KhK=pSrSSKJs Jr SSKJs Jr SSKJrJ r SSK J r J r SSK Jr /SQr\R "S5rSrS rS rS rS r\ "S 5\ "\5S55r\ "S 5\ "\5S55r\ "S 5\ "\5S55rSr\ "S 5\ "\5S55r\ "S 5\ "\5S55rSr\ "S 5\ "\5S55r\ "S 5\ "\5S55r\ "S 5\ "\5S55r\ "S 5\ "\5S55r g)a! Wrapper functions to more user-friendly calling of certain math functions whose output data-type is different than the input data-type in certain domains of the input. For example, for functions like `log` with branch cuts, the versions in this module provide the mathematically valid answers in the complex plane:: >>> import math >>> np.emath.log(-math.exp(1)) == (1+1j*math.pi) True Similarly, `sqrt`, other base logarithms, `power` and trig functions are correctly handled. See their respective docstrings for specific examples. N)asarrayany)array_function_dispatch set_module)isreal) sqrtloglog2lognlog10powerarccosarcsinarctanhg@c |[URR[R[R [R [R[R[R45(aUR[R5$UR[R5$)aConvert its input `arr` to a complex array. The input is returned as a complex array of the smallest type that will fit the original data: types like single, byte, short, etc. become csingle, while others become cdouble. A copy of the input is always made. Parameters ---------- arr : array Returns ------- array An array with the same input data as the input but in complex form. Examples -------- >>> import numpy as np First, consider an input of type short: >>> a = np.array([1,2,3],np.short) >>> ac = np.lib.scimath._tocomplex(a); ac array([1.+0.j, 2.+0.j, 3.+0.j], dtype=complex64) >>> ac.dtype dtype('complex64') If the input is of type double, the output is correspondingly of the complex double type as well: >>> b = np.array([1,2,3],np.double) >>> bc = np.lib.scimath._tocomplex(b); bc array([1.+0.j, 2.+0.j, 3.+0.j]) >>> bc.dtype dtype('complex128') Note that even if the input was complex to begin with, a copy is still made, since the astype() method always copies: >>> c = np.array([1,2,3],np.csingle) >>> cc = np.lib.scimath._tocomplex(c); cc array([1.+0.j, 2.+0.j, 3.+0.j], dtype=complex64) >>> c *= 2; c array([2.+0.j, 4.+0.j, 6.+0.j], dtype=complex64) >>> cc array([1.+0.j, 2.+0.j, 3.+0.j], dtype=complex64) ) issubclassdtypetypentsinglebyteshortubyteushortcsingleastypecdouble)arrs I/var/www/html/env/lib/python3.13/site-packages/numpy/lib/_scimath_impl.py _tocomplexr !slr#))..299bggrxx#%99bjj#:;;zz"**%%zz"**%%cp[U5n[[U5US:-5(a [U5nU$)aoConvert `x` to complex if it has real, negative components. Otherwise, output is just the array version of the input (via asarray). Parameters ---------- x : array_like Returns ------- array Examples -------- >>> import numpy as np >>> np.lib.scimath._fix_real_lt_zero([1,2]) array([1, 2]) >>> np.lib.scimath._fix_real_lt_zero([-1,2]) array([-1.+0.j, 2.+0.j]) r)rrrr xs r_fix_real_lt_zeror%as3.  A 6!9A  qM Hr!cd[U5n[[U5US:-5(aUS-nU$)acConvert `x` to double if it has real, negative components. Otherwise, output is just the array version of the input (via asarray). Parameters ---------- x : array_like Returns ------- array Examples -------- >>> import numpy as np >>> np.lib.scimath._fix_int_lt_zero([1,2]) array([1, 2]) >>> np.lib.scimath._fix_int_lt_zero([-1,2]) array([-1., 2.]) rg?)rrrr#s r_fix_int_lt_zeror'~s3,  A 6!9A  G Hr!c[U5n[[U5[U5S:-5(a [ U5nU$)awConvert `x` to complex if it has real components x_i with abs(x_i)>1. Otherwise, output is just the array version of the input (via asarray). Parameters ---------- x : array_like Returns ------- array Examples -------- >>> import numpy as np >>> np.lib.scimath._fix_real_abs_gt_1([0,1]) array([0, 1]) >>> np.lib.scimath._fix_real_abs_gt_1([0,2]) array([0.+0.j, 2.+0.j]) )rrrabsr r#s r_fix_real_abs_gt_1r+s7,  A 6!9A #$$ qM Hr!cU4$Nr#s r_unary_dispatcherr/s 4Kr!znumpy.lib.scimathcD[U5n[R"U5$)ar Compute the square root of x. For negative input elements, a complex value is returned (unlike `numpy.sqrt` which returns NaN). Parameters ---------- x : array_like The input value(s). Returns ------- out : ndarray or scalar The square root of `x`. If `x` was a scalar, so is `out`, otherwise an array is returned. See Also -------- numpy.sqrt Examples -------- For real, non-negative inputs this works just like `numpy.sqrt`: >>> import numpy as np >>> np.emath.sqrt(1) 1.0 >>> np.emath.sqrt([1, 4]) array([1., 2.]) But it automatically handles negative inputs: >>> np.emath.sqrt(-1) 1j >>> np.emath.sqrt([-1,4]) array([0.