#!/usr/local/bin/ruby

[0] Fix | Delete

#--

[1] Fix | Delete

# matrix.rb -

[2] Fix | Delete

# $Release Version: 1.0$

[3] Fix | Delete

# $Revision: 1.11 $

[4] Fix | Delete

# $Date: 1999/10/06 11:01:53 $

[5] Fix | Delete

# Original Version from Smalltalk-80 version

[6] Fix | Delete

# on July 23, 1985 at 8:37:17 am

[7] Fix | Delete

# by Keiju ISHITSUKA

[8] Fix | Delete

#++

[9] Fix | Delete

#

[10] Fix | Delete

# = matrix.rb

[11] Fix | Delete

#

[12] Fix | Delete

# An implementation of Matrix and Vector classes.

[13] Fix | Delete

#

[14] Fix | Delete

# Author:: Keiju ISHITSUKA

[15] Fix | Delete

# Documentation:: Gavin Sinclair (sourced from <i>Ruby in a Nutshell</i> (Matsumoto, O'Reilly))

[16] Fix | Delete

#

[17] Fix | Delete

# See classes Matrix and Vector for documentation.

[18] Fix | Delete

#

[19] Fix | Delete

[20] Fix | Delete

[21] Fix | Delete

require "e2mmap.rb"

[22] Fix | Delete

[23] Fix | Delete

module ExceptionForMatrix # :nodoc:

[24] Fix | Delete

extend Exception2MessageMapper

[25] Fix | Delete

def_e2message(TypeError, "wrong argument type %s (expected %s)")

[26] Fix | Delete

def_e2message(ArgumentError, "Wrong # of arguments(%d for %d)")

[27] Fix | Delete

[28] Fix | Delete

def_exception("ErrDimensionMismatch", "\#{self.name} dimension mismatch")

[29] Fix | Delete

def_exception("ErrNotRegular", "Not Regular Matrix")

[30] Fix | Delete

def_exception("ErrOperationNotDefined", "This operation(%s) can\\'t defined")

