/** Return the Householder vectors
@return Lower trapezoidal matrix whose columns define the reflections
*/
public CoreMatrix getH()
{
CoreMatrix X = new CoreMatrix(m, n);
double[,] H = X.getArray();
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
if (i >= j)
{
H[i, j] = QR[i, j];
}
else
{
H[i, j] = 0.0;
}
}
}
return X;
}
/* ------------------------
Constructor
* ------------------------ */
/** Check for symmetry, then construct the eigenvalue decomposition
@param A Square matrix
@return Structure to access D and V.
*/
public EigenvalueDecomposition(CoreMatrix Arg)
{
double[,] A = Arg.getArray();
n = Arg.getColumnDimension();
V = new double[n, n];
d = new double[n];
e = new double[n];
issymmetric = true;
for (int j = 0; (j < n) & issymmetric; j++)
{
for (int i = 0; (i < n) & issymmetric; i++)
{
issymmetric = (A[i, j] == A[j, i]);
}
}
if (issymmetric)
{
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
V[i, j] = A[i, j];
}
}
// Tridiagonalize.
tred2();
// Diagonalize.
tql2();
}
else
{
H = new double[n, n];
ort = new double[n];
for (int j = 0; j < n; j++)
{
for (int i = 0; i < n; i++)
{
H[i, j] = A[i, j];
}
}
// Reduce to Hessenberg form.
orthes();
// Reduce Hessenberg to real Schur form.
hqr2();
}
}
/** Return the block diagonal eigenvalue matrix
@return D
*/
public CoreMatrix getD()
{
CoreMatrix X = new CoreMatrix(n, n);
double[,] D = X.getArray();
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
D[i, j] = 0.0;
}
D[i, i] = d[i];
if (e[i] > 0)
{
D[i, i + 1] = e[i];
}
else if (e[i] < 0)
{
D[i, i - 1] = e[i];
}
}
return X;
}
/** Return lower triangular factor
@return L
*/
public CoreMatrix getL()
{
CoreMatrix X = new CoreMatrix(m, n);
double[,] L = X.getArray();
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
if (i > j)
{
L[i, j] = LU[i, j];
}
else if (i == j)
{
L[i, j] = 1.0;
}
else
{
L[i, j] = 0.0;
}
}
}
return X;
}
/** Return upper triangular factor
@return U
*/
public CoreMatrix getU()
{
CoreMatrix X = new CoreMatrix(n, n);
double[,] U = X.getArray();
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
if (i <= j)
{
U[i, j] = LU[i, j];
}
else
{
U[i, j] = 0.0;
}
}
}
return X;
}
/** Get a subCoreMatrix.
@param i0 Initial row index
@param i1 Final row index
@param j0 Initial column index
@param j1 Final column index
@return A(i0:i1,j0:j1)
@exception Exception SubCoreMatrix indices
*/
public CoreMatrix getMatrix(int i0, int i1, int j0, int j1)
{
CoreMatrix X = new CoreMatrix(i1 - i0 + 1, j1 - j0 + 1);
double[,] B = X.getArray();
try
{
for (int i = i0; i <= i1; i++)
{
for (int j = j0; j <= j1; j++)
{
B[i - i0, j - j0] = A[i, j];
}
}
}
catch (Exception)
{
throw new Exception("SubCoreMatrix indices");
}
return X;
}
/** Generate identity CoreMatrix
@param m Number of rows.
@param n Number of colums.
@return An m-by-n CoreMatrix with ones on the diagonal and zeros elsewhere.
*/
public static CoreMatrix identity(int m, int n)
{
CoreMatrix A = new CoreMatrix(m, n);
double[,] X = A.getArray();
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
X[i, j] = (i == j ? 1.0 : 0.0);
}
}
return A;
}
/** Element-by-element left division, C = A.\B
@param B another CoreMatrix
@return A.\B
*/
public CoreMatrix arrayLeftDivide(CoreMatrix B)
{
checkCoreMatrixDimensions(B);
CoreMatrix X = new CoreMatrix(m, n);
double[,] C = X.getArray();
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
C[i, j] = B.A[i, j] / A[i, j];
}
}
return X;
}
/** Multiply a CoreMatrix by a scalar, C = s*A
@param s scalar
@return s*A
*/
public CoreMatrix times(double s)
{
CoreMatrix X = new CoreMatrix(m, n);
double[,] C = X.getArray();
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
C[i, j] = s * A[i, j];
}
}
return X;
}
/** CoreMatrix transpose.
@return A'
*/
public CoreMatrix transpose()
{
CoreMatrix X = new CoreMatrix(n, m);
double[,] C = X.getArray();
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
C[j, i] = A[i, j];
}
}
return X;
}
/** Unary minus
@return -A
*/
public CoreMatrix uminus()
{
CoreMatrix X = new CoreMatrix(m, n);
double[,] C = X.getArray();
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
C[i, j] = -A[i, j];
}
}
return X;
}
/** Get a subCoreMatrix.
