def test_tfm2ss_6(self):
"""Python version of Fortran test program from
-- Bug in TD04AD when ROWCOL='C' #6
This bug was fixed in PR #27"""
m = 1
p = 1
index = np.array([0])
dcoeff = np.array([[0.5]])
ucoeff = np.array([[[32]]])
n, A, B, C, D = transform.td04ad('R', m, p, index, dcoeff, ucoeff)
self.assertEqual(n, 0)
np.testing.assert_array_almost_equal(D, np.array([[64]]))
n, A, B, C, D = transform.td04ad('C', m, p, index, dcoeff, ucoeff)
self.assertEqual(n, 0)
np.testing.assert_array_almost_equal(D, np.array([[64]]))
def test_td04ad_case1(self):
"""td04ad: Convert with both 'C' and 'R' options"""
# for octave:
"""
num = { [0.0, 0.0, 1.0 ], [ 1.0, 0.0 ];
[3.0, -1.0, 1.0 ], [ 0.0, 1.0 ];
[0.0, 0.0, 1.0], [ 0.0, 2.0 ] };
den = { [1.0, 0.4, 3.0], [ 1.0, 1.0 ];
[1.0, 0.4, 3.0], [ 1.0, 1.0 ];
[1.0, 0.4, 3.0], [ 1.0, 1.0 ]};
"""
# common denominators for the inputs
n = 2
m = 2
p = 3
num = np.array([
[ [0.0, 0.0, 1.0 ], [ 1.0, 0.0, 0.0 ] ],
[ [3.0, -1.0, 1.0 ], [ 0.0, 1.0, 0.0 ] ],
[ [0.0, 0.0, 1.0], [ 0.0, 2.0, 0.0 ] ] ])
p, m, d = num.shape
numc = np.zeros((max(1, m, p), max(1, m, p), d), dtype=float)
numc[:p,:m,:] = num
denc = np.array(
[ [1.0, 0.4, 3.0], [ 1.0, 1.0, 0.0 ] ])
indc = np.array(
[ 2, 1 ], dtype=int)
denr = np.array(
[ [1.0, 0.4, 3.0], [ 1.0, 1.0, 0.0 ], [1.0, 0.0, 0.0] ])
indr = np.array(
[ 2, 1, 0 ], dtype=int)
n, A, B, C, D = transform.td04ad('C', 2, 3, indc, denc, numc)
#print('A=\n', A, '\nB=\n', B, '\nC=\n', C, '\nD=\n', D)
Ac = [ [-1, 0, 0], [ 0, -0.4, -0.3], [ 0, 10, 0]]
Bc = [ [0, -1] ,[ 1 , 0], [ 0, 0]]
Cc = [ [1, 0, 0.1], [-1, -2.2, -0.8], [ -2, 0, 0.1] ]
Dc = [ [0, 1], [ 3, 0], [ 0, 0]]
np.testing.assert_array_almost_equal(A, Ac)
np.testing.assert_array_almost_equal(B, Bc)
np.testing.assert_array_almost_equal(C, Cc)
np.testing.assert_array_almost_equal(D, Dc)
resr = transform.td04ad('R', 2, 3, indr, denr, num)
def test_td04ad_c(self):
"""td04ad: Convert with 'C' option"""
# for octave:
"""
num = { [0.0, 0.0, 1.0 ], [ 1.0, 0.0 ];
[3.0, -1.0, 1.0 ], [ 0.0, 1.0 ];
[0.0, 0.0, 1.0], [ 0.0, 2.0 ] };
den = { [1.0, 0.4, 3.0], [ 1.0, 1.0 ];
[1.0, 0.4, 3.0], [ 1.0, 1.0 ];
[1.0, 0.4, 3.0], [ 1.0, 1.0 ]};
"""
m = 2
p = 3
d = 3
num = np.array([
[ [0.0, 0.0, 1.0], [1.0, 0.0, 0.0] ],
[ [3.0, -1.0, 1.0], [0.0, 1.0, 0.0] ],
[ [0.0, 0.0, 1.0], [0.0, 2.0, 0.0] ] ])
numc = np.zeros((max(1, m, p), max(1, m, p), d), dtype=float)
numc[:p,:m,:] = num
denc = np.array(
[ [1.0, 0.4, 3.0], [ 1.0, 1.0, 0.0 ] ])
indc = np.array(
[ 2, 1 ], dtype=int)
nref = 3
Aref = np.array([ [-1, 0, 0],
[ 0, -0.4, -0.3],
[ 0, 10, 0] ])
Bref = np.array([ [0, -1],
[1, 0],
[0, 0] ])
Cref = np.array([ [1, 0, 0.1],
[-1, -2.2, -0.8],
[-2, 0, 0.1] ])
Dref = np.array([ [0, 1],
[3, 0],
[0, 0] ])
nr, A, B, C, D = transform.td04ad('C', m, p, indc, denc, numc)
#print('A=\n', A, '\nB=\n', B, '\nC=\n', C, '\nD=\n', D)
np.testing.assert_equal(nref, nr)
