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src/onset/onsetdetection.c: simplify complex domain computation

--- a/src/onset/onsetdetection.c

+++ b/src/onset/onsetdetection.c

@@ -34,7 +34,6 @@

       cvec_t * fftgrain, fvec_t * onset);

   smpl_t threshold;      /**< minimum norm threshold for phase and specdiff */

   fvec_t *oldmag;        /**< previous norm vector */

-  fft_data_t *meas;      /**< current onset detection measure complex vector */

   fvec_t *dev1 ;         /**< current onset detection measure vector */

   fvec_t *theta1;        /**< previous phase vector, one frame behind */

   fvec_t *theta2;        /**< previous phase vector, two frames behind */

@@ -74,26 +73,14 @@

   for (i=0;i<fftgrain->channels; i++)  {

     onset->data[i][0] = 0.;

     for (j=0;j<nbins; j++)  {

-      o->dev1->data[i][j]    = aubio_unwrap2pi(

-          fftgrain->phas[i][j]

-          -2.0*o->theta1->data[i][j]+

-          o->theta2->data[i][j]);

-#ifdef HAVE_COMPLEX_H

-      o->meas[j] = fftgrain->norm[i][j]*CEXPC(I*o->dev1->data[i][j]);

-      /* sum on all bins */

-      onset->data[i][0]     += //(fftgrain->norm[i][j]);

-          SQRT(SQR( REAL(o->oldmag->data[i][j]-o->meas[j]) )

-            +  SQR( IMAG(o->oldmag->data[i][j]-o->meas[j]) )

-            );

-#else

-      o->meas[j]             = (fftgrain->norm[i][j])*COS(o->dev1->data[i][j]);

-      o->meas[(nbins-1)*2-1-j] = (fftgrain->norm[i][j])*SIN(o->dev1->data[i][j]);

-      /* sum on all bins */

-      onset->data[i][0]     += //(fftgrain->norm[i][j]);

-          SQRT(SQR( (o->oldmag->data[i][j]-o->meas[j]) )

-            +  SQR( (-o->meas[(nbins-1)*2-1-j]) )

-            );

-#endif

+      // compute the predicted phase

+      o->dev1->data[i][j] = 2. * o->theta1->data[i][j] - o->theta2->data[i][j];

+      // compute the euclidean distance in the complex domain

+      // sqrt ( r_1^2 + r_2^2 - 2 * r_1 * r_2 * \cos ( \phi_1 - \phi_2 ) )

+      onset->data[i][0] +=

+        SQRT (ABS (SQR (o->oldmag->data[i][j]) + SQR (fftgrain->norm[i][j])

+              - 2. * o->oldmag->data[i][j] * fftgrain->norm[i][j]

+              * COS (o->dev1->data[i][j] - fftgrain->phas[i][j])));

       /* swap old phase data (need to remember 2 frames behind)*/

       o->theta2->data[i][j] = o->theta1->data[i][j];

       o->theta1->data[i][j] = fftgrain->phas[i][j];

@@ -234,9 +221,6 @@

       /* the other approaches will need some more memory spaces */

     case aubio_onset_complex:

       o->oldmag = new_fvec(rsize,channels);

-      /** bug: must be complex array */

-      o->meas = AUBIO_ARRAY(fft_data_t,size+1);

-      for (i=0; i<size+1; i++) o->meas[i] = 0;

       o->dev1   = new_fvec(rsize,channels);

       o->theta1 = new_fvec(rsize,channels);

       o->theta2 = new_fvec(rsize,channels);

@@ -308,7 +292,6 @@

       break;

       /* the other approaches will need some more memory spaces */

     case aubio_onset_complex:

-      AUBIO_FREE(o->meas);

       del_fvec(o->oldmag);

       del_fvec(o->dev1);

       del_fvec(o->theta1);