= examples/vector/*.rb, examples/matrix/*.rb

* Modified vector and matrix example scripts to use irb/xmp "example printer"
  to better show usage and results.

* Added comments to examples scripts to provide better annotation of examples.

= examples/matrix/a.dat, examples/matrix/b.dat

* Added data files a.dat and b.dat as created by examples/matrix/write.rb and
  used by examples/matrix/read.rb.


git-svn-id: http://rb-gsl.rubyforge.org/svn/trunk/rb-gsl@81 6e764f74-f39f-46f8-8c54-8307d62afe8d

examples/matrix/add.rb

@@ -1,23 +1,45 @@
 #!/usr/bin/env ruby
-require("gsl")
+# Turn on warnings
+$-w = true
 
+require 'irb/xmp'
+require 'gsl'
+
+# Apparently, IRB::Frame has a bug that prevents the defaults from working, so
+# an XMP instance must be created explicitly this way instead of using the
+# otherwise convenient xmp method.
+XMP.new(IRB::Frame.top(-1)).puts <<END
+# Create to 3x3 matrices
 a = GSL::Matrix.alloc([1, 2, 3, 4, 5, 6, 7, 8, 9], 3, 3)
 b = GSL::Matrix.alloc([6, 7, 8], [2, 3, 4], [3, 4, 5])
 
-p a + b
+# Add together to create new matrix
+a + b
 
+# Add b to a, modifying a
 a += b
-p a
 
+# Show that a is modified
+a
+
+# Subtract b from a, modifying a
 a -= b
-p a
 
-p a + 2
+# Add 2 to all elements of a, creating new matrix
+a + 2
 
-p 2 + a
+# Another way to add 2 to all elements of a, creating new matrix
+2 + a
 
+# Add 2 to all elements of a, modifying a
 a += 2
-p a
 
+# Show that a is modified
+a
+
+# Subtract 2 from all elements of a, modifying a
 a -= 2
-p a
+
+# Show that a is modified
+a
+END

examples/matrix/b.dat

@@ -0,0 +1,4 @@
+5
+6
+7
+8

examples/matrix/cat.rb

@@ -1,13 +1,31 @@
 #!/usr/bin/env ruby
-require("gsl")
+# Turn on warnings
+$-w = true
 
+require 'irb/xmp'
+require 'gsl'
+
+# Apparently, IRB::Frame has a bug that prevents the defaults from working, so
+# an XMP instance must be created explicitly this way instead of using the
+# otherwise convenient xmp method.
+XMP.new(IRB::Frame.top(-1)).puts <<END
+# Create a 2x2 Matrix::Int and a 2x3 Matrix::Int
 a = GSL::Matrix::Int[1..4, 2, 2]
 b = GSL::Matrix::Int[5..10, 2, 3]
-p a.horzcat(b)
-p GSL::Matrix::Int.horzcat(a, b)
 
+# Concatenate them horizontally using Matrix::Int#horzcat
+a.horzcat(b)
+
+# Concatenate them horizontally using Matrix::Int.horzcat
+GSL::Matrix::Int.horzcat(a, b)
+
+# Create a 2x2 Matrix::Int and a 3x2 Matrix::Int
 a = GSL::Matrix::Int[1..4, 2, 2]
 b = GSL::Matrix::Int[5..10, 3, 2]
-p b
-p a.vertcat(b)
-p GSL::Matrix::Int.vertcat(a, b)
+
+# Concatenate them vertically using Matrix::Int#vertcat
+a.vertcat(b)
+
+# Concatenate them vertically using Matrix::Int.vertcat
+GSL::Matrix::Int.vertcat(a, b)
+END

examples/matrix/colvectors.rb

@@ -1,13 +1,24 @@
 #!/usr/bin/env ruby
-require("gsl")
+# Turn on warnings
+$-w = true
 
+require 'irb/xmp'
+require 'gsl'
+
+# Apparently, IRB::Frame has a bug that prevents the defaults from working, so
+# an XMP instance must be created explicitly this way instead of using the
+# otherwise convenient xmp method.
+XMP.new(IRB::Frame.top(-1)).puts <<END
+# Create two 3x3 matrices
 m = GSL::Matrix.alloc(1..9, 3, 3)
 n = GSL::Matrix.alloc(11..19, 3, 3)
 
+# Get Vector::Col::View for column 1 of Matrix a
 a = m.col(1)
+
+# Get Vector::Col::View for column 2 of Matrix b
 b = n.col(2)
 
