def MaxInnerProd(ser1, ser2, PSD):
size = Numeric.shape(ser1)[0]
pdlen = size/2
nyquistf = 0.5/15.0 # !!! hardcoded !!!!
freqs = Numeric.arange(0,pdlen+1,dtype='d') * (nyquistf / pdlen)
if(Numeric.shape(ser2)[0] != size):
print "size of time series must be the same"
sys.exit(1)
if(Numeric.shape(PSD)[0] != pdlen):
print "wrong size of psd: ", pdlen, Numeric.shape(PSD)
sys.exit(1)
fourier1 = FFT.fft(ser1)
fourier2 = FFT.fft(ser2)
prod1 = Numeric.zeros(pdlen+1, dtype='d')
prod2 = Numeric.zeros(pdlen+1, dtype='d')
prod1[0] = 0.0
prod1[1:pdlen] = numpy.multiply(fourier1[1:pdlen],numpy.conjugate(fourier2[1:pdlen])) + numpy.multiply(fourier1[-1:pdlen:-1],numpy.conjugate(fourier2[-1:pdlen:-1]))
prod1[pdlen] = fourier1[pdlen]*fourier2[pdlen]
prod2[0] = 0.0
prod2[1:pdlen] = numpy.multiply(fourier1[1:pdlen],numpy.conjugate(fourier2[1:pdlen]*1.j)) + numpy.multiply((fourier1[-1:pdlen:-1]),numpy.conjugate(fourier2[-1:pdlen:-1]*(-1.j)))
prod2[pdlen] = fourier1[pdlen]*fourier2[pdlen]
Numeric.divide(prod1[1:], PSD, prod1[1:])
Numeric.divide(prod2[1:], PSD, prod2[1:])
olap0 = 0.0
olappiby2 = 0.0
for i in xrange(pdlen):
if (freqs[i] > fLow and freqs[i]<= fHigh):
olap0 += prod1[i]
olappiby2 += prod2[i]
olap0 = 2.0*olap0/float(size)
olappiby2 = 2.0*olappiby2/float(size)
# olap0 = 2.0*(numpy.sum(prod1[1:]))/float(size) #it must be scaled by dt
# olappiby2 = 2.0*(numpy.sum(prod2[1:]))/float(size) #it must be scaled by dt
print "angle of maxim. = ", math.atan(olappiby2/olap0)
return sqrt(olap0**2 + olappiby2**2)
def ring(x, y, height, thickness, gaussian_width):
"""
Circular ring (annulus) with Gaussian fall-off after the solid ring-shaped region.
"""
radius = height / 2.0
half_thickness = thickness / 2.0
distance_from_origin = sqrt(x**2 + y**2)
distance_outside_outer_disk = distance_from_origin - radius - half_thickness
distance_inside_inner_disk = radius - half_thickness - distance_from_origin
ring = 1.0 - bitwise_xor(greater_equal(distance_inside_inner_disk, 0.0),
greater_equal(distance_outside_outer_disk, 0.0))
sigmasq = gaussian_width * gaussian_width
if sigmasq == 0.0:
inner_falloff = x * 0.0
outer_falloff = x * 0.0
else:
with float_error_ignore():
inner_falloff = exp(
divide(
-distance_inside_inner_disk * distance_inside_inner_disk,
2.0 * sigmasq))
outer_falloff = exp(
divide(
-distance_outside_outer_disk * distance_outside_outer_disk,
2.0 * sigmasq))
return maximum(inner_falloff, maximum(outer_falloff, ring))
def InnerProd(ser1, ser2, PSD):
size = Numeric.shape(ser1)[0]
pdlen = size/2
nyquistf = 0.5/15.0 # !!! hardcoded !!!!
