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 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 ``` ``````/* Evaluates all fully normalized circular harmonics at the angles phi up to the order nmax. using the recurrence for the Chebyshev polynomials of the first and second kind T has the dimensions length(phi) x 2nmax+1 Implementation by Franz Zotter, Institute of Electronic Music and Acoustics (IEM), University of Music and Dramatic Arts (KUG), Graz, Austria http://iem.at/Members/zotter, 2008. This code is published under the Gnu General Public License, see "LICENSE.txt" */ #include "mtx_spherical_harmonics/chebyshev12.h" Cheby12WorkSpace *chebyshev12_alloc(const size_t nmax, const size_t l) { Cheby12WorkSpace *wc; // memory allocation if ((wc=(Cheby12WorkSpace*)calloc(1,sizeof(Cheby12WorkSpace)))!=0) { wc->l=l; wc->nmax=nmax; if ((wc->t=(double*)calloc(l*(2*nmax+1),sizeof(double)))==0) { free(wc); return 0; } return wc; } return 0; } void chebyshev12_free(Cheby12WorkSpace *wc) { if (wc!=0) { free(wc->t); free(wc); } } void chebyshev12(double *phi, Cheby12WorkSpace *wc) { int l,l0,n; const int incr=2*wc->nmax+1; double *cosphi; double *sinphi; const double oneoversqrt2pi=1.0/sqrt(2.0*M_PI); const double oneoversqrtpi=1.0/sqrt(M_PI); // memory allocation if ((wc!=0)&&(phi!=0)) { if ((cosphi=(double*)calloc(wc->l,sizeof(double)))==0) { return; } if ((sinphi=(double*)calloc(wc->l,sizeof(double)))==0) { free(cosphi); return; } // constants and initialization for (l=0, l0=wc->nmax; ll; l++, l0+=incr) { cosphi[l]=cos(phi[l]); sinphi[l]=sin(phi[l]); // initial value T_0=1 wc->t[l0]=oneoversqrt2pi; wc->t[l0+1]=cosphi[l]*oneoversqrtpi; wc->t[l0-1]=sinphi[l]*oneoversqrtpi; } // recurrence for n>1 for (n=2; n<=wc->nmax; n++) { for (l=0, l0=wc->nmax; ll; l++, l0+=incr) { wc->t[l0+n]=cosphi[l]* wc->t[l0+n-1] - sinphi[l]* wc->t[l0-n+1]; wc->t[l0-n]=sinphi[l]* wc->t[l0+n-1] + cosphi[l]* wc->t[l0-n+1]; } } free(cosphi); free(sinphi); } } ``````