fixed merge conflicts

doc_source/references.bib

@@ -118,4 +118,13 @@ @ARTICLE{ml4pers
 ISSN={2624-8212},   
 }
 
+@misc{polanco2019adaptive,
+      title={Adaptive template systems: Data-driven feature selection for learning with persistence diagrams}, 
+      author={Luis Polanco and Jose A. Perea},
+      year={2019},
+      eprint={1910.06741},
+      archivePrefix={arXiv},
+      primaryClass={cs.LG}
+}
+
 @Comment{jabref-meta: databaseType:bibtex;}

notebooks/kernel_gpu.py

@@ -0,0 +1,72 @@
+@guvectorize(["void(int64[:,:,:], int64[:,:], float64, float64[:])",],"(p,m,n), (m,n), ()->(p)", target='cuda', nopython=True)
+def kernel_gpu(dgms0, dgms1, s, result):
+    """
+
+    This function computes (using gpu) the multiscale heat kernel distance for an array of persistence diagrams based on the formula provided in Ref. :cite:`5 <Reininghaus2015>`.
+    There are three inputs and these are two persistence diagram arrays and the kernel scale sigma.  This function should be used for large size datasets.  Please note this function will not work if you do not have a compatible GPU.
+    Details for compatibility can be found `here <https://numba.readthedocs.io/en/stable/cuda/index.html>`_.
+
+    Parameters
+    ----------
+    dgms0 : ndarray
+        Object array that includes first persistence diagram set.
+    dgms1 : ndarray
+        Object array that includes second persistence diagram set.
+    sigma : float
+        Kernel scale.
+
+    Returns
+    -------
+    result : np array
+        The kernel matrix
+
+    """
+    n_train = len(dgms0)
+    for i in range(n_train):
+        dgm0=dgms0[i]
+        dgm1 = dgms1
+        kSigma0 = 0
+        kSigma1 = 0
+        kSigma2 = 0
+        sigma = s
+        for k in range(dgm0.shape[0]):
+            p = dgm0[k,0:2]
+            if p[0]+p[1]==-2:
+                continue
+            for l in range(dgm0.shape[0]):
+                q = dgm0[l,0:2]
+                if q[0]+q[1]==-2:
+                    continue
+                qc = dgm0[l, 1::-1]
+                pq = (p[0] - q[0])**2 + (p[1] - q[1])**2
+                pqc = (p[0] - qc[0])**2 + (p[1] - qc[1])**2
+                kSigma0 += math.exp(-( pq) / (8 * sigma)) - math.exp(-(pqc) / (8 * sigma))
+        for k in range(dgm1.shape[0]):
+            p = dgm1[k,0:2]
+            if p[0]+p[1]==-2:
+                continue
+            for l in range(dgm1.shape[0]):
+                q = dgm1[l,0:2]
+                if q[0]+q[1]==-2:
+                    continue
+                qc = dgm1[l, 1::-1]
+                pq = (p[0] - q[0])**2 + (p[1] - q[1])**2
+                pqc = (p[0] - qc[0])**2 + (p[1] - qc[1])**2
+                kSigma1 += math.exp(-( pq) / (8 * sigma)) - math.exp(-(pqc) / (8 * sigma))
+        for k in range(dgm0.shape[0]):
+            p = dgm0[k,0:2]
+            if p[0]+p[1]==-2:
+                continue
+            for l in range(dgm1.shape[0]):
+                q = dgm1[l,0:2]
+                if q[0]+q[1]==-2:
+                    continue
+                qc = dgm1[l, 1::-1]
+                pq = (p[0] - q[0])**2 + (p[1] - q[1])**2
+                pqc = (p[0] - qc[0])**2 + (p[1] - qc[1])**2
+                kSigma2 += math.exp(-( pq) / (8 * sigma)) - math.exp(-(pqc) / (8 * sigma))
+
+        kSigma0 = kSigma0/(8 * np.pi * sigma)
+        kSigma1 = kSigma1/(8 * np.pi * sigma)
+        kSigma2 = kSigma2/(8 * np.pi * sigma)
+        result[i] = math.sqrt(kSigma1 + kSigma0-2*kSigma2)