freqs = Numeric.arange(0,pdlen+1,dtype='d') * (nyquistf / pdlen)
if(Numeric.shape(ser2)[0] != size):
print "size of time series must be the same"
sys.exit(1)
if(Numeric.shape(PSD)[0] != pdlen):
print "wrong size of psd: ", pdlen, Numeric.shape(PSD)
sys.exit(1)
fourier1 = FFT.fft(ser1)
fourier2 = FFT.fft(ser2)
prod = Numeric.zeros(pdlen+1, dtype='d')
prod[0] = 0.0
prod[1:pdlen] = numpy.multiply(fourier1[1:pdlen],numpy.conjugate(fourier2[1:pdlen])) + numpy.multiply(fourier1[-1:pdlen:-1],numpy.conjugate(fourier2[-1:pdlen:-1]))
prod[pdlen] = fourier1[pdlen]*fourier2[pdlen]
Numeric.divide(prod[1:], PSD, prod[1:])
olap0 = 0.0
for i in xrange(pdlen):
if (freqs[i] > fLow and freqs[i]<= fHigh):
olap0 += prod[i]
olap0 = 2.0*olap0/float(size)
# olap0 = 2.0*(numpy.sum(prod[1:]))/float(size) #it must be scaled by dt
return olap0
def InnerProd(ser1, ser2, PSD):
size = Numeric.shape(ser1)[0]
pdlen = size/2
nyquistf = 0.5/15.0 # !!! hardcoded !!!!
freqs = Numeric.arange(0,pdlen+1,dtype='d') * (nyquistf / pdlen)
if(Numeric.shape(ser2)[0] != size):
print "size of time series must be the same"
sys.exit(1)
if(Numeric.shape(PSD)[0] != pdlen):
print "wrong size of psd: ", pdlen, Numeric.shape(PSD)
sys.exit(1)
fourier1 = FFT.fft(ser1)
fourier2 = FFT.fft(ser2)
prod = Numeric.zeros(pdlen+1, dtype='d')
prod[0] = 0.0
prod[1:pdlen] = numpy.multiply(fourier1[1:pdlen],numpy.conjugate(fourier2[1:pdlen])) + numpy.multiply(fourier1[-1:pdlen:-1],numpy.conjugate(fourier2[-1:pdlen:-1]))
prod[pdlen] = fourier1[pdlen]*fourier2[pdlen]
Numeric.divide(prod[1:], PSD, prod[1:])
olap0 = 0.0
for i in xrange(pdlen):
if (freqs[i] > 1.e-5 and freqs[i]<0.01):
olap0 += prod[i]
olap0 = 2.0*olap0/float(size)
# olap0 = 2.0*(numpy.sum(prod[1:]))/float(size) #it must be scaled by dt
return olap0
def MaxInnerProd(ser1, ser2, PSD):
size = Numeric.shape(ser1)[0]
pdlen = size/2
nyquistf = 0.5/15.0 # !!! hardcoded !!!!
freqs = Numeric.arange(0,pdlen+1,dtype='d') * (nyquistf / pdlen)
if(Numeric.shape(ser2)[0] != size):
print "size of time series must be the same"
sys.exit(1)
if(Numeric.shape(PSD)[0] != pdlen):
print "wrong size of psd: ", pdlen, Numeric.shape(PSD)
sys.exit(1)
fourier1 = FFT.fft(ser1)
fourier2 = FFT.fft(ser2)
prod1 = Numeric.zeros(pdlen+1, dtype='d')
prod2 = Numeric.zeros(pdlen+1, dtype='d')
prod1[0] = 0.0
prod1[1:pdlen] = numpy.multiply(fourier1[1:pdlen],numpy.conjugate(fourier2[1:pdlen])) + numpy.multiply(fourier1[-1:pdlen:-1],numpy.conjugate(fourier2[-1:pdlen:-1]))
prod1[pdlen] = fourier1[pdlen]*fourier2[pdlen]
prod2[0] = 0.0
prod2[1:pdlen] = numpy.multiply(fourier1[1:pdlen],numpy.conjugate(fourier2[1:pdlen]*1.j)) + numpy.multiply((fourier1[-1:pdlen:-1]),numpy.conjugate(fourier2[-1:pdlen:-1]*(-1.j)))
prod2[pdlen] = fourier1[pdlen]*fourier2[pdlen]
Numeric.divide(prod1[1:], PSD, prod1[1:])
Numeric.divide(prod2[1:], PSD, prod2[1:])
olap0 = 0.0
olappiby2 = 0.0
for i in xrange(pdlen):
if (freqs[i] > 1.e-5 and freqs[i]<0.01):
olap0 += prod1[i]
olappiby2 += prod2[i]
olap0 = 2.0*olap0/float(size)
olappiby2 = 2.0*olappiby2/float(size)
# olap0 = 2.0*(numpy.sum(prod1[1:]))/float(size) #it must be scaled by dt
# olappiby2 = 2.0*(numpy.sum(prod2[1:]))/float(size) #it must be scaled by dt
print "angle of maxim. = ", math.atan(olappiby2/olap0)
return sqrt(olap0**2 + olappiby2**2)
def arc_by_radian(x, y, height, radian_range, thickness, gaussian_width):
"""
Radial arc with Gaussian fall-off after the solid ring-shaped
region with the given thickness, with shape specified by the
(start,end) radian_range.
