replace np.pi with math.pi (avoids Mock() issues) + docstring update …

…in margin

control/ctrlutil.py

@@ -43,17 +43,12 @@
 # Packages that we need access to
 from . import lti
 import numpy as np
-from numpy import pi
-
-# Hack for sphinx.ext.autodoc: if numpy is a mock import, then numpy.pi 
-# will be assigned to _Mock() and this generates a type error
-if not isinstance(pi, float):
-    pi = 3.14
+import math
 
 __all__ = ['unwrap', 'issys', 'db2mag', 'mag2db']
 
 # Utility function to unwrap an angle measurement
-def unwrap(angle, period=2*pi):
+def unwrap(angle, period=2*math.pi):
     """Unwrap a phase angle to give a continuous curve
 
     Parameters

control/freqplot.py

@@ -44,6 +44,7 @@
 import matplotlib.pyplot as plt
 import scipy as sp
 import numpy as np
+import math
 from .ctrlutil import unwrap
 from .bdalg import feedback
 
@@ -128,7 +129,7 @@ def bode_plot(syslist, omega=None, dB=None, Hz=None, deg=None,
         else:
             omega_limits = np.array(omega_limits)
             if Hz:
-                omega_limits *= 2.*np.pi
+                omega_limits *= 2.*math.pi
             if omega_num:
                 omega = sp.logspace(np.log10(omega_limits[0]), np.log10(omega_limits[1]), num=omega_num, endpoint=True)
             else:
@@ -142,7 +143,7 @@ def bode_plot(syslist, omega=None, dB=None, Hz=None, deg=None,
         else:
             omega_sys = np.array(omega)
             if sys.isdtime(True):
-                nyquistfrq = 2. * np.pi * 1. / sys.dt / 2.
+                nyquistfrq = 2. * math.pi * 1. / sys.dt / 2.
                 omega_sys = omega_sys[omega_sys < nyquistfrq]
                 # TODO: What distance to the Nyquist frequency is appropriate?
             else:
@@ -154,9 +155,9 @@ def bode_plot(syslist, omega=None, dB=None, Hz=None, deg=None,
             phase = unwrap(phase)
             nyquistfrq_plot = None
             if Hz:
-                omega_plot = omega_sys / (2. * np.pi)
+                omega_plot = omega_sys / (2. * math.pi)
                 if nyquistfrq:
-                    nyquistfrq_plot = nyquistfrq / (2. * np.pi)
+                    nyquistfrq_plot = nyquistfrq / (2. * math.pi)
             else:
                 omega_plot = omega_sys
                 if nyquistfrq:
@@ -187,7 +188,7 @@ def bode_plot(syslist, omega=None, dB=None, Hz=None, deg=None,
                 # Phase plot
                 ax_phase = plt.subplot(212, sharex=ax_mag);
                 if deg:
-                    phase_plot = phase * 180. / np.pi
+                    phase_plot = phase * 180. / math.pi
                 else:
                     phase_plot = phase
                 ax_phase.semilogx(omega_plot, phase_plot, *args, **kwargs)
@@ -208,8 +209,8 @@ def genZeroCenteredSeries(val_min, val_max, period):
                     ax_phase.set_yticks(genZeroCenteredSeries(ylim[0], ylim[1], 15.), minor=True)
                 else:
                     ylim = ax_phase.get_ylim()
-                    ax_phase.set_yticks(genZeroCenteredSeries(ylim[0], ylim[1], np.pi / 4.))
-                    ax_phase.set_yticks(genZeroCenteredSeries(ylim[0], ylim[1], np.pi / 12.), minor=True)
+                    ax_phase.set_yticks(genZeroCenteredSeries(ylim[0], ylim[1], math.pi / 4.))
+                    ax_phase.set_yticks(genZeroCenteredSeries(ylim[0], ylim[1], math.pi / 12.), minor=True)
                 ax_phase.grid(True, which='both')
                 # ax_mag.grid(which='minor', alpha=0.3)
                 # ax_mag.grid(which='major', alpha=0.9)
@@ -449,7 +450,7 @@ def default_frequency_range(syslist, Hz=None, number_of_samples=None, feature_pe
                 features_ = features_[features_ != 0.0];
                 features = np.concatenate((features, features_))
             elif sys.isdtime(strict=True):
-                fn = np.pi * 1. / sys.dt
+                fn = math.pi * 1. / sys.dt
                 # TODO: What distance to the Nyquist frequency is appropriate?
                 freq_interesting.append(fn * 0.9)
 
