Package org.hipparchus.transform

Class FastHadamardTransformer

java.lang.Object
org.hipparchus.transform.FastHadamardTransformer
All Implemented Interfaces:
Serializable, RealTransformer
public class FastHadamardTransformer extends Object implements RealTransformer, Serializable
Implements the Fast Hadamard Transform (FHT). Transformation of an input vector x to the output vector y.

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).

See Also:

  • Constructor Summary

    Constructors
    Constructor
    Description
    FastHadamardTransformer()
    Empty constructor.

  • Method Summary

    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.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • FastHadamardTransformer

      public FastHadamardTransformer()
      Empty constructor.

      This constructor is not strictly necessary, but it prevents spurious javadoc warnings with JDK 18 and later.

      Since:
      3.0

  • Method Details

    • transform

      public double[] transform(double[] f, TransformType type)
      Returns the (forward, inverse) transform of the specified real data set.
      Specified by:
      transform in interface RealTransformer
      Parameters:
      f - the real data array to be transformed (signal)
      type - the type of transform (forward, inverse) to be performed
      Returns:
      the real transformed array (spectrum)
      Throws:
      MathIllegalArgumentException - if the length of the data array is not a power of two

    • transform

      public 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.
      Specified by:
      transform in interface RealTransformer
      Parameters:
      f - the function to be sampled and transformed
      min - the (inclusive) lower bound for the interval
      max - the (exclusive) upper bound for the interval
      n - the number of sample points
      type - the type of transform (forward, inverse) to be performed
      Returns:
      the real transformed array
      Throws:
      MathIllegalArgumentException - if the lower bound is greater than, or equal to the upper bound
      MathIllegalArgumentException - if the number of sample points is negative
      MathIllegalArgumentException - if the number of sample points is not a power of two

    • transform

      public 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.
      Parameters:
      f - the integer data array to be transformed (signal)
      Returns:
      the integer transformed array (spectrum)
      Throws:
      MathIllegalArgumentException - if the length of the data array is not a power of two

    • fht

      protected double[] fht(double[] x) throws MathIllegalArgumentException
      The FHT (Fast Hadamard Transformation) which uses only subtraction and addition. Requires N * log2(N) = n * 2^n additions.
      1. x is the input vector to be transformed,
      2. y is the output vector (Fast Hadamard transform of x),
      3. a and b are helper rows.
      Short Table of manual calculation for N=8
      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

      How it works

      1. Construct a matrix with N rows and n + 1 columns, hadm[n+1][N].
        (If I use [x][y] it always means [row-offset][column-offset] of a Matrix with n rows and m columns. Its entries go from M[0][0] to M[n][N])
      2. Place the input vector x[N] in the first column of the matrix hadm.
      3. The entries of the submatrix D_top are calculated as follows
        • D_top goes from entry [0][1] to [N / 2 - 1][n + 1],
        • the columns of D_top are the pairwise mutually exclusive sums of the previous column.
      4. The entries of the submatrix D_bottom are calculated as follows
        • D_bottom goes from entry [N / 2][1] to [N][n + 1],
        • the columns of D_bottom are the pairwise differences of the previous column.
      5. The consputation of D_top and D_bottom are best understood with the above example (for N = 8).
      6. The output vector y is now in the last column of hadm.
      7. Algorithm from chipcenter.
      visually
      0123 … n + 1
      0 x0 ↑
      ← Dtop →
      ↓
      1x1
      2x2
      ……
      N / 2 - 1xN/2-1
      N / 2 xN/2 ↑
      ← Dbottom →
      ↓
      N / 2 + 1xN/2+1
      N / 2 + 2xN/2+2
      ……
      NxN
      Parameters:
      x - the real data array to be transformed
      Returns:
      the real transformed array, y
      Throws:
      MathIllegalArgumentException - if the length of the data array is not a power of two

    • fht

      protected int[] fht(int[] x) throws MathIllegalArgumentException
      Returns the forward transform of the specified integer data set. The FHT (Fast Hadamard Transform) uses only subtraction and addition.
      Parameters:
      x - the integer data array to be transformed
      Returns:
      the integer transformed array, y
      Throws:
      MathIllegalArgumentException - if the length of the data array is not a power of two