+ iL^^RIt^RIt^RIt^RIt^RIt^RIHt^RIH t ^RI H t ^RI H t^RI HtHtHtHt.ROt]P(!]P*RR7tRR R/R llt]!]4RR R/R ll4tRR lt]!]4RR l4tRRlt]!]4RRl4tRtRtRRltR#)N) overrides)_array_converter) add_docstring)numeric) asanyarraynanndim result_typenumpy)moduledevicecW3#N)startstopnumendpointretstepdtypeaxisr s&&&&&&&$;/usr/lib/python3/dist-packages/numpy/_core/function_base.py_linspace_dispatcherr =c`\P!V4pV^8d\RV R24hV'd V^, MTp\W4p V P 4wrV P RR7p VfT pRp M%\ P!V\ P4p \P!W\V 4R7p \ P!^W*VR7PR R \V 4,,4p V^8d\ P!V 4pW, pV'dV^8HM&\ P !V^8H4P#4pV'd#W,p V'd W,p M1W,p M(V'd W,p MW,p M\$pW,p W, p V'd V^8dWR &V^8wd\ P&!V ^V4p V 'd\ P(!WR7V P+V P-VRR 74p V'dW3#V #) a` Return evenly spaced numbers over a specified interval. Returns `num` evenly spaced samples, calculated over the interval [`start`, `stop`]. The endpoint of the interval can optionally be excluded. .. versionchanged:: 1.20.0 Values are rounded towards ``-inf`` instead of ``0`` when an integer ``dtype`` is specified. The old behavior can still be obtained with ``np.linspace(start, stop, num).astype(int)`` Parameters ---------- start : array_like The starting value of the sequence. stop : array_like The end value of the sequence, unless `endpoint` is set to False. In that case, the sequence consists of all but the last of ``num + 1`` evenly spaced samples, so that `stop` is excluded. Note that the step size changes when `endpoint` is False. num : int, optional Number of samples to generate. Default is 50. Must be non-negative. endpoint : bool, optional If True, `stop` is the last sample. Otherwise, it is not included. Default is True. retstep : bool, optional If True, return (`samples`, `step`), where `step` is the spacing between samples. dtype : dtype, optional The type of the output array. If `dtype` is not given, the data type is inferred from `start` and `stop`. The inferred dtype will never be an integer; `float` is chosen even if the arguments would produce an array of integers. axis : int, optional The axis in the result to store the samples. Relevant only if start or stop are array-like. By default (0), the samples will be along a new axis inserted at the beginning. Use -1 to get an axis at the end. device : str, optional The device on which to place the created array. Default: None. For Array-API interoperability only, so must be ``"cpu"`` if passed. .. versionadded:: 2.0.0 Returns ------- samples : ndarray There are `num` equally spaced samples in the closed interval ``[start, stop]`` or the half-open interval ``[start, stop)`` (depending on whether `endpoint` is True or False). step : float, optional Only returned if `retstep` is True Size of spacing between samples. See Also -------- arange : Similar to `linspace`, but uses a step size (instead of the number of samples). geomspace : Similar to `linspace`, but with numbers spaced evenly on a log scale (a geometric progression). logspace : Similar to `geomspace`, but with the end points specified as logarithms. :ref:`how-to-partition` Examples -------- >>> import numpy as np >>> np.linspace(2.0, 3.0, num=5) array([2. , 2.25, 2.5 , 2.75, 3. ]) >>> np.linspace(2.0, 3.0, num=5, endpoint=False) array([2. , 2.2, 2.4, 2.6, 2.8]) >>> np.linspace(2.0, 3.0, num=5, retstep=True) (array([2. , 2.25, 2.5 , 2.75, 3. ]), 0.25) Graphical illustration: >>> import matplotlib.pyplot as plt >>> N = 8 >>> y = np.zeros(N) >>> x1 = np.linspace(0, 10, N, endpoint=True) >>> x2 = np.linspace(0, 10, N, endpoint=False) >>> plt.plot(x1, y, 'o') [] >>> plt.plot(x2, y + 0.5, 'o') [] >>> plt.ylim([-0.5, 1]) (-0.5, 1) >>> plt.show() zNumber of samples, z, must be non-negative.T)ensure_inexactF)r)rr )outcopy)))r!.)operatorindex ValueErrorr as_arraysr _nx issubdtypeintegernpsubtracttypearangereshaper isscalarranyrmoveaxisfloorwrapastype)rrrrrrrr divconvdt integer_dtypedeltay _mult_inplacestep any_step_zeros&&&&&&&$ rlinspacer>s@ .. C Qw!