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Commit 4b1f6a5d authored by Saad Jbabdi's avatar Saad Jbabdi
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added expm

parent a5f1bca0
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......@@ -1408,6 +1408,73 @@ ReturnMatrix exp(const Matrix& mat)
return res;
}
// optimised code for calculating matrix exponential
ReturnMatrix expm(const Matrix& mat){
float nmat = sum(mat).Maximum();
int nc=mat.Ncols(),nr=mat.Nrows();
Matrix res(nr,nc);
IdentityMatrix id(nr);
Matrix U(nr,nc),V(nr,nc);
if(nmat <= 1.495585217958292e-002){ // m=3
Matrix mat2(nr,nc);
mat2=mat*mat;
U = mat*(mat2+60.0*id);
V = 12.0*mat2+120.0*id;
res = (-U+V).i()*(U+V);
}
else if(nmat <= 2.539398330063230e-001){ // m=5
Matrix mat2(nr,nc),mat4(nr,nc);
mat2=mat*mat;mat4=mat2*mat2;
U = mat*(mat4+420.0*mat2+15120.0*id);
V = 30.0*mat4+3360.0*mat2+30240.0*id;
res = (-U+V).i()*(U+V);
}
else if(nmat <= 9.504178996162932e-001){ // m=7
Matrix mat2(nr,nc),mat4(nr,nc),mat6(nr,nc);
mat2=mat*mat;mat4=mat2*mat2,mat6=mat4*mat2;
U = mat*(mat6+1512.0*mat4+277200.0*mat2+8648640.0*id);
V = 56.0*mat6+25200.0*mat4+1995840.0*mat2+17297280.0*id;
res = (-U+V).i()*(U+V);
}
else if(nmat <= 2.097847961257068e+000){
Matrix mat2(nr,nc),mat4(nr,nc),mat6(nr,nc),mat8(nr,nc);
mat2=mat*mat;mat4=mat2*mat2,mat6=mat4*mat2,mat8=mat6*mat2;
U = mat*(mat8+3960.0*mat6+2162160.0*mat4+302702400.0*mat2+8821612800.0*id);
V = 90.0*mat8+110880.0*mat6+30270240.0*mat4+2075673600.0*mat2+17643225600.0*id;
res = (-U+V).i()*(U+V);
}
else if(nmat <= 5.371920351148152e+000){
Matrix mat2(nr,nc),mat4(nr,nc),mat6(nr,nc);
mat2=mat*mat;mat4=mat2*mat2,mat6=mat4*mat2;
U = mat*(mat6*(mat6+16380.0*mat4+40840800.0*mat2)+
+33522128640.0*mat6+10559470521600.0*mat4+1187353796428800.0*mat2+32382376266240000.0*id);
V = mat6*(182.0*mat6+960960.0*mat4+1323241920.0*mat2)
+ 670442572800.0*mat6+129060195264000.0*mat4+7771770303897600.0*mat2+64764752532480000.0*id;
res = (-U+V).i()*(U+V);
}
else{
double t;int s;
t = frexp(nmat/5.371920351148152,&s);
if(t==0.5) s--;
t = std::pow(2.0,s);
res = (mat/t);
Matrix mat2(nr,nc),mat4(nr,nc),mat6(nr,nc);
mat2=res*res;mat4=mat2*mat2,mat6=mat4*mat2;
U = res*(mat6*(mat6+16380*mat4+40840800*mat2)+
+33522128640.0*mat6+10559470521600.0*mat4+1187353796428800.0*mat2+32382376266240000.0*id);
V = mat6*(182.0*mat6+960960.0*mat4+1323241920.0*mat2)
+ 670442572800.0*mat6+129060195264000.0*mat4+7771770303897600.0*mat2+64764752532480000.0*id;
res = (-U+V).i()*(U+V);
for(int i=1;i<=s;i++)
res = res*res;
}
res.Release();
return res;
}
ReturnMatrix tanh(const Matrix& mat)
{
Matrix res = mat;
......
......@@ -217,6 +217,7 @@ namespace MISCMATHS {
ReturnMatrix sqrtm(const Matrix& mat);
ReturnMatrix log(const Matrix& mat);
ReturnMatrix exp(const Matrix& mat);
ReturnMatrix expm(const Matrix& mat);
ReturnMatrix tanh(const Matrix& mat);
ReturnMatrix pow(const Matrix& mat, const double exp);
ReturnMatrix sum(const Matrix& mat, const int dim = 1);
......
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