@@ -475,12 +476,12 @@ def default_frequency_range(syslist, Hz=None, number_of_samples=None, feature_pe
         features = np.array([1.]);
 
     if Hz:
-        features /= 2.*np.pi
+        features /= 2.*math.pi
         features = np.log10(features)
         lsp_min = np.floor(np.min(features) - feature_periphery_decade)
         lsp_max = np.ceil(np.max(features) + feature_periphery_decade)
-        lsp_min += np.log10(2.*np.pi)
-        lsp_max += np.log10(2.*np.pi)
+        lsp_min += np.log10(2.*math.pi)
+        lsp_max += np.log10(2.*math.pi)
     else:
         features = np.log10(features)
         lsp_min = np.floor(np.min(features) - feature_periphery_decade)

control/margins.py

@@ -50,11 +50,12 @@
 $Id$
 """
 
+import math
 import numpy as np
+import scipy as sp
 from . import xferfcn
 from .lti import issiso
 from . import frdata
-import scipy as sp
 
 __all__ = ['stability_margins', 'phase_crossover_frequencies', 'margin']
 
@@ -140,7 +141,7 @@ def stability_margins(sysdata, returnall=False, epsw=0.0):
             sys = sysdata
         elif getattr(sysdata, '__iter__', False) and len(sysdata) == 3:
             mag, phase, omega = sysdata
-            sys = frdata.FRD(mag * np.exp(1j * phase * np.pi/180),
+            sys = frdata.FRD(mag * np.exp(1j * phase * math.pi/180),
                              omega, smooth=True)
         else:
             sys = xferfcn._convertToTransferFunction(sysdata)
@@ -336,13 +337,13 @@ def phase_crossover_frequencies(sys):
 
 
 def margin(*args):
-    """margin(sys)
+    """margin(sysdata)
 
     Calculate gain and phase margins and associated crossover frequencies
 
     Parameters
     ----------
-    sysdata: LTI system or (mag, phase, omega) sequence
+    sysdata : LTI system or (mag, phase, omega) sequence
         sys : StateSpace or TransferFunction
             Linear SISO system
         mag, phase, omega : sequence of array_like

control/statesp.py

@@ -51,9 +51,10 @@
 $Id$
 """
 
+import math
 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, matrix, ones, poly, poly1d, roots, shape, sin, \
     zeros, squeeze
 from numpy.random import rand, randn
 from numpy.linalg import solve, eigvals, matrix_rank
@@ -367,7 +368,7 @@ def evalfr(self, omega):
         if isdtime(self, strict=True):
             dt = timebase(self)
             s = exp(1.j * omega * dt)
-            if (omega * dt > pi):
+            if (omega * dt > math.pi):
                 warnings.warn("evalfr: frequency evaluation above Nyquist frequency")
         else:
             s = omega * 1.j
@@ -798,7 +799,7 @@ def _rss_generate(states, inputs, outputs, type):
                 poles[i] = complex(-exp(randn()), 3. * exp(randn()))
             elif type == 'd':
                 mag = rand()
-                phase = 2. * pi * rand()
+                phase = 2. * math.pi * rand()
                 poles[i] = complex(mag * cos(phase),
                     mag * sin(phase))
             poles[i+1] = complex(poles[i].real, -poles[i].imag)