/*
Computes the discrete Fourier transform (DFT) of the given complex vector, storing the result back into the vector.
The vector can have any length. This is a wrapper function.
340830
private static void FFT(double[] real, double[] imag) {
        int n = real.length;
        if (n == 0) {
            return;
        } else if ((n & (n - 1)) == 0)  // Is power of 2
            transformRadix2(real, imag);
        else  // More complicated algorithm for arbitrary sizes
            transformBluestein(real, imag);
    }
237248
public void transform (double data[], int i0, int stride) {
    checkData(data,i0,stride);
    int p, p_1, q;

    if (n == 1) return;		/* identity operation */

    /* bit reverse the ordering of input data for decimation in time algorithm */
    bitreverse(data, i0, stride);

    /* apply fft recursion */
    p = 1; q = n ;
    for (int i = 1; i <= logn; i++) {
      int a, b;

      p_1 = p ;
      p = 2 * p ;
      q = q / 2 ;

      /* a = 0 */

      for (b = 0; b < q; b++) {
	double t0_real = data[i0+stride*b*p] + data[i0+stride*(b*p + p_1)];
	double t1_real = data[i0+stride*b*p] - data[i0+stride*(b*p + p_1)];
	  
	data[i0+stride*b*p] = t0_real;
	data[i0+stride*(b*p + p_1)] = t1_real;
      }

      /* a = 1 ... p_{i-1}/2 - 1 */

      {
	double w_real = 1.0;
	double w_imag = 0.0;

	double theta = - 2.0 * Math.PI / p;
	
	double s = Math.sin(theta);
	double t = Math.sin(theta / 2.0);
	double s2 = 2.0 * t * t;
	
	for (a = 1; a < (p_1)/2; a++) {
	  /* trignometric recurrence for w-> exp(i theta) w */
	    
	  {
	    double tmp_real = w_real - s * w_imag - s2 * w_real;
	    double tmp_imag = w_imag + s * w_real - s2 * w_imag;
	    w_real = tmp_real;
	    w_imag = tmp_imag;
	  }
	    
	  for (b = 0; b < q; b++) {
	    double z0_real = data[i0+stride*(b*p + a)];
	    double z0_imag = data[i0+stride*(b*p + p_1 - a)];
	    double z1_real = data[i0+stride*(b*p + p_1 + a)];
	    double z1_imag = data[i0+stride*(b*p + p - a)];
		
	    /* t0 = z0 + w * z1 */
	    data[i0+stride*(b*p + a)]    =z0_real + w_real * z1_real - w_imag * z1_imag;
	    data[i0+stride*(b*p + p - a)]=z0_imag + w_real * z1_imag + w_imag * z1_real;
	    /* t1 = -(z0 - w * z1) */
	    data[i0+stride*(b*p + p_1 - a)]=z0_real - w_real * z1_real + w_imag * z1_imag;
	    data[i0+stride*(b*p + p_1 + a)]=-(z0_imag - w_real * z1_imag - w_imag * z1_real);
	  }
	}
      }

      if (p_1 >  1) {
	for (b = 0; b < q; b++) {
	  /* a = p_{i-1}/2 */
	  data[i0+stride*(b*p + p - p_1/2)] *= -1 ;
	}}
    }
  }
286401
public void compMult(DoubleVector dv) {
	for (int i = 0; i < len; i++) {
	    vect[i] *= dv.vect[i];
	}
    }
1241662
def scale_fft(in1):
    

    ker = SourceModule("""
                        __global__ void scale_fft_ker(float *in1)
                        {
                            const int len = gridDim.x*blockDim.x;
                            const int col = (blockDim.x * blockIdx.x + threadIdx.x);
                            const int row = (blockDim.y * blockIdx.y + threadIdx.y);
                            const int tid2 = col + len*row;
                            const int szin1 = gridDim.x*blockDim.x*gridDim.y*blockDim.y;

							in1[tid2] = in1[tid2]/szin1;                           
                        }
                       """, keep=True)

    scale_fft_ker = ker.get_function("scale_fft_ker")
    scale_fft_ker(in1, block=(32,32,1), grid=(int(in1.shape[1]//32), int(in1.shape[0]//32)))
589656
def fft(ts):
    
    t_step = ts.index[1] - ts.index[0]
    oc = np.abs(np.fft.fftshift(np.fft.fft(ts.values))) / len(ts.values)
    t = np.fft.fftshift(np.fft.fftfreq(len(oc), d=t_step))
    return Trace(oc, t)
862405
@Override
    public DMatrixRMaj getV(DMatrixRMaj V , boolean transpose , boolean compact ) {
        V = handleV(V, transpose, compact,m,n,min);
        CommonOps_DDRM.setIdentity(V);

