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Conjugate transpose: Difference between revisions
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Matrix is unitary
</pre>
=={{header|Python}}==
Internally, matrices must be represented as rectangular tuples of tuples of complex numbers.
<lang python>def conjugate_transpose(m):
return tuple(tuple(n.conjugate() for n in row) for row in zip(*m))
def mmul( ma, mb):
return tuple(tuple(sum( ea*eb for ea,eb in zip(a,b)) for b in zip(*mb)) for a in ma)
def mi(size):
'Complex Identity matrix'
sz = range(size)
m = [[0 + 0j for i in sz] for j in sz]
for i in range(size):
m[i][i] = 1 + 0j
return tuple(tuple(row) for row in m)
def __allsame(vector):
first, rest = vector[0], vector[1:]
return all(i == first for i in rest)
def __allnearsame(vector, eps=1e-14):
first, rest = vector[0], vector[1:]
return all(abs(first.real - i.real) < eps and abs(first.imag - i.imag) < eps
for i in rest)
def isequal(matrices, eps=1e-14):
'Check any number of matrices for equality within eps'
x = [len(m) for m in matrices]
if not __allsame(x): return False
y = [len(m[0]) for m in matrices]
if not __allsame(y): return False
for s in range(x[0]):
for t in range(y[0]):
if not __allnearsame([m[s][t] for m in matrices], eps): return False
return True
def ishermitian(m, ct):
return isequal([m, ct])
def isnormal(m, ct):
return isequal([mmul(m, ct), mmul(ct, m)])
def isunitary(m, ct):
mct, ctm = mmul(m, ct), mmul(ct, m)
mctx, mcty, cmx, ctmy = len(mct), len(mct[0]), len(ctm), len(ctm[0])
ident = mi(mctx)
return isequal([mct, ctm, ident])
def printm(comment, m):
print(comment)
fields = [['%g%+gj' % (f.real, f.imag) for f in row] for row in m]
width = max(max(len(f) for f in row) for row in fields)
lines = (', '.join('%*s' % (width, f) for f in row) for row in fields)
print('\n'.join(lines))
if __name__ == '__main__':
for matrix in [
((( 3.000+0.000j), (+2.000+1.000j)),
(( 2.000-1.000j), (+1.000+0.000j))),
((( 1.000+0.000j), (+1.000+0.000j), (+0.000+0.000j)),
(( 0.000+0.000j), (+1.000+0.000j), (+1.000+0.000j)),
(( 1.000+0.000j), (+0.000+0.000j), (+1.000+0.000j))),
((( 2**0.5/2+0.000j), (+2**0.5/2+0.000j), (+0.000+0.000j)),
(( 0.000+2**0.5/2j), (+0.000-2**0.5/2j), (+0.000+0.000j)),
(( 0.000+0.000j), (+0.000+0.000j), (+0.000+1.000j)))]:
printm('\nMatrix:', matrix)
ct = conjugate_transpose(matrix)
printm('Its conjugate transpose:', ct)
print('Hermitian? %s.' % ishermitian(matrix, ct))
print('Normal? %s.' % isnormal(matrix, ct))
print('Unitary? %s.' % isunitary(matrix, ct))</lang>
{{out}}
<pre>Matrix:
3+0j, 2+1j
2-1j, 1+0j
Its conjugate transpose:
3-0j, 2+1j
2-1j, 1-0j
Hermitian? True.
Normal? True.
Unitary? False.
Matrix:
1+0j, 1+0j, 0+0j
0+0j, 1+0j, 1+0j
1+0j, 0+0j, 1+0j
Its conjugate transpose:
1-0j, 0-0j, 1-0j
1-0j, 1-0j, 0-0j
0-0j, 1-0j, 1-0j
Hermitian? False.
Normal? True.
Unitary? False.
Matrix:
0.707107+0j, 0.707107+0j, 0+0j
0-0.707107j, 0+0.707107j, 0+0j
0+0j, 0+0j, 0+1j
Its conjugate transpose:
0.707107-0j, 0+0.707107j, 0-0j
0.707107-0j, 0-0.707107j, 0-0j
0-0j, 0-0j, 0-1j
Hermitian? False.
Normal? True.
Unitary? True.</pre>
=={{header|Racket}}==
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#f
</lang>
=={{header|REXX}}==
<lang rexx>/*REXX pgm performs a conjugate transpose on a complex square matrix.*/
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