def __coordinateToIndex(self, coordinates):
col, row = map(int, coordinates)
if row > len(self.rows):
raise IndexError, "invalid row %d" % row
if col > self.rows[row]:
raise IndexError, "invalid column %d" % col
return sum(self.rows[: row]) + col
def __init__(self, rows, **style):
"""Create a layout.
For example,
'BrickLayout((2, 2, 1))'
creates a layout of three rows with two cells in the top and
center rows and one cell in the bottom row.
'rows' -- A sequence of rows. Each row is a sequence of numbers
specifying how many cells in each row. The number of rows is
the length of the sequence."""
rows = map(int, rows)
num_figures = sum(rows)
self.rows = modified.List(rows)
self.figures = modified.List(num_figures * ( None, ))
Layout.__init__(self, style)
self.watch_modified.append(self.figures)
def chiSquareFit1D(histogram, function, variable_name, parameters,
min_count=7, range=None):
"""Perform a one-dimensional chi-square fit of a PDF to a histogram.
Performs a chi-square fit of PDF 'function' to a one-dimensional
histogram. The chi-square is computed using Simpson's rule
(three-point gaussian quadrature) to integrate the PDF for
comparison with histogram bins. Bin errors in 'histogram' are
ignored; 1/sqrt(N) gaussian couning errors are always used.
Therefore, histogram contents should be positive integers (though
zero and small bins are handled; see the 'min_count' parameter
below).
'histogram' -- The histogram to fit to.
'function' -- The PDF. May be an 'Expression' object or a
callable.
'variable_name' -- The name of the variable in 'function'
corresponding to the dependent quantity in 'histogram' (i.e. the
quantity along the histogram axis).
'parameters' -- A sequence of parameters to fit. Each may be simply
a variable name in 'function', or a sequence '(name, initial_value,
step_size, bound_low, bound_hi)'.
'min_count' -- The minimum value for bins in the fit. Bins which
contain a smaller value than this are coalesced with neighboring
bins until all bins contain at least this value.
returns -- A 'Result' object."""
# We'll use this for minimization.
import hep.minimize
import hep.cernlib.minuit
axis = histogram.axis
function = hep.expr.asExpression(function)
parameters = hep.minimize.normalizeParameters(parameters)
num_floating = sum([ 1 for p in parameters if p[2] is not None ])
# Construct the list of bin samples, coalescing bins as necessary.
samples = []
# Figure out which bins are included in the fit.
if range is None:
bins = hep.hist.AxisIterator(axis)
else:
lo, hi = range
bins = xrange(axis(lo), axis(hi))
# Loop over bins.
x0 = None
for bin in bins:
range = axis.getBinRange(bin)
# Are we carrying a bin whose contents don't satisfy the minimum
# so far?
if x0 is None:
# No. Start a new bin
x0, x1 = range
value = histogram.getBinContent(bin)
else:
# Yes. Make sure we are adjacent.
assert x1 == range[0]
# Coalesce this bin with the carried one.
x1 = range[1]
value += histogram.getBinContent(bin)
# Doe the bin we're carrying have enough in it?
if value >= min_count:
# Yes it does. Use it as a sample.
samples.append(((x0, x1), value, ))
x0 = None
# If we're still carrying a bin, it must not have enough in it. But
# we have to do something with it.
if x0 is not None:
# Are there any samples at all so far?
if len(samples) > 0:
# Yes there are. Coalesce the bin we're carrying with the
# last one.
(last_x0, last_x1), last_value = samples.pop(-1)
assert last_x1 == x0
samples.append(((last_x0, x1), last_value + value, ))
else:
# No samples. The whole histogram doesn't have enough in it
# to satisfy the minimum criterion. Oh well, just use one
# sample.
samples.append(((x0, x1), value, ))
# Construct the chi-square function.
chi_sq = ChiSquare1D(function, variable_name, samples)
# Minimize it.
result = hep.cernlib.minuit.minimize(chi_sq, parameters)
# Store the number of degrees of freedom.
dof = len(samples) - num_floating
result.degrees_of_freedom = dof
# Compute the chi-square probability.
result.chi_square_probability = \
dof > 0 and hep.num.chiSquareCDF(result.minimum, dof) or None
# Substitute the fit parameter values into 'function' and store
# that.
result.expression = hep.expr.substitute(function, **result.values)
# Construct a function suitable for plotting. Scale the PDF by the
# bin size, for sensible comparison to the histogram.
bin_size = (axis.range[1] - axis.range[0]) / axis.number_of_bins
scaled_expr = hep.expr.Multiply(
result.expression, hep.expr.Constant(bin_size))
notes = "Results of fit to '%s'\n" % str(function)
notes += " $\chi^2$ / DOF = %.2f / %d\n" \
% (result.minimum, result.degrees_of_freedom, )
if result.chi_square_probability is not None:
notes += " $P_{\chi^2}$ = %.3f\n" % result.chi_square_probability
for name, value in result.values.items():
notes += " %s = %.4f ± %.4f\n" \
% (name, value, result.errors[name])
result.function = hep.hist.Function1D(
scaled_expr, arg_name=variable_name,
axis=hep.hist.Axis(axis.type, range=axis.range), notes=notes)
return result