Merge pull request scikit-learn#5050 from AnishShah/issue5043

DOC Fix documentation of callable kernel

Author: larsmans

doc/modules/svm.rst

@@ -482,15 +482,17 @@ Using Python functions as kernels
 You can also use your own defined kernels by passing a function to the
 keyword ``kernel`` in the constructor.
 
-Your kernel must take as arguments two matrices and return a third matrix.
+Your kernel must take as arguments two matrices of shape
+``(n_samples_1, n_features)``, ``(n_samples_2, n_features)``
+and return a kernel matrix of shape ``(n_samples_1, n_samples_2)``.
 
 The following code defines a linear kernel and creates a classifier
 instance that will use that kernel::
 
     >>> import numpy as np
     >>> from sklearn import svm
-    >>> def my_kernel(x, y):
-    ...     return np.dot(x, y.T)
+    >>> def my_kernel(X, Y):
+    ...     return np.dot(X, Y.T)
     ...
     >>> clf = svm.SVC(kernel=my_kernel)
 

examples/svm/plot_custom_kernel.py

@@ -20,16 +20,16 @@
 Y = iris.target
 
 
-def my_kernel(x, y):
+def my_kernel(X, Y):
     """
     We create a custom kernel:
 
                  (2  0)
-    k(x, y) = x  (    ) y.T
+    k(X, Y) = X  (    ) Y.T
                  (0  1)
     """
     M = np.array([[2, 0], [0, 1.0]])
-    return np.dot(np.dot(x, M), y.T)
+    return np.dot(np.dot(X, M), Y.T)
 
 
 h = .02  # step size in the mesh

sklearn/svm/classes.py

@@ -406,7 +406,8 @@ class SVC(BaseSVC):
          It must be one of 'linear', 'poly', 'rbf', 'sigmoid', 'precomputed' or
          a callable.
          If none is given, 'rbf' will be used. If a callable is given it is
-         used to precompute the kernel matrix.
+         used to pre-compute the kernel matrix from data matrices; that matrix
+         should be an array of shape ``(n_samples, n_samples)``.
 
     degree : int, optional (default=3)
         Degree of the polynomial kernel function ('poly').