def __init__(self, a_ellipsoid, f, name):
'''(INTERNAL) New C{Ecef...}.
'''
try:
E = a_ellipsoid
if f is None:
if isinstance(E, Datum):
self._datum = E
E = E.ellipsoid
elif not isinstance(E, Ellipsoid):
raise TypeError
if not name:
name = E.name
elif isscalar(E) and isscalar(f):
a = float(E)
f_ = (1.0 / f) if f else 0 # sphere
b = None if f_ else a
E = Ellipsoid(a, b, f_, name='_' + name)
else:
raise ValueError
if not (E.a > 0 and E.f < 1):
raise ValueError
except (TypeError, ValueError):
t = unstr(self.classname, a=E, f=f)
raise EcefError('%s invalid: %s' % ('ellipsoid', t))
self._E = E
if name:
self.name = name
def _height(self, lats, lons, Error=HeightError):
if isscalar(lats) and isscalar(lons):
llis = LatLon_(lats, lons)
else:
n, lats = len2(lats)
m, lons = len2(lons)
if n != m:
raise Error('non-matching %s: %s vs %s' % ('len', n, m))
llis = [LatLon_(*ll) for ll in zip(lats, lons)]
return self(llis) # __call__(lli) or __call__(llis)
def _height(self, lats, lons, Error=HeightError):
LLis, d = self._LLis, self.datum
if isscalar(lats) and isscalar(lons):
llis = LLis(lats, lons, datum=d)
else:
n, lats = len2(lats)
m, lons = len2(lons)
if n != m:
# format a LenError, but raise an Error
e = LenError(self.__class__, lats=n, lons=m, txt=None)
raise e if Error is LenError else Error(str(e))
llis = [LLis(*ll, datum=d) for ll in zip(lats, lons)]
return self(llis) # __call__(lli) or __call__(llis)
def fractional(points, fi, LatLon=None, **LatLon_kwds):
'''Return the point at a given I{fractional} index.
@arg points: The points (C{LatLon}[], L{Numpy2LatLon}[],
L{Tuple2LatLon}[] or C{other}[]).
@arg fi: The fractional index (C{float} or C{int}).
@kwarg LatLon: Optional class to return the I{intermediate},
I{fractional} point (C{LatLon}) or C{None}.
@kwarg LatLon_kwds: Optional B{C{LatLon}} keyword arguments,
ignored of B{C{LatLon=None}}.
@return: A B{C{LatLon}} or if B{C{LatLon}} is C{None}, a
L{LatLon2Tuple}C{(lat, lon)} for B{C{points[fi]}} if
I{fractional} index B{C{fi}} is C{int}, otherwise the
intermediate point between B{C{points[int(fi)]}} and
B{C{points[int(fi) + 1]}} for C{float} I{fractional}
index B{C{fi}}.
@raise IndexError: Fractional index B{C{fi}} invalid or
B{C{points}} not subscriptable.
'''
try:
if not (isscalar(fi) and 0 <= fi < len(points)):
raise IndexError
p = _fractional(points, fi)
except (IndexError, TypeError):
raise _IndexError(fractional.__name__, fi)
if LatLon and isinstance(p, LatLon2Tuple):
p = LatLon(*p, **LatLon_kwds)
return p
def fadd(self, iterable):
'''Accumulate more values from an iterable.
@arg iterable: Sequence, list, tuple, etc. (C{scalar}s).
@raise OverflowError: Partial C{2sum} overflow.
@raise TypeError: Non-scalar B{C{iterable}} value.
@raise ValueError: Invalid or non-finite B{C{iterable}} value.
'''
if isscalar(iterable): # for backward compatibility
iterable = tuple(iterable)
ps = self._ps
for a in map(float, iterable): # _iter()
if not isfinite(a):
raise _ValueError(iterable=a, txt=_not_(_finite_))
i = 0
for p in ps:
a, p = _2sum(a, p)
if p:
ps[i] = p
i += 1
ps[i:] = [a]
self._n += 1
# assert self._ps is ps
self._fsum2_ = None
def __imul__(self, other):
'''Multiply this instance by a scalar or an other instance.
@arg other: L{Fsum} instance or C{scalar}.
@return: This instance, updated (L{Fsum}).
@raise TypeError: Invalid B{C{other}} type.
