +04:00
|
|
|
m = self.class.column_vector(m)
|
1998-01-16 15:13:05 +03:00
|
|
|
when Matrix
|
|
|
|
else
|
2010-04-11 22:30:58 +04:00
|
|
|
return apply_through_coercion(m, __method__)
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2014-07-18 14:04:15 +04:00
|
|
|
Matrix.Raise ErrDimensionMismatch unless row_count == m.row_count && column_count == m.column_count
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2012-12-10 20:53:57 +04:00
|
|
|
rows = Array.new(row_count) {|i|
|
|
|
|
Array.new(column_count) {|j|
|
2004-02-01 12:27:17 +03:00
|
|
|
self[i, j] - m[i, j]
|
1998-01-16 15:13:05 +03:00
|
|
|
}
|
|
|
|
}
|
2012-12-10 20:53:57 +04:00
|
|
|
new_matrix rows, column_count
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Matrix division (multiplication by the inverse).
|
|
|
|
# Matrix[[7,6], [3,9]] / Matrix[[2,9], [3,1]]
|
|
|
|
# => -7 1
|
|
|
|
# -3 -6
|
|
|
|
#
|
1999-01-20 07:59:39 +03:00
|
|
|
def /(other)
|
|
|
|
case other
|
|
|
|
when Numeric
|
2008-12-18 10:54:50 +03:00
|
|
|
rows = @rows.collect {|row|
|
2010-06-05 08:17:44 +04:00
|
|
|
row.collect {|e| e / other }
|
1999-01-20 07:59:39 +03:00
|
|
|
}
|
2012-12-10 20:53:57 +04:00
|
|
|
return new_matrix rows, column_count
|
1999-01-20 07:59:39 +03:00
|
|
|
when Matrix
|
|
|
|
return self * other.inverse
|
|
|
|
else
|
2010-04-11 22:30:58 +04:00
|
|
|
return apply_through_coercion(other, __method__)
|
1999-01-20 07:59:39 +03:00
|
|
|
end
|
|
|
|
end
|
1998-01-16 15:13:05 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Returns the inverse of the matrix.
|
2010-01-09 23:35:28 +03:00
|
|
|
# Matrix[[-1, -1], [0, -1]].inverse
|
2003-01-20 10:16:01 +03:00
|
|
|
# => -1 1
|
|
|
|
# 0 -1
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def inverse
|
1999-08-13 09:45:20 +04:00
|
|
|
Matrix.Raise ErrDimensionMismatch unless square?
|
2012-12-10 20:53:57 +04:00
|
|
|
self.class.I(row_count).send(:inverse_from, self)
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
alias inv inverse
|
2003-01-20 10:16:01 +03:00
|
|
|
|
2010-05-02 09:43:29 +04:00
|
|
|
def inverse_from(src) # :nodoc:
|
2012-12-10 20:53:57 +04:00
|
|
|
last = row_count - 1
|
1998-01-16 15:13:05 +03:00
|
|
|
a = src.to_a
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2010-05-02 09:43:29 +04:00
|
|
|
0.upto(last) do |k|
|
2007-03-19 08:39:07 +03:00
|
|
|
i = k
|
|
|
|
akk = a[k][k].abs
|
2010-05-02 09:43:29 +04:00
|
|
|
(k+1).upto(last) do |j|
|
2007-03-19 08:39:07 +03:00
|
|
|
v = a[j][k].abs
|
|
|
|
if v > akk
|
|
|
|
i = j
|
|
|
|
akk = v
|
|
|
|
end
|
|
|
|
end
|
|
|
|
Matrix.Raise ErrNotRegular if akk == 0
|
|
|
|
if i != k
|
2004-02-01 12:27:17 +03:00
|
|
|
a[i], a[k] = a[k], a[i]
|
|
|
|
@rows[i], @rows[k] = @rows[k], @rows[i]
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2007-03-19 08:39:07 +03:00
|
|
|
akk = a[k][k]
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2010-05-02 09:43:29 +04:00
|
|
|
0.upto(last) do |ii|
|
2010-01-26 01:08:29 +03:00
|
|
|
next if ii == k
|
|
|
|
q = a[ii][k].quo(akk)
|
|
|
|
a[ii][k] = 0
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2010-05-02 09:43:29 +04:00
|
|
|
(k + 1).upto(last) do |j|
|
2010-01-26 01:08:29 +03:00
|
|
|
a[ii][j] -= a[k][j] * q
|
2004-02-01 12:27:17 +03:00
|
|
|
end
|
2010-05-02 09:43:29 +04:00
|
|
|
0.upto(last) do |j|
|
2010-01-26 01:08:29 +03:00
|
|
|
@rows[ii][j] -= @rows[k][j] * q
|
2004-02-01 12:27:17 +03:00
|
|
|
end
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2010-05-02 09:43:29 +04:00
|
|
|
(k+1).upto(last) do |j|
|
2005-11-01 16:04:35 +03:00
|
|
|
a[k][j] = a[k][j].quo(akk)
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2010-05-02 09:43:29 +04:00
|
|
|
0.upto(last) do |j|
|
2005-11-01 16:04:35 +03:00
|
|
|
@rows[k][j] = @rows[k][j].quo(akk)
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
end
|
|
|
|
self
|
|
|
|
end
|
2010-05-02 09:43:29 +04:00
|
|
|
private :inverse_from
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
2011-07-01 10:21:24 +04:00
|
|
|
# Matrix exponentiation.
|
2010-05-02 09:43:29 +04:00
|
|
|
# Equivalent to multiplying the matrix by itself N times.
|
2011-07-01 10:21:24 +04:00
|
|
|
# Non integer exponents will be handled by diagonalizing the matrix.
|
|
|
|
#
|
2003-01-20 10:16:01 +03:00
|
|
|
# Matrix[[7,6], [3,9]] ** 2
|
|
|
|
# => 67 96
|
|
|
|
# 48 99
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def ** (other)
|
2010-05-02 09:43:29 +04:00
|
|
|
case other
|
|
|
|
when Integer
|
1998-01-16 15:13:05 +03:00
|
|
|
x = self
|
|
|
|
if other <= 0
|
2004-02-01 12:27:17 +03:00
|
|
|
x = self.inverse
|
2012-12-10 20:53:57 +04:00
|
|
|
return self.class.identity(self.column_count) if other == 0
|
2004-02-01 12:27:17 +03:00
|
|
|
other = -other
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2009-10-25 00:55:40 +04:00
|
|
|
z = nil
|
|
|
|
loop do
|
|
|
|
z = z ? z * x : x if other[0] == 1
|
|
|
|
return z if (other >>= 1).zero?
