public static double[] Subtract(double[] aStore, int aOffset, int aStride, double[] bStore, int bOffset, int bStride, int dimension)
{
double[] store = new double[dimension];
Blas1.dCopy(aStore, aOffset, aStride, store, 0, 1, dimension);
Blas1.dAxpy(-1.0, bStore, bOffset, bStride, store, 0, 1, dimension);
return(store);
}
// Apply a Householder transfrom defined by v to the vector x (which may be
// a column of a matrix, if H is applied from the left, or a row of a matrix
// if H is applied from the right). On exit v is unchanged, x is changed.
// We have H = I - \beta v v^T, so H x = x - (\beta v^T x) v.
public static void ApplyHouseholderReflection(
double[] uStore, int uOffset, int uStride,
double[] yStore, int yOffset, int yStride,
int count
)
{
double s = Blas1.dDot(uStore, uOffset, uStride, yStore, yOffset, yStride, count);
Blas1.dAxpy(-s, uStore, uOffset, uStride, yStore, yOffset, yStride, count);
}
public static double[] Multiply(double alpha, double[] store, int offset, int stride, int dimension)
{
double[] product = new double[dimension];
Blas1.dAxpy(alpha, store, offset, stride, product, 0, 1, dimension);
return(product);
}
// inverts the matrix in place
// the in-place-ness makes this a bit confusing
public static void GaussJordanInvert(double[] store, int dimension)
{
// keep track of row exchanges
int[] ps = new int[dimension];
// iterate over dimensions
for (int k = 0; k < dimension; k++)
{
// look for a pivot in the kth column on any lower row
int p = k;
double q = MatrixAlgorithms.GetEntry(store, dimension, dimension, k, k);
for (int r = k + 1; r < dimension; r++)
{
double s = MatrixAlgorithms.GetEntry(store, dimension, dimension, r, k);
if (Math.Abs(s) > Math.Abs(q))
{
p = r;
q = s;
}
}
ps[k] = p;
// if no non-zero pivot is found, the matrix is singular and cannot be inverted
if (q == 0.0)
{
throw new DivideByZeroException();
}
// if the best pivot was on a lower row, swap it into the kth row
if (p != k)
{
Blas1.dSwap(store, k, dimension, store, p, dimension, dimension);
}
// divide the pivot row by the pivot element, so the diagonal element becomes unity
MatrixAlgorithms.SetEntry(store, dimension, dimension, k, k, 1.0);
Blas1.dScal(1.0 / q, store, k, dimension, dimension);
// add factors to the pivot row to zero all off-diagonal elements in the kth column
for (int r = 0; r < dimension; r++)
{
if (r == k)
{
continue;
}
double a = MatrixAlgorithms.GetEntry(store, dimension, dimension, r, k);
MatrixAlgorithms.SetEntry(store, dimension, dimension, r, k, 0.0);
Blas1.dAxpy(-a, store, k, dimension, store, r, dimension, dimension);
}
}
// unscramble exchanges
for (int k = dimension - 1; k >= 0; k--)
{
int p = ps[k];
if (p != k)
{
Blas1.dSwap(store, dimension * p, 1, store, dimension * k, 1, dimension);
}
}
}
