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 constants 1, i, j, k, etc | quaternion constants 1, i, j and k | empty quaternion or octonion array | 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 | sylvester Solve Sylvester's equation | ||
Random matrices | randf | rando | randq | randv | randvo | randvmf |
Decompositions/factorizations | cd - Cayley-Dickson decomposition | dc - Cayley-Dickson recomposition | factorq - orthogonal factorization | ohd (orthogonal hyperplane decomposition) | opd (orthogonal plane decomposition) | |
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 | convw | convw2 | mustard convolution | |
Discrete and fast Fourier transforms | qdft | qdft2 | qfft | qfft2 | fft | fft2 |
fftflip | fftflip2 | 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 | plot3 3D line plot | quiver3 3D quiver plot | scatter3 3D scatter plot | scatter4 4D scatter plot projected into 2D | scatter4p3 4D scatter plots projected into 3D | |
Other functions | associator Associator | commutator Commutator | kleinfeld Kleinfeld product | frenet Frenet-Serret frames | slerp Spherical linear interpolation | spherical_mean Spherical (geodesic or intrinsic) mean |
Internal | qtfm_helpdb Build or update searchable help database | qtfm_helpup Update HTML help files from XML masters | qtfm_root Display root directory of QTFM installation | qtfm_test Run QTFM test code | qtfm_version Return the QTFM version number (and check for update) |