[31] Fix | Delete

end

[32] Fix | Delete

[33] Fix | Delete

#

[34] Fix | Delete

# The +Matrix+ class represents a mathematical matrix, and provides methods for creating

[35] Fix | Delete

# special-case matrices (zero, identity, diagonal, singular, vector), operating on them

[36] Fix | Delete

# arithmetically and algebraically, and determining their mathematical properties (trace, rank,

[37] Fix | Delete

# inverse, determinant).

[38] Fix | Delete

#

[39] Fix | Delete

# Note that although matrices should theoretically be rectangular, this is not

[40] Fix | Delete

# enforced by the class.

[41] Fix | Delete

#

[42] Fix | Delete

# Also note that the determinant of integer matrices may be incorrectly calculated unless you

[43] Fix | Delete

# also <tt>require 'mathn'</tt>. This may be fixed in the future.

[44] Fix | Delete

#

[45] Fix | Delete

# == Method Catalogue

[46] Fix | Delete

#

[47] Fix | Delete

# To create a matrix:

[48] Fix | Delete

# * <tt> Matrix[*rows] </tt>

[49] Fix | Delete

# * <tt> Matrix.[](*rows) </tt>

[50] Fix | Delete

# * <tt> Matrix.rows(rows, copy = true) </tt>

[51] Fix | Delete

# * <tt> Matrix.columns(columns) </tt>

[52] Fix | Delete

# * <tt> Matrix.diagonal(*values) </tt>

[53] Fix | Delete

# * <tt> Matrix.scalar(n, value) </tt>

[54] Fix | Delete

# * <tt> Matrix.scalar(n, value) </tt>

[55] Fix | Delete

# * <tt> Matrix.identity(n) </tt>

[56] Fix | Delete

# * <tt> Matrix.unit(n) </tt>

[57] Fix | Delete

# * <tt> Matrix.I(n) </tt>

[58] Fix | Delete

# * <tt> Matrix.zero(n) </tt>

[59] Fix | Delete

# * <tt> Matrix.row_vector(row) </tt>

[60] Fix | Delete

# * <tt> Matrix.column_vector(column) </tt>

[61] Fix | Delete

#

[62] Fix | Delete

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

[63] Fix | Delete

# * <tt> [](i, j) </tt>

[64] Fix | Delete

# * <tt> #row_size </tt>

[65] Fix | Delete

# * <tt> #column_size </tt>

[66] Fix | Delete

# * <tt> #row(i) </tt>

[67] Fix | Delete

# * <tt> #column(j) </tt>

[68] Fix | Delete

# * <tt> #collect </tt>

[69] Fix | Delete

# * <tt> #map </tt>

[70] Fix | Delete

# * <tt> #minor(*param) </tt>

[71] Fix | Delete

#

[72] Fix | Delete

# Properties of a matrix:

[73] Fix | Delete

# * <tt> #regular? </tt>

[74] Fix | Delete

# * <tt> #singular? </tt>

[75] Fix | Delete

# * <tt> #square? </tt>

[76] Fix | Delete

#

[77] Fix | Delete

# Matrix arithmetic:

[78] Fix | Delete

# * <tt> *(m) </tt>

[79] Fix | Delete

# * <tt> +(m) </tt>

[80] Fix | Delete

# * <tt> -(m) </tt>

[81] Fix | Delete

# * <tt> #/(m) </tt>

[82] Fix | Delete

# * <tt> #inverse </tt>

[83] Fix | Delete

# * <tt> #inv </tt>

[84] Fix | Delete

# * <tt> ** </tt>

[85] Fix | Delete

#

[86] Fix | Delete

# Matrix functions:

[87] Fix | Delete

# * <tt> #determinant </tt>

[88] Fix | Delete

# * <tt> #det </tt>

[89] Fix | Delete

# * <tt> #rank </tt>

[90] Fix | Delete

# * <tt> #trace </tt>

[91] Fix | Delete

# * <tt> #tr </tt>

[92] Fix | Delete

# * <tt> #transpose </tt>

[93] Fix | Delete

# * <tt> #t </tt>

[94] Fix | Delete

#

[95] Fix | Delete

# Conversion to other data types:

[96] Fix | Delete

# * <tt> #coerce(other) </tt>

[97] Fix | Delete

# * <tt> #row_vectors </tt>

[98] Fix | Delete

# * <tt> #column_vectors </tt>

[99] Fix | Delete

# * <tt> #to_a </tt>

[100] Fix | Delete

#

[101] Fix | Delete

# String representations:

[102] Fix | Delete

# * <tt> #to_s </tt>

[103] Fix | Delete

# * <tt> #inspect </tt>

[104] Fix | Delete

#

[105] Fix | Delete

class Matrix

[106] Fix | Delete

@RCS_ID='-$Id: matrix.rb,v 1.11 1999/10/06 11:01:53 keiju Exp keiju $-'

[107] Fix | Delete

[108] Fix | Delete

# extend Exception2MessageMapper

[109] Fix | Delete

include ExceptionForMatrix

[110] Fix | Delete

[111] Fix | Delete

# instance creations

[112] Fix | Delete

private_class_method :new

[113] Fix | Delete

[114] Fix | Delete

#

[115] Fix | Delete

# Creates a matrix where each argument is a row.

[116] Fix | Delete

# Matrix[ [25, 93], [-1, 66] ]

[117] Fix | Delete

# => 25 93

[118] Fix | Delete

# -1 66

[119] Fix | Delete

#

[120] Fix | Delete

def Matrix.[](*rows)

[121] Fix | Delete

new(:init_rows, rows, false)

[122] Fix | Delete

end

[123] Fix | Delete

[124] Fix | Delete

#

[125] Fix | Delete

# Creates a matrix where +rows+ is an array of arrays, each of which is a row

[126] Fix | Delete

# to the matrix. If the optional argument +copy+ is false, use the given

[127] Fix | Delete

# arrays as the internal structure of the matrix without copying.

[128] Fix | Delete

# Matrix.rows([[25, 93], [-1, 66]])

[129] Fix | Delete

# => 25 93

[130] Fix | Delete

# -1 66

[131] Fix | Delete

def Matrix.rows(rows, copy = true)

[132] Fix | Delete

new(:init_rows, rows, copy)

