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<a href="dgematrix__small-specialized_8hpp.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">//=============================================================================</span><span class="comment"></span>
<a name="l00002"></a>00002 <span class="comment">/*! calculate determinant */</span>
<a name="l00003"></a><a class="code" href="dgematrix__small_8hpp.html#a264abc4b817407bbfed2911a30871a20">00003</a> <span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code" href="dgematrix__small-specialized_8hpp.html#a74dda59225405b0940dc395b6f682596">det</a>(<span class="keyword">const</span> dgemat2&amp; A)
<a name="l00004"></a>00004 {VERBOSE_REPORT;
<a name="l00005"></a>00005   <span class="keywordflow">return</span> A(0,0)*A(1,1)-A(0,1)*A(1,0);
<a name="l00006"></a>00006 }
<a name="l00007"></a>00007 
<a name="l00008"></a>00008 <span class="comment">//=============================================================================</span><span class="comment"></span>
<a name="l00009"></a>00009 <span class="comment">/*! calculate inverse */</span>
<a name="l00010"></a><a class="code" href="dgematrix__small_8hpp.html#a389e4421a8265a3165bebfaad3527117">00010</a> <span class="keyword">inline</span> dgemat2 <a class="code" href="dcovector__small-specialized_8hpp.html#a816188231dc59c47c02a0187291207f1">inv</a>(<span class="keyword">const</span> dgemat2&amp; A)
<a name="l00011"></a>00011 {VERBOSE_REPORT;
<a name="l00012"></a>00012   <span class="keyword">const</span> <span class="keywordtype">double</span> Adet( <a class="code" href="dgematrix__small-specialized_8hpp.html#a74dda59225405b0940dc395b6f682596">det</a>(A) );
<a name="l00013"></a>00013   dgemat2 Ainv;
<a name="l00014"></a>00014   Ainv(0,0)= A(1,1)/Adet;  Ainv(0,1)=-A(0,1)/Adet;
<a name="l00015"></a>00015   Ainv(1,0)=-A(1,0)/Adet;  Ainv(1,1)= A(0,0)/Adet;
<a name="l00016"></a>00016   <span class="keywordflow">return</span> Ainv;
<a name="l00017"></a>00017 }
<a name="l00018"></a>00018 
<a name="l00019"></a>00019 <span class="comment">//=============================================================================</span><span class="comment"></span>
<a name="l00020"></a>00020 <span class="comment">/*! return rotated tensor */</span>
<a name="l00021"></a><a class="code" href="dgematrix__small_8hpp.html#aa9e18a552c758acf0a67ee580783529f">00021</a> <span class="keyword">inline</span> dgemat2 <a class="code" href="dcovector__small-specialized_8hpp.html#a7c6e40d311633e4c71f998cf49ff39f0">rotate</a>(<span class="keyword">const</span> dgemat2&amp; m, <span class="keyword">const</span> <span class="keywordtype">double</span>&amp; theta)
<a name="l00022"></a>00022 {VERBOSE_REPORT;
<a name="l00023"></a>00023   <span class="comment">//dgemat2 R(t2m(theta)); return R*m*t(R);//too slow</span>
<a name="l00024"></a>00024   <span class="keywordtype">double</span> c(cos(theta)), s(sin(theta));
<a name="l00025"></a>00025   <span class="keywordtype">double</span> cc(c*c), cs(c*s), ss(s*s);
<a name="l00026"></a>00026   dgemat2 mat;
<a name="l00027"></a>00027   mat(0,0) =m(0,0)*cc -(m(0,1)+m(1,0))*cs +m(1,1)*ss;
<a name="l00028"></a>00028   mat(0,1) =m(0,1)*cc +(m(0,0)-m(1,1))*cs -m(1,0)*ss;
<a name="l00029"></a>00029   mat(1,0) =m(1,0)*cc +(m(0,0)-m(1,1))*cs -m(0,1)*ss;
<a name="l00030"></a>00030   mat(1,1) =m(1,1)*cc +(m(0,1)+m(1,0))*cs +m(0,0)*ss;
<a name="l00031"></a>00031   <span class="keywordflow">return</span> mat;
<a name="l00032"></a>00032 }
<a name="l00033"></a>00033 
