8000 Merge pull request #7268 from endolith/geomspace · numpy/numpy@70f50b8 · GitHub
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charrischarris
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Merge pull request #7268 from endolith/geomspace
ENH: add geomspace function
2 parents f902cfd + e53570d commit 70f50b8

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‎doc/release/1.12.0-notes.rst

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@@ -162,6 +162,13 @@ from the roots of the polynomial. This is useful for higher order polynomials,
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where expansion into polynomial coefficients is inaccurate at machine
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precision.
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New array creation function ``geomspace`` added
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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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The new function ``geomspace`` generates a geometric sequence. It is similar
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to ``logspace``, but with start and stop specified directly:
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``geomspace(start, stop)`` behaves the same as
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``logspace(log10(start), log10(stop))``.
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Improvements
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============
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‎doc/source/reference/routines.array-creation.rst

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@@ -80,6 +80,7 @@ Numerical ranges
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arange
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linspace
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logspace
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geomspace
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meshgrid
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mgrid
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ogrid

‎numpy/core/function_base.py

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@@ -3,10 +3,12 @@
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import warnings
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import operator
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__all__ = ['logspace', 'linspace']
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from . import numeric as _nx
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from .numeric import result_type, NaN, shares_memory, MAY_SHARE_BOUNDS, TooHardError
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from .numeric import (result_type, NaN, shares_memory, MAY_SHARE_BOUNDS,
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TooHardError)
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__all__ = ['logspace', 'linspace', 'geomspace']
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def _index_deprecate(i, stacklevel=2):
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try:
@@ -73,11 +75,11 @@ def linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None):
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Examples
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--------
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>>> np.linspace(2.0, 3.0, num=5)
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array([ 2. , 2.25, 2.5 , 2.75, 3. ])
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array([ 2. , 2.25, 2.5 , 2.75, 3. ])
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>>> np.linspace(2.0, 3.0, num=5, endpoint=False)
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array([ 2. , 2.2, 2.4, 2.6, 2.8])
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array([ 2. , 2.2, 2.4, 2.6, 2.8])
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>>> np.linspace(2.0, 3.0, num=5, retstep=True)
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(array([ 2. , 2.25, 2.5 , 2.75, 3. ]), 0.25)
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(array([ 2. , 2.25, 2.5 , 2.75, 3. ]), 0.25)
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Graphical illustration:
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@@ -102,8 +104,8 @@ def linspace(start, stop, num=50, endpoint=True, retstep=False, dtype=None):
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div = (num - 1) if endpoint else num
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# Convert float/complex array scalars to float, gh-3504
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start = start * 1.
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stop = stop * 1.
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start = start * 1.0
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stop = stop * 1.0
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dt = result_type(start, stop, float(num))
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if dtype is None:
@@ -156,7 +158,7 @@ def logspace(start, stop, num=50, endpoint=True, base=10.0, dtype=None):
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``base ** stop`` is the final value of the sequence, unless `endpoint`
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is False. In that case, ``num + 1`` values are spaced over the
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interval in log-space, of which all but the last (a sequence of
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length ``num``) are returned.
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length `num`) are returned.
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num : integer, optional
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Number of samples to generate. Default is 50.
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endpoint : boolean, optional
@@ -195,11 +197,11 @@ def logspace(start, stop, num=50, endpoint=True, base=10.0, dtype=None):
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Examples
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--------
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>>> np.logspace(2.0, 3.0, num=4)
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array([ 100. , 215.443469 , 464.15888336, 1000. ])
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array([ 100. , 215.443469 , 464.15888336, 1000. ])
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>>> np.logspace(2.0, 3.0, num=4, endpoint=False)
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array([ 100. , 177.827941 , 316.22776602, 562.34132519])
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array([ 100. , 177.827941 , 316.22776602, 562.34132519])
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>>> np.logspace(2.0, 3.0, num=4, base=2.0)
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array([ 4. , 5.0396842 , 6.34960421, 8. ])
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array([ 4. , 5.0396842 , 6.34960421, 8. ])
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Graphical illustration:
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@@ -221,3 +223,127 @@ def logspace(start, stop, num=50, endpoint=True, base=10.0, dtype=None):
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if dtype is None:
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return _nx.power(base, y)
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return _nx.power(base, y).astype(dtype)
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def geomspace(start, stop, num=50, endpoint=True, dtype=None):
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"""
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Return numbers spaced evenly on a log scale (a geometric progression).
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This is similar to `logspace`, but with endpoints specified directly.
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Each output sample is a constant multiple of the previous.
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Parameters
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----------
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start : scalar
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The starting value of the sequence.
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stop : scalar
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The final value of the sequence, unless `endpoint` is False.
