/// <summary>
/// Returns the result of dividing each element by 'val':
/// <code>b[i,j] = a[i,j]/val</code>
/// </summary>
/// <param name="val">Divisor</param>
/// <returns>Matrix with its elements divided by the specified value.</returns>
/// <see cref="CommonOps_DDRM.divide(DMatrixD1, double)"/>
public override SimpleMatrixD divide(double val)
{
SimpleMatrixD ret = copy();
var rm = ret.getMatrix();
CommonOps_DDRM.divide(rm, val);
return(ret);
}
/**
* <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 creating 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 create random vectors.
* @return Array of N random orthogonal vectors of unit length.
*/
// is there a faster algorithm out there? This one is a bit sluggish
public static DMatrixRMaj[] span(int dimen, int numVectors, IMersenneTwister 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++)
{
// Console.WriteLine(" i = "+i);
DMatrixRMaj a = new DMatrixRMaj(dimen, 1);
DMatrixRMaj r = null;
for (int j = 0; j < i; j++)
{
// Console.WriteLine("j = "+j);
if (j == 0)
{
r = RandomMatrices_DDRM.rectangle(dimen, 1, -1, 1, rand);
}
// find a vector that is normal to vector j
// u[i] = (1/2)*(r + Q[j]*r)
a.set(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 InvalidOperationException("Failed sanity check");
}
CommonOps_DDRM.divide(r, val);
}
u[i] = r;
}
return(u);
}
/**
* This method computes the eigen vector with the largest eigen value by using the
* direct power method. This technique is the easiest to implement, but the slowest to converge.
* Works only if all the eigenvalues are real.
*
* @param A The matrix. Not modified.
* @return If it converged or not.
*/
public bool computeDirect(DMatrixRMaj A)
{
initPower(A);
bool converged = false;
for (int i = 0; i < maxIterations && !converged; i++)
{
// q0.print();
CommonOps_DDRM.mult(A, q0, q1);
double s = NormOps_DDRM.normPInf(q1);
CommonOps_DDRM.divide(q1, s, q2);
converged = checkConverged(A);
}
return(converged);
}
/**
* Computes the most dominant eigen vector of A using an inverted shifted matrix.
* The inverted shifted matrix is defined as <b>B = (A - αI)<sup>-1</sup></b> and
* can converge faster if α is chosen wisely.
*
* @param A An invertible square matrix matrix.
* @param alpha Shifting factor.
* @return If it converged or not.
*/
public bool computeShiftInvert(DMatrixRMaj A, double alpha)
{
initPower(A);
LinearSolverDense <DMatrixRMaj> solver = LinearSolverFactory_DDRM.linear(A.numCols);
SpecializedOps_DDRM.addIdentity(A, B, -alpha);
solver.setA(B);
bool converged = false;
for (int i = 0; i < maxIterations && !converged; i++)
{
solver.solve(q0, q1);
double s = NormOps_DDRM.normPInf(q1);
CommonOps_DDRM.divide(q1, s, q2);
converged = checkConverged(A);
}
return(converged);
}
public void divide(Matrix A, double val, Matrix output)
{
CommonOps_DDRM.divide((DMatrixRMaj)A, (double)val, (DMatrixRMaj)output);
}
/**
* 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;
}
}
}