@see: Method L{Fsum.fmul}.
'''
if isscalar(other):
self.fmul(other)
elif isinstance(other, Fsum):
ps = list(other._ps) # copy
if ps:
s = self.fcopy()
self.fmul(ps.pop())
while ps: # self += s * ps.pop()
p = s.fcopy()
p.fmul(ps.pop())
self.fadd(p._ps)
else:
self._ps = [] # zero
self._fsum2_ = None
else:
raise _TypeError(_SPACE_(self, '*=', repr(other)))
return self
def _x3d2(start, end, wrap, n, hs):
# see <https://www.EdWilliams.org/intersect.htm> (5) ff
a1, b1 = start.philam
if isscalar(end): # bearing, make a point
a2, b2 = _destination2(a1, b1, PI_4, radians(end))
else: # must be a point
_Trll.others(end, name='end' + n)
hs.append(end.height)
a2, b2 = end.philam
db, b2 = unrollPI(b1, b2, wrap=wrap)
if max(abs(db), abs(a2 - a1)) < EPS:
raise ValueError('intersection %s%s null: %r' % ('path', n,
(start, end)))
# note, in EdWilliams.org/avform.htm W is + and E is -
b21, b12 = db * 0.5, -(b1 + b2) * 0.5
sb21, cb21, sb12, cb12, \
sa21, _, sa12, _ = sincos2(b21, b12, a1 - a2, a1 + a2)
x = _Nvector(sa21 * sb12 * cb21 - sa12 * cb12 * sb21,
sa21 * cb12 * cb21 + sa12 * sb12 * sb21,
cos(a1) * cos(a2) * sin(db)) # ll=start
return x.unit(), (db, (a2 - a1)) # negated d
def __mod__(self, arg, **unused):
'''Regular C{%} operator.
@arg arg: A C{scalar} value to be formatted (either
the C{scalar}, or a 1-tuple C{(scalar,)},
or 2-tuple C{(prec, scalar)}.
@raise TypeError: Non-scalar B{C{arg}} value.
@raise ValueError: Invalid B{C{arg}}.
'''
def _error(arg):
n = _DOT_(Fstr.__name__, self.name or self)
return _SPACE_(n, _PERCENT_, repr(arg))
prec = 6 # default std %f and %F
if isinstance(arg, (tuple, list)):
n = len(arg)
if n == 1:
arg = arg[0]
elif n == 2:
prec, arg = arg
else:
raise _ValueError(_error(arg))
if not isscalar(arg):
raise _TypeError(_error(arg))
return self(arg, prec=prec)
def toStr(self,
prec=3,
sep=_SPACE_,
radius=False,
**unused): # PYCHOK expected
'''Return a string representation of this WM coordinate.
@kwarg prec: Optional number of decimals, unstripped (C{int}).
@kwarg sep: Optional separator to join (C{str}) or C{None}
to return an unjoined C{tuple} of C{str}s.
@kwarg radius: Optionally, include radius (C{bool} or C{scalar}).
@return: This WM as "meter meter" (C{str}) plus " radius"
if B{C{radius}} is C{True} or C{scalar}.
@raise WebMercatorError: Invalid B{C{radius}}.
@example:
>>> w = Wm(448251, 5411932.0001)
>>> w.toStr(4) # 448251.0 5411932.0001
>>> w.toStr(sep=', ') # 448251, 5411932
'''
fs = self._x, self._y
if radius in (False, None):
pass
elif radius is True:
fs += (self._radius, )
elif isscalar(radius):
fs += (radius, )
else:
raise WebMercatorError(radius=radius)
t = strs(fs, prec=prec)
return t if sep is None else sep.join(t)
def __init__(self, knots, weight=None, name=NN):
'''New L{HeightLSQBiSpline} interpolator.
@arg knots: The points with known height (C{LatLon}s).
@kwarg weight: Optional weight or weights for each B{C{knot}}
(C{scalar} or C{scalar}s).
@kwarg name: Optional name for this height interpolator (C{str}).
@raise HeightError: Insufficient number of B{C{knots}} or
an invalid B{C{knot}} or B{C{weight}}.
@raise LenError: Number of B{C{knots}} and B{C{weight}}s
don't match.
@raise ImportError: Package C{numpy} or C{scipy} not found
or not installed.
