/**
* @brief Compute the inverse of a matrix
*
* This method will compute the inverse of an affine matrix for purposes of
* forward and inverse Affine computations.
*
* @param a Matrix to invert
*
* @return Affine::AMatrix The inverted matrix
*/
Affine::AMatrix Affine::invert(const AMatrix &a) const throw (iException &) {
// Now compute the inverse affine matrix using singular value
// decomposition A = USV'. So invA = V invS U'. Where ' represents
// the transpose of a matrix and invS is S with the recipricol of the
// diagonal elements
JAMA::SVD<double> svd(a);
AMatrix V;
svd.getV(V);
// The inverse of S is 1 over each diagonal element of S
AMatrix invS;
svd.getS(invS);
for (int i=0; i<invS.dim1(); i++) {
if (invS[i][i] == 0.0) {
string msg = "Affine transform not invertible";
throw iException::Message(iException::Math,msg,_FILEINFO_);
}
invS[i][i] = 1.0 / invS[i][i];
}
// Transpose U
AMatrix U;
svd.getU(U);
AMatrix transU(U.dim2(),U.dim1());
for (int r=0; r<U.dim1(); r++) {
for (int c=0; c<U.dim2(); c++) {
transU[c][r] = U[r][c];
}
}
// Multiply stuff together to get the inverse of the affine
AMatrix VinvS = TNT::matmult(V,invS);
return (TNT::matmult(VinvS,transU));
}
/**
* @brief Checks affine matrix to ensure it is a 3x3 standard form transform
*
* @param am Affine matrix to validate
*/
void Affine::checkDims(const AMatrix &am) const throw (iException &) {
if ((am.dim1() != 3) && (am.dim2() != 3)) {
ostringstream mess;
mess << "Affine matrices must be 3x3 - this one is " << am.dim1()
<< "x" << am.dim2();
throw iException::Message(iException::Programmer, mess.str(), _FILEINFO_);
}
return;
}