<a name="l00034"></a>00034 <span class="comment">//=============================================================================</span><span class="comment"></span>
<a name="l00035"></a>00035 <span class="comment">/*! convert theta to 2x2 rotational matrix */</span>
<a name="l00036"></a><a class="code" href="dgematrix__small_8hpp.html#a387d7b2f1b99fefef322091b0a3107d9">00036</a> <span class="keyword">inline</span> dgemat2 <a class="code" href="dgematrix__small-specialized_8hpp.html#a71e601b6ab60bf9cb2fd3475e394f5bf">t2m</a>(<span class="keyword">const</span> <span class="keywordtype">double</span>&amp; theta)
<a name="l00037"></a>00037 {VERBOSE_REPORT;
<a name="l00038"></a>00038   dgemat2 R;
<a name="l00039"></a>00039   R(0,0)=cos(theta); R(0,1)=-sin(theta);
<a name="l00040"></a>00040   R(1,0)=sin(theta); R(1,1)=cos(theta);
<a name="l00041"></a>00041   <span class="keywordflow">return</span> R;
<a name="l00042"></a>00042 }
<a name="l00043"></a>00043 <span class="comment"></span>
<a name="l00044"></a>00044 <span class="comment">///////////////////////////////////////////////////////////////////////////////</span>
<a name="l00045"></a>00045 <span class="comment">///////////////////////////////////////////////////////////////////////////////</span>
<a name="l00046"></a>00046 <span class="comment">///////////////////////////////////////////////////////////////////////////////</span>
<a name="l00047"></a>00047 <span class="comment">///////////////////////////////////////////////////////////////////////////////</span>
<a name="l00048"></a>00048 <span class="comment">///////////////////////////////////////////////////////////////////////////////</span>
<a name="l00049"></a>00049 <span class="comment">///////////////////////////////////////////////////////////////////////////////</span>
<a name="l00050"></a>00050 <span class="comment">///////////////////////////////////////////////////////////////////////////////</span>
<a name="l00051"></a>00051 <span class="comment">///////////////////////////////////////////////////////////////////////////////</span>
<a name="l00052"></a>00052 <span class="comment">///////////////////////////////////////////////////////////////////////////////</span>
<a name="l00053"></a>00053 <span class="comment"></span>
<a name="l00054"></a>00054 <span class="comment">//=============================================================================</span><span class="comment"></span>
<a name="l00055"></a>00055 <span class="comment">/*! calculate determinant */</span>
<a name="l00056"></a><a class="code" href="dgematrix__small_8hpp.html#a094c91a62212e1c7a4598b612bea1cbd">00056</a> <span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code" href="dgematrix__small-specialized_8hpp.html#a74dda59225405b0940dc395b6f682596">det</a>(<span class="keyword">const</span> dgemat3&amp; A)
<a name="l00057"></a>00057 {VERBOSE_REPORT;
<a name="l00058"></a>00058   <span class="keywordflow">return</span>
<a name="l00059"></a>00059     +A(0,0)*A(1,1)*A(2,2) -A(0,0)*A(1,2)*A(2,1)
<a name="l00060"></a>00060     +A(0,1)*A(1,2)*A(2,0) -A(0,1)*A(1,0)*A(2,2)
<a name="l00061"></a>00061     +A(0,2)*A(1,0)*A(2,1) -A(0,2)*A(1,1)*A(2,0);
<a name="l00062"></a>00062 }
<a name="l00063"></a>00063 
<a name="l00064"></a>00064 <span class="comment">//=============================================================================</span><span class="comment"></span>
<a name="l00065"></a>00065 <span class="comment">/*! calculate inverse */</span>