[133] Fix | Delete

end

[134] Fix | Delete

[135] Fix | Delete

#

[136] Fix | Delete

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

[137] Fix | Delete

# Matrix.columns([[25, 93], [-1, 66]])

[138] Fix | Delete

# => 25 -1

[139] Fix | Delete

# 93 66

[140] Fix | Delete

#

[141] Fix | Delete

#

[142] Fix | Delete

def Matrix.columns(columns)

[143] Fix | Delete

rows = (0 .. columns[0].size - 1).collect {

[144] Fix | Delete

|i|

[145] Fix | Delete

(0 .. columns.size - 1).collect {

[146] Fix | Delete

|j|

[147] Fix | Delete

columns[j][i]

[148] Fix | Delete

}

[149] Fix | Delete

}

[150] Fix | Delete

Matrix.rows(rows, false)

[151] Fix | Delete

end

[152] Fix | Delete

[153] Fix | Delete

#

[154] Fix | Delete

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

[155] Fix | Delete

# Matrix.diagonal(9, 5, -3)

[156] Fix | Delete

# => 9 0 0

[157] Fix | Delete

# 0 5 0

[158] Fix | Delete

# 0 0 -3

[159] Fix | Delete

#

[160] Fix | Delete

def Matrix.diagonal(*values)

[161] Fix | Delete

size = values.size

[162] Fix | Delete

rows = (0 .. size - 1).collect {

[163] Fix | Delete

|j|

[164] Fix | Delete

row = Array.new(size).fill(0, 0, size)

[165] Fix | Delete

row[j] = values[j]

[166] Fix | Delete

row

[167] Fix | Delete

}

[168] Fix | Delete

rows(rows, false)

[169] Fix | Delete

end

[170] Fix | Delete

[171] Fix | Delete

#

[172] Fix | Delete

# Creates an +n+ by +n+ diagonal matrix where each diagonal element is

[173] Fix | Delete

# +value+.

[174] Fix | Delete

# Matrix.scalar(2, 5)

[175] Fix | Delete

# => 5 0

[176] Fix | Delete

# 0 5

[177] Fix | Delete

#

[178] Fix | Delete

def Matrix.scalar(n, value)

[179] Fix | Delete

Matrix.diagonal(*Array.new(n).fill(value, 0, n))

[180] Fix | Delete

end

[181] Fix | Delete

[182] Fix | Delete

#

[183] Fix | Delete

# Creates an +n+ by +n+ identity matrix.

[184] Fix | Delete

# Matrix.identity(2)

[185] Fix | Delete

# => 1 0

[186] Fix | Delete

# 0 1

[187] Fix | Delete

#

[188] Fix | Delete

def Matrix.identity(n)

[189] Fix | Delete

Matrix.scalar(n, 1)

[190] Fix | Delete

end

[191] Fix | Delete

class << Matrix

[192] Fix | Delete

alias unit identity

[193] Fix | Delete

alias I identity

[194] Fix | Delete

end

[195] Fix | Delete

[196] Fix | Delete

#

[197] Fix | Delete

# Creates an +n+ by +n+ zero matrix.

[198] Fix | Delete

# Matrix.zero(2)

[199] Fix | Delete

# => 0 0

[200] Fix | Delete

# 0 0

[201] Fix | Delete

#

[202] Fix | Delete

def Matrix.zero(n)

[203] Fix | Delete

Matrix.scalar(n, 0)

[204] Fix | Delete

end

[205] Fix | Delete

[206] Fix | Delete

#

[207] Fix | Delete

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

[208] Fix | Delete

# +row+.

[209] Fix | Delete

# Matrix.row_vector([4,5,6])

[210] Fix | Delete

# => 4 5 6

[211] Fix | Delete

#

[212] Fix | Delete

def Matrix.row_vector(row)

[213] Fix | Delete

case row

[214] Fix | Delete

when Vector

[215] Fix | Delete

Matrix.rows([row.to_a], false)

[216] Fix | Delete

when Array

[217] Fix | Delete

Matrix.rows([row.dup], false)

[218] Fix | Delete

else

[219] Fix | Delete

Matrix.rows([[row]], false)

