def generate_vector_field(poly_model, pmodel, \
axr = np.arange(-_VF_MAXR,_VF_MAXR+_VF_DELTAR,_VF_DELTAR), \
bxr = np.arange(-_VF_MAXR,_VF_MAXR+_VF_DELTAR,_VF_DELTAR), \
make_grid = True, limit_grid_radius = 0,color = 'k'):
"""
Generates a field of vectors using the base color shift model.
| Has the option to plot vector field.
Args:
:poly_model:
| function handle to model
:pmodel:
| ndarray with model parameters.
:axr:
| np.arange(-_VF_MAXR,_VF_MAXR+_VF_DELTAR,_VF_DELTAR), optional
| Ndarray specifying the a-coordinates at which to apply the model.
:bxr:
| np.arange(-_VF_MAXR,_VF_MAXR+_VF_DELTAR,_VF_DELTAR), optional
| Ndarray specifying the b-coordinates at which to apply the model.
:make_grid:
| True, optional
| True: generate a 2d-grid from :axr:, :bxr:.
:limit_grid_radius:
| 0, optional
| A value of zeros keeps grid as specified by axr,bxr.
| A value > 0 only keeps (a,b) coordinates within :limit_grid_radius:
:color:
| 'k', optional
| For plotting the vector field.
| If :color: == 0, no plot will be generated.
Returns:
:returns:
| If :color: == 0: ndarray of axt,bxt,axr,bxr
| Else: handle to axes used for plotting.
"""
# Generate grid from axr, bxr:
if make_grid == True:
axr, bxr = generate_grid(ax = axr, bx = bxr, out = 'ax,bx', limit_grid_radius = limit_grid_radius)
# Apply model at ref. coordinates:
axt,bxt,Cxt,hxt,axr,bxr,Cxr,hxr = apply_poly_model_at_x(poly_model, pmodel,axr,bxr)
# Plot vectorfield:
if color is not 0:
#plt.plot(axr, bxr,'ro',markersize=2)
plt.quiver(axr, bxr, axt-axr, bxt-bxr, headlength=1,color = color)
plt.xlabel("a'")
plt.ylabel("b'")
return plt.gca()#plt.show(plot1)
else:
return axt,bxt,axr,bxr
def plot(self, ylabel='Spectrum', *args, **kwargs):
"""
Make a plot of the spectral data in SPD instance.
Returns:
:returns:
| handle to current axes.
"""
plt.plot(self.wl, self.value.T, *args, **kwargs)
plt.xlabel('Wavelength (nm)')
plt.ylabel(ylabel)
return plt.gca()
def plot(self, ylabel='Spectrum', wavelength_bar=True, *args, **kwargs):
"""
Make a plot of the spectral data in SPD instance.
Returns:
:returns:
| handle to current axes.
"""
plt.plot(self.wl, self.value.T, *args, **kwargs)
if wavelength_bar == True:
Smax = np.nanmax(self.value)
axh = plot_spectrum_colors(spd=None,
spdmax=Smax,
axh=plt.gca(),
wavelength_height=-0.05)
plt.xlabel('Wavelength (nm)')
plt.ylabel(ylabel)
return plt.gca()
def plot_hue_bins(hbins = 16, start_hue = 0.0, scalef = 100, \
plot_axis_labels = False, bin_labels = '#', plot_edge_lines = True, \
plot_center_lines = False, plot_bin_colors = True, \
axtype = 'polar', ax = None, force_CVG_layout = False):
"""
Makes basis plot for Color Vector Graphic (CVG).
Args:
:hbins:
| 16 or ndarray with sorted hue bin centers (°), optional
:start_hue:
| 0.0, optional
:scalef:
| 100, optional
| Scale factor for graphic.
:plot_axis_labels:
| False, optional
| Turns axis ticks on/off (True/False).
:bin_labels:
| None or list[str] or '#', optional
| Plots labels at the bin center hues.
| - None: don't plot.
| - list[str]: list with str for each bin.
| (len(:bin_labels:) = :nhbins:)
| - '#': plots number.
:plot_edge_lines:
| True or False, optional
| Plot grey bin edge lines with '--'.
:plot_center_lines:
| False or True, optional
| Plot colored lines at 'center' of hue bin.
