# Coverage for pygeodesy/vector3dBase.py : 93%

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Pure Python implementation of vector-based functions by I{(C) Chris Veness 2011-2015} published under the same MIT Licence**, see U{Vector-based geodesy <https://www.Movable-Type.co.UK/scripts/latlong-vectors.html>}. ''' from pygeodesy.basics import copysign0, isnear0, isnear1, isscalar, map1, \ _xinstanceof from pygeodesy.errors import CrossError, _InvalidError, _IsnotError, VectorError from pygeodesy.fmath import euclid_, fdot, hypot_, hypot2_ from pygeodesy.formy import n_xyz2latlon, n_xyz2philam, sincos2 from pygeodesy.interns import EPS, EPS0, NN, PI, PI2, _coincident_, \ _colinear_, _COMMASPACE_, _1_0 from pygeodesy.lazily import _ALL_LAZY, _ALL_MODS as _MODS, _sys_version_info2 from pygeodesy.named import _NamedBase, _NotImplemented, _xother3 from pygeodesy.namedTuples import Vector3Tuple, Vector4Tuple from pygeodesy.props import deprecated_method, Property, Property_RO, \ property_doc_ from pygeodesy.streprs import Fmt, strs from pygeodesy.units import Float, Scalar # from pygeodesy.utily import sincos2 # from .formy from math import atan2 __all__ = _ALL_LAZY.vector3dBase __version__ = '21.12.28' class Vector3dBase(_NamedBase): # XXX or _NamedTuple or Vector3Tuple? '''(INTERNAL) Generic 3-D vector base class. In a geodesy context, these may be used to represent: - n-vector representing a normal to point on earth's surface - earth-centered, earth-fixed cartesian (= spherical n-vector) - great circle normal to vector - motion vector on earth's surface - etc. ''' _crosserrors = True # un/set by .errors.crosserrors _fromll = None # original latlon, '_fromll' _x = 0 # X component _y = 0 # Y component _z = 0 # Z component def __init__(self, x_xyz, y=0, z=0, ll=None, name=NN): '''New L{Vector3d} or C{Vector3dBase} instance. The vector may be normalised or use x, y, z for position and distance from earth centre or height relative to the surface of the earth' sphere or ellipsoid. @arg x_xyz: X component of vector (C{scalar}) or (3-D) vector (C{Cartesian}, C{Nvector}, L{Vector3d} or L{Vector3Tuple}). @kwarg y: Y component of vector (C{scalar}), ignored if B{C{x_xyz}} is not C{scalar}, otherwise same units as B{C{x_xyz}}. @kwarg z: Z component of vector (C{scalar}), ignored if B{C{x_xyz}} is not C{scalar}, otherwise same units as B{C{x_xyz}}. @kwarg ll: Optional latlon reference (C{LatLon}). @kwarg name: Optional name (C{str}). @raise VectorError: Invalid B{C{x_xyz}}. ''' try: self._x, self._y, self._z = (x_xyz, y, z) if isscalar(x_xyz) else x_xyz.xyz except (AttributeError, TypeError, ValueError) as x: raise VectorError(x=x_xyz, y=y, z=z, txt=str(x)) if ll: self._fromll = ll if name: self.name = name def __abs__(self): '''Return the norm of this vector. @return: Norm, unit length (C{float}); ''' return self.length def __add__(self, other): '''Add this to an other vector (L{Vector3d}). @return: Vectorial sum (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self.plus(other) __radd__ = __add__ # PYCHOK no cover def __bool__(self): # PYCHOK PyChecker '''Is this vector non-zero? ''' return bool(self.x or self.y or self.z) def __cmp__(self, other): # Python 2- '''Compare this and an other vector @arg other: The other vector (L{Vector3d}). @return: -1, 0 or +1 (C{int}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return -1 if self.length < other.length else ( +1 if self.length > other.length else 0) cmp = __cmp__ def __divmod__(self, other): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, other) def __eq__(self, other): '''Is this vector equal to an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if equal, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' # self.others(other) return self.isequalTo(other, eps=EPS0) def __floordiv__(self, other): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, other) def __format__(self, *other): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, *other) def __ge__(self, other): '''Is this vector longer than or equal to an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if so, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.length >= other.length # def __getitem__(self, key): # '''Return C{item} at index or slice C{[B{key}]}. # ''' # return self.xyz[key] def __gt__(self, other): '''Is