# the returned state space representation is not guaranteed to
# be of one form for all architectures, so we transform back
# to tf and check for equality then
_, _, _, _, _, dcoeff, ucoeff = transform.tb04ad(
nr, m, p, A, B, C, D)
_, _, _, _, _, dcoeffref, ucoeffref = transform.tb04ad(
nref, m, p, Aref, Bref, Cref, Dref)
np.testing.assert_array_almost_equal(dcoeff,dcoeffref)
np.testing.assert_array_almost_equal(ucoeff,ucoeffref)
def test_mixfeedthrough(self):
"""Test case popping up from control testing"""
# a mix of feedthrough and dynamics. The problem from the control
# package was somewhere else
num = np.array([ [ [ 0.0, 0.0 ], [ 0.0, -0.2 ] ],
[ [ -0.1, 0.0 ], [ 0.0, 0.0 ] ] ])
p, m, d = num.shape
numc = np.zeros((max(1, m, p), max(1, m, p), d), dtype=float)
numc[:p,:m,:] = num
denc = np.array([ [ 1.0, 1.1 ], [ 1.0, 0.0 ] ])
idxc = np.array([ 1, 0 ])
n, A, B, C, D = transform.td04ad('C', 2, 2, idxc, denc, numc)
np.testing.assert_array_almost_equal(D, np.array([[0, 0],[-0.1, 0]]))
def test_td04ad_static(self):
"""Regression: td04ad (TFM -> SS transformation) for static TFM"""
import numpy as np
from itertools import product
# 'C' fails on static TFs
for nout, nin, rc in product(range(1, 6), range(1, 6), ['R']):
num = np.reshape(np.arange(nout * nin), (nout, nin, 1))
if rc == 'R':
den = np.reshape(np.arange(1, 1 + nout), (nout, 1))
else:
den = np.reshape(np.arange(1, 1 + nin), (nin, 1))
index = np.tile([0], den.shape[0])
nr, a, b, c, d = transform.td04ad(rc, nin, nout, index, den, num)
def test_td04ad_static(self):
"""Regression: td04ad (TFM -> SS transformation) for static TFM"""
import numpy as np
from itertools import product
# 'C' fails on static TFs
for nout,nin,rc in product(range(1,6),range(1,6),['R']):
num = np.reshape(np.arange(nout*nin),(nout,nin,1))
if rc == 'R':
den = np.reshape(np.arange(1,1+nout),(nout,1))
else:
den = np.reshape(np.arange(1,1+nin),(nin,1))
index = np.tile([0],den.shape[0])
nr,a,b,c,d = transform.td04ad(rc,nin,nout,index,den,num)
def test_staticgain(self):
"""td04ad: Convert a transferfunction to SS with only static gain"""
# 2 inputs, 3 outputs? columns share a denominator
num = np.array([ [ [1.0], [2.0] ],
[ [0.2], [4.3] ],
[ [1.2], [3.2] ] ])
p, m, d = num.shape
numc = np.zeros((max(1, m, p), max(1, m, p), d), dtype=float)
numc[:p,:m,:] = num
# denc, columns share a common denominator
denc = np.array([ [ 1.0], [0.5] ])
Dc = (num / denc).reshape((3,2))
idxc = np.zeros((2,), dtype=int)
# denr, rows share a common denominator
denr = np.array([ [1.0], [0.5], [3.0] ])
idxr = np.zeros((3,), dtype=int)
Dr = (num / denr[:, np.newaxis]).reshape((3,2))
# fails with:
# On entry to TB01XD parameter number 5 had an illegal value
n, A, B, C, D = transform.td04ad('C', 2, 3, idxc, denc, numc)
#print('A=\n', A, '\nB=\n', B, '\nC=\n', C, '\nD=\n', D)
self.assertEqual(A.shape, (0,0))
self.assertEqual(B.shape, (0,2))
self.assertEqual(C.shape, (3,0))
