ó 2ÄÈ[c @`sdZddlmZmZmZddljjZddl jj Z ddlm Z m Z ddlmZdddd d d d d dg ZejdƒZd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„ZdS(sD 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 >>> from numpy.lib import scimath >>> scimath.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. i(tdivisiontabsolute_importtprint_functionN(tasarraytany(tisrealtsqrttlogtlog2tlogntlog10tpowertarccostarcsintarctanhg@cC`s]t|jjtjtjtjtjtjtj fƒrI|j tj ƒS|j tj ƒSdS(shConvert 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 -------- 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) N( t issubclasstdtypettypetnttsingletbytetshorttubytetushorttcsingletastypetcdouble(tarr((s0/tmp/pip-build-fiC0ax/numpy/numpy/lib/scimath.pyt _tocomplex#s8$cC`s;t|ƒ}tt|ƒ|dk@ƒr7t|ƒ}n|S(sConvert `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 -------- >>> 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]) i(RRRR(tx((s0/tmp/pip-build-fiC0ax/numpy/numpy/lib/scimath.pyt_fix_real_lt_zeroas cC`s9t|ƒ}tt|ƒ|dk@ƒr5|d}n|S(s„Convert `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 -------- >>> np.lib.scimath._fix_int_lt_zero([1,2]) array([1, 2]) >>> np.lib.scimath._fix_int_lt_zero([-1,2]) array([-1., 2.]) igð?(RRR(R((s0/tmp/pip-build-fiC0ax/numpy/numpy/lib/scimath.pyt_fix_int_lt_zero|s  cC`sAt|ƒ}tt|ƒt|ƒdk@ƒr=t|ƒ}n|S(sšConvert `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 -------- >>> 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]) i(RRRtabsR(R((s0/tmp/pip-build-fiC0ax/numpy/numpy/lib/scimath.pyt_fix_real_abs_gt_1–s "cC`st|ƒ}tj|ƒS(s 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`: >>> np.lib.scimath.sqrt(1) 1.0 >>> np.lib.scimath.sqrt([1, 4]) array([ 1., 2.]) But it automatically handles negative inputs: >>> np.lib.scimath.sqrt(-1) (0.0+1.0j) >>> np.lib.scimath.sqrt([-1,4]) array([ 0.+1.j, 2.+0.j]) (RtnxR(R((s0/tmp/pip-build-fiC0ax/numpy/numpy/lib/scimath.pyR°s' cC`st|ƒ}tj|ƒS(sš 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 -------- >>> 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 (RR"R(R((s0/tmp/pip-build-fiC0ax/numpy/numpy/lib/scimath.pyRÚs+ cC`st|ƒ}tj|ƒS(sè 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 -------- (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 ]) (RR"R (R((s0/tmp/pip-build-fiC0ax/numpy/numpy/lib/scimath.pyR s- cC`s2t|ƒ}t|ƒ}tj|ƒtj|ƒS(s´ Take log base n of x. If `x` contains negative inputs, the answer is computed and returned in the complex domain. Parameters ---------- n : int The base 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 -------- >>> np.set_printoptions(precision=4) >>> np.lib.scimath.logn(2, [4, 8]) array([ 2., 3.]) >>> np.lib.scimath.logn(2, [-4, -8, 8]) array([ 2.+4.5324j, 3.+4.5324j, 3.+0.j ]) (RR"R(tnR((s0/tmp/pip-build-fiC0ax/numpy/numpy/lib/scimath.pyR 8s  cC`st|ƒ}tj|ƒS(s´ 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 ]) (RR"R(R((s0/tmp/pip-build-fiC0ax/numpy/numpy/lib/scimath.pyRZs+ cC`s(t|ƒ}t|ƒ}tj||ƒS(sÄ 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 -------- >>> np.set_printoptions(precision=4) >>> np.lib.scimath.power([2, 4], 2) array([ 4, 16]) >>> np.lib.scimath.power([2, 4], -2) array([ 0.25 , 0.0625]) >>> np.lib.scimath.power([-2, 4], 2) array([ 4.+0.j, 16.+0.j]) (RRR"R (Rtp((s0/tmp/pip-build-fiC0ax/numpy/numpy/lib/scimath.pyR ˆs'  cC`st|ƒ}tj|ƒS(sÞ 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 -------- >>> 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!R"R (R((s0/tmp/pip-build-fiC0ax/numpy/numpy/lib/scimath.pyR ³s( cC`st|ƒ}tj|ƒS(sÆ 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 -------- >>> np.set_printoptions(precision=4) >>> np.emath.arcsin(0) 0.0 >>> np.emath.arcsin([0,1]) array([ 0. , 1.5708]) (R!R"R (R((s0/tmp/pip-build-fiC0ax/numpy/numpy/lib/scimath.pyR Þs) cC`st|ƒ}tj|ƒS(sP 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 -------- >>> np.set_printoptions(precision=4) >>> np.emath.arctanh(np.eye(2)) array([[ Inf, 0.], [ 0., Inf]]) >>> np.emath.arctanh([1j]) array([ 0.+0.7854j]) (R!R"R(R((s0/tmp/pip-build-fiC0ax/numpy/numpy/lib/scimath.pyR s+ (t__doc__t __future__RRRtnumpy.core.numerictcoretnumericR"tnumpy.core.numerictypest numerictypesRRRtnumpy.lib.type_checkRt__all__Rt_ln2RRRR!RR R RR R R R(((s0/tmp/pip-build-fiC0ax/numpy/numpy/lib/scimath.pyts*  >    * . 0 " . + + ,