public /**/ double quality()
{
return(SpecializedOps_ZDRM.qualityTriangular(LU));
}
/**
* a specialized version of solve that avoid additional checks that are not needed.
*/
public void _solveVectorInternal(double[] vv)
{
// Solve L*Y = B
solveL(vv);
// Solve U*X = Y;
TriangularSolver_ZDRM.solveU(dataLU, vv, n);
}
public override /**/ double quality()
{
return(SpecializedOps_ZDRM.qualityTriangular(R));
}
/**
* Solves for X using the QR decomposition.
*
* @param B A matrix that is n by m. Not modified.
* @param X An n by m matrix where the solution is written to. Modified.
*/
//@Override
public override void solve(ZMatrixRMaj B, ZMatrixRMaj X)
{
if (X.numRows != numCols)
{
throw new ArgumentException("Unexpected dimensions for X: X rows = " + X.numRows + " expected = " +
numCols);
}
else if (B.numRows != numRows || B.numCols != X.numCols)
{
throw new ArgumentException("Unexpected dimensions for B");
}
int BnumCols = B.numCols;
// solve each column one by one
for (int colB = 0; colB < BnumCols; colB++)
{
// make a copy of this column in the vector
for (int i = 0; i < numRows; i++)
{
int indexB = (i * BnumCols + colB) * 2;
a.data[i * 2] = B.data[indexB];
a.data[i * 2 + 1] = B.data[indexB + 1];
}
// Solve Qa=b
// a = Q'b
// a = Q_{n-1}...Q_2*Q_1*b
//
// Q_n*b = (I-gamma*u*u^T)*b = b - u*(gamma*U^T*b)
for (int n = 0; n < numCols; n++)
{
double[] u = QR[n];
double realVV = u[n * 2];
double imagVV = u[n * 2 + 1];
u[n * 2] = 1;
u[n * 2 + 1] = 0;
QrHelperFunctions_ZDRM.rank1UpdateMultR(a, u, 0, gammas[n], 0, n, numRows, temp.data);
u[n * 2] = realVV;
u[n * 2 + 1] = imagVV;
}
// solve for Rx = b using the standard upper triangular solver
TriangularSolver_ZDRM.solveU(R.data, a.data, numCols);
// save the results
for (int i = 0; i < numCols; i++)
{
int indexB = (i * BnumCols + colB) * 2;
X.data[indexB] = a.data[i * 2];
X.data[indexB + 1] = a.data[i * 2 + 1];
}
}
}
/**
* Used internally to find the solution to a single column vector.
*/
private void solveInternalL()
{
// This takes advantage of the diagonal elements always being real numbers
// solve L*y=b storing y in x
TriangularSolver_ZDRM.solveL_diagReal(t, vv, n);
// solve L^T*x=y
TriangularSolver_ZDRM.solveConjTranL_diagReal(t, vv, n);
}
/**
* Sets the matrix to the inverse using a lower triangular matrix.
*/
public void setToInverseL(double[] a)
{
// the more direct method which takes full advantage of the sparsity of the data structures proved to
// be difficult to get right due to the conjugates and reordering.
// See comparable real number code for an example.
for (int col = 0; col < n; col++)
{
Arrays.Fill(vv, 0);
vv[col * 2] = 1;
TriangularSolver_ZDRM.solveL_diagReal(t, vv, n);
TriangularSolver_ZDRM.solveConjTranL_diagReal(t, vv, n);
for (int i = 0; i < n; i++)
{
a[(i * numCols + col) * 2] = vv[i * 2];
a[(i * numCols + col) * 2 + 1] = vv[i * 2 + 1];
}
}
// NOTE: If you want to make inverse faster take advantage of the sparsity
}
public override /**/ double quality()
{
return(SpecializedOps_ZDRM.qualityTriangular(R));
}
/**
* Solves for X using the QR decomposition.
*
* @param B A matrix that is n by m. Not modified.
* @param X An n by m matrix where the solution is written to. Modified.
*/
//@Override
public override void solve(ZMatrixRMaj B, ZMatrixRMaj 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;
Y.reshape(numRows, 1);
Z.reshape(numRows, 1);
// solve each column one by one
for (int colB = 0; colB < BnumCols; colB++)
{
// make a copy of this column in the vector
for (int i = 0; i < numRows; i++)
{
int indexB = B.getIndex(i, colB);
Y.data[i * 2] = B.data[indexB];
Y.data[i * 2 + 1] = B.data[indexB + 1];
}
// Solve Qa=b
// a = Q'b
CommonOps_ZDRM.mult(Qt, Y, Z);
// solve for Rx = b using the standard upper triangular solver
TriangularSolver_ZDRM.solveU(R.data, Z.data, numCols);
// save the results
for (int i = 0; i < numCols; i++)
{
X.set(i, colB, Z.data[i * 2], Z.data[i * 2 + 1]);
}
}
}
public override /**/ double quality()
{
// even those it is transposed the diagonal elements are at the same
// elements
return(SpecializedOps_ZDRM.qualityTriangular(QR));
}
/**
* Solves for X using the QR decomposition.
