#N canvas 61 39 921 503 10;
#X text 516 377 Franz Zotter \, 2009;
#X text 129 226 for -n<=m<=n:;
#X text 620 241 for m>=0;
#X text 619 257 for m< 0;
#X text 288 118 [mtx_circular_harmonics] requires a numerical creation
argument <nmax> specifyiing the maximum order 0<=n<=nmax.;
#X text 74 54 [mtx_circular_harmonics] circular harmonics evaluated
at a set of points given in phi coordinates.;
#X text 284 160 for an L points 2xL input matrix \, [mtx_spherical_harmonics]
evaluates the (2*nmax+2) circular harmonics at L points and delivers
an Lx(2*nmax+2) output matrix.;
#X text 167 242 PHI_m(phi) = sqrt((2-delta_m) / (2*pi)) * cos(m*phi)
;
#X text 167 258 PHI_m(phi) = 1/sqrt(pi) * sin(m*phi);
#X text 126 291 The order of the harmonics in the output columns is
specified by the linear index k=nmax+m+1.;
#X text 125 328 [mtx_circular_harmonics] uses fully normalized PHI_m.
;
#N canvas 0 0 450 300 (subpatch) 0;
#X array circularharmonic1 100 float 1;
#A 0 0 0.106888 0.209904 0.305318 0.389673 0.459913 0.513495 0.548478
0.563594 0.558297 0.532777 0.48796 0.425469 0.347567 0.257076 0.157273
0.0517736 -0.055601 -0.160962 -0.260492 -0.350588 -0.427984 -0.489879
-0.53403 -0.558838 -0.563404 -0.547564 -0.51189 -0.457675 -0.386883
-0.302078 -0.206331 -0.10311 0.003845 0.110661 0.213468 0.308544 0.392444
0.462129 0.515076 0.549366 0.563758 0.55773 0.5315 0.486019 0.422934
0.34453 0.253647 0.153577 0.0479438 -0.059426 -0.164643 -0.263897 -0.353592
-0.43048 -0.491775 -0.535258 -0.559353 -0.563189 -0.546625 -0.510261
-0.455416 -0.384076 -0.298823 -0.202747 -0.0993281 0.00768981 0.114428
0.217022 0.311755 0.395197 0.464324 0.516633 0.550229 0.563895 0.557136
0.530198 0.484055 0.42038 0.341478 0.250207 0.149874 0.044112 -0.0632482
-0.168317 -0.267289 -0.35658 -0.432955 -0.493648 -0.536461 -0.559843
-0.562947 -0.54566 -0.508609 -0.453136 -0.38125 -0.295555 -0.199155
-0.0955408 0.0115335;
#X coords 0 1 99 -1 200 50 1;
#X restore 720 14 graph;
#N canvas 0 0 450 300 (subpatch) 0;
#X array circularharmonic2 100 float 1;
#A 0 0 0.0714992 0.141845 0.209904 0.274579 0.334825 0.389673 0.438236
0.479734 0.513495 0.538976 0.555766 0.563594 0.562334 0.552006 0.532777
0.504957 0.468995 0.425469 0.375083 0.318648 0.257076 0.191358 0.122554
0.0517737 -0.0198414 -0.0911363 -0.160962 -0.228192 -0.291742 -0.350588
-0.40378 -0.450461 -0.489879 -0.521397 -0.544508 -0.558838 -0.564157
-0.560378 -0.547564 -0.52592 -0.495795 -0.457675 -0.412175 -0.360029
-0.302078 -0.239255 -0.172574 -0.10311 -0.031984 0.0396582 0.110661
0.179879 0.246196 0.308544 0.365916 0.417388 0.462129 0.499418 0.528655
0.549366 0.561219 0.564022 0.55773 0.542444 0.518411 0.486019 0.44579
0.398372 0.344531 0.285133 0.221138 0.153577 0.0835392 0.0121547 -0.0594257
-0.130048 -0.198574 -0.263897 -0.324964 -0.380792 -0.43048 -0.473225
-0.50834 -0.535258 -0.553544 -0.562905 -0.563189 -0.554391 -0.536653
-0.510261 -0.475642 -0.433353 -0.384075 -0.328605 -0.267836 -0.202748
-0.13439 -0.0638651 0.00768928;
#X coords 0 1 99 -1 200 50 1;
#X restore 718 80 graph;
#N canvas 0 0 450 300 (subpatch) 0;
#X array circularharmonic3 100 float 1;