:plot_bin_colors:
| True, optional
| Colorize hue bins.
:axtype:
| 'polar' or 'cart', optional
| Make polar or Cartesian plot.
:ax:
| None or 'new' or 'same', optional
| - None or 'new' creates new plot
| - 'same': continue plot on same axes.
| - axes handle: plot on specified axes.
:force_CVG_layout:
| False or True, optional
| True: Force plot of basis of CVG on first encounter.
Returns:
:returns:
| gcf(), gca(), list with rgb colors for hue bins (for use in
other plotting fcns)
"""
# Setup hbincenters and hsv_hues:
if isinstance(hbins, float) | isinstance(hbins, int):
nhbins = hbins
dhbins = 360 / (nhbins) # hue bin width
hbincenters = np.arange(start_hue + dhbins / 2, 360, dhbins)
hbincenters = np.sort(hbincenters)
else:
hbincenters = hbins
idx = np.argsort(hbincenters)
if isinstance(bin_labels, list) | isinstance(bin_labels, np.ndarray):
bin_labels = bin_labels[idx]
hbincenters = hbincenters[idx]
nhbins = hbincenters.shape[0]
hbincenters = hbincenters * np.pi / 180
# Setup hbin labels:
if bin_labels is '#':
bin_labels = ['#{:1.0f}'.format(i + 1) for i in range(nhbins)]
# initializing the figure
cmap = None
if (ax == None) or (ax == 'new'):
fig = plt.figure()
newfig = True
else:
newfig = False
rect = [0.1, 0.1, 0.8,
0.8] # setting the axis limits in [left, bottom, width, height]
if axtype == 'polar':
# the polar axis:
if newfig == True:
ax = fig.add_axes(rect, polar=True, frameon=False)
else:
#cartesian axis:
if newfig == True:
ax = fig.add_axes(rect)
if (newfig == True) | (force_CVG_layout == True):
# Calculate hue-bin boundaries:
r = np.vstack(
(np.zeros(hbincenters.shape), scalef * np.ones(hbincenters.shape)))
theta = np.vstack((np.zeros(hbincenters.shape), hbincenters))
#t = hbincenters.copy()
dU = np.roll(hbincenters.copy(), -1)
dL = np.roll(hbincenters.copy(), 1)
dtU = dU - hbincenters
dtL = hbincenters - dL
dtU[dtU < 0] = dtU[dtU < 0] + 2 * np.pi
dtL[dtL < 0] = dtL[dtL < 0] + 2 * np.pi
dL = hbincenters - dtL / 2
dU = hbincenters + dtU / 2
dt = (dU - dL)
dM = dL + dt / 2
# Setup color for plotting hue bins:
hsv_hues = hbincenters - 30 * np.pi / 180
hsv_hues = hsv_hues / hsv_hues.max()
edges = np.vstack(
(np.zeros(hbincenters.shape), dL)) # setup hue bin edges array
if axtype == 'cart':
if plot_center_lines == True:
hx = r * np.cos(theta)
hy = r * np.sin(theta)
if bin_labels is not None:
hxv = np.vstack((np.zeros(hbincenters.shape),
1.3 * scalef * np.cos(hbincenters)))
hyv = np.vstack((np.zeros(hbincenters.shape),
1.3 * scalef * np.sin(hbincenters)))
if plot_edge_lines == True:
hxe = np.vstack(
(np.zeros(hbincenters.shape), 1.2 * scalef * np.cos(dL)))
hye = np.vstack(
(np.zeros(hbincenters.shape), 1.2 * scalef * np.sin(dL)))
# Plot hue-bins:
for i in range(nhbins):
# Create color from hue angle:
c = np.abs(np.array(colorsys.hsv_to_rgb(hsv_hues[i], 0.84, 0.9)))
#c = [abs(c[0]),abs(c[1]),abs(c[2])] # ensure all positive elements
if i == 0:
cmap = [c]
else:
cmap.append(c)