*
* @param B A matrix that is n by m. Not modified.
* @param X An n by m matrix where the solution is written to. Modified.
*/
//@Override
public override void solve(ZMatrixRMaj B, ZMatrixRMaj X)
{
if (X.numRows != numCols)
{
throw new ArgumentException("Unexpected dimensions for X: X rows = " + X.numRows + " expected = " +
numCols);
}
else if (B.numRows != numRows || B.numCols != X.numCols)
{
throw new ArgumentException("Unexpected dimensions for B");
}
U = decomposer.getR(U, true);
double[] gammas = decomposer.getGammas();
double[] dataQR = QR.data;
int BnumCols = B.numCols;
// solve each column one by one
for (int colB = 0; colB < BnumCols; colB++)
{
// make a copy of this column in the vector
for (int i = 0; i < numRows; i++)
{
int indexB = (i * BnumCols + colB) * 2;
a[i * 2] = B.data[indexB];
a[i * 2 + 1] = B.data[indexB + 1];
}
// Solve Qa=b
// a = Q'b
// a = Q_{n-1}...Q_2*Q_1*b
//
// Q_n*b = (I-gamma*u*u^H)*b = b - u*(gamma*U^H*b)
for (int n = 0; n < numCols; n++)
{
int indexU = (n * numRows + n + 1) * 2;
double realUb = a[n * 2];
double imagUb = a[n * 2 + 1];
// U^H*b
for (int i = n + 1; i < numRows; i++)
{
double realU = dataQR[indexU++];
double imagU = -dataQR[indexU++];
double realB = a[i * 2];
double imagB = a[i * 2 + 1];
realUb += realU * realB - imagU * imagB;
imagUb += realU * imagB + imagU * realB;
}
// gamma*U^T*b
realUb *= gammas[n];
imagUb *= gammas[n];
a[n * 2] -= realUb;
a[n * 2 + 1] -= imagUb;
indexU = (n * numRows + n + 1) * 2;
for (int i = n + 1; i < numRows; i++)
{
double realU = dataQR[indexU++];
double imagU = dataQR[indexU++];
a[i * 2] -= realU * realUb - imagU * imagUb;
a[i * 2 + 1] -= realU * imagUb + imagU * realUb;
}
}
// solve for Rx = b using the standard upper triangular solver
TriangularSolver_ZDRM.solveU(U.data, a, numCols);
// save the results
for (int i = 0; i < numCols; i++)
{
int indexX = (i * X.numCols + colB) * 2;
X.data[indexX] = a[i * 2];
X.data[indexX + 1] = a[i * 2 + 1];
}
}
}
public override /**/ double quality()
{
return(SpecializedOps_ZDRM.qualityTriangular(QR));
}
/**
* Solves for X using the QR decomposition.
*
* @param B A matrix that is n by m. Not modified.
* @param X An n by m matrix where the solution is writen to. Modified.
*/
//@Override
public override void solve(ZMatrixRMaj B, ZMatrixRMaj 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;
// solve each column one by one
for (int colB = 0; colB < BnumCols; colB++)
{
// make a copy of this column in the vector
for (int i = 0; i < numRows; i++)
{
int indexB = (i * BnumCols + colB) * 2;
a[i * 2] = B.data[indexB];
a[i * 2 + 1] = B.data[indexB + 1];
}
// Solve Qa=b
// a = Q'b
// a = Q_{n-1}...Q_2*Q_1*b
//
// Q_n*b = (I-gamma*u*u^H)*b = b - u*(gamma*U^H*b)
for (int n = 0; n < numCols; n++)
{
u[n * 2] = 1;
u[n * 2 + 1] = 0;
double realUb = a[2 * n];
double imagUb = a[2 * n + 1];
// U^H*b
for (int i = n + 1; i < numRows; i++)
{
int indexQR = (i * QR.numCols + n) * 2;
double realU = u[i * 2] = QR.data[indexQR];
double imagU = u[i * 2 + 1] = QR.data[indexQR + 1];
double realB = a[i * 2];
double imagB = a[i * 2 + 1];
realUb += realU * realB + imagU * imagB;
imagUb += realU * imagB - imagU * realB;
}
// gamma*U^H*b
realUb *= gammas[n];
imagUb *= gammas[n];
for (int i = n; i < numRows; i++)
{
double realU = u[i * 2];
double imagU = u[i * 2 + 1];
a[i * 2] -= realU * realUb - imagU * imagUb;
a[i * 2 + 1] -= realU * imagUb + imagU * realUb;
}
}
// solve for Rx = b using the standard upper triangular solver
TriangularSolver_ZDRM.solveU(QR.data, a, numCols);
// save the results
for (int i = 0; i < numCols; i++)
{
int indexX = (i * X.numCols + colB) * 2;
X.data[indexX] = a[i * 2];
X.data[indexX + 1] = a[i * 2 + 1];
}
}
}