@raise SciPyError: A C{LSQSphereBivariateSpline} issue.
@raise SciPyWarning: A C{LSQSphereBivariateSpline} warning
as exception.
'''
np, spi = self._NumSciPy()
xs, ys, hs = self._xyhs3(knots)
n = len(hs)
w = weight
if isscalar(w):
w = float(w)
if w <= 0:
raise HeightError(weight=w)
w = [w] * n
elif w is not None:
m, w = len2(w)
if m != n:
raise LenError(HeightLSQBiSpline, weight=m, knots=n)
w = map2(float, w)
m = min(w)
if m <= 0:
raise HeightError(_item_sq(weight=w.find(m)), m)
try:
T = 1.0e-4 # like SciPy example
ps = np.array(_ordedup(xs, T, PI2 - T))
ts = np.array(_ordedup(ys, T, PI - T))
self._ev = spi.LSQSphereBivariateSpline(ys,
xs,
hs,
ts,
ps,
eps=EPS,
w=w).ev
except Exception as x:
raise _SciPyIssue(x)
if name:
self.name = name
def _fraction(fraction, n):
f = 1 # int, no fractional indices
if fraction in (None, 1):
pass
elif not (isscalar(fraction) and EPS < fraction < EPS1 and
(float(n) - fraction) < n):
raise FrechetError(fraction=fraction)
elif fraction < EPS1:
f = float(fraction)
return f
def times(self, factor):
'''Multiply this vector by a scalar.
@arg factor: Scale factor (C{scalar}).
@return: New, scaled vector (L{Vector3d}).
@raise TypeError: Non-scalar B{C{factor}}.
'''
if not isscalar(factor):
raise IsnotError('scalar', factor=factor)
return self.classof(self.x * factor, self.y * factor, self.z * factor)
def _gc3(self, start, end, namend, raiser=_points_):
'''(INTERNAL) Return great circle, start and end Nvectors.
'''
s = start.toNvector()
if isscalar(end): # bearing
gc = s.greatCircle(end)
e = None
else:
self.others(end, name=namend)
e = end.toNvector()
gc = s.cross(e, raiser=raiser) # XXX .unit()?
return gc, s, e
def _to3zBhp(zone,
band,
hemipole=NN,
Error=_ValueError): # imported by .epsg, .ups, .utm, .utmups
'''Parse UTM/UPS zone, Band letter and hemisphere/pole letter.
@arg zone: Zone with/-out Band (C{scalar} or C{str}).
@kwarg band: Optional (longitudinal/polar) Band letter (C{str}).
@kwarg hemipole: Optional hemisphere/pole letter (C{str}).
@kwarg Error: Optional error to raise, overriding the default
C{ValueError}.
@return: 3-Tuple (C{zone, Band, hemisphere/pole}) as (C{int,
str, 'N'|'S'}) where C{zone} is C{0} for UPS or
C{1..60} for UTM and C{Band} is C{'A'..'Z'} I{NOT}
checked for valid UTM/UPS bands.
@raise ValueError: Invalid B{C{zone}}, B{C{band}} or B{C{hemipole}}.
'''
try:
B, z = band, _UTMUPS_ZONE_INVALID
if isscalar(zone):
z = int(zone)
elif zone and isstr(zone):
if zone.isdigit():
z = int(zone)
elif len(zone) > 1:
B = zone[-1:]
z = int(zone[:-1])
elif zone in 'AaBbYyZz': # single letter
B = zone
z = _UPS_ZONE
if _UTMUPS_ZONE_MIN <= z <= _UTMUPS_ZONE_MAX:
hp = hemipole[:1].upper()
if hp in _NS_ or not hp:
z = Zone(z)
B = Band(B.upper())
if B.isalpha():
return z, B, (hp or _NS_[B < _N_])
elif not B:
return z, B, hp
t = _invalid_
except (AttributeError, IndexError, TypeError, ValueError) as x:
t = str(x) # no Python 3+ exception chaining
raise Error(zone=zone, band=B, hemipole=hemipole, txt=t)
def fstr(floats, prec=6, fmt='F', ints=False, sep=', '):
'''Convert one or more floats to string, optionally stripped of trailing zero decimals.
@arg floats: Single or a list, sequence, tuple, etc. (C{scalar}s).