|
|
|
|
x *= x
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2011-07-01 10:21:24 +04:00
|
|
|
when Numeric
|
|
|
|
v, d, v_inv = eigensystem
|
2011-09-11 00:23:36 +04:00
|
|
|
v * self.class.diagonal(*d.each(:diagonal).map{|e| e ** other}) * v_inv
|
1998-01-16 15:13:05 +03:00
|
|
|
else
|
2010-01-27 17:28:47 +03:00
|
|
|
Matrix.Raise ErrOperationNotDefined, "**", self.class, other.class
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2014-10-08 00:18:35 +04:00
|
|
|
def +@
|
|
|
|
self
|
|
|
|
end
|
|
|
|
|
|
|
|
def -@
|
|
|
|
collect {|e| -e }
|
|
|
|
end
|
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#--
|
|
|
|
# MATRIX FUNCTIONS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
|
|
|
#++
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
2010-04-01 22:06:08 +04:00
|
|
|
# Returns the determinant of the matrix.
|
2010-04-29 22:19:12 +04:00
|
|
|
#
|
|
|
|
# Beware that using Float values can yield erroneous results
|
|
|
|
# because of their lack of precision.
|
|
|
|
# Consider using exact types like Rational or BigDecimal instead.
|
2005-12-09 19:10:45 +03:00
|
|
|
#
|
2003-01-20 10:16:01 +03:00
|
|
|
# Matrix[[7,6], [3,9]].determinant
|
2010-04-29 22:19:12 +04:00
|
|
|
# => 45
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def determinant
|
2010-04-01 22:06:08 +04:00
|
|
|
Matrix.Raise ErrDimensionMismatch unless square?
|
2010-04-29 22:19:12 +04:00
|
|
|
m = @rows
|
2012-12-10 20:53:57 +04:00
|
|
|
case row_count
|
2010-04-29 22:19:12 +04:00
|
|
|
# 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
|
2010-05-18 01:09:31 +04:00
|
|
|
m0, m1, m2 = m
|
2010-04-29 22:19:12 +04:00
|
|
|
+ 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
|
2010-05-18 01:09:31 +04:00
|
|
|
m0, m1, m2, m3 = m
|
2010-04-29 22:19:12 +04:00
|
|
|
+ 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
|
2008-12-18 10:54:50 +03:00
|
|
|
end
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2010-04-29 22:19:12 +04:00
|
|
|
alias_method :det, :determinant
|
2005-12-09 19:10:45 +03:00
|
|
|
|
|
|
|
#
|
2010-04-29 22:19:12 +04:00
|
|
|
# Private. Use Matrix#determinant
|
2005-12-09 19:10:45 +03:00
|
|
|
#
|
2010-04-29 22:19:12 +04:00
|
|
|
# Returns the determinant of the matrix, using
|
|
|
|
# Bareiss' multistep integer-preserving gaussian elimination.
|
|
|
|
# It has the same computational cost order O(n^3) as standard Gaussian elimination.
|
|
|
|
# Intermediate results are fraction free and of lower complexity.
|
|
|
|
# A matrix of Integers will have thus intermediate results that are also Integers,
|
2010-05-02 09:43:29 +04:00
|
|
|
# with smaller bignums (if any), while a matrix of Float will usually have
|
|
|
|
# intermediate results with better precision.
|
2005-12-09 19:10:45 +03:00
|
|
|
#
|
2010-04-29 22:19:12 +04:00
|
|
|
def determinant_bareiss
|
2012-12-10 20:53:57 +04:00
|
|
|
size = row_count
|
2010-04-29 22:19:12 +04:00
|
|
|
last = size - 1
|
2005-12-09 19:10:45 +03:00
|
|
|
a = to_a
|
2010-04-29 22:19:12 +04:00
|
|
|
no_pivot = Proc.new{ return 0 }
|
|
|
|
sign = +1
|
|
|
|
pivot = 1
|
2009-09-16 08:36:37 +04:00
|
|
|
size.times do |k|
|
2010-04-29 22:19:12 +04:00
|
|
|
previous_pivot = pivot
|
|
|
|
if (pivot = a[k][k]) == 0
|
|
|
|
switch = (k+1 ... size).find(no_pivot) {|row|
|
|
|
|
a[row][k] != 0
|
2009-09-17 01:02:54 +04:00
|
|
|
}
|
2010-04-29 22:19:12 +04:00
|
|
|
a[switch], a[k] = a[k], a[switch]
|
|
|
|
pivot = a[k][k]
|
|
|
|
sign = -sign
|
2005-12-09 19:10:45 +03:00
|
|
|
end
|
2010-04-29 22:19:12 +04:00
|
|
|
(k+1).upto(last) do |i|
|
|
|
|
ai = a[i]
|
|
|
|
(k+1).upto(last) do |j|
|
|
|
|
ai[j] = (pivot * ai[j] - ai[k] * a[k][j]) / previous_pivot
|
2005-12-09 19:10:45 +03:00
|
|
|
end
|
|
|
|
end
|
2008-12-18 10:54:50 +03:00
|
|
|
end
|
2010-04-29 22:19:12 +04:00
|
|
|
sign * pivot
|
|
|
|
end
|
|
|
|
private :determinant_bareiss
|
|
|
|
|
|
|
|
#
|
|
|
|
# deprecated; use Matrix#determinant
|
|
|
|
#
|
|
|
|
def determinant_e
|
|
|
|
warn "#{caller(1)[0]}: warning: Matrix#determinant_e is deprecated; use #determinant"
|
2012-10-28 22:21:17 +04:00
|
|
|
determinant
|
2005-12-09 19:10:45 +03:00
|
|
|
end
|
|
|
|
alias det_e determinant_e
|
|
|
|
|
2014-10-03 07:44:20 +04:00
|
|
|
#
|
|
|
|
# Returns a new matrix resulting by stacking horizontally
|
|
|
|
# the receiver with the given matrices
|
|
|
|
#
|
|
|
|
# x = Matrix[[1, 2], [3, 4]]
|
|
|
|
# y = Matrix[[5, 6], [7, 8]]
|
|
|
|
# x.hstack(y) # => Matrix[[1, 2, 5, 6], [3, 4, 7, 8]]
|
|
|
|
#
|
|
|
|
def hstack(*matrices)
|
|
|
|
self.class.hstack(self, *matrices)
|
|
|
|
end
|
|
|
|
|
2005-12-09 19:10:45 +03:00
|
|
|
#
|
2010-04-29 22:19:12 +04:00
|
|
|
# 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.
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Matrix[[7,6], [3,9]].rank
|
|
|
|
# => 2
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def rank
|
2010-04-29 22:19:12 +04:00
|
|
|
# We currently use Bareiss' multistep integer-preserving gaussian elimination
|
|
|
|
# (see comments on determinant)
|
|
|
|
a = to_a
|
2012-12-10 20:53:57 +04:00
|
|
|
last_column = column_count - 1
|
|
|
|
last_row = row_count - 1
|
2010-04-29 22:19:12 +04:00
|
|
|
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
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2009-09-16 08:36:37 +04:00
|
|
|
end
|
2010-04-29 22:19:12 +04:00
|
|
|
pivot_row
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
|
2005-12-09 19:10:45 +03:00
|
|
|
#
|
2010-04-29 22:19:12 +04:00
|
|
|
# deprecated; use Matrix#rank
|
2005-12-09 19:10:45 +03:00
|
|
|
#
|
|
|
|
def rank_e
|
2010-04-29 22:19:12 +04:00
|
|
|
warn "#{caller(1)[0]}: warning: Matrix#rank_e is deprecated; use #rank"
|
|
|
|
rank
|
2005-12-09 19:10:45 +03:00
|
|
|
end
|
|
|
|
|
2011-07-01 10:10:40 +04:00
|
|
|
# Returns a matrix with entries rounded to the given precision
|
|
|
|
# (see Float#round)
|
|
|
|
#
|
|
|
|
def round(ndigits=0)
|
|
|
|
map{|e| e.round(ndigits)}
|
|
|
|
end
|
2005-12-09 19:10:45 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Returns the trace (sum of diagonal elements) of the matrix.