if axtype == 'polar':
if plot_edge_lines == True:
ax.plot(edges[:, i],
r[:, i] * 1.2,
color='grey',
marker='None',
linestyle=':',
linewidth=3,
markersize=2)
if plot_center_lines == True:
if np.mod(i, 2) == 1:
ax.plot(theta[:, i],
r[:, i],
color=c,
marker=None,
linestyle='--',
linewidth=2)
else:
ax.plot(theta[:, i],
r[:, i],
color=c,
marker='o',
linestyle='-',
linewidth=3,
markersize=10)
if plot_bin_colors == True:
bar = ax.bar(dM[i],
r[1, i],
width=dt[i],
color=c,
alpha=0.15)
if bin_labels is not None:
ax.text(hbincenters[i],
1.3 * scalef,
bin_labels[i],
fontsize=12,
horizontalalignment='center',
verticalalignment='center',
color=np.array([1, 1, 1]) * 0.3)
if plot_axis_labels == False:
ax.set_xticklabels([])
ax.set_yticklabels([])
else:
if plot_edge_lines == True:
ax.plot(hxe[:, i],
hye[:, i],
color='grey',
marker='None',
linestyle=':',
linewidth=3,
markersize=2)
if plot_center_lines == True:
if np.mod(i, 2) == 1:
ax.plot(hx[:, i],
hy[:, i],
color=c,
marker=None,
linestyle='--',
linewidth=2)
else:
ax.plot(hx[:, i],
hy[:, i],
color=c,
marker='o',
linestyle='-',
linewidth=3,
markersize=10)
if bin_labels is not None:
ax.text(hxv[1, i],
hyv[1, i],
bin_labels[i],
fontsize=12,
horizontalalignment='center',
verticalalignment='center',
color=np.array([1, 1, 1]) * 0.3)
ax.axis(1.1 * np.array(
[hxv.min(), hxv.max(),
hyv.min(), hyv.max()]))
if plot_axis_labels == False:
ax.set_xticklabels([])
ax.set_yticklabels([])
else:
plt.xlabel("a'")
plt.ylabel("b'")
plt.plot(0, 0, color='k', marker='o', linestyle=None)
return plt.gcf(), plt.gca(), cmap
def plot_ColorVectorGraphic(jabt, jabr, hbins = 16, start_hue = 0.0, scalef = 100, \
plot_axis_labels = False, bin_labels = None, \
plot_edge_lines = True, plot_center_lines = False, \
plot_bin_colors = True, axtype = 'polar', ax = None,\
force_CVG_layout = False):
"""
Plot Color Vector Graphic (CVG).
Args:
:jabt:
| ndarray with jab data under test SPD
:jabr:
| ndarray with jab data under reference SPD
:hbins:
| 16 or ndarray with sorted hue bin centers (°), optional
:start_hue:
| 0.0, optional
:scalef:
| 100, optional
| Scale factor for graphic.
:plot_axis_labels:
| False, optional
| Turns axis ticks on/off (True/False).
:bin_labels:
| None or list[str] or '#', optional
| Plots labels at the bin center hues.
| - None: don't plot.
| - list[str]: list with str for each bin.
| (len(:bin_labels:) = :nhbins:)
| - '#': plots number.
:plot_edge_lines:
| True or False, optional
| Plot grey bin edge lines with '--'.
:plot_center_lines:
| False or True, optional
| Plot colored lines at 'center' of hue bin.
:plot_bin_colors:
| True, optional
| Colorize hue-bins.
:axtype:
| 'polar' or 'cart', optional
| Make polar or Cartesian plot.
:ax:
| None or 'new' or 'same', optional
| - None or 'new' creates new plot
| - 'same': continue plot on same axes.
| - axes handle: plot on specified axes.
:force_CVG_layout:
| False or True, optional
| True: Force plot of basis of CVG.