#A 0 0 0.0358219 0.0714992 0.106888 0.141845 0.176231 0.209904 0.242731
0.274579 0.305318 0.334825 0.362981 0.389673 0.414791 0.438236 0.459913
0.479734 0.497618 0.513495 0.527299 0.538976 0.548478 0.555766 0.560812
0.563594 0.564102 0.562334 0.558297 0.552006 0.543489 0.532777 0.519916
0.504957 0.48796 0.468995 0.448136 0.425469 0.401085 0.375083 0.347567
0.318648 0.288444 0.257076 0.22467 0.191358 0.157273 0.122554 0.0873399
0.0517737 0.0159984 -0.0198414 -0.055601 -0.0911363 -0.126304 -0.160962
-0.19497 -0.228192 -0.260492 -0.291742 -0.321814 -0.350588 -0.377946
-0.40378 -0.427984 -0.450461 -0.471121 -0.489879 -0.50666 -0.521397
-0.53403 -0.544508 -0.552788 -0.558838 -0.562633 -0.564157 -0.563404
-0.560378 -0.555091 -0.547564 -0.537827 -0.52592 -0.51189 -0.495795
-0.477699 -0.457675 -0.435805 -0.412175 -0.386883 -0.360029 -0.331723
-0.302078 -0.271213 -0.239255 -0.206331 -0.172574 -0.138121 -0.10311
-0.0676836 -0.031984 0.00384473 ;
#X coords 0 1 99 -1 200 50 1;
#X restore 719 146 graph;
#N canvas 0 0 450 300 (subpatch) 0;
#X array circularharmonic4 100 float 1;
#A 0 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942
0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942
0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942
0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942
0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942
0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942
0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942
0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942
0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942
0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942
0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942
0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942 0.398942
0.398942 0.398942 0.398942 0.398942 0.398942;
#X coords 0 1 99 -1 200 50 1;
#X restore 718 217 graph;
#N canvas 0 0 450 300 (subpatch) 0;
#X array circularharmonic5 100 float 1;
#A 0 0.56419 0.563051 0.559641 0.553972 0.546068 0.53596 0.523689 0.509305
0.492866 0.474437 0.454095 0.43192 0.408001 0.382437 0.355329 0.326787
0.296927 0.265868 0.233737 0.200662 0.166777 0.13222 0.097129 0.061646
0.0259142 -0.00992222 -0.0457185 -0.0813303 -0.116614 -0.151427 -0.185629
-0.219082 -0.251651 -0.283204 -0.313614 -0.342759 -0.370521 -0.396788
-0.421453 -0.444418 -0.465589 -0.484881 -0.502217 -0.517526 -0.530747
-0.541826 -0.550718 -0.557388 -0.561809 -0.563963 -0.563841 -0.561443
-0.55678 -0.54987 -0.540741 -0.52943 -0.515983 -0.500453 -0.482904
-0.463407 -0.442039 -0.418887 -0.394045 -0.367613 -0.339697 -0.310411
-0.279872 -0.248204 -0.215534 -0.181994 -0.14772 -0.112849 -0.0775239
-0.0418852 -0.00607772 0.0297543 0.0654664 0.100914 0.135955 0.170447
0.204251 0.237231 0.269253 0.300189 0.329914 0.358307 0.385255 0.410648
0.434383 0.456366 0.476507 0.494725 0.510947 0.525107 0.537148 0.547022
0.554687 0.560115 0.563282 0.564176;
#X coords 0 1 99 -1 200 50 1;
#X restore 718 286 graph;
#X obj 75 109 loadbang;
#N canvas 624 434 600 460 send_to_tables 0;
#X obj 21 14 inlet;
