def _find_gap_voltage(volt_v, curr_a, **kw):
"""Find gap voltage.
Args:
volt_v (ndarray): voltage, in V
curr_a (ndarray): current, in A
Keyword Args:
vgap_threshold (float): the current at the gap voltage
Returns:
float: gap voltage
"""
# Unpack keyword arguments
vgap_threshold = kw.get('vgap_threshold', PARAMS['vgap_threshold'])
# Method 1: current threshold
if vgap_threshold is not None:
idx = np.abs(curr_a - vgap_threshold).argmin()
vgap = volt_v[idx]
return vgap
# Method 2: max derivative
vstep = volt_v[1] - volt_v[0]
mask = (1.5e-3 < volt_v) & (volt_v < 3.5e-3)
der = slope(volt_v[mask], curr_a[mask])
der = gauss_conv(der, sigma=0.2e-3 / vstep)
vgap = volt_v[mask][der.argmax()]
return vgap
def _find_gap_voltage(volt_v, curr_a, **kw):
"""Find gap voltage.
Args:
volt_v (ndarray): voltage, in V
curr_a (ndarray): current, in A
Keyword Args:
vrn (list): Voltage range over which to calculate the normal
resistance, in units [V]
debug (bool): plot for debugging purposes
Returns:
float: gap voltage
"""
# Unpack keyword arguments
vrn = kw.get('vrn', PARAMS['vrn'])
debug = kw.get('debug', PARAMS['debug'])
# Normal resistance slope
mask = (vrn[0] < volt_v) & (volt_v < vrn[1])
vtmp, itmp = volt_v[mask], curr_a[mask]
prn = np.polyfit(vtmp, itmp, 1)
# Find max derivative in I-V curve
vstep = volt_v[1] - volt_v[0]
mask = 2e-3 < volt_v
der = slope(volt_v[mask], curr_a[mask])
der = gauss_conv(der, sigma=0.2e-3 / vstep)
vgap = volt_v[mask][der.argmax()]
# Fit line around max derivative
mask = (vgap - 0.1e-4 < volt_v) & (volt_v < vgap + 0.1e-4)
vtmp, itmp = volt_v[mask], curr_a[mask]
pgap = np.polyfit(vtmp, itmp, 1)
# Find "corner" in I-V curve
vcorner = (pgap[1] - prn[1]) / (prn[0] - pgap[0])
icorner = pgap[0] * vcorner + pgap[1]
# Find gap
igap = icorner / 2
vgap = (igap - pgap[1]) / pgap[0]
if debug:
plt.figure()
plt.plot(volt_v * 1e3, curr_a * 1e6)
plt.plot(volt_v * 1e3, np.polyval(prn, volt_v) * 1e6, 'k--')
plt.plot(volt_v * 1e3, np.polyval(pgap, volt_v) * 1e6, 'r--')
plt.plot([vcorner * 1e3], [icorner * 1e6], 'r*')
plt.plot([vgap * 1e3], [igap * 1e6], 'k*')
plt.xlim([volt_v.min() * 1e3, volt_v.max() * 1e3])
plt.ylim([curr_a.min() * 1e6, curr_a.max() * 1e6])
plt.show()
return vgap
def _sample_curve(voltage, current, max_npts, smear):
"""Sample curve. Sample more often when the curve is curvier.
Args:
voltage (ndarray): DC bias voltage
current (ndarray): current (either DC tunneling or KK)
max_npts (int): maximum number of sample points
smear (float): smear current (only for sampling purposes)
Returns:
list: indices of sample points
"""
# Second derivative
dd_current = np.abs(slope(voltage, slope(voltage, current)))
# Cumulative sum of second derivative
v_step = voltage[1] - voltage[0]
cumsum = np.cumsum(gauss_conv(dd_current, sigma=smear / v_step))
# Build sampling array
idx_list = [0]
# Add indices based on curvy-ness
cumsum_last = 0.
voltage_last = voltage[0]
for idx, v in enumerate(voltage):
condition1 = abs(v) < 0.05 or abs(v - 1) < 0.1 or abs(v + 1) < 0.1
condition2 = v - voltage_last >= 1.
