/**
* An alternative implementation of {@link #multTransA_small} that performs well on large
* matrices. There is a relative performance hit when used on small matrices.
*
* @param A A matrix that is m by n. Not modified.
* @param B A Vector that has length m. Not modified.
* @param C A column vector that has length n. Modified.
*/
public static void multTransA_reorder(DMatrix1Row A, DMatrixD1 B, DMatrixD1 C)
{
if (C.numCols != 1)
{
throw new MatrixDimensionException("C is not a column vector");
}
else if (C.numRows != A.numCols)
{
throw new MatrixDimensionException("C is not the expected length");
}
if (B.numRows == 1)
{
if (A.numRows != B.numCols)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else if (B.numCols == 1)
{
if (A.numRows != B.numRows)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else
{
throw new MatrixDimensionException("B is not a vector");
}
if (A.numRows == 0)
{
CommonOps_DDRM.fill(C, 0);
return;
}
double B_val = B.get(0);
for (int i = 0; i < A.numCols; i++)
{
C.set(i, A.get(i) * B_val);
}
int indexA = A.numCols;
for (int i = 1; i < A.numRows; i++)
{
B_val = B.get(i);
for (int j = 0; j < A.numCols; j++)
{
C.plus(j, A.get(indexA++) * B_val);
}
}
}
/**
* <p>
* Performs a matrix vector multiply.<br>
* <br>
* c = A * b <br>
* and<br>
* c = A * b<sup>T</sup> <br>
* <br>
* c<sub>i</sub> = Sum{ j=1:n, a<sub>ij</sub> * b<sub>j</sub>}<br>
* <br>
* where A is a matrix, b is a column or transposed row vector, and c is a column vector.
* </p>
*
* @param A A matrix that is m by n. Not modified.
* @param B A vector that has length n. Not modified.
* @param C A column vector that has length m. Modified.
*/
public static void mult(DMatrix1Row A, DMatrixD1 B, DMatrixD1 C)
{
if (C.numCols != 1)
{
throw new MatrixDimensionException("C is not a column vector");
}
else if (C.numRows != A.numRows)
{
throw new MatrixDimensionException("C is not the expected length");
}
if (B.numRows == 1)
{
if (A.numCols != B.numCols)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else if (B.numCols == 1)
{
if (A.numCols != B.numRows)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else
{
throw new MatrixDimensionException("B is not a vector");
}
if (A.numCols == 0)
{
CommonOps_DDRM.fill(C, 0);
return;
}
int indexA = 0;
int cIndex = 0;
double b0 = B.get(0);
for (int i = 0; i < A.numRows; i++)
{
double total = A.get(indexA++) * b0;
for (int j = 1; j < A.numCols; j++)
{
total += A.get(indexA++) * B.get(j);
}
C.set(cIndex++, total);
}
}
/**
* <p>
* Multiplies a householder reflection against a vector:<br>
* <br>
* y = (I + γ u u<sup>T</sup>)x<br>
* </p>
* <p>
* The Householder reflection is used in some implementations of QR decomposition.
* </p>
*
* @param u A vector. Not modified.
* @param x a vector. Not modified.
* @param y Vector where the result are written to.
*/
public static void householder(double gamma,
DMatrixD1 u,
DMatrixD1 x, DMatrixD1 y)
{
int n = u.NumElements;
double sum = 0;
for (int i = 0; i < n; i++)
{
sum += u.get(i) * x.get(i);
}
for (int i = 0; i < n; i++)
{
y.set(i, x.get(i) + gamma * u.get(i) * sum);
}
}
/**
* <p>
* Performs a matrix vector multiply.<br>
* <br>
* C = A<sup>T</sup> * B <br>
* where B is a column vector.<br>
* or<br>
* C = A<sup>T</sup> * B<sup>T</sup> <br>
* where B is a row vector. <br>
* <br>
* c<sub>i</sub> = Sum{ j=1:n, a<sub>ji</sub> * b<sub>j</sub>}<br>
* <br>
* where A is a matrix, B is a column or transposed row vector, and C is a column vector.
* </p>
* <p>
* This implementation is optimal for small matrices. There is a huge performance hit when
* used on large matrices due to CPU cache issues.
* </p>
*
* @param A A matrix that is m by n. Not modified.
* @param B A that has length m and is a column. Not modified.
* @param C A column vector that has length n. Modified.
*/
public static void multTransA_small(DMatrix1Row A, DMatrixD1 B, DMatrixD1 C)
{
if (C.numCols != 1)
{
throw new MatrixDimensionException("C is not a column vector");
}
else if (C.numRows != A.numCols)
{
throw new MatrixDimensionException("C is not the expected length");
}
if (B.numRows == 1)
{
if (A.numRows != B.numCols)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else if (B.numCols == 1)
{
if (A.numRows != B.numRows)
{
throw new MatrixDimensionException("A and B are not compatible");
}
}
else
{
throw new MatrixDimensionException("B is not a vector");
}
int cIndex = 0;
for (int i = 0; i < A.numCols; i++)
{
double total = 0.0;
int indexA = i;
for (int j = 0; j < A.numRows; j++)
{
total += A.get(indexA) * B.get(j);
indexA += A.numCols;
}
C.set(cIndex++, total);
}
}
public void set(int row, int col, double value)
{
original.set(row + row0, col + col0, value);
}