|
|
|
|
# Matrix[[7,6], [3,9]].trace
|
|
|
|
# => 16
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def trace
|
2009-10-20 17:35:15 +04:00
|
|
|
Matrix.Raise ErrDimensionMismatch unless square?
|
2012-12-10 20:53:57 +04:00
|
|
|
(0...column_count).inject(0) do |tr, i|
|
2009-09-17 01:02:54 +04:00
|
|
|
tr + @rows[i][i]
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
end
|
|
|
|
alias tr trace
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# 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
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def transpose
|
2012-12-10 20:53:57 +04:00
|
|
|
return self.class.empty(column_count, 0) if row_count.zero?
|
|
|
|
new_matrix @rows.transpose, row_count
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
alias t transpose
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2014-10-03 07:44:20 +04:00
|
|
|
#
|
|
|
|
# Returns a new matrix resulting by stacking vertically
|
|
|
|
# the receiver with the given matrices
|
|
|
|
#
|
|
|
|
# x = Matrix[[1, 2], [3, 4]]
|
|
|
|
# y = Matrix[[5, 6], [7, 8]]
|
|
|
|
# x.vstack(y) # => Matrix[[1, 2], [3, 4], [5, 6], [7, 8]]
|
|
|
|
#
|
|
|
|
def vstack(*matrices)
|
|
|
|
self.class.vstack(self, *matrices)
|
|
|
|
end
|
|
|
|
|
2011-07-01 10:13:35 +04:00
|
|
|
#--
|
|
|
|
# DECOMPOSITIONS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
|
|
|
|
#++
|
|
|
|
|
|
|
|
#
|
|
|
|
# Returns the Eigensystem of the matrix; see +EigenvalueDecomposition+.
|
|
|
|
# m = Matrix[[1, 2], [3, 4]]
|
|
|
|
# v, d, v_inv = m.eigensystem
|
|
|
|
# d.diagonal? # => true
|
|
|
|
# v.inv == v_inv # => true
|
|
|
|
# (v * d * v_inv).round(5) == m # => true
|
|
|
|
#
|
|
|
|
def eigensystem
|
|
|
|
EigenvalueDecomposition.new(self)
|
|
|
|
end
|
|
|
|
alias eigen eigensystem
|
|
|
|
|
2011-07-01 10:23:12 +04:00
|
|
|
#
|
|
|
|
# Returns the LUP decomposition of the matrix; see +LUPDecomposition+.
|
|
|
|
# a = Matrix[[1, 2], [3, 4]]
|
|
|
|
# l, u, p = a.lup
|
|
|
|
# l.lower_triangular? # => true
|
|
|
|
# u.upper_triangular? # => true
|
|
|
|
# p.permutation? # => true
|
2012-12-17 21:36:56 +04:00
|
|
|
# l * u == p * a # => true
|
2011-07-01 10:23:12 +04:00
|
|
|
# a.lup.solve([2, 5]) # => Vector[(1/1), (1/2)]
|
|
|
|
#
|
|
|
|
def lup
|
|
|
|
LUPDecomposition.new(self)
|
|
|
|
end
|
|
|
|
alias lup_decomposition lup
|
|
|
|
|
2010-04-01 22:05:11 +04:00
|
|
|
#--
|
|
|
|
# COMPLEX ARITHMETIC -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
|
|
|
|
#++
|
|
|
|
|
|
|
|
#
|
|
|
|
# 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
|
|
|
|
#
|
|
|
|
def conjugate
|
|
|
|
collect(&:conjugate)
|
|
|
|
end
|
|
|
|
alias conj conjugate
|
|
|
|
|
|
|
|
#
|
|
|
|
# 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
|
|
|
|
#
|
|
|
|
def imaginary
|
|
|
|
collect(&:imaginary)
|
|
|
|
end
|
|
|
|
alias imag imaginary
|
|
|
|
|
|
|
|
#
|
|
|
|
# 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
|
|
|
|
#
|
|
|
|
def real
|
|
|
|
collect(&:real)
|
|
|
|
end
|
|
|
|
|
|
|
|
#
|
|
|
|
# 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
|
|
|
|
#
|
|
|
|
def rect
|
|
|
|
[real, imag]
|
|
|
|
end
|
|
|
|
alias rectangular rect
|
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#--
|
|
|
|
# CONVERTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
|
|
|
#++
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
2010-05-02 09:43:29 +04:00
|
|
|
# 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.
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def coerce(other)
|
|
|
|
case other
|
|
|
|
when Numeric
|
|
|
|
return Scalar.new(other), self
|
1999-08-13 09:45:20 +04:00
|
|
|
else
|
2002-10-02 20:45:35 +04:00
|
|
|
raise TypeError, "#{self.class} can't be coerced into #{other.class}"
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
end
|
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Returns an array of the row vectors of the matrix. See Vector.
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def row_vectors
|
2012-12-10 20:53:57 +04:00
|
|
|
Array.new(row_count) {|i|
|
1998-01-16 15:13:05 +03:00
|
|
|
row(i)
|
|
|
|
}
|
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Returns an array of the column vectors of the matrix. See Vector.
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def column_vectors
|
2012-12-10 20:53:57 +04:00
|
|
|
Array.new(column_count) {|i|
|
1998-01-16 15:13:05 +03:00
|
|
|
column(i)
|
|
|
|
}
|
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Returns an array of arrays that describe the rows of the matrix.
