public virtual void invert(FMatrixRBlock A_inv)
{
FMatrixRBlock T = decomposer.getT(null);
if (A_inv.numRows != T.numRows || A_inv.numCols != T.numCols)
{
throw new ArgumentException("Unexpected number or rows and/or columns");
}
if (temp == null || temp.Length < blockLength * blockLength)
{
temp = new float[blockLength * blockLength];
}
// zero the upper triangular portion of A_inv
MatrixOps_FDRB.zeroTriangle(true, A_inv);
FSubmatrixD1 L = new FSubmatrixD1(T);
FSubmatrixD1 B = new FSubmatrixD1(A_inv);
// invert L from cholesky decomposition and write the solution into the lower
// triangular portion of A_inv
// B = inv(L)
TriangularSolver_FDRB.invert(blockLength, false, L, B, temp);
// B = L^-T * B
// todo could speed up by taking advantage of B being lower triangular
// todo take advantage of symmetry
TriangularSolver_FDRB.solveL(blockLength, L, B, true);
}
private bool decomposeLower()
{
int blockLength = T.blockLength;
subA.set(T);
subB.set(T);
subC.set(T);
for (int i = 0; i < T.numCols; i += blockLength)
{
int widthA = Math.Min(blockLength, T.numCols - i);
subA.col0 = i;
subA.col1 = i + widthA;
subA.row0 = subA.col0;
subA.row1 = subA.col1;
subB.col0 = i;
subB.col1 = i + widthA;
subB.row0 = i + widthA;
subB.row1 = T.numRows;
subC.col0 = i + widthA;
subC.col1 = T.numRows;
subC.row0 = i + widthA;
subC.row1 = T.numRows;
// cholesky on inner block A
if (!InnerCholesky_FDRB.lower(subA))
{
return(false);
}
// on the last block these operations are not needed.
if (widthA == blockLength)
{
// B = L^-1 B
TriangularSolver_FDRB.solveBlock(blockLength, false, subA, subB, false, true);
// C = C - B * B^T
InnerRankUpdate_FDRB.symmRankNMinus_L(blockLength, subC, subB);
}
}
MatrixOps_FDRB.zeroTriangle(true, T);
return(true);
}
public virtual /**/ double quality()
{
return(SpecializedOps_FDRM.qualityTriangular(decomposer.getT(null)));
}
/**
* If X == null then the solution is written into B. Otherwise the solution is copied
* from B into X.
*/
public virtual void solve(FMatrixRBlock B, FMatrixRBlock X)
{
if (B.blockLength != blockLength)
{
throw new ArgumentException("Unexpected blocklength in B.");
}
FSubmatrixD1 L = new FSubmatrixD1(decomposer.getT(null));
if (X != null)
{
if (X.blockLength != blockLength)
{
throw new ArgumentException("Unexpected blocklength in X.");
}
if (X.numRows != L.col1)
{
throw new ArgumentException("Not enough rows in X");
}
}
if (B.numRows != L.col1)
{
throw new ArgumentException("Not enough rows in B");
}
// L * L^T*X = B
// Solve for Y: L*Y = B
TriangularSolver_FDRB.solve(blockLength, false, L, new FSubmatrixD1(B), false);
// L^T * X = Y
TriangularSolver_FDRB.solve(blockLength, false, L, new FSubmatrixD1(B), true);
if (X != null)
{
// copy the solution from B into X
MatrixOps_FDRB.extractAligned(B, X);
}
}
public virtual /**/ double quality()
{
return(SpecializedOps_FDRM.qualityTriangular(decomposer.getQR()));
}
public virtual void solve(FMatrixRBlock B, FMatrixRBlock X)
{
if (B.numCols != X.numCols)
{
throw new ArgumentException("Columns of B and X do not match");
}
if (QR.numCols != X.numRows)
{
throw new ArgumentException("Rows in X do not match the columns in A");
}
if (QR.numRows != B.numRows)
{
throw new ArgumentException("Rows in B do not match the rows in A.");
}
if (B.blockLength != QR.blockLength || X.blockLength != QR.blockLength)
{
throw new ArgumentException("All matrices must have the same block length.");
}
// The system being solved for can be described as:
// Q*R*X = B
// First apply householder reflectors to B
// Y = Q^T*B
decomposer.applyQTran(B);
// Second solve for Y using the upper triangle matrix R and the just computed Y
// X = R^-1 * Y
MatrixOps_FDRB.extractAligned(B, X);
// extract a block aligned matrix
int M = Math.Min(QR.numRows, QR.numCols);
TriangularSolver_FDRB.solve(QR.blockLength, true,
new FSubmatrixD1(QR, 0, M, 0, M), new FSubmatrixD1(X), false);
}
/**
* Invert by solving for against an identity matrix.
*
* @param A_inv Where the inverted matrix saved. Modified.
*/
public virtual void invert(FMatrixRBlock A_inv)
{
int M = Math.Min(QR.numRows, QR.numCols);
if (A_inv.numRows != M || A_inv.numCols != M)
{
throw new ArgumentException("A_inv must be square an have dimension " + M);
}
// Solve for A^-1
// Q*R*A^-1 = I
// Apply householder reflectors to the identity matrix
// y = Q^T*I = Q^T
MatrixOps_FDRB.setIdentity(A_inv);
decomposer.applyQTran(A_inv);
// Solve using upper triangular R matrix
// R*A^-1 = y
// A^-1 = R^-1*y
TriangularSolver_FDRB.solve(QR.blockLength, true,
new FSubmatrixD1(QR, 0, M, 0, M), new FSubmatrixD1(A_inv), false);
}
