Corrected Multivariate Gaussian prior (#775)

* Corrected MultivariateGaussian prior

Some corrections including adapting to current version of pdinv, correcting the expressions of constant, pdf and its gradient, and adding the printing function. After some tests, seems to run as expected, similarly to the Gaussian prior which was already working.

* Added test of MultivariateGaussian prior

Simple unit test for creating a kernel with Multivariate Gaussian prior over the lengthscales, then performing GP regression.

* Took care of case where x of shape (n, 1) for multivariate Gaussian prior

* Got rid of unnecessary asserts in Multivariate Gaussian prior since loss of time

Co-authored-by: and <buisson-fenet@is.mpg.de>

GPy/core/parameterization/priors.py

@@ -200,37 +200,50 @@ class MultivariateGaussian(Prior):
 
     def __new__(cls, mu=0, var=1):  # Singleton:
         if cls._instances:
-            cls._instances[:] = [instance for instance in cls._instances if instance()]
+            cls._instances[:] = [instance for instance in cls._instances if
+                                 instance()]
             for instance in cls._instances:
-                if np.all(instance().mu == mu) and np.all(instance().var == var):
+                if np.all(instance().mu == mu) and np.all(
+                        instance().var == var):
                     return instance()
-        o = super(Prior, cls).__new__(cls, mu, var)
+        newfunc = super(Prior, cls).__new__
+        if newfunc is object.__new__:
+            o = newfunc(cls)
+        else:
+            o = newfunc(cls, mu, var)
         cls._instances.append(weakref.ref(o))
         return cls._instances[-1]()
 
     def __init__(self, mu, var):
         self.mu = np.array(mu).flatten()
         self.var = np.array(var)
-        assert len(self.var.shape) == 2
-        assert self.var.shape[0] == self.var.shape[1]
+        assert len(self.var.shape) == 2, 'Covariance must be a matrix'
+        assert self.var.shape[0] == self.var.shape[1], \
+            'Covariance must be a square matrix'
         assert self.var.shape[0] == self.mu.size
         self.input_dim = self.mu.size
-        self.inv, self.hld = pdinv(self.var)
-        self.constant = -0.5 * self.input_dim * np.log(2 * np.pi) - self.hld
+        self.inv, _, self.hld, _ = pdinv(self.var)
+        self.constant = -0.5 * (self.input_dim * np.log(2 * np.pi) + self.hld)
+
+    def __str__(self):
+        return 'MultiN(' + str(self.mu) + ', ' + str(np.diag(self.var)) + ')'
 
     def summary(self):
         raise NotImplementedError
 
     def pdf(self, x):
+        x = np.array(x).flatten()
         return np.exp(self.lnpdf(x))
 
     def lnpdf(self, x):
+        x = np.array(x).flatten()
         d = x - self.mu
-        return self.constant - 0.5 * np.sum(d * np.dot(d, self.inv), 1)
+        return self.constant - 0.5 * np.dot(d.T, np.dot(self.inv, d))
 
     def lnpdf_grad(self, x):
+        x = np.array(x).flatten()
         d = x - self.mu
-        return -np.dot(self.inv, d)
+        return - np.dot(self.inv, d)
 
     def rvs(self, n):
         return np.random.multivariate_normal(self.mu, self.var, n)
@@ -247,14 +260,15 @@ class MultivariateGaussian(Prior):
         return self.mu, self.var
 
     def __setstate__(self, state):
-        self.mu = state[0]
+        self.mu = np.array(state[0]).flatten()
         self.var = state[1]
-        assert len(self.var.shape) == 2
-        assert self.var.shape[0] == self.var.shape[1]
+        assert len(self.var.shape) == 2, 'Covariance must be a matrix'
+        assert self.var.shape[0] == self.var.shape[1], \
+            'Covariance must be a square matrix'
         assert self.var.shape[0] == self.mu.size
         self.input_dim = self.mu.size
-        self.inv, self.hld = pdinv(self.var)
-        self.constant = -0.5 * self.input_dim * np.log(2 * np.pi) - self.hld
+        self.inv, _, self.hld, _ = pdinv(self.var)
+        self.constant = -0.5 * (self.input_dim * np.log(2 * np.pi) + self.hld)
 
 def gamma_from_EV(E, V):
     warnings.warn("use Gamma.from_EV to create Gamma Prior", FutureWarning)