#&= >   37SC E (D.."KE    .B } uckk:  KK48 4E  3  gedT%[(() Qw U+ {&DAICNN419,E,I,I,K   HA I  IAA IJAC!G'  qy LLAt $ ! !((5u(-.Awrc WV3#rr)rrrrbaserrs&&&&&&&r_logspace_dispatcherrAs  rca\V\\34'gf\P!V4'dJ\P !WV4PoV3RlWV34wrp\P !WFR7p\WW#VR7pVf\P!WG4#\P!WG4PVRR7#)aa Return numbers spaced evenly on a log scale. In linear space, the sequence starts at ``base ** start`` (`base` to the power of `start`) and ends with ``base ** stop`` (see `endpoint` below). .. versionchanged:: 1.25.0 Non-scalar 'base` is now supported Parameters ---------- start : array_like ``base ** start`` is the starting value of the sequence. stop : array_like ``base ** stop`` is the final value of the sequence, unless `endpoint` is False. In that case, ``num + 1`` values are spaced over the interval in log-space, of which all but the last (a sequence of length `num`) are returned. num : integer, optional Number of samples to generate. Default is 50. endpoint : boolean, optional If true, `stop` is the last sample. Otherwise, it is not included. Default is True. base : array_like, optional The base of the log space. The step size between the elements in ``ln(samples) / ln(base)`` (or ``log_base(samples)``) is uniform. Default is 10.0. dtype : dtype The type of the output array. If `dtype` is not given, the data type is inferred from `start` and `stop`. The inferred type will never be an integer; `float` is chosen even if the arguments would produce an array of integers. axis : int, optional The axis in the result to store the samples. Relevant only if start, stop, or base are array-like. By default (0), the samples will be along a new axis inserted at the beginning. Use -1 to get an axis at the end. Returns ------- samples : ndarray `num` samples, equally spaced on a log scale. See Also -------- arange : Similar to linspace, with the step size specified instead of the number of samples. Note that, when used with a float endpoint, the endpoint may or may not be included. linspace : Similar to logspace, but with the samples uniformly distributed in linear space, instead of log space. geomspace : Similar to logspace, but with endpoints specified directly. :ref:`how-to-partition` Notes ----- If base is a scalar, logspace is equivalent to the code >>> y = np.linspace(start, stop, num=num, endpoint=endpoint) ... # doctest: +SKIP >>> power(base, y).astype(dtype) ... # doctest: +SKIP Examples -------- >>> import numpy as np >>> np.logspace(2.0, 3.0, num=4) array([ 100. , 215.443469 , 464.15888336, 1000. ]) >>> np.logspace(2.0, 3.0, num=4, endpoint=False) array([100. , 177.827941 , 316.22776602, 562.34132519]) >>> np.logspace(2.0, 3.0, num=4, base=2.0) array([4. , 5.0396842 , 6.34960421, 8. ]) >>> np.logspace(2.0, 3.0, num=4, base=[2.0, 3.0], axis=-1) array([[ 4. , 5.0396842 , 6.34960421, 8. ], [ 9. , 12.98024613, 18.72075441, 27. ]]) Graphical illustration: >>> import matplotlib.pyplot as plt >>> N = 10 >>> x1 = np.logspace(0.1, 1, N, endpoint=True) >>> x2 = np.logspace(0.1, 1, N, endpoint=False) >>> y = np.zeros(N) >>> plt.plot(x1, y, 'o') [] >>> plt.plot(x2, y + 0.5, 'o') [] >>> plt.ylim([-0.5, 1]) (-0.5, 1) >>> plt.show() c3X<"TFp\P!VRRSR7xK! R#5i)NT)r subokndmin)r*array).0andmaxs& r logspace..&s* ( HHQTU ; ;(s'*)r)rrrFr) isinstancefloatintr*r broadcast expand_dimsr>r'powerr4) rrrrr@rrr:rIs &&&&&&& @rlogspacerRs~ dUCL ) )bggdmm U$/44 4( T~~d.