"""
# Create a circular ring (copied from the ring function)
radius = height/2.0
half_thickness = thickness/2.0
distance_from_origin = sqrt(x**2+y**2)
distance_outside_outer_disk = distance_from_origin - radius - half_thickness
distance_inside_inner_disk = radius - half_thickness - distance_from_origin
ring = 1.0-bitwise_xor(greater_equal(distance_inside_inner_disk,0.0),greater_equal(distance_outside_outer_disk,0.0))
sigmasq = gaussian_width*gaussian_width
if sigmasq==0.0:
inner_falloff = x*0.0
outer_falloff = x*0.0
else:
with float_error_ignore():
inner_falloff = exp(divide(-distance_inside_inner_disk*distance_inside_inner_disk, 2.0*sigmasq))
outer_falloff = exp(divide(-distance_outside_outer_disk*distance_outside_outer_disk, 2.0*sigmasq))
output_ring = maximum(inner_falloff,maximum(outer_falloff,ring))
# Calculate radians (in 4 phases) and cut according to the set range)
# RZHACKALERT:
# Function float_error_ignore() cannot catch the exception when
# both dividend and divisor are 0.0, and when only divisor is 0.0
# it returns 'Inf' rather than 0.0. In x, y and
# distance_from_origin, only one point in distance_from_origin can
# be 0.0 (circle center) and in this point x and y must be 0.0 as
# well. So here is a hack to avoid the 'invalid value encountered
# in divide' error by turning 0.0 to 1e-5 in distance_from_origin.
distance_from_origin += where(distance_from_origin == 0.0, 1e-5, 0)
with float_error_ignore():
sines = divide(y, distance_from_origin)
cosines = divide(x, distance_from_origin)
arcsines = arcsin(sines)
phase_1 = where(logical_and(sines >= 0, cosines >= 0), 2*pi-arcsines, 0)
phase_2 = where(logical_and(sines >= 0, cosines < 0), pi+arcsines, 0)
phase_3 = where(logical_and(sines < 0, cosines < 0), pi+arcsines, 0)
phase_4 = where(logical_and(sines < 0, cosines >= 0), -arcsines, 0)
arcsines = phase_1 + phase_2 + phase_3 + phase_4
if radian_range[0] <= radian_range[1]:
return where(logical_and(arcsines >= radian_range[0], arcsines <= radian_range[1]),
output_ring, 0.0)
else:
return where(logical_or(arcsines >= radian_range[0], arcsines <= radian_range[1]),
output_ring, 0.0)
def arc_by_radian(x, y, height, radian_range, thickness, gaussian_width):
"""
Radial arc with Gaussian fall-off after the solid ring-shaped
region with the given thickness, with shape specified by the
(start,end) radian_range.
