def expBroaden(y, t, expMod):
fy = F.fft(y)
a = N.exp(-1 * expMod * N.arange(0, len(y)) / t)
fa = F.fft(a)
fy1 = fy * fa
yb = (F.ifft(fy1).real) / N.sum(a)
return yb
def test_vector1(self):
"""check that mkl_fft gives the same result of numpy.fft"""
f1 = mkl_fft.fft(self.xz1)
f2 = np_fft.fft(self.xz1)
assert_allclose(f1,f2, rtol=1e-7, atol=2e-12)
f1 = mkl_fft.fft(self.xc1)
f2 = np_fft.fft(self.xc1)
assert_allclose(f1,f2, rtol=2e-6, atol=2e-6)
def generate_dashboard(data):
if len(data) == 0:
return 'Empty data set'
data.sort(key=lambda x: x['timestamp'])
x = map(lambda x: x['timestamp'], data)
# this base_plot is just for xrange synchronization
base_plot = bokeh.plotting.figure(width=800,
height=250,
x_axis_type="datetime")
base_plot.circle(x, x)
figures = []
for key in data[0]['data'].keys():
figure = bokeh.plotting.figure(width=800,
height=250,
title=key,
x_axis_type="datetime",
x_range=base_plot.x_range)
y = map(lambda x: x['data'][key], data)
figure.circle(x, y)
figure2 = bokeh.plotting.figure(width=800,
height=250,
title='FFT: %s' % key)
y2 = map(lambda x: x.real, fftpack.fft(y))
x2 = range(len(y))
figure2.line(x2, y2)
figures.append(bokeh.plotting.hplot(figure, figure2))
return file_html(bokeh.plotting.vplot(*figures), CDN, "my plot")
def rfftn_fix(a, s=None, axes=None, norm=None):
a = numpy.array(a, copy=True, dtype=float)
s, axes = fftpk._cook_nd_args(a, s, axes)
a = rfft_fix(a, s[-1], axes[-1], norm)
for ii in range(len(axes) - 1):
a = fftpk.fft(a, s[ii], axes[ii], norm)
return a
def chebt1(f):
#TODO
"""chebyshev transformation, see chebfun"""
n = len(f)
oncircle = concatenate((f[-1::-1], f[1:-1]))
fftcoef = real(fft(oncircle))/(2*n-2)
return fftcoef[n-1::-1]
def update_data(self, x, taps, psd, syms, table):
try:
eqdata_key = 'dtv_atsc_equalizer0::taps'
symdata_key = 'dtv_atsc_equalizer0::data'
rs_nump_key = 'dtv_atsc_rs_decoder0::num_packets'
rs_numbp_key = 'dtv_atsc_rs_decoder0::num_bad_packets'
rs_numerrs_key = 'dtv_atsc_rs_decoder0::num_errors_corrected'
vt_metrics_key = 'dtv_atsc_viterbi_decoder0::decoder_metrics'
snr_key = 'probe2_f0::SNR'
data = self.radio.getKnobs([])
eqdata = data[eqdata_key]
symdata = data[symdata_key]
rs_num_packets = data[rs_nump_key]
rs_num_bad_packets = data[rs_numbp_key]
rs_num_errors_corrected = data[rs_numerrs_key]
vt_decoder_metrics = data[vt_metrics_key]
snr_est = data[snr_key]
vt_decoder_metrics = numpy.mean(vt_decoder_metrics.value)
self._viterbi_metric.pop()
self._viterbi_metric.insert(0, vt_decoder_metrics)
except TTransportException:
sys.stderr.write("Lost connection, exiting")
sys.exit(1)
ntaps = len(eqdata.value)
taps.set_ydata(eqdata.value)
taps.set_xdata(list(range(ntaps)))
self._sp0.set_xlim(0, ntaps)
self._sp0.set_ylim(min(eqdata.value), max(eqdata.value))
fs = 6.25e6
freq = numpy.linspace(-fs / 2, fs / 2, 10000)
H = numpy.fft.fftshift(fftpack.fft(eqdata.value, 10000))
HdB = 20.0*numpy.log10(abs(H))
psd.set_ydata(HdB)
psd.set_xdata(freq)
self._sp1.set_xlim(0, fs / 2)
self._sp1.set_ylim([min(HdB), max(HdB)])
self._sp1.set_yticks([min(HdB), max(HdB)])
self._sp1.set_yticklabels(["min", "max"])
nsyms = len(symdata.value)
syms.set_ydata(symdata.value)
syms.set_xdata(nsyms*[0,])
self._sp2.set_xlim([-1, 1])
self._sp2.set_ylim([-10, 10])
per = float(rs_num_bad_packets.value) / float(rs_num_packets.value)
ber = float(rs_num_errors_corrected.value) / float(187*rs_num_packets.value)
table._cells[(1,0)]._text.set_text("{0}".format(rs_num_packets.value))
table._cells[(1,1)]._text.set_text("{0:.2g}".format(ber))
table._cells[(1,2)]._text.set_text("{0:.2g}".format(per))
table._cells[(1,3)]._text.set_text("{0:.1f}".format(numpy.mean(self._viterbi_metric)))
table._cells[(1,4)]._text.set_text("{0:.4f}".format(snr_est.value[0]))
return (taps, psd, syms, table)
def rfftn_fix(a, s=None, axes=None, norm=None):
a = numpy.array(a, copy=True, dtype=float)
s, axes = fftpk._cook_nd_args(a, s, axes)
a = rfft_fix(a, s[-1], axes[-1], norm)
for ii in range(len(axes)-1):
a = fftpk.fft(a, s[ii], axes[ii], norm)
return a
def dofft(self, iq):
N = len(iq)
iq_fft = numpy.fft.fftshift(fftpack.fft(iq)) # fft and shift axis
iq_fft = 20 * numpy.log10(abs(
(iq_fft + 1e-15) / N)) # convert to decibels, adjust power
# adding 1e-15 (-300 dB) to protect against value errors if an item in iq_fft is 0
return iq_fft
def chebt1(f):
#TODO
"""chebyshev transformation, see chebfun"""
n = len(f)
oncircle = concatenate((f[-1::-1], f[1:-1]))
fftcoef = real(fft(oncircle))/(2*n-2)
return fftcoef[n-1::-1]
def plot_dft_abs_phase(signal: np.array.__class__,
frequency_discretization=1,
is_in_db=False):
spectrum = fftshift(fft(signal))
fft_frequencies = fftshift(
fftfreq(signal.shape[0], 1 / frequency_discretization))
abs_values = np.abs(spectrum)
if is_in_db:
abs_values = power_samples_in_db(abs_values)
plt.figure()
plt.subplot(211)
plt.plot(fft_frequencies, abs_values, color='b')
plt.ylabel('Amplitude [dB]', color='b')
plt.xlabel('Frequency')
plt.grid()
plt.subplot(212)
plt.plot(fft_frequencies, np.angle(spectrum), color='g')
plt.ylabel('Phase [rad]', color='g')
plt.xlabel('Frequency')
plt.grid()
plt.show()
def chebt2(f):
"""chebyshev transformation, coefficients in expansion using
Chebyshev polynomials T_n(x), see chebfun for details"""
n = len(f)
oncircle = concatenate((f[-1::-1], f[1:-1]))
fftcoef = real(fft(oncircle))/(2*n-2)
#print n, len(fftcoef)
#print fftcoef[n-1:]
#print fftcoef[n-1:0:-1]
fftcoef[n-1:0:-1] += fftcoef[n-1:] # z+conj(z)
return fftcoef[n-1::-1]
def chebt2(f):
"""chebyshev transformation, coefficients in expansion using
Chebyshev polynomials T_n(x), see chebfun for details"""
n = len(f)
oncircle = concatenate((f[-1::-1], f[1:-1]))
fftcoef = real(fft(oncircle))/(2*n-2)
#print n, len(fftcoef)
#print fftcoef[n-1:]
#print fftcoef[n-1:0:-1]
fftcoef[n-1:0:-1] += fftcoef[n-1:] # z+conj(z)
return fftcoef[n-1::-1]
def dofft(iq, reverse=False):
if reverse:
# iq_ifft = np.fft.ifftshift(fftpack.ifft(iq))
iq_ifft = fftpack.ifft(iq)
return iq_ifft
else:
# iq_fft = np.fft.fftshift(fftpack.fft(iq)) # fft and shift axis
iq_fft = fftpack.fft(iq) # fft and shift axis
# iq_fft = fftpack.fft(iq) # fft no shift axis
# iq_fft = 20 * np.log10(abs((iq_fft + 1e-15) / N)) # convert to decibels, adjust power
# adding 1e-15 (-300 dB) to protect against value errors if an item in iq_fft is 0
return iq_fft
def plot_dft_real_image(signal: np.array.__class__,
frequency_discretization=1,
is_in_db=False):
spectrum = fftshift(fft(signal))
if is_in_db:
spectrum = power_samples_in_db(
np.real(spectrum)) + 1j * power_samples_in_db(np.imag(spectrum))
fft_frequencies = fftshift(
fftfreq(signal.shape[0], 1 / frequency_discretization))
plt.subplot(211)
plt.plot(fft_frequencies, np.real(spectrum))
plt.subplot(212)
plt.plot(fft_frequencies, np.imag(spectrum))
# plt.ion()
plt.show()
def hilbert(mag):
"""Compute the modified 1D discrete Hilbert transform
Parameters
----------
mag : ndarray
The magnitude spectrum. Should be 1D with an even length, and
preferably a fast length for FFT/IFFT.