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def to_a
|
2010-06-05 08:17:44 +04:00
|
|
|
@rows.collect(&:dup)
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2005-12-09 19:10:45 +03:00
|
|
|
def elements_to_f
|
2010-05-02 09:43:29 +04:00
|
|
|
warn "#{caller(1)[0]}: warning: Matrix#elements_to_f is deprecated, use map(&:to_f)"
|
2010-04-11 22:45:58 +04:00
|
|
|
map(&:to_f)
|
2005-12-09 19:10:45 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2005-12-09 19:10:45 +03:00
|
|
|
def elements_to_i
|
2010-05-02 09:43:29 +04:00
|
|
|
warn "#{caller(1)[0]}: warning: Matrix#elements_to_i is deprecated, use map(&:to_i)"
|
2010-04-11 22:45:58 +04:00
|
|
|
map(&:to_i)
|
2005-12-09 19:10:45 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2005-12-09 19:10:45 +03:00
|
|
|
def elements_to_r
|
2010-05-02 09:43:29 +04:00
|
|
|
warn "#{caller(1)[0]}: warning: Matrix#elements_to_r is deprecated, use map(&:to_r)"
|
2010-04-11 22:45:58 +04:00
|
|
|
map(&:to_r)
|
2005-12-09 19:10:45 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#--
|
|
|
|
# PRINTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
|
|
|
#++
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Overrides Object#to_s
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def to_s
|
2010-04-01 22:02:27 +04:00
|
|
|
if empty?
|
2012-12-10 20:53:57 +04:00
|
|
|
"#{self.class}.empty(#{row_count}, #{column_count})"
|
2009-10-20 17:35:15 +04:00
|
|
|
else
|
2011-09-11 00:23:36 +04:00
|
|
|
"#{self.class}[" + @rows.collect{|row|
|
2010-04-01 22:01:45 +04:00
|
|
|
"[" + row.collect{|e| e.to_s}.join(", ") + "]"
|
2009-10-20 17:35:15 +04:00
|
|
|
}.join(", ")+"]"
|
|
|
|
end
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Overrides Object#inspect
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def inspect
|
2010-04-01 22:02:27 +04:00
|
|
|
if empty?
|
2012-12-10 20:53:57 +04:00
|
|
|
"#{self.class}.empty(#{row_count}, #{column_count})"
|
2009-10-20 17:35:15 +04:00
|
|
|
else
|
2011-09-11 00:23:36 +04:00
|
|
|
"#{self.class}#{@rows.inspect}"
|
2009-10-20 17:35:15 +04:00
|
|
|
end
|
|
|
|
end
|
|
|
|
|
2010-05-02 09:43:29 +04:00
|
|
|
# Private helper modules
|
|
|
|
|
|
|
|
module ConversionHelper # :nodoc:
|
|
|
|
#
|
|
|
|
# Converts the obj to an Array. If copy is set to true
|
|
|
|
# a copy of obj will be made if necessary.
|
|
|
|
#
|
|
|
|
def convert_to_array(obj, copy = false) # :nodoc:
|
|
|
|
case obj
|
|
|
|
when Array
|
|
|
|
copy ? obj.dup : obj
|
|
|
|
when Vector
|
|
|
|
obj.to_a
|
|
|
|
else
|
|
|
|
begin
|
|
|
|
converted = obj.to_ary
|
|
|
|
rescue Exception => e
|
|
|
|
raise TypeError, "can't convert #{obj.class} into an Array (#{e.message})"
|
|
|
|
end
|
|
|
|
raise TypeError, "#{obj.class}#to_ary should return an Array" unless converted.is_a? Array
|
|
|
|
converted
|
2009-10-20 17:35:15 +04:00
|
|
|
end
|
|
|
|
end
|
2010-05-02 09:43:29 +04:00
|
|
|
private :convert_to_array
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2010-05-02 09:43:29 +04:00
|
|
|
extend ConversionHelper
|
2010-04-11 22:30:58 +04:00
|
|
|
|
2010-04-12 00:10:43 +04:00
|
|
|
module CoercionHelper # :nodoc:
|
2010-05-02 09:43:29 +04:00
|
|
|
#
|
|
|
|
# Applies the operator +oper+ with argument +obj+
|
|
|
|
# through coercion of +obj+
|
|
|
|
#
|
2010-04-11 22:30:58 +04:00
|
|
|
def apply_through_coercion(obj, oper)
|
|
|
|
coercion = obj.coerce(self)
|
|
|
|
raise TypeError unless coercion.is_a?(Array) && coercion.length == 2
|
|
|
|
coercion[0].public_send(oper, coercion[1])
|
|
|
|
rescue
|
|
|
|
raise TypeError, "#{obj.inspect} can't be coerced into #{self.class}"
|
|
|
|
end
|
|
|
|
private :apply_through_coercion
|
2010-04-12 00:10:43 +04:00
|
|
|
|
2010-05-02 09:43:29 +04:00
|
|
|
#
|
2010-04-12 00:10:43 +04:00
|
|
|
# Helper method to coerce a value into a specific class.
|
|
|
|
# Raises a TypeError if the coercion fails or the returned value
|
|
|
|
# is not of the right class.
|
|
|
|
# (from Rubinius)
|
2010-05-02 09:43:29 +04:00
|
|
|
#
|
2010-04-12 00:10:43 +04:00
|
|
|
def self.coerce_to(obj, cls, meth) # :nodoc:
|
|
|
|
return obj if obj.kind_of?(cls)
|
|
|
|
|
|
|
|
begin
|
|
|
|
ret = obj.__send__(meth)
|
|
|
|
rescue Exception => e
|
2012-10-25 18:06:31 +04:00
|
|
|
raise TypeError, "Coercion error: #{obj.inspect}.#{meth} => #{cls} failed:\n" \
|
|
|
|
"(#{e.message})"
|
2010-04-12 00:10:43 +04:00
|
|
|
end
|
|
|
|
raise TypeError, "Coercion error: obj.#{meth} did NOT return a #{cls} (was #{ret.class})" unless ret.kind_of? cls
|
|
|
|
ret
|
|
|
|
end
|
|
|
|
|
|
|
|
def self.coerce_to_int(obj)
|
|
|
|
coerce_to(obj, Integer, :to_int)
|
|
|
|
end
|
2010-04-11 22:30:58 +04:00
|
|
|
end
|
|
|
|
|
|
|
|
include CoercionHelper
|
|
|
|
|
1998-01-16 15:13:05 +03:00
|
|
|
# Private CLASS
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
class Scalar < Numeric # :nodoc:
|
1998-01-16 15:13:05 +03:00
|
|
|
include ExceptionForMatrix
|
2010-04-11 22:30:58 +04:00
|
|
|
include CoercionHelper
|
2009-03-06 06:56:38 +03:00
|
|
|
|
1998-01-16 15:13:05 +03:00
|
|
|
def initialize(value)
|
|
|
|
@value = value
|
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
1998-01-16 15:13:05 +03:00
|
|
|
# ARITHMETIC
|
|
|
|
def +(other)
|
|
|
|
case other
|
|
|
|
when Numeric
|
2004-02-01 12:27:17 +03:00
|
|
|
Scalar.new(@value + other)
|
1998-01-16 15:13:05 +03:00
|
|
|
when Vector, Matrix
|
2010-01-27 17:28:47 +03:00
|
|
|
Scalar.Raise ErrOperationNotDefined, "+", @value.class, other.class
|
1998-01-16 15:13:05 +03:00
|
|
|
else
|
2010-04-11 22:30:58 +04:00
|
|
|
apply_through_coercion(other, __method__)
