/**
* Solves for x in Ax = b, where x is this vector (nx1), A is mxn, b is mx1, and A =
* U*W*transpose(V); U,W,V must be precomputed and can be found by taking the singular value
* decomposition (SVD) of A using the method SVD found in the GMatrix class.
*
* @param U The U matrix produced by the GMatrix method SVD
* @param W The W matrix produced by the GMatrix method SVD
* @param V The V matrix produced by the GMatrix method SVD
* @param b The b vector in the linear equation Ax = b
*/
public final void SVDBackSolve(GMatrix U, GMatrix W, GMatrix V, GVector b) {
if (!(U.nRow == b.getSize() && U.nRow == U.nCol && U.nRow == W.nRow)) {
throw new MismatchedSizeException(VecMathI18N.getString("GVector15"));
}
if (!(W.nCol == values.length && W.nCol == V.nCol && W.nCol == V.nRow)) {
throw new MismatchedSizeException(VecMathI18N.getString("GVector23"));
}
GMatrix tmp = new GMatrix(U.nRow, W.nCol);
tmp.mul(U, V);
tmp.mulTransposeRight(U, W);
tmp.invert();
mul(tmp, b);
}
