Quaternion Functions — Categorized List

Some functions are overloaded for octonions. This is not shown below, but should be noted in the documentation pages themselves. Functions specific to octonions are listed below under the appropriate headings.

Constructor and components

octonion constructor
quaternion constructor
scalar component
vector component
x/y/z components
part access components by index

Display of quaternion values

char
disp
display
displayall
show

Quaternion constants and matrices

octonion operators i, j, k, etc
quaternion operators i, j and k
quaternion identity matrix
quaternion matrix of ones
matrix of zero quaternions
matrix of zero vectors
matrix of zero octonions
matrix of zero pure octonions

Basic quaternion operations

abs absolute value or modulus
conj quaternion conjugate
cross cross or vector product
normo norm or semi-norm of an octonion
normq norm or semi-norm of a quaternion
scalar_product scalar product
sign
unit
vector_product cross or vector product

Arithmetic and logical operations

eq
ldivide
minus
mrdivide
mtimes
ne
plus
power
rdivide
times
uminus
uplus

Trigonometric, hyperbolic, exp/log/sqrt functions

acos
acosh
asin
asinh
atan
atanh
cos
cosh
sin
sinh
tan
tanh

exp
log
sqrt

Polar forms

angle
axis
cdpolar - Cayley-Dickson polar form

Basic matrix operations

bsxfun
arrayfun
cat
horzcat
vertcat

blkdiag
diag
tril
triu

ctranspose conjugate transpose
end
length
ndims
norm
numel
orthogonal
size
subsasgn
subsindex
subsref
transpose

ipermute
permute

repmat
reshape
squeeze

cumprod
cumsum
diff
mean
prod
sum

Matrix operations and decompositions

adjoint
unadjoint

det
eig
expm
funm
inv
linv Octonion left inverse operator
logm
lu
mpower
qr
rinv Octonion right inverse operator
sqrtm
svd
svdj

Random matrices

randf
rando
randq
randv
randvo
randvmf

Cayley-Dickson form

cd - Cayley-Dickson decomposition
dc - Cayley-Dickson recomposition

Conversions

cast
convert
change_basis

Rounding

ceil
fix
floor
round

Complexified quaternion or biquaternion operations

complex construct complexified quaternion
imag imaginary part
real real part
conj quaternion or complex conjugate

Tests of properties

isempty
isfinite
ishermitian
isinf
isnan
ispure
isreal
isunitary

Convolutions

conv
conv2

Discrete and fast Fourier transforms

qdft
qdft2
qfft
qfft2
fft
fft2
fftshift
ifft
ifft2
ifftshift
iqdft
iqdft2
iqfft
iqfft2

Input/output

read matrix
write matrix
image display quaternion array as image
imreadq image read
imwrite image write
fprintf

Plots

scatter3 3D scatter plot
scatter4 3D scatter plot

Other functions

associator Associator
commutator Commutator
frenet Frenet-Serret frames
slerp Spherical linear interpolation

Internal

qtfm_root Display root directory of QTFM installation
qtfm_test Run QTFM test code

© 2008-2013 Stephen J. Sangwine and Nicolas Le Bihan.

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