diff --git a/control/tests/xferfcn_test.py b/control/tests/xferfcn_test.py
index 6e1cf6ce2..ebb781b89 100644
--- a/control/tests/xferfcn_test.py
+++ b/control/tests/xferfcn_test.py
@@ -9,8 +9,9 @@
import control as ct
from control import StateSpace, TransferFunction, rss, evalfr
-from control import ss, ss2tf, tf, tf2ss
-from control import isctime, isdtime, sample_system, defaults
+from control import ss, ss2tf, tf, tf2ss, zpk
+from control import isctime, isdtime, sample_system
+from control import defaults, reset_defaults, set_defaults
from control.statesp import _convert_to_statespace
from control.xferfcn import _convert_to_transfer_function
from control.tests.conftest import slycotonly, matrixfilter
@@ -906,6 +907,128 @@ def test_printing_mimo(self):
assert isinstance(str(sys), str)
assert isinstance(sys._repr_latex_(), str)
+ @pytest.mark.parametrize(
+ "zeros, poles, gain, output",
+ [([0], [-1], 1,
+ '\n'
+ ' s\n'
+ '-----\n'
+ 's + 1\n'),
+ ([-1], [-1], 1,
+ '\n'
+ 's + 1\n'
+ '-----\n'
+ 's + 1\n'),
+ ([-1], [1], 1,
+ '\n'
+ 's + 1\n'
+ '-----\n'
+ 's - 1\n'),
+ ([1], [-1], 1,
+ '\n'
+ 's - 1\n'
+ '-----\n'
+ 's + 1\n'),
+ ([-1], [-1], 2,
+ '\n'
+ '2 (s + 1)\n'
+ '---------\n'
+ ' s + 1\n'),
+ ([-1], [-1], 0,
+ '\n'
+ '0\n'
+ '-\n'
+ '1\n'),
+ ([-1], [1j, -1j], 1,
+ '\n'
+ ' s + 1\n'
+ '-----------------\n'
+ '(s - 1j) (s + 1j)\n'),
+ ([4j, -4j], [2j, -2j], 2,
+ '\n'
+ '2 (s - 4j) (s + 4j)\n'
+ '-------------------\n'
+ ' (s - 2j) (s + 2j)\n'),
+ ([1j, -1j], [-1, -4], 2,
+ '\n'
+ '2 (s - 1j) (s + 1j)\n'
+ '-------------------\n'
+ ' (s + 1) (s + 4)\n'),
+ ([1], [-1 + 1j, -1 - 1j], 1,
+ '\n'
+ ' s - 1\n'
+ '-------------------------\n'
+ '(s + (1-1j)) (s + (1+1j))\n'),
+ ([1], [1 + 1j, 1 - 1j], 1,
+ '\n'
+ ' s - 1\n'
+ '-------------------------\n'
+ '(s - (1+1j)) (s - (1-1j))\n'),
+ ])
+ def test_printing_zpk(self, zeros, poles, gain, output):
+ """Test _tf_polynomial_to_string for constant systems"""
+ G = zpk(zeros, poles, gain, display_format='zpk')
+ res = str(G)
+ assert res == output
+
+ @pytest.mark.parametrize(
+ "zeros, poles, gain, format, output",
+ [([1], [1 + 1j, 1 - 1j], 1, ".2f",
+ '\n'
+ ' 1.00\n'
+ '-------------------------------------\n'
+ '(s + (1.00-1.41j)) (s + (1.00+1.41j))\n'),
+ ([1], [1 + 1j, 1 - 1j], 1, ".3f",
+ '\n'
+ ' 1.000\n'
+ '-----------------------------------------\n'
+ '(s + (1.000-1.414j)) (s + (1.000+1.414j))\n'),
+ ([1], [1 + 1j, 1 - 1j], 1, ".6g",
+ '\n'
+ ' 1\n'
+ '-------------------------------------\n'
+ '(s + (1-1.41421j)) (s + (1+1.41421j))\n')
+ ])
+ def test_printing_zpk_format(self, zeros, poles, gain, format, output):
+ """Test _tf_polynomial_to_string for constant systems"""
+ G = tf([1], [1,2,3], display_format='zpk')
+
+ set_defaults('xferfcn', floating_point_format=format)
+ res = str(G)
+ reset_defaults()
+
+ assert res == output
+
+ @pytest.mark.parametrize(
+ "num, den, output",
+ [([[[11], [21]], [[12], [22]]],
+ [[[1, -3, 2], [1, 1, -6]], [[1, 0, 1], [1, -1, -20]]],
+ ('\n'
+ 'Input 1 to output 1:\n'
+ ' 11\n'
+ '---------------\n'
+ '(s - 2) (s - 1)\n'
+ '\n'
+ 'Input 1 to output 2:\n'
+ ' 12\n'
+ '-----------------\n'
+ '(s - 1j) (s + 1j)\n'
+ '\n'
+ 'Input 2 to output 1:\n'
+ ' 21\n'
+ '---------------\n'
+ '(s - 2) (s + 3)\n'
+ '\n'
+ 'Input 2 to output 2:\n'
+ ' 22\n'
+ '---------------\n'
+ '(s - 5) (s + 4)\n'))])
+ def test_printing_zpk_mimo(self, num, den, output):
+ """Test _tf_polynomial_to_string for constant systems"""
+ G = tf(num, den, display_format='zpk')
+ res = str(G)
+ assert res == output
+
@slycotonly
def test_size_mismatch(self):
"""Test size mismacht"""
diff --git a/control/xferfcn.py b/control/xferfcn.py
index 0bc84e096..6edb26858 100644
--- a/control/xferfcn.py
+++ b/control/xferfcn.py
@@ -69,7 +69,14 @@
# Define module default parameter values
-_xferfcn_defaults = {}
+_xferfcn_defaults = {
+ 'xferfcn.display_format': 'poly',
+ 'xferfcn.floating_point_format': '.4g'
+}
+
+def _float2str(value):
+ _num_format = config.defaults.get('xferfcn.floating_point_format', ':.4g')
+ return f"{value:{_num_format}}"
class TransferFunction(LTI):
@@ -92,6 +99,10 @@ class TransferFunction(LTI):
time, positive number is discrete time with specified
sampling time, None indicates unspecified timebase (either
continuous or discrete time).
