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fix :unitary? and add :adjoint #14

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fix :unitary? and add :adjoint #14

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16 changes: 14 additions & 2 deletions lib/matrix.rb
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Original file line number Diff line number Diff line change
Expand Up @@ -827,6 +827,16 @@ def laplace_expansion(row: nil, column: nil)
end
alias_method :cofactor_expansion, :laplace_expansion

#
# Returns the adjoint of the matrix.
#
# Matrix[ [i,1],[2,-i] ].adjoint
# # => -i 2
# # 1 i
#
def adjoint
conjugate.transpose
end

#--
# TESTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
Expand Down Expand Up @@ -984,11 +994,13 @@ def antisymmetric?
#
def unitary?
raise ErrDimensionMismatch unless square?
rows.each_with_index do |row, i|
adj_conj = adjoint

row_count.times do |i|
column_count.times do |j|
s = 0
row_count.times do |k|
s += row[k].conj * rows[k][j]
s += adj_conj[i, k] * self[k, j]
end
return false unless s == (i == j ? 1 : 0)
end
Expand Down
23 changes: 23 additions & 0 deletions test/matrix/test_matrix.rb
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Expand Up @@ -360,6 +360,20 @@ def test_laplace_expansion
assert_raise(RuntimeError) { Matrix.empty(0, 0).laplace_expansion(row: 0) }
end

def test_adjoint
assert_equal(Matrix.empty, Matrix.empty.adjoint)
assert_equal(Matrix[[1]], Matrix[[1]].adjoint)
assert_equal(Matrix[[9,-6],[-3,7]], Matrix[[9,-3],[-6,7]].adjoint)
assert_equal(Matrix[[45,3,-7],[6,-1,0],[-7,0,0]], Matrix[[45,6,-7],[3,-1,0],[-7,0,0]].adjoint)
assert_equal(@m1.transpose, @m1.adjoint)
assert_equal(@m4.transpose, @m4.adjoint)
assert_equal(Matrix[[Complex(1,-2),1], [Complex(0,-1), 2], [0,3]], @c1.adjoint)
assert_equal(@e1.transpose, @e1.adjoint)
assert_equal(@e2.transpose, @e2.adjoint)
assert_equal(Matrix[[0,Complex(0,1)], [Complex(0, -1), 0]], Matrix[[0,Complex(0,1)], [Complex(0, -1), 0]].adjoint)
assert_equal(Matrix[[Complex(0,1), 0], [0, Complex(0,-1)]], Matrix[[Complex(0, -1), 0], [0, Complex(0, 1)]].adjoint)
end

def test_regular?
assert(Matrix[[1, 0], [0, 1]].regular?)
assert(Matrix[[1, 0, 0], [0, 1, 0], [0, 0, 1]].regular?)
Expand All @@ -379,6 +393,15 @@ def test_square?
assert(!Matrix[[1, 0, 0], [0, 1, 0]].square?)
end

def test_unitary?
assert(Matrix[[0,1], [1,0]].unitary?)
assert(Matrix[[0,Complex(0,-1)], [Complex(0,1),0]].unitary?)
assert(Matrix[[1,0], [0, -1]].unitary?)
assert(!Matrix[[1,1], [1,1]].unitary?)
assert(Matrix[[1,0,0,0], [0,0,1,0], [0,1,0,0], [0,0,0,1]].unitary?)
assert(Matrix[[1,0,0,0], [0,1,0,0], [0,0,0,1], [0,0,1,0]].unitary?)
end

def test_mul
assert_equal(Matrix[[2,4],[6,8]], Matrix[[2,4],[6,8]] * Matrix.I(2))
assert_equal(Matrix[[4,8],[12,16]], Matrix[[2,4],[6,8]] * 2)
Expand Down