+1.j, 2.+0.j]) Different results are expected because: floating point 0.0 and -0.0 are distinct. For more control, explicitly use complex() as follows: >>> np.emath.sqrt(complex(-4.0, 0.0)) 2j >>> np.emath.sqrt(complex(-4.0, -0.0)) -2j )r%nxrr#s rrrsh !A 771:r!cD[U5n[R"U5$)a1 Compute the natural logarithm of `x`. Return the "principal value" (for a description of this, see `numpy.log`) of :math:`log_e(x)`. For real `x > 0`, this is a real number (``log(0)`` returns ``-inf`` and ``log(np.inf)`` returns ``inf``). Otherwise, the complex principle value is returned. Parameters ---------- x : array_like The value(s) whose log is (are) required. Returns ------- out : ndarray or scalar The log of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array is returned. See Also -------- numpy.log Notes ----- For a log() that returns ``NAN`` when real `x < 0`, use `numpy.log` (note, however, that otherwise `numpy.log` and this `log` are identical, i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`, and, notably, the complex principle value if ``x.imag != 0``). Examples -------- >>> import numpy as np >>> np.emath.log(np.exp(1)) 1.0 Negative arguments are handled "correctly" (recall that ``exp(log(x)) == x`` does *not* hold for real ``x < 0``): >>> np.emath.log(-np.exp(1)) == (1 + np.pi * 1j) True r%r1r r#s rr r s\ !A 66!9r!cD[U5n[R"U5$)a| Compute the logarithm base 10 of `x`. Return the "principal value" (for a description of this, see `numpy.log10`) of :math:`log_{10}(x)`. For real `x > 0`, this is a real number (``log10(0)`` returns ``-inf`` and ``log10(np.inf)`` returns ``inf``). Otherwise, the complex principle value is returned. Parameters ---------- x : array_like or scalar The value(s) whose log base 10 is (are) required. Returns ------- out : ndarray or scalar The log base 10 of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array object is returned. See Also -------- numpy.log10 Notes ----- For a log10() that returns ``NAN`` when real `x < 0`, use `numpy.log10` (note, however, that otherwise `numpy.log10` and this `log10` are identical, i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`, and, notably, the complex principle value if ``x.imag != 0``). Examples -------- >>> import numpy as np (We set the printing precision so the example can be auto-tested) >>> np.set_printoptions(precision=4) >>> np.emath.log10(10**1) 1.0 >>> np.emath.log10([-10**1, -10**2, 10**2]) array([1.+1.3644j, 2.+1.3644j, 2.+0.j ]) )r%r1r r#s rr r $s` !A 88A;r!cX4$r-r.nr$s r_logn_dispatcherr8Xs 7Nr!c[U5n[U5n[R"U5[R"U5- $)at Take log base n of x. If `x` contains negative inputs, the answer is computed and returned in the complex domain. Parameters ---------- n : array_like The integer base(s) in which the log is taken. x : array_like The value(s) whose log base `n` is (are) required. Returns ------- out : ndarray or scalar The log base `n` of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array is returned. Examples -------- >>> import numpy as np >>> np.set_printoptions(precision=4) >>> np.emath.logn(2, [4, 8]) array([2., 3.]) >>> np.emath.logn(2, [-4, -8, 8]) array([2.+4.5324j, 3.+4.5324j, 3.+0.j ]) r3r6s rr r \s4B !A!A 66!9RVVAY r!cD[U5n[R"U5$)a2 Compute the logarithm base 2 of `x`. Return the "principal value" (for a description of this, see `numpy.log2`) of :math:`log_2(x)`. For real `x > 0`, this is a real number (``log2(0)`` returns ``-inf`` and ``log2(np.inf)`` returns ``inf``). Otherwise, the complex principle value is returned. Parameters ---------- x : array_like The value(s) whose log base 2 is (are) required. Returns ------- out : ndarray or scalar The log base 2 of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array is returned. See Also -------- numpy.log2 Notes ----- For a log2() that returns ``NAN`` when real `x < 0`, use `numpy.log2` (note, however, that otherwise `numpy.log2` and this `log2` are identical, i.e., both return ``-inf`` for `x = 0`, ``inf`` for `x = inf`, and, notably, the complex principle value if ``x.imag != 0``). Examples -------- We set the printing precision so the example can be auto-tested: >>> np.set_printoptions(precision=4) >>> np.emath.log2(8) 3.0 >>> np.emath.log2([-4, -8, 8]) array([2.+4.5324j, 3.