diff --git a/src/main/java/org/apache/commons/math/transform/FastFourierTransformer.java b/src/main/java/org/apache/commons/math/transform/FastFourierTransformer.java index 2c1cbccb4..a2419aada 100644 --- a/src/main/java/org/apache/commons/math/transform/FastFourierTransformer.java +++ b/src/main/java/org/apache/commons/math/transform/FastFourierTransformer.java @@ -49,12 +49,10 @@ public class FastFourierTransformer implements Serializable { /** Serializable version identifier. */ static final long serialVersionUID = 5138259215438106000L; - /** roots of unity */ + /** The roots of unity. */ private RootsOfUnity roots = new RootsOfUnity(); - /** - * Construct a default transformer. - */ + /** Construct a default transformer. */ public FastFourierTransformer() { super(); } @@ -69,7 +67,7 @@ public class FastFourierTransformer implements Serializable { * @return the complex transformed array * @throws IllegalArgumentException if any parameters are invalid */ - public Complex[] transform(double f[]) + public Complex[] transform(double[] f) throws IllegalArgumentException { return fft(f, false); } @@ -90,7 +88,7 @@ public class FastFourierTransformer implements Serializable { public Complex[] transform(UnivariateFunction f, double min, double max, int n) throws IllegalArgumentException { - double data[] = sample(f, min, max, n); + double[] data = sample(f, min, max, n); return fft(data, false); } @@ -104,7 +102,7 @@ public class FastFourierTransformer implements Serializable { * @return the complex transformed array * @throws IllegalArgumentException if any parameters are invalid */ - public Complex[] transform(Complex f[]) + public Complex[] transform(Complex[] f) throws IllegalArgumentException { roots.computeOmega(f.length); return fft(f); @@ -120,11 +118,11 @@ public class FastFourierTransformer implements Serializable { * @return the complex transformed array * @throws IllegalArgumentException if any parameters are invalid */ - public Complex[] transform2(double f[]) + public Complex[] transform2(double[] f) throws IllegalArgumentException { - double scaling_coefficient = 1.0 / FastMath.sqrt(f.length); - return scaleArray(fft(f, false), scaling_coefficient); + double scalingCoefficient = 1.0 / FastMath.sqrt(f.length); + return scaleArray(fft(f, false), scalingCoefficient); } /** @@ -144,9 +142,9 @@ public class FastFourierTransformer implements Serializable { double min, double max, int n) throws IllegalArgumentException { - double data[] = sample(f, min, max, n); - double scaling_coefficient = 1.0 / FastMath.sqrt(n); - return scaleArray(fft(data, false), scaling_coefficient); + double[] data = sample(f, min, max, n); + double scalingCoefficient = 1.0 / FastMath.sqrt(n); + return scaleArray(fft(data, false), scalingCoefficient); } /** @@ -159,12 +157,12 @@ public class FastFourierTransformer implements Serializable { * @return the complex transformed array * @throws IllegalArgumentException if any parameters are invalid */ - public Complex[] transform2(Complex f[]) + public Complex[] transform2(Complex[] f) throws IllegalArgumentException { roots.computeOmega(f.length); - double scaling_coefficient = 1.0 / FastMath.sqrt(f.length); - return scaleArray(fft(f), scaling_coefficient); + double scalingCoefficient = 1.0 / FastMath.sqrt(f.length); + return scaleArray(fft(f), scalingCoefficient); } /** @@ -177,11 +175,11 @@ public class FastFourierTransformer implements Serializable { * @return the complex inversely transformed array * @throws IllegalArgumentException if any parameters are invalid */ - public Complex[] inverseTransform(double f[]) + public Complex[] inverseTransform(double[] f) throws IllegalArgumentException { - double scaling_coefficient = 1.0 / f.length; - return scaleArray(fft(f, true), scaling_coefficient); + double scalingCoefficient = 1.0 / f.length; + return scaleArray(fft(f, true), scalingCoefficient); } /** @@ -201,9 +199,9 @@ public class FastFourierTransformer implements Serializable { double min, double max, int n) throws IllegalArgumentException { - double data[] = sample(f, min, max, n); - double scaling_coefficient = 1.0 / n; - return scaleArray(fft(data, true), scaling_coefficient); + double[] data = sample(f, min, max, n); + double scalingCoefficient = 1.0 / n; + return scaleArray(fft(data, true), scalingCoefficient); } /** @@ -216,12 +214,12 @@ public class FastFourierTransformer implements Serializable { * @return the complex inversely transformed array * @throws IllegalArgumentException if any parameters are invalid */ - public Complex[] inverseTransform(Complex f[]) + public Complex[] inverseTransform(Complex[] f) throws IllegalArgumentException { roots.computeOmega(-f.length); // pass negative argument - double scaling_coefficient = 1.0 / f.length; - return scaleArray(fft(f), scaling_coefficient); + double scalingCoefficient = 1.0 / f.length; + return scaleArray(fft(f), scalingCoefficient); } /** @@ -234,11 +232,11 @@ public class FastFourierTransformer implements Serializable { * @return the complex inversely transformed array * @throws IllegalArgumentException if any parameters are invalid */ - public Complex[] inverseTransform2(double f[]) + public Complex[] inverseTransform2(double[] f) throws IllegalArgumentException { - double scaling_coefficient = 1.0 / FastMath.sqrt(f.length); - return scaleArray(fft(f, true), scaling_coefficient); + double scalingCoefficient = 1.0 / FastMath.sqrt(f.length); + return scaleArray(fft(f, true), scalingCoefficient); } /** @@ -258,9 +256,9 @@ public class FastFourierTransformer implements Serializable { double min, double max, int n) throws IllegalArgumentException { - double data[] = sample(f, min, max, n); - double scaling_coefficient = 1.0 / FastMath.sqrt(n); - return scaleArray(fft(data, true), scaling_coefficient); + double[] data = sample(f, min, max, n); + double scalingCoefficient = 1.0 / FastMath.sqrt(n); + return scaleArray(fft(data, true), scalingCoefficient); } /** @@ -273,12 +271,12 @@ public class FastFourierTransformer implements Serializable { * @return the complex inversely transformed array * @throws IllegalArgumentException if any parameters are invalid */ - public Complex[] inverseTransform2(Complex f[]) + public Complex[] inverseTransform2(Complex[] f) throws IllegalArgumentException { roots.computeOmega(-f.length); // pass negative argument - double scaling_coefficient = 1.0 / FastMath.sqrt(f.length); - return scaleArray(fft(f), scaling_coefficient); + double scalingCoefficient = 1.0 / FastMath.sqrt(f.length); + return scaleArray(fft(f), scalingCoefficient); } /** @@ -289,42 +287,42 @@ public class FastFourierTransformer implements Serializable { * @return the complex transformed array * @throws IllegalArgumentException if any parameters are invalid */ - protected Complex[] fft(double f[], boolean isInverse) + protected Complex[] fft(double[] f, boolean isInverse) throws IllegalArgumentException { verifyDataSet(f); - Complex F[] = new Complex[f.length]; + Complex[] transformed = new Complex[f.length]; if (f.length == 1) { - F[0] = new Complex(f[0], 0.0); - return F; + transformed[0] = new Complex(f[0], 0.0); + return transformed; } // Rather than the naive real to complex conversion, pack 2N // real numbers into N complex numbers for better performance. - int N = f.length >> 1; - Complex c[] = new Complex[N]; - for (int i = 0; i < N; i++) { - c[i] = new Complex(f[2*i], f[2*i+1]); + int n = f.length >> 1; + Complex[] repacked = new Complex[n]; + for (int i = 0; i < n; i++) { + repacked[i] = new Complex(f[2 * i], f[2 * i + 1]); } - roots.computeOmega(isInverse ? -N : N); - Complex z[] = fft(c); + roots.computeOmega(isInverse ? -n : n); + Complex[] z = fft(repacked); // reconstruct the FFT result for the original array - roots.computeOmega(isInverse ? -2*N : 2*N); - F[0] = new Complex(2 * (z[0].getReal() + z[0].getImaginary()), 0.0); - F[N] = new Complex(2 * (z[0].getReal() - z[0].getImaginary()), 0.0); - for (int i = 1; i < N; i++) { - Complex A = z[N-i].conjugate(); - Complex B = z[i].add(A); - Complex C = z[i].subtract(A); + roots.computeOmega(isInverse ? -2 * n : 2 * n); + transformed[0] = new Complex(2 * (z[0].getReal() + z[0].getImaginary()), 0.0); + transformed[n] = new Complex(2 * (z[0].getReal() - z[0].getImaginary()), 0.0); + for (int i = 1; i < n; i++) { + Complex a = z[n - i].conjugate(); + Complex b = z[i].add(a); + Complex c = z[i].subtract(a); //Complex D = roots.getOmega(i).multiply(Complex.I); - Complex D = new Complex(-roots.getOmegaImaginary(i), + Complex d = new Complex(-roots.getOmegaImaginary(i), roots.getOmegaReal(i)); - F[i] = B.subtract(C.multiply(D)); - F[2*N-i] = F[i].conjugate(); + transformed[i] = b.subtract(c.multiply(d)); + transformed[2 * n - i] = transformed[i].conjugate(); } - return scaleArray(F, 0.5); + return scaleArray(transformed, 0.5); } /** @@ -334,11 +332,11 @@ public class FastFourierTransformer implements Serializable { * @return the complex transformed array * @throws IllegalArgumentException if any parameters are invalid */ - protected Complex[] fft(Complex data[]) + protected Complex[] fft(Complex[] data) throws IllegalArgumentException { final int n = data.length; - final Complex f[] = new Complex[n]; + final Complex[] f = new Complex[n]; // initial simple cases verifyDataSet(data); @@ -365,37 +363,37 @@ public class FastFourierTransformer implements Serializable { // the bottom base-4 round for (int i = 0; i < n; i += 4) { - final Complex a = f[i].add(f[i+1]); - final Complex b = f[i+2].add(f[i+3]); - final Complex c = f[i].subtract(f[i+1]); - final Complex d = f[i+2].subtract(f[i+3]); + final Complex a = f[i].add(f[i + 1]); + final Complex b = f[i + 2].add(f[i + 3]); + final Complex c = f[i].subtract(f[i + 1]); + final Complex d = f[i + 2].subtract(f[i + 3]); final Complex e1 = c.add(d.multiply(Complex.I)); final Complex e2 = c.subtract(d.multiply(Complex.I)); f[i] = a.add(b); - f[i+2] = a.subtract(b); + f[i + 2] = a.subtract(b); // omegaCount indicates forward or inverse transform - f[i+1] = roots.isForward() ? e2 : e1; - f[i+3] = roots.isForward() ? e1 : e2; + f[i + 1] = roots.isForward() ? e2 : e1; + f[i + 3] = roots.isForward() ? e1 : e2; } // iterations from bottom to top take O(N*logN) time for (int i = 4; i < n; i <<= 1) { - final int m = n / (i<<1); - for (int j = 0; j < n; j += i<<1) { + final int m = n / (i << 1); + for (int j = 0; j < n; j += i << 1) { for (int k = 0; k < i; k++) { //z = f[i+j+k].multiply(roots.getOmega(k*m)); - final int k_times_m = k*m; - final double omega_k_times_m_real = roots.getOmegaReal(k_times_m); - final double omega_k_times_m_imaginary = roots.getOmegaImaginary(k_times_m); + final int km = k * m; + final double omegaKmReal = roots.getOmegaReal(km); + final double omegaKmImag = roots.getOmegaImaginary(km); //z = f[i+j+k].multiply(omega[k*m]); final Complex z = new Complex( - f[i+j+k].getReal() * omega_k_times_m_real - - f[i+j+k].getImaginary() * omega_k_times_m_imaginary, - f[i+j+k].getReal() * omega_k_times_m_imaginary + - f[i+j+k].getImaginary() * omega_k_times_m_real); + f[i + j + k].getReal() * omegaKmReal + - f[i + j + k].getImaginary() * omegaKmImag, + f[i + j + k].getReal() * omegaKmImag + + f[i + j + k].getImaginary() * omegaKmReal); - f[i+j+k] = f[j+k].subtract(z); - f[j+k] = f[j+k].add(z); + f[i + j + k] = f[j + k].subtract(z); + f[j + k] = f[j + k].add(z); } } } @@ -427,7 +425,7 @@ public class FastFourierTransformer implements Serializable { } verifyInterval(min, max); - double s[] = new double[n]; + double[] s = new double[n]; double h = (max - min) / n; for (int i = 0; i < n; i++) { s[i] = f.value(min + i * h); @@ -443,7 +441,7 @@ public class FastFourierTransformer implements Serializable { * @param d the real scaling coefficient * @return a reference to the scaled array */ - public static double[] scaleArray(double f[], double d) { + public static double[] scaleArray(double[] f, double d) { for (int i = 0; i < f.length; i++) { f[i] *= d; } @@ -458,7 +456,7 @@ public class FastFourierTransformer implements Serializable { * @param d the real scaling coefficient * @return a reference to the