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In that case, ``num + 1`` values are spaced over the
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interval in log-space, of which all but the last (a sequence of
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length `num`) are returned.
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num : integer, optional
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Number of samples to generate. Default is 50.
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endpoint : boolean, optional
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If true, `stop` is the last sample. Otherwise, it is not included.
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Default is True.
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dtype : dtype
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The type of the output array. If `dtype` is not given, infer the data
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type from the other input arguments.
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Returns
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-------
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samples : ndarray
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`num` samples, equally spaced on a log scale.
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See Also
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--------
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logspace : Similar to geomspace, but with endpoints specified using log
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and base.
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linspace : Similar to geomspace, but with arithmetic instead of geometric
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progression.
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arange : Similar to linspace, with the step size specified instead of the
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number of samples.
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Notes
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-----
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If the inputs or dtype are complex, the output will follow a logarithmic
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spiral in the complex plane. (There are an infinite number of spirals
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passing through two points; the output will follow the shortest such path.)
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Examples
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--------
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>>> np.geomspace(1, 1000, num=4)
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array([ 1., 10., 100., 1000.])
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>>> np.geomspace(1, 1000, num=3, endpoint=False)
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array([ 1., 10., 100.])
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>>> np.geomspace(1, 1000, num=4, endpoint=False)
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array([ 1. , 5.62341325, 31.6227766 , 177.827941 ])
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>>> np.geomspace(1, 256, num=9)
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array([ 1., 2., 4., 8., 16., 32., 64., 128., 256.])
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Note that the above may not produce exact integers:
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>>> np.geomspace(1, 256, num=9, dtype=int)
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array([ 1, 2, 4, 7, 16, 32, 63, 127, 256])
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>>> np.around(np.geomspace(1, 256, num=9)).astype(int)
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array([ 1, 2, 4, 8, 16, 32, 64, 128, 256])
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Negative, decreasing, and complex inputs are allowed:
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>>> geomspace(1000, 1, num=4)
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array([ 1000., 100., 10., 1.])
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>>> geomspace(-1000, -1, num=4)
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array([-1000., -100., -10., -1.])
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>>> geomspace(1j, 1000j, num=4) # Straight line
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array([ 0. +1.j, 0. +10.j, 0. +100.j, 0.+1000.j])
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>>> geomspace(-1+0j, 1+0j, num=5) # Circle
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array([-1.00000000+0.j , -0.70710678+0.70710678j,
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0.00000000+1.j , 0.70710678+0.70710678j,
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1.00000000+0.j ])
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Graphical illustration of ``endpoint`` parameter:
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>>> import matplotlib.pyplot as plt
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>>> N = 10
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>>> y = np.zeros(N)
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>>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=True), y + 1, 'o')
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>>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=False), y + 2, 'o')
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>>> plt.axis([0.5, 2000, 0, 3])
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>>> plt.grid(True, color='0.7', linestyle='-', which='both', axis='both')
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>>> plt.show()
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"""
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if start == 0 or stop == 0:
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raise ValueError('Geometric sequence cannot include zero')
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dt = result_type(start, stop, float(num))
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if dtype is None:
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dtype = dt
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else:
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# complex to dtype('complex128'), for instance
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dtype = _nx.dtype(dtype)
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# Avoid negligible real or imaginary parts in output by rotating to
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# positive real, calculating, then undoing rotation
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out_sign = 1
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if start.real == stop.real == 0:
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start, stop = start.imag, stop.imag
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out_sign = 1j * out_sign
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if _nx.sign(start) == _nx.sign(stop) == -1:
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start, stop = -start, -stop
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out_sign = -out_sign
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# Promote both arguments to the same dtype in case, for instance, one is
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# complex and another is negative and log would produce NaN otherwise
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start = start + (stop - stop)
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stop = stop + (start - start)
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if _nx.issubdtype(dtype, complex):
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start = start + 0j
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stop = stop + 0j
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log_start = _nx.log10(start)
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log_stop = _nx.log10(stop)
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result = out_sign * logspace(log_start, log_stop, num=num,
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endpoint=endpoint, base=10.0, dtype=dtype)
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return result.astype(dtype)

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