Conjugate transpose: Difference between revisions
Added the Common Lisp version--~~~~
Thundergnat (talk | contribs) m (→{{header|Perl 6}}: minor style tweaks) |
(Added the Common Lisp version--~~~~) |
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Complex Matrix A is not normal</pre>
=={{header|Common Lisp}}==
<lang Lisp>
(defun matrix-multiply (m1 m2)
(mapcar
(lambda (row)
(apply #'mapcar
(lambda (&rest column)
(apply #'+ (mapcar #'* row column))) m2)) m1))
(defun identity-p (m &optional (tolerance 1e-6))
"Is m an identity matrix?"
(loop for row in m
for r = 1 then (1+ r) do
(loop for col in row
for c = 1 then (1+ c) do
(if (eql r c)
(unless (< (abs (- col 1)) tolerance) (return-from identity-p nil))
(unless (< (abs col) tolerance) (return-from identity-p nil)) )))
T )
(defun conjugate-transpose (m)
(apply #'mapcar #'list (mapcar #'(lambda (r) (mapcar #'conjugate r)) m)) )
(defun hermitian-p (m)
(equalp m (conjugate-transpose m)))
(defun normal-p (m)
(let ((m* (conjugate-transpose m)))
(equalp (matrix-multiply m m*) (matrix-multiply m* m)) ))
(defun unitary-p (m)
(identity-p (matrix-multiply m (conjugate-transpose m))) )
</lang>
{{out}}
<pre>
(hermitian-p
'((3 #C(2 1))
(#C(2 -1) 1) ))
=> T
(normal-p
'((#C(0 1) 0)
(0 #C(3 -5)) ))
==> T
(unitary-p
'((0.70710677 0.70710677 0)
(#C(0 -0.70710677) #C(0 0.70710677) 0)
(0 0 1) ))
==> T
</pre>
=={{header|D}}==
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