/**
* <p>
* The condition number of a matrix is used to measure the sensitivity of the linear
* system <b>Ax=b</b>. A value near one indicates that it is a well conditioned matrix.<br>
* <br>
* κ<sub>p</sub> = ||A||<sub>p</sub>||A<sup>-1</sup>||<sub>p</sub>
* </p>
* <p>
* If the matrix is not square then the condition of either A<sup>T</sup>A or AA<sup>T</sup> is computed.
* <p>
* @param A The matrix.
* @param p p-norm
* @return The condition number.
*/
public static float conditionP(FMatrixRMaj A, float p)
{
if (p == 2)
{
return(conditionP2(A));
}
else if (A.numRows == A.numCols)
{
// square matrices are the typical case
FMatrixRMaj A_inv = new FMatrixRMaj(A.numRows, A.numCols);
if (!CommonOps_FDRM.invert(A, A_inv))
{
throw new ArgumentException("A can't be inverted.");
}
return(normP(A, p) * normP(A_inv, p));
}
else
{
FMatrixRMaj pinv = new FMatrixRMaj(A.numCols, A.numRows);
CommonOps_FDRM.pinv(A, pinv);
return(normP(A, p) * normP(pinv, p));
}
}
//@Override
public FMatrixRMaj getQ(FMatrixRMaj Q, bool compact)
{
int minLength = Math.Min(Ablock.numRows, Ablock.numCols);
if (Q == null)
{
if (compact)
{
Q = new FMatrixRMaj(Ablock.numRows, minLength);
CommonOps_FDRM.setIdentity(Q);
}
else
{
Q = new FMatrixRMaj(Ablock.numRows, Ablock.numRows);
CommonOps_FDRM.setIdentity(Q);
}
}
FMatrixRBlock Qblock = new FMatrixRBlock();
Qblock.numRows = Q.numRows;
Qblock.numCols = Q.numCols;
Qblock.blockLength = blockLength;
Qblock.data = Q.data;
((QRDecompositionHouseholder_FDRB)alg).getQ(Qblock, compact);
convertBlockToRow(Q.numRows, Q.numCols, Ablock.blockLength, Q.data);
return(Q);
}
/**
* <p>
* To decompose the matrix 'A' it must have full rank. 'A' is a 'm' by 'n' matrix.
* It requires about 2n*m<sup>2</sup>-2m<sup>2</sup>/3 flops.
* </p>
*
* <p>
* The matrix provided here can be of different
* dimension than the one specified in the constructor. It just has to be smaller than or equal
* to it.
* </p>
*/
public override bool decompose(FMatrixRMaj A)
{
setExpectedMaxSize(A.numRows, A.numCols);
convertToColumnMajor(A);
maxAbs = CommonOps_FDRM.elementMaxAbs(A);
// initialize pivot variables
setupPivotInfo();
// go through each column and perform the decomposition
for (int j = 0; j < minLength; j++)
{
if (j > 0)
{
updateNorms(j);
}
swapColumns(j);
// if its degenerate stop processing
if (!householderPivot(j))
{
break;
}
updateA(j);
rank = j + 1;
}
return(true);
}
/**
* <p>
* Returns true if the matrix is symmetric within the tolerance. Only square matrices can be
* symmetric.
* </p>
* <p>
* A matrix is symmetric if:<br>
* |a<sub>ij</sub> - a<sub>ji</sub>| ≤ tol
* </p>
*
* @param m A matrix. Not modified.
* @param tol Tolerance for how similar two elements need to be.
* @return true if it is symmetric and false if it is not.
*/
public static bool isSymmetric(FMatrixRMaj m, float tol)
{
if (m.numCols != m.numRows)
{
return(false);
}
float max = CommonOps_FDRM.elementMaxAbs(m);
for (int i = 0; i < m.numRows; i++)
{
for (int j = 0; j < i; j++)
{
float a = m.get(i, j) / max;
float b = m.get(j, i) / max;
float diff = Math.Abs(a - b);
if (!(diff <= tol))
{
return(false);
}
}
}
return(true);
}
/**
* Returns the orthogonal V matrix.
*
* @param V If not null then the results will be stored here. Otherwise a new matrix will be created.
* @return The extracted Q matrix.