this vector longer than an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if so, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.length > other.length def __iadd__(self, other): '''Add an other vector to this one I{in-place}, C{this += B{other}}. @arg other: The other vector (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.xyz = self.plus(other).xyz def __imatmul__(self, other): # PYCHOK Python 3.5+ '''Cross multiply an other vector and this one I{in-place}, C{this @= B{other}}. @arg other: The other vector (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. @see: Luciano Ramalho, "Fluent Python", page 397-398, O'Reilly 2016. ''' self.xyz = self.cross(other).xyz def __imul__(self, scalar): '''Multiply this vector by a scalar I{in-place}, C{this *= B{scalar}}. @arg scalar: Factor (C{scalar}). @raise TypeError: Non-scalar B{C{scalar}}. ''' self.xyz = self.times(scalar).xyz def __isub__(self, other): '''Subtract an other vector from this one I{in-place}, C{this -= B{other}}. @arg other: The other vector (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.xyz = self.minus(other).xyz def __itruediv__(self, scalar): '''Divide this vector by a scalar I{in-place}, C{this /= B{scalar}}. @arg scalar: The divisor (C{scalar}). @raise TypeError: Non-scalar B{C{scalar}}. ''' self.xyz = self.dividedBy(scalar).xyz def __le__(self, other): # Python 3+ '''Is this vector shorter than or equal to an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if so, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.length <= other.length # def __len__(self): # '''Return C{3}, always. # ''' # return len(self.xyz) def __lt__(self, other): # Python 3+ '''Is this vector shorter than an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if so, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.length < other.length def __matmul__(self, other): # PYCHOK Python 3.5+ '''Compute the cross product of this and an other vector, C{this @ B{other}}. @arg other: The other vector (L{Vector3d}). @return: Cross product (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self.cross(other) def __mod__(self, other): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, other) def __mul__(self, scalar): '''Multiply this vector by a scalar. @arg scalar: Factor (C{scalar}). @return: Product (L{Vector3d}). ''' return self.times(scalar) def __ne__(self, other): '''Is this vector not equal to an other vector? @arg other: The other vector (L{Vector3d}). @return: C{True} if so, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. ''' return not self.__eq__(other) def __pos__(self): # PYCHOK no cover '''Return this vector I{as-is}. @return: This instance (L{Vector3d}) ''' return self def __pow__(self, other, *mod): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, other, *mod) def __rdivmod__ (self, other): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, other) def __rfloordiv__(self, other): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, other) def __rmatmul__(self, other): # PYCHOK Python 3.5+ '''Compute the cross product of an other and this vector, C{B{other} @ this}. @arg other: The other vector (L{Vector3d}). @return: Cross product (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return other.cross(self) def __rmod__(self, other): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, other) def __rmul__(self, scalar): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, scalar) def __round__(self, ndigits=None): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, ndigits=ndigits) def __rpow__(self, other, *mod): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, other, *mod) def __rsub__(self, other): # PYCHOK no cover '''Subtract this vector from an other vector. @arg other: The other vector (L{Vector3d}). @return: Difference (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return other.minus(self) def __rtruediv__(self, scalar): # PYCHOK no cover '''Not implemented.''' return _NotImplemented(self, scalar) def __sub__(self, other): '''Subtract an other vector from this vector. @arg other: The other vector (L{Vector3d}). @return: Difference (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' return self.minus(other) def __truediv__(self, scalar): '''Divide this vector by a scalar. @arg scalar: The divisor (C{scalar}). @return: Quotient (L{Vector3d}). @raise TypeError: Non-scalar B{C{scalar}}. ''' return self.dividedBy(scalar) if _sys_version_info2 < (3, 0): # PYCHOK no cover # <https://docs.Python.org/2/library/operator.html#mapping-operators-to-functions> __div__ = __truediv__ __idiv__ = __itruediv__ __nonzero__ = __bool__ def angleTo(self, other, vSign=None, wrap=False): '''Compute the angle between this and an other vector. @arg other: The other vector (L{Vector3d}). @kwarg vSign: Optional vector, if supplied (and out of the plane of this and the other), angle is signed positive if this->other is clockwise looking along vSign or negative in opposite direction, otherwise angle is unsigned. @kwarg wrap: Wrap/unroll the angle to +/-PI (C{bool}). @return: Angle (C{radians}). @raise TypeError: If B{C{other}} or B{C{vSign}} not a L{Vector3d}. ''' x = self.cross(other) s = x.length # use vSign as reference to set sign of s if s and vSign and x.dot(vSign) < 0: s = -s a = atan2(s, self.dot(other)) if wrap and abs(a) > PI: a -= copysign0(PI2, a) return a def apply(self, fun2, other_x, *y_z, **fun2_kwds): '''Apply a function component-wise to this and an other vector. @arg fun2: 2-Argument callable (C{any(scalar, scalar}). @arg other_x: An other vector factors (L{Vector3dBase}, L{Vector3Tuple}, L{Vector4Tuple}, L{Ecef9Tuple} cartesian) or X scale factor (C{scalar}). @arg y_z: Y and Z scale factors (C{scalar}, C{scalar}). @kwarg fun2_kwds: Optional keyword arguments for B{C{fun2}}. @return: New, applied vector (L{Vector3d}). @raise ValueError: Invalid B{C{other_x}} or B{C{y_z}}. ''' if not callable(fun2): raise _IsnotError(callable.__name__, fun2=fun2) if fun2_kwds: def _f2(a, b): return fun2(a, b, **fun2_kwds) else: _f2 = fun2 xyz = _other_xyz3(other_x, y_z) xyz = (_f2(a, b) for a, b in zip(self.xyz, xyz)) return self.classof(*xyz) def cross(self, other, raiser=None): # raiser=NN '''Compute the cross product of this and an other vector. @arg other: The other vector (L{Vector3d}). @kwarg raiser: Optional, L{CrossError} label if raised (C{str}). @return: Cross product (L{Vector3d}). @raise CrossError: Zero or near-zero cross product and both B{C{raiser}} and L{pygeodesy.crosserrors} set. @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) x = self.y * other.z - self.z * other.y y = self.z * other.x - self.x * other.z z = self.x * other.y - self.y * other.x if raiser and self.crosserrors and max(map1(abs, x, y, z)) < EPS: t = _coincident_ if self.isequalTo(other) else _colinear_ r = getattr(other, '_fromll', None) or other raise CrossError(raiser, r, txt=t) return self.classof(x, y, z) @property_doc_('''raise or ignore L{CrossError} exceptions (C{bool}).''') def crosserrors(self): '''Get L{CrossError} exceptions (C{bool}). ''' return self._crosserrors @crosserrors.setter # PYCHOK setter! def crosserrors(self, raiser): '''Raise L{CrossError} exceptions (C{bool}). ''' self._crosserrors = bool(raiser) 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}}. ''' f = Scalar(factor=factor) try: return self.times(_1_0 / f) except (ValueError, ZeroDivisionError) as x: raise VectorError(factor=factor, txt=str(x)) def dot(self, other): '''Compute the dot (scalar) product of this and an other vector. @arg other: The other vector (L{Vector3d}). @return: Dot product (C{float}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' if other is self: d = self.length2 else: self.others(other) d = fdot(self.xyz, *other.xyz) return d @deprecated_method def equals(self, other, units=False): # PYCHOK no cover '''DEPRECATED, use method C{isequalTo}. ''' return self.isequalTo(other, units=units) @Property_RO def euclid(self): '''Approximate the length (norm, magnitude) of this vector (C{Float}). @see: Properties C{length} and C{length2} and function L{pygeodesy.euclid_}. ''' return Float(euclid=euclid_(self.x, self.y, self.z)) def equirectangular(self, other): '''Approximate the different between this and an other vector. @arg other: Vector to subtract (C{Vector3dBase}). @return: The lenght I{squared} of the difference (C{Float}). @raise TypeError: Incompatible B{C{other}} C{type}. @see: Property C{length2}. ''' d = self.minus(other) return Float(equirectangular=hypot2_(d.x, d.y, d.z)) def intermediateTo(self, other, fraction, **unused): # height=None, wrap=False '''Locate the vector at a given fraction between (or along) this and an other vector. @arg other: The other vector (L{Vector3d}). @arg fraction: Fraction between both vectors (C{scalar}, 0.0 for this and 1.0 for the other vector). @return: Intermediate vector (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' f = Scalar(fraction=fraction) if isnear0(f): r = self elif isnear1(f): r = self.others(other) else: d = self.others(other).minus(self) r = self.plus(d.times(f)) return r def isconjugateTo(self, other, minum=1, eps=EPS): '''Determine whether this and an other vector are conjugates. @arg other: The other vector (L{Vector3d}, C{Vector3Tuple} or C{Vector4Tuple}). @kwarg minum: Minimal number of conjugates (C{int}, 0..3). @kwarg eps: Tolerance for equality and conjugation (C{scalar}), same units as C{x}, C{y}, and C{z}. @return: C{True} if C{x}, C{y} and C{z} of this match the other vector's or at least C{B{minum}} have opposite signs. @raise TypeError: Incompatible B{C{other}} C{type}. @see: Method C{isequalTo}. ''' self.others(other) n = 0 for a, b in zip(self.xyz, other.xyz): if abs(a + b) < eps and (a * b) < 0: n += 1 # conjugate elif abs(a - b) > eps: return False # unequal return bool(n >= minum) def isequalTo(self, other, units=False, eps=EPS): '''Check if this and an other vector are equal or equivalent. @arg other: The other vector (L{Vector3d}). @kwarg units: Optionally, compare the normalized, unit version of both vectors. @kwarg eps: Tolerance for equality (C{scalar}), same units as C{x}, C{y}, and C{z}. @return: C{True} if vectors are identical, C{False} otherwise. @raise TypeError: Incompatible B{C{other}} C{type}. @see: Method C{isconjugateTo}. ''' if units: self.others(other) d = self.unit().minus(other.unit()) else: d = self.minus(other) return max(map(abs, d.xyz)) < eps @Property_RO def length(self): # __dict__ value overwritten by Property_RO C{_united} '''Get the length (norm, magnitude) of this vector (C{Float}). @see: Properties L{length2} and L{euclid}. ''' return Float(length=hypot_(self.x, self.y, self.z)) @Property_RO def length2(self): # __dict__ value overwritten by Property_RO C{_united} '''Get the length I{squared} of this vector (C{Float}). @see: Property L{length} and method C{equirectangular}. ''' return Float(length2=hypot2_(self.x, self.y, self.z)) def minus(self, other): '''Subtract an other vector from this vector. @arg other: The other vector (L{Vector3d}). @return: New vector difference (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.classof(self.x - other.x, self.y - other.y, self.z - other.z) def negate(self): '''Return this vector in opposite direction. @return: New, opposite vector (L{Vector3d}). ''' return self.classof(-self.x, -self.y, -self.z) __neg__ = negate # PYCHOK no cover @Property_RO def _N_vector(self): '''(INTERNAL) Get the (C{nvectorBase._N_vector_}) ''' return _MODS.nvectorBase._N_vector_(*self.xyz, name=self.name) def others(self, *other, **name_other_up): '''Refined class comparison. @arg other: The other vector (L{Vector3d}). @kwarg name_other_up: Overriding C{name=other} and C{up=1} keyword arguments. @return: The B{C{other}} if compatible. @raise TypeError: Incompatible B{C{other}} C{type}. ''' other, name, up = _xother3(self, other, **name_other_up) if not isinstance(other, Vector3dBase): _NamedBase.others(self, other, name=name, up=up + 1) return other def plus(self, other): '''Add this vector and an other vector. @arg other: The other vector (L{Vector3d}). @return: Vectorial sum (L{Vector3d}). @raise TypeError: Incompatible B{C{other}} C{type}. ''' self.others(other) return self.classof(self.x + other.x, self.y + other.y, self.z + other.z) sum = plus # alternate name def rotate(self, axis, theta): '''Rotate this vector around an axis by a specified angle. See U{Rotation matrix from axis and angle <https://WikiPedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle>} and U{Quaternion-derived rotation matrix <https://WikiPedia.org/wiki/Quaternions_and_spatial_rotation#Quaternion-derived_rotation_matrix>}. @arg axis: The axis being rotated around (L{Vector3d}). @arg theta: The angle of rotation (C{radians}). @return: New, rotated vector (L{Vector3d}). @JSname: I{rotateAround}. ''' p = self.unit().xyz # point being rotated r = self.others(axis=axis).unit() # axis being rotated around s, c = sincos2(theta) # rotation angle