@kwarg prec: The C{float} precision, number of decimal digits (0..9).
Trailing zero decimals are stripped if B{C{prec}} is
positive, but kept for negative B{C{prec}} values.
@kwarg fmt: Optional, float format (C{str}).
@kwarg ints: Optionally, remove the decimal dot (C{bool}).
@kwarg sep: Separator joining the B{C{floats}} (C{str}).
@return: The C{sep.join(strs(floats, ...)} joined (C{str}) or single
C{strs((floats,), ...)} (C{str}) if B{C{floats}} is C{scalar}.
'''
if isscalar(floats):
floats = (floats, )
return sep.join(_streprs(prec, floats, fmt, ints, True, None))
def dividedBy(self, factor):
'''Divide this vector by a scalar.
@arg factor: The divisor (C{scalar}).
@return: New, scaled vector (L{Vector3d}).
@raise TypeError: Non-scalar B{C{factor}}.
@raise VectorError: Invalid or zero B{C{factor}}.
'''
if not isscalar(factor):
raise _IsnotError(_scalar_, factor=factor)
try:
return self.times(_1_0 / factor)
except (ValueError, ZeroDivisionError) as x:
raise VectorError(factor=factor, txt=str(x))
def __iadd__(self, other):
'''Add a scalar or an other instance to this instance.
@arg other: L{Fsum} instance or C{scalar}.
@return: This instance, updated (L{Fsum}).
@raise TypeError: Invalid B{C{other}} type.
@see: Method L{Fsum.fadd}.
'''
if isscalar(other):
self.fadd_(other)
elif other is self:
self.fmul(2)
elif isinstance(other, Fsum):
self.fadd(other._ps)
else:
raise _TypeError(_SPACE_(self, '+=', repr(other)))
return self
def __isub__(self, other):
'''Subtract a scalar or an other instance from this instance.
@arg other: L{Fsum} instance or C{scalar}.
@return: This instance, updated (L{Fsum}).
@raise TypeError: Invalid B{C{other}} type.
@see: Method L{Fsum.fadd}.
'''
if isscalar(other):
self.fadd_(-other)
elif other is self:
self._ps = [] # zero
self._fsum2_ = None
elif isinstance(other, Fsum):
self.fadd(-p for p in other._ps)
else:
raise _TypeError(_SPACE_(self, '-=', repr(other)))
return self
def _to3zBhp(zone, band, hemipole=''): # imported by .epsg, .ups, .utm, .utmups
'''Parse UTM/UPS zone, Band letter and hemisphere/pole letter.
@arg zone: Zone with/-out Band (C{scalar} or C{str}).
@kwarg band: Optional (longitudinal/polar) Band letter (C{str}).
@kwarg hemipole: Optional hemisphere/pole letter (C{str}).
@return: 3-Tuple (C{zone, Band, hemisphere/pole}) as (C{int,
str, 'N'|'S'}) where C{zone} is C{0} for UPS or
C{1..60} for UTM and C{Band} is C{'A'..'Z'} I{NOT}
checked for valid UTM/UPS bands.
@raise ValueError: Invalid B{C{zone}}, B{C{band}} or B{C{hemipole}}.
'''
B = band
try:
z = _UTMUPS_ZONE_INVALID
if isscalar(zone) or zone.isdigit():
z = int(zone)
elif zone and isstr(zone):
if len(zone) > 1:
B = zone[-1:]
z = int(zone[:-1])
elif zone in 'AaBbYyZz': # single letter
B = zone
z = _UPS_ZONE
if _UTMUPS_ZONE_MIN <= z <= _UTMUPS_ZONE_MAX:
hp = hemipole[:1].upper()
if hp in ('N', 'S') or not hp:
B = B.upper()
if B.isalpha():
return z, B, (hp or ('S' if B < 'N' else 'N'))
elif not B:
return z, B, hp
except (AttributeError, TypeError, ValueError):
pass
raise ValueError('%s invalid: %r' % (_or('zone', 'band', 'hemipole'),
(zone, B, hemipole)))
def fadd(self, iterable):
'''Accumulate more values from an iterable.
@arg iterable: Sequence, list, tuple, etc. (C{scalar}s).
@raise OverflowError: Partial C{2sum} overflow.