*/
public virtual FMatrixRMaj getV(FMatrixRMaj V, bool transpose, bool compact)
{
V = handleV(V, transpose, compact, m, n, min);
CommonOps_FDRM.setIdentity(V);
// UBV.print();
// todo the very first multiplication can be avoided by setting to the rank1update output
for (int j = min - 1; j >= 0; j--)
{
u[j + 1] = 1;
for (int i = j + 2; i < n; i++)
{
u[i] = UBV.get(j, i);
}
if (transpose)
{
QrHelperFunctions_FDRM.rank1UpdateMultL(V, u, gammasV[j], j + 1, j + 1, n);
}
else
{
QrHelperFunctions_FDRM.rank1UpdateMultR(V, u, gammasV[j], j + 1, j + 1, n, this.b);
}
}
return(V);
}
public virtual FMatrixRMaj getU(FMatrixRMaj U, bool transpose, bool compact)
{
U = BidiagonalDecompositionRow_FDRM.handleU(U, false, compact, m, n, min);
if (compact)
{
// U = Q*U1
FMatrixRMaj Q1 = decompQRP.getQ(null, true);
FMatrixRMaj U1 = decompBi.getU(null, false, true);
CommonOps_FDRM.mult(Q1, U1, U);
}
else
{
// U = [Q1*U1 Q2]
FMatrixRMaj Q = decompQRP.getQ(U, false);
FMatrixRMaj U1 = decompBi.getU(null, false, true);
FMatrixRMaj Q1 = CommonOps_FDRM.extract(Q, 0, Q.numRows, 0, min);
FMatrixRMaj tmp = new FMatrixRMaj(Q1.numRows, U1.numCols);
CommonOps_FDRM.mult(Q1, U1, tmp);
CommonOps_FDRM.insert(tmp, Q, 0, 0);
}
if (transpose)
{
CommonOps_FDRM.transpose(U);
}
return(U);
}
//@Override
public FMatrixRMaj getV(FMatrixRMaj V, bool transpose)
{
if (!prefComputeV)
{
throw new ArgumentException("As requested V was not computed.");
}
if (transpose)
{
if (V == null)
{
return(Vt);
}
V.set(Vt);
}
else
{
if (V == null)
{
V = new FMatrixRMaj(Vt.numCols, Vt.numRows);
}
else
{
V.reshape(Vt.numCols, Vt.numRows);
}
CommonOps_FDRM.transpose(Vt, V);
}
return(V);
}
/**
* Returns the orthogonal U matrix.
*
* @param U If not null then the results will be stored here. Otherwise a new matrix will be created.
* @return The extracted Q matrix.
*/
public virtual FMatrixRMaj getU(FMatrixRMaj U, bool transpose, bool compact)
{
U = handleU(U, transpose, compact, m, n, min);
CommonOps_FDRM.setIdentity(U);
for (int i = 0; i < m; i++)
{
u[i] = 0;
}
for (int j = min - 1; j >= 0; j--)
{
u[j] = 1;
for (int i = j + 1; i < m; i++)
{
u[i] = UBV.get(i, j);
}
if (transpose)
{
QrHelperFunctions_FDRM.rank1UpdateMultL(U, u, gammasU[j], j, j, m);
}
else
{
QrHelperFunctions_FDRM.rank1UpdateMultR(U, u, gammasU[j], j, j, m, this.b);
}
}
return(U);
}
public virtual FMatrixRMaj getT(FMatrixRMaj T)
{
int N = Ablock.numRows;
if (T == null)
{
T = new FMatrixRMaj(N, N);
}
else
{
CommonOps_FDRM.fill(T, 0);
}
float[] diag = new float[N];
float[] off = new float[N];
((TridiagonalDecompositionHouseholder_FDRB)alg).getDiagonal(diag, off);
T.unsafe_set(0, 0, diag[0]);
for (int i = 1; i < N; i++)
{
T.unsafe_set(i, i, diag[i]);
T.unsafe_set(i, i - 1, off[i - 1]);
T.unsafe_set(i - 1, i, off[i - 1]);
}
return(T);
}
//@Override
public FMatrixRMaj getU(FMatrixRMaj U, bool transpose)
{
if (!prefComputeU)
{
throw new ArgumentException("As requested U was not computed.");
}
if (transpose)
{
if (U == null)
{
return(Ut);
}
U.set(Ut);
}
else
{
if (U == null)
{
U = new FMatrixRMaj(Ut.numCols, Ut.numRows);
}
else
{
U.reshape(Ut.numCols, Ut.numRows);
}
CommonOps_FDRM.transpose(Ut, U);
}
return(U);
}
/**
* <p>
* Computes a metric which measures the the quality of an eigen value decomposition. If a
* value is returned that is close to or smaller than 1e-15 then it is within machine precision.
