complexdoublefft_mixed.java

All the tool for build a network able to reconize any shapes. Very complete, a good base for anythi

package jnt.FFT;

/** Computes FFT's of complex, double precision data of arbitrary length n.
  * This class uses the Mixed Radix method; it has special methods to handle
  * factors 2, 3, 4, 5, 6 and 7, as well as a general factor.
  * <P>
  * This method appears to be faster than the Radix2 method, when both methods apply,
  * but requires extra storage (which ComplexDoubleFFT_Mixed manages itself).
  * <P>
  * See {@link ComplexDoubleFFT ComplexDoubleFFT} for details of data layout.
  *
  * @author Bruce R. Miller [e-mail]
  * @author Contribution of the National Institute of Standards and Technology,
  * @author not subject to copyright.
  * @author Derived from GSL (Gnu Scientific Library)
  * @author GSL's FFT Code by Brian Gough [e-mail]
  * @author Since GSL is released under 
  * @author <H HREF="http://www.gnu.org/copyleft/gpl.html">GPL</A>,
  * @author this package must also be.
  */
public class ComplexDoubleFFT_Mixed extends ComplexDoubleFFT{
  static final double PI = Math.PI;

  public ComplexDoubleFFT_Mixed(int n){
    super(n);
    setup_wavetable(n);
  }

  public void transform(double data[], int i0, int stride) {
    checkData(data,i0,stride);
    transform_internal(data, i0, stride, -1); }

  public void backtransform (double data[], int i0, int stride){
    checkData(data,i0,stride);
    transform_internal(data, i0, stride, +1); }

  /*______________________________________________________________________
   Setting up the Wavetable */

  private int factors[];
  // Reversed the last 2 levels of the twiddle array compared to what the C version had.
  private double twiddle[][][];
  private int available_factors[]={7, 6, 5, 4, 3, 2};

  void setup_wavetable(int n){

    if (n <= 0)
      throw new Error("length must be positive integer : "+n);
    this.n = n;

    factors = Factorize.factor(n, available_factors);

    double d_theta = -2.0 * PI / ((double) n);
    int product = 1;
    twiddle = new double[factors.length][][];
    for (int i = 0; i < factors.length; i++) {
      int factor = factors[i];
      int product_1 = product;	/* product_1 = p_(i-1) */
      product *= factor;
      int q = n / product;

      twiddle[i] = new double[q+1][2*(factor-1)];
      double twid[][] = twiddle[i];
      for(int j=1; j<factor; j++){
	twid[0][2*(j-1)]   = 1.0;
	twid[0][2*(j-1)+1] = 0.0; }
      for (int k = 1; k <= q; k++) {
	int m = 0;
	for(int j=1; j<factor; j++){
	  //	  int m = (k*j*product_1) % n;
	  m += k*product_1;
	  m %= n;
	  double theta = d_theta * m;	/*  d_theta*j*k*p_(i-1) */
	  twid[k][2*(j-1)]   = Math.cos(theta);
	  twid[k][2*(j-1)+1] = Math.sin(theta); }}
    }
  }

  /*______________________________________________________________________
    The main transformation driver */
  void transform_internal(double data[], int i0, int stride, int sign){

    if (n == 1) return;		/* FFT of 1 data point is the identity */

    double scratch[] = new double[2*n];
    int product = 1;
    int state = 0;
    double in[], out[];
    int istride, ostride;
    int in0, out0;

    for (int i = 0; i < factors.length; i++) {
      int factor = factors[i];
      product *= factor;

      if (state == 0) {
	in = data;
	in0 = i0;
	istride = stride;
	out = scratch;
	out0 = 0;
	ostride = 2;
	state = 1; }
      else {
	in = scratch;
	in0 = 0;
	istride = 2;
	out = data;
	out0 = i0;
	ostride = stride;
	state = 0; }

      switch(factor){
      case 2: pass_2(i,in, in0, istride, out, out0, ostride, sign, product); break;
      case 3: pass_3(i,in, in0, istride, out, out0, ostride, sign, product); break;
      case 4: pass_4(i,in, in0, istride, out, out0, ostride, sign, product); break;
      case 5: pass_5(i,in, in0, istride, out, out0, ostride, sign, product); break;
      case 6: pass_6(i,in, in0, istride, out, out0, ostride, sign, product); break;
      case 7: pass_7(i,in, in0, istride, out, out0, ostride, sign, product); break;
      default:pass_n(i,in, in0, istride, out, out0, ostride, sign, factor, product);  }
    }
    if (state == 1){	/* copy results back from scratch to data */
      for (int i = 0; i < n; i++) {
	data[i0+stride*i]   = scratch[2*i];
	data[i0+stride*i+1] = scratch[2*i+1]; }}
  }

