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jacobians_Rodrigues.m
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jacobians_Rodrigues.m
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% Steffen Urban email: [email protected]
% Copyright (C) 2016 Steffen Urban
%
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License along
% with this program; if not, write to the Free Software Foundation, Inc.,
% 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
% 28.06.2016 Steffen Urban
% file was created with the Matlab symbolic toolbox
% todo: jacobians would probably a lot easier if I'd use expmap and
% optimize near the identity...
% would need to change the update step from x+dx to exp(dx)*exp(x) or sth
function jacs = jacobians_Rodrigues(X1,Y1,Z1,r1,r2,r3,s1,s2,s3,t1,t2,t3,w1,w2,w3)
t5 = w1.^2;
t6 = w2.^2;
t7 = w3.^2;
t8 = t5+t6+t7;
t9 = sqrt(t8);
t10 = sin(t9);
t11 = 1.0./sqrt(t8);
t12 = cos(t9);
t13 = t12-1.0;
t14 = 1.0./t8;
t16 = t10.*t11.*w3;
t17 = t13.*t14.*w1.*w2;
t19 = t10.*t11.*w2;
t20 = t13.*t14.*w1.*w3;
t24 = t6+t7;
t27 = t16+t17;
t28 = Y1.*t27;
t29 = t19-t20;
t30 = Z1.*t29;
t31 = t13.*t14.*t24;
t32 = t31+1.0;
t33 = X1.*t32;
t15 = t1-t28+t30+t33;
t21 = t10.*t11.*w1;
t22 = t13.*t14.*w2.*w3;
t45 = t5+t7;
t53 = t16-t17;
t54 = X1.*t53;
t55 = t21+t22;
t56 = Z1.*t55;
t57 = t13.*t14.*t45;
t58 = t57+1.0;
t59 = Y1.*t58;
t18 = t2+t54-t56+t59;
t34 = t5+t6;
t38 = t19+t20;
t39 = X1.*t38;
t40 = t21-t22;
t41 = Y1.*t40;
t42 = t13.*t14.*t34;
t43 = t42+1.0;
t44 = Z1.*t43;
t23 = t3-t39+t41+t44;
t25 = 1.0./t8.^(3.0./2.0);
t26 = 1.0./t8.^2;
t35 = t12.*t14.*w1.*w2;
t36 = t5.*t10.*t25.*w3;
t37 = t5.*t13.*t26.*w3.*2.0;
t46 = t10.*t25.*w1.*w3;
t47 = t5.*t10.*t25.*w2;
t48 = t5.*t13.*t26.*w2.*2.0;
t49 = t10.*t11;
t50 = t5.*t12.*t14;
t51 = t13.*t26.*w1.*w2.*w3.*2.0;
t52 = t10.*t25.*w1.*w2.*w3;
t60 = t15.^2;
t61 = t18.^2;
t62 = t23.^2;
t63 = t60+t61+t62;
t64 = t5.*t10.*t25;
t65 = 1.0./sqrt(t63);
t66 = Y1.*r2.*t6;
t67 = Z1.*r3.*t7;
t68 = r1.*t1.*t5;
t69 = r1.*t1.*t6;
t70 = r1.*t1.*t7;
t71 = r2.*t2.*t5;
t72 = r2.*t2.*t6;
t73 = r2.*t2.*t7;
t74 = r3.*t3.*t5;
t75 = r3.*t3.*t6;
t76 = r3.*t3.*t7;
t77 = X1.*r1.*t5;
t78 = X1.*r2.*w1.*w2;
t79 = X1.*r3.*w1.*w3;
t80 = Y1.*r1.*w1.*w2;
t81 = Y1.*r3.*w2.*w3;
t82 = Z1.*r1.*w1.*w3;
t83 = Z1.*r2.*w2.*w3;
t84 = X1.*r1.*t6.*t12;
t85 = X1.*r1.*t7.*t12;
t86 = Y1.*r2.*t5.*t12;
t87 = Y1.*r2.*t7.*t12;
t88 = Z1.*r3.*t5.*t12;
t89 = Z1.*r3.*t6.*t12;
t90 = X1.*r2.*t9.*t10.*w3;
t91 = Y1.*r3.*t9.*t10.*w1;
t92 = Z1.*r1.*t9.*t10.*w2;
t102 = X1.*r3.*t9.*t10.*w2;
t103 = Y1.*r1.*t9.*t10.*w3;
t104 = Z1.*r2.*t9.*t10.*w1;
t105 = X1.*r2.*t12.*w1.*w2;
t106 = X1.*r3.*t12.*w1.*w3;
t107 = Y1.*r1.*t12.*w1.*w2;
t108 = Y1.*r3.*t12.*w2.*w3;
t109 = Z1.*r1.*t12.*w1.*w3;
t110 = Z1.*r2.*t12.*w2.*w3;
t93 = t66+t67+t68+t69+t70+t71+t72+t73+t74+t75+t76+t77+t78+t79+t80+t81+t82+...