@raise TypeError: Non-scalar B{C{iterable}} value.
@raise ValueError: Invalid or non-finite B{C{iterable}} value.
'''
if isscalar(iterable): # for backward compatibility
iterable = tuple(iterable)
# def _iter():
# for a in iterable:
# if isinstance(a, Fsum):
# if a is self:
# self.fmul(2)
# else:
# for a in a._ps:
# yield a
# else:
# yield a
ps = self._ps
for a in iterable: # _iter()
if not isfinite(a):
raise ValueError('%s, not %s: %r' % (self, 'finite', a))
i = 0
for p in ps:
a, p = _2sum(a, p)
if p:
ps[i] = p
i += 1
ps[i:] = [a]
self._n += 1
# assert self._ps is ps
self._fsum2_ = None
def _spherical_datum(radius, name=NN, raiser=False):
'''(INTERNAL) Create a L{Datum} from an L{Ellipsoid}, L{Ellipsoid2} or scalar earth C{radius}.
'''
try:
d = _ellipsoidal_datum(radius, name=name)
except TypeError:
d = None
if d is None:
if not isscalar(radius):
_xinstanceof(Datum,
Ellipsoid,
Ellipsoid2,
a_f2Tuple,
Scalar,
datum=radius)
n = _UNDERSCORE_ + name
r = Radius_(radius, Error=TypeError)
E = Ellipsoid(r, r, name=n)
d = Datum(E, transform=Transforms.Identity, name=n)
elif raiser and not d.isSpherical: # raiser if no spherical
raise _IsnotError(_spherical_, datum=radius)
return d
def fstr(floats, prec=6, fmt=Fmt.F, ints=False, sep=_COMMASPACE_, strepr=None):
'''Convert one or more floats to string, optionally stripped of trailing zero decimals.
@arg floats: Single or a list, sequence, tuple, etc. (C{scalar}s).
@kwarg prec: The C{float} precision, number of decimal digits (0..9).
Trailing zero decimals are stripped if B{C{prec}} is
positive, but kept for negative B{C{prec}} values. In
addition, trailing decimal zeros are stripped for U{alternate,
form '#'<https://docs.Python.org/3/library/stdtypes.html
#printf-style-string-formatting>}.
@kwarg fmt: Optional, C{float} format (C{str}).
@kwarg ints: Optionally, remove the decimal dot for C{int} values (C{bool}).
@kwarg sep: Separator joining the B{C{floats}} (C{str}).
@kwarg strepr: Optional callable to format non-C{floats} (typically
C{repr}, C{str}) or C{None} to raise a TypeError.
@return: The C{sep.join(strs(floats, ...)} joined (C{str}) or single
C{strs((floats,), ...)} (C{str}) if B{C{floats}} is C{scalar}.
'''
if isscalar(floats): # see Fstr.__call__ above
return next(_streprs(prec, (floats, ), fmt, ints, True, strepr))
else:
return sep.join(_streprs(prec, floats, fmt, ints, True, strepr))
def intersection(start1,
end1,
start2,
end2,
height=None,
wrap=False,
LatLon=LatLon,
**LatLon_kwds):
'''Compute the intersection point of two paths both defined
by two points or a start point and bearing from North.
@arg start1: Start point of the first path (L{LatLon}).
@arg end1: End point ofthe first path (L{LatLon}) or
the initial bearing at the first start point
(compass C{degrees360}).
@arg start2: Start point of the second path (L{LatLon}).
@arg end2: End point of the second path (L{LatLon}) or
the initial bearing at the second start point
(compass C{degrees360}).
@kwarg height: Optional height for the intersection point,
overriding the mean height (C{meter}).
@kwarg wrap: Wrap and unroll longitudes (C{bool}).
@kwarg LatLon: Optional class to return the intersection
point (L{LatLon}) or C{None}.
@kwarg LatLon_kwds: Optional, additional B{C{LatLon}} keyword
arguments, ignored if B{C{LatLon=None}}.
@return: The intersection point (B{C{LatLon}}) or a
L{LatLon3Tuple}C{(lat, lon, height)} if B{C{LatLon}}
is C{None}. An alternate intersection point might
be the L{antipode} to the returned result.
@raise TypeError: A B{C{start}} or B{C{end}} point not L{LatLon}.