"""
# Create a circular ring (copied from the ring function)
radius = height/2.0
half_thickness = thickness/2.0
distance_from_origin = sqrt(x**2+y**2)
distance_outside_outer_disk = distance_from_origin - radius - half_thickness
distance_inside_inner_disk = radius - half_thickness - distance_from_origin
ring = 1.0-bitwise_xor(greater_equal(distance_inside_inner_disk,0.0),greater_equal(distance_outside_outer_disk,0.0))
sigmasq = gaussian_width*gaussian_width
if sigmasq==0.0:
inner_falloff = x*0.0
outer_falloff = x*0.0
else:
with float_error_ignore():
inner_falloff = exp(divide(-distance_inside_inner_disk*distance_inside_inner_disk, 2.0*sigmasq))
outer_falloff = exp(divide(-distance_outside_outer_disk*distance_outside_outer_disk, 2.0*sigmasq))
output_ring = maximum(inner_falloff,maximum(outer_falloff,ring))
# Calculate radians (in 4 phases) and cut according to the set range)
# RZHACKALERT:
# Function float_error_ignore() cannot catch the exception when
# both dividend and divisor are 0.0, and when only divisor is 0.0
# it returns 'Inf' rather than 0.0. In x, y and
# distance_from_origin, only one point in distance_from_origin can
# be 0.0 (circle center) and in this point x and y must be 0.0 as
# well. So here is a hack to avoid the 'invalid value encountered
# in divide' error by turning 0.0 to 1e-5 in distance_from_origin.
distance_from_origin += where(distance_from_origin == 0.0, 1e-5, 0)
with float_error_ignore():
sines = divide(y, distance_from_origin)
cosines = divide(x, distance_from_origin)
arcsines = arcsin(sines)
phase_1 = where(logical_and(sines >= 0, cosines >= 0), 2*pi-arcsines, 0)
phase_2 = where(logical_and(sines >= 0, cosines < 0), pi+arcsines, 0)
phase_3 = where(logical_and(sines < 0, cosines < 0), pi+arcsines, 0)
phase_4 = where(logical_and(sines < 0, cosines >= 0), -arcsines, 0)
arcsines = phase_1 + phase_2 + phase_3 + phase_4
if radian_range[0] <= radian_range[1]:
return where(logical_and(arcsines >= radian_range[0], arcsines <= radian_range[1]),
output_ring, 0.0)
else:
return where(logical_or(arcsines >= radian_range[0], arcsines <= radian_range[1]),
output_ring, 0.0)
def exponential(x, y, xscale, yscale):
"""
Two-dimensional oriented exponential decay pattern.
"""
if xscale == 0.0 or yscale == 0.0:
return x * 0.0
with float_error_ignore():
x_w = divide(x, xscale)
y_h = divide(y, yscale)
return exp(-sqrt(x_w * x_w + y_h * y_h))
def exponential(x, y, xscale, yscale):
"""
Two-dimensional oriented exponential decay pattern.
"""
if xscale==0.0 or yscale==0.0:
return x*0.0
with float_error_ignore():
x_w = divide(x,xscale)
y_h = divide(y,yscale)
return exp(-sqrt(x_w*x_w+y_h*y_h))
def gabor(x, y, xsigma, ysigma, frequency, phase):
"""
Gabor pattern (sine grating multiplied by a circular Gaussian).
"""
if xsigma==0.0 or ysigma==0.0:
return x*0.0
with float_error_ignore():
x_w = divide(x,xsigma)
y_h = divide(y,ysigma)
p = exp(-0.5*x_w*x_w + -0.5*y_h*y_h)
return p * 0.5*cos(2*pi*frequency*y + phase)
def gabor(x, y, xsigma, ysigma, frequency, phase):
"""
Gabor pattern (sine grating multiplied by a circular Gaussian).
"""
if xsigma == 0.0 or ysigma == 0.0:
return x * 0.0
with float_error_ignore():
x_w = divide(x, xsigma)
y_h = divide(y, ysigma)
p = exp(-0.5 * x_w * x_w + -0.5 * y_h * y_h)
return p * 0.5 * cos(2 * pi * frequency * y + phase)
def gaussian(x, y, xsigma, ysigma):
"""
Two-dimensional oriented Gaussian pattern (i.e., 2D version of a
bell curve, like a normal distribution but not necessarily summing
to 1.0).
"""
if xsigma == 0.0 or ysigma == 0.0:
return x * 0.0
with float_error_ignore():
x_w = divide(x, xsigma)
y_h = divide(y, ysigma)
return exp(-0.5 * x_w * x_w + -0.5 * y_h * y_h)
def gaussian(x, y, xsigma, ysigma):
"""
Two-dimensional oriented Gaussian pattern (i.e., 2D version of a
bell curve, like a normal distribution but not necessarily summing
to 1.0).
