# Coverage for pygeodesy/utily.py : 97%

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After I{(C) Chris Veness 2011-2015} published under the same MIT Licence**, see U{Latitude/Longitude<https://www.Movable-Type.co.UK/scripts/latlong.html>} and U{Vector-based geodesy<https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>}. @newfield example: Example, Examples ''' from pygeodesy.basics import isint from pygeodesy.errors import _xkwds_get, _ValueError from pygeodesy.interns import PI, PI2, PI_2, R_M, _deg_, _Missing, \ _0_0, _0_5, _1_0, _90_0, _180_0, _360_0 from pygeodesy.lazily import _ALL_LAZY from pygeodesy.units import Feet, Lam_, Meter, Phi_, Radius from math import acos, asin, atan2, cos, degrees, radians, sin, tan # pow __all__ = _ALL_LAZY.utily __version__ = '20.09.10' # <https://Numbers.Computation.Free.FR/Constants/Miscellaneous/digits.html> _1_90 = _1_0 / _90_0 # 0.011111111111111111111111111111111111111111111111 _2_PI = _1_0 / PI_2 # 0.63661977236758134307553505349005744813783858296182 # sqrt(2) + 1 <https://wikipedia.org/wiki/Square_root_of_2> # _R2_1 = 2.4142135623730950488 # 0168872420969807856967187537694807317667973799 _iterNumpy2len = 1 # adjustable for testing purposes def acos1(x): '''Return M{math.acos(max(-1, min(1, x)))}. ''' return acos(max(-_1_0, min(_1_0, x))) def asin1(x): '''Return M{math.asin(max(-1, min(1, x)))}. ''' return asin(max(-_1_0, min(_1_0, x))) def atan2b(y, x): '''Compute C{atan2(y, x)} as degrees M{[0..+360]}. @see: Function L{atan2d}. ''' d = atan2d(y, x) if d < 0: d += _360_0 return d def atan2d(y, x): '''Compute C{atan2(y, x)} as degrees M{[-180..+180]}. @see: I{Karney}'s C++ function U{Math.atan2d <https://GeographicLib.SourceForge.io/html/classGeographicLib_1_1Math.html>}. ''' if abs(y) > abs(x) > 0: if y < 0: # q = 3 d = degrees(atan2(x, -y)) - _90_0 else: # q = 2 d = _90_0 - degrees(atan2(x, y)) elif x < 0: # q = 1 d = (-_180_0 if y < 0 else _180_0) - degrees(atan2(y, -x)) elif x > 0: # q = 0 d = degrees(atan2(y, x)) if y else _0_0 else: d = -_90_0 if y < 0 else (_90_0 if y > 0 else _0_0) return d def degrees90(rad): '''Convert radians to degrees and wrap M{[-270..+90]}. @arg rad: Angle (C{radians}). @return: Angle in degrees, wrapped (C{degrees90}). ''' return _wrap(degrees(rad), _90_0, _360_0) def degrees180(rad): '''Convert radians to degrees and wrap M{[-180..+180]}. @arg rad: Angle (C{radians}). @return: Angle in degrees, wrapped (C{degrees180}). ''' return _wrap(degrees(rad), _180_0, _360_0) def degrees360(rad): '''Convert radians to degrees and wrap M{[0..+360)}. @arg rad: Angle (C{radians}). @return: Angle in degrees, wrapped (C{degrees360}). ''' return _wrap(degrees(rad), _360_0, _360_0) def degrees2m(deg, radius=R_M, lat=0): '''Convert angle to distance along the equator or along a parallel at an other latitude. @arg deg: Angle (C{degrees}). @kwarg radius: Mean earth radius (C{meter}). @kwarg lat: Parallel latitude (C{degrees90}, C{str}). @return: Distance (C{meter}, same units as B{C{radius}}). @raise RangeError: Latitude B{C{lat}} outside valid range and L{rangerrors} set to C{True}. @raise ValueError: Invalid B{C{deg}}, B{C{radius}} or B{C{lat}}. @see: Function L{m2degrees}. ''' m = Lam_(deg, name=_deg_, clip=0) * Radius(radius) if lat: m *= cos(Phi_(lat)) return float(m) def ft2m(feet, usurvey=False): '''Convert I{International} or I{US Survey} feet to meter. @arg feet: Value in feet (C{scalar}). @kwarg usurvery: Convert I{US Survey} feet (C{bool}), I{International} feet otherwise. @return: Value in C{meter} (C{float}). @raise ValueError: Invalid B{C{feet}}. ''' # US Survey 1200./3937. == 0.3048006096012192 return Feet(feet) * (0.3048006096012192 if usurvey else 0.3048) def isNumpy2(obj): '''Check for an B{C{Numpy2LatLon}} points wrapper. @arg obj: The object (any C{type}). @return: C{True} if B{C{obj}} is an B{C{Numpy2LatLon}} instance, C{False} otherwise. ''' # isinstance(self, (Numpy2LatLon, ...)) return getattr(obj, isNumpy2.