<a name="l00066"></a><a class="code" href="dgematrix__small_8hpp.html#a1b11c85a3f5e71ca3194db7f36e8e161">00066</a> <span class="keyword">inline</span> dgemat3 <a class="code" href="dcovector__small-specialized_8hpp.html#a816188231dc59c47c02a0187291207f1">inv</a>(<span class="keyword">const</span> dgemat3&amp; A)
<a name="l00067"></a>00067 {VERBOSE_REPORT;
<a name="l00068"></a>00068   <span class="keyword">const</span> <span class="keywordtype">double</span> Adet( <a class="code" href="dgematrix__small-specialized_8hpp.html#a74dda59225405b0940dc395b6f682596">det</a>(A) );
<a name="l00069"></a>00069   dgemat3 Ainv;
<a name="l00070"></a>00070   Ainv(0,0) =(A(1,1)*A(2,2)-A(1,2)*A(2,1))/Adet;
<a name="l00071"></a>00071   Ainv(0,1) =(A(0,2)*A(2,1)-A(0,1)*A(2,2))/Adet;
<a name="l00072"></a>00072   Ainv(0,2) =(A(0,1)*A(1,2)-A(0,2)*A(1,1))/Adet;
<a name="l00073"></a>00073   Ainv(1,0) =(A(1,2)*A(2,0)-A(1,0)*A(2,2))/Adet;
<a name="l00074"></a>00074   Ainv(1,1) =(A(0,0)*A(2,2)-A(0,2)*A(2,0))/Adet;
<a name="l00075"></a>00075   Ainv(1,2) =(A(0,2)*A(1,0)-A(0,0)*A(1,2))/Adet;
<a name="l00076"></a>00076   Ainv(2,0) =(A(1,0)*A(2,1)-A(1,1)*A(2,0))/Adet;
<a name="l00077"></a>00077   Ainv(2,1) =(A(0,1)*A(2,0)-A(0,0)*A(2,1))/Adet;
<a name="l00078"></a>00078   Ainv(2,2) =(A(0,0)*A(1,1)-A(0,1)*A(1,0))/Adet;
<a name="l00079"></a>00079   <span class="keywordflow">return</span> Ainv;
<a name="l00080"></a>00080 }
<a name="l00081"></a>00081 
<a name="l00082"></a>00082 <span class="comment">//=============================================================================</span><span class="comment"></span>
<a name="l00083"></a>00083 <span class="comment">/*!  */</span>
<a name="l00084"></a><a class="code" href="dgematrix__small_8hpp.html#ae0ba705fe511cc2889c8d35749e108d1">00084</a> <span class="keyword">inline</span> dgemat3 <a class="code" href="dcovector__small-specialized_8hpp.html#a7c6e40d311633e4c71f998cf49ff39f0">rotate</a>(<span class="keyword">const</span> dgemat3&amp; m, <span class="keyword">const</span> dquater&amp; q)
<a name="l00085"></a>00085 {VERBOSE_REPORT;
<a name="l00086"></a>00086   dgemat3 R(<a class="code" href="dcovector__small-specialized_8hpp.html#a0b8662d50893bcd25e2d80f468b721f5">q2m</a>(q));
<a name="l00087"></a>00087   <span class="keywordflow">return</span> R*m*<a class="code" href="__dcovector-calc_8hpp.html#afe5475fdf72e825c1fea5f306d686664">t</a>(R);
<a name="l00088"></a>00088 }
<a name="l00089"></a>00089 
<a name="l00090"></a>00090 <span class="comment">//=============================================================================</span><span class="comment"></span>
<a name="l00091"></a>00091 <span class="comment">/*!  */</span>
<a name="l00092"></a><a class="code" href="dgematrix__small_8hpp.html#ae86d81c42d6b624e10aa38f0ab9c2cc6">00092</a> <span class="keyword">inline</span> dquater <a class="code" href="dgematrix__small-specialized_8hpp.html#af95061266e0d8f58a83c8c36f3778157">m2q</a>(<span class="keyword">const</span> dgemat3&amp; m)
<a name="l00093"></a>00093 {VERBOSE_REPORT;
<a name="l00094"></a>00094   dcovec3 v( m(2,1)-m(1,2), m(0,2)-m(2,0), m(1,0)-m(0,1) );
<a name="l00095"></a>00095   <span class="keywordtype">double</span> <a class="code" href="__dcovector-calc_8hpp.html#afe5475fdf72e825c1fea5f306d686664">t</a>( acos(0.5*(m(0,0)+m(1,1)+m(2,2)-1.)) );
<a name="l00096"></a>00096   <span class="keywordflow">return</span> <a class="code" href="dcovector__small-specialized_8hpp.html#a2ea0dbdf9f1b8de71470bf9d0a356577">vt2q</a>(v,t);
<a name="l00097"></a>00097 }
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