/**
* 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.
*/
//@Override
public ZMatrixRMaj getQ(ZMatrixRMaj Q, bool compact)
{
if (compact)
{
Q = UtilDecompositons_ZDRM.checkIdentity(Q, numRows, minLength);
}
else
{
Q = UtilDecompositons_ZDRM.checkIdentity(Q, numRows, numRows);
}
for (int j = minLength - 1; j >= 0; j--)
{
double[] u = dataQR[j];
double vvReal = u[j * 2];
double vvImag = u[j * 2 + 1];
u[j * 2] = 1;
u[j * 2 + 1] = 0;
double gammaReal = gammas[j];
QrHelperFunctions_ZDRM.rank1UpdateMultR(Q, u, 0, gammaReal, j, j, numRows, v);
u[j * 2] = vvReal;
u[j * 2 + 1] = vvImag;
}
return(Q);
}
/**
* Computes the Q matrix from the information 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.
*/
//@Override
public ZMatrixRMaj getQ(ZMatrixRMaj Q, bool compact)
{
if (compact)
{
Q = UtilDecompositons_ZDRM.checkIdentity(Q, numRows, minLength);
}
else
{
Q = UtilDecompositons_ZDRM.checkIdentity(Q, numRows, numRows);
}
// Unlike applyQ() this takes advantage of zeros in the identity matrix
// by not multiplying across all rows.
for (int j = minLength - 1; j >= 0; j--)
{
int diagIndex = (j * numRows + j) * 2;
double realBefore = QR.data[diagIndex];
double imagBefore = QR.data[diagIndex + 1];
QR.data[diagIndex] = 1;
QR.data[diagIndex + 1] = 0;
QrHelperFunctions_ZDRM.rank1UpdateMultR(Q, QR.data, j * numRows, gammas[j], j, j, numRows, v);
QR.data[diagIndex] = realBefore;
QR.data[diagIndex + 1] = imagBefore;
}
return(Q);
}
/**
* <p>
* Computes the householder vector "u" for the first column of submatrix j. Note this is
* a specialized householder for this problem. There is some protection against
* overfloaw and underflow.
* </p>
* <p>
* Q = I - γuu<sup>T</sup>
* </p>
* <p>
* This function finds the values of 'u' and 'γ'.
* </p>
*
* @param j Which submatrix to work off of.
*/
protected void householder(int j)
{
double[] u = dataQR[j];
// find the largest value in this column
// this is used to normalize the column and mitigate overflow/underflow
double max = QrHelperFunctions_ZDRM.findMax(u, j, numRows - j);
if (max == 0.0)
{
gamma = 0;
error = true;
}
else
{
// computes tau and gamma, and normalizes u by max
gamma = QrHelperFunctions_ZDRM.computeTauGammaAndDivide(j, numRows, u, max, tau);
// divide u by u_0
// double u_0 = u[j] + tau;
double real_u_0 = u[j * 2] + tau.real;
double imag_u_0 = u[j * 2 + 1] + tau.imaginary;
QrHelperFunctions_ZDRM.divideElements(j + 1, numRows, u, 0, real_u_0, imag_u_0);
tau.real *= max;
tau.imaginary *= max;
u[j * 2] = -tau.real;
u[j * 2 + 1] = -tau.imaginary;
}
gammas[j] = gamma;
}
/**
* <p>
* Computes the householder vector "u" for the first column of submatrix j. Note this is
* a specialized householder for this problem. There is some protection against
* overflow and underflow.
* </p>
* <p>
* Q = I - γuu<sup>H</sup>
* </p>
* <p>
* This function finds the values of 'u' and 'γ'.
* </p>
*
* @param j Which submatrix to work off of.
*/
protected void householder(int j)
{
int startQR = j * numRows;
int endQR = startQR + numRows;
startQR += j;
double max = QrHelperFunctions_ZDRM.findMax(QR.data, startQR, numRows - j);
if (max == 0.0)
{
gamma = 0;
error = true;
}
else
{
// computes tau and normalizes u by max
gamma = QrHelperFunctions_ZDRM.computeTauGammaAndDivide(startQR, endQR, QR.data, max, tau);
// divide u by u_0
double realU0 = QR.data[startQR * 2] + tau.real;
double imagU0 = QR.data[startQR * 2 + 1] + tau.imaginary;
QrHelperFunctions_ZDRM.divideElements(startQR + 1, endQR, QR.data, 0, realU0, imagU0);
tau.real *= max;
tau.imaginary *= max;
QR.data[startQR * 2] = -tau.real;
QR.data[startQR * 2 + 1] = -tau.imaginary;
}
gammas[j] = gamma;
}
/**
* A = Q<sup>H</sup>*A
*
* @param A Matrix that is being multiplied by Q<sup>T</sup>. Is modified.
