/**
* <p>
* Solves upper triangular systems:<br>
* <br>
* B = R<sup>-1</sup> B<br>
* <br>
* </p>
*
* <p>Only the first B.numRows rows in R will be processed. Lower triangular elements are ignored.<p>
*
* <p> Reverse or forward substitution is used depending upon L being transposed or not. </p>
*
* @param blockLength
* @param R Upper triangular with dimensions m by m. Not modified.
* @param B A matrix with dimensions m by n. Solution is written into here. Modified.
* @param transR Is the triangular matrix transposed?
*/
public static void solveR(int blockLength,
DSubmatrixD1 R,
DSubmatrixD1 B,
bool transR)
{
int lengthR = B.row1 - B.row0;
if (R.getCols() != lengthR)
{
throw new ArgumentException("Number of columns in R must be equal to the number of rows in B");
}
else if (R.getRows() != lengthR)
{
throw new ArgumentException("Number of rows in R must be equal to the number of rows in B");
}
DSubmatrixD1 Y = new DSubmatrixD1(B.original);
DSubmatrixD1 Rinner = new DSubmatrixD1(R.original);
DSubmatrixD1 Binner = new DSubmatrixD1(B.original);
int startI, stepI;
if (transR)
{
startI = 0;
stepI = blockLength;
}
else
{
startI = lengthR - lengthR % blockLength;
if (startI == lengthR && lengthR >= blockLength)
{
startI -= blockLength;
}
stepI = -blockLength;
}
for (int i = startI;; i += stepI)
{
if (transR)
{
if (i >= lengthR)
{
break;
}
}
else
{
if (i < 0)
{
break;
}
}
// width and height of the inner T(i,i) block
int widthT = Math.Min(blockLength, lengthR - i);
Rinner.col0 = R.col0 + i;
Rinner.col1 = Rinner.col0 + widthT;
Rinner.row0 = R.row0 + i;
Rinner.row1 = Rinner.row0 + widthT;
Binner.col0 = B.col0;
Binner.col1 = B.col1;
Binner.row0 = B.row0 + i;
Binner.row1 = Binner.row0 + widthT;
// solve the top row block
// B(i,:) = T(i,i)^-1 Y(i,:)
solveBlock(blockLength, true, Rinner, Binner, transR, false);
bool updateY;
if (transR)
{
updateY = Rinner.row1 < R.row1;
}
else
{
updateY = Rinner.row0 > 0;
}
if (updateY)
{
// Y[i,:] = Y[i,:] - sum j=1:i-1 { T[i,j] B[j,i] }
// where i is the next block down
// The summation is a block inner product
if (transR)
{
Rinner.col0 = Rinner.col1;
Rinner.col1 = Math.Min(Rinner.col0 + blockLength, R.col1);
Rinner.row0 = R.row0;
//Rinner.row1 = Rinner.row1;
Binner.row0 = B.row0;
//Binner.row1 = Binner.row1;
Y.row0 = Binner.row1;
Y.row1 = Math.Min(Y.row0 + blockLength, B.row1);
}
else
{
Rinner.row1 = Rinner.row0;
Rinner.row0 = Rinner.row1 - blockLength;
Rinner.col1 = R.col1;
// Binner.row0 = Binner.row0;
Binner.row1 = B.row1;
Y.row0 = Binner.row0 - blockLength;
Y.row1 = Binner.row0;
}
// step through each block column
for (int k = B.col0; k < B.col1; k += blockLength)
{
Binner.col0 = k;
Binner.col1 = Math.Min(k + blockLength, B.col1);
Y.col0 = Binner.col0;
Y.col1 = Binner.col1;
if (transR)
{
// Y = Y - T^T * B
MatrixMult_DDRB.multMinusTransA(blockLength, Rinner, Binner, Y);
}
else
{
// Y = Y - T * B
MatrixMult_DDRB.multMinus(blockLength, Rinner, Binner, Y);
}
}
}
}
}
/**
* <p>
* Solves lower triangular systems:<br>
* <br>
* B = L<sup>-1</sup> B<br>
* <br>
* </p>
*
* <p> Reverse or forward substitution is used depending upon L being transposed or not. </p>
*
* @param blockLength
* @param L Lower triangular with dimensions m by m. Not modified.
* @param B A matrix with dimensions m by n. Solution is written into here. Modified.
* @param transL Is the triangular matrix transposed?
*/
public static void solveL(int blockLength,
DSubmatrixD1 L,
DSubmatrixD1 B,
bool transL)
{
DSubmatrixD1 Y = new DSubmatrixD1(B.original);
DSubmatrixD1 Linner = new DSubmatrixD1(L.original);
DSubmatrixD1 Binner = new DSubmatrixD1(B.original);
int lengthL = B.row1 - B.row0;
int startI, stepI;
if (transL)
{
startI = lengthL - lengthL % blockLength;
if (startI == lengthL && lengthL >= blockLength)
{
startI -= blockLength;
}
stepI = -blockLength;
}
else
{
startI = 0;
stepI = blockLength;
}
for (int i = startI;; i += stepI)
{
if (transL)
{
if (i < 0)
{
break;
}
}
else
{
if (i >= lengthL)
{
break;
}
}
// width and height of the inner T(i,i) block
int widthT = Math.Min(blockLength, lengthL - i);
Linner.col0 = L.col0 + i;
Linner.col1 = Linner.col0 + widthT;
Linner.row0 = L.row0 + i;
Linner.row1 = Linner.row0 + widthT;
Binner.col0 = B.col0;
Binner.col1 = B.col1;
Binner.row0 = B.row0 + i;
Binner.row1 = Binner.row0 + widthT;
// solve the top row block
// B(i,:) = T(i,i)^-1 Y(i,:)
solveBlock(blockLength, false, Linner, Binner, transL, false);
bool updateY;
if (transL)
{
updateY = Linner.row0 > 0;
}
else
{
updateY = Linner.row1 < L.row1;
}
if (updateY)
{
// Y[i,:] = Y[i,:] - sum j=1:i-1 { T[i,j] B[j,i] }
// where i is the next block down
// The summation is a block inner product
if (transL)
{
Linner.col1 = Linner.col0;
Linner.col0 = Linner.col1 - blockLength;
Linner.row1 = L.row1;
//Tinner.col1 = Tinner.col1;
// Binner.row0 = Binner.row0;
Binner.row1 = B.row1;
Y.row0 = Binner.row0 - blockLength;
Y.row1 = Binner.row0;
}
else
{
Linner.row0 = Linner.row1;
Linner.row1 = Math.Min(Linner.row0 + blockLength, L.row1);
Linner.col0 = L.col0;
//Tinner.col1 = Tinner.col1;
Binner.row0 = B.row0;
//Binner.row1 = Binner.row1;
Y.row0 = Binner.row1;
Y.row1 = Math.Min(Y.row0 + blockLength, B.row1);
}
// step through each block column
for (int k = B.col0; k < B.col1; k += blockLength)
{
Binner.col0 = k;
Binner.col1 = Math.Min(k + blockLength, B.col1);
Y.col0 = Binner.col0;
Y.col1 = Binner.col1;
if (transL)
{
// Y = Y - T^T * B
MatrixMult_DDRB.multMinusTransA(blockLength, Linner, Binner, Y);
}
else
{
// Y = Y - T * B
MatrixMult_DDRB.multMinus(blockLength, Linner, Binner, Y);
}
}
}
}
}