Conjugate transpose: Difference between revisions
Added 11l
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* MathWorld entry: [http://mathworld.wolfram.com/UnitaryMatrix.html unitary matrix]
<br><br>
=={{header|11l}}==
{{trans|Nim}}
<lang 11l>-V eps = 1e-10
F to_str(m)
V r = ‘’
L(row) m
V i = L.index
r ‘’= I i == 0 {‘[’} E ‘ ’
L(val) row
V j = L.index
I j != 0
r ‘’= ‘ ’
r ‘’= ‘(#2.4, #2.4)’.format(val.real, val.imag)
r ‘’= I i == m.len - 1 {‘]’} E "\n"
R r
F conjugateTransposed(m)
V r = [[0i] * m.len] * m.len
L(i) 0 .< m.len
L(j) 0 .< m.len
r[j][i] = conjugate(m[i][j])
R r
F mmul(m1, m2)
V r = [[0i] * m1.len] * m1.len
L(i) 0 .< m1.len
L(j) 0 .< m1.len
L(k) 0 .< m1.len
r[i][j] += m1[i][k] * m2[k][j]
R r
F isHermitian(m)
L(i) 0 .< m.len
L(j) 0 .< m.len
I m[i][j] != conjugate(m[j][i])
R 0B
R 1B
F isEqual(m1, m2)
L(i) 0 .< m1.len
L(j) 0 .< m1.len
I m1[i][j] != m2[i][j]
R 0B
R 1B
F isNormal(m)
V h = conjugateTransposed(m)
R isEqual(mmul(m, h), mmul(h, m))
F isIdentity(m)
L(i) 0 .< m.len
L(j) 0 .< m.len
I i == j
I abs(m[i][j] - 1.0) > :eps
R 0B
E
I abs(m[i][j]) > :eps
R 0B
R 1B
F isUnitary(m)
V h = conjugateTransposed(m)
R isIdentity(mmul(m, h)) & isIdentity(mmul(h, m))
F test(m)
print(‘Matrix’)
print(‘------’)
print(to_str(m))
print(‘’)
print(‘Conjugate transposed’)
print(‘--------------------’)
print(to_str(conjugateTransposed(m)))
print(‘’)
print(‘Hermitian: ’(I isHermitian(m) {‘true’} E ‘false’))
print(‘Normal: ’(I isNormal(m) {‘true’} E ‘false’))
print(‘Unitary: ’(I isUnitary(m) {‘true’} E ‘false’))
V M2 = [[3.0 + 0.0i, 2.0 + 1.0i],
[2.0 - 1.0i, 1.0 + 0.0i]]
V M3 = [[1.0 + 0.0i, 1.0 + 0.0i, 0.0 + 0.0i],
[0.0 + 0.0i, 1.0 + 0.0i, 1.0 + 0.0i],
[1.0 + 0.0i, 0.0 + 0.0i, 1.0 + 0.0i]]
V SR2 = 1 / sqrt(2.0)
V SR2i = SR2 * 1i
V M4 = [[SR2 + 0.0i, SR2 + 0.0i, 0.0 + 0.0i],
[0.0 + SR2i, 0.0 - SR2i, 0.0 + 0.0i],
[0.0 + 0.0i, 0.0 + 0.0i, 0.0 + 1.0i]]
test(M2)
print("\n")
test(M3)
print("\n")
test(M4)</lang>
{{out}}
<pre>
Matrix
------
[( 3.0000, 0.0000) ( 2.0000, 1.0000)
( 2.0000, -1.0000) ( 1.0000, 0.0000)]
Conjugate transposed
--------------------
[( 3.0000, 0.0000) ( 2.0000, 1.0000)
( 2.0000, -1.0000) ( 1.0000, 0.0000)]
Hermitian: true
Normal: true
Unitary: false
Matrix
------
[( 1.0000, 0.0000) ( 1.0000, 0.0000) ( 0.0000, 0.0000)
( 0.0000, 0.0000) ( 1.0000, 0.0000) ( 1.0000, 0.0000)
( 1.0000, 0.0000) ( 0.0000, 0.0000) ( 1.0000, 0.0000)]
Conjugate transposed
--------------------
[( 1.0000, 0.0000) ( 0.0000, 0.0000) ( 1.0000, 0.0000)
( 1.0000, 0.0000) ( 1.0000, 0.0000) ( 0.0000, 0.0000)
( 0.0000, 0.0000) ( 1.0000, 0.0000) ( 1.0000, 0.0000)]
Hermitian: false
Normal: true
Unitary: false
Matrix
------
[( 0.7071, 0.0000) ( 0.7071, 0.0000) ( 0.0000, 0.0000)
( 0.0000, 0.7071) ( 0.0000, -0.7071) ( 0.0000, 0.0000)
( 0.0000, 0.0000) ( 0.0000, 0.0000) ( 0.0000, 1.0000)]
Conjugate transposed
--------------------
[( 0.7071, 0.0000) ( 0.0000, -0.7071) ( 0.0000, 0.0000)
( 0.7071, 0.0000) ( 0.0000, 0.7071) ( 0.0000, 0.0000)
( 0.0000, 0.0000) ( 0.0000, 0.0000) ( 0.0000, -1.0000)]
Hermitian: false
Normal: true
Unitary: true
</pre>
=={{header|Ada}}==
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