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
1998-01-16 15:13:05 +03:00
|
|
|
def -(other)
|
|
|
|
case other
|
|
|
|
when Numeric
|
2004-02-01 12:27:17 +03:00
|
|
|
Scalar.new(@value - other)
|
1998-01-16 15:13:05 +03:00
|
|
|
when Vector, Matrix
|
2010-01-27 17:28:47 +03:00
|
|
|
Scalar.Raise ErrOperationNotDefined, "-", @value.class, other.class
|
1998-01-16 15:13:05 +03:00
|
|
|
else
|
2010-04-11 22:30:58 +04:00
|
|
|
apply_through_coercion(other, __method__)
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
1998-01-16 15:13:05 +03:00
|
|
|
def *(other)
|
|
|
|
case other
|
|
|
|
when Numeric
|
2004-02-01 12:27:17 +03:00
|
|
|
Scalar.new(@value * other)
|
1998-01-16 15:13:05 +03:00
|
|
|
when Vector, Matrix
|
2004-02-01 12:27:17 +03:00
|
|
|
other.collect{|e| @value * e}
|
1998-01-16 15:13:05 +03:00
|
|
|
else
|
2010-04-11 22:30:58 +04:00
|
|
|
apply_through_coercion(other, __method__)
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
1998-01-16 15:13:05 +03:00
|
|
|
def / (other)
|
|
|
|
case other
|
|
|
|
when Numeric
|
2004-02-01 12:27:17 +03:00
|
|
|
Scalar.new(@value / other)
|
1998-01-16 15:13:05 +03:00
|
|
|
when Vector
|
2010-01-27 17:28:47 +03:00
|
|
|
Scalar.Raise ErrOperationNotDefined, "/", @value.class, other.class
|
1998-01-16 15:13:05 +03:00
|
|
|
when Matrix
|
2009-09-16 08:39:37 +04:00
|
|
|
self * other.inverse
|
1998-01-16 15:13:05 +03:00
|
|
|
else
|
2010-04-11 22:30:58 +04:00
|
|
|
apply_through_coercion(other, __method__)
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
1998-01-16 15:13:05 +03:00
|
|
|
def ** (other)
|
|
|
|
case other
|
|
|
|
when Numeric
|
2004-02-01 12:27:17 +03:00
|
|
|
Scalar.new(@value ** other)
|
1998-01-16 15:13:05 +03:00
|
|
|
when Vector
|
2010-01-27 17:28:47 +03:00
|
|
|
Scalar.Raise ErrOperationNotDefined, "**", @value.class, other.class
|
1998-01-16 15:13:05 +03:00
|
|
|
when Matrix
|
2010-01-27 17:28:47 +03:00
|
|
|
#other.powered_by(self)
|
|
|
|
Scalar.Raise ErrOperationNotImplemented, "**", @value.class, other.class
|
1998-01-16 15:13:05 +03:00
|
|
|
else
|
2010-04-11 22:30:58 +04:00
|
|
|
apply_through_coercion(other, __method__)
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
end
|
|
|
|
end
|
2010-04-11 22:30:58 +04:00
|
|
|
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
|
2004-02-01 12:27:17 +03:00
|
|
|
|
|
|
|
#
|
|
|
|
# The +Vector+ class represents a mathematical vector, which is useful in its own right, and
|
* dln.c, io.c, pack.c, lib/benchmark.rb, lib/cgi.rb, lib/csv.rb,
lib/date.rb, lib/ftools.rb, lib/getoptlong.rb, lib/logger.rb,
lib/matrix.rb, lib/monitor.rb, lib/set.rb, lib/thwait.rb,
lib/timeout.rb, lib/yaml.rb, lib/drb/drb.rb, lib/irb/workspace.rb,
lib/net/ftp.rb, lib/net/http.rb, lib/net/imap.rb, lib/net/pop.rb,
lib/net/telnet.rb, lib/racc/parser.rb, lib/rinda/rinda.rb,
lib/rinda/tuplespace.rb, lib/shell/command-processor.rb,
lib/soap/rpc/soaplet.rb, lib/test/unit/testcase.rb,
lib/test/unit/testsuite.rb: typo fix.
git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@6178 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
2004-04-19 03:19:47 +04:00
|
|
|
# also constitutes a row or column of a Matrix.
|
2004-02-01 12:27:17 +03:00
|
|
|
#
|
|
|
|
# == Method Catalogue
|
|
|
|
#
|
|
|
|
# To create a Vector:
|
2012-01-26 07:04:11 +04:00
|
|
|
# * Vector.[](*array)
|
|
|
|
# * Vector.elements(array, copy = true)
|
2014-10-07 23:29:53 +04:00
|
|
|
# * Vector.basis(size: n, index: k)
|
2004-02-01 12:27:17 +03:00
|
|
|
#
|
|
|
|
# To access elements:
|
2012-01-26 07:04:11 +04:00
|
|
|
# * #[](i)
|
2004-02-01 12:27:17 +03:00
|
|
|
#
|
|
|
|
# To enumerate the elements:
|
2012-01-26 07:04:11 +04:00
|
|
|
# * #each2(v)
|
|
|
|
# * #collect2(v)
|
2004-02-01 12:27:17 +03:00
|
|
|
#
|
2014-11-19 20:44:46 +03:00
|
|
|
# Properties of vectors:
|
|
|
|
# * #angle_with(v)
|
|
|
|
# * Vector.independent?(*vs)
|
|
|
|
# * #independent?(*vs)
|
|
|
|
#
|
2004-02-01 12:27:17 +03:00
|
|
|
# Vector arithmetic:
|
2012-01-26 07:04:11 +04:00
|
|
|
# * #*(x) "is matrix or number"
|
|
|
|
# * #+(v)
|
|
|
|
# * #-(v)
|
2015-05-21 11:29:32 +03:00
|
|
|
# * #/(v)
|
2014-10-08 00:18:35 +04:00
|
|
|
# * #+@
|
|
|
|
# * #-@
|
2004-02-01 12:27:17 +03:00
|
|
|
#
|
|
|
|
# Vector functions:
|
2014-10-29 05:42:56 +03:00
|
|
|
# * #inner_product(v), dot(v)
|
|
|
|
# * #cross_product(v), cross(v)
|
2012-01-26 07:04:11 +04:00
|
|
|
# * #collect
|
|
|
|
# * #magnitude
|
|
|
|
# * #map
|
|
|
|
# * #map2(v)
|
|
|
|
# * #norm
|
|
|
|
# * #normalize
|
|
|
|
# * #r
|
2015-03-06 02:45:42 +03:00
|
|
|
# * #round
|
2012-01-26 07:04:11 +04:00
|
|
|
# * #size
|
2004-02-01 12:27:17 +03:00
|
|
|
#
|
|
|
|
# Conversion to other data types:
|
2012-01-26 07:04:11 +04:00
|
|
|
# * #covector
|
|
|
|
# * #to_a
|
|
|
|
# * #coerce(other)
|
1998-01-16 15:13:05 +03:00
|
|
|
#
|
2004-02-01 12:27:17 +03:00
|
|
|
# String representations:
|
2012-01-26 07:04:11 +04:00
|
|
|
# * #to_s
|
|
|
|
# * #inspect
|
1998-01-16 15:13:05 +03:00
|
|
|
#
|
|
|
|
class Vector
|
|
|
|
include ExceptionForMatrix
|
2010-03-03 10:19:21 +03:00
|
|
|
include Enumerable
|
2010-04-11 22:30:58 +04:00
|
|
|
include Matrix::CoercionHelper
|
2010-05-02 09:43:29 +04:00
|
|
|
extend Matrix::ConversionHelper
|
1998-01-16 15:13:05 +03:00
|
|
|
#INSTANCE CREATION
|
2009-03-06 06:56:38 +03:00
|
|
|
|
1998-01-16 15:13:05 +03:00
|
|
|
private_class_method :new
|
2009-10-20 17:35:15 +04:00
|
|
|
attr_reader :elements
|
|
|
|
protected :elements
|
2010-05-02 09:43:29 +04:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Creates a Vector from a list of elements.
