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- Committer: Package Import Robot
- Author(s): Sébastien Villemot, Sébastien Villemot, Thomas Weber
- Date: 2013-11-06 14:44:29 UTC
- mfrom: (1.1.3)
- Revision ID: package-import@ubuntu.com-20131106144429-1286885ymo2ldcp4
Tags: 2.0.3-1
[ Sébastien Villemot ]
* Imported Upstream version 2.0.3
* debian/copyright: reflect upstream changes.
* Bump Standards-Version to 3.9.5, no changes needed.
[ Thomas Weber ]
* debian/control: Use canonical URLs in Vcs-* fields
* Imported Upstream version 2.0.3
* debian/copyright: reflect upstream changes.
* Bump Standards-Version to 3.9.5, no changes needed.
[ Thomas Weber ]
* debian/control: Use canonical URLs in Vcs-* fields
- files removed:
- doc/functions.texi
- files modified:
- DESCRIPTION
added
removed
doc/functions.texi
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@chapter Quaternions
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@section quaternion
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@findex quaternion
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@deftypefn {Function File} {@var{q} =} quaternion (@var{w})
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@deftypefnx {Function File} {@var{q} =} quaternion (@var{x}, @var{y}, @var{z})
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@deftypefnx {Function File} {@var{q} =} quaternion (@var{w}, @var{x}, @var{y}, @var{z})
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Constructor for quaternions - create or convert to quaternion.
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@example
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q = w + x*i + y*j + z*k
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@end example
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Arguments @var{w}, @var{x}, @var{y} and @var{z} can be scalars,
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matrices or n-dimensional arrays, but they must be real-valued
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and of equal size.
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If scalar part @var{w} or components @var{x}, @var{y} and @var{z}
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of the vector part are not specified, zero matrices of appropriate
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size are assumed.
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@strong{Example}
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@example
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@group
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octave:1> q = quaternion (2)
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q = 2 + 0i + 0j + 0k
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octave:2> q = quaternion (3, 4, 5)
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q = 0 + 3i + 4j + 5k
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octave:3> q = quaternion (2, 3, 4, 5)
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q = 2 + 3i + 4j + 5k
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@end group
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@end example
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@example
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@group
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octave:4> w = [2, 6, 10; 14, 18, 22];
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octave:5> x = [3, 7, 11; 15, 19, 23];
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octave:6> y = [4, 8, 12; 16, 20, 24];
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octave:7> z = [5, 9, 13; 17, 21, 25];
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octave:8> q = quaternion (w, x, y, z)
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q.w =
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2 6 10
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14 18 22
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q.x =
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3 7 11
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15 19 23
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q.y =
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4 8 12
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16 20 24
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q.z =
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5 9 13
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17 21 25
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octave:9>
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@end group
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@end example
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@end deftypefn
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@section qi
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@findex qi
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@deftypefn {Function File} {} qi
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Create x-component of a quaternion's vector part.
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@example
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q = w + x*qi + y*qj + z*qk
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@end example
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@strong{Example}
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@example
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@group
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octave:1> q1 = quaternion (1, 2, 3, 4)
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q1 = 1 + 2i + 3j + 4k
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octave:2> q2 = 1 + 2*qi + 3*qj + 4*qk
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q2 = 1 + 2i + 3j + 4k
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octave:3>
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@end group
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@end example
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@end deftypefn
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@section qj
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@findex qj
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@deftypefn {Function File} {} qj
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Create y-component of a quaternion's vector part.
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@example
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q = w + x*qi + y*qj + z*qk
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@end example
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@strong{Example}
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@example
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@group
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octave:1> q1 = quaternion (1, 2, 3, 4)
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q1 = 1 + 2i + 3j + 4k
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octave:2> q2 = 1 + 2*qi + 3*qj + 4*qk
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q2 = 1 + 2i + 3j + 4k
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octave:3>
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@end group
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@end example
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@end deftypefn
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@section qk
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@findex qk
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@deftypefn {Function File} {} qk
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Create z-component of a quaternion's vector part.
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@example
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q = w + x*qi + y*qj + z*qk
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@end example
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@strong{Example}
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@example
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@group
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octave:1> q1 = quaternion (1, 2, 3, 4)
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q1 = 1 + 2i + 3j + 4k
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octave:2> q2 = 1 + 2*qi + 3*qj + 4*qk
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q2 = 1 + 2i + 3j + 4k
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octave:3>
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@end group
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@end example
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@end deftypefn
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@section q2rot
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@findex q2rot
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@deftypefn {Function File} {[@var{axis}, @var{angle}] =} q2rot (@var{q})
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Extract vector/angle form of a unit quaternion @var{q}.
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@strong{Inputs}
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@table @var
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@item q
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Unit quaternion describing the rotation.
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@end table
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@strong{Outputs}
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@table @var
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@item axis
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Eigenaxis as a 3-d unit vector @code{[x, y, z]}.
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@item angle
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Rotation angle in radians. The positive direction is
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determined by the right-hand rule applied to @var{axis}.