[220] Fix | Delete

end

[221] Fix | Delete

end

[222] Fix | Delete

[223] Fix | Delete

#

[224] Fix | Delete

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

[225] Fix | Delete

# in +column+.

[226] Fix | Delete

# Matrix.column_vector([4,5,6])

[227] Fix | Delete

# => 4

[228] Fix | Delete

# 5

[229] Fix | Delete

# 6

[230] Fix | Delete

#

[231] Fix | Delete

def Matrix.column_vector(column)

[232] Fix | Delete

case column

[233] Fix | Delete

when Vector

[234] Fix | Delete

Matrix.columns([column.to_a])

[235] Fix | Delete

when Array

[236] Fix | Delete

Matrix.columns([column])

[237] Fix | Delete

else

[238] Fix | Delete

Matrix.columns([[column]])

[239] Fix | Delete

end

[240] Fix | Delete

end

[241] Fix | Delete

[242] Fix | Delete

#

[243] Fix | Delete

# This method is used by the other methods that create matrices, and is of no

[244] Fix | Delete

# use to general users.

[245] Fix | Delete

#

[246] Fix | Delete

def initialize(init_method, *argv)

[247] Fix | Delete

self.send(init_method, *argv)

[248] Fix | Delete

end

[249] Fix | Delete

[250] Fix | Delete

def init_rows(rows, copy)

[251] Fix | Delete

if copy

[252] Fix | Delete

@rows = rows.collect{|row| row.dup}

[253] Fix | Delete

else

[254] Fix | Delete

@rows = rows

[255] Fix | Delete

end

[256] Fix | Delete

self

[257] Fix | Delete

end

[258] Fix | Delete

private :init_rows

[259] Fix | Delete

[260] Fix | Delete

#

[261] Fix | Delete

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

[262] Fix | Delete

#

[263] Fix | Delete

def [](i, j)

[264] Fix | Delete

@rows[i][j]

[265] Fix | Delete

end

[266] Fix | Delete

[267] Fix | Delete

#

[268] Fix | Delete

# Returns the number of rows.

[269] Fix | Delete

#

[270] Fix | Delete

def row_size

[271] Fix | Delete

@rows.size

[272] Fix | Delete

end

[273] Fix | Delete

[274] Fix | Delete

#

[275] Fix | Delete

# Returns the number of columns. Note that it is possible to construct a

[276] Fix | Delete

# matrix with uneven columns (e.g. Matrix[ [1,2,3], [4,5] ]), but this is

[277] Fix | Delete

# mathematically unsound. This method uses the first row to determine the

[278] Fix | Delete

# result.

[279] Fix | Delete

#

[280] Fix | Delete

def column_size

[281] Fix | Delete

@rows[0].size

[282] Fix | Delete

end

[283] Fix | Delete

[284] Fix | Delete

#

[285] Fix | Delete

# Returns row vector number +i+ of the matrix as a Vector (starting at 0 like

[286] Fix | Delete

# an array). When a block is given, the elements of that vector are iterated.

[287] Fix | Delete

#

[288] Fix | Delete

def row(i) # :yield: e

[289] Fix | Delete

if block_given?

[290] Fix | Delete

for e in @rows[i]

[291] Fix | Delete

yield e

[292] Fix | Delete

end

[293] Fix | Delete

else

[294] Fix | Delete

Vector.elements(@rows[i])

[295] Fix | Delete

end

[296] Fix | Delete

end

[297] Fix | Delete

[298] Fix | Delete

#

[299] Fix | Delete

# Returns column vector number +j+ of the matrix as a Vector (starting at 0

[300] Fix | Delete

# like an array). When a block is given, the elements of that vector are

[301] Fix | Delete

# iterated.

[302] Fix | Delete

#

[303] Fix | Delete

def column(j) # :yield: e

[304] Fix | Delete

if block_given?