t83+t84+t85+t86+t87+t88+t89+t90+t91+t92-t102-t103-t104-t105-t106-t107-t108-t109-t110;
t94 = t10.*t25.*w1.*w2;
t95 = t6.*t10.*t25.*w3;
t96 = t6.*t13.*t26.*w3.*2.0;
t97 = t12.*t14.*w2.*w3;
t98 = t6.*t10.*t25.*w1;
t99 = t6.*t13.*t26.*w1.*2.0;
t100 = t6.*t10.*t25;
t101 = 1.0./t63.^(3.0./2.0);
t111 = t6.*t12.*t14;
t112 = t10.*t25.*w2.*w3;
t113 = t12.*t14.*w1.*w3;
t114 = t7.*t10.*t25.*w2;
t115 = t7.*t13.*t26.*w2.*2.0;
t116 = t7.*t10.*t25.*w1;
t117 = t7.*t13.*t26.*w1.*2.0;
t118 = t7.*t12.*t14;
t119 = t13.*t24.*t26.*w1.*2.0;
t120 = t10.*t24.*t25.*w1;
t121 = t119+t120;
t122 = t13.*t26.*t34.*w1.*2.0;
t123 = t10.*t25.*t34.*w1;
t131 = t13.*t14.*w1.*2.0;
t124 = t122+t123-t131;
t139 = t13.*t14.*w3;
t125 = -t35+t36+t37+t94-t139;
t126 = X1.*t125;
t127 = t49+t50+t51+t52-t64;
t128 = Y1.*t127;
t129 = t126+t128-Z1.*t124;
t130 = t23.*t129.*2.0;
t132 = t13.*t26.*t45.*w1.*2.0;
t133 = t10.*t25.*t45.*w1;
t138 = t13.*t14.*w2;
t134 = -t46+t47+t48+t113-t138;
t135 = X1.*t134;
t136 = -t49-t50+t51+t52+t64;
t137 = Z1.*t136;
t140 = X1.*s1.*t5;
t141 = Y1.*s2.*t6;
t142 = Z1.*s3.*t7;
t143 = s1.*t1.*t5;
t144 = s1.*t1.*t6;
t145 = s1.*t1.*t7;
t146 = s2.*t2.*t5;
t147 = s2.*t2.*t6;
t148 = s2.*t2.*t7;
t149 = s3.*t3.*t5;
t150 = s3.*t3.*t6;
t151 = s3.*t3.*t7;
t152 = X1.*s2.*w1.*w2;
t153 = X1.*s3.*w1.*w3;
t154 = Y1.*s1.*w1.*w2;
t155 = Y1.*s3.*w2.*w3;
t156 = Z1.*s1.*w1.*w3;
t157 = Z1.*s2.*w2.*w3;
t158 = X1.*s1.*t6.*t12;
t159 = X1.*s1.*t7.*t12;
t160 = Y1.*s2.*t5.*t12;
t161 = Y1.*s2.*t7.*t12;
t162 = Z1.*s3.*t5.*t12;
t163 = Z1.*s3.*t6.*t12;
t164 = X1.*s2.*t9.*t10.*w3;
t165 = Y1.*s3.*t9.*t10.*w1;
t166 = Z1.*s1.*t9.*t10.*w2;
t183 = X1.*s3.*t9.*t10.*w2;
t184 = Y1.*s1.*t9.*t10.*w3;
t185 = Z1.*s2.*t9.*t10.*w1;
t186 = X1.*s2.*t12.*w1.*w2;
t187 = X1.*s3.*t12.*w1.*w3;
t188 = Y1.*s1.*t12.*w1.*w2;
t189 = Y1.*s3.*t12.*w2.*w3;
t190 = Z1.*s1.*t12.*w1.*w3;
t191 = Z1.*s2.*t12.*w2.*w3;
t167 = t140+t141+t142+t143+t144+t145+t146+t147+t148+t149+t150+t151+t152+...