ax, ay, az = r.xyz # quaternion-derived rotation matrix bx, by, bz = r.times(_1_0 - c).xyz sx, sy, sz = r.times(s).xyz return self.classof(fdot(p, ax * bx + c, ax * by - sz, ax * bz + sy), fdot(p, ay * bx + sz, ay * by + c, ay * bz - sx), fdot(p, az * bx - sy, az * by + sx, az * bz + c)) @deprecated_method def rotateAround(self, axis, theta): # PYCHOK no cover '''DEPRECATED, use method C{rotate}.''' return self.rotate(axis, theta) 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}}. ''' s = Scalar(factor=factor) return self.classof(self.x * s, self.y * s, self.z * s) def times_(self, other_x, *y_z): '''Multiply this vector's components by separate scalars. @arg other_x: An other vector factors (L{Vector3dBase}, L{Vector3Tuple}, L{Vector4Tuple}, L{Ecef9Tuple} cartesian) or X scale factor (C{scalar}). @arg y_z: Y and Z scale factors (C{scalar}, C{scalar}), ignored if B{C{other_x}} is not C{scalar}. @return: New, scaled vector (L{Vector3d}). @raise ValueError: Invalid B{C{other_x}} or B{C{y_z}}. ''' x, y, z = _other_xyz3(other_x, y_z) return self.classof(self.x * x, self.y * y, self.z * z) @deprecated_method def to2ab(self): # PYCHOK no cover '''DEPRECATED, use property C{Nvector.philam}. @return: A L{PhiLam2Tuple}C{(phi, lam)}. ''' return n_xyz2philam(self.x, self.y, self.z) @deprecated_method def to2ll(self): # PYCHOK no cover '''DEPRECATED, use property C{Nvector.latlon}. @return: A L{LatLon2Tuple}C{(lat, lon)}. ''' return n_xyz2latlon(self.x, self.y, self.z) @deprecated_method def to3xyz(self): # PYCHOK no cover '''DEPRECATED, use property L{xyz}. ''' return self.xyz def toStr(self, prec=5, fmt=Fmt.PAREN, sep=_COMMASPACE_): # PYCHOK expected '''Return a string representation of this vector. @kwarg prec: Optional number of decimal places (C{int}). @kwarg fmt: Optional, enclosing format to use (C{str}). @kwarg sep: Optional separator between components (C{str}). @return: Vector as "(x, y, z)" (C{str}). ''' t = sep.join(strs(self.xyz, prec=prec)) return (fmt % (t,)) if fmt else t def unit(self, ll=None): '''Normalize this vector to unit length. @kwarg ll: Optional, original location (C{LatLon}). @return: Normalized vector (L{Vector3d}). ''' u = self._united if ll: u._fromll = ll return u @Property_RO def _united(self): # __dict__ value overwritten below '''(INTERNAL) Get normalized vector (L{Vector3d}). ''' n = self.length if n > EPS0 and abs(n - _1_0) > EPS0: u = self._xnamed(self.dividedBy(n)) u._overwrite(length=_1_0, length2=_1_0, _united=u) else: u = self.copy() u._overwrite(_united=u) if self._fromll: u._fromll = self._fromll return u @Property def x(self): '''Get the X component (C{float}). ''' return self._x @x.setter # PYCHOK setter! def x(self, x): '''Set the X component, if different (C{float}). ''' x = Float(x=x) if self.x != x: self._update(True) self._x = x @Property def xyz(self): '''Get the X, Y and Z components (L{Vector3Tuple}C{(x, y, z)}). ''' return Vector3Tuple(self.x, self.y, self.z, name=self.name) @xyz.setter # PYCHOK setter! def xyz(self, xyz): '''Set the X, Y and Z components, if different (L{Vector3dBase}, L{Vector3Tuple} or L{Vector4Tuple}). ''' _xinstanceof(Vector3dBase, Vector3Tuple, Vector4Tuple, xyz=xyz) t3 = xyz.x, xyz.y, xyz.z if (self.x, self.y, self.z) != t3: self._update(True) self.x, self.y, self.z = t3 @Property_RO def x2y2z2(self): '''Get the X, Y and Z components I{squared} (C{Vector3Tuple}C{(x2, y2, z2)}). ''' return Vector3Tuple(self.x**2, self.y**2, self.z**2, name=self.name) @Property def y(self): '''Get the Y component (C{float}). ''' return self._y @y.setter # PYCHOK setter! def y(self, y): '''Set the Y component, if different (C{float}). ''' y = Float(y=y) if self.y != y: self._update(True) self._y = y @Property def z(self): '''Get the Z component (C{float}). ''' return self._z @z.setter # PYCHOK setter! def z(self, z): '''Set the Z component, if different (C{float}). ''' z = Float(z=z) if self.z != z: self._update(True) self._z = z def _other_xyz3(other_x, y_z): '''(INTERNAL) Helper. ''' try: if y_z: y, z = y_z x = Scalar(x=other_x) else: x, y, z = other_x.x, other_x.y, other_x.z except (AttributeError, TypeError, ValueError) as x: raise _InvalidError(other_x=other_x, y_z=y_z, txt=str(x)) return x, y, z # **) MIT License # # Copyright (C) 2016-2022 -- 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.