+ display_format: None, 'poly' or 'zpk'
+ Set the display format used in printing the TransferFunction object.
+ Default behavior is polynomial display and can be changed by
+ changing config.defaults['xferfcn.display_format'].
Attributes
----------
@@ -198,6 +209,17 @@ def __init__(self, *args, **kwargs):
#
# Process keyword arguments
#
+ # During module init, TransferFunction.s and TransferFunction.z
+ # get initialized when defaults are not fully initialized yet.
+ # Use 'poly' in these cases.
+
+ self.display_format = kwargs.pop(
+ 'display_format',
+ config.defaults.get('xferfcn.display_format', 'poly'))
+
+ if self.display_format not in ('poly', 'zpk'):
+ raise ValueError("display_format must be 'poly' or 'zpk',"
+ " got '%s'" % self.display_format)
# Determine if the transfer function is static (needed for dt)
static = True
@@ -432,22 +454,29 @@ def _truncatecoeff(self):
[self.num, self.den] = data
def __str__(self, var=None):
- """String representation of the transfer function."""
+ """String representation of the transfer function.
- mimo = self.ninputs > 1 or self.noutputs > 1
+ Based on the display_format property, the output will be formatted as
+ either polynomials or in zpk form.
+ """
+ mimo = not self.issiso()
if var is None:
- # TODO: replace with standard calls to lti functions
- var = 's' if self.dt is None or self.dt == 0 else 'z'
+ var = 's' if self.isctime() else 'z'
outstr = ""
- for i in range(self.ninputs):
- for j in range(self.noutputs):
+ for ni in range(self.ninputs):
+ for no in range(self.noutputs):
if mimo:
- outstr += "\nInput %i to output %i:" % (i + 1, j + 1)
+ outstr += "\nInput %i to output %i:" % (ni + 1, no + 1)
# Convert the numerator and denominator polynomials to strings.
- numstr = _tf_polynomial_to_string(self.num[j][i], var=var)
- denstr = _tf_polynomial_to_string(self.den[j][i], var=var)
+ if self.display_format == 'poly':
+ numstr = _tf_polynomial_to_string(self.num[no][ni], var=var)
+ denstr = _tf_polynomial_to_string(self.den[no][ni], var=var)
+ elif self.display_format == 'zpk':
+ z, p, k = tf2zpk(self.num[no][ni], self.den[no][ni])
+ numstr = _tf_factorized_polynomial_to_string(z, gain=k, var=var)
+ denstr = _tf_factorized_polynomial_to_string(p, var=var)
# Figure out the length of the separating line
dashcount = max(len(numstr), len(denstr))
@@ -461,10 +490,9 @@ def __str__(self, var=None):
outstr += "\n" + numstr + "\n" + dashes + "\n" + denstr + "\n"
- # See if this is a discrete time system with specific sampling time
- if not (self.dt is None) and type(self.dt) != bool and self.dt > 0:
- # TODO: replace with standard calls to lti functions
- outstr += "\ndt = " + self.dt.__str__() + "\n"
+ # If this is a strict discrete time system, print the sampling time
+ if type(self.dt) != bool and self.isdtime(strict=True):
+ outstr += "\ndt = " + str(self.dt) + "\n"
return outstr
@@ -485,7 +513,7 @@ def __repr__(self):
def _repr_latex_(self, var=None):
"""LaTeX representation of transfer function, for Jupyter notebook"""
- mimo = self.ninputs > 1 or self.noutputs > 1
+ mimo = not self.issiso()
if var is None:
# ! TODO: replace with standard calls to lti functions
@@ -496,18 +524,23 @@ def _repr_latex_(self, var=None):
if mimo:
out.append(r"\begin{bmatrix}")
- for i in range(self.noutputs):
- for j in range(self.ninputs):
+ for no in range(self.noutputs):
+ for ni in range(self.ninputs):
