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takagi fix #394

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merged 12 commits into from
Jul 8, 2024
Merged

takagi fix #394

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c41b49f
added the calculation method of diagonal matrix to `takagi`, and test…
RyosukeNORO Jul 5, 2024
3ff6505
added the related pull request number into CHANGELOG.md.
RyosukeNORO Jul 5, 2024
6e9b2b5
Update thewalrus/tests/test_decompositions.py
RyosukeNORO Jul 5, 2024
137820e
added rtol to np.allclose, corrected the sort of l and U,
RyosukeNORO Jul 5, 2024
1ae82f1
Merge branch 'takagi-sqrtm-fix' of https://github.com/XanaduAI/thewal…
RyosukeNORO Jul 5, 2024
05ed19d
reformat test_decompositions.py using black
RyosukeNORO Jul 5, 2024
7f1a795
Update thewalrus/tests/test_decompositions.py
RyosukeNORO Jul 5, 2024
cf82481
added pylint: disable=too-many-return-statements.
RyosukeNORO Jul 5, 2024
74c05b8
fixed the ordering of the matrix in takagi with diagonal matrix
RyosukeNORO Jul 5, 2024
c81cfbb
reformated test_decompositions.py using black -l 100
RyosukeNORO Jul 6, 2024
6fb38fe
moved the rtol as an optional parameter of takagi
RyosukeNORO Jul 8, 2024
b5fbd06
updeted the description of rtol in takagi
RyosukeNORO Jul 8, 2024
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2 changes: 2 additions & 0 deletions .github/CHANGELOG.md
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Expand Up @@ -15,6 +15,8 @@

### Bug fixes

* Add the calculation method of `takagi` when the matrix is diagonal. [(#394)](https://github.com/XanaduAI/thewalrus/pull/394)

### Documentation

### Contributors
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11 changes: 11 additions & 0 deletions thewalrus/decompositions.py
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Expand Up @@ -202,6 +202,17 @@ def takagi(A, svd_order=True):
vals, U = takagi(Amr, svd_order=svd_order)
return vals, U * np.exp(1j * phi / 2)

# If the matrix is diagonal, Takagi decomposition is easy
if np.allclose(A, np.diag(np.diag(A)), rtol=1e-16):
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I'd suggest you move this rtol as an optional parameter in the signature of the function.

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I have moved rtol as an optional parameter of takagi function.

d = np.diag(A)
U = np.diag(np.exp(1j * 0.5 * np.angle(d)))
l = np.abs(d)
l = np.sort(l)
U = U[np.argsort(l)]
if svd_order:
return l[::-1], U[:, ::-1]
return l, U
Comment on lines +216 to +218
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you can do the same thing on lines 218-220 as well if it helps, but I think this should suffice.

Suggested change
if svd_order:
return l[::-1], U[:, ::-1]
return l, U
return (l[::-1], U[:, ::-1]) if svd_order else (l, U)


u, d, v = np.linalg.svd(A)
U = u @ sqrtm((v @ np.conjugate(u)).T)
if svd_order is False:
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56 changes: 50 additions & 6 deletions thewalrus/tests/test_decompositions.py
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Expand Up @@ -19,7 +19,13 @@

from thewalrus.random import random_interferometer as haar_measure
from thewalrus.random import random_symplectic
from thewalrus.decompositions import williamson, blochmessiah, takagi, pre_iwasawa, iwasawa
from thewalrus.decompositions import (
williamson,
blochmessiah,
takagi,
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did you do black -l 100 file.py it seems to me like this changes should not happen.

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I did black file.py. Should I do black -l 100 file.py instead?

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Yup, that is the standard use in here.

pre_iwasawa,
iwasawa,
)
from thewalrus.symplectic import sympmat as omega
from thewalrus.quantum.gaussian_checks import is_symplectic

Expand Down Expand Up @@ -48,15 +54,19 @@ def _create_cov(nbar):

# interferometer 1
U1 = haar_measure(n)
S1 = np.vstack([np.hstack([U1.real, -U1.imag]), np.hstack([U1.imag, U1.real])])
S1 = np.vstack(
[np.hstack([U1.real, -U1.imag]), np.hstack([U1.imag, U1.real])]
)

# squeezing
r = np.log(0.2 * np.arange(n) + 2)
Sq = block_diag(np.diag(np.exp(-r)), np.diag(np.exp(r)))

# interferometer 2
U2 = haar_measure(n)
S2 = np.vstack([np.hstack([U2.real, -U2.imag]), np.hstack([U2.imag, U2.real])])
S2 = np.vstack(
[np.hstack([U2.real, -U2.imag]), np.hstack([U2.imag, U2.real])]
)

# final symplectic
S_final = S2 @ Sq @ S1
Expand Down Expand Up @@ -99,7 +109,9 @@ def test_even_validation(self):
"""Test that the graph_embed decomposition raises exception if not even number of rows"""
A = np.random.rand(5, 5) + 1j * np.random.rand(5, 5)
A += A.T
with pytest.raises(ValueError, match="must have an even number of rows/columns"):
with pytest.raises(
ValueError, match="must have an even number of rows/columns"
):
williamson(A)

def test_positive_definite_validation(self):
Expand Down Expand Up @@ -172,7 +184,9 @@ def _create_transform(n, passive=True):

# interferometer 1
U1 = haar_measure(n)
S1 = np.vstack([np.hstack([U1.real, -U1.imag]), np.hstack([U1.imag, U1.real])])
S1 = np.vstack(
[np.hstack([U1.real, -U1.imag]), np.hstack([U1.imag, U1.real])]
)

Sq = np.identity(2 * n)
if not passive:
Expand All @@ -182,7 +196,9 @@ def _create_transform(n, passive=True):

# interferometer 2
U2 = haar_measure(n)
S2 = np.vstack([np.hstack([U2.real, -U2.imag]), np.hstack([U2.imag, U2.real])])
S2 = np.vstack(
[np.hstack([U2.real, -U2.imag]), np.hstack([U2.imag, U2.real])]
)

# final symplectic
S_final = S2 @ Sq @ S1
Expand Down Expand Up @@ -324,6 +340,34 @@ def test_takagi_error():
takagi(A)


def test_takagi_diagonal_matrix():
"""Test the takagi decomposition works well for a specific matrix that was not decomposed accurately in a previous implementation.
See more info in PR #393 (https://github.com/XanaduAI/thewalrus/pull/393)"""
A = np.array(
[
[
-8.4509484628125742e-01 + 1.0349426984742664e-16j,
6.3637197288239186e-17 - 7.4398922703555097e-33j,
2.6734481396039929e-32 + 1.7155650257063576e-35j,
],
[
6.3637197288239186e-17 - 7.4398922703555097e-33j,
-2.0594021562561332e-01 + 2.2863956908382538e-17j,
-5.8325863096557049e-17 + 1.6949718400585382e-18j,
],
[
2.6734481396039929e-32 + 1.7155650257063576e-35j,
-5.8325863096557049e-17 + 1.6949718400585382e-18j,
4.4171453199503476e-02 + 1.0022350742842835e-02j,
],
]
)
d, U = takagi(A)
assert np.allclose(A, U @ np.diag(d) @ U.T)
assert np.allclose(U @ np.conjugate(U).T, np.eye(len(U)))
assert np.all(d >= 0)


def test_real_degenerate():
"""Verify that the Takagi decomposition returns a matrix that is unitary and results in a
correct decomposition when input a real but highly degenerate matrix. This test uses the
Expand Down
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