t153+t154+t155+t156+t157+t158+t159+t160+t161+t162+t163+t164+t165+t166-...
t183-t184-t185-t186-t187-t188-t189-t190-t191;
t168 = t13.*t26.*t45.*w2.*2.0;
t169 = t10.*t25.*t45.*w2;
t170 = t168+t169;
t171 = t13.*t26.*t34.*w2.*2.0;
t172 = t10.*t25.*t34.*w2;
t176 = t13.*t14.*w2.*2.0;
t173 = t171+t172-t176;
t174 = -t49+t51+t52+t100-t111;
t175 = X1.*t174;
t177 = t13.*t24.*t26.*w2.*2.0;
t178 = t10.*t24.*t25.*w2;
t192 = t13.*t14.*w1;
t179 = -t97+t98+t99+t112-t192;
t180 = Y1.*t179;
t181 = t49+t51+t52-t100+t111;
t182 = Z1.*t181;
t193 = t13.*t26.*t34.*w3.*2.0;
t194 = t10.*t25.*t34.*w3;
t195 = t193+t194;
t196 = t13.*t26.*t45.*w3.*2.0;
t197 = t10.*t25.*t45.*w3;
t200 = t13.*t14.*w3.*2.0;
t198 = t196+t197-t200;
t199 = t7.*t10.*t25;
t201 = t13.*t24.*t26.*w3.*2.0;
t202 = t10.*t24.*t25.*w3;
t203 = -t49+t51+t52-t118+t199;
t204 = Y1.*t203;
t205 = t1.*2.0;
t206 = Z1.*t29.*2.0;
t207 = X1.*t32.*2.0;
t208 = t205+t206+t207-Y1.*t27.*2.0;
t209 = t2.*2.0;
t210 = X1.*t53.*2.0;
t211 = Y1.*t58.*2.0;
t212 = t209+t210+t211-Z1.*t55.*2.0;
t213 = t3.*2.0;
t214 = Y1.*t40.*2.0;
t215 = Z1.*t43.*2.0;
t216 = t213+t214+t215-X1.*t38.*2.0;
jacs = reshape([t14.*t65.*(X1.*r1.*w1.*2.0+X1.*r2.*w2+X1.*r3.*w3+Y1.*r1.*w2+...
Z1.*r1.*w3+r1.*t1.*w1.*2.0+r2.*t2.*w1.*2.0+r3.*t3.*w1.*2.0+Y1.*r3.*t5.*t12+...
Y1.*r3.*t9.*t10-Z1.*r2.*t5.*t12-Z1.*r2.*t9.*t10-X1.*r2.*t12.*w2-X1.*r3.*t12.*w3-...
Y1.*r1.*t12.*w2+Y1.*r2.*t12.*w1.*2.0-Z1.*r1.*t12.*w3+Z1.*r3.*t12.*w1.*2.0+...
Y1.*r3.*t5.*t10.*t11-Z1.*r2.*t5.*t10.*t11+X1.*r2.*t12.*w1.*w3-...
X1.*r3.*t12.*w1.*w2-Y1.*r1.*t12.*w1.*w3+Z1.*r1.*t12.*w1.*w2-...
Y1.*r1.*t10.*t11.*w1.*w3+Z1.*r1.*t10.*t11.*w1.*w2-...
X1.*r1.*t6.*t10.*t11.*w1-X1.*r1.*t7.*t10.*t11.*w1+X1.*r2.*t5.*t10.*t11.*w2+...
X1.*r3.*t5.*t10.*t11.*w3+Y1.*r1.*t5.*t10.*t11.*w2-Y1.*r2.*t5.*t10.*t11.*w1-...
