Changeset 5639:007b55ab186f

Timestamp:

08/12/07 10:46:30 (6 years ago)

Author:

William Stein <wstein@…>

Branch:

default

Message:

Fix some doctests, etc. and improve function names for matrices over RDF.

File:

• sage/matrix/matrix_real_double_dense.pyx (modified) (2 diffs)

sage/matrix/matrix_real_double_dense.pyx

@@ -404 +404 @@
         return e, [c.parent().span_of_basis([c], check=False) for c in v.columns()]
             
-    def eigen(self):
-        """
-        Computes the eigenvalues and eigenvectors of this matrix acting
-        *from the right*. 
+    def eigen_left(self):
+        """
+        Computes the eigenvalues and *left* eigenvectors of this
+        matrix m acting *from the right*.  I.e., vectors v such that
+        v*m = lambda*m.
 
         OUTPUT:
              eigenvalues -- as a list
-             corresponding eigenvectors -- as an RDF matrix whose columns are
-                           the eigenvectors.
+             corresponding eigenvectors -- as an RDF matrix whose columns
+                           are the eigenvectors.
 
         EXAMPLES:
             sage: m = Matrix(RDF, 3, range(9))
-            sage: m.eigen()           # random-ish platform-dependent output (low order digits)
-            ([13.3484692283, -1.34846922835, -9.96461975961e-16],
-             [-0.440242867236 -0.897878732262  0.408248290464]
-            [-0.567868371314 -0.278434036822 -0.816496580928]
-            [-0.695493875393  0.341010658618  0.408248290464])
+            sage: m.eigen_left()           # random-ish platform-dependent output (low order digits)
+
 
         IMPLEMENTATION:
@@ -431 +429 @@
 
         import numpy
-        v_, m_ = numpy.linalg.eig(numpy.transpose(self.numpy()))
-        return ([sage.rings.complex_double.CDF(x) for x in v_],matrix(m_))
-    
+        v, m = numpy.linalg.eig(numpy.transpose(self.numpy()))
+        return ([sage.rings.complex_double.CDF(x) for x in v],matrix(m))
+    
+    def eigen_right(self):
+        """
+        Computes the eigenvalues and *right* eigenvectors of this
+        matrix m acting *from the left*.  I.e., vectors v such that
+        m * v = lambda*m, where v is viewed as a column vector. 
+
+        OUTPUT:
+             eigenvalues -- as a list
+             corresponding eigenvectors -- as an RDF matrix whose columns
+                           are the eigenvectors.
+
+        EXAMPLES:
+            sage: m = Matrix(RDF, 3, range(9))
+            sage: m.eigen_right()           # random-ish platform-dependent output (low order digits)
+
+        IMPLEMENTATION:
+            Uses numpy.
+        """
+        if not self.is_square():
+            raise ValueError, "self must be square"
+        if self._nrows == 0:
+            return [], self
+
+        import numpy
+        v, m = numpy.linalg.eig(self.numpy())
+        return ([sage.rings.complex_double.CDF(x) for x in v],matrix(m))
+
     def solve_left_LU(self, b):
         """