"""
if xsigma==0.0 or ysigma==0.0:
return x*0.0
with float_error_ignore():
x_w = divide(x,xsigma)
y_h = divide(y,ysigma)
return exp(-0.5*x_w*x_w + -0.5*y_h*y_h)
def log_gaussian(x, y, x_sigma, y_sigma, mu):
"""
Two-dimensional oriented Log Gaussian pattern (i.e., 2D version of a
bell curve with an independent, movable peak). Much like a normal
distribution, but not necessarily placing the peak above the center,
and not necessarily summing to 1.0).
"""
if x_sigma==0.0 or y_sigma==0.0:
return x * 0.0
with float_error_ignore():
x_w = divide(log(x)-mu, x_sigma*x_sigma)
y_h = divide(log(y)-mu, y_sigma*y_sigma)
return exp(-0.5*x_w*x_w + -0.5*y_h*y_h)
def log_gaussian(x, y, x_sigma, y_sigma, mu):
"""
Two-dimensional oriented Log Gaussian pattern (i.e., 2D version of a
bell curve with an independent, movable peak). Much like a normal
distribution, but not necessarily placing the peak above the center,
and not necessarily summing to 1.0).
"""
if x_sigma == 0.0 or y_sigma == 0.0:
return x * 0.0
with float_error_ignore():
x_w = divide(log(x) - mu, x_sigma * x_sigma)
y_h = divide(log(y) - mu, y_sigma * y_sigma)
return exp(-0.5 * x_w * x_w + -0.5 * y_h * y_h)
def concentricrings(x, y, white_thickness, gaussian_width, spacing):
"""
Concetric rings with the solid ring-shaped region, then Gaussian fall-off at the edges.
"""
# To have zero value in middle point this pattern calculates zero-value rings instead of
# the one-value ones. But to be consistent with the rest of functions the parameters
# are connected to one-value rings - like half_thickness is now recalculated for zero-value ring:
half_thickness = ((spacing-white_thickness)/2.0)*greater_equal(spacing-white_thickness,0.0)
distance_from_origin = sqrt(x**2+y**2)
distance_from_ring_middle = fmod(distance_from_origin,spacing)
distance_from_ring_middle = minimum(distance_from_ring_middle,spacing - distance_from_ring_middle)
distance_from_ring = distance_from_ring_middle - half_thickness
ring = 0.0 + greater_equal(distance_from_ring,0.0)
sigmasq = gaussian_width*gaussian_width
with float_error_ignore():
falloff = exp(divide(-distance_from_ring*distance_from_ring, 2.0*sigmasq))
return maximum(falloff,ring)
def function(self,params):
"""Hyperbolic function."""
aspect_ratio = params['aspect_ratio']
x = self.pattern_x/aspect_ratio
y = self.pattern_y
thickness = params['thickness']
gaussian_width = params['smoothing']
size = params['size']
half_thickness = thickness / 2.0
distance_from_vertex_middle = fmod(sqrt(absolute(x**2 - y**2)),size)
distance_from_vertex_middle = minimum(distance_from_vertex_middle,size - distance_from_vertex_middle)
distance_from_vertex = distance_from_vertex_middle - half_thickness
hyperbola = 1.0 - greater_equal(distance_from_vertex,0.0)
sigmasq = gaussian_width*gaussian_width
with float_error_ignore():
falloff = exp(divide(-distance_from_vertex*distance_from_vertex, 2.0*sigmasq))
return maximum(falloff, hyperbola)
def function(self,params):
"""Concentric rings."""
aspect_ratio = params['aspect_ratio']
x = self.pattern_x/aspect_ratio
y = self.pattern_y
thickness = params['thickness']
gaussian_width = params['smoothing']
size = params['size']
half_thickness = thickness / 2.0
distance_from_origin = sqrt(x**2+y**2)
distance_from_ring_middle = fmod(distance_from_origin,size)
distance_from_ring_middle = minimum(distance_from_ring_middle,size - distance_from_ring_middle)
distance_from_ring = distance_from_ring_middle - half_thickness
ring = 1.0 - greater_equal(distance_from_ring,0.0)
sigmasq = gaussian_width*gaussian_width
with float_error_ignore():
falloff = exp(divide(-distance_from_ring*distance_from_ring, 2.0*sigmasq))
return maximum(falloff, ring)
def function(self,params):
"""Archemidean spiral function."""