Y1.*r2.*t7.*t10.*t11.*w1+Z1.*r1.*t5.*t10.*t11.*w3-Z1.*r3.*t5.*t10.*t11.*w1-...
Z1.*r3.*t6.*t10.*t11.*w1+X1.*r2.*t10.*t11.*w1.*w3-X1.*r3.*t10.*t11.*w1.*w2+...
Y1.*r3.*t10.*t11.*w1.*w2.*w3+Z1.*r2.*t10.*t11.*w1.*w2.*w3)-t26.*t65.*t93.*w1.*2.0-...
t14.*t93.*t101.*(t130+t15.*(-X1.*t121+Y1.*(t46+t47+t48-t13.*t14.*w2-t12.*t14.*w1.*w3)+...
Z1.*(t35+t36+t37-t13.*t14.*w3-t10.*t25.*w1.*w2)).*2.0+...
t18.*(t135+t137-Y1.*(t132+t133-t13.*t14.*w1.*2.0)).*2.0).*(1.0./2.0),t14.*t65.*(X1.*s1.*w1.*2.0+X1.*s2.*w2+...
X1.*s3.*w3+Y1.*s1.*w2+Z1.*s1.*w3+s1.*t1.*w1.*2.0+s2.*t2.*w1.*2.0+...
s3.*t3.*w1.*2.0+Y1.*s3.*t5.*t12+Y1.*s3.*t9.*t10-Z1.*s2.*t5.*t12-Z1.*s2.*t9.*t10-X1.*s2.*t12.*w2-...
X1.*s3.*t12.*w3-Y1.*s1.*t12.*w2+Y1.*s2.*t12.*w1.*2.0-Z1.*s1.*t12.*w3+...
Z1.*s3.*t12.*w1.*2.0+Y1.*s3.*t5.*t10.*t11-Z1.*s2.*t5.*t10.*t11+...
X1.*s2.*t12.*w1.*w3-X1.*s3.*t12.*w1.*w2-Y1.*s1.*t12.*w1.*w3+...
Z1.*s1.*t12.*w1.*w2+X1.*s2.*t10.*t11.*w1.*w3-X1.*s3.*t10.*t11.*w1.*w2-...
Y1.*s1.*t10.*t11.*w1.*w3+Z1.*s1.*t10.*t11.*w1.*w2-X1.*s1.*t6.*t10.*t11.*w1-...
X1.*s1.*t7.*t10.*t11.*w1+X1.*s2.*t5.*t10.*t11.*w2+X1.*s3.*t5.*t10.*t11.*w3+...
Y1.*s1.*t5.*t10.*t11.*w2-Y1.*s2.*t5.*t10.*t11.*w1-Y1.*s2.*t7.*t10.*t11.*w1+...
Z1.*s1.*t5.*t10.*t11.*w3-Z1.*s3.*t5.*t10.*t11.*w1-Z1.*s3.*t6.*t10.*t11.*w1+...
Y1.*s3.*t10.*t11.*w1.*w2.*w3+Z1.*s2.*t10.*t11.*w1.*w2.*w3)-...
t14.*t101.*t167.*(t130+t15.*(Y1.*(t46+t47+t48-t113-t138)+...
Z1.*(t35+t36+t37-t94-t139)-X1.*t121).*2.0+t18.*(t135+t137-...
Y1.*(-t131+t132+t133)).*2.0).*(1.0./2.0)-t26.*t65.*t167.*w1.*2.0,t14.*t65.*(X1.*r2.*w1+...
Y1.*r1.*w1+Y1.*r2.*w2.*2.0+Y1.*r3.*w3+Z1.*r2.*w3+r1.*t1.*w2.*2.0+...
r2.*t2.*w2.*2.0+r3.*t3.*w2.*2.0-X1.*r3.*t6.*t12-X1.*r3.*t9.*t10+...
Z1.*r1.*t6.*t12+Z1.*r1.*t9.*t10+X1.*r1.*t12.*w2.*2.0-X1.*r2.*t12.*w1-...
Y1.*r1.*t12.*w1-Y1.*r3.*t12.*w3-Z1.*r2.*t12.*w3+Z1.*r3.*t12.*w2.*2.0-...