|
|
|
|
# Vector[7, 4, ...]
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def Vector.[](*array)
|
2010-06-23 09:32:46 +04:00
|
|
|
new convert_to_array(array, false)
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Creates a vector from an Array. The optional second argument specifies
|
|
|
|
# whether the array itself or a copy is used internally.
|
|
|
|
#
|
2000-07-10 08:49:24 +04:00
|
|
|
def Vector.elements(array, copy = true)
|
2010-05-02 09:43:29 +04:00
|
|
|
new convert_to_array(array, copy)
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2014-10-07 23:29:53 +04:00
|
|
|
#
|
|
|
|
# Returns a standard basis +n+-vector, where k is the index.
|
|
|
|
#
|
|
|
|
# Vector.basis(size:, index:) # => Vector[0, 1, 0]
|
|
|
|
#
|
|
|
|
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
|
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
2009-10-20 17:35:15 +04:00
|
|
|
# Vector.new is private; use Vector[] or Vector.elements to create.
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
2009-10-20 17:35:15 +04:00
|
|
|
def initialize(array)
|
|
|
|
# No checking is done at this point.
|
|
|
|
@elements = array
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
* dln.c, io.c, pack.c, lib/benchmark.rb, lib/cgi.rb, lib/csv.rb,
lib/date.rb, lib/ftools.rb, lib/getoptlong.rb, lib/logger.rb,
lib/matrix.rb, lib/monitor.rb, lib/set.rb, lib/thwait.rb,
lib/timeout.rb, lib/yaml.rb, lib/drb/drb.rb, lib/irb/workspace.rb,
lib/net/ftp.rb, lib/net/http.rb, lib/net/imap.rb, lib/net/pop.rb,
lib/net/telnet.rb, lib/racc/parser.rb, lib/rinda/rinda.rb,
lib/rinda/tuplespace.rb, lib/shell/command-processor.rb,
lib/soap/rpc/soaplet.rb, lib/test/unit/testcase.rb,
lib/test/unit/testsuite.rb: typo fix.
git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@6178 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
2004-04-19 03:19:47 +04:00
|
|
|
# ACCESSING
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Returns element number +i+ (starting at zero) of the vector.
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def [](i)
|
|
|
|
@elements[i]
|
|
|
|
end
|
2005-12-09 19:10:45 +03:00
|
|
|
alias element []
|
|
|
|
alias component []
|
|
|
|
|
|
|
|
def []=(i, v)
|
|
|
|
@elements[i]= v
|
|
|
|
end
|
|
|
|
alias set_element []=
|
|
|
|
alias set_component []=
|
|
|
|
private :[]=, :set_element, :set_component
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2015-03-06 02:45:42 +03:00
|
|
|
# Returns a vector with entries rounded to the given precision
|
|
|
|
# (see Float#round)
|
|
|
|
#
|
|
|
|
def round(ndigits=0)
|
|
|
|
map{|e| e.round(ndigits)}
|
|
|
|
end
|
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Returns the number of elements in the vector.
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def size
|
|
|
|
@elements.size
|
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#--
|
* dln.c, io.c, pack.c, lib/benchmark.rb, lib/cgi.rb, lib/csv.rb,
lib/date.rb, lib/ftools.rb, lib/getoptlong.rb, lib/logger.rb,
lib/matrix.rb, lib/monitor.rb, lib/set.rb, lib/thwait.rb,
lib/timeout.rb, lib/yaml.rb, lib/drb/drb.rb, lib/irb/workspace.rb,
lib/net/ftp.rb, lib/net/http.rb, lib/net/imap.rb, lib/net/pop.rb,
lib/net/telnet.rb, lib/racc/parser.rb, lib/rinda/rinda.rb,
lib/rinda/tuplespace.rb, lib/shell/command-processor.rb,
lib/soap/rpc/soaplet.rb, lib/test/unit/testcase.rb,
lib/test/unit/testsuite.rb: typo fix.
git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@6178 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
2004-04-19 03:19:47 +04:00
|
|
|
# ENUMERATIONS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
2003-01-20 10:16:01 +03:00
|
|
|
#++
|
|
|
|
|
2010-03-03 10:19:21 +03:00
|
|
|
#
|
|
|
|
# Iterate over the elements of this vector
|
|
|
|
#
|
2010-03-03 17:07:53 +03:00
|
|
|
def each(&block)
|
2010-03-03 10:19:21 +03:00
|
|
|
return to_enum(:each) unless block_given?
|
2010-03-03 17:07:53 +03:00
|
|
|
@elements.each(&block)
|
|
|
|
self
|
2010-03-03 10:19:21 +03:00
|
|
|
end
|
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Iterate over the elements of this vector and +v+ in conjunction.
|
|
|
|
#
|
|
|
|
def each2(v) # :yield: e1, e2
|
2010-03-29 15:27:03 +04:00
|
|
|
raise TypeError, "Integer is not like Vector" if v.kind_of?(Integer)
|
1999-08-13 09:45:20 +04:00
|
|
|
Vector.Raise ErrDimensionMismatch if size != v.size
|
2009-12-19 05:07:00 +03:00
|
|
|
return to_enum(:each2, v) unless block_given?
|
2009-09-16 08:36:37 +04:00
|
|
|
size.times do |i|
|
1998-01-16 15:13:05 +03:00
|
|
|
yield @elements[i], v[i]
|
|
|
|
end
|
2010-02-01 15:27:46 +03:00
|
|
|
self
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Collects (as in Enumerable#collect) over the elements of this vector and +v+
|
|
|
|
# in conjunction.
|
|
|
|
#
|
|
|
|
def collect2(v) # :yield: e1, e2
|
2010-03-29 15:27:03 +04:00
|
|
|
raise TypeError, "Integer is not like Vector" if v.kind_of?(Integer)
|
1999-08-13 09:45:20 +04:00
|
|
|
Vector.Raise ErrDimensionMismatch if size != v.size
|
2009-12-19 05:07:00 +03:00
|
|
|
return to_enum(:collect2, v) unless block_given?