aspect_ratio = params['aspect_ratio']
x = self.pattern_x/aspect_ratio
y = self.pattern_y
thickness = params['thickness']
gaussian_width = params['smoothing']
size = params['size']
half_thickness = thickness/2.0
spacing = size*2*pi
distance_from_origin = sqrt(x**2+y**2)
distance_from_spiral_middle = fmod(spacing + distance_from_origin - size*arctan2(y,x),spacing)
distance_from_spiral_middle = minimum(distance_from_spiral_middle,spacing - distance_from_spiral_middle)
distance_from_spiral = distance_from_spiral_middle - half_thickness
spiral = 1.0 - greater_equal(distance_from_spiral,0.0)
sigmasq = gaussian_width*gaussian_width
with float_error_ignore():
falloff = exp(divide(-distance_from_spiral*distance_from_spiral, 2.0*sigmasq))
return maximum(falloff, spiral)
def hyperbola(x, y, thickness, gaussian_width, axis):
"""
Two conjugate hyperbolas with Gaussian fall-off which share the same asymptotes.
abs(x^2/a^2 - y^2/b^2) = 1
As a = b = axis, these hyperbolas are rectangular.
"""
difference = absolute(x**2 - y**2)
hyperbola = 1.0 - bitwise_xor(greater_equal(axis**2,difference),greater_equal(difference,(axis + thickness)**2))
distance_inside_hyperbola = sqrt(difference) - axis
distance_outside_hyperbola = sqrt(difference) - axis - thickness
sigmasq = gaussian_width*gaussian_width
with float_error_ignore():
inner_falloff = exp(divide(-distance_inside_hyperbola*distance_inside_hyperbola, 2.0*sigmasq))
outer_falloff = exp(divide(-distance_outside_hyperbola*distance_outside_hyperbola, 2.0*sigmasq))
return maximum(hyperbola,maximum(inner_falloff,outer_falloff))
def smooth_rectangle(x, y, rec_w, rec_h, gaussian_width_x, gaussian_width_y):
"""
Rectangle with a solid central region, then Gaussian fall-off at the edges.
"""
gaussian_x_coord = abs(x)-rec_w/2.0
gaussian_y_coord = abs(y)-rec_h/2.0
box_x=less(gaussian_x_coord,0.0)
box_y=less(gaussian_y_coord,0.0)
sigmasq_x=gaussian_width_x*gaussian_width_x
sigmasq_y=gaussian_width_y*gaussian_width_y
with float_error_ignore():
falloff_x=x*0.0 if sigmasq_x==0.0 else \
exp(divide(-gaussian_x_coord*gaussian_x_coord,2*sigmasq_x))
falloff_y=y*0.0 if sigmasq_y==0.0 else \
exp(divide(-gaussian_y_coord*gaussian_y_coord,2*sigmasq_y))
return minimum(maximum(box_x,falloff_x), maximum(box_y,falloff_y))
def smooth_rectangle(x, y, rec_w, rec_h, gaussian_width_x, gaussian_width_y):
"""
Rectangle with a solid central region, then Gaussian fall-off at the edges.
"""
gaussian_x_coord = abs(x) - rec_w / 2.0
gaussian_y_coord = abs(y) - rec_h / 2.0
box_x = less(gaussian_x_coord, 0.0)
box_y = less(gaussian_y_coord, 0.0)
sigmasq_x = gaussian_width_x * gaussian_width_x
sigmasq_y = gaussian_width_y * gaussian_width_y
with float_error_ignore():
falloff_x=x*0.0 if sigmasq_x==0.0 else \
exp(divide(-gaussian_x_coord*gaussian_x_coord,2*sigmasq_x))
falloff_y=y*0.0 if sigmasq_y==0.0 else \
exp(divide(-gaussian_y_coord*gaussian_y_coord,2*sigmasq_y))
return minimum(maximum(box_x, falloff_x), maximum(box_y, falloff_y))
def ring(x, y, height, thickness, gaussian_width):
"""
Circular ring (annulus) with Gaussian fall-off after the solid ring-shaped region.