"""
# Adapted based on code by Niranjan Damera-Venkata,
# Brian L. Evans and Shawn R. McCaslin (see refs for `minimum_phase`)
sig = np.zeros(len(mag))
# Leave Nyquist and DC at 0, knowing np.abs(fftfreq(N)[midpt]) == 0.5
midpt = len(mag) // 2
sig[1:midpt] = 1
sig[midpt+1:] = -1
# eventually if we want to support complex filters, we will need a
# np.abs() on the mag inside the log, and should remove the .real
recon = ifft(mag * np.exp(fft(sig * ifft(np.log(mag))))).real
return recon
ptA=N.ones(WINDOW_SIZE);
t_fft=0
t_mult=0
for i in xrange(MAX_ELEMENTS):
tA=N.zeros(WINDOW_SIZE)
for j in xrange(MAX_ISOTOPES):
if A[i][j,0] != 0:
#removed +1 after R)+1 --we're using python which counts from 0
tA[N.round(A[i][j,0]*R)]=A[i][j,1]#; % put isotopic distribution in tA
print 'Calculate FFT...'
t0 = time.clock()
tA=F.fft(tA) # FFT along elements isotopic distribution O(nlogn)
t_fft = time.clock()-t0
print 'Multiply vectors...'
t0 = time.clock()
tA=tA**M[i]# % O(n)
#################
ptA = ptA*tA# % O(n)#this is where it is messing UP
#################
t1 = time.clock()
t_mult=t1-t0
print 'Time for FFT: %4.2f s'%t_fft
print 'Time for multiplications: %4.2f s'%t_mult
print 'Calculate IFFT...'
def fft_real_freq(sig, dt):
S = fft(sig)
S_F = np.linspace(0, 1, len(S) / 2) / dt / 2.0
return S_F, S[0:len(S_F)]
def dofft(self, iq):
N = len(iq)
iq_fft = numpy.fft.fftshift(fftpack.fft(iq)) # fft and shift axis
iq_fft = 20*numpy.log10(abs((iq_fft+1e-15) / N)) # convert to decibels, adjust power
# adding 1e-15 (-300 dB) to protect against value errors if an item in iq_fft is 0
return iq_fft
ptA = N.ones(WINDOW_SIZE)
t_fft = 0
t_mult = 0
for i in xrange(MAX_ELEMENTS):
tA = N.zeros(WINDOW_SIZE)
for j in xrange(MAX_ISOTOPES):
if A[i][j, 0] != 0:
#removed +1 after R)+1 --we're using python which counts from 0
tA[N.round(A[i][j, 0] *
R)] = A[i][j, 1] #; % put isotopic distribution in tA
print 'Calculate FFT...'
t0 = time.clock()
tA = F.fft(tA) # FFT along elements isotopic distribution O(nlogn)
t_fft = time.clock() - t0
print 'Multiply vectors...'
t0 = time.clock()
tA = tA**M[i] # % O(n)
#################
ptA = ptA * tA # % O(n)#this is where it is messing UP
#################
t1 = time.clock()
t_mult = t1 - t0
print 'Time for FFT: %4.2f s' % t_fft
print 'Time for multiplications: %4.2f s' % t_mult
print 'Calculate IFFT...'
t0 = time.clock()
def Proj_F1(s):
N = len(s)
return ifft(Proj_M1(fft(s, 2*N)))[0:N]
def main():
parser = ArgumentParser(conflict_handler="resolve")
parser.add_argument(
"-N",
"--nsamples",
type=int,
default=2000,
help="Set the number of samples to process [default=%(default)r]")
parser.add_argument(
"-S",
"--sps",
type=int,
default=4,
help="Set the samples per symbol [default=%(default)r]")
parser.add_argument("-r",
"--rolloff",
type=eng_float,
default=0.35,
help="Set the rolloff factor [default=%(default)r]")
parser.add_argument(
"-W",
"--bandwidth",
type=eng_float,
default=2 * numpy.pi / 100.0,
help="Set the loop bandwidth (PFB) or gain (M&M) [default=%(default)r]"
)
parser.add_argument(
"-n",
"--ntaps",
type=int,
default=45,
help="Set the number of taps in the filters [default=%(default)r]")
parser.add_argument(
"--noise",
type=eng_float,
default=0.0,
help="Set the simulation noise voltage [default=%(default)r]")
parser.add_argument(
"-f",
"--foffset",
type=eng_float,
default=0.0,
help=
"Set the simulation's normalized frequency offset (in Hz) [default=%(default)r]"
)
parser.add_argument(
"-t",
"--toffset",
type=eng_float,
default=1.0,
help="Set the simulation's timing offset [default=%(default)r]")
parser.add_argument(
"-p",
"--poffset",
type=eng_float,
default=0.0,
help="Set the simulation's phase offset [default=%(default)r]")
parser.add_argument(
"-M",
"--mode",
type=int,
default=0,
help=
"Set the recovery mode (0: polyphase, 1: M&M) [default=%(default)r]")
args = parser.parse_args()
# Adjust N for the interpolation by sps
args.nsamples = args.nsamples // args.sps
# Set up the program-under-test
put = example_timing(args.nsamples, args.sps, args.rolloff, args.ntaps,
args.bandwidth, args.noise, args.foffset,
args.toffset, args.poffset, args.mode)
put.run()
if args.mode == 0:
data_src = numpy.array(put.vsnk_src.data()[20:])
data_clk = numpy.array(put.vsnk_clk.data()[20:])
data_err = numpy.array(put.vsnk_err.data()[20:])
data_rat = numpy.array(put.vsnk_rat.data()[20:])
data_phs = numpy.array(put.vsnk_phs.data()[20:])
f1 = pyplot.figure(1, figsize=(12, 10), facecolor='w')
# Plot the IQ symbols
s1 = f1.add_subplot(2, 2, 1)
s1.plot(data_src.real, data_src.imag, "bo")
s1.plot(data_clk.real, data_clk.imag, "ro")
s1.set_title("IQ")
s1.set_xlabel("Real part")
s1.set_ylabel("Imag part")
s1.set_xlim([-2, 2])
s1.set_ylim([-2, 2])
# Plot the symbols in time
delay = put.delay
m = len(data_clk.real)
s2 = f1.add_subplot(2, 2, 2)
s2.plot(data_src.real, "bs", markersize=10, label="Input")
s2.plot(data_clk.real[delay:], "ro", label="Recovered")
s2.set_title("Symbols")
s2.set_xlabel("Samples")
s2.set_ylabel("Real Part of Signals")
s2.legend()
# Plot the clock recovery loop's error
s3 = f1.add_subplot(2, 2, 3)
s3.plot(data_err, label="Error")
s3.plot(data_rat, 'r', label="Update rate")
s3.set_title("Clock Recovery Loop Error")
s3.set_xlabel("Samples")
s3.set_ylabel("Error")
s3.set_ylim([-0.5, 0.5])
s3.legend()
# Plot the clock recovery loop's error
s4 = f1.add_subplot(2, 2, 4)
s4.plot(data_phs)
s4.set_title("Clock Recovery Loop Filter Phase")
s4.set_xlabel("Samples")
s4.set_ylabel("Filter Phase")
diff_taps = put.dtaps
ntaps = len(diff_taps[0])
nfilts = len(diff_taps)
t = numpy.arange(0, ntaps * nfilts)
f3 = pyplot.figure(3, figsize=(12, 10), facecolor='w')
s31 = f3.add_subplot(2, 1, 1)
s32 = f3.add_subplot(2, 1, 2)
s31.set_title("Differential Filters")