//        UBV.print();

        // todo the very first multiplication can be avoided by setting to the rank1update output
        for( int j = min-1; j >= 0; j-- ) {
            u[j+1] = 1;
            for( int i = j+2; i < n; i++ ) {
                u[i] = UBV.get(j,i);
            }
            if( transpose )
                QrHelperFunctions_DDRM.rank1UpdateMultL(V, u, gammasV[j], j + 1, j + 1, n);
            else
                QrHelperFunctions_DDRM.rank1UpdateMultR(V, u, gammasV[j], j + 1, j + 1, n, this.b);
        }

        return V;
    }
714839
function _Vector(dimension, data) {
  if (!dimension || !Number.isInteger(dimension))
    throw new TypeError('Dimension of the array must be an integer.');

  var _values;
  if (!data || data === undefined)
    _values = [];
  else if (!util.isNumberArray(data))
    throw new TypeError('Invalid values for vector.');
  else
    _values = data;

  if (_values.length < dimension) {
    var zeros = Array(dimension - _values.length).fill(0);
    _values = _values.concat(zeros);
  } else if (_values.length > dimension) {
    _values = _values.slice(0, dimension);
  }

  readonly(this, "dimension", dimension);
  readonly(this, "values", _values);
  readonly(this, "magnitude", _magnitudeOf(_values));
}
722843
private double[] computeResidualVector(double[] vector, int centroidIndex) {
		double[] residualVector = new double[vectorLength];
		for (int i = 0; i < vectorLength; i++) {
			residualVector[i] = coarseQuantizer[centroidIndex][i] - vector[i];
		}
		return residualVector;
	}
1249619
static float vDistSqr(float[] v1, float[] v2) {
        float dx = v2[0] - v1[0];
        float dy = v2[1] - v1[1];
        float dz = v2[2] - v1[2];
        return dx * dx + dy * dy + dz * dz;
    }
867605
public static void FFT2(ComplexNumber[][] data, Direction direction) {
        int n = data.length;
        int m = data[0].length;
        //ComplexNumber[] row = new ComplexNumber[m];//Math.max(m, n)];

        for (int i = 0; i < n; i++) {
            // copy row
            //for ( int j = 0; j < m; j++ )
            //row[j] = data[i][j];
            ComplexNumber[] row = data[i];
            // transform it
            FourierTransform.FFT(row, direction);
            // copy back
            for (int j = 0; j < m; j++)
                data[i][j] = row[j];
        }

        // process columns
        ComplexNumber[] col = new ComplexNumber[n];

        for (int j = 0; j < m; j++) {
            // copy column
            for (int i = 0; i < n; i++)
                col[i] = data[i][j];
            // transform it
            FourierTransform.FFT(col, direction);
            // copy back
            for (int i = 0; i < n; i++)
                data[i][j] = col[i];
        }
    }
521159
public static void applyBoxFilter( GrayF32 input ) {

		// declare storage
		GrayF32 boxImage = new GrayF32(input.width, input.height);
		InterleavedF32 boxTransform = new InterleavedF32(input.width,input.height,2);
		InterleavedF32 transform = new InterleavedF32(input.width,input.height,2);
		GrayF32 blurredImage = new GrayF32(input.width, input.height);
		GrayF32 spatialBlur = new GrayF32(input.width, input.height);

		DiscreteFourierTransform<GrayF32,InterleavedF32> dft =
				DiscreteFourierTransformOps.createTransformF32();


		// Make the image scaled from 0 to 1 to reduce overflow issues
		PixelMath.divide(input,255.0f,input);

		// compute the Fourier Transform
		dft.forward(input,transform);

		// create the box filter which is centered around the pixel.  Note that the filter gets wrapped around
		// the image edges
		for( int y = 0; y < 15; y++ ) {
			int yy = y-7 < 0 ? boxImage.height+(y-7) : y - 7;
			for( int x = 0; x < 15; x++ ) {
				int xx = x-7 < 0 ? boxImage.width+(x-7) : x - 7;
				// Set the value such that it doesn't change the image intensity
				boxImage.set(xx,yy,1.0f/(15*15));
			}
		}

