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matrix.rb
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matrix.rb
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# encoding: utf-8
#
# = matrix.rb
#
# An implementation of Matrix and Vector classes.
#
# See classes Matrix and Vector for documentation.
#
# Current Maintainer:: Marc-André Lafortune
# Original Author:: Keiju ISHITSUKA
# Original Documentation:: Gavin Sinclair (sourced from <i>Ruby in a Nutshell</i> (Matsumoto, O'Reilly))
##
require "e2mmap.rb"
module ExceptionForMatrix # :nodoc:
extend Exception2MessageMapper
def_e2message(TypeError, "wrong argument type %s (expected %s)")
def_e2message(ArgumentError, "Wrong # of arguments(%d for %d)")
def_exception("ErrDimensionMismatch", "\#{self.name} dimension mismatch")
def_exception("ErrNotRegular", "Not Regular Matrix")
def_exception("ErrOperationNotDefined", "Operation(%s) can\\'t be defined: %s op %s")
def_exception("ErrOperationNotImplemented", "Sorry, Operation(%s) not implemented: %s op %s")
end
#
# The +Matrix+ class represents a mathematical matrix. It provides methods for creating
# matrices, operating on them arithmetically and algebraically,
# and determining their mathematical properties (trace, rank, inverse, determinant).
#
# == Method Catalogue
#
# To create a matrix:
# * Matrix[*rows]
# * Matrix.[](*rows)
# * Matrix.rows(rows, copy = true)
# * Matrix.columns(columns)
# * Matrix.build(row_count, column_count, &block)
# * Matrix.diagonal(*values)
# * Matrix.scalar(n, value)
# * Matrix.identity(n)
# * Matrix.unit(n)
# * Matrix.I(n)
# * Matrix.zero(n)
# * Matrix.row_vector(row)
# * Matrix.column_vector(column)
# * Matrix.empty(row_count, column_count)
# * Matrix.hstack(*matrices)
# * Matrix.vstack(*matrices)
#
# To access Matrix elements/columns/rows/submatrices/properties:
# * #[](i, j)
# * #row_count (row_size)
# * #column_count (column_size)
# * #row(i)
# * #column(j)
# * #collect
# * #map
# * #each
# * #each_with_index
# * #find_index
# * #minor(*param)
# * #first_minor(row, column)
# * #cofactor(row, column)
# * #adjugate
# * #laplace_expansion(row_or_column: num)
# * #cofactor_expansion(row_or_column: num)
#
# Properties of a matrix:
# * #diagonal?
# * #empty?
# * #hermitian?
# * #lower_triangular?
# * #normal?
# * #orthogonal?
# * #permutation?
# * #real?
# * #regular?
# * #singular?
# * #square?
# * #symmetric?
# * #unitary?
# * #upper_triangular?
# * #zero?
#
# Matrix arithmetic:
# * #*(m)
# * #+(m)
# * #-(m)
# * #/(m)
# * #inverse
# * #inv
# * #**
# * #+@
# * #-@
#
# Matrix functions:
# * #determinant
# * #det
# * #hstack(*matrices)
# * #rank
# * #round
# * #trace
# * #tr
# * #transpose
# * #t
# * #vstack(*matrices)
#
# Matrix decompositions:
# * #eigen
# * #eigensystem
# * #lup
# * #lup_decomposition
#
# Complex arithmetic:
# * conj
# * conjugate
# * imag
# * imaginary
# * real
# * rect
# * rectangular
#
# Conversion to other data types:
# * #coerce(other)
# * #row_vectors
# * #column_vectors
# * #to_a
#
# String representations:
# * #to_s
# * #inspect
#
class Matrix
include Enumerable
include ExceptionForMatrix
autoload :EigenvalueDecomposition, "matrix/eigenvalue_decomposition"
autoload :LUPDecomposition, "matrix/lup_decomposition"
# instance creations
private_class_method :new
attr_reader :rows
protected :rows
#
# Creates a matrix where each argument is a row.
# Matrix[ [25, 93], [-1, 66] ]
# => 25 93
# -1 66
#
def Matrix.[](*rows)
rows(rows, false)