np.testing.assert_array_almost_equal(D, Dc)
n, A, B, C, D = transform.td04ad('R', 2, 3, idxr, denr, num)
#print('A=\n', A, '\nB=\n', B, '\nC=\n', C, '\nD=\n', D)
self.assertEqual(A.shape, (0,0))
self.assertEqual(B.shape, (0,2))
self.assertEqual(C.shape, (3,0))
np.testing.assert_array_almost_equal(D, Dr)
def test_toandfrom(self):
A = np.array([[-3.0]])
B = np.array([[0.1, 0.0]])
C = np.array([[1.0],[0.0]])
D = np.array([[0.0, 0.0],[0.0, 1.0]])
tfout = transform.tb04ad(1, 2, 2, A, B, C, D)
num = tfout[6]
den = tfout[5]
idxc = np.array([1, 0])
n, At, Bt, Ct, Dt = transform.td04ad('R', 2, 2, idxc, den, num)
np.testing.assert_array_almost_equal(D, Dt)
np.testing.assert_array_almost_equal(A, At)
def test_td04ad_r(self):
"""td04ad: Convert with 'R' option
example program from
http://slicot.org/objects/software/shared/doc/TD04AD.html
"""
m = 2
p = 2
rowcol = 'R'
index = [3, 3]
dcoeff = np.array([ [1.0, 6.0, 11.0, 6.0], [1.0, 6.0, 11.0, 6.0] ])
ucoeff = np.array([ [[1.0, 6.0, 12.0, 7.0], [0.0, 1.0, 4.0, 3.0]],
[[0.0, 0.0, 1.0, 1.0], [1.0, 8.0, 20.0, 15.0]] ])
nref = 3
Aref = np.array([ [ 0.5000, -0.8028, 0.9387],
[ 4.4047, -2.3380, 2.5076],
[-5.5541, 1.6872, -4.1620] ])
Bref = np.array([ [-0.2000, -1.2500],
[ 0.0000, -0.6097],
[ 0.0000, 2.2217] ])
Cref = np.array([ [0.0000, -0.8679, 0.2119],
[0.0000, 0.0000, 0.9002] ])
Dref = np.array([ [1.0000, 0.0000],
[0.0000, 1.0000] ])
nr, A, B, C, D = transform.td04ad(rowcol, m, p, index, dcoeff, ucoeff)
#print('A=\n', A, '\nB=\n', B, '\nC=\n', C, '\nD=\n', D)
np.testing.assert_equal(nref, nr)
# order of states is not guaranteed, so we reorder the reference
rindex = np.flip(np.argsort(np.diag(A)))
Arref = Aref[rindex, :][:, rindex]
Brref = Bref[rindex, :]
Crref = Cref[:, rindex]
Drref = Dref
np.testing.assert_array_almost_equal(A, Arref,decimal=4)
np.testing.assert_array_almost_equal(B, Brref,decimal=4)
np.testing.assert_array_almost_equal(C, Crref,decimal=4)
np.testing.assert_array_almost_equal(D, Drref,decimal=4)
def test_td04ad_static(self):
"""Regression: td04ad (TFM -> SS transformation) for static TFM"""
from itertools import product
for nout, nin, rc in product(range(1, 6), range(1, 6), ['R', 'C']):
Dref = np.zeros((nout, nin))
if rc == 'R':
num = np.reshape(np.arange(nout * nin), (nout, nin, 1))
den = np.reshape(np.arange(1, 1 + nout), (nout, 1))
index = np.repeat(0, nout)
Dref = num[:nout, :nin, 0] / np.broadcast_to(den, (nout, nin))
else:
maxn = max(nout, nin)
num = np.zeros((maxn, maxn, 1))
num[:nout, :nin, 0] = np.reshape(
np.arange(nout * nin), (nout, nin))
den = np.reshape(np.arange(1, 1 + nin), (nin, 1))
index = np.repeat(0, nin)
Dref = num[:nout, :nin, 0] / np.broadcast_to(den.T, (nout, nin))
nr, A, B, C, D = transform.td04ad(rc, nin, nout, index, den, num)
np.testing.assert_equal(nr, 0)
for M in [A, B, C]:
np.testing.assert_equal(M, np.zeros_like(M))
np.testing.assert_almost_equal(D, Dref)