#X obj 72 211 mtx;
#X obj 21 36 t a a;
#X obj 21 59 mtx_size;
#X obj 74 105 until;
#X obj 74 82 t f b;
#X msg 117 82 0;
#X obj 101 124 + 1;
#X obj 74 124 f;
#X obj 73 147 t f f;
#X obj 72 249 s;
#X msg 105 168 symbol circularharmonic\$1;
#X obj 72 230 list prepend 0;
#X msg 73 192 column \$1;
#X connect 0 0 2 0;
#X connect 1 0 12 0;
#X connect 2 0 3 0;
#X connect 2 1 1 1;
#X connect 3 1 5 0;
#X connect 4 0 8 0;
#X connect 5 0 4 0;
#X connect 5 1 6 0;
#X connect 6 0 8 1;
#X connect 7 0 8 1;
#X connect 7 0 9 0;
#X connect 8 0 7 0;
#X connect 9 0 13 0;
#X connect 9 1 11 0;
#X connect 11 0 10 1;
#X connect 12 0 10 0;
#X connect 13 0 1 0;
#X restore 75 179 pd send_to_tables;
#X obj 75 133 mtx_linspace 0 6.29 100;
#X obj 159 114 bng 15 250 50 0 empty empty empty 17 7 0 10 -262144
-1 -1;
#X obj 75 157 mtx_circular_harmonics 3;
#N canvas 0 0 450 300 (subpatch) 0;
#X array circularharmonic6 100 float 1;
#A 0 0.56419 0.559641 0.546068 0.523689 0.492866 0.454095 0.408001
0.355329 0.296927 0.233737 0.166777 0.097129 0.0259142 -0.0457185 -0.116614
-0.185629 -0.251651 -0.313614 -0.370521 -0.421453 -0.465589 -0.502217
-0.530747 -0.550718 -0.561809 -0.563841 -0.55678 -0.540741 -0.515983
-0.482904 -0.442039 -0.394045 -0.339697 -0.279872 -0.215534 -0.14772
-0.0775239 -0.00607772 0.0654664 0.135955 0.204251 0.269253 0.329914
0.385255 0.434383 0.476507 0.510947 0.537148 0.554687 0.563282 0.562794
0.553231 0.534746 0.507639 0.472346 0.429436 0.379601 0.323646 0.262471
0.197064 0.128479 0.0578227 -0.0137663 -0.0851333 -0.155127 -0.22262
-0.286523 -0.345805 -0.399512 -0.446776 -0.486836 -0.519045 -0.542885
-0.557971 -0.564059 -0.561051 -0.548997 -0.528089 -0.498667 -0.461203
-0.416302 -0.364688 -0.307193 -0.244745 -0.17835 -0.10908 -0.0380498
0.0335932 0.104695 0.174108 0.240714 0.303438 0.361269 0.413275 0.458616
0.496562 0.526501 0.54795 0.560563 0.564137;
#X coords 0 1 99 -1 200 50 1;
#X restore 718 356 graph;
#N canvas 0 0 450 300 (subpatch) 0;
#X array circularharmonic7 100 float 1;
#A 0 0.56419 0.553972 0.523689 0.474437 0.408001 0.326787 0.233737
0.13222 0.0259142 -0.0813303 -0.185629 -0.283204 -0.370521 -0.444418
-0.502217 -0.541826 -0.561809 -0.561443 -0.540741 -0.500453 -0.442039
-0.367613 -0.279872 -0.181994 -0.0775239 0.0297544 0.135955 0.237231
0.329914 0.410647 0.476507 0.525107 0.554687 0.564176 0.553231 0.522246
0.472346 0.405336 0.323645 0.230232 0.128479 0.0220729 -0.0851331 -0.189256
-0.286523 -0.373412 -0.446776 -0.503957 -0.542885 -0.562149 -0.561051
-0.539632 -0.498667 -0.439639 -0.364688 -0.276527 -0.17835 -0.0737135
0.0335929 0.139683 0.240714 0.333025 0.413275 0.478555 0.526501 0.555377
0.564137 0.552464 0.520779 0.470232 0.402653 0.320489 0.226717 0.124732
0.0182304 -0.0889317 -0.192873 -0.289828 -0.376285 -0.449113 -0.505674
-0.543919 -0.562462 -0.560633 -0.538497 -0.496857 -0.437219 -0.361746
-0.273169 -0.174699 -0.0698998 0.0374303 0.143405 0.244186 0.336121
0.415882 0.48058 0.527871 0.556041 0.564072;
#X coords 0 1 99 -1 200 50 1;
#X restore 716 422 graph;
#X connect 16 0 18 0;
#X connect 18 0 20 0;
#X connect 19 0 18 0;
#X connect 20 0 17 0;