end
#
# Creates a matrix where +rows+ is an array of arrays, each of which is a row
# of the matrix. If the optional argument +copy+ is false, use the given
# arrays as the internal structure of the matrix without copying.
# Matrix.rows([[25, 93], [-1, 66]])
# => 25 93
# -1 66
#
def Matrix.rows(rows, copy = true)
rows = convert_to_array(rows, copy)
rows.map! do |row|
convert_to_array(row, copy)
end
size = (rows[0] || []).size
rows.each do |row|
raise ErrDimensionMismatch, "row size differs (#{row.size} should be #{size})" unless row.size == size
end
new rows, size
end
#
# Creates a matrix using +columns+ as an array of column vectors.
# Matrix.columns([[25, 93], [-1, 66]])
# => 25 -1
# 93 66
#
def Matrix.columns(columns)
rows(columns, false).transpose
end
#
# Creates a matrix of size +row_count+ x +column_count+.
# It fills the values by calling the given block,
# passing the current row and column.
# Returns an enumerator if no block is given.
#
# m = Matrix.build(2, 4) {|row, col| col - row }
# => Matrix[[0, 1, 2, 3], [-1, 0, 1, 2]]
# m = Matrix.build(3) { rand }
# => a 3x3 matrix with random elements
#
def Matrix.build(row_count, column_count = row_count)
row_count = CoercionHelper.coerce_to_int(row_count)
column_count = CoercionHelper.coerce_to_int(column_count)
raise ArgumentError if row_count < 0 || column_count < 0
return to_enum :build, row_count, column_count unless block_given?
rows = Array.new(row_count) do |i|
Array.new(column_count) do |j|
yield i, j
end
end
new rows, column_count
end
#
# Creates a matrix where the diagonal elements are composed of +values+.
# Matrix.diagonal(9, 5, -3)
# => 9 0 0
# 0 5 0
# 0 0 -3
#
def Matrix.diagonal(*values)
size = values.size
return Matrix.empty if size == 0
rows = Array.new(size) {|j|
row = Array.new(size, 0)
row[j] = values[j]
row
}
new rows
end
#
# Creates an +n+ by +n+ diagonal matrix where each diagonal element is
# +value+.
# Matrix.scalar(2, 5)
# => 5 0
# 0 5
#
def Matrix.scalar(n, value)
diagonal(*Array.new(n, value))
end
#
# Creates an +n+ by +n+ identity matrix.
# Matrix.identity(2)
# => 1 0
# 0 1
#
def Matrix.identity(n)
scalar(n, 1)
end
class << Matrix
alias unit identity
alias I identity
end
#
# Creates a zero matrix.
# Matrix.zero(2)
# => 0 0
# 0 0
#
def Matrix.zero(row_count, column_count = row_count)
rows = Array.new(row_count){Array.new(column_count, 0)}
new rows, column_count
end
#
# Creates a single-row matrix where the values of that row are as given in
# +row+.
# Matrix.row_vector([4,5,6])
# => 4 5 6
#
def Matrix.row_vector(row)
row = convert_to_array(row)
new [row]
end
#
# Creates a single-column matrix where the values of that column are as given
# in +column+.
# Matrix.column_vector([4,5,6])
# => 4
# 5
# 6
#
def Matrix.column_vector(column)
column = convert_to_array(column)
new [column].transpose, 1
end
#
# Creates a empty matrix of +row_count+ x +column_count+.
# At least one of +row_count+ or +column_count+ must be 0.
#
# m = Matrix.empty(2, 0)
# m == Matrix[ [], [] ]
# => true
# n = Matrix.empty(0, 3)
# n == Matrix.columns([ [], [], [] ])
# => true
# m * n
# => Matrix[[0, 0, 0], [0, 0, 0]]
#
def Matrix.empty(row_count = 0, column_count = 0)
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
new([[]]*row_count, column_count)
end
#
# 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
#
# Matrix.new is private; use Matrix.rows, columns, [], etc... to create.
#
def initialize(rows, column_count = rows[0].size)
# No checking is done at this point. rows must be an Array of Arrays.
# column_count must be the size of the first row, if there is one,
# otherwise it *must* be specified and can be any integer >= 0
@rows = rows
@column_count = column_count
end
def new_matrix(rows, column_count = rows[0].size) # :nodoc:
self.class.send(:new, rows, column_count) # bypass privacy of Matrix.new
end
private :new_matrix
#
# Returns element (+i+,+j+) of the matrix. That is: row +i+, column +j+.
#
def [](i, j)
@rows.fetch(i){return nil}[j]
end
alias element []
alias component []
def []=(i, j, v)
@rows[i][j] = v
end
alias set_element []=
alias set_component []=
private :[]=, :set_element, :set_component
#
# Returns the number of rows.
#
def row_count
@rows.size
end
alias_method :row_size, :row_count
#
# Returns the number of columns.
#
attr_reader :column_count
alias_method :column_size, :column_count
#
# 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.
#
def row(i, &block) # :yield: e
if block_given?