*/
public void applyTranQ(ZMatrixRMaj A)
{
for (int j = 0; j < minLength; j++)
{
int diagIndex = (j * numRows + j) * 2;
double realBefore = QR.data[diagIndex];
double imagBefore = QR.data[diagIndex + 1];
QR.data[diagIndex] = 1;
QR.data[diagIndex + 1] = 0;
QrHelperFunctions_ZDRM.rank1UpdateMultR(A, QR.data, j * numRows, gammas[j], 0, j, numRows, v);
QR.data[diagIndex] = realBefore;
QR.data[diagIndex + 1] = imagBefore;
}
}
/**
* Computes the Q matrix from the information 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.
*/
//@Override
public ZMatrixRMaj getQ(ZMatrixRMaj Q, bool compact)
{
if (compact)
{
Q = UtilDecompositons_ZDRM.checkIdentity(Q, numRows, minLength);
}
else
{
Q = UtilDecompositons_ZDRM.checkIdentity(Q, numRows, numRows);
}
for (int j = minLength - 1; j >= 0; j--)
{
QrHelperFunctions_ZDRM.extractHouseholderColumn(QR, j, numRows, j, u, 0);
QrHelperFunctions_ZDRM.rank1UpdateMultR(Q, u, 0, gammas[j], j, j, numRows, v);
}
return(Q);
}
/**
* <p>
* Computes the householder vector "u" for the first column of submatrix j. Note this is
* a specialized householder for this problem. There is some protection against
* overflow and underflow.
* </p>
* <p>
* Q = I - γuu<sup>H</sup>
* </p>
* <p>
* This function finds the values of 'u' and 'γ'.
* </p>
*
* @param j Which submatrix to work off of.
*/
protected void householder(int j)
{
// find the element with the largest absolute value in the column and make a copy
double max = QrHelperFunctions_ZDRM.extractColumnAndMax(QR, j, numRows, j, u, 0);
if (max <= 0.0)
{
gammas[j] = 0;
error = true;
}
else
{
double gamma = QrHelperFunctions_ZDRM.computeTauGammaAndDivide(j, numRows, u, max, tau);
gammas[j] = gamma;
// divide u by u_0
double real_u_0 = u[j * 2] + tau.real;
double imag_u_0 = u[j * 2 + 1] + tau.imaginary;
QrHelperFunctions_ZDRM.divideElements(j + 1, numRows, u, 0, real_u_0, imag_u_0);
// write the reflector into the lower left column of the matrix
for (int i = j + 1; i < numRows; i++)
{
dataQR[(i * numCols + j) * 2] = u[i * 2];
dataQR[(i * numCols + j) * 2 + 1] = u[i * 2 + 1];
}
u[j * 2] = 1;
u[j * 2 + 1] = 0;
QrHelperFunctions_ZDRM.rank1UpdateMultR(QR, u, 0, gamma, j + 1, j, numRows, v);
// since the first element in the householder vector is known to be 1
// store the full upper hessenberg
if (j < numCols)
{
dataQR[(j * numCols + j) * 2] = -tau.real * max;
dataQR[(j * numCols + j) * 2 + 1] = -tau.imaginary * max;
}
}
}
/**
* A = Q*A
*
* @param A Matrix that is being multiplied by Q. Is modified.
*/
public void applyQ(ZMatrixRMaj A)
{
if (A.numRows != numRows)
{
throw new ArgumentException("A must have at least " + numRows + " rows.");
}
for (int j = minLength - 1; j >= 0; j--)
{
int diagIndex = (j * numRows + j) * 2;
double realBefore = QR.data[diagIndex];
double imagBefore = QR.data[diagIndex + 1];
QR.data[diagIndex] = 1;
QR.data[diagIndex + 1] = 0;
QrHelperFunctions_ZDRM.rank1UpdateMultR(A, QR.data, j * numRows, gammas[j], 0, j, numRows, v);
QR.data[diagIndex] = realBefore;
QR.data[diagIndex + 1] = imagBefore;
}
}