+# Create new Matrix from Vector::Col::Views
 c = GSL::Matrix[a, b]
-p m
-p n
-p c
+END

examples/matrix/complex.rb

@@ -1,29 +1,41 @@
 #!/usr/bin/env ruby
-require("gsl")
+# Turn on warnings
+$-w = true
 
-m = GSL::Matrix::Complex.alloc(3, 3)
+require 'irb/xmp'
+require 'gsl'
 
-m.set(1, 2, 3, 5.6)
+# Apparently, IRB::Frame has a bug that prevents the defaults from working, so
+# an XMP instance must be created explicitly this way instead of using the
+# otherwise convenient xmp method.
+XMP.new(IRB::Frame.top(-1)).puts <<END
+# Create 3x3 Matrix::Complex mz
+mz = GSL::Matrix::Complex.alloc(3, 3)
 
-m.print
+# Set element at row 1, column 2 to 3+5.6i
+mz.set(1, 2, GSL::Complex[3, 5.6])
 
-a = m.get(1, 2)
-p a
-p a.class
+# Get element at row 1, column 2
+a = mz.get(1, 2)
 
-m2 = m.submatrix(1, 1, 2, 2)
-p m2
-m2.print
+# Create Matrix::Complex::View of mz
+# starting at row 1, column 1 and
+# spanning 2 rows and 2 columns
+mzv = mz.submatrix(1, 1, 2, 2)
 
-row = m.row(1)
-p row
-col = m.col(2)
-p col
+# Create a Vector::Complex::View for row 1 of mz
+row = mz.row(1)
 
-m.each_row do |v|
+# Create a Vector::Complex::Col::View for column 2 of mz
+col = mz.col(2)
+
+# Iterate through rows of mz
+mz.each_row do |v|
   p v
 end
 
-m.each_col do |v|
+# Iterate through columns of mz
+mz.each_col do |v|
   p v
 end
+END

examples/matrix/det.rb

@@ -1,9 +1,29 @@
 #!/usr/bin/env ruby
-require("gsl")
-p m = GSL::Matrix[[1, 2, 3, 4, 5, 6, 7, 8 ,0], 3, 3]
-puts("m.det = #{m.det}")
-puts("m.trace = #{m.trace}")
+# Turn on warnings
+$-w = true
 
-p m.to_complex.det
-p m.to_complex.trace
+require 'irb/xmp'
+require 'gsl'
 
+# Apparently, IRB::Frame has a bug that prevents the defaults from working, so
+# an XMP instance must be created explicitly this way instead of using the
+# otherwise convenient xmp method.
+XMP.new(IRB::Frame.top(-1)).puts <<END
+# Crete test matrix m
+m = GSL::Matrix[[1, 2, 3, 4, 5, 6, 7, 8 ,0], 3, 3]
+
+# Calculate determinant of m
+m.det
+
+# Calculate trace of m (sum of diagonal elements)
+m.trace
+
+# Convert to Matrix::Complex mz
+mz = m.to_complex
+
+# Calulate determinant of mz
+mz.det
+
+# Calculate trace of mz (sum of diagonal elements)
+mz.trace
+END

examples/matrix/diagonal.rb

@@ -1,6 +1,23 @@
 #!/usr/bin/env ruby
-require("gsl")
-p GSL::Matrix.diagonal(1..3)
-p GSL::Matrix.diagonal([1, 2, 3])
-p GSL::Matrix.diagonal([1, 2, 3].to_gv)
-p GSL::Matrix.diagonal(1, 2, 3)
+# Turn on warnings
+$-w = true
+
+require 'irb/xmp'
+require 'gsl'
+
+# Apparently, IRB::Frame has a bug that prevents the defaults from working, so
+# an XMP instance must be created explicitly this way instead of using the
+# otherwise convenient xmp method.
+XMP.new(IRB::Frame.top(-1)).puts <<END
+# Create matrix with diagonal given by Range
+GSL::Matrix.diagonal(1..3)
+
+# Create matrix with diagonal given by Array
+GSL::Matrix.diagonal([1, 2, 3])
+
+# Create matrix with diagonal given by GSL::Vector
+GSL::Matrix.diagonal(GSL::Vector.indgen(3,1))
+
+# Create matrix with diagonal given by individual elements
+GSL::Matrix.diagonal(1, 2, 3)
+END

examples/matrix/hilbert.rb

@@ -1,14 +1,31 @@
 #!/usr/bin/env ruby
-require("gsl")
+# Turn on warnings
+$-w = true
 
