cattools_lmodel(1) --- Imcat Users Guide --- section: cattools_lmodel --- last changed: Thu Jul 10 HST
cattools_lmodel - cattools_lmodel tools sectionDESCRIPTION
This section contains some tools for fitting data to models which are superposition of mode functions:
a(x) = sum_m a_m f_m(x) where x is some position vector (of arbitrary length), and a is a tensor of arbitrary rank. Possible examples are polynomials, fourier modes, Zernike polynomials etc.. These 'lmodels' are output as lc-format catalogues with the following required header items: string model_type e.g. polynomial, zernike string aname name of dependent variable string xname name of independent variable int xdim length of independent variable and the following optional header items int nmodes double *xorigin and for polynomial models int lmin int lmax and for Zernike models int nmin int nmax and for Fourier models int kmin int kmax double lbox Supported models are model_type = polynomial The mode functions are labelled by a set of indices p[] with same length as x[], the functions are f_p = x0^p0 x1^p1 .... = product x_i^p_i and the order l = sum p_i lies in the inclusive interval lmin-lmax. An alternative parameterisation of the indices is in terms of the order array l[i] = l - sum_i=0^i-1 p[i], in terms of which the p-indices are p[i] = l[i] - l[i+1]. model_type = zernike The Zernike polynomial mode functions are only defined in two dimensions and are given by the functions U_n^m as defined in eq 10 of sec 9.2.1 of Born and Wolf. model_type = fourier The modes are indexed by the vector k[] (which has the same length as x[]) and the auxilliary index i, and the modes are f_k^j(x) where f_k^0(x) = cos(2 pi k.x / L) and f_k^1(x) = sin(2 pi k.x / L) Only one half of k-space needs to be occupied. The standard set of modes are defined to be those for which the first non-zero component of k[] is non-negative. Additionally, the mode k=0, i=1 is not used. COMMANDS
difflmodel - differentiate linear mode superposition model
fitlmodel - fit for linear superposition of mode function
generatelmodel - generate lmodel for catalog of points
generatelmodelimage - generate realisation of a lmodel as a FITS imageAUTHOR
Nick Kaiser -- kaiser@hawaii.edu