Returns:
:returns:
| gcf(), gca(), list with rgb colors for hue bins (for use in
other plotting fcns)
"""
# Plot basis of CVG:
figCVG, ax, cmap = plot_hue_bins(hbins=hbins,
start_hue=start_hue,
scalef=scalef,
axtype=axtype,
ax=ax,
plot_center_lines=plot_center_lines,
plot_edge_lines=plot_edge_lines,
force_CVG_layout=force_CVG_layout,
bin_labels=bin_labels,
plot_bin_colors=plot_bin_colors)
if cmap == []:
cmap = ['k' for i in range(hbins)]
if axtype == 'polar':
jabr_theta, jabr_r = math.cart2pol(jabr[..., 1:3], htype='rad')
jabt_theta, jabt_r = math.cart2pol(jabt[..., 1:3], htype='rad')
#ax.quiver(jabrtheta,jabr_r,jabt[...,1]-jabr[...,1], jabt[...,2]-jabr_binned[...,2], color = 'k', headlength=3, angles='uv', scale_units='y', scale = 2,linewidth = 0.5)
ax.plot(jabt_theta, jabt_r, color='grey', linewidth=2)
for j in range(hbins):
c = cmap[j]
ax.quiver(jabr_theta[j],
jabr_r[j],
jabt[j, 1] - jabr[j, 1],
jabt[j, 2] - jabr[j, 2],
edgecolor='k',
facecolor=c,
headlength=3,
angles='uv',
scale_units='y',
scale=2,
linewidth=0.5)
else:
#ax.quiver(jabr[...,1],jabr[...,2],jabt[...,1]-jabr[...,1], jabt[...,2]-jabr[...,2], color = 'k', headlength=3, angles='uv', scale_units='xy', scale = 1,linewidth = 0.5)
ax.plot(jabt, jabt, color='grey', linewidth=2)
for j in range(hbins):
ax.quiver(jabr[j, 1],
jabr[j, 2],
jabt[j, 1] - jabr[j, 1],
jabt[j, 2] - jabr[j, 2],
color=cmap[j],
headlength=3,
angles='uv',
scale_units='xy',
scale=1,
linewidth=0.5)
if axtype == 'cart':
plt.xlabel("a'")
plt.ylabel("b'")
return plt.gcf(), plt.gca(), cmap
def plot_chromaticity_diagram_colors(diagram_samples = 256, diagram_opacity = 1.0, diagram_lightness = 0.25,\
cieobs = _CIEOBS, cspace = 'Yxy', cspace_pars = {},\
show = True, axh = None,\
show_grid = True, label_fontname = 'Times New Roman', label_fontsize = 12,\
**kwargs):
"""
Plot the chromaticity diagram colors.
Args:
:diagram_samples:
| 256, optional
| Sampling resolution of color space.
:diagram_opacity:
| 1.0, optional
| Sets opacity of chromaticity diagram
:diagram_lightness:
| 0.25, optional
| Sets lightness of chromaticity diagram
:axh:
| None or axes handle, optional
| Determines axes to plot data in.
| None: make new figure.
:show:
| True or False, optional
| Invoke matplotlib.pyplot.show() right after plotting
:cieobs:
| luxpy._CIEOBS or str, optional
| Determines CMF set to calculate spectrum locus or other.
:cspace:
| luxpy._CSPACE or str, optional
| Determines color space / chromaticity diagram to plot data in.
| Note that data is expected to be in specified :cspace:
:cspace_pars:
| {} or dict, optional
| Dict with parameters required by color space specified in :cspace:
| (for use with luxpy.colortf())
:show_grid:
| True, optional
| Show grid (True) or not (False)
:label_fontname:
| 'Times New Roman', optional
| Sets font type of axis labels.
:label_fontsize:
| 12, optional
| Sets font size of axis labels.
:kwargs:
| additional keyword arguments for use with matplotlib.pyplot.