X1.*r3.*t6.*t10.*t11+Z1.*r1.*t6.*t10.*t11+X1.*r2.*t12.*w2.*w3-Y1.*r1.*t12.*w2.*w3+...
Y1.*r3.*t12.*w1.*w2-Z1.*r2.*t12.*w1.*w2-Y1.*r1.*t10.*t11.*w2.*w3+...
Y1.*r3.*t10.*t11.*w1.*w2-Z1.*r2.*t10.*t11.*w1.*w2-X1.*r1.*t6.*t10.*t11.*w2+...
X1.*r2.*t6.*t10.*t11.*w1-X1.*r1.*t7.*t10.*t11.*w2+Y1.*r1.*t6.*t10.*t11.*w1-...
Y1.*r2.*t5.*t10.*t11.*w2-Y1.*r2.*t7.*t10.*t11.*w2+Y1.*r3.*t6.*t10.*t11.*w3-...
Z1.*r3.*t5.*t10.*t11.*w2+Z1.*r2.*t6.*t10.*t11.*w3-Z1.*r3.*t6.*t10.*t11.*w2+...
X1.*r2.*t10.*t11.*w2.*w3+X1.*r3.*t10.*t11.*w1.*w2.*w3+Z1.*r1.*t10.*t11.*w1.*w2.*w3)-...
t26.*t65.*t93.*w2.*2.0-t14.*t93.*t101.*(t18.*(Z1.*(-t35+t94+t95+t96-t13.*t14.*w3)-...
Y1.*t170+X1.*(t97+t98+t99-t13.*t14.*w1-t10.*t25.*w2.*w3)).*2.0+...
t15.*(t180+t182-X1.*(t177+t178-t13.*t14.*w2.*2.0)).*2.0+t23.*(t175+...
Y1.*(t35-t94+t95+t96-t13.*t14.*w3)-Z1.*t173).*2.0).*(1.0./2.0),t14.*t65.*(X1.*s2.*w1+...
Y1.*s1.*w1+Y1.*s2.*w2.*2.0+Y1.*s3.*w3+Z1.*s2.*w3+s1.*t1.*w2.*2.0+s2.*t2.*w2.*2.0+...
s3.*t3.*w2.*2.0-X1.*s3.*t6.*t12-X1.*s3.*t9.*t10+Z1.*s1.*t6.*t12+Z1.*s1.*t9.*t10+...
X1.*s1.*t12.*w2.*2.0-X1.*s2.*t12.*w1-Y1.*s1.*t12.*w1-Y1.*s3.*t12.*w3-Z1.*s2.*t12.*w3+...
Z1.*s3.*t12.*w2.*2.0-X1.*s3.*t6.*t10.*t11+Z1.*s1.*t6.*t10.*t11+X1.*s2.*t12.*w2.*w3-...
Y1.*s1.*t12.*w2.*w3+Y1.*s3.*t12.*w1.*w2-Z1.*s2.*t12.*w1.*w2+X1.*s2.*t10.*t11.*w2.*w3-...
Y1.*s1.*t10.*t11.*w2.*w3+Y1.*s3.*t10.*t11.*w1.*w2-Z1.*s2.*t10.*t11.*w1.*w2-...
X1.*s1.*t6.*t10.*t11.*w2+X1.*s2.*t6.*t10.*t11.*w1-X1.*s1.*t7.*t10.*t11.*w2+...
Y1.*s1.*t6.*t10.*t11.*w1-Y1.*s2.*t5.*t10.*t11.*w2-Y1.*s2.*t7.*t10.*t11.*w2+...
Y1.*s3.*t6.*t10.*t11.*w3-Z1.*s3.*t5.*t10.*t11.*w2+Z1.*s2.*t6.*t10.*t11.*w3-...
Z1.*s3.*t6.*t10.*t11.*w2+X1.*s3.*t10.*t11.*w1.*w2.*w3+Z1.*s1.*t10.*t11.*w1.*w2.*w3)-...
t26.*t65.*t167.*w2.*2.0-t14.*t101.*t167.*(t18.*(X1.*(t97+t98+t99-t112-t192)+...
Z1.*(-t35+t94+t95+t96-t139)-Y1.*t170).*2.0+t15.*(t180+t182-X1.*(-t176+t177+t178)).*2.0+...
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