public static double quality(DMatrixRMaj orig, DMatrixRMaj U, DMatrixRMaj W, DMatrixRMaj Vt)
{
// foundA = U*W*Vt
DMatrixRMaj UW = new DMatrixRMaj(U.numRows, W.numCols);
CommonOps_DDRM.mult(U, W, UW);
DMatrixRMaj foundA = new DMatrixRMaj(UW.numRows, Vt.numCols);
CommonOps_DDRM.mult(UW, Vt, foundA);
double normA = NormOps_DDRM.normF(foundA);
return(SpecializedOps_DDRM.diffNormF(orig, foundA) / normA);
}
/**
* <p>
* Creates a reflector from the provided vector.<br>
* <br>
* Q = I - γ u u<sup>T</sup><br>
* γ = 2/||u||<sup>2</sup>
* </p>
*
* <p>
* In practice {@link VectorVectorMult_DDRM#householder(double, DMatrixD1, DMatrixD1, DMatrixD1)} multHouseholder}
* should be used for performance reasons since there is no need to calculate Q explicitly.
* </p>
*
* @param u A vector. Not modified.
* @return An orthogonal reflector.
*/
public static DMatrixRMaj createReflector(DMatrix1Row u)
{
if (!MatrixFeatures_DDRM.isVector(u))
{
throw new ArgumentException("u must be a vector");
}
double norm = NormOps_DDRM.fastNormF(u);
double gamma = -2.0 / (norm * norm);
DMatrixRMaj Q = CommonOps_DDRM.identity(u.NumElements);
CommonOps_DDRM.multAddTransB(gamma, u, u, Q);
return(Q);
}
/**
* <p>
* Creates a randomly generated set of orthonormal vectors. At most it can generate the same
* number of vectors as the dimension of the vectors.
* </p>
*
* <p>
* This is done by creatingJava.Util.Random vectors then ensuring that they are orthogonal
* to all the ones previously created with reflectors.
* </p>
*
* <p>
* NOTE: This employs a brute force O(N<sup>3</sup>) algorithm.
* </p>
*
* @param dimen dimension of the space which the vectors will span.
* @param numVectors How many vectors it should generate.
* @param rand Used to createJava.Util.Random vectors.
* @return Array of NJava.Util.Random orthogonal vectors of unit Count().
*/
// is there a faster algorithm out there? This one is a bit sluggish
public static DMatrixRMaj[] span(int dimen, int numVectors, Java.Util.Random rand)
{
if (dimen < numVectors)
{
throw new ArgumentException("The number of vectors must be less than or equal to the dimension");
}
DMatrixRMaj[] u = new DMatrixRMaj[numVectors];
u[0] = RandomMatrices_DDRM.rectangle(dimen, 1, -1, 1, rand);
NormOps_DDRM.normalizeF(u[0]);
for (int i = 1; i < numVectors; i++)
{
// System.out.println(" i = "+i);
DMatrixRMaj a = new DMatrixRMaj(dimen, 1);
DMatrixRMaj r = RandomMatrices_DDRM.rectangle(dimen, 1, -1, 1, rand);
for (int j = 0; j < i; j++)
{
// find a vector that is normal to vector j
// u[i] = (1/2)*(r + Q[j]*r)
a.setTo(r);
VectorVectorMult_DDRM.householder(-2.0, u[j], r, a);
CommonOps_DDRM.add(r, a, a);
CommonOps_DDRM.scale(0.5, a);
// UtilEjml.print(a);
DMatrixRMaj t = a;
a = r;
r = t;
// normalize it so it doesn't get too small
double val = NormOps_DDRM.normF(r);
if (val == 0 || Double.IsNaN(val) || Double.IsInfinity(val))
{
throw new SystemException("Failed sanity check");
}
CommonOps_DDRM.divide(r, val);
}
u[i] = r;
}
return(u);
}
/**
* <p>
* Computes the F norm of the difference between the two Matrices:<br>
* <br>
* Sqrt{∑<sub>i=1:m</sub> ∑<sub>j=1:n</sub> ( a<sub>ij</sub> - b<sub>ij</sub>)<sup>2</sup>}
* </p>
* <p>
* This is often used as a cost function.
* </p>
*
* @param a m by n matrix. Not modified.
* @param b m by n matrix. Not modified.
* @return The F normal of the difference matrix.
* @see NormOps_DDRM#fastNormF
*/
public static double diffNormF(DMatrixD1 a, DMatrixD1 b)
{
if (a.numRows != b.numRows || a.numCols != b.numCols)
{
throw new ArgumentException("Both matrices must have the same shape.");
}
int size = a.NumElements;
DMatrixRMaj diff = new DMatrixRMaj(size, 1);
for (int i = 0; i < size; i++)
{
diff.set(i, b.get(i) - a.get(i));
}
return(NormOps_DDRM.normF(diff));
}
public double normF(Matrix A)
{
return(NormOps_DDRM.normF((DMatrixRMaj)A));
}