Returns:
"""
offset = _EPS
ii, jj = np.meshgrid(np.linspace(offset, 1 + offset, diagram_samples), np.linspace(1+offset, offset, diagram_samples))
ij = np.dstack((ii, jj))
SL = _CMF[cieobs]['bar'][1:4].T
SL = np.vstack((SL,SL[0]))
SL = 100.0*SL/SL[:,1,None]
SL = colortf(SL, tf = cspace, tfa0 = cspace_pars)
Y,x,y = asplit(SL)
SL = np.vstack((x,y)).T
ij2D = ij.reshape((diagram_samples**2,2))
ij2D = np.hstack((diagram_lightness*100*np.ones((ij2D.shape[0],1)), ij2D))
xyz = colortf(ij2D, tf = cspace + '>xyz', tfa0 = cspace_pars)
xyz[xyz < 0] = 0
xyz[np.isinf(xyz.sum(axis=1)),:] = np.nan
xyz[np.isnan(xyz.sum(axis=1)),:] = offset
srgb = xyz_to_srgb(xyz)
srgb = srgb/srgb.max()
srgb = srgb.reshape((diagram_samples,diagram_samples,3))
if show == True:
if axh is None:
fig = plt.figure()
axh = fig.add_subplot(111)
polygon = Polygon(SL, facecolor='none', edgecolor='none')
axh.add_patch(polygon)
image = axh.imshow(
srgb,
interpolation='bilinear',
extent = (0.0, 1, -0.05, 1),
clip_path=None,
alpha=diagram_opacity)
image.set_clip_path(polygon)
plt.plot(x,y, color = 'darkgray')
if cspace == 'Yxy':
plt.xlim([0,1])
plt.ylim([0,1])
elif cspace == 'Yuv':
plt.xlim([0,0.6])
plt.ylim([0,0.6])
if (cspace is not None):
xlabel = _CSPACE_AXES[cspace][1]
ylabel = _CSPACE_AXES[cspace][2]
if (label_fontname is not None) & (label_fontsize is not None):
plt.xlabel(xlabel, fontname = label_fontname, fontsize = label_fontsize)
plt.ylabel(ylabel, fontname = label_fontname, fontsize = label_fontsize)
if show_grid == True:
plt.grid()
#plt.show()
return axh
else:
return None
def plot_color_data(x,y,z=None, axh=None, show = True, cieobs =_CIEOBS, \
cspace = _CSPACE, formatstr = 'k-', **kwargs):
"""
Plot color data from x,y [,z].
Args:
:x:
| float or ndarray with x-coordinate data
:y:
| float or ndarray with y-coordinate data
:z:
| None or float or ndarray with Z-coordinate data, optional
| If None: make 2d plot.
:axh:
| None or axes handle, optional
| Determines axes to plot data in.
| None: make new figure.
:show:
| True or False, optional
| Invoke matplotlib.pyplot.show() right after plotting
:cieobs:
| luxpy._CIEOBS or str, optional
| Determines CMF set to calculate spectrum locus or other.
:cspace:
| luxpy._CSPACE or str, optional
| Determines color space / chromaticity diagram to plot data in.
| Note that data is expected to be in specified :cspace:
:formatstr:
| 'k-' or str, optional
| Format str for plotting (see ?matplotlib.pyplot.plot)
:kwargs:
| additional keyword arguments for use with matplotlib.pyplot.
Returns:
:returns:
| None (:show: == True)
| or
| handle to current axes (:show: == False)
"""
x = np.atleast_1d(x)
y = np.atleast_1d(y)
if 'grid' in kwargs.keys():
plt.grid(kwargs['grid']);kwargs.pop('grid')
if z is not None:
z = np.atleast_1d(z)
if axh is None:
fig = plt.figure()
axh = plt.axes(projection='3d')
axh.plot3D(x,y,z,formatstr, linewidth = 2,**kwargs)
plt.zlabel(_CSPACE_AXES[cspace][0], kwargs)
else:
plt.plot(x,y,formatstr,linewidth = 2,**kwargs)
plt.xlabel(_CSPACE_AXES[cspace][1], kwargs)
plt.ylabel(_CSPACE_AXES[cspace][2], kwargs)
if 'label' in kwargs.keys():
plt.legend()
if show == True:
plt.show()
else:
return plt.gca()
def plotellipse(v, cspace_in = 'Yxy', cspace_out = None, nsamples = 100, \
show = True, axh = None, \
line_color = 'darkgray', line_style = ':', line_width = 1, line_marker = '', line_markersize = 4,\
plot_center = False, center_marker = 'o', center_color = 'darkgray', center_markersize = 4,\
show_grid = True, label_fontname = 'Times New Roman', label_fontsize = 12,\
out = None):
"""
Plot ellipse(s) given in v-format [Rmax,Rmin,xc,yc,theta].
Args:
:v:
| (Nx5) ndarray
| ellipse parameters [Rmax,Rmin,xc,yc,theta]
:cspace_in:
| 'Yxy', optional
| Color space of v.
| If None: no color space assumed. Axis labels assumed ('x','y').