__name__, False) def isPoints2(obj): '''Check for an B{C{LatLon2psxy}} points wrapper. @arg obj: The object (any C{type}). @return: C{True} if B{C{obj}} is an B{C{LatLon2psxy}} instance, C{False} otherwise. ''' # isinstance(self, (LatLon2psxy, ...)) return getattr(obj, isPoints2.__name__, False) def isTuple2(obj): '''Check for an B{C{Tuple2LatLon}} points wrapper. @arg obj: The object (any). @return: C{True} if B{C{obj}} is an B{C{Tuple2LatLon}} instance, C{False} otherwise. ''' # isinstance(self, (Tuple2LatLon, ...)) return getattr(obj, isTuple2.__name__, False) def iterNumpy2(obj): '''Iterate over Numpy2 wrappers or other sequences exceeding the threshold. @arg obj: Points array, list, sequence, set, etc. (any). @return: C{True} do, C{False} don't iterate. ''' try: return isNumpy2(obj) or len(obj) > _iterNumpy2len except TypeError: return False def iterNumpy2over(n=None): '''Get or set the L{iterNumpy2} threshold. @kwarg n: Optional, new threshold (C{int}). @return: Previous threshold (C{int}). @raise ValueError: Invalid B{C{n}}. ''' global _iterNumpy2len p = _iterNumpy2len if n is not None: try: i = int(n) if i > 0: _iterNumpy2len = i else: raise ValueError except (TypeError, ValueError): raise _ValueError(n=n) return p def m2degrees(meter, radius=R_M, lat=0): '''Convert distance to angle along equator or along a parallel at an other latitude. @arg meter: Distance (C{meter}, same units as B{C{radius}}). @kwarg radius: Mean earth radius (C{meter}). @kwarg lat: Parallel latitude (C{degrees90}, C{str}). @return: Angle (C{degrees}). @raise RangeError: Latitude B{C{lat}} outside valid range and L{rangerrors} set to C{True}. @raise ValueError: Invalid B{C{meter}}, B{C{radius}} or B{C{lat}}. @see: Function L{degrees2m}. ''' r = Radius(radius) if lat: r *= cos(Phi_(lat)) return degrees(Meter(meter) / r) def m2ft(meter, usurvey=False): '''Convert meter to I{International} or I{US Survey} feet (C{ft}). @arg meter: Value in meter (C{scalar}). @kwarg usurvery: Convert to I{US Survey} feet (C{bool}), I{International} feet otherwise. @return: Value in C{feet} (C{float}). @raise ValueError: Invalid B{C{meter}}. ''' # US Survey == 3937./1200. = 3.2808333333333333 return Meter(meter) * (3.2808333333333333 if usurvey else 3.2808399) def m2km(meter): '''Convert meter to kilo meter (km). @arg meter: Value in meter (C{scalar}). @return: Value in km (C{float}). @raise ValueError: Invalid B{C{meter}}. ''' return Meter(meter) * 1.0e-3 def m2NM(meter): '''Convert meter to nautical miles (NM). @arg meter: Value in meter (C{scalar}). @return: Value in NM (C{float}). @raise ValueError: Invalid B{C{meter}}. ''' return Meter(meter) * 5.39956804e-4 # == * _1_0 / 1852.0 def m2SM(meter): '''Convert meter to statute miles (SM). @arg meter: Value in meter (C{scalar}). @return: Value in SM (C{float}). @raise ValueError: Invalid B{C{meter}}. ''' return Meter(meter) * 6.21369949e-4 # == _1_0 / 1609.344 def radiansPI(deg): '''Convert and wrap degrees to radians M{[-PI..+PI]}. @arg deg: Angle (C{degrees}). @return: Radians, wrapped (C{radiansPI}) ''' return _wrap(radians(deg), PI, PI2) def radiansPI2(deg): '''Convert and wrap degrees to radians M{[0..