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Allow static gain StateSpace objects to be straightforwardly created. #107

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e8ee43f
BugFix?: allow straightforward creation of static gain StateSpace obj…
roryyorke Aug 11, 2016
7382644
BugFix: fix Python 2.7 failure.
roryyorke Aug 11, 2016
2794260
MessageFix: remove extra 'C'
roryyorke Aug 12, 2016
e640b17
BugFix: allow empty (no input or output) StateSpace objects.
roryyorke Sep 18, 2016
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76 changes: 41 additions & 35 deletions control/statesp.py
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Original file line number Diff line number Diff line change
Expand Up @@ -52,7 +52,7 @@

import numpy as np
from numpy import all, angle, any, array, asarray, concatenate, cos, delete, \
dot, empty, exp, eye, matrix, ones, pi, poly, poly1d, roots, shape, sin, \
dot, empty, exp, eye, ones, pi, poly, poly1d, roots, shape, sin, \
zeros, squeeze
from numpy.random import rand, randn
from numpy.linalg import solve, eigvals, matrix_rank
Expand All @@ -66,6 +66,19 @@

__all__ = ['StateSpace', 'ss', 'rss', 'drss', 'tf2ss', 'ssdata']


def _matrix(a):
"""_matrix(a) -> numpy.matrix
a - passed to numpy.matrix
Wrapper around numpy.matrix; unlike that function, _matrix([]) will be 0x0
"""
from numpy import matrix
am = matrix(a)
if (1,0) == am.shape:
am.shape = (0,0)
return am


class StateSpace(LTI):
"""A class for representing state-space models

Expand Down Expand Up @@ -122,34 +135,35 @@ def __init__(self, *args):
else:
raise ValueError("Needs 1 or 4 arguments; received %i." % len(args))

# Here we're going to convert inputs to matrices, if the user gave a
# non-matrix type.
#! TODO: [A, B, C, D] = map(matrix, [A, B, C, D])?
matrices = [A, B, C, D]
for i in range(len(matrices)):
# Convert to matrix first, if necessary.
matrices[i] = matrix(matrices[i])
[A, B, C, D] = matrices
A, B, C, D = [_matrix(M) for M in (A, B, C, D)]

LTI.__init__(self, B.shape[1], C.shape[0], dt)
# TODO: use super here?
LTI.__init__(self, inputs=D.shape[1], outputs=D.shape[0], dt=dt)
self.A = A
self.B = B
self.C = C
self.D = D

self.states = A.shape[0]
self.states = A.shape[1]

if 0 == self.states:
# static gain
# matrix's default "empty" shape is 1x0
A.shape = (0,0)
B.shape = (0,self.inputs)
C.shape = (self.outputs,0)

# Check that the matrix sizes are consistent.
if self.states != A.shape[1]:
if self.states != A.shape[0]:
raise ValueError("A must be square.")
if self.states != B.shape[0]:
raise ValueError("B must have the same row size as A.")
raise ValueError("A and B must have the same number of rows.")
if self.states != C.shape[1]:
raise ValueError("C must have the same column size as A.")
if self.inputs != D.shape[1]:
raise ValueError("D must have the same column size as B.")
if self.outputs != D.shape[0]:
raise ValueError("D must have the same row size as C.")
raise ValueError("A and C must have the same number of columns.")
if self.inputs != B.shape[1]:
raise ValueError("B and D must have the same number of columns.")
if self.outputs != C.shape[0]:
raise ValueError("C and D must have the same number of rows.")

# Check for states that don't do anything, and remove them.
self._remove_useless_states()
Expand Down Expand Up @@ -179,17 +193,10 @@ def _remove_useless_states(self):
useless.append(i)

# Remove the useless states.
if all(useless == range(self.states)):
# All the states were useless.
self.A = zeros((1, 1))
self.B = zeros((1, self.inputs))
self.C = zeros((self.outputs, 1))
else:
# A more typical scenario.
self.A = delete(self.A, useless, 0)
self.A = delete(self.A, useless, 1)
self.B = delete(self.B, useless, 0)
self.C = delete(self.C, useless, 1)
self.A = delete(self.A, useless, 0)
self.A = delete(self.A, useless, 1)
self.B = delete(self.B, useless, 0)
self.C = delete(self.C, useless, 1)

self.states = self.A.shape[0]
self.inputs = self.B.shape[1]
Expand Down Expand Up @@ -333,8 +340,9 @@ def __rmul__(self, other):
return _convertToStateSpace(other) * self

# try to treat this as a matrix
# TODO: doesn't _convertToStateSpace do this anyway?
try:
X = matrix(other)
X = _matrix(other)
C = X * self.C
D = X * self.D
return StateSpace(self.A, self.B, C, D, self.dt)
Expand Down Expand Up @@ -692,11 +700,9 @@ def _convertToStateSpace(sys, **kw):

