/**
* 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);
}
/**
* 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];
}
/**
* Multiplies the transpose of vector v1 (ie, v1 becomes a row vector with respect to the
* multiplication) times matrix m1 and places the result into this vector (this =
* transpose(v1)*m1). The result is technically a row vector, but the GVector class only knows
* about column vectors, and so the result is stored as a column vector.
*
* @param m1 The matrix in the multiplication
* @param v1 The vector that is temporarily transposed
*/
public final void mul(GVector v1, GMatrix m1) {
if (m1.getNumRow() != v1.length)
throw new MismatchedSizeException(VecMathI18N.getString("GVector12"));
if (length != m1.getNumCol())
throw new MismatchedSizeException(VecMathI18N.getString("GVector13"));
double v[];
if (v1 != this) {
v = v1.values;
} else {
v = (double[]) values.clone();
}
for (int j = length - 1; j >= 0; j--) {
values[j] = 0.0;
for (int i = v1.length - 1; i >= 0; i--) {
values[j] += m1.values[i][j] * v[i];
}
}
}