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git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@3362 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
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gsinclair 2003-01-20 07:16:01 +00:00
parent 971d5f8480
commit 181edd12a0
1 changed files with 375 additions and 27 deletions
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398
lib/matrix.rb
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@ -183,6 +183,19 @@ module ExceptionForMatrix
def_exception("ErrOperationNotDefined", "This operation(%s) can\\'t defined")
end
#
# Represents a mathematical matrix, and provides methods for creating
# special-case matrices (zero, identity, diagonal, singular, vector), operating
# on them arithmetically and algebraically, and determining their mathematical
# properties (trace, rank, inverse, determinant).
#
# The capabilities of the class indicated in the above paragraph are probably
# not exhaustive. Browse the methods and their documentation for more
# information.
#
# Note that although matrices should theoretically be rectangular, this is not
# enforced by the class.
#
class Matrix
@RCS_ID='-$Id: matrix.rb,v 1.11 1999/10/06 11:01:53 keiju Exp keiju $-'
@ -192,14 +205,34 @@ class Matrix
# instance creations
private_class_method :new
#
# Creates a matrix where each argument is a row.
# Matrix[ [25, 93], [-1, 66] ]
# => 25 93
# -1 66
#
def Matrix.[](*rows)
new(:init_rows, rows, false)
end
#
# Creates a matrix where +rows+ is an array of arrays, each of which is a row
# to 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)
new(:init_rows, rows, copy)
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 = (0 .. columns[0].size - 1).collect {
|i|
@ -211,6 +244,13 @@ class Matrix
Matrix.rows(rows, false)
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
rows = (0 .. size - 1).collect {
@ -222,10 +262,23 @@ class Matrix
rows(rows, false)
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)
Matrix.diagonal(*Array.new(n).fill(value, 0, n))
end
#
# Creates an +n+ by +n+ identity matrix.
# Matrix.identity(2)
# => 1 0
# 0 1
#
def Matrix.identity(n)
Matrix.scalar(n, 1)
end
@ -234,10 +287,22 @@ class Matrix
alias I identity
end
#
# Creates an +n+ by +n+ zero matrix.
# Matrix.zero(2)
# => 0 0
# 0 0
#
def Matrix.zero(n)
Matrix.scalar(n, 0)
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)
case row
when Vector
@ -249,6 +314,14 @@ class Matrix
end
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)
case column
when Vector
@ -260,7 +333,10 @@ class Matrix
end
end
# initializing
#
# This method is used by the other methods that create matrices, and is of no
# use to general users.
#
def initialize(init_method, *argv)
self.send(init_method, *argv)
end
@ -275,31 +351,50 @@ class Matrix
end
private :init_rows
#accessing
#
# Returns element (+i+,+j+) of the matrix. That is: row +i+, column +j+.
#
def [](i, j)
@rows[i][j]
end
#
# Returns the number of rows.
#
def row_size
@rows.size
end
#
# Returns the number of columns. Note that it is possible to construct a
# matrix with uneven columns (e.g. Matrix[ [1,2,3], [4,5] ]), but this is
# mathematically unsound. This method uses the first row to determine the
# result.
#
def column_size
@rows[0].size
end
def row(i)
#
# 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) # :yield: e
if block_given?
for e in @rows[i]
yield e
end
else
Vector.elements(@rows[i])
end
end
def column(j)
#
# 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?
0.upto(row_size - 1) do
|i|
@ -314,15 +409,27 @@ class Matrix
end
end
def collect
#
# 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 { |i| i**2 }
# => 1 4
# 9 16
#
def collect # :yield: e
rows = @rows.collect{|row| row.collect{|e| yield e}}
Matrix.rows(rows, false)
end
alias map collect
#
# param: (from_row, row_size, from_col, size_col)
# (from_row..to_row, from_col..to_col)
# Returns a section of the matrix. The parameters are either:
# * start_row, nrows, start_col, ncols; OR
# * col_range, row_range
#
# Matrix.diagonal(9, 5, -3).minor(0..1, 0..2)
# => 9 0 0
# 0 5 0
#
def minor(*param)
case param.size
@ -347,20 +454,39 @@ class Matrix
Matrix.rows(rows, false)
end
# TESTING
#--
# TESTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Returns +true+ if this is a regular matrix.
#
def regular?
square? and rank == column_size
end
#
# Returns +true+ is this is a singular (i.e. non-regular) matrix.
#
def singular?
not regular?
end
#
# Returns +true+ is this is a square matrix. See note in column_size about this
# being unreliable, though.
#
def square?
column_size == row_size
end
# COMPARING
#--
# OBJECT METHODS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Returns +true+ if and only if the two matrices contain equal elements.