* </p>
* <p>
* EVD quality is defined as:<br>
* <br>
* Quality = ||A*V - V*D|| / ||A*V||.
* </p>
*
* @param orig The original matrix. Not modified.
* @param eig EVD of the original matrix. Not modified.
* @return The quality of the decomposition.
*/
public static float quality(FMatrixRMaj orig, EigenDecomposition_F32 <FMatrixRMaj> eig)
{
FMatrixRMaj A = orig;
FMatrixRMaj V = EigenOps_FDRM.createMatrixV(eig);
FMatrixRMaj D = EigenOps_FDRM.createMatrixD(eig);
// L = A*V
FMatrixRMaj L = new FMatrixRMaj(A.numRows, V.numCols);
CommonOps_FDRM.mult(A, V, L);
// R = V*D
FMatrixRMaj R = new FMatrixRMaj(V.numRows, D.numCols);
CommonOps_FDRM.mult(V, D, R);
FMatrixRMaj diff = new FMatrixRMaj(L.numRows, L.numCols);
CommonOps_FDRM.subtract(L, R, diff);
float top = NormOps_FDRM.normF(diff);
float bottom = NormOps_FDRM.normF(L);
float error = top / bottom;
return(error);
}
/**
* <p>
* Element wise p-norm:<br>
* <br>
* norm = {∑<sub>i=1:m</sub> ∑<sub>j=1:n</sub> { |a<sub>ij</sub>|<sup>p</sup>}}<sup>1/p</sup>
* </p>
*
* <p>
* This is not the same as the induced p-norm used on matrices, but is the same as the vector p-norm.
* </p>
*
* @param A Matrix. Not modified.
* @param p p value.
* @return The norm's value.
*/
public static float elementP(FMatrix1Row A, float p)
{
if (p == 1)
{
return(CommonOps_FDRM.elementSumAbs(A));
}
if (p == 2)
{
return(normF(A));
}
else
{
float max = CommonOps_FDRM.elementMaxAbs(A);
if (max == 0.0f)
{
return(0.0f);
}
float total = 0;
int size = A.getNumElements();
for (int i = 0; i < size; i++)
{
float a = A.get(i) / max;
total += (float)Math.Pow(Math.Abs(a), p);
}
return(max * (float)Math.Pow(total, 1.0f / p));
}
}
/**
* <p>
* Computes W from the householder reflectors stored in the columns of the row block
* submatrix Y.
* </p>
*
* <p>
* Y = v<sup>(1)</sup><br>
* W = -β<sub>1</sub>v<sup>(1)</sup><br>
* for j=2:r<br>
* z = -β(I +WY<sup>T</sup>)v<sup>(j)</sup> <br>
* W = [W z]<br>
* Y = [Y v<sup>(j)</sup>]<br>
* end<br>
* <br>
* where v<sup>(.)</sup> are the house holder vectors, and r is the block length. Note that
* Y already contains the householder vectors so it does not need to be modified.
* </p>
*
* <p>
* Y and W are assumed to have the same number of rows and columns.
* </p>
*/
public static void computeW_row(int blockLength,
FSubmatrixD1 Y, FSubmatrixD1 W,
float[] beta, int betaIndex)
{
int heightY = Y.row1 - Y.row0;
CommonOps_FDRM.fill(W.original, 0);
// W = -beta*v(1)
BlockHouseHolder_FDRB.scale_row(blockLength, Y, W, 0, 1, -beta[betaIndex++]);
int min = Math.Min(heightY, W.col1 - W.col0);
// set up rest of the rows
for (int i = 1; i < min; i++)
{
// w=-beta*(I + W*Y^T)*u
float b = -beta[betaIndex++];
// w = w -beta*W*(Y^T*u)
for (int j = 0; j < i; j++)
{
float yv = BlockHouseHolder_FDRB.innerProdRow(blockLength, Y, i, Y, j, 1);
VectorOps_FDRB.add_row(blockLength, W, i, 1, W, j, b * yv, W, i, 1, Y.col1 - Y.col0);
}
//w=w -beta*u + stuff above
BlockHouseHolder_FDRB.add_row(blockLength, Y, i, b, W, i, 1, W, i, 1, Y.col1 - Y.col0);
}
}
public virtual FMatrixRBlock getT(FMatrixRBlock T)
{
if (T == null)
{
T = new FMatrixRBlock(A.numRows, A.numCols, A.blockLength);
}
else
{
if (T.numRows != A.numRows || T.numCols != A.numCols)
{
throw new ArgumentException("T must have the same dimensions as the input matrix");
}
CommonOps_FDRM.fill(T, 0);
}
T.set(0, 0, A.data[0]);
for (int i = 1; i < A.numRows; i++)
{
float d = A.get(i - 1, i);
T.set(i, i, A.get(i, i));
T.set(i - 1, i, d);
T.set(i, i - 1, d);
}
return(T);
}
/**
* <p>
* Checks to see if a matrix is orthogonal or isometric.
