/**
* Writes the lower triangular matrix into the specified matrix.
*
* @param lower Where the lower triangular matrix is written to.
*/
public virtual DMatrixRMaj getLower(DMatrixRMaj lower)
{
int numRows = LU.numRows;
int numCols = LU.numRows < LU.numCols ? LU.numRows : LU.numCols;
lower = UtilDecompositons_DDRM.checkZerosUT(lower, numRows, numCols);
for (int i = 0; i < numCols; i++)
{
lower.unsafe_set(i, i, 1.0);
for (int j = 0; j < i; j++)
{
lower.unsafe_set(i, j, LU.unsafe_get(i, j));
}
}
if (numRows > numCols)
{
for (int i = numCols; i < numRows; i++)
{
for (int j = 0; j < numCols; j++)
{
lower.unsafe_set(i, j, LU.unsafe_get(i, j));
}
}
}
return(lower);
}
public virtual DMatrixRMaj getT(DMatrixRMaj T)
{
// write the values to T
if (lower)
{
T = UtilDecompositons_DDRM.checkZerosUT(T, n, n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j <= i; j++)
{
T.unsafe_set(i, j, this.T.unsafe_get(i, j));
}
}
}
else
{
T = UtilDecompositons_DDRM.checkZerosLT(T, n, n);
for (int i = 0; i < n; i++)
{
for (int j = i; j < n; j++)
{
T.unsafe_set(i, j, this.T.unsafe_get(i, j));
}
}
}
return(T);
}
/**
* An orthogonal matrix that has the following property: H = Q<sup>T</sup>AQ
*
* @param Q If not null then the results will be stored here. Otherwise a new matrix will be created.
* @return The extracted Q matrix.
*/
public DMatrixRMaj getQ(DMatrixRMaj Q)
{
Q = UtilDecompositons_DDRM.checkIdentity(Q, N, N);
for (int j = N - 2; j >= 0; j--)
{
u[j + 1] = 1;
for (int i = j + 2; i < N; i++)
{
u[i] = QH.get(i, j);
}
QrHelperFunctions_DDRM.rank1UpdateMultR(Q, u, gammas[j], j + 1, j + 1, N, b);
}
return(Q);
}
/**
* An upper Hessenberg matrix from the decomposition.
*
* @param H If not null then the results will be stored here. Otherwise a new matrix will be created.
* @return The extracted H matrix.
*/
public DMatrixRMaj getH(DMatrixRMaj H)
{
H = UtilDecompositons_DDRM.checkZeros(H, N, N);
// copy the first row
Array.Copy(QH.data, 0, H.data, 0, N);
for (int i = 1; i < N; i++)
{
for (int j = i - 1; j < N; j++)
{
H.set(i, j, QH.get(i, j));
}
}
return(H);
}
/**
* Writes the upper triangular matrix into the specified matrix.
*
* @param upper Where the upper triangular matrix is writen to.
*/
public virtual DMatrixRMaj getUpper(DMatrixRMaj upper)
{
int numRows = LU.numRows < LU.numCols ? LU.numRows : LU.numCols;
int numCols = LU.numCols;
upper = UtilDecompositons_DDRM.checkZerosLT(upper, numRows, numCols);
for (int i = 0; i < numRows; i++)
{
for (int j = i; j < numCols; j++)
{
upper.unsafe_set(i, j, LU.unsafe_get(i, j));
}
}
return(upper);
}
/**
* Extracts the tridiagonal matrix found in the decomposition.
*
* @param T If not null then the results will be stored here. Otherwise a new matrix will be created.
* @return The extracted T matrix.
*/
public DMatrixRMaj getT(DMatrixRMaj T)
{
T = UtilDecompositons_DDRM.checkZeros(T, N, N);
T.data[0] = QT.data[0];
T.data[1] = QT.data[1];
for (int i = 1; i < N - 1; i++)
{
T.set(i, i, QT.get(i, i));
T.set(i, i + 1, QT.get(i, i + 1));
T.set(i, i - 1, QT.get(i - 1, i));
}
T.data[(N - 1) * N + N - 1] = QT.data[(N - 1) * N + N - 1];
T.data[(N - 1) * N + N - 2] = QT.data[(N - 2) * N + N - 1];
return(T);
}
/**
* An orthogonal matrix that has the following property: T = Q<sup>T</sup>AQ
*
* @param Q If not null then the results will be stored here. Otherwise a new matrix will be created.