+require 'irb/xmp'
+require 'gsl'
+
+# Apparently, IRB::Frame has a bug that prevents the defaults from working, so
+# an XMP instance must be created explicitly this way instead of using the
+# otherwise convenient xmp method.
+XMP.new(IRB::Frame.top(-1)).puts <<END
+# Create 3x3 Hilbert matrix m
 m = GSL::Matrix.hilbert(3)
-p m
 
+# Compute inverse of m
 invm = m.inv
+
+# Create inverse of 3x3 Hilbert matrix directly
 invm2 = GSL::Matrix.invhilbert(3)
 
-p invm
+# Show that both inverse matrices are inverses of m
+m*invm
+m*invm2
+
+# Show that the two inverse matrices are equal
+# to absolute accuracy eps = 1e-10
+invm == invm2
 
-p m*invm
-p m*invm2
-p invm == invm2
+# Show that they may not be exactly equal
+invm - invm2
+END

examples/matrix/iterator.rb

@@ -1,9 +1,19 @@
 #!/usr/bin/env ruby
-require("gsl")
+# Turn on warnings
+$-w = true
 
+require 'irb/xmp'
+require 'gsl'
+
+# Apparently, IRB::Frame has a bug that prevents the defaults from working, so
+# an XMP instance must be created explicitly this way instead of using the
+# otherwise convenient xmp method.
+XMP.new(IRB::Frame.top(-1)).puts <<END
+# Create test matrix
 m = GSL::Matrix.alloc([1, 2, 3, 4, 5, 6, 7, 8 ,9], 3, 3)
 
+# Iterate through columns
 m.each_col do |v|
   p v
 end
-
+END

examples/matrix/matrix.rb

@@ -1,45 +1,57 @@
 #!/usr/bin/env ruby
-require("gsl") 
+# Turn on warnings
+$-w = true
 
-m = GSL::Matrix.alloc([1, 2, 3, 4, 5, 6, 7, 8, 9], 3, 3)
+require 'irb/xmp'
+require 'gsl'
 
-p m
+# Apparently, IRB::Frame has a bug that prevents the defaults from working, so
+# an XMP instance must be created explicitly this way instead of using the
+# otherwise convenient xmp method.
+XMP.new(IRB::Frame.top(-1)).puts <<END
+# Create test matrix m
+m = GSL::Matrix.alloc([1, 2, 3, 4, 5, 6, 7, 8, 9], 3, 3)
 
-m.set([6,5, 6], [4, 5,7], [8, 5, 21])
-m.print
+# Set rows of m from Arrays
+m.set([6, 5, 6], [4, 5, 7], [8, 5, 21])
 
-m.set_col(1, [12, 3, 55].to_gv)
-#m.print
+# Set column 1 of m from GSL::Vector
+m.set_col(1, GSL::Vector[12, 3, 55])
 
+# Create transpose of m
 m2 = m.transpose
-m.print
-m2.print
 
+# Swap rows 1 and 2 of m
 m.swap_rows(1, 2)
-m.print 
 
+# Create Vector::Col::View for column 0 of m
 v = m.col(0)
-p v.to_a
 
+# Create Vector::View of diagonal of m
+m.diagonal
+
+# Create Array containing diagonal elements of m
 m.diagonal.to_a
 
+# Create another test matrix m
 m = GSL::Matrix.alloc([1, 2, 3], [6, 5, 4], [7, 8, 1])
-p m.get(1, 2)
-m.print
 
-m3 = m.LU_decomp
-p m3
+# Get element at row 1, column 2
+m.get(1, 2)
+
+# Perform LU decomposition of m
+lu, perm, sign = m.LU_decomp
 
-m3 = GSL::Matrix.alloc(5, 5)
+# Create 5x5 zero matrix m5
+m5 = GSL::Matrix.alloc(5, 5)
 
+# Initialize elements of m5
 for i in 0...5 do
   for j in 0...5 do
-    val = 0.5*(i+0.4)*(j+1.2)
-    m3.set(i, j, val)
+    m5[i, j] = 0.5*(i+0.4)*(j+1.2)
   end
 end
 
-m3.print
-
-
-
+# Show m5
+m5
+END