"""
radius = height/2.0
half_thickness = thickness/2.0
distance_from_origin = sqrt(x**2+y**2)
distance_outside_outer_disk = distance_from_origin - radius - half_thickness
distance_inside_inner_disk = radius - half_thickness - distance_from_origin
ring = 1.0-bitwise_xor(greater_equal(distance_inside_inner_disk,0.0),greater_equal(distance_outside_outer_disk,0.0))
sigmasq = gaussian_width*gaussian_width
if sigmasq==0.0:
inner_falloff = x*0.0
outer_falloff = x*0.0
else:
with float_error_ignore():
inner_falloff = exp(divide(-distance_inside_inner_disk*distance_inside_inner_disk, 2.0*sigmasq))
outer_falloff = exp(divide(-distance_outside_outer_disk*distance_outside_outer_disk, 2.0*sigmasq))
return maximum(inner_falloff,maximum(outer_falloff,ring))
def line(y, thickness, gaussian_width):
"""
Infinite-length line with a solid central region, then Gaussian fall-off at the edges.
"""
distance_from_line = abs(y)
gaussian_y_coord = distance_from_line - thickness/2.0
sigmasq = gaussian_width*gaussian_width
if sigmasq==0.0:
falloff = y*0.0
else:
with float_error_ignore():
falloff = exp(divide(-gaussian_y_coord*gaussian_y_coord,2*sigmasq))
return where(gaussian_y_coord<=0, 1.0, falloff)
def line(y, thickness, gaussian_width):
"""
Infinite-length line with a solid central region, then Gaussian fall-off at the edges.
"""
distance_from_line = abs(y)
gaussian_y_coord = distance_from_line - thickness/2.0
sigmasq = gaussian_width*gaussian_width
if sigmasq==0.0:
falloff = x*0.0
else:
with float_error_ignore():
falloff = exp(divide(-gaussian_y_coord*gaussian_y_coord,2*sigmasq))
return where(gaussian_y_coord<=0, 1.0, falloff)
def disk(x, y, height, gaussian_width):
"""
Circular disk with Gaussian fall-off after the solid central region.
"""
disk_radius = height/2.0
distance_from_origin = sqrt(x**2+y**2)
distance_outside_disk = distance_from_origin - disk_radius
sigmasq = gaussian_width*gaussian_width
if sigmasq==0.0:
falloff = x*0.0
else:
with float_error_ignore():
falloff = exp(divide(-distance_outside_disk*distance_outside_disk,
2*sigmasq))
return where(distance_outside_disk<=0,1.0,falloff)
def disk(x, y, height, gaussian_width):
"""
Circular disk with Gaussian fall-off after the solid central region.
"""
disk_radius = height/2.0
distance_from_origin = sqrt(x**2+y**2)
distance_outside_disk = distance_from_origin - disk_radius
sigmasq = gaussian_width*gaussian_width
if sigmasq==0.0:
falloff = x*0.0
else:
with float_error_ignore():
falloff = exp(divide(-distance_outside_disk*distance_outside_disk,
2*sigmasq))
return where(distance_outside_disk<=0,1.0,falloff)
def radial(x, y, wide, gaussian_width):
"""
Radial grating - A sector of a circle with Gaussian fall-off.
Parameter wide determines in wide of sector in radians.
"""
angle = absolute(arctan2(y,x))
half_wide = wide/2
radius = 1.0 - greater_equal(angle,half_wide)
distance = angle - half_wide
sigmasq = gaussian_width*gaussian_width
with float_error_ignore():
falloff = exp(divide(-distance*distance, 2.0*sigmasq))
return maximum(radius,falloff)
def _normalize(self,a,range_):
"""
Normalize an array s to be in the range 0 to 1.0.
For an array of identical elements, returns an array of ones
if the elements are greater than zero, and zeros if the
elements are less than or equal to zero.