#
def ==(other)
return false unless Matrix === other
@ -368,6 +494,9 @@ class Matrix
end
alias eql? ==
#
# Not really intended for general consumption.
#
def compare_by_row_vectors(rows)
return false unless @rows.size == rows.size
@ -378,10 +507,17 @@ class Matrix
true
end
#
# Returns a clone of the matrix, so that the contents of each do not reference
# identical objects.
#
def clone
Matrix.rows(@rows)
end
#
# Returns a hash-code for the matrix.
#
def hash
value = 0
for row in @rows
@ -392,8 +528,16 @@ class Matrix
return value
end
# ARITHMETIC
#--
# 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
@ -431,6 +575,12 @@ class Matrix
end
end
#
# Matrix addition.
# Matrix.scalar(2,5) + Matrix[[1,0], [-4,7]]
# => 6 0
# -4 12
#
def +(m)
case m
when Numeric
@ -455,6 +605,12 @@ class Matrix
Matrix.rows(rows, false)
end
#
# Matrix subtraction.
# Matrix[[1,5], [4,2]] - Matrix[[9,3], [-4,1]]
# => -8 2
# 8 1
#
def -(m)
case m
when Numeric
@ -479,6 +635,12 @@ class Matrix
Matrix.rows(rows, false)
end
#
# Matrix division (multiplication by the inverse).
# Matrix[[7,6], [3,9]] / Matrix[[2,9], [3,1]]
# => -7 1
# -3 -6
#
def /(other)
case other
when Numeric
@ -498,12 +660,21 @@ class Matrix
end
end
#
# Returns the inverse of the matrix.
# Matrix[[1, 2], [2, 1]].inverse
# => -1 1
# 0 -1
#
def inverse
Matrix.Raise ErrDimensionMismatch unless square?
Matrix.I(row_size).inverse_from(self)
end
alias inv inverse
#
# Not for public consumption?
#
def inverse_from(src)
size = row_size - 1
a = src.to_a
@ -547,6 +718,13 @@ class Matrix
end
#alias reciprocal inverse
#
# Matrix exponentiation. Defined for integer powers only. Equivalent to
# multiplying the matrix by itself N times.
# Matrix[[7,6], [3,9]] ** 2
# => 67 96
# 48 99
#
def ** (other)
if other.kind_of?(Integer)
x = self
@ -574,8 +752,16 @@ class Matrix
end
end
# Matrix functions
#--
# MATRIX FUNCTIONS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Returns the determinant of the matrix. If the matrix is not square, the
# result is 0.
# Matrix[[7,6], [3,9]].determinant
# => 63
#
def determinant
return 0 unless square?
@ -608,6 +794,13 @@ class Matrix
end
alias det determinant
#
# Returns the rank of the matrix. Beware that using Float values, with their
# usual lack of precision, can affect the value returned by this method. Use
# Rational values instead if this is important to you.
# Matrix[[7,6], [3,9]].rank
# => 2
#
def rank
if column_size > row_size
a = transpose.to_a
@ -666,6 +859,11 @@ class Matrix
return rank
end
#
# Returns the trace (sum of diagonal elements) of the matrix.
# Matrix[[7,6], [3,9]].trace
# => 16
#
def trace
tr = 0
0.upto(column_size - 1) do
@ -676,13 +874,28 @@ class Matrix
end
alias tr trace
#
# Returns the transpose of the matrix.
# Matrix[[1,2], [3,4], [5,6]]
# => 1 2
# 3 4
# 5 6
# Matrix[[1,2], [3,4], [5,6]].transpose
# => 1 3 5
# 2 4 6
#
def transpose
Matrix.columns(@rows)
end
alias t transpose
# CONVERTING
#--
# CONVERTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# FIXME: describe #coerce.
#
def coerce(other)
case other
when Numeric
@ -692,6 +905,9 @@ class Matrix
end
end
#
# Returns an array of the row vectors of the matrix. See Vector.
#
def row_vectors
rows = (0 .. row_size - 1).collect {
|i|
@ -700,6 +916,9 @@ class Matrix
rows
end
#
# Returns an array of the column vectors of the matrix. See Vector.
#
def column_vectors
columns = (0 .. column_size - 1).collect {
|i|
@ -708,23 +927,41 @@ class Matrix
columns
end
#
# Returns an array of arrays that describe the rows of the matrix.
#
def to_a
@rows.collect{|row| row.collect{|e| e}}
end
#
# Applies #to_f to all elements to return a new matrix.
#
def to_f
collect{|e| e.to_f}
end
#
# Applies #to_i to all elements to return a new matrix.
#
def to_i
collect{|e| e.to_i}
end
#
# Applies #to_r to all elements to return a new matrix.
#
def to_r
collect{|e| e.to_r}
end
# PRINTING
#--
# PRINTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Overrides Object#to_s
#
def to_s
"Matrix[" + @rows.collect{
|row|
@ -732,13 +969,16 @@ class Matrix
}.join(", ")+"]"
end
#
# Overrides Object#inspect
#
def inspect
"Matrix"+@rows.inspect
end
# Private CLASS
class Scalar < Numeric
class Scalar < Numeric # :nodoc:
include ExceptionForMatrix
def initialize(value)
