/**
* Returns the Q matrix.
*/
public DMatrixRMaj getQ()
{
DMatrixRMaj Q = CommonOps_DDRM.identity(QR.numRows);
DMatrixRMaj Q_k = new DMatrixRMaj(QR.numRows, QR.numRows);
DMatrixRMaj u = new DMatrixRMaj(QR.numRows, 1);
DMatrixRMaj temp = new DMatrixRMaj(QR.numRows, QR.numRows);
int N = Math.Min(QR.numCols, QR.numRows);
// compute Q by first extracting the householder vectors from the columns of QR and then applying it to Q
for (int j = N - 1; j >= 0; j--)
{
CommonOps_DDRM.extract(QR, j, QR.numRows, j, j + 1, u, j, 0);
u.set(j, 1.0);
// A = (I - γ*u*u<sup>T</sup>)*A<br>
CommonOps_DDRM.setIdentity(Q_k);
CommonOps_DDRM.multAddTransB(-gammas[j], u, u, Q_k);
CommonOps_DDRM.mult(Q_k, Q, temp);
Q.set(temp);
}
return(Q);
}
public virtual DMatrixRMaj getU(DMatrixRMaj U, bool transpose, bool compact)
{
U = BidiagonalDecompositionRow_DDRM.handleU(U, false, compact, m, n, min);
if (compact)
{
// U = Q*U1
DMatrixRMaj Q1 = decompQRP.getQ(null, true);
DMatrixRMaj U1 = decompBi.getU(null, false, true);
CommonOps_DDRM.mult(Q1, U1, U);
}
else
{
// U = [Q1*U1 Q2]
DMatrixRMaj Q = decompQRP.getQ(U, false);
DMatrixRMaj U1 = decompBi.getU(null, false, true);
DMatrixRMaj Q1 = CommonOps_DDRM.extract(Q, 0, Q.numRows, 0, min);
DMatrixRMaj tmp = new DMatrixRMaj(Q1.numRows, U1.numCols);
CommonOps_DDRM.mult(Q1, U1, tmp);
CommonOps_DDRM.insert(tmp, Q, 0, 0);
}
if (transpose)
{
CommonOps_DDRM.transpose(U);
}
return(U);
}
/**
* <p>
* Returns the null-space from the singular value decomposition. The null space is a set of non-zero vectors that
* when multiplied by the original matrix return zero.
* </p>
*
* <p>
* The null space is found by extracting the columns in V that are associated singular values less than
* or equal to the threshold. In some situations a non-compact SVD is required.
* </p>
*
* @param svd A precomputed decomposition. Not modified.
* @param nullSpace Storage for null space. Will be reshaped as needed. Modified.
* @param tol Threshold for selecting singular values. Try UtilEjml.EPS.
* @return The null space.
*/
public static DMatrixRMaj nullSpace(SingularValueDecomposition_F64 <DMatrixRMaj> svd,
DMatrixRMaj nullSpace, double tol)
{
int N = svd.numberOfSingularValues();
double[] s = svd.getSingularValues();
DMatrixRMaj V = svd.getV(null, true);
if (V.numRows != svd.numCols())
{
throw new ArgumentException(
"Can't compute the null space using a compact SVD for a matrix of this size.");
}
// first determine the size of the null space
int numVectors = svd.numCols() - N;
for (int i = 0; i < N; i++)
{
if (s[i] <= tol)
{
numVectors++;
}
}
// declare output data
if (nullSpace == null)
{
nullSpace = new DMatrixRMaj(numVectors, svd.numCols());
}
else
{
nullSpace.reshape(numVectors, svd.numCols());
}
// now extract the vectors
int count = 0;
for (int i = 0; i < N; i++)
{
if (s[i] <= tol)
{
CommonOps_DDRM.extract(V, i, i + 1, 0, V.numCols, nullSpace, count++, 0);
}
}
for (int i = N; i < svd.numCols(); i++)
{
CommonOps_DDRM.extract(V, i, i + 1, 0, V.numCols, nullSpace, count++, 0);
}
CommonOps_DDRM.transpose(nullSpace);
return(nullSpace);
}
/**
* Returns a vector from the PCA's basis.
*
* @param which Which component's vector is to be returned.
* @return Vector from the PCA basis.