@raise ValueError: Intersection is ambiguous or infinite or
the paths are parallel, coincident or null
or invalid B{C{height}}.
@example:
>>> p = LatLon(51.8853, 0.2545)
>>> s = LatLon(49.0034, 2.5735)
>>> i = intersection(p, 108.547, s, 32.435) # '50.9078°N, 004.5084°E'
'''
_Trll.others(start1, name='start1')
_Trll.others(start2, name='start2')
hs = [start1.height, start2.height]
a1, b1 = start1.philam
a2, b2 = start2.philam
db, b2 = unrollPI(b1, b2, wrap=wrap)
r12 = haversine_(a2, a1, db)
if abs(r12) < EPS: # [nearly] coincident points
a, b = favg(a1, a2), favg(b1, b2)
# see <https://www.EdWilliams.org/avform.htm#Intersection>
elif isscalar(end1) and isscalar(end2): # both bearings
sa1, ca1, sa2, ca2, sr12, cr12 = sincos2(a1, a2, r12)
x1, x2 = (sr12 * ca1), (sr12 * ca2)
if abs(x1) < EPS or abs(x2) < EPS:
raise ValueError('intersection %s: %r vs %r' % ('parallel',
(start1, end1),
(start2, end2)))
# handle domain error for equivalent longitudes,
# see also functions asin_safe and acos_safe at
# <https://www.EdWilliams.org/avform.htm#Math>
t1, t2 = map1(acos1, (sa2 - sa1 * cr12) / x1, (sa1 - sa2 * cr12) / x2)
if sin(db) > 0:
t12, t21 = t1, PI2 - t2
else:
t12, t21 = PI2 - t1, t2
t13, t23 = map1(radiansPI2, end1, end2)
x1, x2 = map1(
wrapPI,
t13 - t12, # angle 2-1-3
t21 - t23) # angle 1-2-3
sx1, cx1, sx2, cx2 = sincos2(x1, x2)
if sx1 == 0 and sx2 == 0: # max(abs(sx1), abs(sx2)) < EPS
raise ValueError('intersection %s: %r vs %r' % ('infinite',
(start1, end1),
(start2, end2)))
sx3 = sx1 * sx2
# if sx3 < 0:
# raise ValueError('intersection %s: %r vs %r' % ('ambiguous',
# (start1, end1), (start2, end2)))
x3 = acos1(cr12 * sx3 - cx2 * cx1)
r13 = atan2(sr12 * sx3, cx2 + cx1 * cos(x3))
a, b = _destination2(a1, b1, r13, t13)
# choose antipode for opposing bearings
if _xb(a1, b1, end1, a, b, wrap) < 0 or \
_xb(a2, b2, end2, a, b, wrap) < 0:
a, b = antipode_(a, b) # PYCHOK PhiLam2Tuple
else: # end point(s) or bearing(s)
x1, d1 = _x3d2(start1, end1, wrap, '1', hs)
x2, d2 = _x3d2(start2, end2, wrap, '2', hs)
x = x1.cross(x2)
if x.length < EPS: # [nearly] colinear or parallel paths
raise ValueError('intersection %s: %r vs %r' % ('colinear',
(start1, end1),
(start2, end2)))
a, b = x.philam
# choose intersection similar to sphericalNvector
d1 = _xdot(d1, a1, b1, a, b, wrap)
if d1:
d2 = _xdot(d2, a2, b2, a, b, wrap)
if (d2 < 0 and d1 > 0) or (d2 > 0 and d1 < 0):
a, b = antipode_(a, b) # PYCHOK PhiLam2Tuple
h = fmean(hs) if height is None else Height(height)
return _latlon3(degrees90(a), degrees180(b), h, intersection, LatLon,
**LatLon_kwds)
def _2epoch(epoch): # imported by .ellipsoidalBase.py
'''(INTERNAL) Validate an C{epoch}.
'''
if isscalar(epoch) and epoch > 0: # XXX 1970?
return _F(epoch)
raise IsnotError('scalar', epoch=epoch)
def _2epoch(epoch): # imported by .ellipsoidalBase
'''(INTERNAL) Validate an C{epoch}.
'''
if isscalar(epoch) and epoch > 0: # XXX 1970?
return _F(epoch)
raise _TypeError(epoch=epoch, txt=_not_scalar_)