* </p>
*
* @param Q The matrix being tested. Not modified.
* @param tol Tolerance.
* @return True if it passes the test.
*/
public static bool isOrthogonal(FMatrixRMaj Q, float tol)
{
if (Q.numRows < Q.numCols)
{
throw new ArgumentException("The number of rows must be more than or equal to the number of columns");
}
FMatrixRMaj[] u = CommonOps_FDRM.columnsToVector(Q, null);
for (int i = 0; i < u.Length; i++)
{
FMatrixRMaj a = u[i];
for (int j = i + 1; j < u.Length; j++)
{
float val = VectorVectorMult_FDRM.innerProd(a, u[j]);
if (!(Math.Abs(val) <= tol))
{
return(false);
}
}
}
return(true);
}
private bool extractSeparate(int numCols)
{
if (!computeEigenValues())
{
return(false);
}
// ---- set up the helper to decompose the same tridiagonal matrix
// swap arrays instead of copying them to make it slightly faster
helper.reset(numCols);
diagSaved = helper.swapDiag(diagSaved);
offSaved = helper.swapOff(offSaved);
// extract the orthogonal from the similar transform
V = decomp.getQ(V, true);
// tell eigenvector algorithm to update this matrix as it computes the rotators
vector.setQ(V);
// extract eigenvectors
if (!vector.process(-1, null, null, values))
{
return(false);
}
// the ordering of the eigenvalues might have changed
values = helper.copyEigenvalues(values);
// the V matrix contains the eigenvectors. Convert those into column vectors
eigenvectors = CommonOps_FDRM.rowsToVector(V, eigenvectors);
return(true);
}
/**
* <p>
* Creates a pivot matrix that exchanges the rows in a matrix:
* <br>
* A' = P*A<br>
* </p>
* <p>
* For example, if element 0 in 'pivots' is 2 then the first row in A' will be the 3rd row in A.
* </p>
*
* @param ret If null then a new matrix is declared otherwise the results are written to it. Is modified.
* @param pivots Specifies the new order of rows in a matrix.
* @param numPivots How many elements in pivots are being used.
* @param transposed If the transpose of the matrix is returned.
* @return A pivot matrix.
*/
public static FMatrixRMaj pivotMatrix(FMatrixRMaj ret, int[] pivots, int numPivots, bool transposed)
{
if (ret == null)
{
ret = new FMatrixRMaj(numPivots, numPivots);
}
else
{
if (ret.numCols != numPivots || ret.numRows != numPivots)
{
throw new ArgumentException("Unexpected matrix dimension");
}
CommonOps_FDRM.fill(ret, 0);
}
if (transposed)
{
for (int i = 0; i < numPivots; i++)
{
ret.set(pivots[i], i, 1);
}
}
else
{
for (int i = 0; i < numPivots; i++)
{
ret.set(i, pivots[i], 1);
}
}
return(ret);
}
public virtual bool setA(FMatrixRMaj A)
{
pinv.reshape(A.numCols, A.numRows, false);
if (!svd.decompose(A))
{
return(false);
}
svd.getU(U_t, true);
svd.getV(V, false);
float[] S = svd.getSingularValues();
int N = Math.Min(A.numRows, A.numCols);
// compute the threshold for singular values which are to be zeroed
float maxSingular = 0;
for (int i = 0; i < N; i++)
{
if (S[i] > maxSingular)
{
maxSingular = S[i];
}
}
float tau = threshold * Math.Max(A.numCols, A.numRows) * maxSingular;
// computer the pseudo inverse of A
if (maxSingular != 0.0f)
{
for (int i = 0; i < N; i++)
{
float s = S[i];
if (s < tau)
{
S[i] = 0;
}
else
{
S[i] = 1.0f / S[i];
}
}
}
// V*W
for (int i = 0; i < V.numRows; i++)
{
int index = i * V.numCols;
for (int j = 0; j < V.numCols; j++)
{
V.data[index++] *= S[j];
}
}
// V*W*U^T
CommonOps_FDRM.mult(V, U_t, pinv);
return(true);
}
public void minus(FMatrixRMaj A, /**/ float b, FMatrixRMaj output)
{
CommonOps_FDRM.subtract(A, b, output);
}
public void plus(FMatrixRMaj A, /**/ float b, FMatrixRMaj output)
{
CommonOps_FDRM.add(A, b, output);
}
/**
* Makes a draw on the distribution. The results are added to parameter 'x'
*/
public void next(FMatrixRMaj x)
{
for (int i = 0; i < r.numRows; i++)
{
r.set(i, 0, (float)rand.NextGaussian());
}
CommonOps_FDRM.multAdd(A, r, x);
}
/**
* <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.F_EPS.
