/**
* Discrete fourier transform 2d
*
* @param input the input to transform
* @param rows the number of rows in the transformed output matrix
* @param cols the number of columns in the transformed output matrix
* @return the discrete fourier transform of the input
*/
public static ComplexDoubleMatrix complexDisceteFourierTransform(
ComplexDoubleMatrix input, int rows, int cols) {
ComplexDoubleMatrix base;
// pad
if (input.rows < rows || input.columns < cols)
base = MatrixUtil.complexPadWithZeros(input, rows, cols);
// truncation
else if (input.rows > rows || input.columns > cols) {
base = input.dup();
base =
base.get(
MatrixUtil.toIndices(RangeUtils.interval(0, rows)),
MatrixUtil.toIndices(RangeUtils.interval(0, cols)));
} else base = input.dup();
ComplexDoubleMatrix temp = new ComplexDoubleMatrix(base.rows, base.columns);
ComplexDoubleMatrix ret = new ComplexDoubleMatrix(base.rows, base.columns);
for (int i = 0; i < base.columns; i++) {
ComplexDoubleMatrix column = base.getColumn(i);
temp.putColumn(i, complexDiscreteFourierTransform1d(column));
}
for (int i = 0; i < ret.rows; i++) {
ComplexDoubleMatrix row = temp.getRow(i);
ret.putRow(i, complexDiscreteFourierTransform1d(row));
}
return ret;
}
/**
* Compute the singular values of a complex matrix.
*
* @param A ComplexDoubleMatrix of dimension m * n
* @return A real-valued (!) min(m, n) vector of singular values.
*/
public static DoubleMatrix SVDValues(ComplexDoubleMatrix A) {
int m = A.rows;
int n = A.columns;
DoubleMatrix S = new DoubleMatrix(min(m, n));
double[] rwork = new double[5 * min(m, n)];
int info =
NativeBlas.zgesvd(
'N',
'N',
m,
n,
A.dup().data,
0,
m,
S.data,
0,
null,
0,
1,
null,
0,
min(m, n),
rwork,
0);
if (info > 0) {
throw new LapackConvergenceException(
"GESVD", info + " superdiagonals of an intermediate bidiagonal form failed to converge.");
}
return S;
}
/**
* Compute a singular-value decomposition of A.
*
* @return A ComplexDoubleMatrix[3] array of U, S, V such that A = U * diag(S) * V'
*/
public static ComplexDoubleMatrix[] fullSVD(ComplexDoubleMatrix A) {
int m = A.rows;
int n = A.columns;
ComplexDoubleMatrix U = new ComplexDoubleMatrix(m, m);
DoubleMatrix S = new DoubleMatrix(min(m, n));
ComplexDoubleMatrix V = new ComplexDoubleMatrix(n, n);
double[] rwork = new double[5 * min(m, n)];
int info =
NativeBlas.zgesvd(
'A', 'A', m, n, A.dup().data, 0, m, S.data, 0, U.data, 0, m, V.data, 0, n, rwork, 0);
if (info > 0) {
throw new LapackConvergenceException(
"GESVD", info + " superdiagonals of an intermediate bidiagonal form failed to converge.");
}
return new ComplexDoubleMatrix[] {U, new ComplexDoubleMatrix(S), V.hermitian()};
}