# Convert the numerator and denominator polynomials to strings.
- numstr = _tf_polynomial_to_string(self.num[i][j], var=var)
- denstr = _tf_polynomial_to_string(self.den[i][j], var=var)
+ if self.display_format == 'poly':
+ numstr = _tf_polynomial_to_string(self.num[no][ni], var=var)
+ denstr = _tf_polynomial_to_string(self.den[no][ni], var=var)
+ elif self.display_format == 'zpk':
+ z, p, k = tf2zpk(self.num[no][ni], self.den[no][ni])
+ numstr = _tf_factorized_polynomial_to_string(z, gain=k, var=var)
+ denstr = _tf_factorized_polynomial_to_string(p, var=var)
numstr = _tf_string_to_latex(numstr, var=var)
denstr = _tf_string_to_latex(denstr, var=var)
out += [r"\frac{", numstr, "}{", denstr, "}"]
- if mimo and j < self.noutputs - 1:
+ if mimo and ni < self.ninputs - 1:
out.append("&")
if mimo:
@@ -1285,7 +1318,7 @@ def _tf_polynomial_to_string(coeffs, var='s'):
N = len(coeffs) - 1
for k in range(len(coeffs)):
- coefstr = '%.4g' % abs(coeffs[k])
+ coefstr = _float2str(abs(coeffs[k]))
power = (N - k)
if power == 0:
if coefstr != '0':
@@ -1323,6 +1356,48 @@ def _tf_polynomial_to_string(coeffs, var='s'):
return thestr
+def _tf_factorized_polynomial_to_string(roots, gain=1, var='s'):
+ """Convert a factorized polynomial to a string"""
+
+ if roots.size == 0:
+ return _float2str(gain)
+
+ factors = []
+ for root in sorted(roots, reverse=True):
+ if np.isreal(root):
+ if root == 0:
+ factor = f"{var}"
+ factors.append(factor)
+ elif root > 0:
+ factor = f"{var} - {_float2str(np.abs(root))}"
+ factors.append(factor)
+ else:
+ factor = f"{var} + {_float2str(np.abs(root))}"
+ factors.append(factor)
+ elif np.isreal(root * 1j):
+ if root.imag > 0:
+ factor = f"{var} - {_float2str(np.abs(root))}j"
+ factors.append(factor)
+ else:
+ factor = f"{var} + {_float2str(np.abs(root))}j"
+ factors.append(factor)
+ else:
+ if root.real > 0:
+ factor = f"{var} - ({_float2str(root)})"
+ factors.append(factor)
+ else:
+ factor = f"{var} + ({_float2str(-root)})"
+ factors.append(factor)
+
+ multiplier = ''
+ if round(gain, 4) != 1.0:
+ multiplier = _float2str(gain) + " "
+
+ if len(factors) > 1 or multiplier:
+ factors = [f"({factor})" for factor in factors]
+
+ return multiplier + " ".join(factors)
+
def _tf_string_to_latex(thestr, var='s'):
""" make sure to superscript all digits in a polynomial string
and convert float coefficients in scientific notation
@@ -1486,6 +1561,10 @@ def tf(*args, **kwargs):
Polynomial coefficients of the numerator
den: array_like, or list of list of array_like
Polynomial coefficients of the denominator
+ display_format: None, 'poly' or 'zpk'
+ Set the display format used in printing the TransferFunction object.
+ Default behavior is polynomial display and can be changed by
+ changing config.defaults['xferfcn.display_format']..
Returns
-------
@@ -1538,7 +1617,7 @@ def tf(*args, **kwargs):
>>> # Create a variable 's' to allow algebra operations for SISO systems
>>> s = tf('s')
- >>> G = (s + 1)/(s**2 + 2*s + 1)
+ >>> G = (s + 1) / (s**2 + 2*s + 1)
>>> # Convert a StateSpace to a TransferFunction object.
>>> sys_ss = ss("1. -2; 3. -4", "5.; 7", "6. 8", "9.")
@@ -1609,12 +1688,24 @@ def zpk(zeros, poles, gain, *args, **kwargs):
name : string, optional
System name (used for specifying signals). If unspecified, a generic
name <sys[id]> is generated with a unique integer id.
+ display_format: None, 'poly' or 'zpk'
+ Set the display format used in printing the TransferFunction object.
+ Default behavior is polynomial display and can be changed by
+ changing config.defaults['xferfcn.display_format'].
Returns
-------
out: :class:`TransferFunction`
Transfer function with given zeros, poles, and gain.
+ Examples
+ --------
+ >>> from control import tf
+ >>> G = zpk([1],[2, 3], gain=1, display_format='zpk')
+ >>> G
+ s - 1
+ ---------------
+ (s - 2) (s - 3)
"""
num, den = zpk2tf(zeros, poles, gain)
return TransferFunction(num, den, *args, **kwargs)