s32.set_title("FFT of Differential Filters")
for i, d in enumerate(diff_taps):
D = 20.0 * numpy.log10(
1e-20 + abs(numpy.fft.fftshift(fftpack.fft(d, 10000))))
s31.plot(t[i::nfilts].real, d, "-o")
s32.plot(D)
s32.set_ylim([-120, 10])
# If testing the M&M clock recovery loop
else:
data_src = numpy.array(put.vsnk_src.data()[20:])
data_clk = numpy.array(put.vsnk_clk.data()[20:])
data_err = numpy.array(put.vsnk_err.data()[20:])
f1 = pyplot.figure(1, figsize=(12, 10), facecolor='w')
# Plot the IQ symbols
s1 = f1.add_subplot(2, 2, 1)
s1.plot(data_src.real, data_src.imag, "o")
s1.plot(data_clk.real, data_clk.imag, "ro")
s1.set_title("IQ")
s1.set_xlabel("Real part")
s1.set_ylabel("Imag part")
s1.set_xlim([-2, 2])
s1.set_ylim([-2, 2])
# Plot the symbols in time
s2 = f1.add_subplot(2, 2, 2)
s2.plot(data_src.real, "bs", markersize=10, label="Input")
s2.plot(data_clk.real, "ro", label="Recovered")
s2.set_title("Symbols")
s2.set_xlabel("Samples")
s2.set_ylabel("Real Part of Signals")
s2.legend()
# Plot the clock recovery loop's error
s3 = f1.add_subplot(2, 2, 3)
s3.plot(data_err)
s3.set_title("Clock Recovery Loop Error")
s3.set_xlabel("Samples")
s3.set_ylabel("Error")
pyplot.show()
def cal_isotopic(self):
MAX_ELEMENTS=5+1 # add 1 due to mass correction 'element'
MAX_ISOTOPES=4 # maxiumum # of isotopes for one element
CUTOFF=1e-4 # relative intensity cutoff for plotting
WINDOW_SIZE = 500
#WINDOW_SIZE=input('Window size (in Da) ---> ');
#RESOLUTION=input('Resolution (in Da) ----> '); % mass unit used in vectors
RESOLUTION = 1
if RESOLUTION < 0.00001:# % minimal mass step allowed
RESOLUTION = 0.00001
elif RESOLUTION > 0.5: # maximal mass step allowed
RESOLUTION = 0.5
R=0.00001/RESOLUTION# % R is used to scale nuclide masses (see below)
WINDOW_SIZE=WINDOW_SIZE/RESOLUTION;
self.xx=WINDOW_SIZE # convert window size to new mass units
WINDOW_SIZE=self.next2pow(); # fast radix-2 fast-Fourier transform algorithm
if WINDOW_SIZE < np.round(496708*R)+1:
WINDOW_SIZE = self.next2pow(np.round(496708*R)+1) # just to make sure window is big enough
#H378 C254 N65 O75 S6
M=np.array([int(self.H),int(self.C),int(self.N),int(self.O),0,0]) #% empiric formula, e.g. bovine insulin
# isotopic abundances stored in matrix A (one row for each element)
A=np.zeros((MAX_ELEMENTS,MAX_ISOTOPES,2));
A[0][0,:] = [100783,0.9998443]# % 1H
A[0][1,:] = [201410,0.0001557]# % 2H
A[1][0,:] = [100000,0.98889]# % 12C
A[1][1,:] = [200336,0.01111]# % 13C
A[2][0,:] = [100307,0.99634]# % 14N
A[2][1,:] = [200011,0.00366]# % 15N
A[3][0,:] = [99492,0.997628]# % 16O
A[3][1,:] = [199913,0.000372]# % 17O
A[3][2,:] = [299916,0.002000]# % 18O
A[4][0,:] = [97207,0.95018]# % 32S
A[4][1,:] = [197146,0.00750]# % 33S
A[4][2,:] = [296787,0.04215]# % 34S
A[4][3,:] = [496708,0.00017]# % 36S
A[5][0,:] = [100000,1.00000]# % for shifting mass so that Mmi is
# % near left limit of window
Mmi=np.array([np.round(100783*R), np.round(100000*R),\
np.round(100307*R),np.round(99492*R), np.round(97207*R), 0])*M# % (Virtual) monoisotopic mass in new units
Mmi = Mmi.sum()
#% mass shift so Mmi is in left limit of window:
FOLDED=np.floor(Mmi/(WINDOW_SIZE-1))+1# % folded FOLDED times (always one folding due to shift below)
#% shift distribution to 1 Da from lower window limit:
M[MAX_ELEMENTS-1]=np.ceil(((WINDOW_SIZE-1)-np.mod(Mmi,WINDOW_SIZE-1)+np.round(100000*R))*RESOLUTION)
MASS_REMOVED=np.array([0,11,13,15,31,-1])*M#% correction for 'virtual' elements and mass shift
begin=WINDOW_SIZE*RESOLUTION+MASS_REMOVED.sum()
end=2*(WINDOW_SIZE-1)*RESOLUTION+MASS_REMOVED.sum()
ptA=np.ones(WINDOW_SIZE);
t_fft=0
t_mult=0
for i in xrange(MAX_ELEMENTS):
tA=np.zeros(WINDOW_SIZE)
for j in xrange(MAX_ISOTOPES):
if A[i][j,0] != 0:
#removed +1 after R)+1 --we're using python
tA[np.round(A[i][j,0]*R)]=A[i][j,1]#; % put isotopic distribution in tA
t0 = time.clock()
tA=F.fft(tA) # FFT along elements isotopic distribution O(nlogn)
t_fft = time.clock()-t0
t0 = time.clock()
tA=tA**M[i]# % O(n)
#################
ptA = ptA*tA# % O(n)#this is where it is messing UP
#################
t1 = time.clock()
t_mult=t1-t0
t0=time.clock()
ptA=F.ifft(ptA).real#; % O(nlogn)
t0=time.clock()
MA=np.linspace(begin,end,WINDOW_SIZE-1)
ind=np.where(ptA>CUTOFF)[0]
self.x = MA[ind]
self.y = ptA[ind]
self.x_min=int(np.min(self.x)-(np.max(self.x)-np.min(self.x)))
self.x_max=int(np.min(self.x)+(np.max(self.x)-np.min(self.x)))
self.mass_y=np.ones(len(self.x))
mass_diff=np.ones(len(self.x))
mzInd= np.logical_and((self.mz>=self.x_min),(self.mz<=self.x_max))
self.mass_y=self.mass[mzInd]
self.mass_x=self.mz[mzInd]
# for i in range(len(self.x)):
# self.mass_y[i]=self.mass[int(self.x[i])]
self.massy=np.max(self.mass_y)
print self.massy
self.mass_y=self.mass_y/max(self.mass_y)*100
self.y=self.y/max(self.y)*100
# k=(self.mass_y*self.y).sum()/(self.mass_y*self.mass_y).sum()
# self.fit=((k*self.mass_y-self.y)*(k*self.mass_y-self.y)).sum()/(self.y*self.y).sum()
for i in range(len(self.y)):
mass_diff[i]=np.abs(self.mass_y[i]-self.y[i])/(self.mass_y[i]+self.y[i])
self.mass_diff=(1-mass_diff.sum()/len(mass_diff))*100