  /*______________________________________________________________________*/

  void pass_2(int fi, 
	      double in[],  int in0, int istride,
	      double out[], int out0, int ostride,
	      int sign, int product) {
    int k, k1;

    int factor = 2;
    int m = n / factor;
    int q = n / product;
    int product_1 = product / factor;

    int di = istride * m;
    int dj = ostride * product_1;
    int i = in0, j = out0;
    double x_real, x_imag;
    for (k = 0; k < q; k++) {
      double twids[] = twiddle[fi][k];
      double w_real =       twids[0];
      double w_imag = -sign*twids[1];

      for (k1 = 0; k1 < product_1; k1++) {
	double z0_real = in[i];
	double z0_imag = in[i+1];
	double z1_real = in[i+di];
	double z1_imag = in[i+di+1];
	i += istride;

	/* compute x = W(2) z */

	/* apply twiddle factors */
	  
	/* out0 = 1 * (z0 + z1) */
	out[j]   = z0_real + z1_real;
	out[j+1] = z0_imag + z1_imag;
	  
	/* out1 = w * (z0 - z1) */
	x_real = z0_real - z1_real;
	x_imag = z0_imag - z1_imag;
	out[j+dj]   = w_real * x_real - w_imag * x_imag;
	out[j+dj+1] = w_real * x_imag + w_imag * x_real;
	  
	j += ostride;
      }
      j += (factor-1)*dj;
    }}
  /*______________________________________________________________________*/

  void pass_3(int fi, 
	      double in[],  int in0, int istride,
	      double out[], int out0, int ostride,
	      int sign, int product) {
      int k, k1;

      int factor = 3;
      int m = n / factor;
      int q = n / product;
      int product_1 = product / factor;
      int jump = (factor - 1) * product_1;

      double tau = sign * Math.sqrt(3.0) / 2.0;
      int di = istride * m;
      int dj = ostride * product_1;
      int i = in0, j = out0;
      double x_real, x_imag;
      for (k = 0; k < q; k++) {
	double twids[] = twiddle[fi][k];
	double w1_real =       twids[0];
	double w1_imag = -sign*twids[1];
	double w2_real =       twids[2];
	double w2_imag = -sign*twids[3];

	for (k1 = 0; k1 < product_1; k1++) {
	  double z0_real = in[i];
	  double z0_imag = in[i+1];
	  double z1_real = in[i+di];
	  double z1_imag = in[i+di+1];
	  double z2_real = in[i+2*di];
	  double z2_imag = in[i+2*di+1];
	  i += istride;

	  /* compute x = W(3) z */

	  /* t1 = z1 + z2 */
	  double t1_real = z1_real + z2_real;
	  double t1_imag = z1_imag + z2_imag;
	  
	  /* t2 = z0 - t1/2 */
	  double t2_real = z0_real - t1_real / 2.0;
	  double t2_imag = z0_imag - t1_imag / 2.0;
	  
	  /* t3 = (+/-) sin(pi/3)*(z1 - z2) */
	  double t3_real = tau * (z1_real - z2_real);
	  double t3_imag = tau * (z1_imag - z2_imag);
	  
  	  /* apply twiddle factors */

	  /* out0 = 1 * (z0 + t1) */
	  out[j]   = z0_real + t1_real;
	  out[j+1] = z0_imag + t1_imag;
	  
	  /* out1 = w1 * (t2 + i t3) */
	  x_real = t2_real - t3_imag;
	  x_imag = t2_imag + t3_real;
	  out[j+dj]   = w1_real * x_real - w1_imag * x_imag;
	  out[j+dj+1] = w1_real * x_imag + w1_imag * x_real;
	  