|
2010-06-05 08:17:44 +04:00
|
|
|
Array.new(size) do |i|
|
1998-01-16 15:13:05 +03:00
|
|
|
yield @elements[i], v[i]
|
|
|
|
end
|
|
|
|
end
|
|
|
|
|
2014-11-19 20:44:46 +03:00
|
|
|
#--
|
|
|
|
# PROPERTIES -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
|
|
|
#++
|
|
|
|
|
|
|
|
#
|
|
|
|
# Returns +true+ iff all of vectors are linearly independent.
|
|
|
|
#
|
|
|
|
# Vector.independent?(Vector[1,0], Vector[0,1])
|
|
|
|
# => true
|
|
|
|
#
|
|
|
|
# Vector.independent?(Vector[1,2], Vector[2,4])
|
|
|
|
# => false
|
|
|
|
#
|
|
|
|
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
|
|
|
|
|
|
|
|
#
|
|
|
|
# Returns +true+ iff all of vectors are linearly independent.
|
|
|
|
#
|
|
|
|
# Vector[1,0].independent?(Vector[0,1])
|
|
|
|
# => true
|
|
|
|
#
|
|
|
|
# Vector[1,2].independent?(Vector[2,4])
|
|
|
|
# => false
|
|
|
|
#
|
|
|
|
def independent?(*vs)
|
|
|
|
self.class.independent?(self, *vs)
|
|
|
|
end
|
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#--
|
|
|
|
# COMPARING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
|
|
|
#++
|
|
|
|
|
|
|
|
#
|
|
|
|
# Returns +true+ iff the two vectors have the same elements in the same order.
|
|
|
|
#
|
1999-01-20 07:59:39 +03:00
|
|
|
def ==(other)
|
2000-07-10 08:49:24 +04:00
|
|
|
return false unless Vector === other
|
2009-10-20 17:35:15 +04:00
|
|
|
@elements == other.elements
|
1999-01-20 07:59:39 +03:00
|
|
|
end
|
2009-10-20 17:35:15 +04:00
|
|
|
|
2008-09-15 16:02:39 +04:00
|
|
|
def eql?(other)
|
|
|
|
return false unless Vector === other
|
2009-10-20 17:35:15 +04:00
|
|
|
@elements.eql? other.elements
|
2008-09-15 16:02:39 +04:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
2014-11-27 04:03:46 +03:00
|
|
|
# Returns a copy of the vector.
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
1999-01-20 07:59:39 +03:00
|
|
|
def clone
|
2011-09-11 00:23:36 +04:00
|
|
|
self.class.elements(@elements)
|
1999-01-20 07:59:39 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
2014-11-27 04:03:46 +03:00
|
|
|
# Returns a hash-code for the vector.
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
1999-01-20 07:59:39 +03:00
|
|
|
def hash
|
|
|
|
@elements.hash
|
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#--
|
|
|
|
# ARITHMETIC -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
|
|
|
#++
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
2015-02-22 23:22:31 +03:00
|
|
|
# Multiplies the vector by +x+, where +x+ is a number or a matrix.
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
def *(x)
|
1998-01-16 15:13:05 +03:00
|
|
|
case x
|
|
|
|
when Numeric
|
|
|
|
els = @elements.collect{|e| e * x}
|
2011-09-11 00:23:36 +04:00
|
|
|
self.class.elements(els, false)
|
1998-01-16 15:13:05 +03:00
|
|
|
when Matrix
|
2001-12-09 17:11:30 +03:00
|
|
|
Matrix.column_vector(self) * x
|
2010-01-27 17:28:47 +03:00
|
|
|
when Vector
|
|
|
|
Vector.Raise ErrOperationNotDefined, "*", self.class, x.class
|
1998-01-16 15:13:05 +03:00
|
|
|
else
|
2010-04-11 22:30:58 +04:00
|
|
|
apply_through_coercion(x, __method__)
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
end
|
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Vector addition.
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def +(v)
|
|
|
|
case v
|
|
|
|
when Vector
|
1999-08-13 09:45:20 +04:00
|
|
|
Vector.Raise ErrDimensionMismatch if size != v.size
|
2008-12-18 10:54:50 +03:00
|
|
|
els = collect2(v) {|v1, v2|
|
2004-02-01 12:27:17 +03:00
|
|
|
v1 + v2
|
1998-01-16 15:13:05 +03:00
|
|
|
}
|
2011-09-11 00:23:36 +04:00
|
|
|
self.class.elements(els, false)
|
1998-01-16 15:13:05 +03:00
|
|
|
when Matrix
|
|
|
|
Matrix.column_vector(self) + v
|
|
|
|
else
|
2010-04-11 22:30:58 +04:00
|
|
|
apply_through_coercion(v, __method__)
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
end
|
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Vector subtraction.
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def -(v)
|
|
|
|
case v
|
|
|
|
when Vector
|
1999-08-13 09:45:20 +04:00
|
|
|
Vector.Raise ErrDimensionMismatch if size != v.size
|
2008-12-18 10:54:50 +03:00
|
|
|
els = collect2(v) {|v1, v2|
|
2004-02-01 12:27:17 +03:00
|
|
|
v1 - v2
|
1998-01-16 15:13:05 +03:00
|
|
|
}
|
2011-09-11 00:23:36 +04:00
|
|
|
self.class.elements(els, false)
|
1998-01-16 15:13:05 +03:00
|
|
|
when Matrix
|
|
|
|
Matrix.column_vector(self) - v
|
|
|
|
else
|
2010-04-11 22:30:58 +04:00
|
|
|
apply_through_coercion(v, __method__)
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2010-01-27 17:28:47 +03:00
|
|
|
#
|
|
|
|
# Vector division.
|
|
|
|
#
|
|
|
|
def /(x)
|
|
|
|
case x
|
|
|
|
when Numeric
|
|
|
|
els = @elements.collect{|e| e / x}
|
2011-09-11 00:23:36 +04:00
|
|
|
self.class.elements(els, false)
|
2010-01-27 17:28:47 +03:00
|
|
|
when Matrix, Vector
|
|
|
|
Vector.Raise ErrOperationNotDefined, "/", self.class, x.class
|
|
|
|
else
|
2010-04-11 22:30:58 +04:00
|
|
|
apply_through_coercion(x, __method__)
|
2010-01-27 17:28:47 +03:00
|
|
|
end
|
|
|
|
end
|
|
|
|
|
2014-10-08 00:18:35 +04:00
|
|
|
def +@
|
|
|
|
self
|
|
|
|
end
|
|
|
|
|
|
|
|
def -@
|
|
|
|
collect {|e| -e }
|
|
|
|
end
|
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#--
|
|
|
|
# VECTOR FUNCTIONS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
|
|
|
#++
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Returns the inner product of this vector with the other.
