public static bool isTranspose(DMatrixSparseCSC A, DMatrixSparseCSC B, double tol)
{
if (A.numCols != B.numRows || A.numRows != B.numCols)
{
return(false);
}
if (A.nz_length != B.nz_length)
{
return(false);
}
if (!A.indicesSorted)
{
throw new ArgumentException("A must have sorted indicies");
}
DMatrixSparseCSC Btran = new DMatrixSparseCSC(B.numCols, B.numRows, B.nz_length);
CommonOps_DSCC.transpose(B, Btran, null);
Btran.sortIndices(null);
for (int i = 0; i < B.nz_length; i++)
{
if (A.nz_rows[i] != Btran.nz_rows[i])
{
return(false);
}
if (Math.Abs(A.nz_values[i] - Btran.nz_values[i]) > tol)
{
return(false);
}
}
return(true);
}
/**
* <p>
* Checks to see if a matrix is orthogonal or isometric.
* </p>
*
* @param Q The matrix being tested. Not modified.
* @param tol Tolerance.
* @return True if it passes the test.
*/
public static bool isOrthogonal(DMatrixSparseCSC Q, double tol)
{
if (Q.numRows < Q.numCols)
{
throw new ArgumentException("The number of rows must be more than or equal to the number of columns");
}
IGrowArray gw = new IGrowArray();
DGrowArray gx = new DGrowArray();
for (int i = 0; i < Q.numRows; i++)
{
for (int j = i + 1; j < Q.numCols; j++)
{
double val = CommonOps_DSCC.dotInnerColumns(Q, i, Q, j, gw, gx);
if (!(Math.Abs(val) <= tol))
{
return(false);
}
}
}
return(true);
}
public static DMatrixSparseCSC triangleUpper(int dimen, int hessenberg, int nz_total,
double min, double max, IMersenneTwister rand)
{
DMatrixSparseCSC L = triangleLower(dimen, hessenberg, nz_total, min, max, rand);
DMatrixSparseCSC U = (DMatrixSparseCSC)L.createLike();
CommonOps_DSCC.transpose(L, U, null);
return(U);
}
public static double normF(DMatrixSparseCSC A)
{
double total = 0;
double max = CommonOps_DSCC.elementMaxAbs(A);
for (int i = 0; i < A.nz_length; i++)
{
double x = A.nz_values[i] / max;
total += x * x;
}
return(max * Math.Sqrt(total));
}
/**
* Creates a random symmetric positive definite matrix.
* @param width number of columns and rows
* @param nz_total Used to adjust number of non-zero values. Exact amount in matrix will be more than this.
* @param rand random number generator
* @return Random matrix
*/
public static DMatrixSparseCSC symmetricPosDef(int width, int nz_total, IMersenneTwister rand)
{
DMatrixSparseCSC A = rectangle(width, width, nz_total, rand);
// to ensure it's SPD assign non-zero values to all the diagonal elements
for (int i = 0; i < width; i++)
{
A.set(i, i, Math.Max(0.5, rand.NextDouble()));
}
DMatrixSparseCSC spd = new DMatrixSparseCSC(width, width, 0);
CommonOps_DSCC.multTransB(A, A, spd, null, null);
return(spd);
}