Feature #10073 » implement_Matrix#laplace_expansion.patch
| NEWS | ||
|---|---|---|
|
by deleting the specified row and column.
|
||
|
* Matrix#cofactor(row, column) returns the (row, column) cofactor
|
||
|
which is obtained by multiplying the first minor by (-1)**(row + column).
|
||
|
* Matrix#laplace_expansion(num, row_or_column) returns the laplace_expansion
|
||
|
along +num+ -th +row_or_column+.
|
||
|
* Matrix#@+ and Matrix#@- .
|
||
|
* Vector
|
||
| lib/matrix.rb | ||
|---|---|---|
|
# * #minor(*param)
|
||
|
# * #first_minor(row, column)
|
||
|
# * #cofactor(row, column)
|
||
|
# * #laplace_expansion(num, row_or_column)
|
||
|
# * #cofactor_expansion(num, row_or_column)
|
||
|
# * #cofact_exp(num, row_or_column)
|
||
|
#
|
||
|
# Properties of a matrix:
|
||
|
# * #diagonal?
|
||
| ... | ... | |
|
det_of_minor * (-1) ** (row + column)
|
||
|
end
|
||
|
#
|
||
|
# Returns the laplace_expansion along +num+ -th +row_or_column+
|
||
|
#
|
||
|
# Matrix[[Vector[1, 0], Vector[0, 1]], [2, 3]].laplace_expansion(0, :row)
|
||
|
# => Vector[3, -2]
|
||
|
#
|
||
|
# Matrix[[7,6], [3,9]].laplace_expansion(1, :column)
|
||
|
# => 45
|
||
|
#
|
||
|
def laplace_expansion(num, row_or_column)
|
||
|
Matrix.Raise ErrDimensionMismatch unless square?
|
||
|
raise RuntimeError, "laplace_expansion of empty matrix is not defined" if empty?
|
||
|
raise ArgumentError, "#{row_or_column} should be :row or :column" unless %i(row column).include?(row_or_column)
|
||
|
unless 0 <= num && num < row_count
|
||
|
raise ArgumentError, "invalid num (#{num.inspect} for 0..#{row_count - 1})"
|
||
|
end
|
||
|
send(row_or_column, num).map.with_index { |e, k|
|
||
|
e * cofactor(*(row_or_column == :row ? [num, k] : [k,num]))
|
||
|
}.inject(:+)
|
||
|
end
|
||
|
alias_method :cofactor_expansion, :laplace_expansion
|
||
|
alias_method :cofact_exp, :laplace_expansion
|
||
|
#--
|
||
|
# TESTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
|
||
|
#++
|
||
| test/matrix/test_matrix.rb | ||
|---|---|---|
|
assert_raise(ExceptionForMatrix::ErrDimensionMismatch) { Matrix[[2,0,1],[0,-2,2]].cofactor(0, 0) }
|
||
|
end
|
||
|
def test_laplace_expansion
|
||
|
assert_equal(1, Matrix[[1]].laplace_expansion(0, :row))
|
||
|
assert_equal(45, Matrix[[7,6], [3,9]].laplace_expansion(1, :row))
|
||
|
assert_equal(0, Matrix[[0,0],[0,0]].laplace_expansion(0, :column))
|
||
|
assert_equal(-7, Matrix[[0,0,1],[0,7,6],[1,3,9]].laplace_expansion(2, :column))
|
||
|
assert_equal(Vector[3, -2], Matrix[[Vector[1, 0], Vector[0, 1]], [2, 3]].laplace_expansion(0, :row))
|
||
|
assert_raise(ExceptionForMatrix::ErrDimensionMismatch) { @m1.laplace_expansion(1, :row) }
|
||
|
assert_raise(ArgumentError) { Matrix[[7,6], [3,9]].laplace_expansion(2, :row) }
|
||
|
assert_raise(ArgumentError) { Matrix[[0,0,1],[0,7,6],[1,3,9]].laplace_expansion(-1, :column) }
|
||
|
assert_raise(ArgumentError) { Matrix[[7,6], [3,9]].laplace_expansion(1, :foo) }
|
||
|
assert_raise(RuntimeError) { Matrix.empty(0, 0).laplace_expansion(0, :row) }
|
||
|
end
|
||
|
def test_regular?
|
||
|
assert(Matrix[[1, 0], [0, 1]].regular?)
|
||
|
assert(Matrix[[1, 0, 0], [0, 1, 0], [0, 0, 1]].regular?)
|
||