* @return The null space.
*/
public static FMatrixRMaj nullSpace(SingularValueDecomposition_F32 <FMatrixRMaj> svd,
FMatrixRMaj nullSpace, float tol)
{
int N = svd.numberOfSingularValues();
float[] s = svd.getSingularValues();
FMatrixRMaj 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 FMatrixRMaj(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_FDRM.extract(V, i, i + 1, 0, V.numCols, nullSpace, count++, 0);
}
}
for (int i = N; i < svd.numCols(); i++)
{
CommonOps_FDRM.extract(V, i, i + 1, 0, V.numCols, nullSpace, count++, 0);
}
CommonOps_FDRM.transpose(nullSpace);
return(nullSpace);
}
/**
* Computes the p=∞ norm. If A is a matrix then the induced norm is computed.
*
* @param A Matrix or vector.
* @return The norm.
*/
public static float normPInf(FMatrixRMaj A)
{
if (MatrixFeatures_FDRM.isVector(A))
{
return(CommonOps_FDRM.elementMaxAbs(A));
}
else
{
return(inducedPInf(A));
}
}
/**
* Compute the A matrix from the Q and R matrices.
*
* @return The A matrix.
*/
public override FMatrixRMaj getA()
{
if (A.data.Length < numRows * numCols)
{
A = new FMatrixRMaj(numRows, numCols);
}
A.reshape(numRows, numCols, false);
CommonOps_FDRM.mult(Q, R, A);
return(A);
}
public static void invert(LinearSolverDense <FMatrixRMaj> solver, FMatrix1Row A, FMatrixRMaj A_inv)
{
if (A.numRows != A_inv.numRows || A.numCols != A_inv.numCols)
{
throw new ArgumentException("A and A_inv must have the same dimensions");
}
CommonOps_FDRM.setIdentity(A_inv);
solver.solve(A_inv, A_inv);
}
public override void invert(FMatrixRMaj A_inv)
{
if (A_inv.numCols != numRows || A_inv.numRows != numCols)
{
throw new ArgumentException("Unexpected dimensions for A_inv");
}
I.reshape(numRows, numRows);
CommonOps_FDRM.setIdentity(I);
solve(I, A_inv);
}
public override void solve(FMatrixRMaj B, FMatrixRMaj X)
{
if (X.numRows != numCols)
{
throw new ArgumentException("Unexpected dimensions for X");
}
else if (B.numRows != numRows || B.numCols != X.numCols)
{
throw new ArgumentException("Unexpected dimensions for B");
}
int BnumCols = B.numCols;
// get the pivots and transpose them
int[] pivots = decomposition.getColPivots();
// solve each column one by one
for (int colB = 0; colB < BnumCols; colB++)
{
x_basic.reshape(numRows, 1);
Y.reshape(numRows, 1);
// make a copy of this column in the vector
for (int i = 0; i < numRows; i++)
{
Y.data[i] = B.get(i, colB);
}
// Solve Q*a=b => a = Q'*b
CommonOps_FDRM.multTransA(Q, Y, x_basic);
// solve for Rx = b using the standard upper triangular solver
TriangularSolver_FDRM.solveU(R11.data, x_basic.data, rank);
// finish the basic solution by filling in zeros
x_basic.reshape(numCols, 1, true);
for (int i = rank; i < numCols; i++)
{
x_basic.data[i] = 0;
}
if (norm2Solution && rank < numCols)
{
upgradeSolution(x_basic);
}
// save the results
for (int i = 0; i < numCols; i++)
{
X.set(pivots[i], colB, x_basic.data[i]);
}
}
}
/**
* An alternative implementation of {@link #multTransA_small} that performs well on large
* matrices. There is a relative performance hit when used on small matrices.
*
* @param A A matrix that is m by n. Not modified.
* @param B A Vector that has length m. Not modified.
* @param C A column vector that has length n. Modified.