+2PI)}. @arg deg: Angle (C{degrees}). @return: Radians, wrapped (C{radiansPI2}) ''' return _wrap(radians(deg), PI2, PI2) def radiansPI_2(deg): '''Convert and wrap degrees to radians M{[-3PI/2..+PI/2]}. @arg deg: Angle (C{degrees}). @return: Radians, wrapped (C{radiansPI_2}) ''' return _wrap(radians(deg), PI_2, PI2) def _sincos2(q, r): '''(INTERNAL) 2-tuple (C{sin(r), cos(r)}) in quadrant M{0 <= q <= 3}. ''' if r: s, c = sin(r), cos(r) t = s, c, -s, -c, s else: t = _0_0, _1_0, -_0_0, -_1_0, _0_0 # q &= 3 return t[q], t[q + 1] def sincos2(*rad): '''Return the C{sine} and C{cosine} of angle(s). @arg rad: One or more angles (C{radians}). @return: The C{sin(rad)} and C{cos(rad)} for each angle. @see: U{GeographicLib<https://GeographicLib.SourceForge.io/html/ classGeographicLib_1_1Math.html#sincosd>} function U{sincosd <https://SourceForge.net/p/geographiclib/code/ci/release/tree/ python/geographiclib/geomath.py#l155>} and C++ U{sincosd <https://SourceForge.net/p/geographiclib/code/ci/release/tree/ include/GeographicLib/Math.hpp#l558>}. ''' for r in rad: q = int(r * _2_PI) # int(math.floor) if r < 0: q -= 1 s, c = _sincos2(q & 3, r - q * PI_2) # _0_0 <= r < PI_2 yield s yield c def sincos2d(*deg): '''Return the C{sine} and C{cosine} of angle(s) in C{degrees}. @arg deg: One or more angles (C{degrees}). @return: The C{sin(deg)} and C{cos(deg)} for each angle. @see: U{GeographicLib<https://GeographicLib.SourceForge.io/html/ classGeographicLib_1_1Math.html#sincosd>} function U{sincosd <https://SourceForge.net/p/geographiclib/code/ci/release/tree/ python/geographiclib/geomath.py#l155>} and C++ U{sincosd <https://SourceForge.net/p/geographiclib/code/ci/release/tree/ include/GeographicLib/Math.hpp#l558>}. ''' for d in deg: q = int(d * _1_90) # int(math.floor) if d < 0: q -= 1 s, c = _sincos2(q & 3, radians(d - q * _90_0)) # _0_0 <= r < PI_2 yield s yield c def splice(iterable, n=2, **fill): '''Split an iterable into C{n} slices. @arg iterable: Items to be spliced (C{list}, C{tuple}, ...). @kwarg n: Number of slices to generate (C{int}). @kwarg fill: Optional fill value for missing items. @return: A generator for each of B{C{n}} slices, M{iterable[i::n] for i=0..n}. @raise ValueError: Invalid B{C{n}}. @note: Each generated slice is a C{tuple} or a C{list}, the latter only if the B{C{iterable}} is a C{list}. @example: >>> from pygeodesy import splice >>> a, b = splice(range(10)) >>> a, b ((0, 2, 4, 6, 8), (1, 3, 5, 7, 9)) >>> a, b, c = splice(range(10), n=3) >>> a, b, c ((0, 3, 6, 9), (1, 4, 7), (2, 5, 8)) >>> a, b, c = splice(range(10), n=3, fill=-1) >>> a, b, c ((0, 3, 6, 9), (1, 4, 7, -1), (2, 5, 8, -1)) >>> tuple(splice(list(range(9)), n=5)) ([0, 5], [1, 6], [2, 7], [3, 8], [4]) >>> splice(range(9), n=1) <generator object splice at 0x0...> ''' if not (isint(n) and n > 0): raise _ValueError(n=n) t = iterable if not isinstance(t, (list, tuple)): t = tuple(t) # force tuple, also for PyPy3 if n > 1: fill = _xkwds_get(fill, fill=_Missing) if fill is not _Missing: m = len(t) % n if m > 0: # fill with same type t += type(t)((fill,)) * (n - m) for i in range(n): yield t[i::n] # slice [i:None:n] pychok -Tb ... else: yield t def tan_2(rad): '''Compute the tangent of half angle. @arg rad: Angle (C{radians}). @return: M{tan(rad / 2)} (C{float}). ''' return tan(rad * _0_5) def tanPI_2_2(rad): '''Compute the tangent of half angle, 90 degrees rotated. @arg rad: Angle (C{radians}). @return: M{tan((rad + PI/2) / 2)} (C{float}). ''' return tan((rad + PI_2) * _0_5) def unroll180(lon1, lon2, wrap=True): '''Unroll longitudinal delta and wrap longitude in degrees. @arg lon1: Start longitude (C{degrees}). @arg lon2: End longitude (C{degrees}). @kwarg wrap: Wrap and unroll to the M{(-180..