scaled array */ - public static Complex[] scaleArray(Complex f[], double d) { + public static Complex[] scaleArray(Complex[] f, double d) { for (int i = 0; i < f.length; i++) { f[i] = new Complex(d * f[i].getReal(), d * f[i].getImaginary()); } @@ -481,7 +479,7 @@ public class FastFourierTransformer implements Serializable { * @param d the data array * @throws IllegalArgumentException if array length is not power of 2 */ - public static void verifyDataSet(double d[]) throws IllegalArgumentException { + public static void verifyDataSet(double[] d) throws IllegalArgumentException { if (!isPowerOf2(d.length)) { throw MathRuntimeException.createIllegalArgumentException( LocalizedFormats.NOT_POWER_OF_TWO_CONSIDER_PADDING, d.length); @@ -494,7 +492,7 @@ public class FastFourierTransformer implements Serializable { * @param o the data array * @throws IllegalArgumentException if array length is not power of 2 */ - public static void verifyDataSet(Object o[]) throws IllegalArgumentException { + public static void verifyDataSet(Object[] o) throws IllegalArgumentException { if (!isPowerOf2(o.length)) { throw MathRuntimeException.createIllegalArgumentException( LocalizedFormats.NOT_POWER_OF_TWO_CONSIDER_PADDING, o.length); @@ -687,7 +685,7 @@ public class FastFourierTransformer implements Serializable { } if (vector.length != dimensionSize.length) { throw MathRuntimeException.createIllegalArgumentException( - LocalizedFormats.DIMENSIONS_MISMATCH_SIMPLE, vector.length,dimensionSize.length); + LocalizedFormats.DIMENSIONS_MISMATCH_SIMPLE, vector.length, dimensionSize.length); } Object[] lastDimension = (Object[]) multiDimensionalComplexArray; @@ -710,7 +708,7 @@ public class FastFourierTransformer implements Serializable { } /** - * Get the underlying storage array + * Get the underlying storage array. * @return underlying storage array */ public Object getArray() { @@ -738,7 +736,7 @@ public class FastFourierTransformer implements Serializable { size *= dimensionSize[i]; } int[][] vectorList = new int[size][dimensionSize.length]; - for (int[] nextVector: vectorList) { + for (int[] nextVector : vectorList) { System.arraycopy(vector, 0, nextVector, 0, dimensionSize.length); for (int i = 0; i < dimensionSize.length; i++) { @@ -751,7 +749,7 @@ public class FastFourierTransformer implements Serializable { } } - for (int[] nextVector: vectorList) { + for (int[] nextVector : vectorList) { mdcm.set(get(nextVector), nextVector); } } @@ -782,7 +780,7 @@ public class FastFourierTransformer implements Serializable { private boolean isForward; /** - * Build an engine for computing then th roots of unity + * Build an engine for computing then th roots of unity. */ public RootsOfUnity() { @@ -844,10 +842,10 @@ public class FastFourierTransformer implements Serializable { omegaImaginaryForward[0] = 0.0; omegaImaginaryInverse[0] = 0.0; for (int i = 1; i < absN; i++) { - omegaReal[i] = - omegaReal[i-1] * cosT + omegaImaginaryForward[i-1] * sinT; - omegaImaginaryForward[i] = - omegaImaginaryForward[i-1] * cosT - omegaReal[i-1] * sinT; + omegaReal[i] = omegaReal[i - 1] * cosT + + omegaImaginaryForward[i - 1] * sinT; + omegaImaginaryForward[i] = omegaImaginaryForward[i - 1] * cosT + - omegaReal[i - 1] * sinT; omegaImaginaryInverse[i] = -omegaImaginaryForward[i]; } omegaCount = absN; @@ -855,7 +853,7 @@ public class FastFourierTransformer implements Serializable { } /** - * Get the real part of the kth nth root of unity + * Get the real part of the kth nth root of unity. * @param k index of the nth root of unity * @return real part of the kth nth root of unity * @throws IllegalStateException if no roots of unity have been computed yet @@ -877,7 +875,7 @@ public class FastFourierTransformer implements Serializable { } /** - * Get the imaginary part of the kth nth root of unity + * Get the imaginary part of the kth nth root of unity. * @param k index of the nth root of unity * @return imaginary part of the kth nth root of unity * @throws IllegalStateException if no roots of unity have been computed yet