[305] Fix | Delete

0.upto(row_size - 1) do

[306] Fix | Delete

|i|

[307] Fix | Delete

yield @rows[i][j]

[308] Fix | Delete

end

[309] Fix | Delete

else

[310] Fix | Delete

col = (0 .. row_size - 1).collect {

[311] Fix | Delete

|i|

[312] Fix | Delete

@rows[i][j]

[313] Fix | Delete

}

[314] Fix | Delete

Vector.elements(col, false)

[315] Fix | Delete

end

[316] Fix | Delete

end

[317] Fix | Delete

[318] Fix | Delete

#

[319] Fix | Delete

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

[320] Fix | Delete

# elements of the matrix.

[321] Fix | Delete

# Matrix[ [1,2], [3,4] ].collect { |i| i**2 }

[322] Fix | Delete

# => 1 4

[323] Fix | Delete

# 9 16

[324] Fix | Delete

#

[325] Fix | Delete

def collect # :yield: e

[326] Fix | Delete

rows = @rows.collect{|row| row.collect{|e| yield e}}

[327] Fix | Delete

Matrix.rows(rows, false)

[328] Fix | Delete

end

[329] Fix | Delete

alias map collect

[330] Fix | Delete

[331] Fix | Delete

#

[332] Fix | Delete

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

[333] Fix | Delete

# * start_row, nrows, start_col, ncols; OR

[334] Fix | Delete

# * col_range, row_range

[335] Fix | Delete

#

[336] Fix | Delete

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

[337] Fix | Delete

# => 9 0 0

[338] Fix | Delete

# 0 5 0

[339] Fix | Delete

#

[340] Fix | Delete

def minor(*param)

[341] Fix | Delete

case param.size

[342] Fix | Delete

when 2

[343] Fix | Delete

from_row = param[0].first

[344] Fix | Delete

size_row = param[0].end - from_row

[345] Fix | Delete

size_row += 1 unless param[0].exclude_end?

[346] Fix | Delete

from_col = param[1].first

[347] Fix | Delete

size_col = param[1].end - from_col

[348] Fix | Delete

size_col += 1 unless param[1].exclude_end?

[349] Fix | Delete

when 4

[350] Fix | Delete

from_row = param[0]

[351] Fix | Delete

size_row = param[1]

[352] Fix | Delete

from_col = param[2]

[353] Fix | Delete

size_col = param[3]

[354] Fix | Delete

else

[355] Fix | Delete

Matrix.Raise ArgumentError, param.inspect

[356] Fix | Delete

end

[357] Fix | Delete

[358] Fix | Delete

rows = @rows[from_row, size_row].collect{

[359] Fix | Delete

|row|

[360] Fix | Delete

row[from_col, size_col]

[361] Fix | Delete

}

[362] Fix | Delete

Matrix.rows(rows, false)

[363] Fix | Delete

end

[364] Fix | Delete

[365] Fix | Delete

#--

[366] Fix | Delete

# TESTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

[367] Fix | Delete

#++

[368] Fix | Delete

[369] Fix | Delete

#

[370] Fix | Delete

# Returns +true+ if this is a regular matrix.

[371] Fix | Delete

#

[372] Fix | Delete

def regular?

[373] Fix | Delete

square? and rank == column_size

[374] Fix | Delete

end

[375] Fix | Delete

[376] Fix | Delete

#

[377] Fix | Delete

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

[378] Fix | Delete

#

[379] Fix | Delete

def singular?

[380] Fix | Delete

not regular?

[381] Fix | Delete

end

[382] Fix | Delete

[383] Fix | Delete

#

[384] Fix | Delete

# Returns +true+ is this is a square matrix. See note in column_size about this

[385] Fix | Delete

# being unreliable, though.

[386] Fix | Delete

#

[387] Fix | Delete

def square?

[388] Fix | Delete

column_size == row_size

[389] Fix | Delete

end

[390] Fix | Delete

[391] Fix | Delete

#--

[392] Fix | Delete

# OBJECT METHODS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

[393] Fix | Delete

#++

[394] Fix | Delete

[395] Fix | Delete

#

[396] Fix | Delete

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

[397] Fix | Delete

#

[398] Fix | Delete

def ==(other)

[399] Fix | Delete

return false unless Matrix === other

[400] Fix | Delete

[401] Fix | Delete

other.compare_by_row_vectors(@rows)

[402] Fix | Delete

end

[403] Fix | Delete

alias eql? ==

[404] Fix | Delete

[405] Fix | Delete

#

[406] Fix | Delete

# Not really intended for general consumption.

[407] Fix | Delete

#

[408] Fix | Delete

def compare_by_row_vectors(rows)