* @return The extracted Q matrix.
*/
public DMatrixRMaj getQ(DMatrixRMaj Q)
{
Q = UtilDecompositons_DDRM.checkIdentity(Q, N, N);
for (int i = 0; i < N; i++)
{
w[i] = 0;
}
for (int j = N - 2; j >= 0; j--)
{
w[j + 1] = 1;
for (int i = j + 2; i < N; i++)
{
w[i] = QT.get(j, i);
}
QrHelperFunctions_DDRM.rank1UpdateMultR(Q, w, gammas[j + 1], j + 1, j + 1, N, b);
// Q.print();
}
return(Q);
}
/**
* Extracts the tridiagonal matrix found in the decomposition.
*
* @param T If not null then the results will be stored here. Otherwise a new matrix will be created.
* @return The extracted T matrix.
*/
//@Override
public DMatrixRMaj getT(DMatrixRMaj T)
{
T = UtilDecompositons_DDRM.checkZeros(T, N, N);
T.data[0] = QT.data[0];
for (int i = 1; i < N; i++)
{
T.set(i, i, QT.get(i, i));
double a = QT.get(i - 1, i);
T.set(i - 1, i, a);
T.set(i, i - 1, a);
}
if (N > 1)
{
T.data[(N - 1) * N + N - 1] = QT.data[(N - 1) * N + N - 1];
T.data[(N - 1) * N + N - 2] = QT.data[(N - 2) * N + N - 1];
}
return(T);
}
/**
* Computes the Q matrix from the imformation stored in the QR matrix. This
* operation requires about 4(m<sup>2</sup>n-mn<sup>2</sup>+n<sup>3</sup>/3) flops.
*
* @param Q The orthogonal Q matrix.
*/
public virtual DMatrixRMaj getQ(DMatrixRMaj Q, bool compact)
{
if (compact)
{
Q = UtilDecompositons_DDRM.checkIdentity(Q, numRows, minLength);
}
else
{
Q = UtilDecompositons_DDRM.checkIdentity(Q, numRows, numRows);
}
for (int j = minLength - 1; j >= 0; j--)
{
double[] u = dataQR[j];
double vv = u[j];
u[j] = 1;
QrHelperFunctions_DDRM.rank1UpdateMultR(Q, u, gammas[j], j, j, numRows, v);
u[j] = vv;
}
return(Q);
}
/**
* Returns an upper triangular matrix which is the R in the QR decomposition. If compact then the input
* expected to be size = [min(rows,cols) , numCols] otherwise size = [numRows,numCols].
*
* @param R Storage for upper triangular matrix.
* @param compact If true then a compact matrix is expected.
*/
public virtual DMatrixRMaj getR(DMatrixRMaj R, bool compact)
{
if (compact)
{
R = UtilDecompositons_DDRM.checkZerosLT(R, minLength, numCols);
}
else
{
R = UtilDecompositons_DDRM.checkZerosLT(R, numRows, numCols);
}
for (int j = 0; j < numCols; j++)
{
double[] colR = dataQR[j];
int l = Math.Min(j, numRows - 1);
for (int i = 0; i <= l; i++)
{
double val = colR[i];
R.set(i, j, val);
}
}
return(R);
}
/**
* An orthogonal matrix that has the following property: T = Q<sup>T</sup>AQ
*
* @param Q If not null then the results will be stored here. Otherwise a new matrix will be created.
* @return The extracted Q matrix.
*/
//@Override
public DMatrixRMaj getQ(DMatrixRMaj Q, bool transposed)
{
Q = UtilDecompositons_DDRM.checkIdentity(Q, N, N);
for (int i = 0; i < N; i++)
{
w[i] = 0;
}
if (transposed)
{
for (int j = N - 2; j >= 0; j--)
{
w[j + 1] = 1;
for (int i = j + 2; i < N; i++)
{
w[i] = QT.data[j * N + i];
}
QrHelperFunctions_DDRM.rank1UpdateMultL(Q, w, gammas[j + 1], j + 1, j + 1, N);
}
}
else
{
for (int j = N - 2; j >= 0; j--)
{
w[j + 1] = 1;
for (int i = j + 2; i < N; i++)
{
w[i] = QT.get(j, i);
}
QrHelperFunctions_DDRM.rank1UpdateMultR(Q, w, gammas[j + 1], j + 1, j + 1, N, b);
}
}
return(Q);
}
