/**
* LU Decomposition Back Solve; this method takes the LU matrix and the permutation vector
* produced by the GMatrix method LUD and solves the equation (LU)*x = b by placing the solution
* vector x into this vector. This vector should be the same length or longer than b.
*
* @param LU The matrix into which the lower and upper decompostions have been placed
* @param b The b vector in the equation (LU)*x = b
* @param permutation The row permuations that were necessary to produce the LU matrix parameter
*/
public final void LUDBackSolve(GMatrix LU, GVector b, GVector permutation) {
int size = LU.nRow * LU.nCol;
double[] temp = new double[size];
double[] result = new double[size];
int[] row_perm = new int[b.getSize()];
int i, j;
if (LU.nRow != b.getSize()) {
throw new MismatchedSizeException(VecMathI18N.getString("GVector16"));
}
if (LU.nRow != permutation.getSize()) {
throw new MismatchedSizeException(VecMathI18N.getString("GVector24"));
}
if (LU.nRow != LU.nCol) {
throw new MismatchedSizeException(VecMathI18N.getString("GVector25"));
}
for (i = 0; i < LU.nRow; i++) {
for (j = 0; j < LU.nCol; j++) {
temp[i * LU.nCol + j] = LU.values[i][j];
}
}
for (i = 0; i < size; i++) result[i] = 0.0;
for (i = 0; i < LU.nRow; i++) result[i * LU.nCol] = b.values[i];
for (i = 0; i < LU.nCol; i++) row_perm[i] = (int) permutation.values[i];
GMatrix.luBacksubstitution(LU.nRow, temp, row_perm, result);
for (i = 0; i < LU.nRow; i++) this.values[i] = result[i * LU.nCol];
}
/**
* Creates a new object of the same class as this object.
*
* @return a clone of this instance.
* @exception OutOfMemoryError if there is not enough memory.
* @see java.lang.Cloneable
* @since vecmath 1.3
*/
public Object clone() {
GVector v1 = null;
try {
v1 = (GVector) super.clone();
} catch (CloneNotSupportedException e) {
// this shouldn't happen, since we are Cloneable
throw new InternalError();
}
// Also need to clone array of values
v1.values = new double[length];
for (int i = 0; i < length; i++) {
v1.values[i] = values[i];
}
return v1;
}
/**
* 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);
}
/**
* Returns the (n-space) angle in radians between this vector and the vector parameter; the return
* value is constrained to the range [0,PI].
*
* @param v1 The other vector
* @return The angle in radians in the range [0,PI]
*/
public final double angle(GVector v1) {
return (Math.acos(this.dot(v1) / (this.norm() * v1.norm())));
}