# Original data exp_data = [0.0, 65.60500001907349, 1825.5309998989105, 1861.1949999332428, 3616.5469999313354, 3652.177999973297, 5413.882999897003, 5449.318000078201, 7207.401999950409, 7243.092000007629, 8328.25200009346, 9006.778000116348, 9042.30999994278, 10797.611999988556, 10863.18799996376, 12623.076999902725, 12658.436000108719, 14415.46900010109, 14450.895999908447, 16213.163000106812, 16248.641000032425, 18005.18600010872, 18070.802999973297, 18522.302000045776, 19803.196000099182, 19868.661999940872, 20802.37299990654, 21594.209000110626, 21659.77800011635, 23422.048000097275, 23457.487999916077, 25214.668999910355, 25250.15300011635, 27011.65199995041, 27047.0569999218, 28803.25200009346, 28868.885999917984, 30222.260999917984, 30599.648000001907, 30665.289000034332, 32419.674999952316, 32455.194000005722, 34214.93099999428, 34250.35400009155, 36008.079999923706, 36043.68400001526, 37804.78500008583, 37870.19900012016, 38442.32400012016, 39594.3789999485, 39665.11899995804, 41424.59200000763, 41460.00900006294, 43217.22499990463, 43252.643000125885, 45012.87599992752, 45048.49799990654, 46848.959000110626, 46914.168999910355, 47809.790999889374, 47874.954999923706, 48406.518000125885, 48471.700000047684] N = 50000 # Test 1 T = N / 80 # T = 625 k = randint(0, T) x = [1 if i%T == k else 0 for i in range(N)] y = fft(x) y_real = [yi.real for yi in y] y_imag = [yi.imag for yi in y] y_phase = [cmath.phase(yi) for yi in y] y_magnitude = [magnitude(yi) for yi in y] # Test 2 T1 = N / 80 # T1 = 625 T2 = N / 200 # T2 = 250 k1 = randint(0, T) k2 = randint(0, T)
import pylab as P
MAX_ELEMENTS = 5
MAX_MASS = 2**13 #% fast radix-2 fast-Fourier transform algorithm is used
M = N.array([378,234,65,75,6]) #% empirical formula, e.g. bovine insulin
A = N.zeros((MAX_ELEMENTS,MAX_MASS))# % isotopic abundancies stored in A
A[0,1:3]=[0.9998443,0.0001557]# % H
A[1,12:14]=[0.98889,0.01111]# % C
A[2,14:16]=[0.99634,0.00366]# % N
A[3,16:19]=[0.997628,0.000372,0.002000]# % O
A[4,32:37]=[0.95018,0.00750,0.04215,0,0.00017]# % S (extend to other elements as needed)
tA=F.fft(A,axis=1)# % FFT along each element's isotopic distribution
ptA=N.ones(MAX_MASS);
for i in xrange(MAX_ELEMENTS-1):
ptA = ptA*(tA[i,:]**M[i])#; % multiply transforms (elementwise)
riptA=F.ifft(ptA).real# % inverse FFT to get convolutions
id=N.zeros(MAX_MASS)
id[0:MAX_MASS-1]=riptA[1:MAX_MASS]#; % shift to real mass
print id.argmax(), id.max()
P.plot(riptA)
P.show()
def Proj_F1(s):
N = len(s)
return ifft(Proj_M1(fft(s, 2 * N)))[0:N]
MAX_MASS = 2**13 #% fast radix-2 fast-Fourier transform algorithm is used
M = N.array([378, 234, 65, 75, 6]) #% empirical formula, e.g. bovine insulin
A = N.zeros((MAX_ELEMENTS,
MAX_MASS)) # % isotopic abundancies stored in A
A[0, 1:3] = [0.9998443, 0.0001557] # % H
A[1, 12:14] = [0.98889, 0.01111] # % C
A[2, 14:16] = [0.99634, 0.00366] # % N
A[3, 16:19] = [0.997628, 0.000372, 0.002000] # % O
A[4, 32:37] = [0.95018, 0.00750, 0.04215, 0,
0.00017] # % S (extend to other elements as needed)
tA = F.fft(
A, axis=1
) # % FFT along each element's isotopic distribution
ptA = N.ones(MAX_MASS)
for i in xrange(MAX_ELEMENTS - 1):
ptA = ptA * (tA[i, :]**M[i]
) #; % multiply transforms (elementwise)
riptA = F.ifft(ptA).real # % inverse FFT to get convolutions
id = N.zeros(MAX_MASS)
id[0:MAX_MASS - 1] = riptA[1:MAX_MASS] #; % shift to real mass
print id.argmax(), id.max()
P.plot(riptA)
P.show()
def taylor_coeff(fun, N):
"""From L. Trefethen, Ten digits algorithms """
zz = exp(2j*pi*(array(list(range(N))))/N)
c = fft(fun(zz))/N
return real(c)
def isotopefn(givenmass):
def next2pow(x):
return 2**int(N.ceil(N.log(float(x))/N.log(2.0)))
MAX_ELEMENTS=5+1 # add 1 due to mass correction 'element'
MAX_ISOTOPES=4 # maxiumum # of isotopes for one element
CUTOFF=1e-8 # relative intensity cutoff for plotting
WINDOW_SIZE = 500
#WINDOW_SIZE=input('Window size (in Da) ---> ');
#RESOLUTION=input('Resolution (in Da) ----> '); % mass unit used in vectors
RESOLUTION = 0.5
if RESOLUTION < 0.00001:# % minimal mass step allowed
RESOLUTION = 0.00001
elif RESOLUTION > 0.5: # maximal mass step allowed
RESOLUTION = 0.5
R=0.00001/RESOLUTION# % R is used to scale nuclide masses (see below)
WINDOW_SIZE=WINDOW_SIZE/RESOLUTION; # convert window size to new mass units
WINDOW_SIZE=next2pow(WINDOW_SIZE); # fast radix-2 fast-Fourier transform algorithm
if WINDOW_SIZE < N.round(496708*R)+1:
WINDOW_SIZE = nextpow2(N.round(496708*R)+1) # just to make sure window is big enough
#print 'Vector size: 1x%d'%WINDOW_SIZE
#H378 C254 N65 O75 S6
resnumber=N.round(float(givenmass)/110,0)
#print resnumber
abuns=[7.593,4.869,1.351,1.492,0.051]
myarr=[N.round(resnumber*k,0) for k in abuns]
#myarr=[98,63,18,13,1]
myarr.append(0)
#print myarr
M=N.array(myarr) #% empiric formula, e.g. bovine insulin
# isotopic abundances stored in matrix A (one row for each element)
A=N.zeros((MAX_ELEMENTS,MAX_ISOTOPES,2));
A[0][0,:] = [100783,0.9998443]# % 1H
A[0][1,:] = [201410,0.0001557]# % 2H
A[1][0,:] = [100000,0.98889]# % 12C
A[1][1,:] = [200336,0.01111]# % 13C
A[2][0,:] = [100307,0.99634]# % 14N
A[2][1,:] = [200011,0.00366]# % 15N
A[3][0,:] = [99492,0.997628]# % 16O
A[3][1,:] = [199913,0.000372]# % 17O
A[3][2,:] = [299916,0.002000]# % 18O
A[4][0,:] = [97207,0.95018]# % 32S
A[4][1,:] = [197146,0.00750]# % 33S
A[4][2,:] = [296787,0.04215]# % 34S
A[4][2,:] = [496708,0.00017]# % 36S
A[5][0,:] = [100000,1.00000]# % for shifting mass so that Mmi is
# % near left limit of window
Mmi=N.array([N.round(100783*R), N.round(100000*R),\
N.round(100307*R), N.round(99492*R), N.round(97207*R), 0])*M# % (Virtual) monoisotopic mass in new units
Mmi = Mmi.sum()
#% mass shift so Mmi is in left limit of window:
#print "Mmi",Mmi
#print "Window", WINDOW_SIZE
FOLDED=N.floor(Mmi/(WINDOW_SIZE-1))+1# % folded FOLDED times (always one folding due to shift below)
#% shift distribution to 1 Da from lower window limit:
M[MAX_ELEMENTS-1]=N.ceil(((WINDOW_SIZE-1)-N.mod(Mmi,WINDOW_SIZE-1)+N.round(100000*R))*RESOLUTION)
MASS_REMOVED=N.array([0,11,13,15,31,-1])*M#'; % correction for 'virtual' elements and mass shift
MASS_REMOVED = MASS_REMOVED.sum()
ptA=N.ones(WINDOW_SIZE);
t_fft=0
t_mult=0
for i in xrange(MAX_ELEMENTS):
tA=N.zeros(WINDOW_SIZE)
for j in xrange(MAX_ISOTOPES):
if A[i][j,0] != 0:
#removed +1 after R)+1 --we're using python
tA[N.round(A[i][j,0]*R)]=A[i][j,1]#; % put isotopic distribution in tA
#print 'Calculate FFT...'