	  /* out2 = w2 * (t2 - i t3) */
	  x_real = t2_real + t3_imag;
	  x_imag = t2_imag - t3_real;
	  out[j+2*dj]   = w2_real * x_real - w2_imag * x_imag;
	  out[j+2*dj+1] = w2_real * x_imag + w2_imag * x_real;
  
	  j += ostride;
	}
	j += (factor-1) * dj;
      }}
  /*______________________________________________________________________*/

  void pass_4(int fi, 
	      double in[],  int in0, int istride,
	      double out[], int out0, int ostride,
	      int sign, int product) {
    int k, k1;

    int factor = 4;
    int m = n / factor;
    int q = n / product;
    int p_1 = product / factor;
    int jump = (factor - 1) * p_1;
    int i = in0, j = out0;
    int di = istride * m;
    int dj = ostride * p_1;
    double x_real, x_imag;
    for (k = 0; k < q; k++) {
      double twids[] = twiddle[fi][k];
      double w1_real =       twids[0];
      double w1_imag = -sign*twids[1];
      double w2_real =       twids[2];
      double w2_imag = -sign*twids[3];
      double w3_real =       twids[4];
      double w3_imag = -sign*twids[5];

      for (k1 = 0; k1 < p_1; k1++) {
	double z0_real = in[i];
	double z0_imag = in[i+1];
	double z1_real = in[i+di];
	double z1_imag = in[i+di+1];
	double z2_real = in[i+2*di];
	double z2_imag = in[i+2*di+1];
	double z3_real = in[i+3*di];
	double z3_imag = in[i+3*di+1];
	i += istride;

	/* compute x = W(4) z */
	  
	/* t1 = z0 + z2 */
	double t1_real = z0_real + z2_real;
	double t1_imag = z0_imag + z2_imag;
	  
	/* t2 = z1 + z3 */
	double t2_real = z1_real + z3_real;
	double t2_imag = z1_imag + z3_imag;
	  
	/* t3 = z0 - z2 */
	double t3_real = z0_real - z2_real;
	double t3_imag = z0_imag - z2_imag;
	  
	/* t4 = (+/-) (z1 - z3) */
	double t4_real = sign * (z1_real - z3_real);
	double t4_imag = sign * (z1_imag - z3_imag);

	/* apply twiddle factors */

	/* out0 = 1 * (t1 + t2) */
	out[j]   = t1_real + t2_real;
	out[j+1] = t1_imag + t2_imag;

	/* out1 = w1 * (t3 + i t4) */
	x_real = t3_real - t4_imag;
	x_imag = t3_imag + t4_real;
	out[j + dj]   = w1_real * x_real - w1_imag * x_imag;
	out[j + dj+1] = w1_real * x_imag + w1_imag * x_real;
	  
	/* out2 = w2 * (t1 - t2) */
	x_real = t1_real - t2_real;
	x_imag = t1_imag - t2_imag;
	out[j + 2 * dj]   = w2_real * x_real - w2_imag * x_imag;
	out[j + 2 * dj+1] = w2_real * x_imag + w2_imag * x_real;
	  
	/* out3 = w3 * (t3 - i t4) */
	x_real = t3_real + t4_imag;
	x_imag = t3_imag - t4_real;
	out[j + 3 * dj]   = w3_real * x_real - w3_imag * x_imag;
	out[j + 3 * dj+1] = w3_real * x_imag + w3_imag * x_real;
	  
	j += ostride;
      }
      j += (factor - 1)*dj;
    }}
  /*______________________________________________________________________*/

  void pass_5(int fi, 
	      double in[],  int in0, int istride,
	      double out[], int out0, int ostride,
	      int sign, int product) {
    int k, k1;

    int factor = 5;
    int m = n / factor;
    int q = n / product;
    int p_1 = product / factor;
    int jump = (factor - 1) * p_1;
    double tau = (Math.sqrt (5.0) / 4.0);
    double sin_2pi_by_5 =  sign * Math.sin (2.0 * PI / 5.0);
    double sin_2pi_by_10 = sign * Math.sin (2.0 * PI / 10.0);
    int i = in0, j = out0;
    int di = istride * m;
    int dj = ostride * p_1;
    double x_real, x_imag;
    for (k = 0; k < q; k++) {
      double twids[] = twiddle[fi][k];
      double w1_real =       twids[0];
      double w1_imag = -sign*twids[1];
      double w2_real =       twids[2];
      double w2_imag = -sign*twids[3];
      double w3_real =       twids[4];
      double w3_imag = -sign*twids[5];
      double w4_real =       twids[6];
      double w4_imag = -sign*twids[7];

      for (k1 = 0; k1 < p_1; k1++) {
	double z0_real = in[i];
	double z0_imag = in[i+1];
	double z1_real = in[i + di];
	double z1_imag = in[i + di+1];
	double z2_real = in[i + 2*di];
	double z2_imag = in[i + 2*di+1];
	double z3_real = in[i + 3*di];
	double z3_imag = in[i + 3*di+1];
	double z4_real = in[i + 4*di];
	double z4_imag = in[i + 4*di+1];
	i += istride;

