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* lib/matrix.rb: add Matrix#determinant_e, Matrix#rank_e.
[ruby-dev:27820] and related thread. git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@9666 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
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@ -1,3 +1,8 @@
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Sat Dec 10 01:06:06 2005 Keiju Ishitsuka <keiju@ruby-lang.org>
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* lib/matrix.rb: add Matrix#determinant_e, Matrix#rank_e.
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[ruby-dev:27820] and related thread.
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Sat Dec 10 00:31:42 2005 Nobuyoshi Nakada <nobu@ruby-lang.org>
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* eval.c (calling_scope_t): gave names to magic numbers for rb_call().
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150
lib/matrix.rb
150
lib/matrix.rb
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@ -1,9 +1,9 @@
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#!/usr/local/bin/ruby
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#--
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# matrix.rb -
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# $Release Version: 1.0$
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# $Revision: 1.11 $
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# $Date: 1999/10/06 11:01:53 $
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# $Release Version: 1.0$
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# $Revision: 1.13 $
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# $Date: 2001/12/09 14:22:23 $
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# Original Version from Smalltalk-80 version
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# on July 23, 1985 at 8:37:17 am
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# by Keiju ISHITSUKA
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@ -105,7 +105,7 @@ end
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# * <tt> #inspect </tt>
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#
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class Matrix
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@RCS_ID='-$Id: matrix.rb,v 1.11 1999/10/06 11:01:53 keiju Exp keiju $-'
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@RCS_ID='-$Id: matrix.rb,v 1.13 2001/12/09 14:22:23 keiju Exp keiju $-'
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# extend Exception2MessageMapper
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include ExceptionForMatrix
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@ -265,6 +265,15 @@ class Matrix
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def [](i, j)
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@rows[i][j]
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end
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alias element []
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alias component []
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def []=(i, j, v)
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@rows[i][j] = v
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end
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alias set_element []=
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alias set_component []=
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private :[]=, :set_element, :set_component
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#
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# Returns the number of rows.
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@ -320,7 +329,7 @@ class Matrix
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#
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# Returns a matrix that is the result of iteration of the given block over all
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# elements of the matrix.
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# Matrix[ [1,2], [3,4] ].collect { |i| i**2 }
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# Matrix[ [1,2], [3,4] ].collect { |e| e**2 }
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# => 1 4
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# 9 16
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#
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@ -668,9 +677,13 @@ class Matrix
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#
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# Returns the determinant of the matrix. If the matrix is not square, the
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# result is 0.
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# result is 0. This method's algorism is Gaussian elimination method
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# and using Numeric#quo(). Beware that using Float values, with their
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# usual lack of precision, can affect the value returned by this method. Use
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# Rational values or Matrix#det_e instead if this is important to you.
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#
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# Matrix[[7,6], [3,9]].determinant
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# => 63
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# => 63.0
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#
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def determinant
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return 0 unless square?
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@ -703,11 +716,56 @@ class Matrix
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det
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end
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alias det determinant
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#
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# Returns the determinant of the matrix. If the matrix is not square, the
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# result is 0. This method's algorism is Gaussian elimination method.
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# This method uses Euclidean algorism. If all elements are integer,
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# really exact value. But, if an element is a float, can't return
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# exact value.
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#
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# Matrix[[7,6], [3,9]].determinant
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# => 63
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#
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def determinant_e
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return 0 unless square?
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size = row_size - 1
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a = to_a
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det = 1
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k = 0
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begin
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if a[k][k].zero?
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i = k
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begin
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return 0 if (i += 1) > size
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end while a[i][k].zero?
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a[i], a[k] = a[k], a[i]
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det *= -1
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end
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(k + 1).upto(size) do |i|
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q = a[i][k] / a[k][k]
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k.upto(size) do |j|
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a[i][j] -= a[k][j] * q
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end
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unless a[i][k].zero?
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a[i], a[k] = a[k], a[i]
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det *= -1
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redo
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end
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end
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det *= a[k][k]
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end while (k += 1) <= size
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det
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end
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alias det_e determinant_e
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#
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# Returns the rank of the matrix. Beware that using Float values,
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# probably return faild value. Use Rational values or Matrix#rank_e
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# for getting exact result.
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#
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# Returns the rank of the matrix. Beware that using Float values, with their
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# usual lack of precision, can affect the value returned by this method. Use
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# Rational values instead if this is important to you.
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# Matrix[[7,6], [3,9]].rank
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# => 2
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#
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@ -769,6 +827,41 @@ class Matrix
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return rank
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end
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#
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# Returns the rank of the matrix. This method uses Euclidean
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# algorism. If all elements are integer, really exact value. But, if
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# an element is a float, can't return exact value.
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#
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# Matrix[[7,6], [3,9]].rank
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# => 2
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#
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def rank_e
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a = to_a
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a_column_size = column_size
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a_row_size = row_size
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pi = 0
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(0 ... a_column_size).each do |j|
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if i = (pi ... a_row_size).find{|i0| !a[i0][j].zero?}
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if i != pi
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a[pi], a[i] = a[i], a[pi]
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end
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(pi + 1 ... a_row_size).each do |k|
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q = a[k][j] / a[pi][j]
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(pi ... a_column_size).each do |j0|
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a[k][j0] -= q * a[pi][j0]
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end
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if k > pi && !a[k][j].zero?
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a[k], a[pi] = a[pi], a[k]
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redo
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end
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end
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pi += 1
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end
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end
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pi
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end
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#
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# Returns the trace (sum of diagonal elements) of the matrix.
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# Matrix[[7,6], [3,9]].trace
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@ -844,6 +937,18 @@ class Matrix
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@rows.collect{|row| row.collect{|e| e}}
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end
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def elements_to_f
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collect{|e| e.to_f}
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end
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def elements_to_i
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collect{|e| e.to_i}
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end
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def elements_to_r
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collect{|e| e.to_r}
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end
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#--
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# PRINTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
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#++
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@ -922,7 +1027,7 @@ class Matrix
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when Vector
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Scalar.Raise WrongArgType, other.class, "Numeric or Scalar or Matrix"
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when Matrix
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self * _M.inverse
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self * other.inverse
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else
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x, y = other.coerce(self)
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x.quo(y)
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@ -1034,6 +1139,15 @@ class Vector
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def [](i)
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@elements[i]
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end
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alias element []
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alias component []
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def []=(i, v)
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@elements[i]= v
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end
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alias set_element []=
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alias set_component []=
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private :[]=, :set_element, :set_component
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#
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# Returns the number of elements in the vector.
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@ -1236,6 +1350,18 @@ class Vector
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@elements.dup
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end
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def elements_to_f
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collect{|e| e.to_f}
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end
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def elements_to_i
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collect{|e| e.to_i}
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end
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def elements_to_r
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collect{|e| e.to_r}
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end
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#
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# FIXME: describe Vector#coerce.
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#
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