Add ab04md

[KybernetikJo]

Add ab04md

TODO:

• add docstring
• add unit tests
• check behavior: intent(in, out, copy, ...), see Bugfix ab13bd #200

import slycot
import numpy as np

A = np.array([[1.0, 0.5],
              [0.5, 1.0]])
B = np.array([[0.0, -1.0],
              [1.0, 0.0]])
C = np.array([[-1.0, 0.0],
              [0.0, 1.0]])
D = np.array([[1.0, 0.0],
              [0.0, -1.0]])

Ad = np.array([[-1.0, -4.0],
               [-4.0, -1.0]])
Bd = np.array([[2.8284, 0.0],
               [0.0, -2.8284]])
Cd = np.array([[0.0, 2.8284],
               [-2.8284, 0.0]])
Dd = np.array([[-1.0, 0.0],
               [0.0, -3.0]])

n = 2
m = 2
p = 2

Ad_t, Bd_t, Cd_t, Dd_t = slycot.ab04md('C',n,m,p,A,B,C,D)

print("Ad_t = \n", Ad_t)
print("Bd_t = \n", Bd_t)
print("Cd_t = \n", Cd_t)
print("Dd_t = \n", Dd_t)

Ac_t, Bc_t, Cc_t, Dc_t = slycot.ab04md('D',n,m,p,Ad_t,Bd_t,Cd_t,Dd_t)

print("Ac_t = \n", Ac_t)
print("Bc_t = \n", Bc_t)
print("Cc_t = \n", Cc_t)
print("Dc_t = \n", Dc_t)

print(np.allclose(A,Ac_t))
print(np.allclose(B,Bc_t))
print(np.allclose(C,Cc_t))
print(np.allclose(D,Dc_t))

output

Ad_t = 
 [[-1. -4.]
 [-4. -1.]]
Bd_t = 
 [[-2.82842712 -0.        ]
 [-0.          2.82842712]]
Cd_t = 
 [[-0.          2.82842712]
 [-2.82842712  0.        ]]
Dd_t = 
 [[3. 0.]
 [0. 1.]]
Ac_t = 
 [[1.  0.5]
 [0.5 1. ]]
Bc_t = 
 [[ 0. -1.]
 [ 1. -0.]]
Cc_t = 
 [[-1.  0.]
 [-0.  1.]]
Dc_t = 
 [[ 1.  0.]
 [ 0. -1.]]
True
True
True
True

[KybernetikJo]

I have added the docstring, 2 unittests and discussed f2py behavior in #200. I would also keep here f2py intent(in,out,copy) for the state space matrices A,B,C,D.

Remark:
There is quite a bit of variation in the style of docstrings and unittests in slycot.

[bnavigator]

Please increase the count from above.

A reformat of the whle ab block seems in order, too

[bnavigator]

#205

[bnavigator]

Sorry for not being responsive as usual. I made a few remarks about formal things.

[KybernetikJo]

I have incorporated the suggestions and tried to improve the docstrings.
However, the .pfy, .py files and the docstring are very different in slycot in general and specifically in the analysis module.

I think we would need templates to unify the docstrings of all routines to meet the numpydoc specification.
Currently, only a few routines like ab01nd meet the numpydoc specification.

[bnavigator]

Suggested change

	""" At,Bt,Ct,Dt = ab04md(type_bn, n, m, p, A, B, C, D, [alpha, beta,ldwork])
	""" At,Bt,Ct,Dt = ab04md(type_t, n, m, p, A, B, C, D, [alpha, beta, ldwork])

[bnavigator]

Suggested change

	alpha : double
	alpha : double, optional

[bnavigator]

unittest.TestCase not needed