[409] Fix | Delete

return false unless @rows.size == rows.size

[410] Fix | Delete

[411] Fix | Delete

0.upto(@rows.size - 1) do

[412] Fix | Delete

|i|

[413] Fix | Delete

return false unless @rows[i] == rows[i]

[414] Fix | Delete

end

[415] Fix | Delete

true

[416] Fix | Delete

end

[417] Fix | Delete

[418] Fix | Delete

#

[419] Fix | Delete

# Returns a clone of the matrix, so that the contents of each do not reference

[420] Fix | Delete

# identical objects.

[421] Fix | Delete

#

[422] Fix | Delete

def clone

[423] Fix | Delete

Matrix.rows(@rows)

[424] Fix | Delete

end

[425] Fix | Delete

[426] Fix | Delete

#

[427] Fix | Delete

# Returns a hash-code for the matrix.

[428] Fix | Delete

#

[429] Fix | Delete

def hash

[430] Fix | Delete

value = 0

[431] Fix | Delete

for row in @rows

[432] Fix | Delete

for e in row

[433] Fix | Delete

value ^= e.hash

[434] Fix | Delete

end

[435] Fix | Delete

end

[436] Fix | Delete

return value

[437] Fix | Delete

end

[438] Fix | Delete

[439] Fix | Delete

#--

[440] Fix | Delete

# ARITHMETIC -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

[441] Fix | Delete

#++

[442] Fix | Delete

[443] Fix | Delete

#

[444] Fix | Delete

# Matrix multiplication.

[445] Fix | Delete

# Matrix[[2,4], [6,8]] * Matrix.identity(2)

[446] Fix | Delete

# => 2 4

[447] Fix | Delete

# 6 8

[448] Fix | Delete

#

[449] Fix | Delete

def *(m) # m is matrix or vector or number

[450] Fix | Delete

case(m)

[451] Fix | Delete

when Numeric

[452] Fix | Delete

rows = @rows.collect {

[453] Fix | Delete

|row|

[454] Fix | Delete

row.collect {

[455] Fix | Delete

|e|

[456] Fix | Delete

e * m

[457] Fix | Delete

}

[458] Fix | Delete

}

[459] Fix | Delete

return Matrix.rows(rows, false)

[460] Fix | Delete

when Vector

[461] Fix | Delete

m = Matrix.column_vector(m)

[462] Fix | Delete

r = self * m

[463] Fix | Delete

return r.column(0)

[464] Fix | Delete

when Matrix

[465] Fix | Delete

Matrix.Raise ErrDimensionMismatch if column_size != m.row_size

[466] Fix | Delete

[467] Fix | Delete

rows = (0 .. row_size - 1).collect {

[468] Fix | Delete

|i|

[469] Fix | Delete

(0 .. m.column_size - 1).collect {

[470] Fix | Delete

|j|

[471] Fix | Delete

vij = 0

[472] Fix | Delete

0.upto(column_size - 1) do

[473] Fix | Delete

|k|

[474] Fix | Delete

vij += self[i, k] * m[k, j]

[475] Fix | Delete

end

[476] Fix | Delete

vij

[477] Fix | Delete

}

[478] Fix | Delete

}

[479] Fix | Delete

return Matrix.rows(rows, false)

[480] Fix | Delete

else

[481] Fix | Delete

x, y = m.coerce(self)

[482] Fix | Delete

return x * y

[483] Fix | Delete

end

[484] Fix | Delete

end

[485] Fix | Delete

[486] Fix | Delete

#

[487] Fix | Delete

# Matrix addition.

[488] Fix | Delete

# Matrix.scalar(2,5) + Matrix[[1,0], [-4,7]]

[489] Fix | Delete

# => 6 0

[490] Fix | Delete

# -4 12

[491] Fix | Delete

#

[492] Fix | Delete

def +(m)

[493] Fix | Delete

case m

[494] Fix | Delete

when Numeric

[495] Fix | Delete

Matrix.Raise ErrOperationNotDefined, "+"

[496] Fix | Delete

when Vector

[497] Fix | Delete

m = Matrix.column_vector(m)

[498] Fix | Delete

when Matrix

[499] Fix | Delete