condition3 = (cumsum[idx] - cumsum_last) * max_npts / cumsum[-1] > 1
condition4 = idx < 3 or idx > len(voltage) - 4
if condition1 or condition2 or condition3 or condition4:
if idx != idx_list[-1]:
idx_list.append(idx)
voltage_last = v
cumsum_last = cumsum[idx]
# Add 10 to start/end
for i in range(0, int(1 / VSTEP), int(1 / VSTEP / 10)):
idx_list.append(i)
for i in range(
len(voltage) - int(1 / VSTEP) - 1, len(voltage),
int(1 / VSTEP / 10)):
idx_list.append(i)
# Add 30 pts to middle
ind_low = np.abs(voltage + 1.).argmin()
ind_high = np.abs(voltage - 1.).argmin()
npts = ind_high - ind_low
for i in range(ind_low, ind_high, npts // 30):
idx_list.append(i)
idx_list = list(set(idx_list))
idx_list.sort()
return idx_list
def __init__(self, **params):
params = _default_params(params)
if params['verbose']:
print("Generating response function:")
# Reflect about y-axis
voltage = np.copy(VINIT)
current = iv.perfect(voltage)
if params['v_smear'] is None:
voltage = np.r_[-voltage[::-1][:-1], voltage]
current = np.r_[-current[::-1][:-1], current]
# KK transform
current_kk = iv.perfect_kk(voltage)
# Place interpolations into hidden attributes
self._f_idc = iv.perfect
self._f_ikk = iv.perfect_kk
self._f_didc = None
self._f_dikk = None
# Save DC I-V curve and KK transform as attributes
self.voltage = voltage
self.current = current
self.voltage_kk = voltage
self.current_kk = current_kk
# Smear IV curve (optional)
else:
tmp = np.zeros_like(voltage)
idx = np.abs(voltage - 1.).argmin()
tmp[idx] = 1.
v_step = voltage[1] - voltage[0]
current = gauss_conv(tmp, sigma=params['v_smear']/v_step) + \
iv.perfect(voltage)
if params['verbose']:
print(" - Voltage smear: {:.4f}".format(params['v_smear']))
RespFn.__init__(self, voltage, current, **params)
def __init__(self, voltage, current, **params):
params = _default_params(params)
if params['verbose']:
print("Generating response function:")
assert voltage[0] == 0., "First voltage value must be zero"
assert voltage[-1] > 5, "Voltage must extend to at least 5"
# Reflect about y-axis
voltage = np.r_[-voltage[::-1][:-1], voltage]
current = np.r_[-current[::-1][:-1], current]
# Smear DC I-V curve (optional)
if params['v_smear'] is not None:
v_step = voltage[1] - voltage[0]
current = gauss_conv(current - voltage,
sigma=params['v_smear'] / v_step) + voltage
if params['verbose']:
print(" - Voltage smear: {:.4f}".format(params['v_smear']))
# Calculate Kramers-Kronig (KK) transform
current_kk = kk_trans(voltage, current, params['kk_n'])
# Interpolate
f_interp = _setup_interpolation(voltage, current, current_kk, **params)
# Place interpolation objects into hidden attributes
self._f_idc = f_interp[0]
self._f_ikk = f_interp[1]
self._f_didc = f_interp[2]
self._f_dikk = f_interp[3]
# Save DC I-V curve and KK transform as attributes
self.voltage = voltage
self.current = current
self.voltage_kk = voltage
self.current_kk = current_kk
params['t_cold'] = args.tcold
# Plot data
if args.verbose:
print(' - Generating figure')
fig, ax = plt.subplots(figsize=(args.width, args.height))
for filename in args.file:
if args.verbose:
print(" - Importing: " + filename)
# Import and plot noise temperature
data = if_response(filename, ifresp_delimiter=args.delimiter)
freq, tn = data[0], data[1]
# Filter
if args.filter is not None:
tn = gauss_conv(tn, args.filter)
plt.plot(freq, tn, label=filename)
# Figure properties
if args.verbose:
print(' - Customizing figure')
plt.xlabel(r'Frequency (GHz)')
plt.ylabel(r'Noise Temperature (K)')
if args.xmax is not None:
plt.xlim([0, args.xmax])
if args.ymax is not None:
plt.ylim([0, args.ymax])
else:
plt.ylim([0, 500])
plt.legend(loc=0)
if args.title is not None:
def _load_if(ifdata, dc, **kwargs):
"""Import IF data.
Args:
ifdata: IF data. A Numpy array. The data
should have two columns: the first for voltage, and the second
for IF power.
dc (qmix.exp.iv_data.DCIVData): DC I-V metadata.