*/
public static void multTransA_reorder(FMatrix1Row A, FMatrixD1 B, FMatrixD1 C)
{
if (C.numCols != 1)
{
throw new MatrixDimensionException("C is not a column vector");
}
else if (C.numRows != A.numCols)
{
throw new MatrixDimensionException("C is not the expected length");
}
if (B.numRows == 1)
{
if (A.numRows != B.numCols)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else if (B.numCols == 1)
{
if (A.numRows != B.numRows)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else
{
throw new MatrixDimensionException("B is not a vector");
}
if (A.numRows == 0)
{
CommonOps_FDRM.fill(C, 0);
return;
}
float B_val = B.get(0);
for (int i = 0; i < A.numCols; i++)
{
C.set(i, A.get(i) * B_val);
}
int indexA = A.numCols;
for (int i = 1; i < A.numRows; i++)
{
B_val = B.get(i);
for (int j = 0; j < A.numCols; j++)
{
C.plus(j, A.get(indexA++) * B_val);
}
}
}
/**
* <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 FMatrixRMaj[] 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");
}
FMatrixRMaj[] u = new FMatrixRMaj[numVectors];
u[0] = RandomMatrices_FDRM.rectangle(dimen, 1, -1, 1, rand);
NormOps_FDRM.normalizeF(u[0]);
for (int i = 1; i < numVectors; i++)
{
// Console.WriteLine(" i = "+i);
FMatrixRMaj a = new FMatrixRMaj(dimen, 1);
FMatrixRMaj r = null;
for (int j = 0; j < i; j++)
{
// Console.WriteLine("j = "+j);
if (j == 0)
{
r = RandomMatrices_FDRM.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_FDRM.householder(-2.0f, u[j], r, a);
CommonOps_FDRM.add(r, a, a);
CommonOps_FDRM.scale(0.5f, a);
// UtilEjml.print(a);
FMatrixRMaj t = a;
a = r;
r = t;
// normalize it so it doesn't get too small
float val = NormOps_FDRM.normF(r);
if (val == 0 || float.IsNaN(val) || float.IsInfinity(val))
{
throw new InvalidOperationException("Failed sanity check");
}
CommonOps_FDRM.divide(r, val);
}
u[i] = r;
}
return(u);
}
/**
* Creates a new random symmetric matrix that will have the specified real eigenvalues.
*
* @param num Dimension of the resulting matrix.
* @param rand Random number generator.
* @param eigenvalues Set of real eigenvalues that the matrix will have.
* @return A random matrix with the specified eigenvalues.
*/
public static FMatrixRMaj symmetricWithEigenvalues(int num, IMersenneTwister rand, float[] eigenvalues)
{
FMatrixRMaj V = RandomMatrices_FDRM.orthogonal(num, num, rand);
FMatrixRMaj D = CommonOps_FDRM.diag(eigenvalues);
FMatrixRMaj temp = new FMatrixRMaj(num, num);
CommonOps_FDRM.mult(V, D, temp);
CommonOps_FDRM.multTransB(temp, V, D);
return(D);
}
/**
* <p>
* Performs a matrix vector multiply.<br>
* <br>
* c = A * b <br>
* and<br>
* c = A * b<sup>T</sup> <br>
* <br>
* c<sub>i</sub> = Sum{ j=1:n, a<sub>ij</sub> * b<sub>j</sub>}<br>
* <br>
* where A is a matrix, b is a column or transposed row vector, and c is a column vector.
* </p>
*
* @param A A matrix that is m by n. Not modified.
* @param B A vector that has length n. Not modified.
* @param C A column vector that has length m. Modified.
*/
public static void mult(FMatrix1Row A, FMatrixD1 B, FMatrixD1 C)
{
if (C.numCols != 1)
{
throw new MatrixDimensionException("C is not a column vector");
}
else if (C.numRows != A.numRows)
{
throw new MatrixDimensionException("C is not the expected length");
}
if (B.numRows == 1)
{
if (A.numCols != B.numCols)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else if (B.numCols == 1)
{
if (A.numCols != B.numRows)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else
{
throw new MatrixDimensionException("B is not a vector");
}
if (A.numCols == 0)
{
CommonOps_FDRM.fill(C, 0);
return;
}
int indexA = 0;
int cIndex = 0;
float b0 = B.get(0);
for (int i = 0; i < A.numRows; i++)
{
float total = A.get(indexA++) * b0;
for (int j = 1; j < A.numCols; j++)
{
total += A.get(indexA++) * B.get(j);
}
C.set(cIndex++, total);
}
}