/**
* 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;
}
/**
* 1d discrete fourier transform, note that this will throw an exception if the passed in input
* isn't a vector. See matlab's fft2 for more information
*
* @param inputC the input to transform
* @return the the discrete fourier transform of the passed in input
*/
public static ComplexNDArray complexDiscreteFourierTransform1d(ComplexNDArray inputC) {
if (inputC.shape().length != 1)
throw new IllegalArgumentException("Illegal input: Must be a vector");
double len = Math.max(inputC.rows, inputC.columns);
ComplexDouble c2 = new ComplexDouble(0, -2).muli(FastMath.PI).divi(len);
ComplexDoubleMatrix range = MatrixUtil.complexRangeVector(0, len);
ComplexDoubleMatrix matrix = exp(range.mmul(range.transpose().mul(c2)));
ComplexDoubleMatrix complexRet = matrix.mmul(inputC);
return ComplexNDArray.wrap(inputC, complexRet);
}
public static DoubleMatrix conv2d(DoubleMatrix input, DoubleMatrix kernel, Type type) {
DoubleMatrix xShape = new DoubleMatrix(1, 2);
xShape.put(0, input.rows);
xShape.put(1, input.columns);
DoubleMatrix yShape = new DoubleMatrix(1, 2);
yShape.put(0, kernel.rows);
yShape.put(1, kernel.columns);
DoubleMatrix zShape = xShape.addi(yShape).subi(1);
int retRows = (int) zShape.get(0);
int retCols = (int) zShape.get(1);
ComplexDoubleMatrix fftInput = complexDisceteFourierTransform(input, retRows, retCols);
ComplexDoubleMatrix fftKernel = complexDisceteFourierTransform(kernel, retRows, retCols);
ComplexDoubleMatrix mul = fftKernel.muli(fftInput);
ComplexDoubleMatrix retComplex = complexInverseDisceteFourierTransform(mul);
DoubleMatrix ret = retComplex.getReal();
if (type == Type.VALID) {
DoubleMatrix validShape = xShape.subi(yShape).addi(1);
DoubleMatrix start = zShape.subi(validShape).divi(2);
DoubleMatrix end = start.addi(validShape);
if (start.get(0) < 1 || start.get(1) < 1)
throw new IllegalStateException("Illegal row index " + start);
if (end.get(0) < 1 || end.get(1) < 1)
throw new IllegalStateException("Illegal column index " + end);
ret =
ret.get(
RangeUtils.interval((int) start.get(0), (int) end.get(0)),
RangeUtils.interval((int) start.get(1), (int) end.get(1)));
}
return ret;
}
/**
* 1d discrete fourier transform, note that this will throw an exception if the passed in input
* isn't a vector. See matlab's fft2 for more information
*
* @param inputC the input to transform
* @return the the discrete fourier transform of the passed in input
*/
public static ComplexDoubleMatrix complexDiscreteFourierTransform1d(ComplexDoubleMatrix inputC) {
if (inputC.rows != 1 && inputC.columns != 1)
throw new IllegalArgumentException("Illegal input: Must be a vector");
double len = Math.max(inputC.rows, inputC.columns);
ComplexDouble c2 = new ComplexDouble(0, -2).muli(FastMath.PI).divi(len);
ComplexDoubleMatrix range = MatrixUtil.complexRangeVector(0, len);
ComplexDoubleMatrix matrix = exp(range.mmul(range.transpose().mul(c2)));
ComplexDoubleMatrix complexRet =
inputC.isRowVector() ? matrix.mmul(inputC) : inputC.mmul(matrix);
return complexRet;
}