"""
if range_: # i.e. not False, not None (expecting a tuple)
range_min = float(range_[0])
range_max = float(range_[1])
if range_min==range_max:
if range_min>0:
resu = ones(a.shape)
else:
resu = zeros(a.shape)
else:
a_offset = a - range_min
resu = a_offset/(range_max-range_min)
return resu
else:
if range_ is None:
if not hasattr(self,'value_range'):
self.value_range=(a.min(),a.max())
else:
# If normalizing multiple matrices, take the largest values
self.value_range=(min(self.value_range[0],a.min()),
max(self.value_range[1],a.max()))
return None # (indicate that array was not scaled)
else: # i.e. range_ is False
a_offset = a-a.min()
max_a_offset = a_offset.max()
if max_a_offset>0:
a = divide(a_offset,float(max_a_offset))
else:
if min(a.ravel())<=0:
a=zeros(a.shape,Float)
else:
a=ones(a.shape,Float)
return a
def _normalize(self, a, range_):
"""
Normalize an array s to be in the range 0 to 1.0.
For an array of identical elements, returns an array of ones
if the elements are greater than zero, and zeros if the
elements are less than or equal to zero.
"""
if range_: # i.e. not False, not None (expecting a tuple)
range_min = float(range_[0])
range_max = float(range_[1])
if range_min == range_max:
if range_min > 0:
resu = ones(a.shape)
else:
resu = zeros(a.shape)
else:
a_offset = a - range_min
resu = a_offset / (range_max - range_min)
return resu
else:
if range_ is None:
if not hasattr(self, 'value_range'):
self.value_range = (a.min(), a.max())
else:
# If normalizing multiple matrices, take the largest values
self.value_range = (min(self.value_range[0], a.min()),
max(self.value_range[1], a.max()))
return None # (indicate that array was not scaled)
else: # i.e. range_ is False
a_offset = a - a.min()
max_a_offset = a_offset.max()
if max_a_offset > 0:
a = divide(a_offset, float(max_a_offset))
else:
if min(a.ravel()) <= 0:
a = zeros(a.shape, Float)
else:
a = ones(a.shape, Float)
return a
def function(self,params):
"""Radial function."""
aspect_ratio = params['aspect_ratio']
x = self.pattern_x/aspect_ratio
y = self.pattern_y
gaussian_width = params['smoothing']
angle = absolute(arctan2(y,x))
half_length = params['arc_length']/2
radius = 1.0 - greater_equal(angle,half_length)
distance = angle - half_length
sigmasq = gaussian_width*gaussian_width
with float_error_ignore():
falloff = exp(divide(-distance*distance, 2.0*sigmasq))
return maximum(radius, falloff)
def spiral(x, y, thickness, gaussian_width, density):
"""
Archemidean spiral with Gaussian fall-off outside the spiral curve.
"""
half_thickness = thickness/2.0
spacing = density*2*pi
distance_from_origin = sqrt(x**2+y**2)
distance_from_spiral_middle = fmod(spacing + distance_from_origin - density*arctan2(y,x),spacing)
distance_from_spiral_middle = minimum(distance_from_spiral_middle,spacing - distance_from_spiral_middle)
distance_from_spiral = distance_from_spiral_middle - half_thickness
spiral = 1.0 - greater_equal(distance_from_spiral,0.0)
sigmasq = gaussian_width*gaussian_width
with float_error_ignore():
falloff = exp(divide(-distance_from_spiral*distance_from_spiral, 2.0*sigmasq))
return maximum(falloff,spiral)
def __div__(self, other):
if isVector(other):
raise TypeError, "Can't divide by a vector"
else:
return Vector(Numeric.divide(self.array, 1. * other))
def normal(self):
"Returns a normalized copy."
len = Numeric.sqrt(Numeric.add.reduce(self.array * self.array))
if len == 0:
raise ZeroDivisionError, "Can't normalize a zero-length vector"
return Vector(Numeric.divide(self.array, len))
def __div__(self, other): if isVector(other): raise TypeError, "Can't divide by a vector" else: return Vector(Numeric.divide(self.array,1.*other))
def normal(self):
"Returns a normalized copy."
len = Numeric.sqrt(Numeric.add.reduce(self.array*self.array))
if len == 0:
raise ZeroDivisionError, "Can't normalize a zero-length vector"
return Vector(Numeric.divide(self.array, len))
