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Returns the trace (sum of diagonal elements) of the matrix.

Matrix[[7,6], [3,9]].trace
  => 16

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

Returns a new matrix resulting by stacking vertically the receiver with the given matrices

x = Matrix[[1, 2], [3, 4]]
y = Matrix[[5, 6], [7, 8]]
x.vstack(y) # => Matrix[[1, 2], [3, 4], [5, 6], [7, 8]]

Returns the Eigensystem of the matrix; see EigenvalueDecomposition.

m = Matrix[[1, 2], [3, 4]]
v, d, v_inv = m.eigensystem
d.diagonal? # => true
v.inv == v_inv # => true
(v * d * v_inv).round(5) == m # => true

Returns the imaginary part of the matrix.

Matrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]]
  => 1+2i  i  0
        1  2  3
Matrix[[Complex(1,2), Complex(0,1), 0], [1, 2, 3]].imaginary
  =>   2i  i  0
        0  0  0

Overrides Object#inspect

Returns true iff all of vectors are linearly independent.

Vector.independent?(Vector[1,0], Vector[0,1])
  => true

Vector.independent?(Vector[1,2], Vector[2,4])
  => false

Returns true iff all of vectors are linearly independent.

Vector[1,0].independent?(Vector[0,1])
  => true

Vector[1,2].independent?(Vector[2,4])
  => false

Overrides Object#inspect

Returns an incremented value of default according to arg.

Terminates option parsing. Optional parameter arg is a string pushed back to be the first non-option argument.

Puts option summary into to and returns to. Yields each line if a block is given.

to

Output destination, which must have method <<. Defaults to [].

width

Width of left side, defaults to @summary_width.

max

Maximum length allowed for left side, defaults to width - 1.

indent

Indentation, defaults to @summary_indent.

Returns the number of elements in the match array.

m = /(.)(.)(\d+)(\d)/.match("THX1138.")
m.length   #=> 5
m.size     #=> 5

Returns the offset of the start of the nth element of the match array in the string. n can be a string or symbol to reference a named capture.

m = /(.)(.)(\d+)(\d)/.match("THX1138.")
m.begin(0)       #=> 1
m.begin(2)       #=> 2

m = /(?<foo>.)(.)(?<bar>.)/.match("hoge")
p m.begin(:foo)  #=> 0
p m.begin(:bar)  #=> 2

Returns a printable version of mtch.

puts /.$/.match("foo").inspect
#=> #<MatchData "o">

puts /(.)(.)(.)/.match("foo").inspect
#=> #<MatchData "foo" 1:"f" 2:"o" 3:"o">

puts /(.)(.)?(.)/.match("fo").inspect
#=> #<MatchData "fo" 1:"f" 2:nil 3:"o">

puts /(?<foo>.)(?<bar>.)(?<baz>.)/.match("hoge").inspect
#=> #<MatchData "hog" foo:"h" bar:"o" baz:"g">

Increases left margin after newline with indent for line breaks added in the block.

Returns true if value is a prime number, else returns false.

Parameters

value

an arbitrary integer to be checked.

generator

optional. A pseudo-prime generator.

Opens a new transaction for the data store. Code executed inside a block passed to this method may read and write data to and from the data store file.

At the end of the block, changes are committed to the data store automatically. You may exit the transaction early with a call to either PStore#commit or PStore#abort. See those methods for details about how changes are handled. Raising an uncaught Exception in the block is equivalent to calling PStore#abort.

If read_only is set to true, you will only be allowed to read from the data store during the transaction and any attempts to change the data will raise a PStore::Error.

Note that PStore does not support nested transactions.

Create the tasks defined by this task lib.