@param r Array of row indices.
@param i0 Initial column index
@param i1 Final column index
@return A(r(:),j0:j1)
@exception Exception SubCoreMatrix indices
*/
public CoreMatrix getMatrix(int[] r, int j0, int j1)
{
CoreMatrix X = new CoreMatrix(r.Length, j1 - j0 + 1);
double[,] B = X.getArray();
try
{
for (int i = 0; i < r.Length; i++)
{
for (int j = j0; j <= j1; j++)
{
B[i, j - j0] = A[r[i], j];
}
}
}
catch (Exception)
{
throw new Exception("SubCoreMatrix indices");
}
return X;
}
/** Get a subCoreMatrix.
@param i0 Initial row index
@param i1 Final row index
@param c Array of column indices.
@return A(i0:i1,c(:))
@exception Exception SubCoreMatrix indices
*/
public CoreMatrix getMatrix(int i0, int i1, int[] c)
{
CoreMatrix X = new CoreMatrix(i1 - i0 + 1, c.Length);
double[,] B = X.getArray();
try
{
for (int i = i0; i <= i1; i++)
{
for (int j = 0; j < c.Length; j++)
{
B[i - i0, j] = A[i, c[j]];
}
}
}
catch (Exception)
{
throw new Exception("SubCoreMatrix indices");
}
return X;
}
/** Get a subCoreMatrix.
@param r Array of row indices.
@param c Array of column indices.
@return A(r(:),c(:))
@exception Exception SubCoreMatrix indices
*/
public CoreMatrix getMatrix(int[] r, int[] c)
{
CoreMatrix X = new CoreMatrix(r.Length, c.Length);
double[,] B = X.getArray();
try
{
for (int i = 0; i < r.Length; i++)
{
for (int j = 0; j < c.Length; j++)
{
B[i, j] = A[r[i], c[j]];
}
}
}
catch (Exception)
{
throw new Exception("SubCoreMatrix indices");
}
return X;
}
/** Return the upper triangular factor
@return R
*/
public CoreMatrix getR()
{
CoreMatrix X = new CoreMatrix(n, n);
double[,] R = X.getArray();
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
if (i < j)
{
R[i, j] = QR[i, j];
}
else if (i == j)
{
R[i, j] = Rdiag[i];
}
else
{
R[i, j] = 0.0;
}
}
}
return X;
}
/** Linear algebraic CoreMatrix multiplication, A * B
@param B another CoreMatrix
@return CoreMatrix product, A * B
@exception IllegalArgumentException CoreMatrix inner dimensions must agree.
*/
public CoreMatrix times(CoreMatrix B)
{
if (B.m != n)
{
throw new Exception("CoreMatrix inner dimensions must agree.");
}
CoreMatrix X = new CoreMatrix(m, B.n);
double[,] C = X.getArray();
double[] Bcolj = new double[n];
for (int j = 0; j < B.n; j++)
{
for (int k = 0; k < n; k++)
{
Bcolj[k] = B.A[k, j];
}
for (int i = 0; i < m; i++)
{
double[] Arowi = new double[n];
for (int z = 0; z < n; z++)
Arowi[z] = A[i, z];
double s = 0;
for (int k = 0; k < n; k++)
{
s += Arowi[k] * Bcolj[k];
}
C[i, j] = s;
}
}
return X;
}
/** Generate and return the (economy-sized) orthogonal factor
@return Q
*/
public CoreMatrix getQ()
{
CoreMatrix X = new CoreMatrix(m, n);
double[,] Q = X.getArray();
for (int k = n - 1; k >= 0; k--)
{
for (int i = 0; i < m; i++)
{
Q[i, k] = 0.0;
}
Q[k, k] = 1.0;
for (int j = k; j < n; j++)
{
if (QR[k, k] != 0)
{
double s = 0.0;
for (int i = k; i < m; i++)
{
s += QR[i, k] * Q[i, j];
}
s = -s / QR[k, k];
for (int i = k; i < m; i++)
{
Q[i, j] += s * QR[i, k];
}
}
}
}
return X;
}
/* ------------------------
Public Methods
* ------------------------ */
/** Construct a CoreMatrix from a copy of a 2-D array.
@param A Two-dimensional array of doubles.
@exception IllegalArgumentException All rows must have the same length
*/
public static CoreMatrix constructWithCopy(double[,] A)
{
int m = A.GetLength(0);
int n = A.GetLength(1);
CoreMatrix X = new CoreMatrix(m, n);
double[,] C = X.getArray();
for (int i = 0; i < m; i++)
{
for (int j = 0; j < n; j++)
{
C[i, j] = A[i, j];
}
}
return X;
}