:cspace_out:
| None, optional
| Color space to plot ellipse(s) in.
| If None: plot in cspace_in.
:nsamples:
| 100 or int, optional
| Number of points (samples) in ellipse boundary
:show:
| True or boolean, optional
| Plot ellipse(s) (True) or not (False)
:axh:
| None, optional
| Ax-handle to plot ellipse(s) in.
| If None: create new figure with axes.
:line_color:
| 'darkgray', optional
| Color to plot ellipse(s) in.
:line_style:
| ':', optional
| Linestyle of ellipse(s).
:line_width':
| 1, optional
| Width of ellipse boundary line.
:line_marker:
| 'none', optional
| Marker for ellipse boundary.
:line_markersize:
| 4, optional
| Size of markers in ellipse boundary.
:plot_center:
| False, optional
| Plot center of ellipse: yes (True) or no (False)
:center_color:
| 'darkgray', optional
| Color to plot ellipse center in.
:center_marker:
| 'o', optional
| Marker for ellipse center.
:center_markersize:
| 4, optional
| Size of marker of ellipse center.
:show_grid:
| True, optional
| Show grid (True) or not (False)
:label_fontname:
| 'Times New Roman', optional
| Sets font type of axis labels.
:label_fontsize:
| 12, optional
| Sets font size of axis labels.
:out:
| None, optional
| Output of function
| If None: returns None. Can be used to output axh of newly created
| figure axes or to return Yxys an ndarray with coordinates of
| ellipse boundaries in cspace_out (shape = (nsamples,3,N))
Returns:
:returns: None, or whatever set by :out:.
"""
Yxys = np.zeros((nsamples,3,v.shape[0]))
ellipse_vs = np.zeros((v.shape[0],5))
for i,vi in enumerate(v):
# Set sample density of ellipse boundary:
t = np.linspace(0, 2*np.pi, nsamples)
a = vi[0] # major axis
b = vi[1] # minor axis
xyc = vi[2:4,None] # center
theta = vi[-1] # rotation angle
# define rotation matrix:
R = np.hstack(( np.vstack((np.cos(theta), np.sin(theta))), np.vstack((-np.sin(theta), np.cos(theta)))))
# Calculate ellipses:
Yxyc = np.vstack((1, xyc)).T
Yxy = np.vstack((np.ones((1,nsamples)), xyc + np.dot(R, np.vstack((a*np.cos(t), b*np.sin(t))) ))).T
Yxys[:,:,i] = Yxy
# Convert to requested color space:
if (cspace_out is not None) & (cspace_in is not None):
Yxy = colortf(Yxy, cspace_in + '>' + cspace_out)
Yxyc = colortf(Yxyc, cspace_in + '>' + cspace_out)
Yxys[:,:,i] = Yxy
# get ellipse parameters in requested color space:
ellipse_vs[i,:] = math.fit_ellipse(Yxy[:,1:])
#de = np.sqrt((Yxy[:,1]-Yxyc[:,1])**2 + (Yxy[:,2]-Yxyc[:,2])**2)
#ellipse_vs[i,:] = np.hstack((de.max(),de.min(),Yxyc[:,1],Yxyc[:,2],np.nan)) # nan because orientation is xy, but request is some other color space. Change later to actual angle when fitellipse() has been implemented
# plot ellipses:
if show == True:
if (axh is None) & (i == 0):
fig = plt.figure()
axh = fig.add_subplot(111)
if (cspace_in is None):
xlabel = 'x'
ylabel = 'y'
else:
xlabel = _CSPACE_AXES[cspace_in][1]
ylabel = _CSPACE_AXES[cspace_in][2]
if (cspace_out is not None):
xlabel = _CSPACE_AXES[cspace_out][1]
ylabel = _CSPACE_AXES[cspace_out][2]
if plot_center == True:
plt.plot(Yxyc[:,1],Yxyc[:,2],color = center_color, linestyle = 'none', marker = center_marker, markersize = center_markersize)
plt.plot(Yxy[:,1],Yxy[:,2],color = line_color, linestyle = line_style, linewidth = line_width, marker = line_marker, markersize = line_markersize)
plt.xlabel(xlabel, fontname = label_fontname, fontsize = label_fontsize)
plt.ylabel(ylabel, fontname = label_fontname, fontsize = label_fontsize)
if show_grid == True:
plt.grid()
#plt.show()
Yxys = np.transpose(Yxys,axes=(0,2,1))
if out is not None:
return eval(out)
else:
return None
def demo_opt(f, args=(), xrange=None, options={}):
"""
DEMO_OPT: Multi-objective optimization using the DEMO
This function uses the Differential Evolution for Multi-objective
Optimization (a.k.a. DEMO) to solve a multi-objective problem. The
result is a set of nondominated points that are (hopefully) very close
to the true Pareto front.