@rows.fetch(i){return self}.each(&block)
self
else
Vector.elements(@rows.fetch(i){return nil})
end
end
#
# 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
if block_given?
return self if j >= column_count || j < -column_count
row_count.times do |i|
yield @rows[i][j]
end
self
else
return nil if j >= column_count || j < -column_count
col = Array.new(row_count) {|i|
@rows[i][j]
}
Vector.elements(col, false)
end
end
#
# Returns a matrix that is the result of iteration of the given block over all
# elements of the matrix.
# Matrix[ [1,2], [3,4] ].collect { |e| e**2 }
# => 1 4
# 9 16
#
def collect(&block) # :yield: e
return to_enum(:collect) unless block_given?
rows = @rows.collect{|row| row.collect(&block)}
new_matrix rows, column_count
end
alias map collect
#
# Yields all elements of the matrix, starting with those of the first row,
# or returns an Enumerator if no block given.
# 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
#
# Matrix[ [1,2], [3,4] ].each { |e| puts e }
# # => prints the numbers 1 to 4
# 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?
last = column_count - 1
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|
column_count.times do |col_index|
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|
[row_index, column_count].min.times do |col_index|
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
raise ArgumentError, "expected #{which.inspect} to be one of :all, :diagonal, :off_diagonal, :lower, :strict_lower, :strict_upper or :upper"
end
self
end
#
# Same as #each, but the row index and column index in addition to the element
#
# Matrix[ [1,2], [3,4] ].each_with_index do |e, row, col|
# puts "#{e} at #{row}, #{col}"
# end
# # => 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?
last = column_count - 1
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|
column_count.times do |col_index|
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
end
when :strict_lower
@rows.each_with_index do |row, row_index|
[row_index, column_count].min.times do |col_index|
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
raise ArgumentError, "expected #{which.inspect} to be one of :all, :diagonal, :off_diagonal, :lower, :strict_lower, :strict_upper or :upper"
end
self
end
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
#
# Returns a section of the matrix. The parameters are either:
# * start_row, nrows, start_col, ncols; OR
# * row_range, col_range
#
# Matrix.diagonal(9, 5, -3).minor(0..1, 0..2)
# => 9 0 0
# 0 5 0
#
# Like Array#[], negative indices count backward from the end of the
# row or column (-1 is the last element). Returns nil if the starting
# row or column is greater than row_count or column_count respectively.
#
def minor(*param)
case param.size
when 2
row_range, col_range = param
from_row = row_range.first
from_row += row_count if from_row < 0
to_row = row_range.end
to_row += row_count if to_row < 0
to_row += 1 unless row_range.exclude_end?
size_row = to_row - from_row
from_col = col_range.first
from_col += column_count if from_col < 0
to_col = col_range.end
to_col += column_count if to_col < 0
to_col += 1 unless col_range.exclude_end?
size_col = to_col - from_col
when 4
from_row, size_row, from_col, size_col = param
return nil if size_row < 0 || size_col < 0
from_row += row_count if from_row < 0
from_col += column_count if from_col < 0
else
raise ArgumentError, param.inspect
end
return nil if from_row > row_count || from_col > column_count || from_row < 0 || from_col < 0
rows = @rows[from_row, size_row].collect{|row|
row[from_col, size_col]
}
new_matrix rows, [column_count - from_col, size_col].min
end
#
# 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
#
# 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
#
# 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
#
# 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
#--
# TESTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Returns +true+ if this is a diagonal matrix.
# Raises an error if matrix is not square.
#
def diagonal?
Matrix.Raise ErrDimensionMismatch unless square?
each(:off_diagonal).all?(&:zero?)
end
#
# Returns +true+ if this is an empty matrix, i.e. if the number of rows
# or the number of columns is 0.
#
def empty?
column_count == 0 || row_count == 0
end
#
# Returns +true+ if this is an hermitian matrix.
# Raises an error if matrix is not square.
#
def hermitian?