@ -827,18 +1067,33 @@ class Vector
#INSTANCE CREATION
private_class_method :new
#
# Creates a Vector from a list of elements.
# Vector[7, 4, ...]
#
def Vector.[](*array)
new(:init_elements, array, copy = false)
end
#
# Creates a vector from an Array. The optional second argument specifies
# whether the array itself or a copy is used internally.
#
def Vector.elements(array, copy = true)
new(:init_elements, array, copy)
end
#
# For internal use.
#
def initialize(method, array, copy)
self.send(method, array, copy)
end
#
# For internal use.
#
def init_elements(array, copy)
if copy
@elements = array.dup
@ -849,16 +1104,28 @@ class Vector
# ACCSESSING
#
# Returns element number +i+ (starting at zero) of the vector.
#
def [](i)
@elements[i]
end
#
# Returns the number of elements in the vector.
#
def size
@elements.size
end
# ENUMRATIONS
def each2(v)
#--
# ENUMRATIONS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Iterate over the elements of this vector and +v+ in conjunction.
#
def each2(v) # :yield: e1, e2
Vector.Raise ErrDimensionMismatch if size != v.size
0.upto(size - 1) do
|i|
@ -866,7 +1133,11 @@ class Vector
end
end
def collect2(v)
#
# Collects (as in Enumerable#collect) over the elements of this vector and +v+
# in conjunction.
#
def collect2(v) # :yield: e1, e2
Vector.Raise ErrDimensionMismatch if size != v.size
(0 .. size - 1).collect do
|i|
@ -874,7 +1145,13 @@ class Vector
end
end
# COMPARING
#--
# COMPARING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Returns +true+ iff the two vectors have the same elements in the same order.
#
def ==(other)
return false unless Vector === other
@ -882,21 +1159,35 @@ class Vector
end
alias eqn? ==
#
# For internal use.
#
def compare_by(elements)
@elements == elements
end
#
# Return a copy of the vector.
#
def clone
Vector.elements(@elements)
end
#
# Return a hash-code for the vector.
#
def hash
@elements.hash
end
# ARITHMETIC
#--
# ARITHMETIC -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
def *(x) #x is matrix or number
#
# Multiplies the vector by +x+, where +x+ is a number or another vector.
#
def *(x)
case x
when Numeric
els = @elements.collect{|e| e * x}
@ -909,6 +1200,9 @@ class Vector
end
end
#
# Vector addition.
#
def +(v)
case v
when Vector
@ -926,6 +1220,9 @@ class Vector
end
end
#
# Vector subtraction.
#
def -(v)
case v
when Vector
@ -943,8 +1240,14 @@ class Vector
end
end
# VECTOR FUNCTIONS
#--
# VECTOR FUNCTIONS -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Returns the inner product of this vector with the other.
# Vector[4,7].inner_product Vector[10,1] => 47
#
def inner_product(v)
Vector.Raise ErrDimensionMismatch if size != v.size
@ -956,7 +1259,10 @@ class Vector
p
end
def collect
#
# Like Array#collect.
#
def collect # :yield: e
els = @elements.collect {
|v|
yield v
@ -965,7 +1271,10 @@ class Vector
end
alias map collect
def map2(v)
#
# Like Vector#collect2, but returns a Vector instead of an Array.
#
def map2(v) # :yield: e1, e2
els = collect2(v) {
|v1, v2|
yield v1, v2
@ -973,6 +1282,10 @@ class Vector
Vector.elements(els, false)
end
#
# Returns the modulus (Pythagorean distance) of the vector.
# Vector[5,8,2].r => 9.643650761
#
def r
v = 0
for e in @elements
@ -981,27 +1294,48 @@ class Vector
return Math.sqrt(v)
end
#--
# CONVERTING
#++
#
# Creates a single-row matrix from this vector.
#
def covector
Matrix.row_vector(self)
end
#
# Returns the elements of the vector in an array.
#
def to_a
@elements.dup
end
#
# Applies #to_f to each element to produce a new vector.
#
def to_f
collect{|e| e.to_f}
end
#
# Applies #to_i to each element to produce a new vector.
#
def to_i
collect{|e| e.to_i}
end
#
# Applies #to_f to each element to produce a new vector.
#
def to_r
collect{|e| e.to_r}
end
#
# FIXME: describe Vector#coerce.
#
def coerce(other)
case other
when Numeric
@ -1011,13 +1345,27 @@ class Vector
end
end
# PRINTING
#--
# PRINTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
#++
#
# Overrides Object#to_s
#
def to_s
"Vector[" + @elements.join(", ") + "]"
end
#
# Overrides Object#inspect
#
def inspect
str = "Vector"+@elements.inspect
end
end
# Documentation comments:
# - Matrix#coerce and Vector#coerce need to be documented
# - Matrix class methods (aliases) unit and I don't appear in RDoc output
# becuase of "class << Matrix". This is an RDoc issue.