Serializable
, RealTransformer
public class FastHadamardTransformer extends Object implements RealTransformer, Serializable
In addition to transformation of real vectors, the Hadamard transform can transform integer vectors into integer vectors. However, this integer transform cannot be inverted directly. Due to a scaling factor it may lead to rational results. As an example, the inverse transform of integer vector (0, 1, 0, 1) is rational vector (1/2, -1/2, 0, 0).
Constructor | Description |
---|---|
FastHadamardTransformer() |
Modifier and Type | Method | Description |
---|---|---|
protected double[] |
fht(double[] x) |
The FHT (Fast Hadamard Transformation) which uses only subtraction and
addition.
|
protected int[] |
fht(int[] x) |
Returns the forward transform of the specified integer data set.
|
double[] |
transform(double[] f,
TransformType type) |
Returns the (forward, inverse) transform of the specified real data set.
|
int[] |
transform(int[] f) |
Returns the forward transform of the specified integer data set.The
integer transform cannot be inverted directly, due to a scaling factor
which may lead to double results.
|
double[] |
transform(UnivariateFunction f,
double min,
double max,
int n,
TransformType type) |
Returns the (forward, inverse) transform of the specified real function,
sampled on the specified interval.
|
public double[] transform(double[] f, TransformType type)
transform
in interface RealTransformer
f
- the real data array to be transformed (signal)type
- the type of transform (forward, inverse) to be performedMathIllegalArgumentException
- if the length of the data array is
not a power of twopublic double[] transform(UnivariateFunction f, double min, double max, int n, TransformType type)
transform
in interface RealTransformer
f
- the function to be sampled and transformedmin
- the (inclusive) lower bound for the intervalmax
- the (exclusive) upper bound for the intervaln
- the number of sample pointstype
- the type of transform (forward, inverse) to be performedMathIllegalArgumentException
- if the lower bound is greater than, or equal to the upper boundMathIllegalArgumentException
- if the number of sample points is negativeMathIllegalArgumentException
- if the number of sample points is not a power of twopublic int[] transform(int[] f)
f
- the integer data array to be transformed (signal)MathIllegalArgumentException
- if the length of the data array is not a power of twoprotected double[] fht(double[] x) throws MathIllegalArgumentException
N * log2(N) = n * 2^n
additions.
x | a | b | y |
---|---|---|---|
x0 | a0 = x0 + x1 | b0 = a0 + a1 | y0 = b0+ b1 |
x1 | a1 = x2 + x3 | b0 = a2 + a3 | y0 = b2 + b3 |
x2 | a2 = x4 + x5 | b0 = a4 + a5 | y0 = b4 + b5 |
x3 | a3 = x6 + x7 | b0 = a6 + a7 | y0 = b6 + b7 |
x4 | a0 = x0 - x1 | b0 = a0 - a1 | y0 = b0 - b1 |
x5 | a1 = x2 - x3 | b0 = a2 - a3 | y0 = b2 - b3 |
x6 | a2 = x4 - x5 | b0 = a4 - a5 | y0 = b4 - b5 |
x7 | a3 = x6 - x7 | b0 = a6 - a7 | y0 = b6 - b7 |
N
rows and n + 1
columns,
hadm[n+1][N]
.x[N]
in the first column of the
matrix hadm
.D_top
are calculated as follows
D_top
goes from entry [0][1]
to
[N / 2 - 1][n + 1]
,D_top
are the pairwise mutually
exclusive sums of the previous column.D_bottom
are calculated as
follows
D_bottom
goes from entry [N / 2][1]
to
[N][n + 1]
,D_bottom
are the pairwise differences
of the previous column.D_top
and D_bottom
are best
understood with the above example (for N = 8
).
y
is now in the last column of
hadm
.0 | 1 | 2 | 3 | … | n + 1 | |
---|---|---|---|---|---|---|
0 | x0 |
↑ ← Dtop → ↓ |
||||
1 | x1 | |||||
2 | x2 | |||||
… | … | |||||
N / 2 - 1 | xN/2-1 | |||||
N / 2 | xN/2 |
↑ ← Dbottom → ↓ |
||||
N / 2 + 1 | xN/2+1 | |||||
N / 2 + 2 | xN/2+2 | |||||
… | … | |||||
N | xN |
x
- the real data array to be transformedy
MathIllegalArgumentException
- if the length of the data array is not a power of twoprotected int[] fht(int[] x) throws MathIllegalArgumentException
x
- the integer data array to be transformedy
MathIllegalArgumentException
- if the length of the data array is not a power of twoCopyright © 2016–2018 Hipparchus.org. All rights reserved.