Matrix.Raise ErrDimensionMismatch unless square?
each_with_index(:upper).all? do |e, row, col|
e == rows[col][row].conj
end
end
#
# Returns +true+ if this is a lower triangular matrix.
#
def lower_triangular?
each(:strict_upper).all?(&:zero?)
end
#
# Returns +true+ if this is a normal matrix.
# 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
#
# Returns +true+ if this is an orthogonal matrix
# Raises an error if matrix is not square.
#
def orthogonal?
Matrix.Raise ErrDimensionMismatch unless square?
rows.each_with_index do |row, i|
column_count.times do |j|
s = 0
row_count.times do |k|
s += row[k] * rows[k][j]
end
return false unless s == (i == j ? 1 : 0)
end
end
true
end
#
# Returns +true+ if this is a permutation matrix
# Raises an error if matrix is not square.
#
def permutation?
Matrix.Raise ErrDimensionMismatch unless square?
cols = Array.new(column_count)
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
#
# Returns +true+ if all entries of the matrix are real.
#
def real?
all?(&:real?)
end
#
# Returns +true+ if this is a regular (i.e. non-singular) matrix.
#
def regular?
not singular?
end
#
# Returns +true+ if this is a singular matrix.
#
def singular?
determinant == 0
end
#
# Returns +true+ if this is a square matrix.
#
def square?
column_count == row_count
end
#
# Returns +true+ if this is a symmetric matrix.
# Raises an error if matrix is not square.
#
def symmetric?
Matrix.Raise ErrDimensionMismatch unless square?
each_with_index(:strict_upper) do |e, row, col|
return false if e != rows[col][row]
end
true
end
#
# Returns +true+ if this is a unitary matrix
# Raises an error if matrix is not square.
#
def unitary?
Matrix.Raise ErrDimensionMismatch unless square?
rows.each_with_index do |row, i|
column_count.times do |j|
s = 0
row_count.times do |k|
s += row[k].conj * rows[k][j]
end
return false unless s == (i == j ? 1 : 0)
end
end
true
end
#
# Returns +true+ if this is an upper triangular matrix.
#
def upper_triangular?
each(:strict_lower).all?(&:zero?)
end
#
# Returns +true+ if this is a matrix with only zero elements
#
def zero?
all?(&:zero?)
end
#--
# OBJECT METHODS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Returns +true+ if and only if the two matrices contain equal elements.
#
def ==(other)
return false unless Matrix === other &&
column_count == other.column_count # necessary for empty matrices
rows == other.rows
end
def eql?(other)
return false unless Matrix === other &&
column_count == other.column_count # necessary for empty matrices
rows.eql? other.rows
end
#
# Returns a clone of the matrix, so that the contents of each do not reference
# identical objects.
# There should be no good reason to do this since Matrices are immutable.
#
def clone
new_matrix @rows.map(&:dup), column_count
end
#
# Returns a hash-code for the matrix.
#
def hash
@rows.hash
end
#--
# ARITHMETIC -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Matrix multiplication.
# Matrix[[2,4], [6,8]] * Matrix.identity(2)
# => 2 4
# 6 8
#
def *(m) # m is matrix or vector or number
case(m)
when Numeric
rows = @rows.collect {|row|
row.collect {|e| e * m }
}
return new_matrix rows, column_count
when Vector
m = self.class.column_vector(m)
r = self * m
return r.column(0)
when Matrix
Matrix.Raise ErrDimensionMismatch if column_count != m.row_count
rows = Array.new(row_count) {|i|
Array.new(m.column_count) {|j|
(0 ... column_count).inject(0) do |vij, k|
vij + self[i, k] * m[k, j]
end
}
}
return new_matrix rows, m.column_count
else
return apply_through_coercion(m, __method__)
end
end
#
# Matrix addition.
# Matrix.scalar(2,5) + Matrix[[1,0], [-4,7]]
# => 6 0
# -4 12
#
def +(m)
case m
when Numeric
Matrix.Raise ErrOperationNotDefined, "+", self.class, m.class
when Vector
m = self.class.column_vector(m)
when Matrix
else
return apply_through_coercion(m, __method__)
end
Matrix.Raise ErrDimensionMismatch unless row_count == m.row_count && column_count == m.column_count
rows = Array.new(row_count) {|i|
Array.new(column_count) {|j|