	/* compute x = W(5) z */

	/* t1 = z1 + z4 */
	double t1_real = z1_real + z4_real;
	double t1_imag = z1_imag + z4_imag;
	  
	/* t2 = z2 + z3 */
	double t2_real = z2_real + z3_real;
	double t2_imag = z2_imag + z3_imag;
	  
	/* t3 = z1 - z4 */
	double t3_real = z1_real - z4_real;
	double t3_imag = z1_imag - z4_imag;
	  
	/* t4 = z2 - z3 */
	double t4_real = z2_real - z3_real;
	double t4_imag = z2_imag - z3_imag;
	  
	/* t5 = t1 + t2 */
	double t5_real = t1_real + t2_real;
	double t5_imag = t1_imag + t2_imag;
	  
	/* t6 = (sqrt(5)/4)(t1 - t2) */
	double t6_real = tau * (t1_real - t2_real);
	double t6_imag = tau * (t1_imag - t2_imag);
	  
	/* t7 = z0 - ((t5)/4) */
	double t7_real = z0_real - t5_real / 4.0;
	double t7_imag = z0_imag - t5_imag / 4.0;
	  
	/* t8 = t7 + t6 */
	double t8_real = t7_real + t6_real;
	double t8_imag = t7_imag + t6_imag;
	  
	/* t9 = t7 - t6 */
	double t9_real = t7_real - t6_real;
	double t9_imag = t7_imag - t6_imag;
	  
	/* t10 = sin(2 pi/5) t3 + sin(2 pi/10) t4 */
	double t10_real = sin_2pi_by_5 * t3_real + sin_2pi_by_10 * t4_real;
	double t10_imag = sin_2pi_by_5 * t3_imag + sin_2pi_by_10 * t4_imag;
	  
	/* t11 = sin(2 pi/10) t3 - sin(2 pi/5) t4 */
	double t11_real = sin_2pi_by_10 * t3_real - sin_2pi_by_5 * t4_real;
	double t11_imag = sin_2pi_by_10 * t3_imag - sin_2pi_by_5 * t4_imag;
      
	/* apply twiddle factors */
	  
	/* out0 = 1 * (z0 + t5) */
	out[j]   = z0_real + t5_real;
	out[j+1] = z0_imag + t5_imag;
	  
	/* out1 = w1 * (t8 + i t10) */
	x_real = t8_real - t10_imag;
	x_imag = t8_imag + t10_real;
	out[j + dj]   = w1_real * x_real - w1_imag * x_imag;
	out[j + dj+1] = w1_real * x_imag + w1_imag * x_real;
	  
	/* out2 = w2 * (t9 + i t11) */
	x_real = t9_real - t11_imag;
	x_imag = t9_imag + t11_real;
	out[j+2*dj]   = w2_real * x_real - w2_imag * x_imag;
	out[j+2*dj+1] = w2_real * x_imag + w2_imag * x_real;
	  
	/* out3 = w3 * (t9 - i t11) */
	x_real = t9_real + t11_imag;
	x_imag = t9_imag - t11_real;
	out[j+3*dj]   = w3_real * x_real - w3_imag * x_imag;
	out[j+3*dj+1] = w3_real * x_imag + w3_imag * x_real;
	  
	/* out4 = w4 * (t8 - i t10) */
	x_real = t8_real + t10_imag;
	x_imag = t8_imag - t10_real;
	out[j+4*dj]   = w4_real * x_real - w4_imag * x_imag;
	out[j+4*dj+1] = w4_real * x_imag + w4_imag * x_real;
	  
	j += ostride;
      }
      j += (factor - 1)*dj;
    }}
  /*______________________________________________________________________*/

  void pass_6(int fi, 
	      double in[],  int in0, int istride,
	      double out[], int out0, int ostride,
	      int sign, int product) {

    int k, k1;

    int factor = 6;
    int m = n / factor;
    int q = n / product;
    int p_1 = product / factor;
    int jump = (factor - 1) * p_1;
    double tau = sign * Math.sqrt (3.0) / 2.0;
    int i = in0, j = out0;
    int di = istride * m;
    int dj = ostride * p_1;
    double x_real, x_imag;
    for (k = 0; k < q; k++) {
      double twids[] = twiddle[fi][k];
      double w1_real =       twids[0];
      double w1_imag = -sign*twids[1];