tA=F.fft(tA) # FFT along elements isotopic distribution O(nlogn)
#print 'Multiply vectors...'
tA=tA**M[i]# % O(n)
#################
ptA = ptA*tA# % O(n)#this is where it is messing UP
#################
#rint 'Time for FFT: %4.2f s'%t_fft
#print 'Time for multiplications: %4.2f s'%t_mult
#print 'Calculate IFFT...'
ptA=F.ifft(ptA).real#; % O(nlogn)
#print 'Time for IFFT: %4.2f s'%(time.clock()-t0)
#print 'Plotting...'
start = (FOLDED*(WINDOW_SIZE-1)+1)*RESOLUTION+MASS_REMOVED,(FOLDED+1)*(WINDOW_SIZE-1)*RESOLUTION+MASS_REMOVED
stop = WINDOW_SIZE - 1
MA=N.linspace((FOLDED*(WINDOW_SIZE-1)+1)*RESOLUTION+MASS_REMOVED,(FOLDED+1)*(WINDOW_SIZE-1)*RESOLUTION+MASS_REMOVED, WINDOW_SIZE-1)
ind=N.where(ptA>CUTOFF)[0]
y = ptA[ind]
y2=[x/y[0] for x in y]
return y2
def isotopefn(sequence, ion_number):
massDict = mass.Composition(sequence[:ion_number])
massDict['C'] -= 1
massDict['H'] -= 2
massDict['O'] -= 2
if 'S' not in massDict:
massDict['S'] = 0
def next2pow(x):
return 2**int(np.ceil(np.log(float(x)) / np.log(2.0)))
MAX_ELEMENTS = 5 + 1 # add 1 due to mass correction 'element'
MAX_ISOTOPES = 4 # maxiumum # of isotopes for one element
CUTOFF = 1e-8 # relative intensity cutoff for plotting
WINDOW_SIZE = 500
# WINDOW_SIZE=input('Window size (in Da) ---> ');
# RESOLUTION=input('Resolution (in Da) ----> '); % mass unit used in vectors
RESOLUTION = 0.5
if RESOLUTION < 0.00001: # % minimal mass step allowed
RESOLUTION = 0.00001
elif RESOLUTION > 0.5: # maximal mass step allowed
RESOLUTION = 0.5
R = 0.00001 / RESOLUTION # % R is used to scale nuclide masses (see below)
WINDOW_SIZE = WINDOW_SIZE / RESOLUTION
# convert window size to new mass units
WINDOW_SIZE = next2pow(WINDOW_SIZE)
# fast radix-2 fast-Fourier transform algorithm
if WINDOW_SIZE < np.round(496708 * R) + 1:
WINDOW_SIZE = next2pow(np.round(496708 * R) +
1) # just to make sure window is big enough
# print 'Vector size: 1x%d'%WINDOW_SIZE
# H378 C254 N65 O75 S6
M = np.array([
massDict['H'], massDict['C'], massDict['N'], massDict['O'],
massDict['S'], 1
])
# isotopic abundances stored in matrix A (one row for each element)
A = np.zeros((MAX_ELEMENTS, MAX_ISOTOPES, 2))
A[0][0, :] = [100783, 0.9998443] # % 1H
A[0][1, :] = [201410, 0.0001557] # % 2H
A[1][0, :] = [100000, 0.98889] # % 12C
A[1][1, :] = [200336, 0.01111] # % 13C
A[2][0, :] = [100307, 0.99634] # % 14N
A[2][1, :] = [200011, 0.00366] # % 15N
A[3][0, :] = [99492, 0.997628] # % 16O
A[3][1, :] = [199913, 0.000372] # % 17O
A[3][2, :] = [299916, 0.002000] # % 18O
A[4][0, :] = [97207, 0.95018] # % 32S
A[4][1, :] = [197146, 0.00750] # % 33S
A[4][2, :] = [296787, 0.04215] # % 34S
A[4][2, :] = [496708, 0.00017] # % 36S
A[5][0, :] = [100000, 1.00000] # % for shifting mass so that Mmi is
# % near left limit of window
Mmi = np.array([np.round(100783 * R), np.round(100000 * R), \
np.round(100307 * R), np.round(99492 * R), np.round(97207 * R),
0]) * M # % (Virtual) monoisotopic mass in new units
Mmi = Mmi.sum()
# % mass shift so Mmi is in left limit of window:
# print "Mmi",Mmi
# print "Window", WINDOW_SIZE
FOLDED = np.floor(
Mmi / (WINDOW_SIZE - 1)
) + 1 # % folded FOLDED times (always one folding due to shift below)
# % shift distribution to 1 Da from lower window limit:
M[MAX_ELEMENTS - 1] = np.ceil(
((WINDOW_SIZE - 1) - np.mod(Mmi, WINDOW_SIZE - 1) +
np.round(100000 * R)) * RESOLUTION)
MASS_REMOVED = np.array([
0, 11, 13, 15, 31, -1
]) * M # '; % correction for 'virtual' elements and mass shift
MASS_REMOVED = MASS_REMOVED.sum()
ptA = np.ones(WINDOW_SIZE)
t_fft = 0
t_mult = 0
for i in xrange(MAX_ELEMENTS):
tA = np.zeros(WINDOW_SIZE)
for j in xrange(MAX_ISOTOPES):
if A[i][j, 0] != 0:
# removed +1 after R)+1 --we're using python
tA[np.int(np.round(
A[i][j, 0] *
R))] = A[i][j, 1] # ; % put isotopic distribution in tA
# print 'Calculate FFT...'
tA = F.fft(tA) # FFT along elements isotopic distribution O(nlogn)
# print 'Multiply vectors...'
tA = tA**M[i] # % O(n)
#################
ptA = ptA * tA # % O(n)#this is where it is messing UP
#################
# rint 'Time for FFT: %4.2f s'%t_fft
# print 'Time for multiplications: %4.2f s'%t_mult
# print 'Calculate IFFT...'
ptA = F.ifft(ptA).real # ; % O(nlogn)
# print 'Time for IFFT: %4.2f s'%(time.clock()-t0)
# print 'Plotting...'
start = (FOLDED * (WINDOW_SIZE - 1) + 1) * RESOLUTION + MASS_REMOVED, (
FOLDED + 1) * (WINDOW_SIZE - 1) * RESOLUTION + MASS_REMOVED
stop = WINDOW_SIZE - 1
MA = np.linspace(
(FOLDED * (WINDOW_SIZE - 1) + 1) * RESOLUTION + MASS_REMOVED,
(FOLDED + 1) * (WINDOW_SIZE - 1) * RESOLUTION + MASS_REMOVED,
WINDOW_SIZE - 1)
ind = np.where(ptA > CUTOFF)[0]
y = ptA[ind]
y2 = y / np.max(y)
return y2
def taylor_coeff(fun, N):
"""From L. Trefethen, Ten digits algorithms """
zz = exp(2j*pi*(array(range(N)))/N)
c = fft(fun(zz))/N
return real(c)
def update_data(self, x, taps, psd, syms, table):
try:
eqdata_key = 'dtv_atsc_equalizer0::taps'
symdata_key = 'dtv_atsc_equalizer0::data'
rs_nump_key = 'dtv_atsc_rs_decoder0::num_packets'
rs_numbp_key = 'dtv_atsc_rs_decoder0::num_bad_packets'
rs_numerrs_key = 'dtv_atsc_rs_decoder0::num_errors_corrected'
vt_metrics_key = 'dtv_atsc_viterbi_decoder0::decoder_metrics'
snr_key = 'probe2_f0::SNR'
data = self.radio.getKnobs([])
eqdata = data[eqdata_key]
symdata = data[symdata_key]
rs_num_packets = data[rs_nump_key]
rs_num_bad_packets = data[rs_numbp_key]
rs_num_errors_corrected = data[rs_numerrs_key]
vt_decoder_metrics = data[vt_metrics_key]
snr_est = data[snr_key]
vt_decoder_metrics = numpy.mean(vt_decoder_metrics.value)
self._viterbi_metric.pop()
self._viterbi_metric.insert(0, vt_decoder_metrics)
except TTransportException:
sys.stderr.write("Lost connection, exiting")
sys.exit(1)
ntaps = len(eqdata.value)
taps.set_ydata(eqdata.value)
taps.set_xdata(list(range(ntaps)))
self._sp0.set_xlim(0, ntaps)
self._sp0.set_ylim(min(eqdata.value), max(eqdata.value))
fs = 6.25e6
freq = numpy.linspace(-fs / 2, fs / 2, 10000)
H = numpy.fft.fftshift(fftpack.fft(eqdata.value, 10000))
HdB = 20.0 * numpy.log10(abs(H))
psd.set_ydata(HdB)
psd.set_xdata(freq)
self._sp1.set_xlim(0, fs / 2)
self._sp1.set_ylim([min(HdB), max(HdB)])
self._sp1.set_yticks([min(HdB), max(HdB)])
self._sp1.set_yticklabels(["min", "max"])
nsyms = len(symdata.value)
syms.set_ydata(symdata.value)
syms.set_xdata(nsyms * [
0,
])
self._sp2.set_xlim([-1, 1])
self._sp2.set_ylim([-10, 10])
per = float(rs_num_bad_packets.value) / float(rs_num_packets.value)
ber = float(rs_num_errors_corrected.value) / float(
187 * rs_num_packets.value)
table._cells[(1, 0)]._text.set_text("{0}".format(rs_num_packets.value))
table._cells[(1, 1)]._text.set_text("{0:.2g}".format(ber))
table._cells[(1, 2)]._text.set_text("{0:.2g}".format(per))
table._cells[(1, 3)]._text.set_text("{0:.1f}".format(
numpy.mean(self._viterbi_metric)))
table._cells[(1, 4)]._text.set_text("{0:.4f}".format(snr_est.value[0]))
return (taps, psd, syms, table)
def isotope(fVec,DAbund):
'''
%
% Calculates isotopic distributions including isotopic fine structure
% of molecules using FFT and various scaling 'tricks'. Easily adopted
% to molecules of any elemental composition (by altering MAX_ELEMENTS
% and the nuclide matrix A). To simulate spectra, convolute with peak
% shape using FFT.
%
% (C) 1999 by Magnus Palmblad, Division of Ion Physics, Uppsala Univ.
% Acknowledgements:
% Lars Larsson-Cohn, Dept. of Mathematical Statistics, Uppsala Univ.,
% for help on theory of convolutions and FFT.
% Jan Axelsson, Div. of Ion Physics, Uppsala Univ. for comments and ideas
%
% Contact Magnus Palmblad at [email protected] if you should
% have any questions or comments.
%
Converted to Python 1/10/08 by
Brian H. Clowers [email protected]
October 31, 2014
Added Phosphorous and chemical formula parsing
Added conditional specification of stable isotope composition
Ben Bowen, [email protected]
fVec is a vector representing the chemical formula including deuterium
# [H, C, N, O, S, P, D]
DAbund is the amount of deuterium [0-1], 0.05 is typical
'''
import numpy as np
import numpy.fft.fftpack as F
# import time
# import pylab as P
def next2pow(x):
return 2**int(np.ceil(np.log(float(x))/np.log(2.0)))
scaleFactor = 100000
MAX_ELEMENTS=7+1 # add 1 due to mass correction 'element'
MAX_ISOTOPES=4 # maxiumum # of isotopes for one element
CUTOFF=1e-4 # relative intensity cutoff for plotting
WINDOW_SIZE = 500
#WINDOW_SIZE=input('Window size (in Da) ---> ');
#RESOLUTION=input('Resolution (in Da) ----> '); % mass unit used in vectors
RESOLUTION = 0.5
if RESOLUTION < 0.00001:# % minimal mass step allowed
RESOLUTION = 0.00001
elif RESOLUTION > 0.5: # maximal mass step allowed
RESOLUTION = 0.5
R=0.00001/RESOLUTION# % R is used to scale nuclide masses (see below)
WINDOW_SIZE=WINDOW_SIZE/RESOLUTION; # convert window size to new mass units
WINDOW_SIZE=next2pow(WINDOW_SIZE); # fast radix-2 fast-Fourier transform algorithm
if WINDOW_SIZE < np.round(496708*R)+1:
WINDOW_SIZE = nextpow2(np.round(496708*R)+1) # just to make sure window is big enough
# print 'Vector size: 1x%d'%WINDOW_SIZE
#H378 C254 N65 O75 S6
# M=np.array([378,254,65,75,6,0]) #% empiric formula, e.g. bovine insulin
M=np.array(fVec) #% empiric formula, e.g. bovine insulin
# isotopic abundances stored in matrix A (one row for each element)
A=np.zeros((MAX_ELEMENTS,MAX_ISOTOPES,2));
A[0][0,:] = [100783,0.9998443]# % 1H
A[0][1,:] = [201410,0.0001557]# % 2H
A[1][0,:] = [100000,0.98889]# % 12C
A[1][1,:] = [200336,0.01111]# % 13C