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@end table
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@strong{Example}
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@example
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@group
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octave:1> axis = [0, 0, 1]
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axis =
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0 0 1
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octave:2> angle = pi/4
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angle = 0.78540
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octave:3> q = rot2q (axis, angle)
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q = 0.9239 + 0i + 0j + 0.3827k
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octave:4> [vv, th] = q2rot (q)
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vv =
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0 0 1
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th = 0.78540
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octave:5> theta = th*180/pi
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theta = 45.000
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octave:6>
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@end group
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@end example
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@end deftypefn
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@section rot2q
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@findex rot2q
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@deftypefn {Function File} {@var{q} =} rot2q (@var{axis}, @var{angle})
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Create unit quaternion @var{q} which describes a rotation of
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@var{angle} radians about the vector @var{axis}. This function uses
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the active convention where the vector @var{axis} is rotated by @var{angle}
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radians. If the coordinate frame should be rotated by @var{angle}
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radians, also called the passive convention, this is equivalent
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to rotating the @var{axis} by @var{-angle} radians.
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@strong{Inputs}
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@table @var
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@item axis
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Vector @code{[x, y, z]} describing the axis of rotation.
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@item angle
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Rotation angle in radians. The positive direction is
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determined by the right-hand rule applied to @var{axis}.
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@end table
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@strong{Outputs}
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@table @var
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@item q
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Unit quaternion describing the rotation.
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@end table
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@strong{Example}
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@example
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@group
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octave:1> axis = [0, 0, 1];
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octave:2> angle = pi/4;
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octave:3> q = rot2q (axis, angle)
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q = 0.9239 + 0i + 0j + 0.3827k
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octave:4> v = quaternion (1, 1, 0)
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v = 0 + 1i + 1j + 0k
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octave:5> vr = q * v * conj (q)
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vr = 0 + 0i + 1.414j + 0k
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octave:6>
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@end group
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@end example
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@end deftypefn
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@chapter Quaternion Methods
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@section @@quaternion/abs
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@findex abs
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@deftypefn {Function File} {@var{qabs} =} abs (@var{q})
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Modulus of a quaternion.
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@example
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q = w + x*i + y*j + z*k
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abs (q) = sqrt (w.^2 + x.^2 + y.^2 + z.^2)
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@end example
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@end deftypefn
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@section @@quaternion/blkdiag
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@findex blkdiag
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@deftypefn {Function File} {@var{q} =} blkdiag (@var{q1}, @var{q2}, @dots{})
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Block-diagonal concatenation of quaternions.
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@end deftypefn
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@section @@quaternion/cat
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@findex cat
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@deftypefn {Function File} {@var{q} =} cat (@var{dim}, @var{q1}, @var{q2}, @dots{})
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Concatenation of quaternions along dimension @var{dim}.
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@end deftypefn
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@section @@quaternion/columns
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@findex columns
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@deftypefn {Function File} {@var{nc} =} columns (@var{q})
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Return number of columns @var{nc} of quaternion array @var{q}.
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@end deftypefn
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@section @@quaternion/conj
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@findex conj
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@deftypefn {Function File} {@var{q} =} conj (@var{q})
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Return conjugate of a quaternion.
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@example
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q = w + x*i + y*j + z*k
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conj (q) = w - x*i - y*j - z*k
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@end example
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@end deftypefn
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@section @@quaternion/diag
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@findex diag
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@deftypefn {Function File} {@var{q} =} diag (@var{v})
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@deftypefnx {Function File} {@var{q} =} diag (@var{v}, @var{k})
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Return a diagonal quaternion matrix with quaternion vector V on diagonal K.
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The second argument is optional. If it is positive,
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the vector is placed on the K-th super-diagonal.
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If it is negative, it is placed on the -K-th sub-diagonal.
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The default value of K is 0, and the vector is placed
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on the main diagonal.
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Given a matrix argument, instead of a vector, @command{diag}
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extracts the @var{K}-th diagonal of the matrix.
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@end deftypefn
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@section @@quaternion/diff
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@findex diff
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@deftypefn {Function File} {@var{qdot} =} diff (@var{q}, @var{omega})
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Derivative of a quaternion.
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Let Q be a quaternion to transform a vector from a fixed frame to
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a rotating frame. If the rotating frame is rotating about the
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[x, y, z] axes at angular rates [wx, wy, wz], then the derivative
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of Q is given by
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@example
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Q' = diff(Q, omega)
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@end example
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If the passive convention is used (rotate the frame, not the vector),
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then
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@example
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Q' = diff(Q,-omega)
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@end example
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@end deftypefn
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@section @@quaternion/exp
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@findex exp
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@deftypefn {Function File} {@var{qexp} =} exp (@var{q})
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Exponential of a quaternion.
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@end deftypefn
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@section @@quaternion/inv
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@findex inv
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@deftypefn {Function File} {@var{qinv} =} inv (@var{q})
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Return inverse of a quaternion.