Keyword arguments:
v_fmt (str): units for voltage ('V', 'mV', 'uV')
ifdata_sigma (float): Standard deviation of Gaussian used for
filtering, in units [V]
ifdata_npts (float): evenly interpolate data to have this many data
points
rseries (float): series resistance of measurement system
Returns: IF data (in matrix form)
"""
# Unpack keyword arguments
v_multiplier = kwargs.get('v_multiplier', PARAMS['v_multiplier'])
sigma = kwargs.get('ifdata_sigma', PARAMS['ifdata_sigma'])
vmax = kwargs.get('vmax', PARAMS['vmax'])
npts = kwargs.get('ifdata_npts', PARAMS['ifdata_npts'])
rseries = kwargs.get('rseries', PARAMS['rseries'])
v_fmt = kwargs.get('v_fmt', PARAMS['v_fmt'])
# Import raw IF data
ifdata = ifdata.copy()
assert isinstance(ifdata, np.ndarray), 'IF data should be a Numpy array.'
assert ifdata.ndim == 2, 'IF data should be 2-dimensional.'
assert ifdata.shape[1] == 2, 'IF data should have 2 columns.'
# Units for voltage
ifdata[:, 0] *= _vfmt_dict[v_fmt]
# Clean
ifdata = remove_nans_matrix(ifdata)
ifdata = ifdata[np.argsort(ifdata[:, 0])]
ifdata = remove_doubles_matrix(ifdata)
# Correct errors in experimental system
ifdata[:, 0] *= v_multiplier
# Correct for offset
ifdata[:, 0] = ifdata[:, 0] - dc.offset[0]
# Correct for series resistance
if rseries is not None:
v = ifdata[:, 0]
rstatic = dc.vraw / dc.iraw
rstatic[rstatic < 0] = 0.
rstatic = np.interp(v, dc.vraw, rstatic)
iraw = np.interp(v, dc.vraw, dc.iraw)
rj = rstatic - rseries
v0 = iraw * rj
ifdata[:, 0] = v0
# Normalize voltage to gap voltage
ifdata[:, 0] /= dc.vgap
# Set to common voltage (so that data can be stacked)
v, p = ifdata[:, 0], ifdata[:, 1]
# assert v.max() > vmax / dc.vgap, \
# 'vmax ({0}) outside data range ({1})'.format(vmax / dc.vgap, v.max())
# assert v.min() < 0., 'V=0 not included in IF data'
v_out = np.linspace(0, vmax / dc.vgap, npts)
p_out = np.interp(v_out, v, p, left=0, right=0)
ifdata = np.vstack((v_out, p_out)).T
# Smooth IF data
if sigma is not None:
step = (ifdata[1, 0] - ifdata[0, 0]) * dc.vgap
# Backwards compatibility
if sigma > 0.5:
sigma = sigma * step
ifdata[:, 1] = gauss_conv(ifdata[:, 1], sigma / step)
return ifdata
def _correct_offset(volt_v, curr_a, **kw):
"""Find and correct any I/V offset.
The experimental data often has an offset in both V and I. This can be
corrected by using the leakage current. This is found by looking at the
derivative and correcting based on where the peak of the derivative is.
Args:
volt_v (ndarray): voltage, in V
curr_a (ndarray): current, in A
Keyword Args:
voffset: voltage offset, in V
ioffset: current offset, in A
voffset_range (list): Voltage range over which to search for offset,
in units [V].
voffset_sigma: std dev of Gaussian filter when searching for offset
Returns:
tuple: corrected voltage, corrected current, I/V offset
"""
# Unpack keyword arguments
voffset_range = kw.get('voffset_range', PARAMS['voffset_range'])
voffset_sigma = kw.get('voffset_sigma', PARAMS['voffset_sigma'])
voffset = kw.get('voffset', PARAMS['voffset'])
ioffset = kw.get('ioffset', PARAMS['ioffset'])
if voffset is None: # Find voffset and ioffset
# Search over a limited voltage range
if isinstance(voffset_range, tuple):
mask = (voffset_range[0] < volt_v) & (volt_v < voffset_range[1])
else: # if int or float
mask = (-voffset_range < volt_v) & (volt_v < voffset_range)
v = volt_v[mask]
i = curr_a[mask]
# Find derivative of I-V curve
vstep = v[1] - v[0]
sigma = voffset_sigma / vstep
der = slope(v, i)
der_smooth = gauss_conv(der, sigma=sigma)
# Offset is at max derivative
idx = der_smooth.argmax()
voffset = v[idx]
# ioffset = np.interp(voffset, v, i)
ioffset = (np.interp(voffset - 0.1e-3, v, i) +
np.interp(voffset + 0.1e-3, v, i)) / 2
if ioffset is None: # Find ioffset
ioffset = np.interp(voffset, volt_v, curr_a)
# Correct for the offset
volt_v -= voffset
curr_a -= ioffset
return volt_v, curr_a, (voffset, ioffset)
def _load_if(ifdata, dc, **kwargs):
"""Import IF data.