#tDA }yy!! 99T  $ $U $ 77rcW3#rr)rrrrrrs&&&&&&r_geomspace_dispatcherrT1rrc \V4p\V4p\P!V^8H4'g \P!V^8H4'd \R4h\ W\ V4\P !RV44pVfTpM\P!V4pVPVRR7pVPVRR7p\P!V4pW,pW, p\P!V4p\P!V4p \WVVRVR7p V^8dW ^&V^8d V'dWR&W,p V^8wd\P!V ^V4p V PVRR7#) a Return numbers spaced evenly on a log scale (a geometric progression). This is similar to `logspace`, but with endpoints specified directly. Each output sample is a constant multiple of the previous. Parameters ---------- start : array_like The starting value of the sequence. stop : array_like The final value of the sequence, unless `endpoint` is False. In that case, ``num + 1`` values are spaced over the interval in log-space, of which all but the last (a sequence of length `num`) are returned. num : integer, optional Number of samples to generate. Default is 50. endpoint : boolean, optional If true, `stop` is the last sample. Otherwise, it is not included. Default is True. dtype : dtype The type of the output array. If `dtype` is not given, the data type is inferred from `start` and `stop`. The inferred dtype will never be an integer; `float` is chosen even if the arguments would produce an array of integers. axis : int, optional The axis in the result to store the samples. Relevant only if start or stop are array-like. By default (0), the samples will be along a new axis inserted at the beginning. Use -1 to get an axis at the end. Returns ------- samples : ndarray `num` samples, equally spaced on a log scale. See Also -------- logspace : Similar to geomspace, but with endpoints specified using log and base. linspace : Similar to geomspace, but with arithmetic instead of geometric progression. arange : Similar to linspace, with the step size specified instead of the number of samples. :ref:`how-to-partition` Notes ----- 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.) Examples -------- >>> import numpy as np >>> np.geomspace(1, 1000, num=4) array([ 1., 10., 100., 1000.]) >>> np.geomspace(1, 1000, num=3, endpoint=False) array([ 1., 10., 100.]) >>> np.geomspace(1, 1000, num=4, endpoint=False) array([ 1. , 5.62341325, 31.6227766 , 177.827941 ]) >>> np.geomspace(1, 256, num=9) array([ 1., 2., 4., 8., 16., 32., 64., 128., 256.]) Note that the above may not produce exact integers: >>> np.geomspace(1, 256, num=9, dtype=int) array([ 1, 2, 4, 7, 16, 32, 63, 127, 256]) >>> np.around(np.geomspace(1, 256, num=9)).astype(int) array([ 1, 2, 4, 8, 16, 32, 64, 128, 256]) Negative, decreasing, and complex inputs are allowed: >>> np.geomspace(1000, 1, num=4) array([1000., 100., 10., 1.]) >>> np.geomspace(-1000, -1, num=4) array([-1000., -100., -10., -1.]) >>> np.geomspace(1j, 1000j, num=4) # Straight line array([0. +1.j, 0. +10.j, 0. +100.j, 0.+1000.j]) >>> np.geomspace(-1+0j, 1+0j, num=5) # Circle array([-1.00000000e+00+1.22464680e-16j, -7.07106781e-01+7.07106781e-01j, 6.12323400e-17+1.00000000e+00j, 7.07106781e-01+7.07106781e-01j, 1.00000000e+00+0.00000000e+00j]) Graphical illustration of `endpoint` parameter: >>> import matplotlib.pyplot as plt >>> N = 10 >>> y = np.zeros(N) >>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=True), y + 1, 'o') [] >>> plt.semilogx(np.geomspace(1, 1000, N, endpoint=False), y + 2, 'o') [] >>> plt.axis([0.5, 2000, 0, 3]) [0.5, 2000, 0, 3] >>> plt.grid(True, color='0.7', linestyle='-', which='both', axis='both') >>> plt.show() z&Geometric sequence cannot include zeroTr$@)rrr@rFrr!) rr'r0r%r rMzerosrr4signlog10rRr1) rrrrrrr7out_sign log_startlog_stopresults &&&&&& r geomspacer^6sIH u E d D wwuzcggdai00ABB U%*ciiE.B CB } %  LL$L 'E ;;r; %D xxH E ?D % IyyH is'd">F  Qwq 7x2J F qyfa. ==U= ++rcRp\V\P\P\34'dR#\V\ 4'dVP V,'dR#R#)z Returns true if the only way to set the docstring of `obj` from python is via add_docstring. This function errs on the side of being overly conservative. FTi)rLtypes FunctionType MethodTypepropertyr, __flags__)objPy_TPFLAGS_HEAPTYPEs& r_needs_add_docstringrgsO!#**E,<,r^)NNNNN)2TFNr)rTrVNr)NNNN)rTNr)T) functoolsr#r`rjr r* numpy._corernumpy._core._multiarray_umathrnumpy._core.multiarrayrrr'rrr r __all__partialarray_function_dispatchrr>rArRrTr^rgrpr~rrrrs !:077 /$++ %%g7:> -.`#`/`F -.j8/j8Z ./M,0M,`$  ;r