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@end deftypefn
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@section @@quaternion/ispure
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@findex ispure
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@deftypefn {Function File} {@var{flg} =} ispure (@var{q})
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Return 1 if scalar part of quaternion is zero, otherwise return 0
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@end deftypefn
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@section @@quaternion/log
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@findex log
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@deftypefn {Function File} {@var{qlog} =} log (@var{q})
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Logarithmus naturalis of a quaternion.
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@end deftypefn
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@section @@quaternion/norm
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@findex norm
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@deftypefn {Function File} {@var{n} =} norm (@var{q})
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Norm of a quaternion.
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@end deftypefn
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@section @@quaternion/rows
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@findex rows
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@deftypefn {Function File} {@var{nr} =} rows (@var{q})
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Return number of rows @var{nr} of quaternion array @var{q}.
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@end deftypefn
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@section @@quaternion/size
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@findex size
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@deftypefn {Function File} {@var{nvec} =} size (@var{q})
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@deftypefnx {Function File} {@var{n} =} size (@var{q}, @var{dim})
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@deftypefnx {Function File} {[@var{nx}, @var{ny}, @dots{}] =} size (@var{q})
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Return size of quaternion arrays.
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@strong{Inputs}
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@table @var
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@item q
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Quaternion object.
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@item dim
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If given a second argument, @command{size} will return the size of the
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corresponding dimension.
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@end table
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@strong{Outputs}
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@table @var
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@item nvec
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Row vector. The first element is the number of rows and the second
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element the number of columns. If @var{q} is an n-dimensional array
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of quaternions, the n-th element of @var{nvec} corresponds to the
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size of the n-th dimension of @var{q}.
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@item n
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Scalar value. The size of the dimension @var{dim}.
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@item nx
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Number of rows.
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@item ny
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Number of columns.
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@item @dots{}
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Sizes of the 3rd to n-th dimensions.
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@end table
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@end deftypefn
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@section @@quaternion/size_equal
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@findex size_equal
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@deftypefn {Function File} {@var{bool} =} size_equal (@var{a}, @var{b}, @dots{})
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Return true if quaternions (and matrices) @var{a}, @var{b}, @dots{}
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are of equal size and false otherwise.
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@end deftypefn
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@section @@quaternion/unit
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@findex unit
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@deftypefn {Function File} {@var{qn} =} unit (@var{q})
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Normalize quaternion to length 1 (unit quaternion).
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@example
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q = w + x*i + y*j + z*k
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unit (q) = q ./ sqrt (w.^2 + x.^2 + y.^2 + z.^2)
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@end example
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@end deftypefn
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@chapter Overloaded Quaternion Operators
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@section @@quaternion/ctranspose
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@findex ctranspose
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Conjugate transpose of a quaternion. Used by Octave for "q'".
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@section @@quaternion/eq
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@findex eq
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Equal to operator for two quaternions. Used by Octave for "q1 == q2".
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@section @@quaternion/horzcat
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@findex horzcat
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Horizontal concatenation of quaternions. Used by Octave for "[q1, q2]".
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@section @@quaternion/ldivide
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@findex ldivide
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Element-wise left division for quaternions. Used by Octave for "q1 .\ q2".
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@section @@quaternion/minus
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@findex minus
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Subtraction of two quaternions. Used by Octave for "q1 - q2".
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@section @@quaternion/mldivide
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@findex mldivide
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Matrix left division for quaternions. Used by Octave for "q1 \ q2".
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@section @@quaternion/mpower
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@findex mpower
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Matrix power operator of quaternions. Used by Octave for "q^x".
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@section @@quaternion/mrdivide
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@findex mrdivide
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Matrix right division for quaternions. Used by Octave for "q1 / q2".
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@section @@quaternion/mtimes
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@findex mtimes
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Matrix multiplication of two quaternions. Used by Octave for "q1 * q2".
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@section @@quaternion/plus
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@findex plus
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Addition of two quaternions. Used by Octave for "q1 + q2".
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@section @@quaternion/power
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@findex power
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Power operator of quaternions. Used by Octave for "q.^x".
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Exponent x can be scalar or of appropriate size.
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@section @@quaternion/rdivide
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@findex rdivide
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Element-wise right division for quaternions. Used by Octave for "q1 ./ q2".
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@section @@quaternion/subsasgn
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@findex subsasgn
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Subscripted assignment for quaternions.
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Used by Octave for "q.key = value".
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@section @@quaternion/subsref
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@findex subsref
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Subscripted reference for quaternions. Used by Octave for "q.w".
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@section @@quaternion/times
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@findex times
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Element-wise multiplication of two quaternions. Used by Octave for "q1 .* q2".
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@section @@quaternion/transpose
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@findex transpose
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Transpose of a quaternion. Used by Octave for "q.'".
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@section @@quaternion/uminus
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@findex uminus
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Unary minus of a quaternion. Used by Octave for "-q".
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@section @@quaternion/uplus
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@findex uplus
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Unary plus of a quaternion. Used by Octave for "+q".
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@section @@quaternion/vertcat
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@findex vertcat
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Vertical concatenation of quaternions. Used by Octave for "[q1; q2]".
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