A[2][0,:] = [100307,0.99634]# % 14N
A[2][1,:] = [200011,0.00366]# % 15N
A[3][0,:] = [99492,0.997628]# % 16O
A[3][1,:] = [199913,0.000372]# % 17O
A[3][2,:] = [299916,0.002000]# % 18O
A[4][0,:] = [97207,0.95018]# % 32S
A[4][1,:] = [197146,0.00750]# % 33S
A[4][2,:] = [296787,0.04215]# % 34S
A[4][3,:] = [496708,0.00017]# % 36S
A[5][0,:] = [97376,1.0]# Phosphorous
A[6][0,:] = [100783,1.0-DAbund]# % 1H
A[6][1,:] = [201410,DAbund]# % 2H
A[7][0,:] = [100000,1.00000]# % for shifting mass so that Mmi is
# % near left limit of window
mass_removed_vec = [0,11,13,15,31,30,0,-1]
monoisotopic = 0.0
for i,e in enumerate(fVec):
monoisotopic = monoisotopic + ( (mass_removed_vec[i]*scaleFactor+A[i][0,0])*e / scaleFactor)
Mmi=np.array([np.round(100783*R), np.round(100000*R),\
np.round(100307*R), np.round(99492*R), np.round(97207*R), np.round(97376*R), np.round(100783*R), 0])*M# % (Virtual) monoisotopic mass in new units
Mmi = Mmi.sum()
#% mass shift so Mmi is in left limit of window:
#print "Mmi",Mmi
#print "Window", WINDOW_SIZE
FOLDED=np.floor(Mmi/(WINDOW_SIZE-1))+1# % folded FOLDED times (always one folding due to shift below)
#% shift distribution to 1 Da from lower window limit:
M[MAX_ELEMENTS-1]=np.ceil(((WINDOW_SIZE-1)-np.mod(Mmi,WINDOW_SIZE-1)+np.round(100000*R))*RESOLUTION)
MASS_REMOVED=np.array(mass_removed_vec)*M#'; % correction for 'virtual' elements and mass shift
MASS_REMOVED = MASS_REMOVED.sum()
ptA=np.ones(WINDOW_SIZE);
t_fft=0
t_mult=0
for i in xrange(MAX_ELEMENTS):
tA=np.zeros(WINDOW_SIZE)
for j in xrange(MAX_ISOTOPES):
if A[i][j,0] != 0:
tA[np.round(A[i][j,0]*R)]=A[i][j,1]#; % put isotopic distribution in tA
tA=F.fft(tA) # FFT along elements isotopic distribution O(nlogn)
tA=tA**M[i]# % O(n)
ptA = ptA*tA# % O(n)#this is where it is messing UP
ptA=F.ifft(ptA).real#; % O(nlogn)
start = (FOLDED*(WINDOW_SIZE-1)+1)*RESOLUTION+MASS_REMOVED,(FOLDED+1)*(WINDOW_SIZE-1)*RESOLUTION+MASS_REMOVED
stop = WINDOW_SIZE - 1
MA=np.linspace((FOLDED*(WINDOW_SIZE-1)+1)*RESOLUTION+MASS_REMOVED,(FOLDED+1)*(WINDOW_SIZE-1)*RESOLUTION+MASS_REMOVED, WINDOW_SIZE-1)
ind=np.where(ptA>CUTOFF)[0]
x = MA[ind]
y = ptA[ind]
for i,xi in enumerate(x):
x[i] = monoisotopic + (i*1.003355)
return x,y,monoisotopic
def fft_real_freq(sig, dt):
S = fft(sig)
S_F = np.linspace(0, 1, len(S)/2) / dt / 2.0
return S_F, S[0:len(S_F)]
def isotope(fVec,DAbund): ''' % % Calculates isotopic distributions including isotopic fine structure % of molecules using FFT and various scaling 'tricks'. Easily adopted % to molecules of any elemental composition (by altering MAX_ELEMENTS % and the nuclide matrix A). To simulate spectra, convolute with peak % shape using FFT. % % (C) 1999 by Magnus Palmblad, Division of Ion Physics, Uppsala Univ. % Acknowledgements: % Lars Larsson-Cohn, Dept. of Mathematical Statistics, Uppsala Univ., % for help on theory of convolutions and FFT. % Jan Axelsson, Div. of Ion Physics, Uppsala Univ. for comments and ideas % % Contact Magnus Palmblad at [email protected] if you should % have any questions or comments. % Converted to Python 1/10/08 by Brian H. Clowers [email protected] October 31, 2014 Added Phosphorous and chemical formula parsing Added conditional specification of stable isotope composition Ben Bowen, [email protected] fVec is a vector representing the chemical formula including deuterium # [H, C, N, O, S, P, D] DAbund is the amount of deuterium [0-1], 0.05 is typical ''' import numpy as np import numpy.fft.fftpack as F # import time # import pylab as P def next2pow(x): return 2**int(np.ceil(np.log(float(x))/np.log(2.0))) scaleFactor = 100000 MAX_ELEMENTS=7+1 # add 1 due to mass correction 'element' MAX_ISOTOPES=4 # maxiumum # of isotopes for one element CUTOFF=1e-4 # relative intensity cutoff for plotting WINDOW_SIZE = 500 #WINDOW_SIZE=input('Window size (in Da) ---> '); #RESOLUTION=input('Resolution (in Da) ----> '); % mass unit used in vectors RESOLUTION = 0.5 if RESOLUTION < 0.00001:# % minimal mass step allowed RESOLUTION = 0.00001 elif RESOLUTION > 0.5: # maximal mass step allowed RESOLUTION = 0.5 R=0.00001/RESOLUTION# % R is used to scale nuclide masses (see below) WINDOW_SIZE=WINDOW_SIZE/RESOLUTION; # convert window size to new mass units WINDOW_SIZE=next2pow(WINDOW_SIZE); # fast radix-2 fast-Fourier transform algorithm if WINDOW_SIZE < np.round(496708*R)+1: WINDOW_SIZE = nextpow2(np.round(496708*R)+1) # just to make sure window is big enough # print 'Vector size: 1x%d'%WINDOW_SIZE #H378 C254 N65 O75 S6 # M=np.array([378,254,65,75,6,0]) #% empiric formula, e.g. bovine insulin M=np.array(fVec) #% empiric formula, e.g. bovine insulin # isotopic abundances stored in matrix A (one row for each element) A=np.zeros((MAX_ELEMENTS,MAX_ISOTOPES,2)); A[0][0,:] = [100783,0.9998443]# % 1H A[0][1,:] = [201410,0.0001557]# % 2H A[1][0,:] = [100000,0.98889]# % 12C A[1][1,:] = [200336,0.01111]# % 13C A[2][0,:] = [100307,0.99634]# % 14N A[2][1,:] = [200011,0.00366]# % 15N A[3][0,:] = [99492,0.997628]# % 16O A[3][1,:] = [199913,0.000372]# % 17O A[3][2,:] = [299916,0.002000]# % 18O A[4][0,:] = [97207,0.95018]# % 32S A[4][1,:] = [197146,0.00750]# % 33S A[4][2,:] = [296787,0.04215]# % 34S A[4][3,:] = [496708,0.00017]# % 36S A[5][0,:] = [97376,1.0]# Phosphorous A[6][0,:] = [100783,1.0-DAbund]# % 1H A[6][1,:] = [201410,DAbund]# % 2H A[7][0,:] = [100000,1.00000]# % for shifting mass so that Mmi is # % near left limit of window mass_removed_vec = [0,11,13,15,31,30,0,-1] monoisotopic = 0.0 for i,e in enumerate(fVec): monoisotopic = monoisotopic + ( (mass_removed_vec[i]*scaleFactor+A[i][0,0])*e / scaleFactor) Mmi=np.array([np.round(100783*R), np.round(100000*R),\ np.round(100307*R), np.round(99492*R), np.round(97207*R), np.round(97376*R), np.round(100783*R), 0])*M# % (Virtual) monoisotopic mass in new