		// compute the DFT for the box filter
		dft.forward(boxImage,boxTransform);

		// Visualize the Fourier Transform for the input image and the box filter
		displayTransform(transform,"Input Image");
		displayTransform(boxTransform,"Box Filter");

		// apply the filter. convolution in spacial domain is the same as multiplication in the frequency domain
		DiscreteFourierTransformOps.multiplyComplex(transform,boxTransform,transform);

		// convert the image back and display the results
		dft.inverse(transform,blurredImage);
		// undo change of scale
		PixelMath.multiply(blurredImage,255.0f,blurredImage);
		PixelMath.multiply(input,255.0f,input);

		// For sake of comparison, let's compute the box blur filter in the spatial domain
		// NOTE: The image border will be different since the frequency domain wraps around and this implementation
		// of the spacial domain adapts the kernel size
		BlurImageOps.mean(input,spatialBlur,7,null,null);

		// Convert to BufferedImage for output
		BufferedImage originOut = ConvertBufferedImage.convertTo(input, null);
		BufferedImage spacialOut = ConvertBufferedImage.convertTo(spatialBlur, null);
		BufferedImage blurredOut = ConvertBufferedImage.convertTo(blurredImage, null);

		ListDisplayPanel listPanel = new ListDisplayPanel();
		listPanel.addImage(originOut,"Original Image");
		listPanel.addImage(spacialOut,"Spacial Domain Box");
		listPanel.addImage(blurredOut,"Frequency Domain Box");

		ShowImages.showWindow(listPanel,"Box Blur in Spacial and Frequency Domain of Input Image");
	}
1213969
function (vector) {
        var len = Math.sqrt(vector[0] * vector[0] + vector[1] * vector[1]);
        return [vector[0] / len, vector[1] / len];
    }
467293
void transform_internal(float data[], int i0, int stride, int sign){

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

    float scratch[] = new float[2*n];
    int product = 1;
    int state = 0;
    float 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]; }}
  }
459185
public static void FFTShift2D(double[][] x, Direction direction) {
        FFTShift2D(x, direction, 1);
        FFTShift2D(x, direction, 2);
    }
978048
public static void multiplyRealComplex( GrayF realA ,
											ImageInterleaved complexB , ImageInterleaved complexC ) {
		if( complexB instanceof InterleavedF32 ) {
			DiscreteFourierTransformOps.multiplyRealComplex((GrayF32) realA, (InterleavedF32) complexB, (InterleavedF32) complexC);
		} else if( complexB instanceof InterleavedF64 ) {
			DiscreteFourierTransformOps.multiplyRealComplex((GrayF64) realA, (InterleavedF64) complexB, (InterleavedF64) complexC);
		} else {
			throw new IllegalArgumentException("Unknown image type");
		}
	}
500618
function svdJs() {
                var A = this;
                var V = Matrix$b.I(A.rows());
                var S = A.transpose();
                var U = Matrix$b.I(A.cols());
                var err = Number.MAX_VALUE;
                var i = 0;
                var maxLoop = 100;

                while(err > 2.2737e-13 && i < maxLoop) {
                    var qr = S.transpose().qrJs();
                    S = qr.R;
                    V = V.x(qr.Q);
                    qr = S.transpose().qrJs();
                    U = U.x(qr.Q);
                    S = qr.R;

                    var e = S.triu(1).unroll().norm();
                    var f = S.diagonal().norm();

                    if(f == 0)
                        f = 1;

                    err = e / f;

                    i++;
                }

                var ss = S.diagonal();
                var s = [];

                for(var i = 1; i <= ss.cols(); i++) {
                    var ssn = ss.e(i);
                    s.push(Math.abs(ssn));

                    if(ssn < 0) {
                        for(var j = 0; j < U.rows(); j++) {
                            V.elements[j][i - 1] = -(V.elements[j][i - 1]);
                        }
                    }
                }

                return {U: U, S: $V(s).toDiagonalMatrix(), V: V};
            }
107289
public static double[][] diag(double[] vector){

		// Note: According to the Java Language spec, an array is initialized with the default value, here 0.
		double[][] diagonalMatrix = new double[vector.length][vector.length];

		for(int index = 0; index < vector.length; index++) {
			diagonalMatrix[index][index] = vector[index];
		}

		return diagonalMatrix;
	}