/**
* <p>
* x<sup>T</sup>A<sup>T</sup>y
* </p>
*
* @param x A vector with n elements. Not modified.
* @param A A matrix with n by n elements. Not modified.
* @param y A vector with n elements. Not modified.
* @return The results.
*/
// TODO better name for this
public static double innerProdTranA(DMatrixD1 x, DMatrixD1 A, DMatrixD1 y)
{
int n = A.numRows;
if (n != A.numCols)
{
throw new ArgumentException("A must be square");
}
if (x.NumElements != n)
{
throw new ArgumentException("Unexpected number of elements in x");
}
if (y.NumElements != n)
{
throw new ArgumentException("Unexpected number of elements in y");
}
double result = 0;
for (int i = 0; i < n; i++)
{
double total = 0;
for (int j = 0; j < n; j++)
{
total += x.get(j) * A.unsafe_get(i, j);
}
result += total * y.get(i);
}
return(result);
}
/**
* <p>
* return = x<sup>T</sup>*A*y
* </p>
*
* @param x A vector with n elements. Not modified.
* @param A A matrix with n by m elements. Not modified.
* @param y A vector with m elements. Not modified.
* @return The results.
*/
public static double innerProdA(DMatrixD1 x, DMatrixD1 A, DMatrixD1 y)
{
int n = A.numRows;
int m = A.numCols;
if (x.getNumElements() != n)
{
throw new ArgumentException("Unexpected number of elements in x");
}
if (y.getNumElements() != m)
{
throw new ArgumentException("Unexpected number of elements in y");
}
double result = 0;
for (int i = 0; i < m; i++)
{
double total = 0;
for (int j = 0; j < n; j++)
{
total += x.get(j) * A.unsafe_get(j, i);
}
result += total * y.get(i);
}
return(result);
}
/**
* Computes the quality of a triangular matrix, where the quality of a matrix
* is defined in {@link LinearSolverDense#quality()}. In
* this situation the quality os the absolute value of the product of
* each diagonal element divided by the magnitude of the largest diagonal element.
* If all diagonal elements are zero then zero is returned.
*
* @param T A matrix.
* @return the quality of the system.
*/
public static double qualityTriangular(DMatrixD1 T)
{
int N = Math.Min(T.numRows, T.numCols);
// TODO make faster by just checking the upper triangular portion
double max = elementDiagonalMaxAbs(T);
if (max == 0.0)
{
return(0.0);
}
double quality = 1.0;
for (int i = 0; i < N; i++)
{
quality *= T.unsafe_get(i, i) / max;
}
return(Math.Abs(quality));
}