|
|
|
|
# Vector[4,7].inner_product Vector[10,1] => 47
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def inner_product(v)
|
1999-08-13 09:45:20 +04:00
|
|
|
Vector.Raise ErrDimensionMismatch if size != v.size
|
2009-03-06 06:56:38 +03:00
|
|
|
|
1998-01-16 15:13:05 +03:00
|
|
|
p = 0
|
2008-12-18 10:54:50 +03:00
|
|
|
each2(v) {|v1, v2|
|
2013-01-30 08:53:58 +04:00
|
|
|
p += v1 * v2.conj
|
1998-01-16 15:13:05 +03:00
|
|
|
}
|
|
|
|
p
|
|
|
|
end
|
2014-10-29 05:42:56 +03:00
|
|
|
alias_method :dot, :inner_product
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2013-04-13 07:08:28 +04:00
|
|
|
#
|
2014-10-29 05:43:52 +03:00
|
|
|
# Returns the cross product of this vector with the others.
|
2013-04-13 07:08:28 +04:00
|
|
|
# Vector[1, 0, 0].cross_product Vector[0, 1, 0] => Vector[0, 0, 1]
|
|
|
|
#
|
2014-10-29 05:43:52 +03:00
|
|
|
# It is generalized to other dimensions to return a vector perpendicular
|
|
|
|
# to the arguments.
|
|
|
|
# Vector[1, 2].cross_product # => Vector[-2, 1]
|
|
|
|
# Vector[1, 0, 0, 0].cross_product(
|
|
|
|
# Vector[0, 1, 0, 0],
|
|
|
|
# Vector[0, 0, 1, 0]
|
|
|
|
# ) #=> Vector[0, 0, 0, 1]
|
|
|
|
#
|
|
|
|
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
|
2013-04-13 07:08:28 +04:00
|
|
|
end
|
2014-10-29 05:42:56 +03:00
|
|
|
alias_method :cross, :cross_product
|
2013-04-13 07:08:28 +04:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Like Array#collect.
|
|
|
|
#
|
2009-09-16 08:36:37 +04:00
|
|
|
def collect(&block) # :yield: e
|
2009-10-20 17:35:15 +04:00
|
|
|
return to_enum(:collect) unless block_given?
|
2009-09-16 08:36:37 +04:00
|
|
|
els = @elements.collect(&block)
|
2011-09-11 00:23:36 +04:00
|
|
|
self.class.elements(els, false)
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
alias map collect
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Returns the modulus (Pythagorean distance) of the vector.
|
|
|
|
# Vector[5,8,2].r => 9.643650761
|
|
|
|
#
|
2011-06-29 05:13:22 +04:00
|
|
|
def magnitude
|
2012-09-03 09:49:06 +04:00
|
|
|
Math.sqrt(@elements.inject(0) {|v, e| v + e.abs2})
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
2011-06-29 05:13:22 +04:00
|
|
|
alias r magnitude
|
2011-07-09 06:41:14 +04:00
|
|
|
alias norm magnitude
|
|
|
|
|
|
|
|
#
|
|
|
|
# Like Vector#collect2, but returns a Vector instead of an Array.
|
|
|
|
#
|
|
|
|
def map2(v, &block) # :yield: e1, e2
|
|
|
|
return to_enum(:map2, v) unless block_given?
|
|
|
|
els = collect2(v, &block)
|
2011-09-11 00:23:36 +04:00
|
|
|
self.class.elements(els, false)
|
2011-07-09 06:41:14 +04:00
|
|
|
end
|
|
|
|
|
|
|
|
class ZeroVectorError < StandardError
|
|
|
|
end
|
|
|
|
#
|
|
|
|
# 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
|
|
|
|
#
|
|
|
|
def normalize
|
|
|
|
n = magnitude
|
|
|
|
raise ZeroVectorError, "Zero vectors can not be normalized" if n == 0
|
|
|
|
self / n
|
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2014-11-19 20:32:58 +03:00
|
|
|
#
|
|
|
|
# Returns an angle with another vector. Result is within the [0...Math::PI].
|
|
|
|
# Vector[1,0].angle_with(Vector[0,1])
|
|
|
|
# # => Math::PI / 2
|
|
|
|
#
|
|
|
|
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
|
|
|
|
|
|
|
|
Math.acos( inner_product(v) / prod )
|
|
|
|
end
|
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#--
|
1998-01-16 15:13:05 +03:00
|
|
|
# CONVERTING
|
2003-01-20 10:16:01 +03:00
|
|
|
#++
|
|
|
|
|
|
|
|
#
|
|
|
|
# Creates a single-row matrix from this vector.
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def covector
|
|
|
|
Matrix.row_vector(self)
|
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Returns the elements of the vector in an array.
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def to_a
|
|
|
|
@elements.dup
|
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2005-12-09 19:10:45 +03:00
|
|
|
def elements_to_f
|
2010-04-11 22:50:51 +04:00
|
|
|
warn "#{caller(1)[0]}: warning: Vector#elements_to_f is deprecated"
|
|
|
|
map(&:to_f)
|
2005-12-09 19:10:45 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2005-12-09 19:10:45 +03:00
|
|
|
def elements_to_i
|
2010-04-11 22:50:51 +04:00
|
|
|
warn "#{caller(1)[0]}: warning: Vector#elements_to_i is deprecated"
|
|
|
|
map(&:to_i)
|
2005-12-09 19:10:45 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2005-12-09 19:10:45 +03:00
|
|
|
def elements_to_r
|
2010-04-11 22:50:51 +04:00
|
|
|
warn "#{caller(1)[0]}: warning: Vector#elements_to_r is deprecated"
|
|
|
|
map(&:to_r)
|
2005-12-09 19:10:45 +03:00
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
2010-05-02 09:43:29 +04:00
|
|
|
# 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.
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def coerce(other)
|
|
|
|
case other
|
|
|
|
when Numeric
|
2007-09-18 17:12:47 +04:00
|
|
|
return Matrix::Scalar.new(other), self
|
1999-08-13 09:45:20 +04:00
|
|
|
else
|
2002-10-02 20:45:35 +04:00
|
|
|
raise TypeError, "#{self.class} can't be coerced into #{other.class}"
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#--
|
|
|
|
# PRINTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
|
|
|
#++
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Overrides Object#to_s
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def to_s
|
|
|
|
"Vector[" + @elements.join(", ") + "]"
|
|
|
|
end
|
2009-03-06 06:56:38 +03:00
|
|
|
|
2003-01-20 10:16:01 +03:00
|
|
|
#
|
|
|
|
# Overrides Object#inspect
|
|
|
|
#
|
1998-01-16 15:13:05 +03:00
|
|
|
def inspect
|
2010-06-23 09:32:46 +04:00
|
|
|
"Vector" + @elements.inspect
|
1998-01-16 15:13:05 +03:00
|
|
|
end
|
|
|
|
end
|