# If this is a matrix, try to create a constant feedthrough
try:
D = matrix(sys)
outputs, inputs = D.shape

return StateSpace(0., zeros((1, inputs)), zeros((outputs, 1)), D)
except Exception(e):
D = _matrix(sys)
return StateSpace([], [], [], D)
except Exception as e:
print("Failure to assume argument is matrix-like in" \
" _convertToStateSpace, result %s" % e)

Expand Down
90 changes: 88 additions & 2 deletions control/tests/statesp_test.py
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Original file line number Diff line number Diff line change
Expand Up @@ -5,9 +5,10 @@

import unittest
import numpy as np
from scipy.linalg import eigvals
from numpy.linalg import solve
from scipy.linalg import eigvals, block_diag
from control import matlab
from control.statesp import StateSpace, _convertToStateSpace
from control.statesp import StateSpace, _convertToStateSpace,tf2ss
from control.xferfcn import TransferFunction

class TestStateSpace(unittest.TestCase):
Expand Down Expand Up @@ -235,6 +236,91 @@ def test_dcgain(self):
sys3 = StateSpace(0., 1., 1., 0.)
np.testing.assert_equal(sys3.dcgain(), np.nan)


def test_scalarStaticGain(self):
"""Regression: can we create a scalar static gain?"""
g1=StateSpace([],[],[],[2])
g2=StateSpace([],[],[],[3])

# make sure StateSpace internals, specifically ABC matrix
# sizes, are OK for LTI operations
g3 = g1*g2
self.assertEqual(6, g3.D[0,0])
g4 = g1+g2
self.assertEqual(5, g4.D[0,0])
g5 = g1.feedback(g2)
self.assertAlmostEqual(2./7, g5.D[0,0])
g6 = g1.append(g2)
np.testing.assert_array_equal(np.diag([2,3]),g6.D)


def test_matrixStaticGain(self):
"""Regression: can we create matrix static gains?"""
d1 = np.matrix([[1,2,3],[4,5,6]])
d2 = np.matrix([[7,8],[9,10],[11,12]])
g1=StateSpace([],[],[],d1)

# _remove_useless_states was making A = [[0]]
self.assertEqual((0,0), g1.A.shape)

g2=StateSpace([],[],[],d2)
g3=StateSpace([],[],[],d2.T)

h1 = g1*g2
np.testing.assert_array_equal(d1*d2, h1.D)
h2 = g1+g3
np.testing.assert_array_equal(d1+d2.T, h2.D)
h3 = g1.feedback(g2)
np.testing.assert_array_almost_equal(solve(np.eye(2)+d1*d2,d1), h3.D)
h4 = g1.append(g2)
np.testing.assert_array_equal(block_diag(d1,d2),h4.D)


def test_remove_useless_states(self):
"""Regression: _remove_useless_states gives correct ABC sizes"""
g1 = StateSpace(np.zeros((3,3)),
np.zeros((3,4)),
np.zeros((5,3)),
np.zeros((5,4)))
self.assertEqual((0,0), g1.A.shape)
self.assertEqual((0,4), g1.B.shape)
self.assertEqual((5,0), g1.C.shape)
self.assertEqual((5,4), g1.D.shape)


def test_BadEmptyMatrices(self):
"""Mismatched ABCD matrices when some are empty"""
self.assertRaises(ValueError,StateSpace, [1], [], [], [1])
self.assertRaises(ValueError,StateSpace, [1], [1], [], [1])
self.assertRaises(ValueError,StateSpace, [1], [], [1], [1])
self.assertRaises(ValueError,StateSpace, [], [1], [], [1])
self.assertRaises(ValueError,StateSpace, [], [1], [1], [1])
self.assertRaises(ValueError,StateSpace, [], [], [1], [1])
self.assertRaises(ValueError,StateSpace, [1], [1], [1], [])


def test_Empty(self):
"""Regression: can we create an empty StateSpace object?"""
g1=StateSpace([],[],[],[])
self.assertEqual(0,g1.states)
self.assertEqual(0,g1.inputs)
self.assertEqual(0,g1.outputs)


def test_MatrixToStateSpace(self):
"""_convertToStateSpace(matrix) gives ss([],[],[],D)"""
D = np.matrix([[1,2,3],[4,5,6]])
g = _convertToStateSpace(D)
def empty(shape):
m = np.matrix([])
m.shape = shape
return m
np.testing.assert_array_equal(empty((0,0)), g.A)
np.testing.assert_array_equal(empty((0,D.shape[1])), g.B)
np.testing.assert_array_equal(empty((D.shape[0],0)), g.C)
np.testing.assert_array_equal(D,g.D)


class TestRss(unittest.TestCase):
"""These are tests for the proper functionality of statesp.rss."""

Expand Down