BUG: branch choices for geomspace on complex arguments #25644
Description
Describe the issue:
The docs for np.geomspace state:
If the inputs or dtype are complex, the output will follow a logarithmic spiral in the complex plane. (There are an infinite number of spirals passing through two points; the output will follow the shortest such path.)
But the function does not appear to obey this rule. I'm not sure how it is in fact choosing branch cuts.
Searching a bit, this may be altered by #25441 but I believe that is not in any released version yet.
Reproduce the code example:
import numpy as np
np.geomspace(-1j, 0.001 + 1j, 5) # semicircle to the right, via +1
np.geomspace(-1j, -0.001 + 1j, 5) # semicircle to the left, via -1, as documented
x = 1.2 + 3.4j # also x = 1+1j
delta = 0.01j
np.geomspace(x, -x + delta, 5) # crosses real line near 3.5, middle point 3.4-1.2j
np.geomspace(x, -x - delta, 5) # goes the same way!Error message:
No error message. Numerical result is:
>>> x = 1.2 + 3.4j # also x = 1+1j
>>> delta = 0.01j
>>> np.geomspace(x, -x + delta, 5) # crosses real line near 3.5, middle point 3.4-1.2j
array([ 1.2 +3.4j , 3.2509223 +1.5538648j ,
3.39499673-1.20000116j, 1.55032927-3.24738677j,
-1.2 -3.39j ])
>>> np.geomspace(x, -x - delta, 5) # goes the same way!
array([ 1.2 +3.4j , 3.25445784+1.55740034j,
3.40499673-1.20000115j, 1.56093588-3.25799337j,
-1.2 -3.41j ])Python and NumPy Versions:
1.26.3
3.11.7 (main, Jan 16 2024, 14:42:22) [Clang 14.0.0 (clang-1400.0.29.202)]
Runtime Environment:
[{'numpy_version': '1.26.3',
'python': '3.11.7 (main, Jan 16 2024, 14:42:22) [Clang 14.0.0 '
'(clang-1400.0.29.202)]',
'uname': uname_result(system='Darwin', node='ArmBook.local', release='21.6.0', version='Darwin Kernel Version 21.6.0: Sun Nov 6 23:29:57 PST 2022; root:xnu-8020.240.14~1/RELEASE_ARM64_T8101', machine='arm64')},
{'simd_extensions': {'baseline': ['NEON', 'NEON_FP16', 'NEON_VFPV4', 'ASIMD'],
'found': ['ASIMDHP'],
'not_found': ['ASIMDFHM']}},
{'architecture': 'armv8',
'filepath': '/opt/homebrew/lib/python3.11/site-packages/numpy/.dylibs/libopenblas64_.0.dylib',
'internal_api': 'openblas',
'num_threads': 8,
'prefix': 'libopenblas',
'threading_layer': 'pthreads',
'user_api': 'blas',
'version': '0.3.23.dev'}]
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