+4.5324j, 3.+0.j ]) )r%r1r r#s rr r s\ !A 771:r!cX4$r-r.r$ps r_power_dispatcherr>s 6Mr!cZ[U5n[U5n[R"X5$)a Return x to the power p, (x**p). If `x` contains negative values, the output is converted to the complex domain. Parameters ---------- x : array_like The input value(s). p : array_like of ints The power(s) to which `x` is raised. If `x` contains multiple values, `p` has to either be a scalar, or contain the same number of values as `x`. In the latter case, the result is ``x[0]**p[0], x[1]**p[1], ...``. Returns ------- out : ndarray or scalar The result of ``x**p``. If `x` and `p` are scalars, so is `out`, otherwise an array is returned. See Also -------- numpy.power Examples -------- >>> import numpy as np >>> np.set_printoptions(precision=4) >>> np.emath.power(2, 2) 4 >>> np.emath.power([2, 4], 2) array([ 4, 16]) >>> np.emath.power([2, 4], -2) array([0.25 , 0.0625]) >>> np.emath.power([-2, 4], 2) array([ 4.-0.j, 16.+0.j]) >>> np.emath.power([2, 4], [2, 4]) array([ 4, 256]) )r%r'r1r r<s rr r s'd !AA 88A>r!cD[U5n[R"U5$)a Compute the inverse cosine of x. Return the "principal value" (for a description of this, see `numpy.arccos`) of the inverse cosine of `x`. For real `x` such that `abs(x) <= 1`, this is a real number in the closed interval :math:`[0, \pi]`. Otherwise, the complex principle value is returned. Parameters ---------- x : array_like or scalar The value(s) whose arccos is (are) required. Returns ------- out : ndarray or scalar The inverse cosine(s) of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array object is returned. See Also -------- numpy.arccos Notes ----- For an arccos() that returns ``NAN`` when real `x` is not in the interval ``[-1,1]``, use `numpy.arccos`. Examples -------- >>> import numpy as np >>> np.set_printoptions(precision=4) >>> np.emath.arccos(1) # a scalar is returned 0.0 >>> np.emath.arccos([1,2]) array([0.-0.j , 0.-1.317j]) )r+r1rr#s rrrsV 1A 99Q<r!cD[U5n[R"U5$)ac Compute the inverse sine of x. Return the "principal value" (for a description of this, see `numpy.arcsin`) of the inverse sine of `x`. For real `x` such that `abs(x) <= 1`, this is a real number in the closed interval :math:`[-\pi/2, \pi/2]`. Otherwise, the complex principle value is returned. Parameters ---------- x : array_like or scalar The value(s) whose arcsin is (are) required. Returns ------- out : ndarray or scalar The inverse sine(s) of the `x` value(s). If `x` was a scalar, so is `out`, otherwise an array object is returned. See Also -------- numpy.arcsin Notes ----- For an arcsin() that returns ``NAN`` when real `x` is not in the interval ``[-1,1]``, use `numpy.arcsin`. Examples -------- >>> import numpy as np >>> np.set_printoptions(precision=4) >>> np.emath.arcsin(0) 0.0 >>> np.emath.arcsin([0,1]) array([0. , 1.5708]) )r+r1rr#s rrrsX 1A 99Q<r!cD[U5n[R"U5$)a Compute the inverse hyperbolic tangent of `x`. Return the "principal value" (for a description of this, see `numpy.arctanh`) of ``arctanh(x)``. For real `x` such that ``abs(x) < 1``, this is a real number. If `abs(x) > 1`, or if `x` is complex, the result is complex. Finally, `x = 1` returns``inf`` and ``x=-1`` returns ``-inf``. Parameters ---------- x : array_like The value(s) whose arctanh is (are) required. Returns ------- out : ndarray or scalar The inverse hyperbolic tangent(s) of the `x` value(s). If `x` was a scalar so is `out`, otherwise an array is returned. See Also -------- numpy.arctanh Notes ----- For an arctanh() that returns ``NAN`` when real `x` is not in the interval ``(-1,1)``, use `numpy.arctanh` (this latter, however, does return +/-inf for ``x = +/-1``). Examples -------- >>> import numpy as np >>> np.set_printoptions(precision=4) >>> np.emath.arctanh(0.5) 0.5493061443340549 >>> from numpy.testing import suppress_warnings >>> with suppress_warnings() as sup: ... sup.filter(RuntimeWarning) ... np.emath.arctanh(np.eye(2)) array([[inf, 0.], [ 0., inf]]) >>> np.emath.arctanh([1j]) array([0.+0.7854j]) )r+r1rr#s rrrNsh 1A ::a=r!)!__doc__numpy._core.numeric_corenumericr1numpy._core.numerictypes numerictypesrrrnumpy._core.overridesrrnumpy.lib._type_check_implr__all__r _ln2r r%r'r+r/rr r8r r r>r rrrr.r!rrMs ! %%,E-   vvc{=&@ : 8 8  *+3,!3l  *+-,!-`  *+/,!/d  )*!+!!H  *+-,!-`  *+2,!2j  *+*,!*Z  *++,!+\  *+3,!3r!