+180]} range (C{bool}). @return: 2-Tuple (B{C{lon2-lon1}}, B{C{lon2}}) unrolled (C{degrees}, C{degrees}). @see: Capability C{LONG_UNROLL} in U{GeographicLib <https://GeographicLib.SourceForge.io/html/python/interface.html#outmask>}. ''' d = lon2 - lon1 if wrap and abs(d) > _180_0: u = _wrap(d, _180_0, _360_0) if u != d: return u, lon1 + u return d, lon2 def unrollPI(rad1, rad2, wrap=True): '''Unroll longitudinal delta and wrap longitude in radians. @arg rad1: Start longitude (C{radians}). @arg rad2: End longitude (C{radians}). @kwarg wrap: Wrap and unroll to the M{(-PI..+PI]} range (C{bool}). @return: 2-Tuple (B{C{rad2 - rad1}}, B{C{rad2}}) unrolled (C{radians}, C{radians}). @see: Capability C{LONG_UNROLL} in U{GeographicLib <https://GeographicLib.SourceForge.io/html/python/interface.html#outmask>}. ''' r = rad2 - rad1 if wrap and abs(r) > PI: u = _wrap(r, PI, PI2) if u != r: return u, rad1 + u return r, rad2 def _wrap(angle, wrap, modulo): '''(INTERNAL) Angle wrapper M{((wrap-modulo)..+wrap]}. @arg angle: Angle (C{degrees} or C{radians}). @arg wrap: Range (C{degrees} or C{radians}). @arg modulo: Upper limit (360 C{degrees} or PI2 C{radians}). @return: The B{C{angle}}, wrapped (C{degrees} or C{radians}). ''' if wrap > angle >= (wrap - modulo): angle = float(angle) else: # math.fmod(-1.5, 3.14) == -1.5, but -1.5 % 3.14 == 1.64 # math.fmod(-1.5, 360) == -1.5, but -1.5 % 360 == 358.5 angle %= modulo if angle > wrap: angle -= modulo return angle def wrap90(deg): '''Wrap degrees to M{[-270..+90]}. @arg deg: Angle (C{degrees}). @return: Degrees, wrapped (C{degrees90}). ''' return _wrap(deg, _90_0, _360_0) def wrap180(deg): '''Wrap degrees to M{[-180..+180]}. @arg deg: Angle (C{degrees}). @return: Degrees, wrapped (C{degrees180}). ''' return _wrap(deg, _180_0, _360_0) def wrap360(deg): '''Wrap degrees to M{[0..+360)}. @arg deg: Angle (C{degrees}). @return: Degrees, wrapped (C{degrees360}). ''' return _wrap(deg, _360_0, _360_0) def wrapPI(rad): '''Wrap radians to M{[-PI..+PI]}. @arg rad: Angle (C{radians}). @return: Radians, wrapped (C{radiansPI}). ''' return _wrap(rad, PI, PI2) def wrapPI2(rad): '''Wrap radians to M{[0..+2PI)}. @arg rad: Angle (C{radians}). @return: Radians, wrapped (C{radiansPI2}). ''' return _wrap(rad, PI2, PI2) def wrapPI_2(rad): '''Wrap radians to M{[-3PI/2..+PI/2]}. @arg rad: Angle (C{radians}). @return: Radians, wrapped (C{radiansPI_2}). ''' return _wrap(rad, PI_2, PI2) # **) MIT License # # Copyright (C) 2016-2020 -- mrJean1 at Gmail -- All Rights Reserved. # # Permission is hereby granted, free of charge, to any person obtaining a # copy of this software and associated documentation files (the "Software"), # to deal in the Software without restriction, including without limitation # the rights to use, copy, modify, merge, publish, distribute, sublicense, # and/or sell copies of the Software, and to permit persons to whom the # Software is furnished to do so, subject to the following conditions: # # The above copyright notice and this permission notice shall be included # in all copies or substantial portions of the Software. # # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS # OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL # THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR # OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, # ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR # OTHER DEALINGS IN THE SOFTWARE.