Args:
:f:
| handle to objective function.
| The output must be, for each point, a column vector of size m x 1,
| with m > 1 the number of objectives.
:args: (), optional
| Input arguments required for f.
:xrange: None, optional
| ndarray with lower and upperbounds.
| If n is the dimension, it will be a n x 2 matrix, such that the
| first column contains the lower bounds,
| and the second, the upper bounds.
| None defaults to no bounds ( [-Inf, Inf] ndarray).
:options:
| None, optional
| dict with internal parameters of the algorithm.
| None initializes default values.
| keys:
| - 'F': the scale factor to be used in the mutation (default: 0.5);
| - 'CR': the crossover factor used in the recombination (def.: 0.3);
| - 'mu': the population size (number of individuals) (def.: 100);
| - 'kmax': maximum number of iterations (def.: 300);
| - 'display': 'on' to display the population while the algorithm is
| being executed, and 'off' to not (default: 'off');
| If any of the parameters is not set, the default ones are used
| instead.
Returns: fopt, xopt
:fopt: the m x mu_opt ndarray with the mu_opt best objectives
:xopt: the n x mu_opt ndarray with the mu_opt best individuals
"""
# Initialize the parameters of the algorithm with values contained in dict:
options = init_options(options=options)
# Initial considerations
n = xrange.shape[0] #dimension of the problem
P = {'x': np.random.rand(n, options['mu'])} #initial decision variables
P['f'] = fobjeval(f, P['x'], args,
xrange) #evaluates the initial population
m = P['f'].shape[0] #number of objectives
k = 0 #iterations counter
# Beginning of the main loop
Pfirst = P.copy()
axh = None
while (k <= options['kmax']):
# Plot the current population (if desired):
if options['display'] == True:
if (k == 0) & (m < 4):
fig = plt.gcf()
fig.show()
fig.canvas.draw()
if m == 2:
# fig = plt.figure()
axh = plt.axes()
plt.plot(P['f'][0], P['f'][1], 'o')
plt.title('Objective values during the execution')
plt.xlabel('f_1')
plt.ylabel('f_2')
fig.canvas.draw()
del axh.lines[0]
elif m == 3:
# fig = plt.figure()
axh = plt.axes(projection='3d')
# print(P['f'])
axh.plot3D(P['f'][0], P['f'][1], P['f'][2], 'o')
plt.title('Objective values during the execution')
axh.set_xlabel('f_1')
axh.set_ylabel('f_2')
axh.set_zlabel('f_3')
fig.canvas.draw()
plt.pause(0.01)
del axh.lines[0]
# Perform the variation operation (mutation and recombination):
O = {'x': mutation(P['x'], options)} #mutation
O['x'] = recombination(P['x'].copy(), O['x'], options) #recombination
O['x'] = repair(
O['x']) #assure the offspring do not cross the search limits
O['f'] = fobjeval(f, O['x'], args,
xrange) #compute objective functions
# Selection and updates
P = selection(P, O, options)
print('Iteration #{:1.0f} of {:1.0f}'.format(k, options['kmax']))
k += 1
# Return the final population:
# First, unnormalize it
Xmin = xrange[:,
0][:,
None] # * np.ones(options['mu']) #replicate lower bound
Xmax = xrange[:,
1][:,
None] # * np.ones(options['mu']) #replicate upper limit
Xun = (Xmax - Xmin) * P['x'] + Xmin
# Then, return the nondominated front:
ispar = ndset(P['f'])
fopt = P['f'][:, ispar]
xopt = Xun[:, ispar]
return fopt, xopt
