change ab05md docstring sections to numpydoc style

Author: KybernetikJo

slycot/analysis.py

@@ -144,76 +144,84 @@ def ab01nd(n, m, A, B, jobz='N', tol=0, ldwork=None):
         Z = None
     return Ac, Bc, ncont, indcon, nblk, Z, tau
 
-
 def ab05md(n1,m1,p1,n2,p2,A1,B1,C1,D1,A2,B2,C2,D2,uplo='U'):
     """ n,a,b,c,d = ab05md(n1,m1,p1,n2,p2,a1,b1,c1,d1,a2,b2,c2,d2,[uplo])
 
     To obtain the state-space model (A,B,C,D) for the cascaded
     inter-connection of two systems, each given in state-space form.
 
-    Required arguments:
-        n1 : input int
-            The number of state variables in the first system, i.e. the order
-            of the matrix A1.  n1 > 0.
-        m1 : input int
-            The number of input variables for the first system. m1 > 0.
-        p1 : input int
-            The number of output variables from the first system and the number
-            of input variables for the second system. p1 > 0.
-        n2 : input int
-            The number of state variables in the second system, i.e. the order
-            of the matrix A2.  n2 > 0.
-        p2 : input int
-            The number of output variables from the second system. p2 > 0.
-        A1 : input rank-2 array('d') with bounds (n1,n1)
-            The leading n1-by-n1 part of this array must contain the state
-            transition matrix A1 for the first system.
-        B1 : input rank-2 array('d') with bounds (n1,m1)
-            The leading n1-by-m1 part of this array must contain the input/state
-            matrix B1 for the first system.
-        C1 : input rank-2 array('d') with bounds (p1,n1)
-            The leading p1-by-n1 part of this array must contain the state/output
-            matrix C1 for the first system.
-        D1 : input rank-2 array('d') with bounds (p1,m1)
-            The leading p1-by-m1 part of this array must contain the input/output
-            matrix D1 for the first system.
-        A2 : input rank-2 array('d') with bounds (n2,n2)
-            The leading n2-by-n2 part of this array must contain the state
-            transition matrix A2 for the second system.
-        B2 : input rank-2 array('d') with bounds (n2,p1)
-            The leading n2-by-p1 part of this array must contain the input/state
-            matrix B2 for the second system.
-        C2 : input rank-2 array('d') with bounds (p2,n2)
-            The leading p2-by-n2 part of this array must contain the state/output
-            matrix C2 for the second system.
-        D2 : input rank-2 array('d') with bounds (p2,p1)
-            The leading p2-by-p1 part of this array must contain the input/output
-            matrix D2 for the second system.
-    Optional arguments:
-        uplo := 'U' input string(len=1)
-            Indicates whether the user wishes to obtain the matrix A in
-            the upper or lower block diagonal form, as follows:
-                = 'U':  Obtain A in the upper block diagonal form;
-                = 'L':  Obtain A in the lower block diagonal form.
-    Return objects:
-        n : int
-            The number of state variables (n1 + n2) in the resulting system,
-            i.e. the order of the matrix A, the number of rows of B and
-            the number of columns of C.
-        A : rank-2 array('d') with bounds (n1+n2,n1+n2)
-            The leading N-by-N part of this array contains the state transition
-            matrix A for the cascaded system.
-        B : rank-2 array('d') with bounds (n1+n2,m1)
-            The leading n-by-m1 part of this array contains the input/state
-            matrix B for the cascaded system.
-        C : rank-2 array('d') with bounds (p2,n1+n2)
-            The leading p2-by-n part of this array contains the state/output
-            matrix C for the cascaded system.
-        D : rank-2 array('d') with bounds (p2,m1)
-            The leading p2-by-m1 part of this array contains the input/output
-            matrix D for the cascaded system.
-
-    Notes:
+    Parameters
+    ----------
+    n1 : int
+        The number of state variables in the first system, i.e. the order
+        of the matrix A1.  n1 > 0.
+    m1 : int
+        The number of input variables for the first system. m1 > 0.
+    p1 : int
+        The number of output variables from the first system and the number
+        of input variables for the second system. p1 > 0.
+    n2 : int
+        The number of state variables in the second system, i.e. the order
+        of the matrix A2.  n2 > 0.
+    p2 : int
+        The number of output variables from the second system. p2 > 0.
+    A1 : (n1,n1) array_like
+        The leading n1-by-n1 part of this array must contain the state
+        transition matrix A1 for the first system.
+    B1 : (n1,m1) array_like
+        The leading n1-by-m1 part of this array must contain the input/state
+        matrix B1 for the first system.
+    C1 : (p1,n1) array_like
+        The leading p1-by-n1 part of this array must contain the state/output
+        matrix C1 for the first system.
+    D1 : (p1,m1) array_like
+        The leading p1-by-m1 part of this array must contain the input/output
+        matrix D1 for the first system.
+    A2 : (n2,n2) array_like
+        The leading n2-by-n2 part of this array must contain the state
+        transition matrix A2 for the second system.
+    B2 : (n2,p1) array_like
+        The leading n2-by-p1 part of this array must contain the input/state
+        matrix B2 for the second system.
+    C2 : (p2,n2) array_like
+        The leading p2-by-n2 part of this array must contain the state/output
+        matrix C2 for the second system.
+    D2 : (p2,p1) array_like
+        The leading p2-by-p1 part of this array must contain the input/output
+        matrix D2 for the second system.
+    uplo :  {'U', 'L'}, optional
+        Indicates whether the user wishes to obtain the matrix A in
+        the upper or lower block diagonal form, as follows:
+            = 'U':  Obtain A in the upper block diagonal form;
+            = 'L':  Obtain A in the lower block diagonal form.
+        Default is `U`.
+
+    Returns
+    -------
+    n : int
+        The number of state variables (n1 + n2) in the resulting system,
+        i.e. the order of the matrix A, the number of rows of B and
+        the number of columns of C.
+    A : (n1+n2,n1+n2) ndarray
+        The leading N-by-N part of this array contains the state transition
+        matrix A for the cascaded system.
+    B : (n1+n2,m1) ndarray
+        The leading n-by-m1 part of this array contains the input/state
+        matrix B for the cascaded system.
+    C : (p2,n1+n2) ndarray
+        The leading p2-by-n part of this array contains the state/output
+        matrix C for the cascaded system.
+    D : (p2,m1) ndarray
+        The leading p2-by-m1 part of this array contains the input/output
+        matrix D for the cascaded system.
+
+    Raises
+    ------
+    SlycotParameterError
+        :info = -i: the i-th argument had an illegal value
+
+    Notes
+    -----
         The implemented methods rely on accuracy enhancing square-root or
         balancing-free square-root techniques.
         The algorithms require less than 30N^3  floating point operations.