*/
public double[] getBasisVector(int which)
{
if (which < 0 || which >= numComponents)
{
throw new ArgumentException("Invalid component");
}
DMatrixRMaj v = new DMatrixRMaj(1, A.numCols);
CommonOps_DDRM.extract(V_t, which, which + 1, 0, A.numCols, v, 0, 0);
return(v.data);
}
public override bool setA(DMatrixRMaj A)
{
_setA(A);
if (!decomposition.decompose(A))
{
return(false);
}
rank = decomposition.getRank();
R.reshape(numRows, numCols);
decomposition.getR(R, false);
// extract the r11 triangle sub matrix
R11.reshape(rank, rank);
CommonOps_DDRM.extract(R, 0, rank, 0, rank, R11, 0, 0);
if (norm2Solution && rank < numCols)
{
// extract the R12 sub-matrix
W.reshape(rank, numCols - rank);
CommonOps_DDRM.extract(R, 0, rank, rank, numCols, W, 0, 0);
// W=inv(R11)*R12
TriangularSolver_DDRM.solveU(R11.data, 0, R11.numCols, R11.numCols, W.data, 0, W.numCols, W.numCols);
// set the identity matrix in the upper portion
W.reshape(numCols, W.numCols, true);
for (int i = 0; i < numCols - rank; i++)
{
for (int j = 0; j < numCols - rank; j++)
{
if (i == j)
{
W.set(i + rank, j, -1);
}
else
{
W.set(i + rank, j, 0);
}
}
}
}
return(true);
}
public bool process(DMatrixRMaj A, int numSingularValues, DMatrixRMaj nullspace)
{
decomposition.decompose(A);
if (A.numRows > A.numCols)
{
Q.reshape(A.numCols, Math.Min(A.numRows, A.numCols));
decomposition.getQ(Q, true);
}
else
{
Q.reshape(A.numCols, A.numCols);
decomposition.getQ(Q, false);
}
nullspace.reshape(Q.numRows, numSingularValues);
CommonOps_DDRM.extract(Q, 0, Q.numRows, Q.numCols - numSingularValues, Q.numCols, nullspace, 0, 0);
return(true);
}
private void solveWithLU(double real, int index, DMatrixRMaj r)
{
DMatrixRMaj A = new DMatrixRMaj(index, index);
CommonOps_DDRM.extract(_implicit.A, 0, index, 0, index, A, 0, 0);
for (int i = 0; i < index; i++)
{
A.add(i, i, -real);
}
r.reshape(index, 1, false);
SpecializedOps_DDRM.subvector(_implicit.A, 0, index, index, false, 0, r);
CommonOps_DDRM.changeSign(r);
// TODO this must be very inefficient
if (!solver.setA(A))
{
throw new InvalidOperationException("Solve failed");
}
solver.solve(r, r);
}
public void extract(Matrix src, int srcY0, int srcY1, int srcX0, int srcX1, Matrix dst, int dstY0, int dstX0)
{
CommonOps_DDRM.extract((DMatrixRMaj)src, srcY0, srcY1, srcX0, srcX1, (DMatrixRMaj)dst, dstY0, dstX0);
}
/**
* Computes the QR decomposition of the provided matrix.
*
* @param A Matrix which is to be decomposed. Not modified.
*/
public void decompose(DMatrixRMaj A)
{
this.QR = (DMatrixRMaj)A.copy();
int N = Math.Min(A.numCols, A.numRows);
gammas = new double[A.numCols];
DMatrixRMaj A_small = new DMatrixRMaj(A.numRows, A.numCols);
DMatrixRMaj A_mod = new DMatrixRMaj(A.numRows, A.numCols);
DMatrixRMaj v = new DMatrixRMaj(A.numRows, 1);
DMatrixRMaj Q_k = new DMatrixRMaj(A.numRows, A.numRows);
for (int i = 0; i < N; i++)
{
// reshape temporary variables
A_small.reshape(QR.numRows - i, QR.numCols - i, false);
A_mod.reshape(A_small.numRows, A_small.numCols, false);
v.reshape(A_small.numRows, 1, false);
Q_k.reshape(v.getNumElements(), v.getNumElements(), false);
// use extract matrix to get the column that is to be zeroed
CommonOps_DDRM.extract(QR, i, QR.numRows, i, i + 1, v, 0, 0);
double max = CommonOps_DDRM.elementMaxAbs(v);
if (max > 0 && v.getNumElements() > 1)
{
// normalize to reduce overflow issues
CommonOps_DDRM.divide(v, max);
// compute the magnitude of the vector
double tau = NormOps_DDRM.normF(v);
if (v.get(0) < 0)
{
tau *= -1.0;
}
double u_0 = v.get(0) + tau;
double gamma = u_0 / tau;
CommonOps_DDRM.divide(v, u_0);
v.set(0, 1.0);
// extract the submatrix of A which is being operated on
CommonOps_DDRM.extract(QR, i, QR.numRows, i, QR.numCols, A_small, 0, 0);
// A = (I - γ*u*u<sup>T</sup>)A
CommonOps_DDRM.setIdentity(Q_k);
CommonOps_DDRM.multAddTransB(-gamma, v, v, Q_k);
CommonOps_DDRM.mult(Q_k, A_small, A_mod);
// save the results
CommonOps_DDRM.insert(A_mod, QR, i, i);
CommonOps_DDRM.insert(v, QR, i, i);
QR.unsafe_set(i, i, -tau * max);
// save gamma for recomputing Q later on
gammas[i] = gamma;
}
}
}