units Mmi = Mmi.sum() #% mass shift so Mmi is in left limit of window: #print "Mmi",Mmi #print "Window", WINDOW_SIZE FOLDED=np.floor(Mmi/(WINDOW_SIZE-1))+1# % folded FOLDED times (always one folding due to shift below) #% shift distribution to 1 Da from lower window limit: M[MAX_ELEMENTS-1]=np.ceil(((WINDOW_SIZE-1)-np.mod(Mmi,WINDOW_SIZE-1)+np.round(100000*R))*RESOLUTION) MASS_REMOVED=np.array(mass_removed_vec)*M#'; % correction for 'virtual' elements and mass shift MASS_REMOVED = MASS_REMOVED.sum() ptA=np.ones(WINDOW_SIZE); t_fft=0 t_mult=0 for i in xrange(MAX_ELEMENTS): tA=np.zeros(WINDOW_SIZE) for j in xrange(MAX_ISOTOPES): if A[i][j,0] != 0: tA[np.round(A[i][j,0]*R)]=A[i][j,1]#; % put isotopic distribution in tA tA=F.fft(tA) # FFT along elements isotopic distribution O(nlogn) tA=tA**M[i]# % O(n) ptA = ptA*tA# % O(n)#this is where it is messing UP ptA=F.ifft(ptA).real#; % O(nlogn) start = (FOLDED*(WINDOW_SIZE-1)+1)*RESOLUTION+MASS_REMOVED,(FOLDED+1)*(WINDOW_SIZE-1)*RESOLUTION+MASS_REMOVED stop = WINDOW_SIZE - 1 MA=np.linspace((FOLDED*(WINDOW_SIZE-1)+1)*RESOLUTION+MASS_REMOVED,(FOLDED+1)*(WINDOW_SIZE-1)*RESOLUTION+MASS_REMOVED, WINDOW_SIZE-1) ind=np.where(ptA>CUTOFF)[0] x = MA[ind] y = ptA[ind] for i,xi in enumerate(x): x[i] = monoisotopic + (i*1.003355) return x,y,monoisotopic
def main():
parser = ArgumentParser(conflict_handler="resolve")
parser.add_argument("-N", "--nsamples", type=int, default=2000,
help="Set the number of samples to process [default=%(default)r]")
parser.add_argument("-S", "--sps", type=int, default=4,
help="Set the samples per symbol [default=%(default)r]")
parser.add_argument("-r", "--rolloff", type=eng_float, default=0.35,
help="Set the rolloff factor [default=%(default)r]")
parser.add_argument("-W", "--bandwidth", type=eng_float, default=2*numpy.pi/100.0,
help="Set the loop bandwidth (PFB) or gain (M&M) [default=%(default)r]")
parser.add_argument("-n", "--ntaps", type=int, default=45,
help="Set the number of taps in the filters [default=%(default)r]")
parser.add_argument("--noise", type=eng_float, default=0.0,
help="Set the simulation noise voltage [default=%(default)r]")
parser.add_argument("-f", "--foffset", type=eng_float, default=0.0,
help="Set the simulation's normalized frequency offset (in Hz) [default=%(default)r]")
parser.add_argument("-t", "--toffset", type=eng_float, default=1.0,
help="Set the simulation's timing offset [default=%(default)r]")
parser.add_argument("-p", "--poffset", type=eng_float, default=0.0,
help="Set the simulation's phase offset [default=%(default)r]")
parser.add_argument("-M", "--mode", type=int, default=0,
help="Set the recovery mode (0: polyphase, 1: M&M) [default=%(default)r]")
args = parser.parse_args()
# Adjust N for the interpolation by sps
args.nsamples = args.nsamples // args.sps
# Set up the program-under-test
put = example_timing(args.nsamples, args.sps, args.rolloff,
args.ntaps, args.bandwidth, args.noise,
args.foffset, args.toffset, args.poffset,
args.mode)
put.run()
if args.mode == 0:
data_src = numpy.array(put.vsnk_src.data()[20:])
data_clk = numpy.array(put.vsnk_clk.data()[20:])
data_err = numpy.array(put.vsnk_err.data()[20:])
data_rat = numpy.array(put.vsnk_rat.data()[20:])
data_phs = numpy.array(put.vsnk_phs.data()[20:])
f1 = pyplot.figure(1, figsize=(12,10), facecolor='w')
# Plot the IQ symbols
s1 = f1.add_subplot(2,2,1)
s1.plot(data_src.real, data_src.imag, "bo")
s1.plot(data_clk.real, data_clk.imag, "ro")
s1.set_title("IQ")
s1.set_xlabel("Real part")
s1.set_ylabel("Imag part")
s1.set_xlim([-2, 2])
s1.set_ylim([-2, 2])
# Plot the symbols in time
delay = put.delay
m = len(data_clk.real)
s2 = f1.add_subplot(2,2,2)
s2.plot(data_src.real, "bs", markersize=10, label="Input")
s2.plot(data_clk.real[delay:], "ro", label="Recovered")
s2.set_title("Symbols")
s2.set_xlabel("Samples")
s2.set_ylabel("Real Part of Signals")
s2.legend()
# Plot the clock recovery loop's error
s3 = f1.add_subplot(2,2,3)
s3.plot(data_err, label="Error")
s3.plot(data_rat, 'r', label="Update rate")
s3.set_title("Clock Recovery Loop Error")
s3.set_xlabel("Samples")
s3.set_ylabel("Error")
s3.set_ylim([-0.5, 0.5])
s3.legend()
# Plot the clock recovery loop's error
s4 = f1.add_subplot(2,2,4)
s4.plot(data_phs)
s4.set_title("Clock Recovery Loop Filter Phase")
s4.set_xlabel("Samples")
s4.set_ylabel("Filter Phase")
diff_taps = put.dtaps
ntaps = len(diff_taps[0])
nfilts = len(diff_taps)
t = numpy.arange(0, ntaps*nfilts)
f3 = pyplot.figure(3, figsize=(12,10), facecolor='w')
s31 = f3.add_subplot(2,1,1)
s32 = f3.add_subplot(2,1,2)
s31.set_title("Differential Filters")
s32.set_title("FFT of Differential Filters")
for i,d in enumerate(diff_taps):
D = 20.0*numpy.log10(1e-20+abs(numpy.fft.fftshift(fftpack.fft(d, 10000))))
s31.plot(t[i::nfilts].real, d, "-o")
s32.plot(D)
s32.set_ylim([-120, 10])
# If testing the M&M clock recovery loop
else:
data_src = numpy.array(put.vsnk_src.data()[20:])
data_clk = numpy.array(put.vsnk_clk.data()[20:])
data_err = numpy.array(put.vsnk_err.data()[20:])
f1 = pyplot.figure(1, figsize=(12,10), facecolor='w')
# Plot the IQ symbols
s1 = f1.add_subplot(2,2,1)
s1.plot(data_src.real, data_src.imag, "o")
s1.plot(data_clk.real, data_clk.imag, "ro")
s1.set_title("IQ")
s1.set_xlabel("Real part")
s1.set_ylabel("Imag part")
s1.set_xlim([-2, 2])
s1.set_ylim([-2, 2])
# Plot the symbols in time
s2 = f1.add_subplot(2,2,2)
s2.plot(data_src.real, "bs", markersize=10, label="Input")
s2.plot(data_clk.real, "ro", label="Recovered")
s2.set_title("Symbols")
s2.set_xlabel("Samples")
s2.set_ylabel("Real Part of Signals")
s2.legend()
# Plot the clock recovery loop's error
s3 = f1.add_subplot(2,2,3)
s3.plot(data_err)
s3.set_title("Clock Recovery Loop Error")
s3.set_xlabel("Samples")
s3.set_ylabel("Error")
pyplot.show()