Args:
ifdata: IF data. Either a CSV data file or a Numpy array. The data
should have two columns: the first for voltage, and the second
for IF power. If you are using a CSV file, the properties of
the CSV file can be set through additional keyword arguments
(see below).
dc (qmix.exp.iv_data.DCIVData): DC I-V metadata.
Keyword arguments:
delimiter (str): delimiter used in data files
v_fmt (str): units for voltage ('V', 'mV', 'uV')
usecols (tuple): columns for voltage and current (e.g., ``(0,1)``)
ifdata_sigma (float): Standard deviation of Gaussian used for
filtering, in units [V]
ifdata_npts (float): evenly interpolate data to have this many data
points
rseries (float): series resistance of measurement system
skip_header: number of rows to skip at the beginning of the file
Returns: IF data (in matrix form)
"""
# Unpack keyword arguments
v_multiplier = kwargs.get('v_multiplier', PARAMS['v_multiplier'])
skip_header = kwargs.get('skip_header', PARAMS['skip_header'])
sigma = kwargs.get('ifdata_sigma', PARAMS['ifdata_sigma'])
vmax = kwargs.get('vmax', PARAMS['vmax'])
npts = kwargs.get('ifdata_npts', PARAMS['ifdata_npts'])
delim = kwargs.get('delimiter', PARAMS['delimiter'])
usecols = kwargs.get('usecols', PARAMS['usecols'])
rseries = kwargs.get('rseries', PARAMS['rseries'])
v_fmt = kwargs.get('v_fmt', PARAMS['v_fmt'])
# Import raw IF data
if isinstance(ifdata, str): # assume CSV data file
ifdata = np.genfromtxt(ifdata,
delimiter=delim,
usecols=usecols,
skip_header=skip_header)
elif isinstance(ifdata, np.ndarray): # Numpy array
ifdata = ifdata.copy()
assert ifdata.ndim == 2, 'I-V data should be 2-dimensional.'
assert ifdata.shape[1] == 2, 'I-V data should have 2 columns.'
else:
raise ValueError("Input data type not recognized.")
# Units for voltage
ifdata[:, 0] *= _vfmt_dict[v_fmt]
# Clean
ifdata = remove_nans_matrix(ifdata)
ifdata = ifdata[np.argsort(ifdata[:, 0])]
ifdata = remove_doubles_matrix(ifdata)
# Correct errors in experimental system
ifdata[:, 0] *= v_multiplier
# Correct for offset
ifdata[:, 0] = ifdata[:, 0] - dc.offset[0]
# Correct for series resistance
if rseries is not None:
v = ifdata[:, 0]
rstatic = dc.vraw / dc.iraw
rstatic[rstatic < 0] = 0.
rstatic = np.interp(v, dc.vraw, rstatic)
iraw = np.interp(v, dc.vraw, dc.iraw)
rj = rstatic - rseries
v0 = iraw * rj
ifdata[:, 0] = v0
# Normalize voltage to gap voltage
ifdata[:, 0] /= dc.vgap
# Set to common voltage (so that data can be stacked)
v, p = ifdata[:, 0], ifdata[:, 1]
assert v.max() > vmax / dc.vgap, \
'vmax ({0}) outside data range ({1})'.format(vmax / dc.vgap, v.max())
assert v.min() < 0., 'V=0 not included in IF data'
v_out = np.linspace(0, vmax / dc.vgap, npts)
p_out = np.interp(v_out, v, p)
ifdata = np.vstack((v_out, p_out)).T
# Smooth IF data
if sigma is not None:
step = (ifdata[1, 0] - ifdata[0, 0]) * dc.vgap
# Backwards compatibility
if sigma > 0.5:
sigma = sigma * step
ifdata[:, 1] = gauss_conv(ifdata[:, 1], sigma / step)
return ifdata